TSTP Solution File: SWW225+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW225+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n004.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 : Sat Sep 2 14:05:26 EDT 2023
% Result : Theorem 2.83s 0.91s
% Output : Refutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1709
% Syntax : Number of formulae : 4907 (1633 unt; 0 def)
% Number of atoms : 11308 (2222 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 9962 (3561 ~;3558 |; 754 &)
% (1240 <=>; 849 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 1042 (1040 usr; 942 prp; 0-4 aty)
% Number of functors : 89 ( 89 usr; 13 con; 0-4 aty)
% Number of variables : 6675 (;6474 !; 201 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15400,plain,
$false,
inference(avatar_sat_refutation,[],[f5986,f5991,f5996,f6001,f6006,f6011,f6016,f6021,f6026,f6031,f6036,f6041,f6046,f6051,f6056,f6061,f6066,f6071,f6076,f6081,f6086,f6091,f6096,f6101,f6106,f6111,f6116,f6121,f6126,f6131,f6136,f6141,f6146,f6151,f6156,f6161,f6166,f6171,f6176,f6181,f6186,f6191,f6196,f6201,f6206,f6211,f6216,f6221,f6226,f6231,f6236,f6241,f6246,f6251,f6256,f6261,f6266,f6271,f6276,f6281,f6286,f6291,f6296,f6301,f6306,f6311,f6316,f6321,f6326,f6331,f6336,f6341,f6346,f6351,f6356,f6361,f6366,f6371,f6376,f6381,f6386,f6391,f6396,f6401,f6406,f6411,f6416,f6421,f6426,f6431,f6436,f6441,f6446,f6451,f6456,f6461,f6466,f6471,f6476,f6481,f6486,f6491,f6496,f6501,f6506,f6511,f6516,f6521,f6526,f6531,f6536,f6541,f6546,f6551,f6556,f6561,f6566,f6571,f6576,f6581,f6586,f6591,f6596,f6601,f6606,f6611,f6616,f6621,f6626,f6631,f6636,f6641,f6646,f6651,f6656,f6661,f6666,f6671,f6676,f6681,f6686,f6691,f6696,f6701,f6706,f6711,f6716,f6721,f6726,f6731,f6736,f6741,f6746,f6751,f6756,f6761,f6766,f6771,f6776,f6781,f6786,f6791,f6796,f6801,f6806,f6811,f6816,f6821,f6826,f6831,f6836,f6841,f6846,f6851,f6856,f6861,f6866,f6871,f6876,f6881,f6886,f6891,f6896,f6901,f6906,f6911,f6916,f6921,f6926,f6931,f6936,f6941,f6946,f6951,f6956,f6961,f6966,f6971,f6976,f6981,f6986,f6991,f6996,f7001,f7006,f7011,f7016,f7021,f7026,f7031,f7036,f7041,f7047,f7052,f7057,f7062,f7068,f7073,f7077,f7081,f7085,f7089,f7093,f7098,f7103,f7109,f7114,f7119,f7124,f7129,f7133,f7137,f7141,f7145,f7149,f7153,f7157,f7161,f7165,f7169,f7173,f7177,f7181,f7185,f7189,f7193,f7197,f7201,f7205,f7209,f7213,f7217,f7221,f7225,f7229,f7233,f7237,f7241,f7245,f7249,f7253,f7257,f7261,f7265,f7269,f7273,f7277,f7281,f7285,f7289,f7293,f7297,f7301,f7305,f7309,f7313,f7317,f7321,f7325,f7329,f7333,f7337,f7341,f7345,f7349,f7353,f7357,f7361,f7365,f7369,f7373,f7377,f7381,f7385,f7389,f7393,f7397,f7401,f7405,f7409,f7413,f7418,f7423,f7428,f7433,f7438,f7443,f7448,f7453,f7458,f7463,f7468,f7472,f7476,f7480,f7484,f7488,f7492,f7496,f7500,f7504,f7508,f7512,f7516,f7520,f7524,f7528,f7532,f7536,f7545,f7558,f7562,f7566,f7570,f7574,f7578,f7582,f7586,f7590,f7594,f7598,f7602,f7606,f7610,f7614,f7618,f7622,f7626,f7630,f7634,f7638,f7642,f7646,f7650,f7654,f7659,f7664,f7668,f7672,f7676,f7681,f7704,f7712,f7717,f7722,f7726,f7730,f7734,f7738,f7742,f7746,f7750,f7754,f7758,f7762,f7766,f7770,f7774,f7778,f7782,f7786,f7790,f7794,f7798,f7802,f7806,f7810,f7814,f7818,f7822,f7826,f7831,f7835,f7839,f7843,f7847,f7851,f7855,f7859,f7863,f7867,f7871,f7875,f7879,f7883,f7887,f7891,f7895,f7899,f7903,f7907,f7911,f7915,f7919,f7923,f7927,f7931,f7945,f7993,f8036,f8052,f8070,f8075,f8079,f8083,f8087,f8092,f8096,f8100,f8104,f8108,f8112,f8116,f8120,f8124,f8128,f8132,f8136,f8140,f8144,f8148,f8152,f8156,f8160,f8164,f8168,f8172,f8176,f8180,f8184,f8188,f8192,f8196,f8200,f8204,f8208,f8212,f8216,f8220,f8224,f8228,f8232,f8236,f8240,f8259,f8263,f8267,f8271,f8275,f8279,f8283,f8287,f8291,f8295,f8300,f8304,f8308,f8312,f8316,f8320,f8324,f8328,f8332,f8336,f8340,f8345,f8350,f8354,f8358,f8362,f8366,f8370,f8374,f8378,f8382,f8387,f8391,f8395,f8399,f8403,f8407,f8411,f8415,f8421,f8530,f8576,f8716,f8735,f8788,f8792,f8796,f8800,f8804,f8808,f8812,f8816,f8820,f8824,f8828,f8832,f8836,f8840,f8844,f8848,f8852,f8856,f8861,f8865,f8869,f8873,f8877,f8881,f8885,f8889,f8893,f8897,f8901,f8905,f8909,f8913,f8917,f8921,f8925,f8929,f8933,f8937,f8941,f8945,f8949,f8953,f8957,f8961,f8967,f8977,f8981,f8985,f8989,f8995,f8999,f9003,f9007,f9011,f9016,f9021,f9025,f9029,f9033,f9037,f9256,f9530,f9546,f9550,f9563,f9587,f9591,f9595,f9599,f9603,f9607,f9611,f9615,f9619,f9623,f9627,f9631,f9635,f9639,f9647,f9651,f9655,f9659,f9663,f9667,f9671,f9675,f9679,f9683,f9699,f9703,f9707,f9711,f9715,f9719,f9723,f9727,f9731,f9735,f9745,f9749,f9753,f9757,f9761,f9765,f9769,f9773,f9777,f9781,f9790,f9794,f9798,f9802,f9806,f9810,f9814,f9818,f9822,f9826,f9841,f9845,f9849,f9853,f9857,f9861,f9865,f9869,f9873,f9877,f9881,f9885,f9889,f9893,f9897,f9901,f9905,f9909,f9913,f9917,f9921,f9925,f9929,f9933,f9937,f9941,f9945,f9949,f9953,f9957,f9961,f9965,f9969,f9973,f9977,f9981,f9985,f9989,f9993,f9997,f10001,f10005,f10009,f10013,f10017,f10021,f10120,f10256,f11085,f11100,f11105,f11110,f11131,f11135,f11139,f11143,f11147,f11151,f11155,f11159,f11163,f11167,f11171,f11175,f11179,f11183,f11187,f11191,f11195,f11199,f11203,f11207,f11211,f11215,f11219,f11223,f11227,f11231,f11235,f11239,f11243,f11247,f11252,f11256,f11260,f11264,f11268,f11272,f11276,f11280,f11284,f11288,f11292,f11296,f11300,f11304,f11308,f11312,f11316,f11320,f11324,f11328,f11332,f11336,f11340,f11344,f11348,f11352,f11356,f11360,f11364,f11368,f11372,f11376,f11380,f11385,f11389,f11395,f11399,f11403,f11407,f11411,f11415,f11419,f11423,f11428,f11433,f11586,f11841,f11991,f12089,f12245,f12308,f12312,f12316,f12320,f12324,f12328,f12332,f12336,f12340,f12344,f12348,f12352,f12356,f12361,f12365,f12369,f12373,f12377,f12381,f12385,f12389,f12393,f12397,f12401,f12405,f12409,f12413,f12417,f12421,f12425,f12429,f12433,f12437,f12441,f12445,f12449,f12453,f12457,f12461,f12465,f12469,f12473,f12477,f12481,f12485,f12489,f12493,f12497,f12501,f12505,f12509,f12513,f12517,f12521,f12525,f12529,f12533,f12537,f12541,f12545,f12549,f12553,f12557,f12561,f12565,f12569,f12573,f12577,f12581,f12585,f12589,f12593,f12597,f12601,f12696,f12876,f12953,f13190,f13884,f13888,f13894,f13925,f13929,f13933,f13937,f13948,f13952,f13956,f13960,f13964,f13968,f13972,f13976,f13981,f13985,f13993,f13997,f14001,f14005,f14009,f14013,f14017,f14021,f14025,f14029,f14034,f14038,f14042,f14046,f14050,f14054,f14058,f14062,f14066,f14070,f14096,f14100,f14104,f14108,f14112,f14116,f14120,f14124,f14128,f14132,f14140,f14144,f14148,f14152,f14156,f14160,f14164,f14168,f14172,f14176,f14180,f14184,f14188,f14192,f14196,f14200,f14204,f14208,f14212,f14216,f14220,f14225,f14229,f14233,f14237,f14241,f14245,f14249,f14253,f14257,f14261,f14265,f14269,f14273,f14277,f14281,f14285,f14289,f14293,f14297,f14301,f14305,f14326,f14330,f14334,f14338,f14342,f14346,f14350,f14354,f14358,f14362,f14366,f14370,f14599,f14896,f15399]) ).
fof(f15399,plain,
( ~ spl104_753
| ~ spl104_536
| spl104_941 ),
inference(avatar_split_clause,[],[f15102,f14893,f8895,f11425]) ).
fof(f11425,plain,
( spl104_753
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_753])]) ).
fof(f8895,plain,
( spl104_536
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_536])]) ).
fof(f14893,plain,
( spl104_941
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____)),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_941])]) ).
fof(f15102,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____)))
| ~ spl104_536
| spl104_941 ),
inference(resolution,[],[f14895,f8896]) ).
fof(f8896,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ spl104_536 ),
inference(avatar_component_clause,[],[f8895]) ).
fof(f14895,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____)),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____))))
| spl104_941 ),
inference(avatar_component_clause,[],[f14893]) ).
fof(f14896,plain,
( ~ spl104_941
| spl104_226
| ~ spl104_859 ),
inference(avatar_split_clause,[],[f14691,f14007,f7106,f14893]) ).
fof(f7106,plain,
( spl104_226
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_226])]) ).
fof(f14007,plain,
( spl104_859
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_859])]) ).
fof(f14691,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____)),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____))))
| spl104_226
| ~ spl104_859 ),
inference(resolution,[],[f14008,f7108]) ).
fof(f7108,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____)))))
| spl104_226 ),
inference(avatar_component_clause,[],[f7106]) ).
fof(f14008,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ spl104_859 ),
inference(avatar_component_clause,[],[f14007]) ).
fof(f14599,plain,
( spl104_940
| ~ spl104_840
| ~ spl104_852 ),
inference(avatar_split_clause,[],[f13977,f13974,f13892,f14597]) ).
fof(f14597,plain,
( spl104_940
<=> ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_Osucc(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) != X0
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_940])]) ).
fof(f13892,plain,
( spl104_840
<=> ! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X0)) = c_Int_Osucc(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_840])]) ).
fof(f13974,plain,
( spl104_852
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X2))) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_852])]) ).
fof(f13977,plain,
( ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,c_Int_Osucc(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) != X0
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
| ~ spl104_840
| ~ spl104_852 ),
inference(forward_demodulation,[],[f13975,f13893]) ).
fof(f13893,plain,
( ! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X0)) = c_Int_Osucc(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ spl104_840 ),
inference(avatar_component_clause,[],[f13892]) ).
fof(f13975,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X2))) != X0 )
| ~ spl104_852 ),
inference(avatar_component_clause,[],[f13974]) ).
fof(f14370,plain,
spl104_939,
inference(avatar_split_clause,[],[f5903,f14368]) ).
fof(f14368,plain,
( spl104_939
<=> ! [X0,X1] :
( c_Int_OPls = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_939])]) ).
fof(f5903,plain,
! [X0,X1] :
( c_Int_OPls = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0)) ),
inference(forward_demodulation,[],[f5902,f4101]) ).
fof(f4101,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
inference(cnf_transformation,[],[f525]) ).
fof(f525,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Pls__def) ).
fof(f5902,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 ),
inference(forward_demodulation,[],[f4922,f4101]) ).
fof(f4922,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 ),
inference(cnf_transformation,[],[f3673]) ).
fof(f3673,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0)) ) ),
inference(flattening,[],[f3672]) ).
fof(f3672,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0)) ) ),
inference(nnf_transformation,[],[f1817]) ).
fof(f1817,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ) ),
inference(rectify,[],[f884]) ).
fof(f884,axiom,
! [X18,X23] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X23)),X18))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X23 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__less__zpower__abs__iff) ).
fof(f14366,plain,
spl104_938,
inference(avatar_split_clause,[],[f5826,f14364]) ).
fof(f14364,plain,
( spl104_938
<=> ! [X0,X1] :
( c_Int_OPls = X1
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_938])]) ).
fof(f5826,plain,
! [X0,X1] :
( c_Int_OPls = X1
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f5825,f4101]) ).
fof(f5825,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f4808,f4101]) ).
fof(f4808,plain,
! [X0,X1] :
( 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_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f3614]) ).
fof(f3614,plain,
! [X0,X1] :
( ( sP2(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
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f3613]) ).
fof(f3613,plain,
! [X1,X0] :
( ( sP2(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
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f3612]) ).
fof(f3612,plain,
! [X1,X0] :
( ( sP2(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
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f3345]) ).
fof(f3345,plain,
! [X1,X0] :
( sP2(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,[sP2])]) ).
fof(f14362,plain,
spl104_937,
inference(avatar_split_clause,[],[f5824,f14360]) ).
fof(f14360,plain,
( spl104_937
<=> ! [X0,X1] :
( c_Int_OPls = X1
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_937])]) ).
fof(f5824,plain,
! [X0,X1] :
( c_Int_OPls = X1
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f5823,f4101]) ).
fof(f5823,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f4809,f4101]) ).
fof(f4809,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f3614]) ).
fof(f14358,plain,
spl104_936,
inference(avatar_split_clause,[],[f5822,f14356]) ).
fof(f14356,plain,
( spl104_936
<=> ! [X0,X1] :
( c_Int_OPls = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_936])]) ).
fof(f5822,plain,
! [X0,X1] :
( c_Int_OPls = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
| ~ sP2(X0,X1) ),
inference(forward_demodulation,[],[f4810,f4101]) ).
fof(f4810,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
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f3614]) ).
fof(f14354,plain,
spl104_935,
inference(avatar_split_clause,[],[f5783,f14352]) ).
fof(f14352,plain,
( spl104_935
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Nat__Transfer_Otsub(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_935])]) ).
fof(f5783,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Nat__Transfer_Otsub(X1,X0)) ),
inference(forward_demodulation,[],[f5782,f4101]) ).
fof(f5782,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Nat__Transfer_Otsub(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(forward_demodulation,[],[f5781,f4101]) ).
fof(f5781,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Nat__Transfer_Otsub(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(forward_demodulation,[],[f4698,f4101]) ).
fof(f4698,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f2628]) ).
fof(f2628,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(flattening,[],[f2627]) ).
fof(f2627,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(ennf_transformation,[],[f1721]) ).
fof(f1721,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X1,X0)) ) ),
inference(rectify,[],[f519]) ).
fof(f519,axiom,
! [X22,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X22)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Nat__Transfer_Otsub(X3,X22)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) ).
fof(f14350,plain,
spl104_934,
inference(avatar_split_clause,[],[f5777,f14348]) ).
fof(f14348,plain,
( spl104_934
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
| c_Int_OPls = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_934])]) ).
fof(f5777,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
| c_Int_OPls = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f5776,f4101]) ).
fof(f5776,plain,
! [X0,X1] :
( c_Int_OPls = c_Divides_Odiv__class_Odiv(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_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(forward_demodulation,[],[f4696,f4101]) ).
fof(f4696,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,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f2624]) ).
fof(f2624,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,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(flattening,[],[f2623]) ).
fof(f2623,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,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ),
inference(ennf_transformation,[],[f1719]) ).
fof(f1719,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0) ) ),
inference(rectify,[],[f937]) ).
fof(f937,axiom,
! [X11,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X12)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X12,X11)
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X12,X11) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_div__pos__pos__trivial) ).
fof(f14346,plain,
spl104_933,
inference(avatar_split_clause,[],[f5770,f14344]) ).
fof(f14344,plain,
( spl104_933
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| c_Int_OPls = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_933])]) ).
fof(f5770,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| c_Int_OPls = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(forward_demodulation,[],[f5769,f4101]) ).
fof(f5769,plain,
! [X0,X1] :
( c_Int_OPls = 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)) ),
inference(forward_demodulation,[],[f4693,f4101]) ).
fof(f4693,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)) ),
inference(cnf_transformation,[],[f2619]) ).
fof(f2619,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)) ),
inference(flattening,[],[f2618]) ).
fof(f2618,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)) ),
inference(ennf_transformation,[],[f1716]) ).
fof(f1716,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1)
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0) ) ),
inference(rectify,[],[f933]) ).
fof(f933,axiom,
! [X11,X12] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X12,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X11,X12)
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X12,X11) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_div__neg__neg__trivial) ).
fof(f14342,plain,
spl104_932,
inference(avatar_split_clause,[],[f5715,f14340]) ).
fof(f14340,plain,
( spl104_932
<=> ! [X0,X1] :
( c_Nat__Numeral_Oneg(X0)
| c_Int_Onumber__class_Onumber__of(X1,X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ class_Int_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_932])]) ).
fof(f5715,plain,
! [X0,X1] :
( c_Nat__Numeral_Oneg(X0)
| c_Int_Onumber__class_Onumber__of(X1,X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f4533,f4155]) ).
fof(f4155,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = X0,
inference(cnf_transformation,[],[f1293]) ).
fof(f1293,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = X0,
inference(rectify,[],[f472]) ).
fof(f472,axiom,
! [X14] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X14) = X14,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_number__of__is__id) ).
fof(f4533,plain,
! [X0,X1] :
( c_Int_Onumber__class_Onumber__of(X1,X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f2463]) ).
fof(f2463,plain,
! [X0,X1] :
( ( ( c_Int_Onumber__class_Onumber__of(X1,X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) )
& ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ) )
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f1596]) ).
fof(f1596,plain,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0))
=> c_Int_Onumber__class_Onumber__of(X1,X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0))
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ) ),
inference(rectify,[],[f747]) ).
fof(f747,axiom,
! [X48,X4] :
( class_Int_Onumber__ring(X4)
=> ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X48))
=> c_Int_Onumber__class_Onumber__of(X4,X48) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48)) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X48))
=> c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_of__nat__number__of__eq) ).
fof(f14338,plain,
spl104_931,
inference(avatar_split_clause,[],[f5675,f14336]) ).
fof(f14336,plain,
( spl104_931
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_931])]) ).
fof(f5675,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(forward_demodulation,[],[f5674,f4119]) ).
fof(f4119,plain,
c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f186]) ).
fof(f186,axiom,
c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_One__nat__def) ).
fof(f5674,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(forward_demodulation,[],[f4328,f4119]) ).
fof(f4328,plain,
! [X0] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(cnf_transformation,[],[f2396]) ).
fof(f2396,plain,
! [X0] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(flattening,[],[f2395]) ).
fof(f2395,plain,
! [X0] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(ennf_transformation,[],[f1455]) ).
fof(f1455,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f331]) ).
fof(f331,axiom,
! [X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
=> ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X3
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X3 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__lt__two__imp__zero__or__one) ).
fof(f14334,plain,
spl104_930,
inference(avatar_split_clause,[],[f5542,f14332]) ).
fof(f14332,plain,
( spl104_930
<=> ! [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,[spl104_930])]) ).
fof(f5542,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,[],[f3240]) ).
fof(f3240,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,[],[f3239]) ).
fof(f3239,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,[],[f2224]) ).
fof(f2224,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,[],[f40]) ).
fof(f40,axiom,
! [X25,X3,X22,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X22,X3)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X25,X22)
=> c_Orderings_Oord__class_Oless__eq(X4,X25,X3) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_xt1_I6_J) ).
fof(f14330,plain,
spl104_929,
inference(avatar_split_clause,[],[f5541,f14328]) ).
fof(f14328,plain,
( spl104_929
<=> ! [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,[spl104_929])]) ).
fof(f5541,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,[],[f3238]) ).
fof(f3238,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,[],[f3237]) ).
fof(f3237,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,[],[f2223]) ).
fof(f2223,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,[],[f219]) ).
fof(f219,axiom,
! [X25,X3,X22,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X22,X3)
=> ( c_Orderings_Oord__class_Oless(X4,X25,X22)
=> c_Orderings_Oord__class_Oless(X4,X25,X3) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_xt1_I8_J) ).
fof(f14326,plain,
spl104_928,
inference(avatar_split_clause,[],[f5539,f14324]) ).
fof(f14324,plain,
( spl104_928
<=> ! [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,[spl104_928])]) ).
fof(f5539,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,[],[f3234]) ).
fof(f3234,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,[],[f3233]) ).
fof(f3233,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,[],[f2221]) ).
fof(f2221,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
inference(rectify,[],[f217]) ).
fof(f217,axiom,
! [X25,X3,X22,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X22,X3)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X25,X22)
=> c_Orderings_Oord__class_Oless(X4,X25,X3) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_xt1_I7_J) ).
fof(f14305,plain,
spl104_927,
inference(avatar_split_clause,[],[f5538,f14303]) ).
fof(f14303,plain,
( spl104_927
<=> ! [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,[spl104_927])]) ).
fof(f5538,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,[],[f3232]) ).
fof(f3232,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,[],[f3231]) ).
fof(f3231,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,[],[f2220]) ).
fof(f2220,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X0,X2)
=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
inference(rectify,[],[f165]) ).
fof(f165,axiom,
! [X25,X3,X22,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X22,X3)
=> ( c_Orderings_Oord__class_Oless(X4,X25,X22)
=> c_Orderings_Oord__class_Oless(X4,X25,X3) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_xt1_I10_J) ).
fof(f14301,plain,
spl104_926,
inference(avatar_split_clause,[],[f5534,f14299]) ).
fof(f14299,plain,
( spl104_926
<=> ! [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,[spl104_926])]) ).
fof(f5534,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,[],[f3224]) ).
fof(f3224,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,[],[f3223]) ).
fof(f3223,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,[],[f2216]) ).
fof(f2216,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,[],[f42]) ).
fof(f42,axiom,
! [X25,X22,X3,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X22)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X22,X25)
=> c_Orderings_Oord__class_Oless__eq(X4,X3,X25) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_order__trans) ).
fof(f14297,plain,
spl104_925,
inference(avatar_split_clause,[],[f5533,f14295]) ).
fof(f14295,plain,
( spl104_925
<=> ! [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,[spl104_925])]) ).
fof(f5533,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,[],[f3222]) ).
fof(f3222,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,[],[f3221]) ).
fof(f3221,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,[],[f2215]) ).
fof(f2215,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,[],[f218]) ).
fof(f218,axiom,
! [X25,X22,X3,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X22)
=> ( c_Orderings_Oord__class_Oless(X4,X22,X25)
=> c_Orderings_Oord__class_Oless(X4,X3,X25) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_order__le__less__trans) ).
fof(f14293,plain,
spl104_924,
inference(avatar_split_clause,[],[f5532,f14291]) ).
fof(f14291,plain,
( spl104_924
<=> ! [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,[spl104_924])]) ).
fof(f5532,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,[],[f3220]) ).
fof(f3220,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,[],[f3219]) ).
fof(f3219,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,[],[f2214]) ).
fof(f2214,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,[],[f216]) ).
fof(f216,axiom,
! [X25,X22,X3,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X22)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X22,X25)
=> c_Orderings_Oord__class_Oless(X4,X3,X25) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_order__less__le__trans) ).
fof(f14289,plain,
spl104_923,
inference(avatar_split_clause,[],[f5531,f14287]) ).
fof(f14287,plain,
( spl104_923
<=> ! [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,[spl104_923])]) ).
fof(f5531,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,[],[f3218]) ).
fof(f3218,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,[],[f3217]) ).
fof(f3217,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Opreorder(X3) ),
inference(ennf_transformation,[],[f2213]) ).
fof(f2213,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Opreorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( c_Orderings_Oord__class_Oless(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
inference(rectify,[],[f164]) ).
fof(f164,axiom,
! [X25,X22,X3,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X22)
=> ( c_Orderings_Oord__class_Oless(X4,X22,X25)
=> c_Orderings_Oord__class_Oless(X4,X3,X25) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_order__less__trans) ).
fof(f14285,plain,
spl104_922,
inference(avatar_split_clause,[],[f5527,f14283]) ).
fof(f14283,plain,
( spl104_922
<=> ! [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,[spl104_922])]) ).
fof(f5527,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,[],[f3853]) ).
fof(f3853,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,[],[f3852]) ).
fof(f3852,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,[],[f3215]) ).
fof(f3215,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,[],[f2211]) ).
fof(f2211,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,[],[f343]) ).
fof(f343,axiom,
! [X0,X1,X4,X24] :
( class_Orderings_Oord(X24)
=> ( c_Orderings_Oord__class_Oless(tc_fun(X4,X24),X1,X0)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X24),X0,X1)
& c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X24),X1,X0) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__fun__def) ).
fof(f14281,plain,
spl104_921,
inference(avatar_split_clause,[],[f5526,f14279]) ).
fof(f14279,plain,
( spl104_921
<=> ! [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,[spl104_921])]) ).
fof(f5526,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,[],[f3853]) ).
fof(f14277,plain,
spl104_920,
inference(avatar_split_clause,[],[f5503,f14275]) ).
fof(f14275,plain,
( spl104_920
<=> ! [X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X0,X1)
| X0 != X2
| ~ class_Groups_Ocancel__semigroup__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_920])]) ).
fof(f5503,plain,
! [X2,X3,X0,X1] :
( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X0,X1)
| X0 != X2
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(cnf_transformation,[],[f3851]) ).
fof(f3851,plain,
! [X0,X1,X2,X3] :
( ( ( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X0,X1)
| X0 != X2 )
& ( 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(nnf_transformation,[],[f3187]) ).
fof(f3187,plain,
! [X0,X1,X2,X3] :
( ( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X0,X1)
<=> X0 = X2 )
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(ennf_transformation,[],[f2188]) ).
fof(f2188,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,[],[f57]) ).
fof(f57,axiom,
! [X8,X9,X7,X4] :
( class_Groups_Ocancel__semigroup__add(X4)
=> ( c_Groups_Oplus__class_Oplus(X4,X8,X9) = c_Groups_Oplus__class_Oplus(X4,X7,X9)
<=> X7 = X8 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__right__cancel) ).
fof(f14273,plain,
spl104_919,
inference(avatar_split_clause,[],[f5501,f14271]) ).
fof(f14271,plain,
( spl104_919
<=> ! [X0,X3,X2,X1] :
( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X2,X0)
| X0 != X1
| ~ class_Groups_Ocancel__semigroup__add(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_919])]) ).
fof(f5501,plain,
! [X2,X3,X0,X1] :
( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X2,X0)
| X0 != X1
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(cnf_transformation,[],[f3850]) ).
fof(f3850,plain,
! [X0,X1,X2,X3] :
( ( ( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X2,X0)
| 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(nnf_transformation,[],[f3186]) ).
fof(f3186,plain,
! [X0,X1,X2,X3] :
( ( c_Groups_Oplus__class_Oplus(X3,X2,X1) = c_Groups_Oplus__class_Oplus(X3,X2,X0)
<=> X0 = X1 )
| ~ class_Groups_Ocancel__semigroup__add(X3) ),
inference(ennf_transformation,[],[f2187]) ).
fof(f2187,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,[],[f58]) ).
fof(f58,axiom,
! [X8,X7,X9,X4] :
( class_Groups_Ocancel__semigroup__add(X4)
=> ( c_Groups_Oplus__class_Oplus(X4,X9,X8) = c_Groups_Oplus__class_Oplus(X4,X9,X7)
<=> X7 = X8 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__left__cancel) ).
fof(f14269,plain,
spl104_918,
inference(avatar_split_clause,[],[f5499,f14267]) ).
fof(f14267,plain,
( spl104_918
<=> ! [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,[spl104_918])]) ).
fof(f5499,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,[],[f3185]) ).
fof(f3185,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,[],[f3184]) ).
fof(f3184,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,[],[f2186]) ).
fof(f2186,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,[],[f56]) ).
fof(f56,axiom,
! [X10,X11,X12,X4] :
( class_Groups_Ocancel__semigroup__add(X4)
=> ( c_Groups_Oplus__class_Oplus(X4,X12,X10) = c_Groups_Oplus__class_Oplus(X4,X12,X11)
=> X10 = X11 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__left__imp__eq) ).
fof(f14265,plain,
spl104_917,
inference(avatar_split_clause,[],[f5498,f14263]) ).
fof(f14263,plain,
( spl104_917
<=> ! [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,[spl104_917])]) ).
fof(f5498,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,[],[f3183]) ).
fof(f3183,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,[],[f3182]) ).
fof(f3182,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,[],[f2185]) ).
fof(f2185,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,[],[f54]) ).
fof(f54,axiom,
! [X10,X12,X11,X4] :
( class_Groups_Ocancel__semigroup__add(X4)
=> ( c_Groups_Oplus__class_Oplus(X4,X10,X12) = c_Groups_Oplus__class_Oplus(X4,X11,X12)
=> X10 = X11 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__right__imp__eq) ).
fof(f14261,plain,
spl104_916,
inference(avatar_split_clause,[],[f5496,f14259]) ).
fof(f14259,plain,
( spl104_916
<=> ! [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,[spl104_916])]) ).
fof(f5496,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,[],[f3180]) ).
fof(f3180,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,[],[f3179]) ).
fof(f3179,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,[],[f2183]) ).
fof(f2183,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,[],[f55]) ).
fof(f55,axiom,
! [X10,X11,X12,X4] :
( class_Groups_Ocancel__ab__semigroup__add(X4)
=> ( c_Groups_Oplus__class_Oplus(X4,X12,X10) = c_Groups_Oplus__class_Oplus(X4,X12,X11)
=> X10 = X11 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__imp__eq) ).
fof(f14257,plain,
spl104_915,
inference(avatar_split_clause,[],[f5434,f14255]) ).
fof(f14255,plain,
( spl104_915
<=> ! [X0,X3,X2,X1] :
( sP22(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_915])]) ).
fof(f5434,plain,
! [X2,X3,X0,X1] :
( sP22(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f3840]) ).
fof(f3840,plain,
! [X0,X1,X2,X3] :
( ( sP22(X0,X1,X2,X3)
| ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ) ) )
& ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
& c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless(X2,X0,X1)
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) )
| ~ sP22(X0,X1,X2,X3) ) ),
inference(rectify,[],[f3839]) ).
fof(f3839,plain,
! [X2,X0,X3,X1] :
( ( sP22(X2,X0,X3,X1)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) )
& ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X2,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
| ~ sP22(X2,X0,X3,X1) ) ),
inference(flattening,[],[f3838]) ).
fof(f3838,plain,
! [X2,X0,X3,X1] :
( ( sP22(X2,X0,X3,X1)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) )
& ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X2,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) )
| ~ sP22(X2,X0,X3,X1) ) ),
inference(nnf_transformation,[],[f3379]) ).
fof(f3379,plain,
! [X2,X0,X3,X1] :
( sP22(X2,X0,X3,X1)
<=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X2)
& c_Orderings_Oord__class_Oless(X3,X1,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X2,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
fof(f14253,plain,
spl104_914,
inference(avatar_split_clause,[],[f5433,f14251]) ).
fof(f14251,plain,
( spl104_914
<=> ! [X0,X3,X2,X1] :
( sP22(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_914])]) ).
fof(f5433,plain,
! [X2,X3,X0,X1] :
( sP22(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ),
inference(cnf_transformation,[],[f3840]) ).
fof(f14249,plain,
spl104_913,
inference(avatar_split_clause,[],[f5431,f14247]) ).
fof(f14247,plain,
( spl104_913
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ sP22(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_913])]) ).
fof(f5431,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ sP22(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3840]) ).
fof(f14245,plain,
spl104_912,
inference(avatar_split_clause,[],[f5430,f14243]) ).
fof(f14243,plain,
( spl104_912
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP22(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_912])]) ).
fof(f5430,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP22(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3840]) ).
fof(f14241,plain,
spl104_911,
inference(avatar_split_clause,[],[f5425,f14239]) ).
fof(f14239,plain,
( spl104_911
<=> ! [X0,X3,X2,X1] :
( sP20(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_911])]) ).
fof(f5425,plain,
! [X2,X3,X0,X1] :
( sP20(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) ),
inference(cnf_transformation,[],[f3835]) ).
fof(f3835,plain,
! [X0,X1,X2,X3] :
( ( sP20(X0,X1,X2,X3)
| ( ( ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ) ) )
& ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
& c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless(X2,X0,X1)
& c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) )
| ~ sP20(X0,X1,X2,X3) ) ),
inference(rectify,[],[f3834]) ).
fof(f3834,plain,
! [X1,X0,X3,X2] :
( ( sP20(X1,X0,X3,X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X1,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) )
| ~ sP20(X1,X0,X3,X2) ) ),
inference(flattening,[],[f3833]) ).
fof(f3833,plain,
! [X1,X0,X3,X2] :
( ( sP20(X1,X0,X3,X2)
| ( ( ~ c_Orderings_Oord__class_Oless(X3,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
& ( ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| ~ c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X1,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) )
| ~ sP20(X1,X0,X3,X2) ) ),
inference(nnf_transformation,[],[f3376]) ).
fof(f3376,plain,
! [X1,X0,X3,X2] :
( sP20(X1,X0,X3,X2)
<=> ( ( c_Orderings_Oord__class_Oless(X3,X0,X1)
& c_Orderings_Oord__class_Oless(X3,X2,c_Groups_Ozero__class_Ozero(X3)) )
| ( c_Orderings_Oord__class_Oless(X3,X1,X0)
& c_Orderings_Oord__class_Oless(X3,c_Groups_Ozero__class_Ozero(X3),X2) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).
fof(f14237,plain,
spl104_910,
inference(avatar_split_clause,[],[f5424,f14235]) ).
fof(f14235,plain,
( spl104_910
<=> ! [X0,X3,X2,X1] :
( sP20(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_910])]) ).
fof(f5424,plain,
! [X2,X3,X0,X1] :
( sP20(X0,X1,X2,X3)
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3) ),
inference(cnf_transformation,[],[f3835]) ).
fof(f14233,plain,
spl104_909,
inference(avatar_split_clause,[],[f5422,f14231]) ).
fof(f14231,plain,
( spl104_909
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ sP20(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_909])]) ).
fof(f5422,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,c_Groups_Ozero__class_Ozero(X2),X3)
| ~ sP20(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3835]) ).
fof(f14229,plain,
spl104_908,
inference(avatar_split_clause,[],[f5421,f14227]) ).
fof(f14227,plain,
( spl104_908
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP20(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_908])]) ).
fof(f5421,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X3,c_Groups_Ozero__class_Ozero(X2))
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP20(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3835]) ).
fof(f14225,plain,
( ~ spl104_907
| spl104_886
| ~ spl104_368
| ~ spl104_730 ),
inference(avatar_split_clause,[],[f12061,f11330,f7732,f14138,f14222]) ).
fof(f14222,plain,
( spl104_907
<=> class_Groups_Ogroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_907])]) ).
fof(f14138,plain,
( spl104_886
<=> ! [X13] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X13 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_886])]) ).
fof(f7732,plain,
( spl104_368
<=> ! [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,[spl104_368])]) ).
fof(f11330,plain,
( spl104_730
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ominus__class_Ominus(X2,X1,X0) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_730])]) ).
fof(f12061,plain,
( ! [X13] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X13
| ~ class_Groups_Ogroup__add(tc_Nat_Onat) )
| ~ spl104_368
| ~ spl104_730 ),
inference(trivial_inequality_removal,[],[f12060]) ).
fof(f12060,plain,
( ! [X13] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X13
| ~ class_Groups_Ogroup__add(tc_Nat_Onat) )
| ~ spl104_368
| ~ spl104_730 ),
inference(superposition,[],[f11331,f7733]) ).
fof(f7733,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)
| ~ spl104_368 ),
inference(avatar_component_clause,[],[f7732]) ).
fof(f11331,plain,
( ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) != c_Groups_Ozero__class_Ozero(X2)
| X0 = X1
| ~ class_Groups_Ogroup__add(X2) )
| ~ spl104_730 ),
inference(avatar_component_clause,[],[f11330]) ).
fof(f14220,plain,
spl104_906,
inference(avatar_split_clause,[],[f5359,f14218]) ).
fof(f14218,plain,
( spl104_906
<=> ! [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,[spl104_906])]) ).
fof(f5359,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,[],[f3809]) ).
fof(f3809,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,[],[f2093]) ).
fof(f2093,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,[],[f34]) ).
fof(f34,axiom,
! [X18,X17,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X17),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X18))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X18) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__add__left__cancel__le) ).
fof(f14216,plain,
spl104_905,
inference(avatar_split_clause,[],[f5358,f14214]) ).
fof(f14214,plain,
( spl104_905
<=> ! [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,[spl104_905])]) ).
fof(f5358,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,[],[f3809]) ).
fof(f14212,plain,
spl104_904,
inference(avatar_split_clause,[],[f5357,f14210]) ).
fof(f14210,plain,
( spl104_904
<=> ! [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,[spl104_904])]) ).
fof(f5357,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,[],[f3808]) ).
fof(f3808,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,[],[f2092]) ).
fof(f2092,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,[],[f258]) ).
fof(f258,axiom,
! [X18,X17,X20] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X17),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X18))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__add__left__cancel__less) ).
fof(f14208,plain,
spl104_903,
inference(avatar_split_clause,[],[f5356,f14206]) ).
fof(f14206,plain,
( spl104_903
<=> ! [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,[spl104_903])]) ).
fof(f5356,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,[],[f3808]) ).
fof(f14204,plain,
spl104_902,
inference(avatar_split_clause,[],[f5355,f14202]) ).
fof(f14202,plain,
( spl104_902
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))))
| ~ sP19(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_902])]) ).
fof(f5355,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))))
| ~ sP19(X2,X0,X1) ),
inference(cnf_transformation,[],[f3807]) ).
fof(f3807,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))))
| ~ sP19(X2,X0,X1) )
& ( sP19(X2,X0,X1)
| ~ hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))) ) ),
inference(nnf_transformation,[],[f3375]) ).
fof(f3375,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))))
<=> sP19(X2,X0,X1) ),
inference(definition_folding,[],[f3046,f3374]) ).
fof(f3374,plain,
! [X2,X0,X1] :
( sP19(X2,X0,X1)
<=> ( ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f3046,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))))
<=> ( ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) ) ),
inference(ennf_transformation,[],[f2091]) ).
fof(f2091,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1)
=> hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)))) ) ) ),
inference(rectify,[],[f749]) ).
fof(f749,axiom,
! [X26,X23,X41] :
( hBOOL(hAPP(X41,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X23,X26))))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X26)
=> hBOOL(hAPP(X41,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X26,X23)
=> hBOOL(hAPP(X41,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26)))) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zdiff__int__split) ).
fof(f14200,plain,
spl104_901,
inference(avatar_split_clause,[],[f5354,f14198]) ).
fof(f14198,plain,
( spl104_901
<=> ! [X2,X0,X1] :
( sP19(X2,X0,X1)
| ~ hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_901])]) ).
fof(f5354,plain,
! [X2,X0,X1] :
( sP19(X2,X0,X1)
| ~ hBOOL(hAPP(X2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))) ),
inference(cnf_transformation,[],[f3807]) ).
fof(f14196,plain,
spl104_900,
inference(avatar_split_clause,[],[f5343,f14194]) ).
fof(f14194,plain,
( spl104_900
<=> ! [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,[spl104_900])]) ).
fof(f5343,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,[],[f3801]) ).
fof(f3801,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,[],[f2088]) ).
fof(f2088,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,[],[f304]) ).
fof(f304,axiom,
! [X35,X20,X42] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X20),X35)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X42,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X20)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__diff__conv) ).
fof(f14192,plain,
spl104_899,
inference(avatar_split_clause,[],[f5342,f14190]) ).
fof(f14190,plain,
( spl104_899
<=> ! [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,[spl104_899])]) ).
fof(f5342,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,[],[f3801]) ).
fof(f14188,plain,
spl104_898,
inference(avatar_split_clause,[],[f5341,f14186]) ).
fof(f14186,plain,
( spl104_898
<=> ! [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,[spl104_898])]) ).
fof(f5341,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,[],[f3800]) ).
fof(f3800,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,[],[f2087]) ).
fof(f2087,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,[],[f176]) ).
fof(f176,axiom,
! [X20,X42,X35] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X35,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X42,X20))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X35,X20),X42) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__diff__conv) ).
fof(f14184,plain,
spl104_897,
inference(avatar_split_clause,[],[f5340,f14182]) ).
fof(f14182,plain,
( spl104_897
<=> ! [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,[spl104_897])]) ).
fof(f5340,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,[],[f3800]) ).
fof(f14180,plain,
spl104_896,
inference(avatar_split_clause,[],[f5333,f14178]) ).
fof(f14178,plain,
( spl104_896
<=> ! [X2,X4,X0,X1] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1
| ~ sP18(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_896])]) ).
fof(f5333,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f3798]) ).
fof(f3798,plain,
! [X0,X1,X2] :
( ( sP18(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK99(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK99(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) ) )
| ~ sP18(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK99])],[f3796,f3797]) ).
fof(f3797,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
=> ( ~ hBOOL(hAPP(X0,sK99(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK99(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f3796,plain,
! [X0,X1,X2] :
( ( sP18(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) ) )
| ~ sP18(X0,X1,X2) ) ),
inference(rectify,[],[f3795]) ).
fof(f3795,plain,
! [X2,X1,X0] :
( ( sP18(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) ) )
| ~ sP18(X2,X1,X0) ) ),
inference(flattening,[],[f3794]) ).
fof(f3794,plain,
! [X2,X1,X0] :
( ( sP18(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) ) )
| ~ sP18(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3372]) ).
fof(f3372,plain,
! [X2,X1,X0] :
( sP18(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,[sP18])]) ).
fof(f14176,plain,
spl104_895,
inference(avatar_split_clause,[],[f5325,f14174]) ).
fof(f14174,plain,
( spl104_895
<=> ! [X2,X4,X0,X1] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1
| ~ sP17(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_895])]) ).
fof(f5325,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(X0,X4))
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X4) != X1
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f3792]) ).
fof(f3792,plain,
! [X0,X1,X2] :
( ( sP17(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK98(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK98(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) ) )
| ~ sP17(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK98])],[f3790,f3791]) ).
fof(f3791,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X3) = X1 )
=> ( ~ hBOOL(hAPP(X0,sK98(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,sK98(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f3790,plain,
! [X0,X1,X2] :
( ( sP17(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) ) )
| ~ sP17(X0,X1,X2) ) ),
inference(rectify,[],[f3789]) ).
fof(f3789,plain,
! [X2,X1,X0] :
( ( sP17(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) ) )
| ~ sP17(X2,X1,X0) ) ),
inference(flattening,[],[f3788]) ).
fof(f3788,plain,
! [X2,X1,X0] :
( ( sP17(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) ) )
| ~ sP17(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3370]) ).
fof(f3370,plain,
! [X2,X1,X0] :
( sP17(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,[sP17])]) ).
fof(f14172,plain,
spl104_894,
inference(avatar_split_clause,[],[f5273,f14170]) ).
fof(f14170,plain,
( spl104_894
<=> ! [X2,X0,X1] :
( 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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_894])]) ).
fof(f5273,plain,
! [X2,X0,X1] :
( 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(cnf_transformation,[],[f3752]) ).
fof(f3752,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,[],[f3032]) ).
fof(f3032,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,[],[f3031]) ).
fof(f3031,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,[],[f2077]) ).
fof(f2077,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,[],[f365]) ).
fof(f365,axiom,
! [X26,X23,X4] :
( ( class_Int_Oring__char__0(X4)
& class_Int_Onumber__ring(X4) )
=> ( c_Int_Onumber__class_Onumber__of(X4,X23) = c_Int_Onumber__class_Onumber__of(X4,X26)
<=> X23 = X26 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_eq__number__of) ).
fof(f14168,plain,
spl104_893,
inference(avatar_split_clause,[],[f5272,f14166]) ).
fof(f14166,plain,
( spl104_893
<=> ! [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,[spl104_893])]) ).
fof(f5272,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,[],[f3752]) ).
fof(f14164,plain,
spl104_892,
inference(avatar_split_clause,[],[f5208,f14162]) ).
fof(f14162,plain,
( spl104_892
<=> ! [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,[spl104_892])]) ).
fof(f5208,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,[],[f2966]) ).
fof(f2966,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,[],[f2031]) ).
fof(f2031,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,[],[f31]) ).
fof(f31,axiom,
! [X14,X15,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,X15)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X14),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__le__mono1) ).
fof(f14160,plain,
spl104_891,
inference(avatar_split_clause,[],[f5207,f14158]) ).
fof(f14158,plain,
( spl104_891
<=> ! [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,[spl104_891])]) ).
fof(f5207,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,[],[f2965]) ).
fof(f2965,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,[],[f2030]) ).
fof(f2030,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,[],[f238]) ).
fof(f238,axiom,
! [X19,X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X19),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,X19)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__le__mono) ).
fof(f14156,plain,
spl104_890,
inference(avatar_split_clause,[],[f5206,f14154]) ).
fof(f14154,plain,
( spl104_890
<=> ! [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,[spl104_890])]) ).
fof(f5206,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,[],[f2964]) ).
fof(f2964,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,[],[f2029]) ).
fof(f2029,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,[],[f239]) ).
fof(f239,axiom,
! [X19,X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X5),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X19,X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__le__mono2) ).
fof(f14152,plain,
spl104_889,
inference(avatar_split_clause,[],[f5205,f14150]) ).
fof(f14150,plain,
( spl104_889
<=> ! [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,[spl104_889])]) ).
fof(f5205,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,[],[f2963]) ).
fof(f2963,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,[],[f2028]) ).
fof(f2028,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,[],[f974]) ).
fof(f974,axiom,
! [X14,X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X6,X14),c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X5,X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_div__le__mono) ).
fof(f14148,plain,
spl104_888,
inference(avatar_split_clause,[],[f5204,f14146]) ).
fof(f14146,plain,
( spl104_888
<=> ! [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,[spl104_888])]) ).
fof(f5204,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,[],[f2962]) ).
fof(f2962,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,[],[f2027]) ).
fof(f2027,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,[],[f303]) ).
fof(f303,axiom,
! [X6,X5,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X6),X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__add__diff) ).
fof(f14144,plain,
spl104_887,
inference(avatar_split_clause,[],[f5196,f14142]) ).
fof(f14142,plain,
( spl104_887
<=> ! [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,[spl104_887])]) ).
fof(f5196,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,[],[f2951]) ).
fof(f2951,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,[],[f2019]) ).
fof(f2019,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,[],[f439]) ).
fof(f439,axiom,
! [X14,X15,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,X15)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X16),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,X15)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zadd__left__mono) ).
fof(f14140,plain,
( ~ spl104_885
| spl104_886
| ~ spl104_368
| ~ spl104_729 ),
inference(avatar_split_clause,[],[f12046,f11326,f7732,f14138,f14134]) ).
fof(f14134,plain,
( spl104_885
<=> class_Groups_Oab__group__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_885])]) ).
fof(f11326,plain,
( spl104_729
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ominus__class_Ominus(X2,X1,X0) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_729])]) ).
fof(f12046,plain,
( ! [X13] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X13
| ~ class_Groups_Oab__group__add(tc_Nat_Onat) )
| ~ spl104_368
| ~ spl104_729 ),
inference(trivial_inequality_removal,[],[f12045]) ).
fof(f12045,plain,
( ! [X13] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X13
| ~ class_Groups_Oab__group__add(tc_Nat_Onat) )
| ~ spl104_368
| ~ spl104_729 ),
inference(superposition,[],[f11327,f7733]) ).
fof(f11327,plain,
( ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) != c_Groups_Ozero__class_Ozero(X2)
| X0 = X1
| ~ class_Groups_Oab__group__add(X2) )
| ~ spl104_729 ),
inference(avatar_component_clause,[],[f11326]) ).
fof(f14132,plain,
spl104_884,
inference(avatar_split_clause,[],[f5193,f14130]) ).
fof(f14130,plain,
( spl104_884
<=> ! [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,[spl104_884])]) ).
fof(f5193,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,[],[f2946]) ).
fof(f2946,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,[],[f2016]) ).
fof(f2016,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,[],[f77]) ).
fof(f77,axiom,
! [X25,X22,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X22)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X25,X3),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X25,X22)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__add__left__mono) ).
fof(f14128,plain,
spl104_883,
inference(avatar_split_clause,[],[f5187,f14126]) ).
fof(f14126,plain,
( spl104_883
<=> ! [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,[spl104_883])]) ).
fof(f5187,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,[],[f2935]) ).
fof(f2935,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,[],[f2010]) ).
fof(f2010,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,[],[f261]) ).
fof(f261,axiom,
! [X14,X15,X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X15)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X14),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__less__mono1) ).
fof(f14124,plain,
spl104_882,
inference(avatar_split_clause,[],[f5179,f14122]) ).
fof(f14122,plain,
( spl104_882
<=> ! [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,[spl104_882])]) ).
fof(f5179,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,[],[f2925]) ).
fof(f2925,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,[],[f2002]) ).
fof(f2002,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,[],[f430]) ).
fof(f430,axiom,
! [X14,X15,X16] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X16,X15)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X16,X14),c_Groups_Oplus__class_Oplus(tc_Int_Oint,X15,X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zadd__strict__right__mono) ).
fof(f14120,plain,
spl104_881,
inference(avatar_split_clause,[],[f5149,f14118]) ).
fof(f14118,plain,
( spl104_881
<=> ! [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,[spl104_881])]) ).
fof(f5149,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,[],[f3719]) ).
fof(f3719,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,[],[f3718]) ).
fof(f3718,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,[],[f2893]) ).
fof(f2893,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,[],[f1983]) ).
fof(f1983,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,[],[f203]) ).
fof(f203,axiom,
! [X26,X23,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X23,X26)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(X4,X26,X23)
& c_Orderings_Oord__class_Oless__eq(X4,X23,X26) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__le__not__le) ).
fof(f14116,plain,
spl104_880,
inference(avatar_split_clause,[],[f5117,f14114]) ).
fof(f14114,plain,
( spl104_880
<=> ! [X2,X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1)
| X0 != X1
| ~ class_Nat_Osemiring__char__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_880])]) ).
fof(f5117,plain,
! [X2,X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1)
| X0 != X1
| ~ class_Nat_Osemiring__char__0(X2) ),
inference(cnf_transformation,[],[f3715]) ).
fof(f3715,plain,
! [X0,X1,X2] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1) ) )
| ~ class_Nat_Osemiring__char__0(X2) ),
inference(nnf_transformation,[],[f2857]) ).
fof(f2857,plain,
! [X0,X1,X2] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1)
<=> X0 = X1 )
| ~ class_Nat_Osemiring__char__0(X2) ),
inference(ennf_transformation,[],[f1956]) ).
fof(f1956,plain,
! [X0,X1,X2] :
( class_Nat_Osemiring__char__0(X2)
=> ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1)
<=> X0 = X1 ) ),
inference(rectify,[],[f598]) ).
fof(f598,axiom,
! [X18,X17,X4] :
( class_Nat_Osemiring__char__0(X4)
=> ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X17) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X18)
<=> X17 = X18 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_of__nat__eq__iff) ).
fof(f14112,plain,
spl104_879,
inference(avatar_split_clause,[],[f5116,f14110]) ).
fof(f14110,plain,
( spl104_879
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1)
| ~ class_Nat_Osemiring__char__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_879])]) ).
fof(f5116,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1)
| ~ class_Nat_Osemiring__char__0(X2) ),
inference(cnf_transformation,[],[f3715]) ).
fof(f14108,plain,
spl104_878,
inference(avatar_split_clause,[],[f5027,f14106]) ).
fof(f14106,plain,
( spl104_878
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Oabs__class_Oabs(X2,X1)),X0))
| ~ class_Rings_Olinordered__idom(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_878])]) ).
fof(f5027,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Oabs__class_Oabs(X2,X1)),X0))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(cnf_transformation,[],[f2735]) ).
fof(f2735,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Oabs__class_Oabs(X2,X1)),X0))
| ~ class_Rings_Olinordered__idom(X2) ),
inference(ennf_transformation,[],[f1885]) ).
fof(f1885,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__idom(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Power_Opower__class_Opower(X2),c_Groups_Oabs__class_Oabs(X2,X1)),X0)) ),
inference(rectify,[],[f910]) ).
fof(f910,axiom,
! [X5,X12,X4] :
( class_Rings_Olinordered__idom(X4)
=> c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Oabs__class_Oabs(X4,X12)),X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__le__power__abs) ).
fof(f14104,plain,
spl104_877,
inference(avatar_split_clause,[],[f5008,f14102]) ).
fof(f14102,plain,
( spl104_877
<=> ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_877])]) ).
fof(f5008,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) ),
inference(cnf_transformation,[],[f3691]) ).
fof(f3691,plain,
! [X0,X1,X2] :
( ( sP9(X0,X1,X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
& c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1)) )
| ( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
& c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) )
| ~ sP9(X0,X1,X2) ) ),
inference(rectify,[],[f3690]) ).
fof(f3690,plain,
! [X0,X2,X1] :
( ( sP9(X0,X2,X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
| ~ sP9(X0,X2,X1) ) ),
inference(flattening,[],[f3689]) ).
fof(f3689,plain,
! [X0,X2,X1] :
( ( sP9(X0,X2,X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
| ~ sP9(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f3357]) ).
fof(f3357,plain,
! [X0,X2,X1] :
( sP9(X0,X2,X1)
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f14100,plain,
spl104_876,
inference(avatar_split_clause,[],[f5007,f14098]) ).
fof(f14098,plain,
( spl104_876
<=> ! [X2,X0,X1] :
( sP9(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_876])]) ).
fof(f5007,plain,
! [X2,X0,X1] :
( sP9(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2) ),
inference(cnf_transformation,[],[f3691]) ).
fof(f14096,plain,
spl104_875,
inference(avatar_split_clause,[],[f5006,f14094]) ).
fof(f14094,plain,
( spl104_875
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_875])]) ).
fof(f5006,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f3691]) ).
fof(f14070,plain,
spl104_874,
inference(avatar_split_clause,[],[f5005,f14068]) ).
fof(f14068,plain,
( spl104_874
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_874])]) ).
fof(f5005,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f3691]) ).
fof(f14066,plain,
spl104_873,
inference(avatar_split_clause,[],[f5004,f14064]) ).
fof(f14064,plain,
( spl104_873
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_873])]) ).
fof(f5004,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Ozero__class_Ozero(X1))
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f3691]) ).
fof(f14062,plain,
spl104_872,
inference(avatar_split_clause,[],[f5003,f14060]) ).
fof(f14060,plain,
( spl104_872
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ sP9(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_872])]) ).
fof(f5003,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X2,c_Groups_Ozero__class_Ozero(X1))
| c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X2)
| ~ sP9(X0,X1,X2) ),
inference(cnf_transformation,[],[f3691]) ).
fof(f14058,plain,
spl104_871,
inference(avatar_split_clause,[],[f4999,f14056]) ).
fof(f14056,plain,
( spl104_871
<=> ! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_871])]) ).
fof(f4999,plain,
! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0)) ),
inference(cnf_transformation,[],[f3686]) ).
fof(f3686,plain,
! [X0,X1,X2] :
( ( sP7(X0,X1,X2)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| ~ c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
& c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0)) )
| ( c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
& c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2) )
| ~ sP7(X0,X1,X2) ) ),
inference(rectify,[],[f3685]) ).
fof(f3685,plain,
! [X2,X0,X1] :
( ( sP7(X2,X0,X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
| ~ sP7(X2,X0,X1) ) ),
inference(flattening,[],[f3684]) ).
fof(f3684,plain,
! [X2,X0,X1] :
( ( sP7(X2,X0,X1)
| ( ( ~ c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) )
| ~ sP7(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3354]) ).
fof(f3354,plain,
! [X2,X0,X1] :
( sP7(X2,X0,X1)
<=> ( ( c_Orderings_Oord__class_Oless__eq(X2,X0,c_Groups_Ozero__class_Ozero(X2))
& c_Orderings_Oord__class_Oless__eq(X2,X1,c_Groups_Ozero__class_Ozero(X2)) )
| ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X0)
& c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f14054,plain,
spl104_870,
inference(avatar_split_clause,[],[f4998,f14052]) ).
fof(f14052,plain,
( spl104_870
<=> ! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_870])]) ).
fof(f4998,plain,
! [X2,X0,X1] :
( sP7(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2) ),
inference(cnf_transformation,[],[f3686]) ).
fof(f14050,plain,
spl104_869,
inference(avatar_split_clause,[],[f4997,f14048]) ).
fof(f14048,plain,
( spl104_869
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_869])]) ).
fof(f4997,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f3686]) ).
fof(f14046,plain,
spl104_868,
inference(avatar_split_clause,[],[f4996,f14044]) ).
fof(f14044,plain,
( spl104_868
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_868])]) ).
fof(f4996,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f3686]) ).
fof(f14042,plain,
spl104_867,
inference(avatar_split_clause,[],[f4995,f14040]) ).
fof(f14040,plain,
( spl104_867
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_867])]) ).
fof(f4995,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X1)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f3686]) ).
fof(f14038,plain,
spl104_866,
inference(avatar_split_clause,[],[f4994,f14036]) ).
fof(f14036,plain,
( spl104_866
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ sP7(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_866])]) ).
fof(f4994,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X2,c_Groups_Ozero__class_Ozero(X0))
| c_Orderings_Oord__class_Oless__eq(X0,c_Groups_Ozero__class_Ozero(X0),X2)
| ~ sP7(X0,X1,X2) ),
inference(cnf_transformation,[],[f3686]) ).
fof(f14034,plain,
spl104_865,
inference(avatar_split_clause,[],[f4983,f14032]) ).
fof(f14032,plain,
( spl104_865
<=> ! [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,[spl104_865])]) ).
fof(f4983,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,[],[f3681]) ).
fof(f3681,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,[],[f2706]) ).
fof(f2706,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,[],[f1864]) ).
fof(f1864,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,[],[f183]) ).
fof(f183,axiom,
! [X7,X9,X4] :
( class_Groups_Oordered__ab__group__add(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X9,X7)
<=> c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ominus__class_Ominus(X4,X9,X7),c_Groups_Ozero__class_Ozero(X4)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__iff__diff__le__0) ).
fof(f14029,plain,
spl104_864,
inference(avatar_split_clause,[],[f4982,f14027]) ).
fof(f14027,plain,
( spl104_864
<=> ! [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,[spl104_864])]) ).
fof(f4982,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,[],[f3681]) ).
fof(f14025,plain,
spl104_863,
inference(avatar_split_clause,[],[f4981,f14023]) ).
fof(f14023,plain,
( spl104_863
<=> ! [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,[spl104_863])]) ).
fof(f4981,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,[],[f3680]) ).
fof(f3680,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,[],[f2705]) ).
fof(f2705,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,[],[f1863]) ).
fof(f1863,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,[],[f137]) ).
fof(f137,axiom,
! [X7,X9,X4] :
( class_Groups_Oordered__ab__group__add(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X9,X7)
<=> c_Orderings_Oord__class_Oless(X4,c_Groups_Ominus__class_Ominus(X4,X9,X7),c_Groups_Ozero__class_Ozero(X4)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__iff__diff__less__0) ).
fof(f14021,plain,
spl104_862,
inference(avatar_split_clause,[],[f4980,f14019]) ).
fof(f14019,plain,
( spl104_862
<=> ! [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,[spl104_862])]) ).
fof(f4980,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,[],[f3680]) ).
fof(f14017,plain,
spl104_861,
inference(avatar_split_clause,[],[f4915,f14015]) ).
fof(f14015,plain,
( spl104_861
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_861])]) ).
fof(f4915,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3668]) ).
fof(f3668,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ) ),
inference(nnf_transformation,[],[f1814]) ).
fof(f1814,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f686]) ).
fof(f686,axiom,
! [X18,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X18) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zle__int) ).
fof(f14013,plain,
spl104_860,
inference(avatar_split_clause,[],[f4914,f14011]) ).
fof(f14011,plain,
( spl104_860
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_860])]) ).
fof(f4914,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
inference(cnf_transformation,[],[f3668]) ).
fof(f14009,plain,
spl104_859,
inference(avatar_split_clause,[],[f4913,f14007]) ).
fof(f4913,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3667]) ).
fof(f3667,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ) ),
inference(nnf_transformation,[],[f1813]) ).
fof(f1813,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f69]) ).
fof(f69,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X18),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X17))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__of__nat__le__iff) ).
fof(f14005,plain,
spl104_858,
inference(avatar_split_clause,[],[f4912,f14003]) ).
fof(f14003,plain,
( spl104_858
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_858])]) ).
fof(f4912,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ),
inference(cnf_transformation,[],[f3667]) ).
fof(f14001,plain,
spl104_857,
inference(avatar_split_clause,[],[f4904,f13999]) ).
fof(f13999,plain,
( spl104_857
<=> ! [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 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_857])]) ).
fof(f4904,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f3662]) ).
fof(f3662,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ) ),
inference(flattening,[],[f3661]) ).
fof(f3661,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)) ) ),
inference(nnf_transformation,[],[f1810]) ).
fof(f1810,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,[],[f869]) ).
fof(f869,axiom,
! [X18,X23] :
( 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),X23),X18))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X23)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__less__power__nat__eq) ).
fof(f13997,plain,
spl104_856,
inference(avatar_split_clause,[],[f4900,f13995]) ).
fof(f13995,plain,
( spl104_856
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_856])]) ).
fof(f4900,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3659]) ).
fof(f3659,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ) ),
inference(nnf_transformation,[],[f1808]) ).
fof(f1808,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f683]) ).
fof(f683,axiom,
! [X26,X23] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X23,X26) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Nat__Transfer_Otransfer__int__nat__relations_I2_J) ).
fof(f13993,plain,
spl104_855,
inference(avatar_split_clause,[],[f4899,f13991]) ).
fof(f13991,plain,
( spl104_855
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_855])]) ).
fof(f4899,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
inference(cnf_transformation,[],[f3659]) ).
fof(f13985,plain,
spl104_854,
inference(avatar_split_clause,[],[f4898,f13983]) ).
fof(f13983,plain,
( spl104_854
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_854])]) ).
fof(f4898,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3658]) ).
fof(f3658,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ) ),
inference(nnf_transformation,[],[f1807]) ).
fof(f1807,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f187]) ).
fof(f187,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X18),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X17))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,X17) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__of__nat__less__iff) ).
fof(f13981,plain,
spl104_853,
inference(avatar_split_clause,[],[f4897,f13979]) ).
fof(f13979,plain,
( spl104_853
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_853])]) ).
fof(f4897,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ),
inference(cnf_transformation,[],[f3658]) ).
fof(f13976,plain,
spl104_852,
inference(avatar_split_clause,[],[f4759,f13974]) ).
fof(f4759,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X2))) != X0 ),
inference(cnf_transformation,[],[f3570]) ).
fof(f3570,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X2))) != X0 )
& ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(sK81(X0,X1)))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK81])],[f3568,f3569]) ).
fof(f3569,plain,
! [X0,X1] :
( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X3))) = X0
=> c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(sK81(X0,X1)))) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3568,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X2))) != X0 )
& ( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X3))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(rectify,[],[f3567]) ).
fof(f3567,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X2))) != X0 )
& ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X2))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
inference(nnf_transformation,[],[f1762]) ).
fof(f1762,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
<=> ? [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X2))) = X0 ),
inference(rectify,[],[f736]) ).
fof(f736,axiom,
! [X55,X50] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X55)
<=> ? [X30] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X50,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X30))) = X55 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zless__iff__Suc__zadd) ).
fof(f13972,plain,
spl104_851,
inference(avatar_split_clause,[],[f4742,f13970]) ).
fof(f13970,plain,
( spl104_851
<=> ! [X0,X1] :
( X0 = X1
| hAPP(X1,sK80(X0,X1)) != hAPP(X0,sK80(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_851])]) ).
fof(f4742,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X1,sK80(X0,X1)) != hAPP(X0,sK80(X0,X1)) ),
inference(cnf_transformation,[],[f3557]) ).
fof(f3557,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X1,sK80(X0,X1)) != hAPP(X0,sK80(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK80])],[f2682,f3556]) ).
fof(f3556,plain,
! [X0,X1] :
( ? [X2] : hAPP(X1,X2) != hAPP(X0,X2)
=> hAPP(X1,sK80(X0,X1)) != hAPP(X0,sK80(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f2682,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] : hAPP(X1,X2) != hAPP(X0,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ! [X2] : hAPP(X1,X2) = hAPP(X0,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_ext) ).
fof(f13968,plain,
spl104_850,
inference(avatar_split_clause,[],[f4531,f13966]) ).
fof(f13966,plain,
( spl104_850
<=> ! [X0,X1] :
( c_Int_Onumber__class_Onumber__of(X1,c_Int_Osucc(X0)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Int_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_850])]) ).
fof(f4531,plain,
! [X0,X1] :
( c_Int_Onumber__class_Onumber__of(X1,c_Int_Osucc(X0)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f2462]) ).
fof(f2462,plain,
! [X0,X1] :
( c_Int_Onumber__class_Onumber__of(X1,c_Int_Osucc(X0)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f1595]) ).
fof(f1595,plain,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> c_Int_Onumber__class_Onumber__of(X1,c_Int_Osucc(X0)) = c_Groups_Oplus__class_Oplus(X1,c_Groups_Oone__class_Oone(X1),c_Int_Onumber__class_Onumber__of(X1,X0)) ),
inference(rectify,[],[f514]) ).
fof(f514,axiom,
! [X14,X4] :
( class_Int_Onumber__ring(X4)
=> c_Int_Onumber__class_Onumber__of(X4,c_Int_Osucc(X14)) = c_Groups_Oplus__class_Oplus(X4,c_Groups_Oone__class_Oone(X4),c_Int_Onumber__class_Onumber__of(X4,X14)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_number__of__succ) ).
fof(f13964,plain,
spl104_849,
inference(avatar_split_clause,[],[f4410,f13962]) ).
fof(f13962,plain,
( spl104_849
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),c_Complex_Ocis(X0)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_849])]) ).
fof(f4410,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),c_Complex_Ocis(X0)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)),
inference(cnf_transformation,[],[f1508]) ).
fof(f1508,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X1)),c_Complex_Ocis(X0)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X1,X0)),
inference(rectify,[],[f857]) ).
fof(f857,axiom,
! [X11,X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocis(X12)),c_Complex_Ocis(X11)) = c_Complex_Ocis(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,X12,X11)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_cis__mult) ).
fof(f13960,plain,
spl104_848,
inference(avatar_split_clause,[],[f4409,f13958]) ).
fof(f13958,plain,
( spl104_848
<=> ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_848])]) ).
fof(f4409,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f1507]) ).
fof(f1507,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(rectify,[],[f112]) ).
fof(f112,axiom,
! [X5,X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Nat_OSuc(X5)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__Suc__eq__diff__pred) ).
fof(f13956,plain,
spl104_847,
inference(avatar_split_clause,[],[f4408,f13954]) ).
fof(f13954,plain,
( spl104_847
<=> ! [X0,X1] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X1)),c_Complex_Oexpi(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_847])]) ).
fof(f4408,plain,
! [X0,X1] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X1)),c_Complex_Oexpi(X0)),
inference(cnf_transformation,[],[f1506]) ).
fof(f1506,plain,
! [X0,X1] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X1,X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X1)),c_Complex_Oexpi(X0)),
inference(rectify,[],[f802]) ).
fof(f802,axiom,
! [X11,X12] : c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,X12,X11)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oexpi(X12)),c_Complex_Oexpi(X11)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_expi__add) ).
fof(f13952,plain,
spl104_846,
inference(avatar_split_clause,[],[f4376,f13950]) ).
fof(f13950,plain,
( spl104_846
<=> ! [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 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_846])]) ).
fof(f4376,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,[],[f3427]) ).
fof(f3427,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,[],[f1479]) ).
fof(f1479,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,[],[f834]) ).
fof(f834,axiom,
! [X23] :
( ~ 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),X23),X23))
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = X23 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__real__square__gt__zero) ).
fof(f13948,plain,
spl104_845,
inference(avatar_split_clause,[],[f4375,f13946]) ).
fof(f13946,plain,
( spl104_845
<=> ! [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,[spl104_845])]) ).
fof(f4375,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,[],[f3427]) ).
fof(f13937,plain,
spl104_844,
inference(avatar_split_clause,[],[f4334,f13935]) ).
fof(f13935,plain,
( spl104_844
<=> ! [X4,X0,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X3),hAPP(X0,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ c_SEQ_Osubseq(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_844])]) ).
fof(f4334,plain,
! [X3,X0,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X3),hAPP(X0,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4)
| ~ c_SEQ_Osubseq(X0) ),
inference(cnf_transformation,[],[f3404]) ).
fof(f3404,plain,
! [X0] :
( ( c_SEQ_Osubseq(X0)
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,sK32(X0)),hAPP(X0,sK33(X0)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK32(X0),sK33(X0)) ) )
& ( ! [X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X3),hAPP(X0,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) )
| ~ c_SEQ_Osubseq(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33])],[f3402,f3403]) ).
fof(f3403,plain,
! [X0] :
( ? [X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,sK32(X0)),hAPP(X0,sK33(X0)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK32(X0),sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f3402,plain,
! [X0] :
( ( c_SEQ_Osubseq(X0)
| ? [X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
& ( ! [X3,X4] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X3),hAPP(X0,X4))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X4) )
| ~ c_SEQ_Osubseq(X0) ) ),
inference(rectify,[],[f3401]) ).
fof(f3401,plain,
! [X0] :
( ( c_SEQ_Osubseq(X0)
| ? [X1,X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) )
& ( ! [X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) )
| ~ c_SEQ_Osubseq(X0) ) ),
inference(nnf_transformation,[],[f2398]) ).
fof(f2398,plain,
! [X0] :
( c_SEQ_Osubseq(X0)
<=> ! [X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,X2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2) ) ),
inference(ennf_transformation,[],[f1459]) ).
fof(f1459,plain,
! [X0] :
( c_SEQ_Osubseq(X0)
<=> ! [X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,X2)) ) ),
inference(rectify,[],[f291]) ).
fof(f291,axiom,
! [X1] :
( c_SEQ_Osubseq(X1)
<=> ! [X34,X30] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X34,X30)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X34),hAPP(X1,X30)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_subseq__def) ).
fof(f13933,plain,
spl104_843,
inference(avatar_split_clause,[],[f4323,f13931]) ).
fof(f13931,plain,
( spl104_843
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK29(X0))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_843])]) ).
fof(f4323,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK29(X0))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[],[f3393]) ).
fof(f3393,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK29(X0))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK29(X0)),X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f2390,f3392]) ).
fof(f3392,plain,
! [X0] :
( ? [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X1)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),X0) )
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(sK29(X0))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK29(X0)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f2390,plain,
! [X0] :
( ? [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X1)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(ennf_transformation,[],[f1451]) ).
fof(f1451,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
=> ? [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X1)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),X0) ) ),
inference(rectify,[],[f413]) ).
fof(f413,axiom,
! [X53] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X53)
=> ? [X30] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X53,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X30)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X30),X53) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_reals__Archimedean6a) ).
fof(f13929,plain,
spl104_842,
inference(avatar_split_clause,[],[f4224,f13927]) ).
fof(f13927,plain,
( spl104_842
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_842])]) ).
fof(f4224,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls) ),
inference(cnf_transformation,[],[f2296]) ).
fof(f2296,plain,
! [X0] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(X0))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls) ) ),
inference(ennf_transformation,[],[f1357]) ).
fof(f1357,plain,
! [X0] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(X0)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(rectify,[],[f551]) ).
fof(f551,axiom,
! [X48] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,c_Int_OPls)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Opred(X48)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X48,c_Int_OPls)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__number__of__diff__1) ).
fof(f13925,plain,
spl104_841,
inference(avatar_split_clause,[],[f4213,f13923]) ).
fof(f13923,plain,
( spl104_841
<=> ! [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,[spl104_841])]) ).
fof(f4213,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,[],[f1351]) ).
fof(f1351,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,[],[f774]) ).
fof(f774,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X6))),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__cube) ).
fof(f13894,plain,
( spl104_840
| ~ spl104_370
| ~ spl104_419
| ~ spl104_439
| ~ spl104_839 ),
inference(avatar_split_clause,[],[f13890,f13886,f8138,f7990,f7740,f13892]) ).
fof(f7740,plain,
( spl104_370
<=> ! [X0] : c_Int_Osucc(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_370])]) ).
fof(f7990,plain,
( spl104_419
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Osucc(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_419])]) ).
fof(f8138,plain,
( spl104_439
<=> ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_439])]) ).
fof(f13886,plain,
( spl104_839
<=> ! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_839])]) ).
fof(f13890,plain,
( ! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X0)) = c_Int_Osucc(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ spl104_370
| ~ spl104_419
| ~ spl104_439
| ~ spl104_839 ),
inference(forward_demodulation,[],[f13889,f8470]) ).
fof(f8470,plain,
( ! [X1] : c_Int_Osucc(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Osucc(c_Int_OPls),X1)
| ~ spl104_370
| ~ spl104_419
| ~ spl104_439 ),
inference(forward_demodulation,[],[f8459,f7992]) ).
fof(f7992,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Osucc(c_Int_OPls)
| ~ spl104_419 ),
inference(avatar_component_clause,[],[f7990]) ).
fof(f8459,plain,
( ! [X1] : c_Int_Osucc(X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| ~ spl104_370
| ~ spl104_439 ),
inference(superposition,[],[f8139,f7741]) ).
fof(f7741,plain,
( ! [X0] : c_Int_Osucc(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl104_370 ),
inference(avatar_component_clause,[],[f7740]) ).
fof(f8139,plain,
( ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0)
| ~ spl104_439 ),
inference(avatar_component_clause,[],[f8138]) ).
fof(f13889,plain,
( ! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Osucc(c_Int_OPls),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ spl104_419
| ~ spl104_839 ),
inference(forward_demodulation,[],[f13887,f7992]) ).
fof(f13887,plain,
( ! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ spl104_839 ),
inference(avatar_component_clause,[],[f13886]) ).
fof(f13888,plain,
spl104_839,
inference(avatar_split_clause,[],[f4212,f13886]) ).
fof(f4212,plain,
! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f1350]) ).
fof(f1350,plain,
! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(rectify,[],[f737]) ).
fof(f737,axiom,
! [X6] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nat_OSuc(X6)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_int__Suc) ).
fof(f13884,plain,
spl104_838,
inference(avatar_split_clause,[],[f4211,f13882]) ).
fof(f13882,plain,
( spl104_838
<=> ! [X0] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_838])]) ).
fof(f4211,plain,
! [X0] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f1349]) ).
fof(f1349,plain,
! [X0] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X0)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rectify,[],[f86]) ).
fof(f86,axiom,
! [X5] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X5)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__of__nat__Suc) ).
fof(f13190,plain,
( spl104_837
| ~ spl104_222
| ~ spl104_564 ),
inference(avatar_split_clause,[],[f9551,f9019,f7087,f13188]) ).
fof(f13188,plain,
( spl104_837
<=> ! [X0] :
( sP4(c_Int_OPls,X0)
| ~ sP3(X0,c_Int_OPls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_837])]) ).
fof(f7087,plain,
( spl104_222
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_222])]) ).
fof(f9019,plain,
( spl104_564
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| sP4(X0,X1)
| ~ sP3(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_564])]) ).
fof(f9551,plain,
( ! [X0] :
( sP4(c_Int_OPls,X0)
| ~ sP3(X0,c_Int_OPls) )
| ~ spl104_222
| ~ spl104_564 ),
inference(resolution,[],[f9020,f7088]) ).
fof(f7088,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0)
| ~ spl104_222 ),
inference(avatar_component_clause,[],[f7087]) ).
fof(f9020,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| sP4(X0,X1)
| ~ sP3(X1,X0) )
| ~ spl104_564 ),
inference(avatar_component_clause,[],[f9019]) ).
fof(f12953,plain,
( spl104_836
| ~ spl104_541 ),
inference(avatar_split_clause,[],[f9289,f8915,f12951]) ).
fof(f12951,plain,
( spl104_836
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_836])]) ).
fof(f8915,plain,
( spl104_541
<=> ! [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,[spl104_541])]) ).
fof(f9289,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl104_541 ),
inference(factoring,[],[f8916]) ).
fof(f8916,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) )
| ~ spl104_541 ),
inference(avatar_component_clause,[],[f8915]) ).
fof(f12876,plain,
( ~ spl104_835
| ~ spl104_370
| ~ spl104_419
| ~ spl104_553 ),
inference(avatar_split_clause,[],[f8973,f8965,f7990,f7740,f12873]) ).
fof(f12873,plain,
( spl104_835
<=> c_Int_OPls = c_Int_Osucc(c_Int_Osucc(c_Int_Osucc(c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_835])]) ).
fof(f8965,plain,
( spl104_553
<=> ! [X0] : c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Osucc(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_553])]) ).
fof(f8973,plain,
( c_Int_OPls != c_Int_Osucc(c_Int_Osucc(c_Int_Osucc(c_Int_OPls)))
| ~ spl104_370
| ~ spl104_419
| ~ spl104_553 ),
inference(forward_demodulation,[],[f8970,f7992]) ).
fof(f8970,plain,
( c_Int_OPls != c_Int_Osucc(c_Int_Osucc(c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl104_370
| ~ spl104_553 ),
inference(superposition,[],[f8966,f7741]) ).
fof(f8966,plain,
( ! [X0] : c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Osucc(X0),X0)
| ~ spl104_553 ),
inference(avatar_component_clause,[],[f8965]) ).
fof(f12696,plain,
( spl104_834
| ~ spl104_495 ),
inference(avatar_split_clause,[],[f8746,f8380,f12694]) ).
fof(f12694,plain,
( spl104_834
<=> ! [X0] :
( sP3(c_Int_OPls,X0)
| c_Int_OPls != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_834])]) ).
fof(f8380,plain,
( spl104_495
<=> ! [X0,X1] :
( c_Int_OPls != X0
| sP3(X0,X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_495])]) ).
fof(f8746,plain,
( ! [X0] :
( sP3(c_Int_OPls,X0)
| c_Int_OPls != X0 )
| ~ spl104_495 ),
inference(equality_resolution,[],[f8381]) ).
fof(f8381,plain,
( ! [X0,X1] :
( c_Int_OPls != X0
| sP3(X0,X1)
| X0 != X1 )
| ~ spl104_495 ),
inference(avatar_component_clause,[],[f8380]) ).
fof(f12601,plain,
spl104_833,
inference(avatar_split_clause,[],[f5883,f12599]) ).
fof(f12599,plain,
( spl104_833
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
| 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,[spl104_833])]) ).
fof(f5883,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) ),
inference(forward_demodulation,[],[f5882,f4119]) ).
fof(f5882,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(forward_demodulation,[],[f4893,f4119]) ).
fof(f4893,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f3655]) ).
fof(f3655,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) ) ),
inference(flattening,[],[f3654]) ).
fof(f3654,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) ) ),
inference(nnf_transformation,[],[f1805]) ).
fof(f1805,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
<=> ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f874]) ).
fof(f874,axiom,
! [X17,X23] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X23),X17)
<=> ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X23
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X17 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__power__eq__Suc__0__iff) ).
fof(f12597,plain,
spl104_832,
inference(avatar_split_clause,[],[f5812,f12595]) ).
fof(f12595,plain,
( spl104_832
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_RComplete_Onatfloor(X1)),X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_832])]) ).
fof(f5812,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_RComplete_Onatfloor(X1)),X0)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ),
inference(forward_demodulation,[],[f4724,f4184]) ).
fof(f4184,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,[],[f1322]) ).
fof(f1322,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,[],[f324]) ).
fof(f324,axiom,
! [X5] : c_Nat_OSuc(X5) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__eq__plus1) ).
fof(f4724,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(cnf_transformation,[],[f2663]) ).
fof(f2663,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(ennf_transformation,[],[f1745]) ).
fof(f1745,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ),
inference(rectify,[],[f464]) ).
fof(f464,axiom,
! [X5,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(X25),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X25,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_ge__natfloor__plus__one__imp__gt) ).
fof(f12593,plain,
spl104_831,
inference(avatar_split_clause,[],[f5775,f12591]) ).
fof(f12591,plain,
( spl104_831
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_831])]) ).
fof(f5775,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0)) ),
inference(forward_demodulation,[],[f5774,f4101]) ).
fof(f5774,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,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(forward_demodulation,[],[f4695,f4101]) ).
fof(f4695,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,[],[f2622]) ).
fof(f2622,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,[],[f1718]) ).
fof(f1718,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,[],[f870]) ).
fof(f870,axiom,
! [X5,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X3)
=> 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),X3),X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).
fof(f12589,plain,
spl104_830,
inference(avatar_split_clause,[],[f5716,f12587]) ).
fof(f12587,plain,
( spl104_830
<=> ! [X0,X1] :
( ~ c_Nat__Numeral_Oneg(X0)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ class_Int_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_830])]) ).
fof(f5716,plain,
! [X0,X1] :
( ~ c_Nat__Numeral_Oneg(X0)
| c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f4532,f4155]) ).
fof(f4532,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0))
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f2463]) ).
fof(f12585,plain,
spl104_829,
inference(avatar_split_clause,[],[f5714,f12583]) ).
fof(f12583,plain,
( spl104_829
<=> ! [X0,X1] :
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) = c_RealVector_Onorm__class_Onorm(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0))
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_829])]) ).
fof(f5714,plain,
! [X0,X1] :
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) = c_RealVector_Onorm__class_Onorm(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0))
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(forward_demodulation,[],[f4455,f4106]) ).
fof(f4106,plain,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f596]) ).
fof(f596,axiom,
c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__of__nat__def) ).
fof(f4455,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X0)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(cnf_transformation,[],[f2408]) ).
fof(f2408,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X0)
| ~ class_RealVector_Oreal__normed__algebra__1(X1) ),
inference(ennf_transformation,[],[f1545]) ).
fof(f1545,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__algebra__1(X1)
=> c_RealVector_Onorm__class_Onorm(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X0) ),
inference(rectify,[],[f613]) ).
fof(f613,axiom,
! [X5,X4] :
( class_RealVector_Oreal__normed__algebra__1(X4)
=> c_RealVector_Onorm__class_Onorm(X4,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X5)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_norm__of__nat) ).
fof(f12581,plain,
( spl104_828
| ~ spl104_481 ),
inference(avatar_split_clause,[],[f8719,f8322,f12579]) ).
fof(f12579,plain,
( spl104_828
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_828])]) ).
fof(f8322,plain,
( spl104_481
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 != X1
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_481])]) ).
fof(f8719,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,X1)
| ~ class_Orderings_Oorder(X0) )
| ~ spl104_481 ),
inference(equality_resolution,[],[f8323]) ).
fof(f8323,plain,
( ! [X2,X0,X1] :
( X0 != X1
| c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| ~ class_Orderings_Oorder(X2) )
| ~ spl104_481 ),
inference(avatar_component_clause,[],[f8322]) ).
fof(f12577,plain,
spl104_827,
inference(avatar_split_clause,[],[f5661,f12575]) ).
fof(f12575,plain,
( spl104_827
<=> ! [X0] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X0)) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_827])]) ).
fof(f5661,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X0)) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ),
inference(forward_demodulation,[],[f4221,f4185]) ).
fof(f4185,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,[],[f1323]) ).
fof(f1323,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,[],[f323]) ).
fof(f323,axiom,
! [X5] : c_Nat_OSuc(X5) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__eq__plus1__left) ).
fof(f4221,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ),
inference(cnf_transformation,[],[f2294]) ).
fof(f2294,plain,
! [X0] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ) ),
inference(ennf_transformation,[],[f1355]) ).
fof(f1355,plain,
! [X0] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
inference(rectify,[],[f523]) ).
fof(f523,axiom,
! [X48] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Int_OPls)
=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X48)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X48,c_Int_OPls)
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__1__add__number__of) ).
fof(f12573,plain,
spl104_826,
inference(avatar_split_clause,[],[f5540,f12571]) ).
fof(f12571,plain,
( spl104_826
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| X0 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_826])]) ).
fof(f5540,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| X0 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f3236]) ).
fof(f3236,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| X0 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f3235]) ).
fof(f3235,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| X0 != X2
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f2222]) ).
fof(f2222,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( X0 = X2
=> c_Orderings_Oord__class_Oless__eq(X3,X0,X1) ) ) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X10,X12,X11,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X11,X12)
=> ( X10 = X11
=> c_Orderings_Oord__class_Oless__eq(X4,X10,X12) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_xt1_I4_J) ).
fof(f12569,plain,
spl104_825,
inference(avatar_split_clause,[],[f5537,f12567]) ).
fof(f12567,plain,
( spl104_825
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| X0 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_825])]) ).
fof(f5537,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| X0 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f3230]) ).
fof(f3230,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| X0 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f3229]) ).
fof(f3229,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X1)
| X0 != X2
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f2219]) ).
fof(f2219,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( X0 = X2
=> c_Orderings_Oord__class_Oless(X3,X0,X1) ) ) ),
inference(rectify,[],[f163]) ).
fof(f163,axiom,
! [X10,X12,X11,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X11,X12)
=> ( X10 = X11
=> c_Orderings_Oord__class_Oless(X4,X10,X12) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_xt1_I2_J) ).
fof(f12565,plain,
spl104_824,
inference(avatar_split_clause,[],[f5536,f12563]) ).
fof(f12563,plain,
( spl104_824
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_824])]) ).
fof(f5536,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f3228]) ).
fof(f3228,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f3227]) ).
fof(f3227,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f2218]) ).
fof(f2218,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( X1 = X2
=> ( c_Orderings_Oord__class_Oless__eq(X3,X0,X1)
=> c_Orderings_Oord__class_Oless__eq(X3,X0,X2) ) ) ),
inference(rectify,[],[f46]) ).
fof(f46,axiom,
! [X10,X11,X12,X4] :
( class_Orderings_Oorder(X4)
=> ( X11 = X12
=> ( c_Orderings_Oord__class_Oless__eq(X4,X10,X11)
=> c_Orderings_Oord__class_Oless__eq(X4,X10,X12) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_xt1_I3_J) ).
fof(f12561,plain,
spl104_823,
inference(avatar_split_clause,[],[f5535,f12559]) ).
fof(f12559,plain,
( spl104_823
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X1)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_823])]) ).
fof(f5535,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X1)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f3226]) ).
fof(f3226,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X1)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f3225]) ).
fof(f3225,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X0,X2)
| ~ c_Orderings_Oord__class_Oless(X3,X0,X1)
| X1 != X2
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f2217]) ).
fof(f2217,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( X1 = X2
=> ( c_Orderings_Oord__class_Oless(X3,X0,X1)
=> c_Orderings_Oord__class_Oless(X3,X0,X2) ) ) ),
inference(rectify,[],[f161]) ).
fof(f161,axiom,
! [X10,X11,X12,X4] :
( class_Orderings_Oorder(X4)
=> ( X11 = X12
=> ( c_Orderings_Oord__class_Oless(X4,X10,X11)
=> c_Orderings_Oord__class_Oless(X4,X10,X12) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_xt1_I1_J) ).
fof(f12557,plain,
spl104_822,
inference(avatar_split_clause,[],[f5525,f12555]) ).
fof(f12555,plain,
( spl104_822
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| X0 != X1
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_822])]) ).
fof(f5525,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| X0 != X1
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f3214]) ).
fof(f3214,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| X0 != X1
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oord(X3) ),
inference(flattening,[],[f3213]) ).
fof(f3213,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| X0 != X1
| ~ c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
| ~ class_Orderings_Oord(X3) ),
inference(ennf_transformation,[],[f2210]) ).
fof(f2210,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oord(X3)
=> ( c_Orderings_Oord__class_Oless__eq(X3,X2,X1)
=> ( X0 = X1
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ) ),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X10,X11,X12,X4] :
( class_Orderings_Oord(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X12,X11)
=> ( X10 = X11
=> c_Orderings_Oord__class_Oless__eq(X4,X12,X10) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_ord__le__eq__trans) ).
fof(f12553,plain,
spl104_821,
inference(avatar_split_clause,[],[f5524,f12551]) ).
fof(f12551,plain,
( spl104_821
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| X0 != X1
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_821])]) ).
fof(f5524,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| X0 != X1
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f3212]) ).
fof(f3212,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| X0 != X1
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oord(X3) ),
inference(flattening,[],[f3211]) ).
fof(f3211,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| X0 != X1
| ~ c_Orderings_Oord__class_Oless(X3,X2,X1)
| ~ class_Orderings_Oord(X3) ),
inference(ennf_transformation,[],[f2209]) ).
fof(f2209,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oord(X3)
=> ( c_Orderings_Oord__class_Oless(X3,X2,X1)
=> ( X0 = X1
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
inference(rectify,[],[f162]) ).
fof(f162,axiom,
! [X10,X11,X12,X4] :
( class_Orderings_Oord(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X12,X11)
=> ( X10 = X11
=> c_Orderings_Oord__class_Oless(X4,X12,X10) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_ord__less__eq__trans) ).
fof(f12549,plain,
spl104_820,
inference(avatar_split_clause,[],[f5523,f12547]) ).
fof(f12547,plain,
( spl104_820
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| X1 != X2
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_820])]) ).
fof(f5523,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| X1 != X2
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f3210]) ).
fof(f3210,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| X1 != X2
| ~ class_Orderings_Oord(X3) ),
inference(flattening,[],[f3209]) ).
fof(f3209,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
| X1 != X2
| ~ class_Orderings_Oord(X3) ),
inference(ennf_transformation,[],[f2208]) ).
fof(f2208,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oord(X3)
=> ( X1 = X2
=> ( c_Orderings_Oord__class_Oless__eq(X3,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(X3,X2,X0) ) ) ),
inference(rectify,[],[f47]) ).
fof(f47,axiom,
! [X10,X11,X12,X4] :
( class_Orderings_Oord(X4)
=> ( X11 = X12
=> ( c_Orderings_Oord__class_Oless__eq(X4,X11,X10)
=> c_Orderings_Oord__class_Oless__eq(X4,X12,X10) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_ord__eq__le__trans) ).
fof(f12545,plain,
spl104_819,
inference(avatar_split_clause,[],[f5522,f12543]) ).
fof(f12543,plain,
( spl104_819
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| X1 != X2
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_819])]) ).
fof(f5522,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| X1 != X2
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f3208]) ).
fof(f3208,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| X1 != X2
| ~ class_Orderings_Oord(X3) ),
inference(flattening,[],[f3207]) ).
fof(f3207,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless(X3,X2,X0)
| ~ c_Orderings_Oord__class_Oless(X3,X1,X0)
| X1 != X2
| ~ class_Orderings_Oord(X3) ),
inference(ennf_transformation,[],[f2207]) ).
fof(f2207,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oord(X3)
=> ( X1 = X2
=> ( c_Orderings_Oord__class_Oless(X3,X1,X0)
=> c_Orderings_Oord__class_Oless(X3,X2,X0) ) ) ),
inference(rectify,[],[f160]) ).
fof(f160,axiom,
! [X10,X11,X12,X4] :
( class_Orderings_Oord(X4)
=> ( X11 = X12
=> ( c_Orderings_Oord__class_Oless(X4,X11,X10)
=> c_Orderings_Oord__class_Oless(X4,X12,X10) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_ord__eq__less__trans) ).
fof(f12541,plain,
spl104_818,
inference(avatar_split_clause,[],[f5432,f12539]) ).
fof(f12539,plain,
( spl104_818
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP22(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_818])]) ).
fof(f5432,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP22(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3840]) ).
fof(f12537,plain,
( spl104_817
| ~ spl104_480 ),
inference(avatar_split_clause,[],[f8718,f8318,f12535]) ).
fof(f12535,plain,
( spl104_817
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,X1)
| ~ class_Orderings_Oorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_817])]) ).
fof(f8318,plain,
( spl104_480
<=> ! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_480])]) ).
fof(f8718,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,X1)
| ~ class_Orderings_Oorder(X0) )
| ~ spl104_480 ),
inference(equality_resolution,[],[f8319]) ).
fof(f8319,plain,
( ! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) )
| ~ spl104_480 ),
inference(avatar_component_clause,[],[f8318]) ).
fof(f12533,plain,
spl104_816,
inference(avatar_split_clause,[],[f5423,f12531]) ).
fof(f12531,plain,
( spl104_816
<=> ! [X0,X3,X2,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP20(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_816])]) ).
fof(f5423,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless(X2,X1,X0)
| c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ sP20(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f3835]) ).
fof(f12529,plain,
spl104_815,
inference(avatar_split_clause,[],[f5332,f12527]) ).
fof(f12527,plain,
( spl104_815
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ sP18(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_815])]) ).
fof(f5332,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)
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f3798]) ).
fof(f12525,plain,
spl104_814,
inference(avatar_split_clause,[],[f5324,f12523]) ).
fof(f12523,plain,
( spl104_814
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X2)
| ~ sP17(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_814])]) ).
fof(f5324,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)
| ~ sP17(X0,X1,X2) ),
inference(cnf_transformation,[],[f3792]) ).
fof(f12521,plain,
spl104_813,
inference(avatar_split_clause,[],[f5188,f12519]) ).
fof(f12519,plain,
( spl104_813
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_813])]) ).
fof(f5188,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(cnf_transformation,[],[f2937]) ).
fof(f2937,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(flattening,[],[f2936]) ).
fof(f2936,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) ),
inference(ennf_transformation,[],[f2011]) ).
fof(f2011,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),X0) ) ),
inference(rectify,[],[f248]) ).
fof(f248,axiom,
! [X14,X15,X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X15)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X16),X14) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__trans__Suc) ).
fof(f12517,plain,
spl104_812,
inference(avatar_split_clause,[],[f5159,f12515]) ).
fof(f12515,plain,
( spl104_812
<=> ! [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,[spl104_812])]) ).
fof(f5159,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,[],[f2913]) ).
fof(f2913,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,[],[f2912]) ).
fof(f2912,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,[],[f1993]) ).
fof(f1993,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,[],[f41]) ).
fof(f41,axiom,
! [X3,X22,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X22,X3)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X3,X22)
=> X3 = X22 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_xt1_I5_J) ).
fof(f12513,plain,
spl104_811,
inference(avatar_split_clause,[],[f5150,f12511]) ).
fof(f12511,plain,
( spl104_811
<=> ! [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,[spl104_811])]) ).
fof(f5150,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,[],[f2895]) ).
fof(f2895,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,[],[f2894]) ).
fof(f2894,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,[],[f1984]) ).
fof(f1984,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,[],[f208]) ).
fof(f208,axiom,
! [X11,X12,X4] :
( class_Orderings_Oorder(X4)
=> ( X11 != X12
=> ( c_Orderings_Oord__class_Oless__eq(X4,X12,X11)
=> c_Orderings_Oord__class_Oless(X4,X12,X11) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_order__neq__le__trans) ).
fof(f12509,plain,
spl104_810,
inference(avatar_split_clause,[],[f5078,f12507]) ).
fof(f12507,plain,
( spl104_810
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 != X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_810])]) ).
fof(f5078,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 != X1
| c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f3705]) ).
fof(f3705,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,[],[f2811]) ).
fof(f2811,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,[],[f2810]) ).
fof(f2810,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,[],[f1927]) ).
fof(f1927,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,[],[f207]) ).
fof(f207,axiom,
! [X26,X23,X4] :
( class_Orderings_Olinorder(X4)
=> ( ~ c_Orderings_Oord__class_Oless(X4,X23,X26)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X23,X26)
<=> X23 = X26 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_linorder__antisym__conv1) ).
fof(f12505,plain,
spl104_809,
inference(avatar_split_clause,[],[f5077,f12503]) ).
fof(f12503,plain,
( spl104_809
<=> ! [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,[spl104_809])]) ).
fof(f5077,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,[],[f3705]) ).
fof(f12501,plain,
spl104_808,
inference(avatar_split_clause,[],[f5069,f12499]) ).
fof(f12499,plain,
( spl104_808
<=> ! [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,[spl104_808])]) ).
fof(f5069,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,[],[f2797]) ).
fof(f2797,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,[],[f2796]) ).
fof(f2796,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,[],[f1920]) ).
fof(f1920,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,[],[f138]) ).
fof(f138,axiom,
! [X22,X3,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X22,X3)
| X3 = X22
| c_Orderings_Oord__class_Oless(X4,X3,X22) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_linorder__less__linear) ).
fof(f12497,plain,
spl104_807,
inference(avatar_split_clause,[],[f5030,f12495]) ).
fof(f12495,plain,
( spl104_807
<=> ! [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,[spl104_807])]) ).
fof(f5030,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,[],[f2739]) ).
fof(f2739,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,[],[f2738]) ).
fof(f2738,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,[],[f1888]) ).
fof(f1888,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,[],[f349]) ).
fof(f349,axiom,
! [X22,X3,X4] :
( class_Rings_Olinordered__idom(X4)
=> ( X3 != X22
=> ( ~ c_Orderings_Oord__class_Oless(X4,X3,X22)
=> c_Orderings_Oord__class_Oless(X4,X22,X3) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_linorder__neqE__linordered__idom) ).
fof(f12493,plain,
( spl104_806
| ~ spl104_478 ),
inference(avatar_split_clause,[],[f8712,f8310,f12491]) ).
fof(f12491,plain,
( spl104_806
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_806])]) ).
fof(f8310,plain,
( spl104_478
<=> ! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_478])]) ).
fof(f8712,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X0,X1,X1)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl104_478 ),
inference(equality_resolution,[],[f8311]) ).
fof(f8311,plain,
( ! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) )
| ~ spl104_478 ),
inference(avatar_component_clause,[],[f8310]) ).
fof(f12489,plain,
spl104_805,
inference(avatar_split_clause,[],[f4884,f12487]) ).
fof(f12487,plain,
( spl104_805
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_805])]) ).
fof(f4884,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f3650]) ).
fof(f3650,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
inference(flattening,[],[f3649]) ).
fof(f3649,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
inference(nnf_transformation,[],[f1801]) ).
fof(f1801,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
inference(rectify,[],[f757]) ).
fof(f757,axiom,
! [X18,X17] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X18)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X17 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__is__0) ).
fof(f12485,plain,
spl104_804,
inference(avatar_split_clause,[],[f4877,f12483]) ).
fof(f12483,plain,
( spl104_804
<=> ! [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,[spl104_804])]) ).
fof(f4877,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,[],[f3646]) ).
fof(f3646,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,[],[f3645]) ).
fof(f3645,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,[],[f1799]) ).
fof(f1799,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,[],[f785]) ).
fof(f785,axiom,
! [X18,X17] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X17),X18)
<=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X18
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X17 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__mult__eq__1__iff) ).
fof(f12481,plain,
spl104_803,
inference(avatar_split_clause,[],[f4876,f12479]) ).
fof(f12479,plain,
( spl104_803
<=> ! [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,[spl104_803])]) ).
fof(f4876,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,[],[f3646]) ).
fof(f12477,plain,
spl104_802,
inference(avatar_split_clause,[],[f4794,f12475]) ).
fof(f12475,plain,
( spl104_802
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_802])]) ).
fof(f4794,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 ),
inference(cnf_transformation,[],[f3604]) ).
fof(f3604,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ( ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK86(X0,X1),X0)
& c_Nat_OSuc(sK86(X0,X1)) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK86])],[f3602,f3603]) ).
fof(f3603,plain,
! [X0,X1] :
( ? [X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X0)
& c_Nat_OSuc(X3) = X1 )
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK86(X0,X1),X0)
& c_Nat_OSuc(sK86(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f3602,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ( ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
& ( ? [X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X0)
& c_Nat_OSuc(X3) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(rectify,[],[f3601]) ).
fof(f3601,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ( ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
& ( ? [X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& c_Nat_OSuc(X2) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(flattening,[],[f3600]) ).
fof(f3600,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ( ! [X2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
| c_Nat_OSuc(X2) != X1 )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) )
& ( ? [X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& c_Nat_OSuc(X2) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
inference(nnf_transformation,[],[f1777]) ).
fof(f1777,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> ( ? [X2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X0)
& c_Nat_OSuc(X2) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
inference(rectify,[],[f120]) ).
fof(f120,axiom,
! [X18,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18))
<=> ( ? [X37] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,X18)
& c_Nat_OSuc(X37) = X17 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X17 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__Suc__eq__0__disj) ).
fof(f12473,plain,
spl104_801,
inference(avatar_split_clause,[],[f4777,f12471]) ).
fof(f12471,plain,
( spl104_801
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_801])]) ).
fof(f4777,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) != X0 ),
inference(cnf_transformation,[],[f3586]) ).
fof(f3586,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) != X0 )
& ( c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK83(X0,X1))) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK83])],[f3584,f3585]) ).
fof(f3585,plain,
! [X0,X1] :
( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) = X0
=> c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK83(X0,X1))) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3584,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) != X0 )
& ( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
inference(rectify,[],[f3583]) ).
fof(f3583,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) != X0 )
& ( ? [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
inference(nnf_transformation,[],[f1770]) ).
fof(f1770,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
<=> ? [X2] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)) = X0 ),
inference(rectify,[],[f690]) ).
fof(f690,axiom,
! [X55,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X55)
<=> ? [X30] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X50,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30)) = X55 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zle__iff__zadd) ).
fof(f12469,plain,
spl104_800,
inference(avatar_split_clause,[],[f4767,f12467]) ).
fof(f12467,plain,
( spl104_800
<=> ! [X0,X1] :
( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK82(X0,X1))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_800])]) ).
fof(f4767,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK82(X0,X1))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3578]) ).
fof(f3578,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,sK82(X0,X1))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK82])],[f3576,f3577]) ).
fof(f3577,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,sK82(X0,X1))) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3576,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,[],[f3575]) ).
fof(f3575,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,[],[f1766]) ).
fof(f1766,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,[],[f308]) ).
fof(f308,axiom,
! [X18,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
<=> ? [X21] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X21)) = X18 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__iff__Suc__add) ).
fof(f12465,plain,
spl104_799,
inference(avatar_split_clause,[],[f4706,f12463]) ).
fof(f12463,plain,
( spl104_799
<=> ! [X0,X1] :
( c_Nat_OSuc(X0) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_799])]) ).
fof(f4706,plain,
! [X0,X1] :
( c_Nat_OSuc(X0) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f2638]) ).
fof(f2638,plain,
! [X0,X1] :
( c_Nat_OSuc(X0) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(flattening,[],[f2637]) ).
fof(f2637,plain,
! [X0,X1] :
( c_Nat_OSuc(X0) = X1
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(ennf_transformation,[],[f1727]) ).
fof(f1727,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Nat_OSuc(X0) = X1 ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Nat_OSuc(X5))
=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5)
=> c_Nat_OSuc(X5) = X6 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__SucE) ).
fof(f12461,plain,
spl104_798,
inference(avatar_split_clause,[],[f4669,f12459]) ).
fof(f12459,plain,
( spl104_798
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_798])]) ).
fof(f4669,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f2591]) ).
fof(f2591,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)),X1)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ),
inference(ennf_transformation,[],[f1698]) ).
fof(f1698,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Nat_OSuc(X0)),X1) ),
inference(rectify,[],[f146]) ).
fof(f146,axiom,
! [X16,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,c_Nat_OSuc(X16)),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__Suc__less) ).
fof(f12457,plain,
spl104_797,
inference(avatar_split_clause,[],[f4636,f12455]) ).
fof(f12455,plain,
( spl104_797
<=> ! [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,[spl104_797])]) ).
fof(f4636,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,[],[f2560]) ).
fof(f2560,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,[],[f1676]) ).
fof(f1676,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,[],[f302]) ).
fof(f302,axiom,
! [X6,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X6)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X5)) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__add__diff__inverse) ).
fof(f12453,plain,
spl104_796,
inference(avatar_split_clause,[],[f4635,f12451]) ).
fof(f12451,plain,
( spl104_796
<=> ! [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,[spl104_796])]) ).
fof(f4635,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,[],[f2559]) ).
fof(f2559,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,[],[f1675]) ).
fof(f1675,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,[],[f237]) ).
fof(f237,axiom,
! [X5,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,X5)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,X16)) = X16 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__diff__cancel) ).
fof(f12449,plain,
( spl104_795
| ~ spl104_235
| ~ spl104_465 ),
inference(avatar_split_clause,[],[f8610,f8257,f7147,f12447]) ).
fof(f12447,plain,
( spl104_795
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_795])]) ).
fof(f7147,plain,
( spl104_235
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_235])]) ).
fof(f8257,plain,
( spl104_465
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_465])]) ).
fof(f8610,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Nat_OSuc(X0)),X0)
| ~ spl104_235
| ~ spl104_465 ),
inference(resolution,[],[f8258,f7148]) ).
fof(f7148,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0)
| ~ spl104_235 ),
inference(avatar_component_clause,[],[f7147]) ).
fof(f8258,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
| ~ spl104_465 ),
inference(avatar_component_clause,[],[f8257]) ).
fof(f12445,plain,
spl104_794,
inference(avatar_split_clause,[],[f4626,f12443]) ).
fof(f12443,plain,
( spl104_794
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| c_Nat_OSuc(X1) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_794])]) ).
fof(f4626,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| c_Nat_OSuc(X1) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2548]) ).
fof(f2548,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| c_Nat_OSuc(X1) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(flattening,[],[f2547]) ).
fof(f2547,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
| c_Nat_OSuc(X1) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1666]) ).
fof(f1666,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> ( c_Nat_OSuc(X1) != X0
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ) ),
inference(rectify,[],[f247]) ).
fof(f247,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X5)
=> ( c_Nat_OSuc(X6) != X5
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X6),X5) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__lessI) ).
fof(f12441,plain,
spl104_793,
inference(avatar_split_clause,[],[f4611,f12439]) ).
fof(f12439,plain,
( spl104_793
<=> ! [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,[spl104_793])]) ).
fof(f4611,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,[],[f2532]) ).
fof(f2532,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,[],[f1652]) ).
fof(f1652,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,[],[f177]) ).
fof(f177,axiom,
! [X5,X6] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X5)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X5)) = X6 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__diff__inverse) ).
fof(f12437,plain,
spl104_792,
inference(avatar_split_clause,[],[f4589,f12435]) ).
fof(f12435,plain,
( spl104_792
<=> ! [X0,X1] :
( c_SEQ_Oincseq(X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK67(X0,X1),sK68(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_792])]) ).
fof(f4589,plain,
! [X0,X1] :
( c_SEQ_Oincseq(X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK67(X0,X1),sK68(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f3512]) ).
fof(f3512,plain,
! [X0,X1] :
( ( ( c_SEQ_Oincseq(X1,X0)
| ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK67(X0,X1)),hAPP(X0,sK68(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK67(X0,X1),sK68(X0,X1)) ) )
& ( ! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X0,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) )
| ~ c_SEQ_Oincseq(X1,X0) ) )
| ~ class_Orderings_Oorder(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f3510,f3511]) ).
fof(f3511,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X2),hAPP(X0,X3))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
=> ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK67(X0,X1)),hAPP(X0,sK68(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK67(X0,X1),sK68(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3510,plain,
! [X0,X1] :
( ( ( c_SEQ_Oincseq(X1,X0)
| ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X2),hAPP(X0,X3))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ) )
& ( ! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X0,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) )
| ~ c_SEQ_Oincseq(X1,X0) ) )
| ~ class_Orderings_Oorder(X1) ),
inference(rectify,[],[f3509]) ).
fof(f3509,plain,
! [X0,X1] :
( ( ( c_SEQ_Oincseq(X1,X0)
| ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X2),hAPP(X0,X3))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ) )
& ( ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X2),hAPP(X0,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
| ~ c_SEQ_Oincseq(X1,X0) ) )
| ~ class_Orderings_Oorder(X1) ),
inference(nnf_transformation,[],[f2516]) ).
fof(f2516,plain,
! [X0,X1] :
( ( c_SEQ_Oincseq(X1,X0)
<=> ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X2),hAPP(X0,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ) )
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f1642]) ).
fof(f1642,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> ( c_SEQ_Oincseq(X1,X0)
<=> ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
=> c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X2),hAPP(X0,X3)) ) ) ),
inference(rectify,[],[f83]) ).
fof(f83,axiom,
! [X33,X4] :
( class_Orderings_Oorder(X4)
=> ( c_SEQ_Oincseq(X4,X33)
<=> ! [X34,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X30)
=> c_Orderings_Oord__class_Oless__eq(X4,hAPP(X33,X34),hAPP(X33,X30)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_incseq__def) ).
fof(f12433,plain,
spl104_791,
inference(avatar_split_clause,[],[f4586,f12431]) ).
fof(f12431,plain,
( spl104_791
<=> ! [X0,X1] :
( c_SEQ_Odecseq(X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK65(X0,X1),sK66(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_791])]) ).
fof(f4586,plain,
! [X0,X1] :
( c_SEQ_Odecseq(X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK65(X0,X1),sK66(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f3508]) ).
fof(f3508,plain,
! [X0,X1] :
( ( ( c_SEQ_Odecseq(X1,X0)
| ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK66(X0,X1)),hAPP(X0,sK65(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK65(X0,X1),sK66(X0,X1)) ) )
& ( ! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X5),hAPP(X0,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) )
| ~ c_SEQ_Odecseq(X1,X0) ) )
| ~ class_Orderings_Oorder(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65,sK66])],[f3506,f3507]) ).
fof(f3507,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
=> ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK66(X0,X1)),hAPP(X0,sK65(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK65(X0,X1),sK66(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3506,plain,
! [X0,X1] :
( ( ( c_SEQ_Odecseq(X1,X0)
| ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ) )
& ( ! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X5),hAPP(X0,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) )
| ~ c_SEQ_Odecseq(X1,X0) ) )
| ~ class_Orderings_Oorder(X1) ),
inference(rectify,[],[f3505]) ).
fof(f3505,plain,
! [X0,X1] :
( ( ( c_SEQ_Odecseq(X1,X0)
| ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ) )
& ( ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
| ~ c_SEQ_Odecseq(X1,X0) ) )
| ~ class_Orderings_Oorder(X1) ),
inference(nnf_transformation,[],[f2515]) ).
fof(f2515,plain,
! [X0,X1] :
( ( c_SEQ_Odecseq(X1,X0)
<=> ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) ) )
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f1641]) ).
fof(f1641,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> ( c_SEQ_Odecseq(X1,X0)
<=> ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
=> c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2)) ) ) ),
inference(rectify,[],[f82]) ).
fof(f82,axiom,
! [X33,X4] :
( class_Orderings_Oorder(X4)
=> ( c_SEQ_Odecseq(X4,X33)
<=> ! [X34,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X30)
=> c_Orderings_Oord__class_Oless__eq(X4,hAPP(X33,X30),hAPP(X33,X34)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_decseq__def) ).
fof(f12429,plain,
spl104_790,
inference(avatar_split_clause,[],[f4583,f12427]) ).
fof(f12427,plain,
( spl104_790
<=> ! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK63(X0,X1),sK64(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_790])]) ).
fof(f4583,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK63(X0,X1),sK64(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f3504]) ).
fof(f3504,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK64(X0,X1)),hAPP(X0,sK63(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK63(X0,X1),sK64(X0,X1)) )
| ~ class_Orderings_Oorder(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK63,sK64])],[f2514,f3503]) ).
fof(f3503,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
=> ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK64(X0,X1)),hAPP(X0,sK63(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK63(X0,X1),sK64(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2514,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
| ~ class_Orderings_Oorder(X1) ),
inference(flattening,[],[f2513]) ).
fof(f2513,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f1640]) ).
fof(f1640,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> ( ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
=> c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2)) )
=> c_SEQ_Omonoseq(X1,X0) ) ),
inference(rectify,[],[f99]) ).
fof(f99,axiom,
! [X33,X4] :
( class_Orderings_Oorder(X4)
=> ( ! [X34,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X30)
=> c_Orderings_Oord__class_Oless__eq(X4,hAPP(X33,X30),hAPP(X33,X34)) )
=> c_SEQ_Omonoseq(X4,X33) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_monoI2) ).
fof(f12425,plain,
spl104_789,
inference(avatar_split_clause,[],[f4581,f12423]) ).
fof(f12423,plain,
( spl104_789
<=> ! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK61(X0,X1),sK62(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_789])]) ).
fof(f4581,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK61(X0,X1),sK62(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f3502]) ).
fof(f3502,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK61(X0,X1)),hAPP(X0,sK62(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK61(X0,X1),sK62(X0,X1)) )
| ~ class_Orderings_Oorder(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61,sK62])],[f2512,f3501]) ).
fof(f3501,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X2),hAPP(X0,X3))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
=> ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK61(X0,X1)),hAPP(X0,sK62(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK61(X0,X1),sK62(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2512,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X2),hAPP(X0,X3))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
| ~ class_Orderings_Oorder(X1) ),
inference(flattening,[],[f2511]) ).
fof(f2511,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X2),hAPP(X0,X3))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f1639]) ).
fof(f1639,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> ( ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
=> c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X2),hAPP(X0,X3)) )
=> c_SEQ_Omonoseq(X1,X0) ) ),
inference(rectify,[],[f100]) ).
fof(f100,axiom,
! [X33,X4] :
( class_Orderings_Oorder(X4)
=> ( ! [X34,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X30)
=> c_Orderings_Oord__class_Oless__eq(X4,hAPP(X33,X34),hAPP(X33,X30)) )
=> c_SEQ_Omonoseq(X4,X33) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_monoI1) ).
fof(f12421,plain,
spl104_788,
inference(avatar_split_clause,[],[f4551,f12419]) ).
fof(f12419,plain,
( spl104_788
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_788])]) ).
fof(f4551,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,[],[f3494]) ).
fof(f3494,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0) ) )
| ~ class_Groups_Ozero(X1) ),
inference(nnf_transformation,[],[f2476]) ).
fof(f2476,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X1,X0)
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X1)) = X0 )
| ~ class_Groups_Ozero(X1) ),
inference(ennf_transformation,[],[f1609]) ).
fof(f1609,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,[],[f361]) ).
fof(f361,axiom,
! [X49,X4] :
( class_Groups_Ozero(X4)
=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(X4,X49)
<=> c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(X4)) = X49 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_psize__eq__0__iff) ).
fof(f12417,plain,
spl104_787,
inference(avatar_split_clause,[],[f4550,f12415]) ).
fof(f12415,plain,
( spl104_787
<=> ! [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,[spl104_787])]) ).
fof(f4550,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,[],[f3494]) ).
fof(f12413,plain,
spl104_786,
inference(avatar_split_clause,[],[f4522,f12411]) ).
fof(f12411,plain,
( spl104_786
<=> ! [X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0) = c_Groups_Oabs__class_Oabs(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0))
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_786])]) ).
fof(f4522,plain,
! [X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0) = c_Groups_Oabs__class_Oabs(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f2454]) ).
fof(f2454,plain,
! [X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0) = c_Groups_Oabs__class_Oabs(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(ennf_transformation,[],[f1587]) ).
fof(f1587,plain,
! [X0,X1] :
( class_Rings_Olinordered__idom(X1)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0) = c_Groups_Oabs__class_Oabs(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)) ),
inference(rectify,[],[f579]) ).
fof(f579,axiom,
! [X5,X4] :
( class_Rings_Olinordered__idom(X4)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X5) = c_Groups_Oabs__class_Oabs(X4,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__of__nat) ).
fof(f12409,plain,
spl104_785,
inference(avatar_split_clause,[],[f4521,f12407]) ).
fof(f12407,plain,
( spl104_785
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_785])]) ).
fof(f4521,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f3489]) ).
fof(f3489,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(nnf_transformation,[],[f2453]) ).
fof(f2453,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1586]) ).
fof(f1586,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f387]) ).
fof(f387,axiom,
! [X9,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oabs__class_Oabs(X4,X9),c_Groups_Ozero__class_Ozero(X4))
<=> c_Groups_Ozero__class_Ozero(X4) = X9 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__le__zero__iff) ).
fof(f12405,plain,
( spl104_784
| ~ spl104_78
| ~ spl104_218
| ~ spl104_452 ),
inference(avatar_split_clause,[],[f8543,f8190,f7070,f6368,f12403]) ).
fof(f12403,plain,
( spl104_784
<=> ! [X3] : c_Int_OPls = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_784])]) ).
fof(f6368,plain,
( spl104_78
<=> class_Groups_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_78])]) ).
fof(f7070,plain,
( spl104_218
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl104_218])]) ).
fof(f8190,plain,
( spl104_452
<=> ! [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,[spl104_452])]) ).
fof(f8543,plain,
( ! [X3] : c_Int_OPls = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X3)
| ~ spl104_78
| ~ spl104_218
| ~ spl104_452 ),
inference(forward_demodulation,[],[f8541,f7072]) ).
fof(f7072,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls
| ~ spl104_218 ),
inference(avatar_component_clause,[],[f7070]) ).
fof(f8541,plain,
( ! [X3] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X3)
| ~ spl104_78
| ~ spl104_452 ),
inference(resolution,[],[f8191,f6370]) ).
fof(f6370,plain,
( class_Groups_Ogroup__add(tc_Int_Oint)
| ~ spl104_78 ),
inference(avatar_component_clause,[],[f6368]) ).
fof(f8191,plain,
( ! [X0,X1] :
( ~ class_Groups_Ogroup__add(X1)
| c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0) )
| ~ spl104_452 ),
inference(avatar_component_clause,[],[f8190]) ).
fof(f12401,plain,
spl104_783,
inference(avatar_split_clause,[],[f4520,f12399]) ).
fof(f12399,plain,
( spl104_783
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_783])]) ).
fof(f4520,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f3489]) ).
fof(f12397,plain,
spl104_782,
inference(avatar_split_clause,[],[f4519,f12395]) ).
fof(f12395,plain,
( spl104_782
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_782])]) ).
fof(f4519,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f3488]) ).
fof(f3488,plain,
! [X0,X1] :
( ( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| c_Groups_Ozero__class_Ozero(X1) = X0 )
& ( c_Groups_Ozero__class_Ozero(X1) != X0
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(nnf_transformation,[],[f2452]) ).
fof(f2452,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
<=> c_Groups_Ozero__class_Ozero(X1) != X0 )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1585]) ).
fof(f1585,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
<=> c_Groups_Ozero__class_Ozero(X1) != X0 ) ),
inference(rectify,[],[f390]) ).
fof(f390,axiom,
! [X9,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Oabs__class_Oabs(X4,X9))
<=> c_Groups_Ozero__class_Ozero(X4) != X9 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__less__abs__iff) ).
fof(f12393,plain,
spl104_781,
inference(avatar_split_clause,[],[f4518,f12391]) ).
fof(f12391,plain,
( spl104_781
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) != X0
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_781])]) ).
fof(f4518,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) != X0
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f3488]) ).
fof(f12389,plain,
spl104_780,
inference(avatar_split_clause,[],[f4509,f12387]) ).
fof(f12387,plain,
( spl104_780
<=> ! [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,[spl104_780])]) ).
fof(f4509,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,[],[f2442]) ).
fof(f2442,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,[],[f2441]) ).
fof(f2441,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,[],[f1577]) ).
fof(f1577,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,[],[f956]) ).
fof(f956,axiom,
! [X12,X4] :
( class_Divides_Osemiring__div(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) != X12
=> c_Groups_Oone__class_Oone(X4) = c_Divides_Odiv__class_Odiv(X4,X12,X12) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_div__self) ).
fof(f12385,plain,
spl104_779,
inference(avatar_split_clause,[],[f4495,f12383]) ).
fof(f12383,plain,
( spl104_779
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_779])]) ).
fof(f4495,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,[],[f3481]) ).
fof(f3481,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,[],[f2432]) ).
fof(f2432,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,[],[f1568]) ).
fof(f1568,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,[],[f273]) ).
fof(f273,axiom,
! [X9,X4] :
( class_Groups_Olinordered__ab__group__add(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) = c_Groups_Oplus__class_Oplus(X4,X9,X9)
<=> c_Groups_Ozero__class_Ozero(X4) = X9 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_double__zero__sym) ).
fof(f12381,plain,
spl104_778,
inference(avatar_split_clause,[],[f4494,f12379]) ).
fof(f12379,plain,
( spl104_778
<=> ! [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,[spl104_778])]) ).
fof(f4494,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,[],[f3481]) ).
fof(f12377,plain,
spl104_777,
inference(avatar_split_clause,[],[f4485,f12375]) ).
fof(f12375,plain,
( spl104_777
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_777])]) ).
fof(f4485,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,[],[f3466]) ).
fof(f3466,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,[],[f2427]) ).
fof(f2427,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,[],[f1563]) ).
fof(f1563,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,[],[f483]) ).
fof(f483,axiom,
! [X23,X4] :
( class_RealVector_Oreal__normed__vector(X4)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X23),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Groups_Ozero__class_Ozero(X4) = X23 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_norm__le__zero__iff) ).
fof(f12373,plain,
spl104_776,
inference(avatar_split_clause,[],[f4484,f12371]) ).
fof(f12371,plain,
( spl104_776
<=> ! [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,[spl104_776])]) ).
fof(f4484,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,[],[f3466]) ).
fof(f12369,plain,
spl104_775,
inference(avatar_split_clause,[],[f4483,f12367]) ).
fof(f12367,plain,
( spl104_775
<=> ! [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,[spl104_775])]) ).
fof(f4483,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,[],[f3465]) ).
fof(f3465,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,[],[f2426]) ).
fof(f2426,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,[],[f1562]) ).
fof(f1562,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,[],[f484]) ).
fof(f484,axiom,
! [X23,X4] :
( class_RealVector_Oreal__normed__vector(X4)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,X23))
<=> c_Groups_Ozero__class_Ozero(X4) != X23 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__less__norm__iff) ).
fof(f12365,plain,
spl104_774,
inference(avatar_split_clause,[],[f4482,f12363]) ).
fof(f12363,plain,
( spl104_774
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_774])]) ).
fof(f4482,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,[],[f3465]) ).
fof(f12361,plain,
( spl104_773
| ~ spl104_311
| ~ spl104_363
| ~ spl104_428 ),
inference(avatar_split_clause,[],[f8425,f8094,f7709,f7460,f12358]) ).
fof(f12358,plain,
( spl104_773
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_773])]) ).
fof(f7460,plain,
( spl104_311
<=> c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_311])]) ).
fof(f7709,plain,
( spl104_363
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_363])]) ).
fof(f8094,plain,
( spl104_428
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_428])]) ).
fof(f8425,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl104_311
| ~ spl104_363
| ~ spl104_428 ),
inference(forward_demodulation,[],[f8424,f7711]) ).
fof(f7711,plain,
( c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl104_363 ),
inference(avatar_component_clause,[],[f7709]) ).
fof(f8424,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl104_311
| ~ spl104_428 ),
inference(superposition,[],[f8095,f7462]) ).
fof(f7462,plain,
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ spl104_311 ),
inference(avatar_component_clause,[],[f7460]) ).
fof(f8095,plain,
( ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X0)))
| ~ spl104_428 ),
inference(avatar_component_clause,[],[f8094]) ).
fof(f12356,plain,
spl104_772,
inference(avatar_split_clause,[],[f4439,f12354]) ).
fof(f12354,plain,
( spl104_772
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_772])]) ).
fof(f4439,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f2402]) ).
fof(f2402,plain,
! [X0,X1] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(ennf_transformation,[],[f1535]) ).
fof(f1535,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
inference(rectify,[],[f813]) ).
fof(f813,axiom,
! [X5,X6] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X6
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X5) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X5)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X6
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X5) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__eq__if) ).
fof(f12352,plain,
spl104_771,
inference(avatar_split_clause,[],[f4437,f12350]) ).
fof(f12350,plain,
( spl104_771
<=> ! [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 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_771])]) ).
fof(f4437,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,[],[f2401]) ).
fof(f2401,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,[],[f1534]) ).
fof(f1534,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,[],[f883]) ).
fof(f883,axiom,
! [X86,X6] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X6
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X86),X6) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X86),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X86),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X6
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X86),X6) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_power__eq__if) ).
fof(f12348,plain,
spl104_770,
inference(avatar_split_clause,[],[f4407,f12346]) ).
fof(f12346,plain,
( spl104_770
<=> ! [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,[spl104_770])]) ).
fof(f4407,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,[],[f1505]) ).
fof(f1505,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,[],[f767]) ).
fof(f767,axiom,
! [X5,X6] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),X6),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__mult__commute) ).
fof(f12344,plain,
spl104_769,
inference(avatar_split_clause,[],[f4406,f12342]) ).
fof(f12342,plain,
( spl104_769
<=> ! [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,[spl104_769])]) ).
fof(f4406,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,[],[f1504]) ).
fof(f1504,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,[],[f609]) ).
fof(f609,axiom,
! [X32,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),X32) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X32),X25),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zmult__commute) ).
fof(f12340,plain,
spl104_768,
inference(avatar_split_clause,[],[f4405,f12338]) ).
fof(f12338,plain,
( spl104_768
<=> ! [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,[spl104_768])]) ).
fof(f4405,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,[],[f1503]) ).
fof(f1503,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,[],[f765]) ).
fof(f765,axiom,
! [X32,X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X25),X32) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),X32),X25),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__mult__commute) ).
fof(f12336,plain,
spl104_767,
inference(avatar_split_clause,[],[f4368,f12334]) ).
fof(f12334,plain,
( spl104_767
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_767])]) ).
fof(f4368,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f3423]) ).
fof(f3423,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ) ),
inference(nnf_transformation,[],[f1475]) ).
fof(f1475,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(rectify,[],[f352]) ).
fof(f352,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X18))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__of__nat__gt__zero__cancel__iff) ).
fof(f12332,plain,
spl104_766,
inference(avatar_split_clause,[],[f4367,f12330]) ).
fof(f12330,plain,
( spl104_766
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_766])]) ).
fof(f4367,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ),
inference(cnf_transformation,[],[f3423]) ).
fof(f12328,plain,
spl104_765,
inference(avatar_split_clause,[],[f4333,f12326]) ).
fof(f12326,plain,
( spl104_765
<=> ! [X0] :
( c_SEQ_Osubseq(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,sK31(X0)),hAPP(X0,c_Nat_OSuc(sK31(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_765])]) ).
fof(f4333,plain,
! [X0] :
( c_SEQ_Osubseq(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,sK31(X0)),hAPP(X0,c_Nat_OSuc(sK31(X0)))) ),
inference(cnf_transformation,[],[f3400]) ).
fof(f3400,plain,
! [X0] :
( ( c_SEQ_Osubseq(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,sK31(X0)),hAPP(X0,c_Nat_OSuc(sK31(X0)))) )
& ( ! [X2] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X2),hAPP(X0,c_Nat_OSuc(X2)))
| ~ c_SEQ_Osubseq(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f3398,f3399]) ).
fof(f3399,plain,
! [X0] :
( ? [X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,c_Nat_OSuc(X1)))
=> ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,sK31(X0)),hAPP(X0,c_Nat_OSuc(sK31(X0)))) ),
introduced(choice_axiom,[]) ).
fof(f3398,plain,
! [X0] :
( ( c_SEQ_Osubseq(X0)
| ? [X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,c_Nat_OSuc(X1))) )
& ( ! [X2] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X2),hAPP(X0,c_Nat_OSuc(X2)))
| ~ c_SEQ_Osubseq(X0) ) ),
inference(rectify,[],[f3397]) ).
fof(f3397,plain,
! [X0] :
( ( c_SEQ_Osubseq(X0)
| ? [X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,c_Nat_OSuc(X1))) )
& ( ! [X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,c_Nat_OSuc(X1)))
| ~ c_SEQ_Osubseq(X0) ) ),
inference(nnf_transformation,[],[f1458]) ).
fof(f1458,plain,
! [X0] :
( c_SEQ_Osubseq(X0)
<=> ! [X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X1),hAPP(X0,c_Nat_OSuc(X1))) ),
inference(rectify,[],[f328]) ).
fof(f328,axiom,
! [X1] :
( c_SEQ_Osubseq(X1)
<=> ! [X30] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X1,X30),hAPP(X1,c_Nat_OSuc(X30))) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_subseq__Suc__iff) ).
fof(f12324,plain,
spl104_764,
inference(avatar_split_clause,[],[f4325,f12322]) ).
fof(f12322,plain,
( spl104_764
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK30(X0)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_764])]) ).
fof(f4325,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK30(X0)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[],[f3395]) ).
fof(f3395,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK30(X0)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK30(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f2391,f3394]) ).
fof(f3394,plain,
! [X0] :
( ? [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) )
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK30(X0)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,sK30(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f2391,plain,
! [X0] :
( ? [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(ennf_transformation,[],[f1452]) ).
fof(f1452,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
=> ? [X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0) ) ),
inference(rectify,[],[f410]) ).
fof(f410,axiom,
! [X53] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X53)
=> ? [X30] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X53,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X30))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X30,c_Groups_Oone__class_Oone(tc_Nat_Onat))),X53) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_reals__Archimedean6) ).
fof(f12320,plain,
spl104_763,
inference(avatar_split_clause,[],[f4322,f12318]) ).
fof(f12318,plain,
( spl104_763
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK29(X0)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_763])]) ).
fof(f4322,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),sK29(X0)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[],[f3393]) ).
fof(f12316,plain,
( spl104_762
| ~ spl104_327
| ~ spl104_416 ),
inference(avatar_split_clause,[],[f8056,f7925,f7526,f12314]) ).
fof(f12314,plain,
( spl104_762
<=> ! [X2,X0,X1] :
( sP13(X1,X2,X0)
| c_Nat__Numeral_Oneg(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_762])]) ).
fof(f7526,plain,
( spl104_327
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| c_Nat__Numeral_Oneg(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_327])]) ).
fof(f7925,plain,
( spl104_416
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
| sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_416])]) ).
fof(f8056,plain,
( ! [X2,X0,X1] :
( sP13(X1,X2,X0)
| c_Nat__Numeral_Oneg(X0) )
| ~ spl104_327
| ~ spl104_416 ),
inference(resolution,[],[f7926,f7527]) ).
fof(f7527,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| c_Nat__Numeral_Oneg(X0) )
| ~ spl104_327 ),
inference(avatar_component_clause,[],[f7526]) ).
fof(f7926,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
| sP13(X0,X1,X2) )
| ~ spl104_416 ),
inference(avatar_component_clause,[],[f7925]) ).
fof(f12312,plain,
spl104_761,
inference(avatar_split_clause,[],[f4319,f12310]) ).
fof(f12310,plain,
( spl104_761
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_761])]) ).
fof(f4319,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[],[f2387]) ).
fof(f2387,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0)),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
inference(ennf_transformation,[],[f1448]) ).
fof(f1448,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0)),X0) ),
inference(rectify,[],[f453]) ).
fof(f453,axiom,
! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X3)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X3)),X3) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__natfloor__le) ).
fof(f12308,plain,
spl104_760,
inference(avatar_split_clause,[],[f4314,f12306]) ).
fof(f12306,plain,
( spl104_760
<=> ! [X0] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_760])]) ).
fof(f4314,plain,
! [X0] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f2382]) ).
fof(f2382,plain,
! [X0] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(ennf_transformation,[],[f1443]) ).
fof(f1443,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X0 ),
inference(rectify,[],[f114]) ).
fof(f114,axiom,
! [X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,c_Groups_Oone__class_Oone(tc_Nat_Onat))) = X5 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__pred_H) ).
fof(f12245,plain,
( ~ spl104_759
| ~ spl104_31
| ~ spl104_325
| ~ spl104_394 ),
inference(avatar_split_clause,[],[f8023,f7837,f7518,f6133,f12242]) ).
fof(f12242,plain,
( spl104_759
<=> c_Nat__Numeral_Oneg(c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_759])]) ).
fof(f6133,plain,
( spl104_31
<=> class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_31])]) ).
fof(f7518,plain,
( spl104_325
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| ~ c_Nat__Numeral_Oneg(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_325])]) ).
fof(f7837,plain,
( spl104_394
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_394])]) ).
fof(f8023,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint)
| ~ c_Nat__Numeral_Oneg(c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Int_OPls))
| ~ spl104_325
| ~ spl104_394 ),
inference(resolution,[],[f7838,f7519]) ).
fof(f7519,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| ~ c_Nat__Numeral_Oneg(X0) )
| ~ spl104_325 ),
inference(avatar_component_clause,[],[f7518]) ).
fof(f7838,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) )
| ~ spl104_394 ),
inference(avatar_component_clause,[],[f7837]) ).
fof(f12089,plain,
( spl104_758
| ~ spl104_325
| ~ spl104_391 ),
inference(avatar_split_clause,[],[f8005,f7824,f7518,f12087]) ).
fof(f12087,plain,
( spl104_758
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Nat__Numeral_Oneg(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_758])]) ).
fof(f7824,plain,
( spl104_391
<=> ! [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,[spl104_391])]) ).
fof(f8005,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Nat__Numeral_Oneg(X0) )
| ~ spl104_325
| ~ spl104_391 ),
inference(resolution,[],[f7825,f7519]) ).
fof(f7825,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) )
| ~ spl104_391 ),
inference(avatar_component_clause,[],[f7824]) ).
fof(f11991,plain,
( spl104_757
| ~ spl104_373
| ~ spl104_387 ),
inference(avatar_split_clause,[],[f7984,f7808,f7752,f11989]) ).
fof(f11989,plain,
( spl104_757
<=> ! [X3] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(c_Nat_OSuc(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_757])]) ).
fof(f7752,plain,
( spl104_373
<=> ! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_373])]) ).
fof(f7808,plain,
( spl104_387
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_387])]) ).
fof(f7984,plain,
( ! [X3] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,c_Nat_OSuc(c_Nat_OSuc(X3)))
| ~ spl104_373
| ~ spl104_387 ),
inference(superposition,[],[f7809,f7753]) ).
fof(f7753,plain,
( ! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0)
| ~ spl104_373 ),
inference(avatar_component_clause,[],[f7752]) ).
fof(f7809,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)))
| ~ spl104_387 ),
inference(avatar_component_clause,[],[f7808]) ).
fof(f11841,plain,
( spl104_756
| ~ spl104_97
| ~ spl104_381 ),
inference(avatar_split_clause,[],[f7974,f7784,f6463,f11838]) ).
fof(f11838,plain,
( spl104_756
<=> c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_756])]) ).
fof(f6463,plain,
( spl104_97
<=> class_Int_Onumber__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_97])]) ).
fof(f7784,plain,
( spl104_381
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OPls)
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_381])]) ).
fof(f7974,plain,
( c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OPls)
| ~ spl104_97
| ~ spl104_381 ),
inference(resolution,[],[f7785,f6465]) ).
fof(f6465,plain,
( class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ spl104_97 ),
inference(avatar_component_clause,[],[f6463]) ).
fof(f7785,plain,
( ! [X0] :
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OPls) )
| ~ spl104_381 ),
inference(avatar_component_clause,[],[f7784]) ).
fof(f11586,plain,
( spl104_755
| ~ spl104_78
| ~ spl104_218
| ~ spl104_222
| ~ spl104_452
| ~ spl104_687 ),
inference(avatar_split_clause,[],[f11564,f11157,f8190,f7087,f7070,f6368,f11584]) ).
fof(f11584,plain,
( spl104_755
<=> ! [X0] : c_Int_OPls = c_Nat__Transfer_Otsub(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_755])]) ).
fof(f11157,plain,
( spl104_687
<=> ! [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,[spl104_687])]) ).
fof(f11564,plain,
( ! [X0] : c_Int_OPls = c_Nat__Transfer_Otsub(X0,X0)
| ~ spl104_78
| ~ spl104_218
| ~ spl104_222
| ~ spl104_452
| ~ spl104_687 ),
inference(forward_demodulation,[],[f11543,f8543]) ).
fof(f11543,plain,
( ! [X0] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,X0) = c_Nat__Transfer_Otsub(X0,X0)
| ~ spl104_222
| ~ spl104_687 ),
inference(resolution,[],[f11158,f7088]) ).
fof(f11158,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) )
| ~ spl104_687 ),
inference(avatar_component_clause,[],[f11157]) ).
fof(f11433,plain,
( spl104_754
| ~ spl104_98
| ~ spl104_381 ),
inference(avatar_split_clause,[],[f7971,f7784,f6468,f11430]) ).
fof(f11430,plain,
( spl104_754
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_754])]) ).
fof(f6468,plain,
( spl104_98
<=> class_Int_Onumber__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_98])]) ).
fof(f7971,plain,
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OPls)
| ~ spl104_98
| ~ spl104_381 ),
inference(resolution,[],[f7785,f6470]) ).
fof(f6470,plain,
( class_Int_Onumber__ring(tc_RealDef_Oreal)
| ~ spl104_98 ),
inference(avatar_component_clause,[],[f6468]) ).
fof(f11428,plain,
( spl104_753
| ~ spl104_440
| ~ spl104_677 ),
inference(avatar_split_clause,[],[f11101,f11097,f8142,f11425]) ).
fof(f8142,plain,
( spl104_440
<=> ! [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,[spl104_440])]) ).
fof(f11097,plain,
( spl104_677
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_677])]) ).
fof(f11101,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____)))
| ~ spl104_440
| ~ spl104_677 ),
inference(forward_demodulation,[],[f11099,f8143]) ).
fof(f8143,plain,
( ! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1)
| ~ spl104_440 ),
inference(avatar_component_clause,[],[f8142]) ).
fof(f11099,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))
| ~ spl104_677 ),
inference(avatar_component_clause,[],[f11097]) ).
fof(f11423,plain,
spl104_752,
inference(avatar_split_clause,[],[f5964,f11421]) ).
fof(f11421,plain,
( spl104_752
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ sP19(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_752])]) ).
fof(f5964,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ sP19(X0,X1,X2) ),
inference(forward_demodulation,[],[f5349,f4101]) ).
fof(f5349,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1)
| ~ sP19(X0,X1,X2) ),
inference(cnf_transformation,[],[f3806]) ).
fof(f3806,plain,
! [X0,X1,X2] :
( ( sP19(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
| ( ~ hBOOL(hAPP(X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ) )
& ( ( ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
& ( hBOOL(hAPP(X0,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ) )
| ~ sP19(X0,X1,X2) ) ),
inference(rectify,[],[f3805]) ).
fof(f3805,plain,
! [X2,X0,X1] :
( ( sP19(X2,X0,X1)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) )
& ( ( ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) )
| ~ sP19(X2,X0,X1) ) ),
inference(flattening,[],[f3804]) ).
fof(f3804,plain,
! [X2,X0,X1] :
( ( sP19(X2,X0,X1)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) )
& ( ( ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) )
& ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X1) ) )
| ~ sP19(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3374]) ).
fof(f11419,plain,
spl104_751,
inference(avatar_split_clause,[],[f5963,f11417]) ).
fof(f11417,plain,
( spl104_751
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,c_Int_OPls))
| sP19(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_751])]) ).
fof(f5963,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,c_Int_OPls))
| sP19(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(forward_demodulation,[],[f5352,f4101]) ).
fof(f5352,plain,
! [X2,X0,X1] :
( sP19(X0,X1,X2)
| ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X2) ),
inference(cnf_transformation,[],[f3806]) ).
fof(f11415,plain,
spl104_750,
inference(avatar_split_clause,[],[f5869,f11413]) ).
fof(f11413,plain,
( spl104_750
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Osucc(X0))
| X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_750])]) ).
fof(f5869,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Osucc(X0))
| X0 = X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f4853,f4183]) ).
fof(f4183,plain,
! [X0] : c_Int_Osucc(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f1321]) ).
fof(f1321,plain,
! [X0] : c_Int_Osucc(X0) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(rectify,[],[f513]) ).
fof(f513,axiom,
! [X14] : c_Int_Osucc(X14) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_succ__def) ).
fof(f4853,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,[],[f3633]) ).
fof(f3633,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,[],[f3632]) ).
fof(f3632,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,[],[f1790]) ).
fof(f1790,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,[],[f419]) ).
fof(f419,axiom,
! [X55,X50] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X55,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( X50 = X55
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X55) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zless__add1__eq) ).
fof(f11411,plain,
spl104_749,
inference(avatar_split_clause,[],[f5712,f11409]) ).
fof(f11409,plain,
( spl104_749
<=> ! [X0,X1] :
( ~ c_Nat__Numeral_Oneg(X1)
| c_Nat_OSuc(X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_749])]) ).
fof(f5712,plain,
! [X0,X1] :
( ~ c_Nat__Numeral_Oneg(X1)
| c_Nat_OSuc(X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),X0)) ),
inference(forward_demodulation,[],[f5711,f4155]) ).
fof(f5711,plain,
! [X0,X1] :
( c_Nat_OSuc(X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),X0))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(forward_demodulation,[],[f4441,f4185]) ).
fof(f4441,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),X0))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(cnf_transformation,[],[f2403]) ).
fof(f2403,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X1)),X0)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),X0))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ) ),
inference(ennf_transformation,[],[f1536]) ).
fof(f1536,plain,
! [X0,X1] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X1)),X0) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),X0)) ) ),
inference(rectify,[],[f506]) ).
fof(f506,axiom,
! [X5,X48] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X48))
=> c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48),X5)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X48)),X5) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X48))
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),X5) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48),X5)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__nat__number__of__add) ).
fof(f11407,plain,
spl104_748,
inference(avatar_split_clause,[],[f5700,f11405]) ).
fof(f11405,plain,
( spl104_748
<=> ! [X2,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,sK37(X0))
| ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_748])]) ).
fof(f5700,plain,
! [X2,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,sK37(X0))
| ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(forward_demodulation,[],[f4383,f4101]) ).
fof(f4383,plain,
! [X2,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK37(X0))
| ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(cnf_transformation,[],[f3438]) ).
fof(f3438,plain,
! [X0] :
( ( ( hBOOL(hAPP(X0,sK37(X0)))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK37(X0)) )
| ! [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
& ( hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK38(X0))))
| ! [X4] :
( ~ hBOOL(hAPP(X0,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38])],[f3435,f3437,f3436]) ).
fof(f3436,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP(X0,X1))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) )
=> ( hBOOL(hAPP(X0,sK37(X0)))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK37(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f3437,plain,
! [X0] :
( ? [X3] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
=> hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK38(X0)))) ),
introduced(choice_axiom,[]) ).
fof(f3435,plain,
! [X0] :
( ( ? [X1] :
( hBOOL(hAPP(X0,X1))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) )
| ! [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
& ( ? [X3] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
| ! [X4] :
( ~ hBOOL(hAPP(X0,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) ) ) ),
inference(rectify,[],[f3434]) ).
fof(f3434,plain,
! [X0] :
( ( ? [X1] :
( hBOOL(hAPP(X0,X1))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) )
| ! [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
& ( ? [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ! [X1] :
( ~ hBOOL(hAPP(X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ) ),
inference(nnf_transformation,[],[f1482]) ).
fof(f1482,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP(X0,X1))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) )
<=> ? [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(rectify,[],[f677]) ).
fof(f677,axiom,
! [X41] :
( ? [X2] :
( hBOOL(hAPP(X41,X2))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) )
<=> ? [X2] : hBOOL(hAPP(X41,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_transfer__int__nat__quantifiers_I2_J) ).
fof(f11403,plain,
spl104_747,
inference(avatar_split_clause,[],[f5699,f11401]) ).
fof(f11401,plain,
( spl104_747
<=> ! [X0,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,sK36(X0))
| hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_747])]) ).
fof(f5699,plain,
! [X3,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,sK36(X0))
| hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3))) ),
inference(forward_demodulation,[],[f4379,f4101]) ).
fof(f4379,plain,
! [X3,X0] :
( hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK36(X0)) ),
inference(cnf_transformation,[],[f3433]) ).
fof(f3433,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP(X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) )
| ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK35(X0)))) )
& ( ! [X3] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
| ( ~ hBOOL(hAPP(X0,sK36(X0)))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK36(X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36])],[f3430,f3432,f3431]) ).
fof(f3431,plain,
! [X0] :
( ? [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
=> ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK35(X0)))) ),
introduced(choice_axiom,[]) ).
fof(f3432,plain,
! [X0] :
( ? [X4] :
( ~ hBOOL(hAPP(X0,X4))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) )
=> ( ~ hBOOL(hAPP(X0,sK36(X0)))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK36(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f3430,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP(X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) )
| ? [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
& ( ! [X3] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
| ? [X4] :
( ~ hBOOL(hAPP(X0,X4))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X4) ) ) ),
inference(rectify,[],[f3429]) ).
fof(f3429,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP(X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) )
| ? [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
& ( ! [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ? [X1] :
( ~ hBOOL(hAPP(X0,X1))
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) ) ) ),
inference(nnf_transformation,[],[f2399]) ).
fof(f2399,plain,
! [X0] :
( ! [X1] :
( hBOOL(hAPP(X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1) )
<=> ! [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(ennf_transformation,[],[f1481]) ).
fof(f1481,plain,
! [X0] :
( ! [X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1)
=> hBOOL(hAPP(X0,X1)) )
<=> ! [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(rectify,[],[f676]) ).
fof(f676,axiom,
! [X41] :
( ! [X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2)
=> hBOOL(hAPP(X41,X2)) )
<=> ! [X2] : hBOOL(hAPP(X41,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_transfer__int__nat__quantifiers_I1_J) ).
fof(f11399,plain,
spl104_746,
inference(avatar_split_clause,[],[f5691,f11397]) ).
fof(f11397,plain,
( spl104_746
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_746])]) ).
fof(f5691,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(forward_demodulation,[],[f4369,f4101]) ).
fof(f4369,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
inference(cnf_transformation,[],[f3424]) ).
fof(f3424,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ) ),
inference(nnf_transformation,[],[f1476]) ).
fof(f1476,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(rectify,[],[f744]) ).
fof(f744,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__less__int__conv) ).
fof(f11395,plain,
spl104_745,
inference(avatar_split_clause,[],[f5690,f11393]) ).
fof(f11393,plain,
( spl104_745
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_745])]) ).
fof(f5690,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(forward_demodulation,[],[f4370,f4101]) ).
fof(f4370,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f3424]) ).
fof(f11389,plain,
spl104_744,
inference(avatar_split_clause,[],[f5673,f11387]) ).
fof(f11387,plain,
( spl104_744
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_744])]) ).
fof(f5673,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)) ),
inference(forward_demodulation,[],[f5672,f4101]) ).
fof(f5672,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(forward_demodulation,[],[f4326,f4101]) ).
fof(f4326,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f2392]) ).
fof(f2392,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(ennf_transformation,[],[f1453]) ).
fof(f1453,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)) ),
inference(rectify,[],[f422]) ).
fof(f422,axiom,
! [X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__imp__0__less) ).
fof(f11385,plain,
( spl104_743
| ~ spl104_363
| ~ spl104_378 ),
inference(avatar_split_clause,[],[f7968,f7772,f7709,f11382]) ).
fof(f11382,plain,
( spl104_743
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_743])]) ).
fof(f7772,plain,
( spl104_378
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_378])]) ).
fof(f7968,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ spl104_363
| ~ spl104_378 ),
inference(superposition,[],[f7773,f7711]) ).
fof(f7773,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
| ~ spl104_378 ),
inference(avatar_component_clause,[],[f7772]) ).
fof(f11380,plain,
spl104_742,
inference(avatar_split_clause,[],[f5655,f11378]) ).
fof(f11378,plain,
( spl104_742
<=> ! [X0] :
( c_Nat__Numeral_Oneg(X0)
| c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_742])]) ).
fof(f5655,plain,
! [X0] :
( c_Nat__Numeral_Oneg(X0)
| c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ),
inference(forward_demodulation,[],[f4217,f4155]) ).
fof(f4217,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ),
inference(cnf_transformation,[],[f2292]) ).
fof(f2292,plain,
! [X0] :
( ( c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ) ),
inference(ennf_transformation,[],[f1353]) ).
fof(f1353,plain,
! [X0] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0))
=> c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0))
=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
inference(rectify,[],[f503]) ).
fof(f503,axiom,
! [X48] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X48))
=> hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48)) = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X48) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X48))
=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__of__nat__number__of) ).
fof(f11376,plain,
spl104_741,
inference(avatar_split_clause,[],[f5347,f11374]) ).
fof(f11374,plain,
( spl104_741
<=> ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_741])]) ).
fof(f5347,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f3803]) ).
fof(f3803,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,[],[f2090]) ).
fof(f2090,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,[],[f65]) ).
fof(f65,axiom,
! [X18,X17,X20] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X17) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X18)
<=> X17 = X18 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__add__left__cancel) ).
fof(f11372,plain,
spl104_740,
inference(avatar_split_clause,[],[f5346,f11370]) ).
fof(f11370,plain,
( spl104_740
<=> ! [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,[spl104_740])]) ).
fof(f5346,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,[],[f3803]) ).
fof(f11368,plain,
spl104_739,
inference(avatar_split_clause,[],[f5345,f11366]) ).
fof(f11366,plain,
( spl104_739
<=> ! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)
| X0 != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_739])]) ).
fof(f5345,plain,
! [X2,X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X2,X1)
| X0 != X2 ),
inference(cnf_transformation,[],[f3802]) ).
fof(f3802,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,[],[f2089]) ).
fof(f2089,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,[],[f64]) ).
fof(f64,axiom,
! [X18,X20,X17] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X20) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X18,X20)
<=> X17 = X18 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__add__right__cancel) ).
fof(f11364,plain,
spl104_738,
inference(avatar_split_clause,[],[f5344,f11362]) ).
fof(f11362,plain,
( spl104_738
<=> ! [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,[spl104_738])]) ).
fof(f5344,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,[],[f3802]) ).
fof(f11360,plain,
spl104_737,
inference(avatar_split_clause,[],[f5218,f11358]) ).
fof(f11358,plain,
( spl104_737
<=> ! [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,[spl104_737])]) ).
fof(f5218,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,[],[f2977]) ).
fof(f2977,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,[],[f2976]) ).
fof(f2976,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,[],[f2041]) ).
fof(f2041,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,[],[f18]) ).
fof(f18,axiom,
! [X14,X15,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,X15)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X15,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X16,X14) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__trans) ).
fof(f11356,plain,
spl104_736,
inference(avatar_split_clause,[],[f5197,f11354]) ).
fof(f11354,plain,
( spl104_736
<=> ! [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,[spl104_736])]) ).
fof(f5197,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,[],[f2953]) ).
fof(f2953,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,[],[f2952]) ).
fof(f2952,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,[],[f2020]) ).
fof(f2020,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,[],[f438]) ).
fof(f438,axiom,
! [X14,X15,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,X15)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X15,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X16,X14) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zle__trans) ).
fof(f11352,plain,
spl104_735,
inference(avatar_split_clause,[],[f5194,f11350]) ).
fof(f11350,plain,
( spl104_735
<=> ! [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,[spl104_735])]) ).
fof(f5194,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,[],[f2948]) ).
fof(f2948,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,[],[f2947]) ).
fof(f2947,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,[],[f2017]) ).
fof(f2017,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,[],[f79]) ).
fof(f79,axiom,
! [X14,X15,X16] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,X15)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X15,X14)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X16,X14) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__le__trans) ).
fof(f11348,plain,
spl104_734,
inference(avatar_split_clause,[],[f5121,f11346]) ).
fof(f11346,plain,
( spl104_734
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_734])]) ).
fof(f5121,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,[],[f3716]) ).
fof(f3716,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,[],[f2862]) ).
fof(f2862,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,[],[f1959]) ).
fof(f1959,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,[],[f278]) ).
fof(f278,axiom,
! [X9,X7,X4] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)
=> ( c_Groups_Oplus__class_Oplus(X4,X7,X9) = X7
<=> c_Groups_Ozero__class_Ozero(X4) = X9 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__0__iff) ).
fof(f11344,plain,
spl104_733,
inference(avatar_split_clause,[],[f5120,f11342]) ).
fof(f11342,plain,
( spl104_733
<=> ! [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,[spl104_733])]) ).
fof(f5120,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,[],[f3716]) ).
fof(f11340,plain,
( spl104_732
| ~ spl104_344
| ~ spl104_372 ),
inference(avatar_split_clause,[],[f7952,f7748,f7608,f11338]) ).
fof(f11338,plain,
( spl104_732
<=> ! [X2] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_732])]) ).
fof(f7608,plain,
( spl104_344
<=> ! [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,[spl104_344])]) ).
fof(f7748,plain,
( spl104_372
<=> ! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_372])]) ).
fof(f7952,plain,
( ! [X2] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl104_344
| ~ spl104_372 ),
inference(superposition,[],[f7609,f7749]) ).
fof(f7749,plain,
( ! [X0] : c_Nat_OSuc(X0) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl104_372 ),
inference(avatar_component_clause,[],[f7748]) ).
fof(f7609,plain,
( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0)
| ~ spl104_344 ),
inference(avatar_component_clause,[],[f7608]) ).
fof(f11336,plain,
spl104_731,
inference(avatar_split_clause,[],[f5051,f11334]) ).
fof(f11334,plain,
( spl104_731
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
| X0 != X1
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_731])]) ).
fof(f5051,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
| X0 != X1
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f3701]) ).
fof(f3701,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
| X0 != X1 )
& ( X0 = X1
| c_Groups_Ominus__class_Ominus(X2,X1,X0) != c_Groups_Ozero__class_Ozero(X2) ) )
| ~ class_Groups_Ogroup__add(X2) ),
inference(nnf_transformation,[],[f2765]) ).
fof(f2765,plain,
! [X0,X1,X2] :
( ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
<=> X0 = X1 )
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f1904]) ).
fof(f1904,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
<=> X0 = X1 ) ),
inference(rectify,[],[f139]) ).
fof(f139,axiom,
! [X7,X9,X4] :
( class_Groups_Ogroup__add(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) = c_Groups_Ominus__class_Ominus(X4,X9,X7)
<=> X7 = X9 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_right__minus__eq) ).
fof(f11332,plain,
spl104_730,
inference(avatar_split_clause,[],[f5050,f11330]) ).
fof(f5050,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ominus__class_Ominus(X2,X1,X0) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f3701]) ).
fof(f11328,plain,
spl104_729,
inference(avatar_split_clause,[],[f5049,f11326]) ).
fof(f5049,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ominus__class_Ominus(X2,X1,X0) != c_Groups_Ozero__class_Ozero(X2)
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f3700]) ).
fof(f3700,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| c_Groups_Ominus__class_Ominus(X2,X1,X0) != c_Groups_Ozero__class_Ozero(X2) )
& ( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
| X0 != X1 ) )
| ~ class_Groups_Oab__group__add(X2) ),
inference(nnf_transformation,[],[f2764]) ).
fof(f2764,plain,
! [X0,X1,X2] :
( ( X0 = X1
<=> c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2) )
| ~ class_Groups_Oab__group__add(X2) ),
inference(ennf_transformation,[],[f1903]) ).
fof(f1903,plain,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> ( X0 = X1
<=> c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2) ) ),
inference(rectify,[],[f136]) ).
fof(f136,axiom,
! [X7,X9,X4] :
( class_Groups_Oab__group__add(X4)
=> ( X7 = X9
<=> c_Groups_Ozero__class_Ozero(X4) = c_Groups_Ominus__class_Ominus(X4,X9,X7) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_eq__iff__diff__eq__0) ).
fof(f11324,plain,
spl104_728,
inference(avatar_split_clause,[],[f5048,f11322]) ).
fof(f11322,plain,
( spl104_728
<=> ! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
| X0 != X1
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_728])]) ).
fof(f5048,plain,
! [X2,X0,X1] :
( c_Groups_Ominus__class_Ominus(X2,X1,X0) = c_Groups_Ozero__class_Ozero(X2)
| X0 != X1
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f3700]) ).
fof(f11320,plain,
spl104_727,
inference(avatar_split_clause,[],[f5026,f11318]) ).
fof(f11318,plain,
( spl104_727
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_727])]) ).
fof(f5026,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(cnf_transformation,[],[f2734]) ).
fof(f2734,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(flattening,[],[f2733]) ).
fof(f2733,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X2) ),
inference(ennf_transformation,[],[f1884]) ).
fof(f1884,plain,
! [X0,X1,X2] :
( class_Groups_Oordered__ab__group__add__abs(X2)
=> ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Oabs__class_Oabs(X2,X1),X0)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
inference(rectify,[],[f369]) ).
fof(f369,axiom,
! [X11,X12,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oabs__class_Oabs(X4,X12),X11)
=> c_Orderings_Oord__class_Oless__eq(X4,X12,X11) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__le__D1) ).
fof(f11316,plain,
spl104_726,
inference(avatar_split_clause,[],[f4888,f11314]) ).
fof(f11314,plain,
( spl104_726
<=> ! [X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_726])]) ).
fof(f4888,plain,
! [X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f3652]) ).
fof(f3652,plain,
! [X0,X1] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ) ),
inference(nnf_transformation,[],[f1803]) ).
fof(f1803,plain,
! [X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
<=> X0 = X1 ),
inference(rectify,[],[f779]) ).
fof(f779,axiom,
! [X26,X23] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X23) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X26)
<=> X23 = X26 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Nat__Transfer_Otransfer__int__nat__relations_I1_J) ).
fof(f11312,plain,
spl104_725,
inference(avatar_split_clause,[],[f4887,f11310]) ).
fof(f11310,plain,
( spl104_725
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_725])]) ).
fof(f4887,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f3652]) ).
fof(f11308,plain,
spl104_724,
inference(avatar_split_clause,[],[f4886,f11306]) ).
fof(f11306,plain,
( spl104_724
<=> ! [X0,X1] :
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_724])]) ).
fof(f4886,plain,
! [X0,X1] :
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f3651]) ).
fof(f3651,plain,
! [X0,X1] :
( ( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1) ) ),
inference(nnf_transformation,[],[f1802]) ).
fof(f1802,plain,
! [X0,X1] :
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1)
<=> X0 = X1 ),
inference(rectify,[],[f76]) ).
fof(f76,axiom,
! [X17,X18] :
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X18) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X17)
<=> X17 = X18 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__of__nat__inject) ).
fof(f11304,plain,
spl104_723,
inference(avatar_split_clause,[],[f4885,f11302]) ).
fof(f11302,plain,
( spl104_723
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_723])]) ).
fof(f4885,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f3651]) ).
fof(f11300,plain,
spl104_722,
inference(avatar_split_clause,[],[f4875,f11298]) ).
fof(f11298,plain,
( spl104_722
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_722])]) ).
fof(f4875,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ),
inference(cnf_transformation,[],[f3644]) ).
fof(f3644,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
inference(flattening,[],[f3643]) ).
fof(f3643,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
inference(nnf_transformation,[],[f2685]) ).
fof(f2685,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
inference(ennf_transformation,[],[f1798]) ).
fof(f1798,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_OPls) ) ),
inference(rectify,[],[f543]) ).
fof(f543,axiom,
! [X66,X52] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X52),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X66))
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52,X66)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52,c_Int_OPls) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__nat__number__of) ).
fof(f11296,plain,
( spl104_721
| ~ spl104_346
| ~ spl104_372 ),
inference(avatar_split_clause,[],[f7950,f7748,f7616,f11294]) ).
fof(f11294,plain,
( spl104_721
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Nat_OSuc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_721])]) ).
fof(f7616,plain,
( spl104_346
<=> ! [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,[spl104_346])]) ).
fof(f7950,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Nat_OSuc(X0))
| ~ spl104_346
| ~ spl104_372 ),
inference(superposition,[],[f7617,f7749]) ).
fof(f7617,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,X1))
| ~ spl104_346 ),
inference(avatar_component_clause,[],[f7616]) ).
fof(f11292,plain,
spl104_720,
inference(avatar_split_clause,[],[f4874,f11290]) ).
fof(f11290,plain,
( spl104_720
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_720])]) ).
fof(f4874,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3644]) ).
fof(f11288,plain,
spl104_719,
inference(avatar_split_clause,[],[f4864,f11286]) ).
fof(f11286,plain,
( spl104_719
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_719])]) ).
fof(f4864,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ),
inference(cnf_transformation,[],[f3639]) ).
fof(f3639,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,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(tc_Int_Oint,c_Int_OPls,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
inference(flattening,[],[f3638]) ).
fof(f3638,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,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(tc_Int_Oint,c_Int_OPls,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
inference(nnf_transformation,[],[f2684]) ).
fof(f2684,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ) ),
inference(ennf_transformation,[],[f1794]) ).
fof(f1794,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,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(tc_Int_Oint,c_Int_OPls,X0) ) ) ),
inference(rectify,[],[f542]) ).
fof(f542,axiom,
! [X66,X52] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X52),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X66))
<=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X52,X66)
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X52,X66)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X66) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__nat__number__of) ).
fof(f11284,plain,
spl104_718,
inference(avatar_split_clause,[],[f4859,f11282]) ).
fof(f11282,plain,
( spl104_718
<=> ! [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,[spl104_718])]) ).
fof(f4859,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,[],[f3635]) ).
fof(f3635,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,[],[f1792]) ).
fof(f1792,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,[],[f130]) ).
fof(f130,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X18,X17))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__less__diff) ).
fof(f11280,plain,
spl104_717,
inference(avatar_split_clause,[],[f4858,f11278]) ).
fof(f11278,plain,
( spl104_717
<=> ! [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,[spl104_717])]) ).
fof(f4858,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,[],[f3635]) ).
fof(f11276,plain,
spl104_716,
inference(avatar_split_clause,[],[f4785,f11274]) ).
fof(f11274,plain,
( spl104_716
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK85(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_716])]) ).
fof(f4785,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK85(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3597]) ).
fof(f3597,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK85(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK85])],[f3595,f3596]) ).
fof(f3596,plain,
! [X0,X1] :
( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK85(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3595,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,[],[f3594]) ).
fof(f3594,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,[],[f1774]) ).
fof(f1774,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,[],[f74]) ).
fof(f74,axiom,
! [X29,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X20,X29)
<=> ? [X30] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X20,X30) = X29 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__Suc__ex__iff) ).
fof(f11272,plain,
spl104_715,
inference(avatar_split_clause,[],[f4783,f11270]) ).
fof(f11270,plain,
( spl104_715
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK84(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_715])]) ).
fof(f4783,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK84(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3593]) ).
fof(f3593,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ! [X2] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK84(X0,X1)) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK84])],[f3591,f3592]) ).
fof(f3592,plain,
! [X0,X1] :
( ? [X3] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X3) = X0
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,sK84(X0,X1)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3591,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,[],[f3590]) ).
fof(f3590,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,[],[f1773]) ).
fof(f1773,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,[],[f35]) ).
fof(f35,axiom,
! [X18,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X18)
<=> ? [X21] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X21) = X18 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__iff__add) ).
fof(f11268,plain,
spl104_714,
inference(avatar_split_clause,[],[f4770,f11266]) ).
fof(f11266,plain,
( spl104_714
<=> ! [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,[spl104_714])]) ).
fof(f4770,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,[],[f3579]) ).
fof(f3579,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,[],[f1767]) ).
fof(f1767,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,[],[f342]) ).
fof(f342,axiom,
! [X26,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X26)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X23,X26),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__le__eq__diff) ).
fof(f11264,plain,
spl104_713,
inference(avatar_split_clause,[],[f4769,f11262]) ).
fof(f11262,plain,
( spl104_713
<=> ! [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,[spl104_713])]) ).
fof(f4769,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,[],[f3579]) ).
fof(f11260,plain,
spl104_712,
inference(avatar_split_clause,[],[f4719,f11258]) ).
fof(f11258,plain,
( spl104_712
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_712])]) ).
fof(f4719,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),X0) ),
inference(cnf_transformation,[],[f2656]) ).
fof(f2656,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),X0) ),
inference(ennf_transformation,[],[f1740]) ).
fof(f1740,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X1),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_RComplete_Onatfloor(X0)) ),
inference(rectify,[],[f454]) ).
fof(f454,axiom,
! [X12,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3),X12)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_RComplete_Onatfloor(X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__natfloor) ).
fof(f11256,plain,
spl104_711,
inference(avatar_split_clause,[],[f4718,f11254]) ).
fof(f11254,plain,
( spl104_711
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_711])]) ).
fof(f4718,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ),
inference(cnf_transformation,[],[f2655]) ).
fof(f2655,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ),
inference(ennf_transformation,[],[f1739]) ).
fof(f1739,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),X0) ),
inference(rectify,[],[f399]) ).
fof(f399,axiom,
! [X12,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X12))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3),X12) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_natceiling__le) ).
fof(f11252,plain,
( ~ spl104_710
| ~ spl104_363
| ~ spl104_366 ),
inference(avatar_split_clause,[],[f7939,f7724,f7709,f11249]) ).
fof(f11249,plain,
( spl104_710
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_710])]) ).
fof(f7724,plain,
( spl104_366
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_366])]) ).
fof(f7939,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl104_363
| ~ spl104_366 ),
inference(superposition,[],[f7725,f7711]) ).
fof(f7725,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ spl104_366 ),
inference(avatar_component_clause,[],[f7724]) ).
fof(f11247,plain,
spl104_709,
inference(avatar_split_clause,[],[f4643,f11245]) ).
fof(f11245,plain,
( spl104_709
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_709])]) ).
fof(f4643,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,[],[f3532]) ).
fof(f3532,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,[],[f2569]) ).
fof(f2569,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,[],[f1683]) ).
fof(f1683,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,[],[f310]) ).
fof(f310,axiom,
! [X18,X17] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X18)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X17))
<=> X17 = X18 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__less__Suc__eq) ).
fof(f11243,plain,
spl104_708,
inference(avatar_split_clause,[],[f4612,f11241]) ).
fof(f11241,plain,
( spl104_708
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_708])]) ).
fof(f4612,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,[],[f2534]) ).
fof(f2534,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,[],[f2533]) ).
fof(f2533,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,[],[f1653]) ).
fof(f1653,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,[],[f245]) ).
fof(f245,axiom,
! [X6,X5] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X6)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,c_Nat_OSuc(X6))
=> X5 = X6 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__antisym) ).
fof(f11239,plain,
spl104_707,
inference(avatar_split_clause,[],[f4569,f11237]) ).
fof(f11237,plain,
( spl104_707
<=> ! [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,[spl104_707])]) ).
fof(f4569,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,[],[f2494]) ).
fof(f2494,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,[],[f1627]) ).
fof(f1627,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,[],[f566]) ).
fof(f566,axiom,
! [X12,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ozero__class_Ozero(X4)),X12) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(f11235,plain,
spl104_706,
inference(avatar_split_clause,[],[f4568,f11233]) ).
fof(f11233,plain,
( spl104_706
<=> ! [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,[spl104_706])]) ).
fof(f4568,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,[],[f2493]) ).
fof(f2493,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,[],[f1626]) ).
fof(f1626,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,[],[f567]) ).
fof(f567,axiom,
! [X12,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),c_Groups_Ozero__class_Ozero(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f11231,plain,
spl104_705,
inference(avatar_split_clause,[],[f4567,f11229]) ).
fof(f11229,plain,
( spl104_705
<=> ! [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,[spl104_705])]) ).
fof(f4567,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,[],[f2492]) ).
fof(f2492,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,[],[f1625]) ).
fof(f1625,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,[],[f846]) ).
fof(f846,axiom,
! [X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> c_Groups_Oone__class_Oone(X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(f11227,plain,
spl104_704,
inference(avatar_split_clause,[],[f4561,f11225]) ).
fof(f11225,plain,
( spl104_704
<=> ! [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,[spl104_704])]) ).
fof(f4561,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(cnf_transformation,[],[f2486]) ).
fof(f2486,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(ennf_transformation,[],[f1619]) ).
fof(f1619,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,[],[f888]) ).
fof(f888,axiom,
! [X5,X4] :
( class_Groups_Omonoid__mult(X4)
=> c_Groups_Oone__class_Oone(X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X4),c_Groups_Oone__class_Oone(X4)),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_power__one) ).
fof(f11223,plain,
spl104_703,
inference(avatar_split_clause,[],[f4557,f11221]) ).
fof(f11221,plain,
( spl104_703
<=> ! [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,[spl104_703])]) ).
fof(f4557,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Power_Opower(X1) ),
inference(cnf_transformation,[],[f2482]) ).
fof(f2482,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Power_Opower(X1) ),
inference(ennf_transformation,[],[f1615]) ).
fof(f1615,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,[],[f902]) ).
fof(f902,axiom,
! [X12,X4] :
( class_Power_Opower(X4)
=> c_Groups_Oone__class_Oone(X4) = hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_power__0) ).
fof(f11219,plain,
spl104_702,
inference(avatar_split_clause,[],[f4553,f11217]) ).
fof(f11217,plain,
( spl104_702
<=> ! [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,[spl104_702])]) ).
fof(f4553,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,[],[f2478]) ).
fof(f2478,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,[],[f1611]) ).
fof(f1611,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,[],[f568]) ).
fof(f568,axiom,
! [X12,X4] :
( class_Rings_Omult__zero(X4)
=> c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ozero__class_Ozero(X4)),X12) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__zero__left) ).
fof(f11215,plain,
spl104_701,
inference(avatar_split_clause,[],[f4552,f11213]) ).
fof(f11213,plain,
( spl104_701
<=> ! [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,[spl104_701])]) ).
fof(f4552,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,[],[f2477]) ).
fof(f2477,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,[],[f1610]) ).
fof(f1610,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,[],[f569]) ).
fof(f569,axiom,
! [X12,X4] :
( class_Rings_Omult__zero(X4)
=> c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),c_Groups_Ozero__class_Ozero(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__zero__right) ).
fof(f11211,plain,
spl104_700,
inference(avatar_split_clause,[],[f4517,f11209]) ).
fof(f11209,plain,
( spl104_700
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oabs__class_Oabs(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_700])]) ).
fof(f4517,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oabs__class_Oabs(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f3487]) ).
fof(f3487,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oabs__class_Oabs(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oabs__class_Oabs(X1,X0) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(nnf_transformation,[],[f2451]) ).
fof(f2451,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oabs__class_Oabs(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1584]) ).
fof(f1584,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Oabs__class_Oabs(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f367]) ).
fof(f367,axiom,
! [X9,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) = c_Groups_Oabs__class_Oabs(X4,X9)
<=> c_Groups_Ozero__class_Ozero(X4) = X9 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__eq__0) ).
fof(f11207,plain,
spl104_699,
inference(avatar_split_clause,[],[f4516,f11205]) ).
fof(f11205,plain,
( spl104_699
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oabs__class_Oabs(X1,X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_699])]) ).
fof(f4516,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Oabs__class_Oabs(X1,X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f3487]) ).
fof(f11203,plain,
spl104_698,
inference(avatar_split_clause,[],[f4515,f11201]) ).
fof(f11201,plain,
( spl104_698
<=> ! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_698])]) ).
fof(f4515,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f2450]) ).
fof(f2450,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(flattening,[],[f2449]) ).
fof(f2449,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1583]) ).
fof(f1583,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),X0)
=> c_Groups_Oabs__class_Oabs(X1,X0) = X0 ) ),
inference(rectify,[],[f388]) ).
fof(f388,axiom,
! [X12,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X12)
=> c_Groups_Oabs__class_Oabs(X4,X12) = X12 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__of__nonneg) ).
fof(f11199,plain,
spl104_697,
inference(avatar_split_clause,[],[f4514,f11197]) ).
fof(f11197,plain,
( spl104_697
<=> ! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_697])]) ).
fof(f4514,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f2448]) ).
fof(f2448,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(flattening,[],[f2447]) ).
fof(f2447,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = X0
| ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1582]) ).
fof(f1582,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( c_Orderings_Oord__class_Oless(X1,c_Groups_Ozero__class_Ozero(X1),X0)
=> c_Groups_Oabs__class_Oabs(X1,X0) = X0 ) ),
inference(rectify,[],[f391]) ).
fof(f391,axiom,
! [X12,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> ( c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X12)
=> c_Groups_Oabs__class_Oabs(X4,X12) = X12 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__of__pos) ).
fof(f11195,plain,
spl104_696,
inference(avatar_split_clause,[],[f4493,f11193]) ).
fof(f11193,plain,
( spl104_696
<=> ! [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,[spl104_696])]) ).
fof(f4493,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,[],[f2431]) ).
fof(f2431,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,[],[f1567]) ).
fof(f1567,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,[],[f642]) ).
fof(f642,axiom,
! [X12,X4] :
( class_Rings_Olinordered__ring(X4)
=> c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__le__square) ).
fof(f11191,plain,
spl104_695,
inference(avatar_split_clause,[],[f4492,f11189]) ).
fof(f11189,plain,
( spl104_695
<=> ! [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,[spl104_695])]) ).
fof(f4492,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,[],[f2430]) ).
fof(f2430,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,[],[f1566]) ).
fof(f1566,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,[],[f659]) ).
fof(f659,axiom,
! [X12,X4] :
( class_Rings_Olinordered__ring(X4)
=> ~ c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X12),c_Groups_Ozero__class_Ozero(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__square__less__zero) ).
fof(f11187,plain,
spl104_694,
inference(avatar_split_clause,[],[f4481,f11185]) ).
fof(f11185,plain,
( spl104_694
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_694])]) ).
fof(f4481,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(cnf_transformation,[],[f3464]) ).
fof(f3464,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_RealVector_Onorm__class_Onorm(X1,X0) ) )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(nnf_transformation,[],[f2425]) ).
fof(f2425,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1561]) ).
fof(f1561,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,[],[f477]) ).
fof(f477,axiom,
! [X23,X4] :
( class_RealVector_Oreal__normed__vector(X4)
=> ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X4,X23)
<=> c_Groups_Ozero__class_Ozero(X4) = X23 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_norm__eq__zero) ).
fof(f11183,plain,
spl104_693,
inference(avatar_split_clause,[],[f4480,f11181]) ).
fof(f11181,plain,
( spl104_693
<=> ! [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,[spl104_693])]) ).
fof(f4480,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,[],[f3464]) ).
fof(f11179,plain,
spl104_692,
inference(avatar_split_clause,[],[f4473,f11177]) ).
fof(f11177,plain,
( spl104_692
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK45(X0,X1))
| ~ c_SEQ_OBseq(X1,X0)
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_692])]) ).
fof(f4473,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK45(X0,X1))
| ~ c_SEQ_OBseq(X1,X0)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f3453]) ).
fof(f3453,plain,
! [X0,X1] :
( ( ( c_SEQ_OBseq(X1,X0)
| ! [X2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,sK44(X0,X1,X2))),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) )
& ( ( ! [X5] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,X5)),sK45(X0,X1))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK45(X0,X1)) )
| ~ c_SEQ_OBseq(X1,X0) ) )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45])],[f3450,f3452,f3451]) ).
fof(f3451,plain,
! [X0,X1,X2] :
( ? [X3] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,X3)),X2)
=> ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,sK44(X0,X1,X2))),X2) ),
introduced(choice_axiom,[]) ).
fof(f3452,plain,
! [X0,X1] :
( ? [X4] :
( ! [X5] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,X5)),X4)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4) )
=> ( ! [X5] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,X5)),sK45(X0,X1))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK45(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3450,plain,
! [X0,X1] :
( ( ( c_SEQ_OBseq(X1,X0)
| ! [X2] :
( ? [X3] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,X3)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) )
& ( ? [X4] :
( ! [X5] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,X5)),X4)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X4) )
| ~ c_SEQ_OBseq(X1,X0) ) )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(rectify,[],[f3449]) ).
fof(f3449,plain,
! [X0,X1] :
( ( ( c_SEQ_OBseq(X1,X0)
| ! [X2] :
( ? [X3] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,X3)),X2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) )
& ( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,X3)),X2)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
| ~ c_SEQ_OBseq(X1,X0) ) )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(nnf_transformation,[],[f2422]) ).
fof(f2422,plain,
! [X0,X1] :
( ( c_SEQ_OBseq(X1,X0)
<=> ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,X3)),X2)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) )
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1558]) ).
fof(f1558,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> ( c_SEQ_OBseq(X1,X0)
<=> ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,X3)),X2)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ) ),
inference(rectify,[],[f518]) ).
fof(f518,axiom,
! [X33,X4] :
( class_RealVector_Oreal__normed__vector(X4)
=> ( c_SEQ_OBseq(X4,X33)
<=> ? [X61] :
( ! [X30] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,hAPP(X33,X30)),X61)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Bseq__def) ).
fof(f11175,plain,
spl104_691,
inference(avatar_split_clause,[],[f4471,f11173]) ).
fof(f11173,plain,
( spl104_691
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK43(X0,X1))
| ~ c_SEQ_OBseq(X1,X0)
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_691])]) ).
fof(f4471,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK43(X0,X1))
| ~ c_SEQ_OBseq(X1,X0)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f3448]) ).
fof(f3448,plain,
! [X0,X1] :
( ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,X3)),sK43(X0,X1))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK43(X0,X1)) )
| ~ c_SEQ_OBseq(X1,X0)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK43])],[f2421,f3447]) ).
fof(f3447,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,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(X0,X3)),sK43(X0,X1))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK43(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2421,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,X3)),X2)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
| ~ c_SEQ_OBseq(X1,X0)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(flattening,[],[f2420]) ).
fof(f2420,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,X3)),X2)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
| ~ c_SEQ_OBseq(X1,X0)
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1557]) ).
fof(f1557,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> ( c_SEQ_OBseq(X1,X0)
=> ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(X0,X3)),X2)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ) ),
inference(rectify,[],[f521]) ).
fof(f521,axiom,
! [X33,X4] :
( class_RealVector_Oreal__normed__vector(X4)
=> ( c_SEQ_OBseq(X4,X33)
=> ? [X61] :
( ! [X30] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,hAPP(X33,X30)),X61)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_BseqD) ).
fof(f11171,plain,
spl104_690,
inference(avatar_split_clause,[],[f4458,f11169]) ).
fof(f11169,plain,
( spl104_690
<=> ! [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,[spl104_690])]) ).
fof(f4458,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,[],[f2411]) ).
fof(f2411,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,[],[f1548]) ).
fof(f1548,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,[],[f564]) ).
fof(f564,axiom,
! [X22,X4] :
( class_RealVector_Oreal__normed__algebra(X4)
=> c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Ozero__class_Ozero(X4)),X22) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__left_Ozero) ).
fof(f11167,plain,
( spl104_689
| ~ spl104_417
| ~ spl104_676 ),
inference(avatar_split_clause,[],[f11113,f11083,f7929,f11165]) ).
fof(f11165,plain,
( spl104_689
<=> ! [X2,X3] : sP12(X2,X3,c_Int_Opred(c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_689])]) ).
fof(f7929,plain,
( spl104_417
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
| sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_417])]) ).
fof(f11083,plain,
( spl104_676
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_Opred(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_676])]) ).
fof(f11113,plain,
( ! [X2,X3] : sP12(X2,X3,c_Int_Opred(c_Int_OPls))
| ~ spl104_417
| ~ spl104_676 ),
inference(resolution,[],[f11084,f7930]) ).
fof(f7930,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
| sP12(X0,X1,X2) )
| ~ spl104_417 ),
inference(avatar_component_clause,[],[f7929]) ).
fof(f11084,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_Opred(X0))
| ~ spl104_676 ),
inference(avatar_component_clause,[],[f11083]) ).
fof(f11163,plain,
spl104_688,
inference(avatar_split_clause,[],[f4456,f11161]) ).
fof(f11161,plain,
( spl104_688
<=> ! [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,[spl104_688])]) ).
fof(f4456,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,[],[f2409]) ).
fof(f2409,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,[],[f1546]) ).
fof(f1546,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,[],[f563]) ).
fof(f563,axiom,
! [X12,X4] :
( class_RealVector_Oreal__normed__algebra(X4)
=> c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),c_Groups_Ozero__class_Ozero(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult_Ozero__right) ).
fof(f11159,plain,
spl104_687,
inference(avatar_split_clause,[],[f4448,f11157]) ).
fof(f4448,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,[],[f2406]) ).
fof(f2406,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,[],[f1539]) ).
fof(f1539,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,[],[f515]) ).
fof(f515,axiom,
! [X3,X22] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X3)
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X3,X22) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X22,X3)
=> c_Nat__Transfer_Otsub(X3,X22) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X3,X22) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_tsub__def) ).
fof(f11155,plain,
spl104_686,
inference(avatar_split_clause,[],[f4384,f11153]) ).
fof(f11153,plain,
( spl104_686
<=> ! [X2,X0] :
( hBOOL(hAPP(X0,sK37(X0)))
| ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_686])]) ).
fof(f4384,plain,
! [X2,X0] :
( hBOOL(hAPP(X0,sK37(X0)))
| ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(cnf_transformation,[],[f3438]) ).
fof(f11151,plain,
spl104_685,
inference(avatar_split_clause,[],[f4380,f11149]) ).
fof(f11149,plain,
( spl104_685
<=> ! [X0,X3] :
( hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
| ~ hBOOL(hAPP(X0,sK36(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_685])]) ).
fof(f4380,plain,
! [X3,X0] :
( hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
| ~ hBOOL(hAPP(X0,sK36(X0))) ),
inference(cnf_transformation,[],[f3433]) ).
fof(f11147,plain,
spl104_684,
inference(avatar_split_clause,[],[f4372,f11145]) ).
fof(f11145,plain,
( spl104_684
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_684])]) ).
fof(f4372,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f3425]) ).
fof(f3425,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(nnf_transformation,[],[f1477]) ).
fof(f1477,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f350]) ).
fof(f350,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X18),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__of__nat__le__zero__cancel__iff) ).
fof(f11143,plain,
spl104_683,
inference(avatar_split_clause,[],[f4371,f11141]) ).
fof(f11141,plain,
( spl104_683
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_683])]) ).
fof(f4371,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f3425]) ).
fof(f11139,plain,
spl104_682,
inference(avatar_split_clause,[],[f4336,f11137]) ).
fof(f11137,plain,
( spl104_682
<=> ! [X0] :
( c_SEQ_Osubseq(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,sK32(X0)),hAPP(X0,sK33(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_682])]) ).
fof(f4336,plain,
! [X0] :
( c_SEQ_Osubseq(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,sK32(X0)),hAPP(X0,sK33(X0))) ),
inference(cnf_transformation,[],[f3404]) ).
fof(f11135,plain,
spl104_681,
inference(avatar_split_clause,[],[f4281,f11133]) ).
fof(f11133,plain,
( spl104_681
<=> ! [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,[spl104_681])]) ).
fof(f4281,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,[],[f2350]) ).
fof(f2350,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,[],[f1411]) ).
fof(f1411,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,[],[f330]) ).
fof(f330,axiom,
! [X4] :
( class_Rings_Olinordered__semidom(X4)
=> c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Oplus__class_Oplus(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Oone__class_Oone(X4))) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__less__two) ).
fof(f11131,plain,
spl104_680,
inference(avatar_split_clause,[],[f4210,f11129]) ).
fof(f11129,plain,
( spl104_680
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_680])]) ).
fof(f4210,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0))),
inference(cnf_transformation,[],[f1348]) ).
fof(f1348,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0))),
inference(rectify,[],[f461]) ).
fof(f461,axiom,
! [X3] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,X3,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X3))),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__natfloor__gt__diff__one) ).
fof(f11110,plain,
( spl104_679
| ~ spl104_678 ),
inference(avatar_split_clause,[],[f11106,f11103,f11108]) ).
fof(f11108,plain,
( spl104_679
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_RComplete_Onatfloor(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_679])]) ).
fof(f11103,plain,
( spl104_678
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_678])]) ).
fof(f11106,plain,
( ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_RComplete_Onatfloor(X0))))
| ~ spl104_678 ),
inference(forward_demodulation,[],[f11104,f4211]) ).
fof(f11104,plain,
( ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ spl104_678 ),
inference(avatar_component_clause,[],[f11103]) ).
fof(f11105,plain,
spl104_678,
inference(avatar_split_clause,[],[f4209,f11103]) ).
fof(f4209,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(cnf_transformation,[],[f1347]) ).
fof(f1347,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X0)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(rectify,[],[f459]) ).
fof(f459,axiom,
! [X3] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X3,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatfloor(X3)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__natfloor__add__one__gt) ).
fof(f11100,plain,
spl104_677,
inference(avatar_split_clause,[],[f4133,f11097]) ).
fof(f4133,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____),hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact__096N1_A_L_AN2_A_060_061_Af_A_IN1_A_L_AN2_J_096) ).
fof(f11085,plain,
( spl104_676
| ~ spl104_236
| ~ spl104_671 ),
inference(avatar_split_clause,[],[f10817,f10011,f7151,f11083]) ).
fof(f7151,plain,
( spl104_236
<=> ! [X0] : c_Int_Osucc(c_Int_Opred(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_236])]) ).
fof(f10011,plain,
( spl104_671
<=> ! [X2] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Osucc(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_671])]) ).
fof(f10817,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_Opred(X0))
| ~ spl104_236
| ~ spl104_671 ),
inference(superposition,[],[f10012,f7152]) ).
fof(f7152,plain,
( ! [X0] : c_Int_Osucc(c_Int_Opred(X0)) = X0
| ~ spl104_236 ),
inference(avatar_component_clause,[],[f7151]) ).
fof(f10012,plain,
( ! [X2] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Osucc(X2),X2)
| ~ spl104_671 ),
inference(avatar_component_clause,[],[f10011]) ).
fof(f10256,plain,
( spl104_675
| ~ spl104_401
| ~ spl104_577 ),
inference(avatar_split_clause,[],[f9828,f9597,f7865,f10254]) ).
fof(f10254,plain,
( spl104_675
<=> ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Opred(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_675])]) ).
fof(f7865,plain,
( spl104_401
<=> ! [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,[spl104_401])]) ).
fof(f9597,plain,
( spl104_577
<=> ! [X2] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_577])]) ).
fof(f9828,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Opred(X1),X1)
| ~ spl104_401
| ~ spl104_577 ),
inference(resolution,[],[f9598,f7866]) ).
fof(f7866,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
| ~ spl104_401 ),
inference(avatar_component_clause,[],[f7865]) ).
fof(f9598,plain,
( ! [X2] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X2),X2)
| ~ spl104_577 ),
inference(avatar_component_clause,[],[f9597]) ).
fof(f10120,plain,
( spl104_674
| ~ spl104_401
| ~ spl104_548 ),
inference(avatar_split_clause,[],[f9685,f8943,f7865,f10118]) ).
fof(f10118,plain,
( spl104_674
<=> ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_Osucc(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_674])]) ).
fof(f8943,plain,
( spl104_548
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_Osucc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_548])]) ).
fof(f9685,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_Osucc(X1))
| ~ spl104_401
| ~ spl104_548 ),
inference(resolution,[],[f8944,f7866]) ).
fof(f8944,plain,
( ! [X0] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_Osucc(X0))
| ~ spl104_548 ),
inference(avatar_component_clause,[],[f8943]) ).
fof(f10021,plain,
spl104_673,
inference(avatar_split_clause,[],[f5957,f10019]) ).
fof(f10019,plain,
( spl104_673
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,sK94(X0,X1,X2))
| sP12(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_673])]) ).
fof(f5957,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,sK94(X0,X1,X2))
| sP12(X0,X1,X2) ),
inference(forward_demodulation,[],[f5301,f4101]) ).
fof(f5301,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK94(X0,X1,X2)) ),
inference(cnf_transformation,[],[f3773]) ).
fof(f3773,plain,
! [X0,X1,X2] :
( ( sP12(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK93(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK93(X0,X1,X2)),sK94(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK94(X0,X1,X2),X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK94(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)
| ~ sP12(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK93,sK94])],[f3770,f3772,f3771]) ).
fof(f3771,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,sK93(X0,X1,X2)))
& ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK93(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(f3772,plain,
! [X0,X1,X2] :
( ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK93(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),sK93(X0,X1,X2)),sK94(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,sK94(X0,X1,X2),X2)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),sK94(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3770,plain,
! [X0,X1,X2] :
( ( sP12(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)
| ~ sP12(X0,X1,X2) ) ),
inference(rectify,[],[f3769]) ).
fof(f3769,plain,
! [X2,X1,X0] :
( ( sP12(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)
| ~ sP12(X2,X1,X0) ) ),
inference(flattening,[],[f3768]) ).
fof(f3768,plain,
! [X2,X1,X0] :
( ( sP12(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)
| ~ sP12(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3362]) ).
fof(f3362,plain,
! [X2,X1,X0] :
( sP12(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,[sP12])]) ).
fof(f10017,plain,
spl104_672,
inference(avatar_split_clause,[],[f5952,f10015]) ).
fof(f10015,plain,
( spl104_672
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK92(X0,X1,X2),c_Int_OPls)
| sP13(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_672])]) ).
fof(f5952,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK92(X0,X1,X2),c_Int_OPls)
| sP13(X0,X1,X2) ),
inference(forward_demodulation,[],[f5296,f4101]) ).
fof(f5296,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK92(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3767]) ).
fof(f3767,plain,
! [X0,X1,X2] :
( ( sP13(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK91(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK91(X0,X1,X2)),sK92(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK92(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK92(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))
| ~ sP13(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK91,sK92])],[f3764,f3766,f3765]) ).
fof(f3765,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,sK91(X0,X1,X2)))
& ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK91(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(f3766,plain,
! [X0,X1,X2] :
( ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK91(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),sK91(X0,X1,X2)),sK92(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,sK92(X0,X1,X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK92(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f3764,plain,
! [X0,X1,X2] :
( ( sP13(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))
| ~ sP13(X0,X1,X2) ) ),
inference(rectify,[],[f3763]) ).
fof(f3763,plain,
! [X2,X1,X0] :
( ( sP13(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))
| ~ sP13(X2,X1,X0) ) ),
inference(flattening,[],[f3762]) ).
fof(f3762,plain,
! [X2,X1,X0] :
( ( sP13(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))
| ~ sP13(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3363]) ).
fof(f3363,plain,
! [X2,X1,X0] :
( sP13(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,[sP13])]) ).
fof(f10013,plain,
( spl104_671
| ~ spl104_371
| ~ spl104_499 ),
inference(avatar_split_clause,[],[f8757,f8397,f7744,f10011]) ).
fof(f7744,plain,
( spl104_371
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_371])]) ).
fof(f8397,plain,
( spl104_499
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Osucc(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_499])]) ).
fof(f8757,plain,
( ! [X2] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Osucc(X2),X2)
| ~ spl104_371
| ~ spl104_499 ),
inference(resolution,[],[f8398,f7745]) ).
fof(f7745,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X0)
| ~ spl104_371 ),
inference(avatar_component_clause,[],[f7744]) ).
fof(f8398,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Osucc(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
| ~ spl104_499 ),
inference(avatar_component_clause,[],[f8397]) ).
fof(f10009,plain,
spl104_670,
inference(avatar_split_clause,[],[f5950,f10007]) ).
fof(f10007,plain,
( spl104_670
<=> ! [X2,X0,X1] :
( c_Int_OPls != X0
| hBOOL(hAPP(X2,c_Int_OPls))
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_670])]) ).
fof(f5950,plain,
! [X2,X0,X1] :
( c_Int_OPls != X0
| hBOOL(hAPP(X2,c_Int_OPls))
| ~ sP14(X0,X1,X2) ),
inference(forward_demodulation,[],[f5949,f4101]) ).
fof(f5949,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ sP14(X0,X1,X2) ),
inference(forward_demodulation,[],[f5288,f4101]) ).
fof(f5288,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f3761]) ).
fof(f3761,plain,
! [X0,X1,X2] :
( ( sP14(X0,X1,X2)
| ~ sP13(X2,X1,X0)
| ~ sP12(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP13(X2,X1,X0)
& sP12(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP14(X0,X1,X2) ) ),
inference(flattening,[],[f3760]) ).
fof(f3760,plain,
! [X0,X1,X2] :
( ( sP14(X0,X1,X2)
| ~ sP13(X2,X1,X0)
| ~ sP12(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP13(X2,X1,X0)
& sP12(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP14(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f3364]) ).
fof(f3364,plain,
! [X0,X1,X2] :
( sP14(X0,X1,X2)
<=> ( sP13(X2,X1,X0)
& sP12(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,[sP14])]) ).
fof(f10005,plain,
spl104_669,
inference(avatar_split_clause,[],[f5862,f10003]) ).
fof(f10003,plain,
( spl104_669
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_669])]) ).
fof(f5862,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f4843,f4119]) ).
fof(f4843,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f3629]) ).
fof(f3629,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP6(X0,X1) ) ),
inference(flattening,[],[f3628]) ).
fof(f3628,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP6(X0,X1) ) ),
inference(nnf_transformation,[],[f3352]) ).
fof(f3352,plain,
! [X0,X1] :
( sP6(X0,X1)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f10001,plain,
spl104_668,
inference(avatar_split_clause,[],[f5861,f9999]) ).
fof(f9999,plain,
( spl104_668
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_668])]) ).
fof(f5861,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f5860,f4119]) ).
fof(f5860,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f4845,f4119]) ).
fof(f4845,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f3629]) ).
fof(f9997,plain,
spl104_667,
inference(avatar_split_clause,[],[f5859,f9995]) ).
fof(f9995,plain,
( spl104_667
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_667])]) ).
fof(f5859,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f4846,f4119]) ).
fof(f4846,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f3629]) ).
fof(f9993,plain,
spl104_666,
inference(avatar_split_clause,[],[f5858,f9991]) ).
fof(f9991,plain,
( spl104_666
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
| sP6(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_666])]) ).
fof(f5858,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
| sP6(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(forward_demodulation,[],[f4847,f4119]) ).
fof(f4847,plain,
! [X0,X1] :
( sP6(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f3629]) ).
fof(f9989,plain,
spl104_665,
inference(avatar_split_clause,[],[f5857,f9987]) ).
fof(f9987,plain,
( spl104_665
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| sP6(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_665])]) ).
fof(f5857,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| sP6(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(forward_demodulation,[],[f4848,f4119]) ).
fof(f4848,plain,
! [X0,X1] :
( sP6(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f3629]) ).
fof(f9985,plain,
spl104_664,
inference(avatar_split_clause,[],[f5854,f9983]) ).
fof(f9983,plain,
( spl104_664
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_664])]) ).
fof(f5854,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f4835,f4119]) ).
fof(f4835,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f3626]) ).
fof(f3626,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP5(X0,X1) ) ),
inference(flattening,[],[f3625]) ).
fof(f3625,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP5(X0,X1) ) ),
inference(nnf_transformation,[],[f3350]) ).
fof(f3350,plain,
! [X0,X1] :
( sP5(X0,X1)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f9981,plain,
spl104_663,
inference(avatar_split_clause,[],[f5853,f9979]) ).
fof(f9979,plain,
( spl104_663
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_663])]) ).
fof(f5853,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f5852,f4119]) ).
fof(f5852,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f4837,f4119]) ).
fof(f4837,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f3626]) ).
fof(f9977,plain,
spl104_662,
inference(avatar_split_clause,[],[f5851,f9975]) ).
fof(f9975,plain,
( spl104_662
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_662])]) ).
fof(f5851,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f4838,f4119]) ).
fof(f4838,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f3626]) ).
fof(f9973,plain,
spl104_661,
inference(avatar_split_clause,[],[f5850,f9971]) ).
fof(f9971,plain,
( spl104_661
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
| sP5(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_661])]) ).
fof(f5850,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
| sP5(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(forward_demodulation,[],[f4839,f4119]) ).
fof(f4839,plain,
! [X0,X1] :
( sP5(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f3626]) ).
fof(f9969,plain,
( spl104_660
| ~ spl104_371
| ~ spl104_497 ),
inference(avatar_split_clause,[],[f8747,f8389,f7744,f9967]) ).
fof(f9967,plain,
( spl104_660
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Osucc(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_660])]) ).
fof(f8389,plain,
( spl104_497
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Osucc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_497])]) ).
fof(f8747,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Osucc(X0),X0)
| ~ spl104_371
| ~ spl104_497 ),
inference(resolution,[],[f8390,f7745]) ).
fof(f8390,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Osucc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
| ~ spl104_497 ),
inference(avatar_component_clause,[],[f8389]) ).
fof(f9965,plain,
spl104_659,
inference(avatar_split_clause,[],[f5849,f9963]) ).
fof(f9963,plain,
( spl104_659
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| sP5(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_659])]) ).
fof(f5849,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| sP5(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(forward_demodulation,[],[f4840,f4119]) ).
fof(f4840,plain,
! [X0,X1] :
( sP5(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f3626]) ).
fof(f9961,plain,
spl104_658,
inference(avatar_split_clause,[],[f5820,f9959]) ).
fof(f9959,plain,
( spl104_658
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| sP2(X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_658])]) ).
fof(f5820,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| sP2(X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X1) ),
inference(forward_demodulation,[],[f4812,f4101]) ).
fof(f4812,plain,
! [X0,X1] :
( sP2(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,[],[f3614]) ).
fof(f9957,plain,
spl104_657,
inference(avatar_split_clause,[],[f5819,f9955]) ).
fof(f9955,plain,
( spl104_657
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| sP2(X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_657])]) ).
fof(f5819,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| sP2(X0,X1)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f4813,f4101]) ).
fof(f4813,plain,
! [X0,X1] :
( sP2(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,[],[f3614]) ).
fof(f9953,plain,
spl104_656,
inference(avatar_split_clause,[],[f5814,f9951]) ).
fof(f9951,plain,
( spl104_656
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_656])]) ).
fof(f5814,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f4753,f4101]) ).
fof(f4753,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,[],[f3564]) ).
fof(f3564,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,[],[f1760]) ).
fof(f1760,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,[],[f428]) ).
fof(f428,axiom,
! [X29,X20] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,X29)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X20,X29),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__bin__lemma) ).
fof(f9949,plain,
spl104_655,
inference(avatar_split_clause,[],[f5813,f9947]) ).
fof(f9947,plain,
( spl104_655
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_655])]) ).
fof(f5813,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X1,X0),c_Int_OPls)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f4754,f4101]) ).
fof(f4754,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,[],[f3564]) ).
fof(f9945,plain,
spl104_654,
inference(avatar_split_clause,[],[f5703,f9943]) ).
fof(f9943,plain,
( spl104_654
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_654])]) ).
fof(f5703,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0)),
inference(forward_demodulation,[],[f4404,f4101]) ).
fof(f4404,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0)),
inference(cnf_transformation,[],[f1502]) ).
fof(f1502,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X1)),X0)),
inference(rectify,[],[f880]) ).
fof(f880,axiom,
! [X5,X3] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,X3)),X5)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__le__zpower__abs) ).
fof(f9941,plain,
spl104_653,
inference(avatar_split_clause,[],[f5693,f9939]) ).
fof(f9939,plain,
( spl104_653
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_653])]) ).
fof(f5693,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(forward_demodulation,[],[f4373,f4101]) ).
fof(f4373,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3426]) ).
fof(f3426,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| 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_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(nnf_transformation,[],[f1478]) ).
fof(f1478,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f724]) ).
fof(f724,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_int__le__0__conv) ).
fof(f9937,plain,
spl104_652,
inference(avatar_split_clause,[],[f5692,f9935]) ).
fof(f9935,plain,
( spl104_652
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_652])]) ).
fof(f5692,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(forward_demodulation,[],[f4374,f4101]) ).
fof(f4374,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f3426]) ).
fof(f9933,plain,
spl104_651,
inference(avatar_split_clause,[],[f5667,f9931]) ).
fof(f9931,plain,
( spl104_651
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK28(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_651])]) ).
fof(f5667,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK28(X0)) = X0 ),
inference(forward_demodulation,[],[f4313,f4101]) ).
fof(f4313,plain,
! [X0] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK28(X0)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f3391]) ).
fof(f3391,plain,
! [X0] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK28(X0)) = X0
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK28(X0)) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f2381,f3390]) ).
fof(f3390,plain,
! [X0] :
( ? [X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
=> ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK28(X0)) = X0
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK28(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f2381,plain,
! [X0] :
( ? [X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(ennf_transformation,[],[f1442]) ).
fof(f1442,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> ? [X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1) ) ),
inference(rectify,[],[f840]) ).
fof(f840,axiom,
! [X14] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X14)
=> ? [X30] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30) = X14
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X30) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__less__imp__eq__int) ).
fof(f9929,plain,
spl104_650,
inference(avatar_split_clause,[],[f5662,f9927]) ).
fof(f9927,plain,
( spl104_650
<=> ! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_650])]) ).
fof(f5662,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ),
inference(forward_demodulation,[],[f4220,f4185]) ).
fof(f4220,plain,
! [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),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls) ),
inference(cnf_transformation,[],[f2294]) ).
fof(f9925,plain,
( spl104_649
| ~ spl104_371
| ~ spl104_473 ),
inference(avatar_split_clause,[],[f8695,f8289,f7744,f9923]) ).
fof(f9923,plain,
( spl104_649
<=> ! [X1] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_Opred(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_649])]) ).
fof(f8289,plain,
( spl104_473
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_473])]) ).
fof(f8695,plain,
( ! [X1] : ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_Opred(X1))
| ~ spl104_371
| ~ spl104_473 ),
inference(resolution,[],[f8290,f7745]) ).
fof(f8290,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) )
| ~ spl104_473 ),
inference(avatar_component_clause,[],[f8289]) ).
fof(f9921,plain,
spl104_648,
inference(avatar_split_clause,[],[f5656,f9919]) ).
fof(f9919,plain,
( spl104_648
<=> ! [X0] :
( ~ c_Nat__Numeral_Oneg(X0)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_648])]) ).
fof(f5656,plain,
! [X0] :
( ~ c_Nat__Numeral_Oneg(X0)
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ),
inference(forward_demodulation,[],[f4216,f4155]) ).
fof(f4216,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ),
inference(cnf_transformation,[],[f2292]) ).
fof(f9917,plain,
spl104_647,
inference(avatar_split_clause,[],[f5653,f9915]) ).
fof(f9915,plain,
( spl104_647
<=> ! [X0] :
( c_Nat__Numeral_Oneg(X0)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X0)) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_647])]) ).
fof(f5653,plain,
! [X0] :
( c_Nat__Numeral_Oneg(X0)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X0)) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ),
inference(forward_demodulation,[],[f4215,f4155]) ).
fof(f4215,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X0)) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ),
inference(cnf_transformation,[],[f2291]) ).
fof(f2291,plain,
! [X0] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X0)) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ) ),
inference(ennf_transformation,[],[f1352]) ).
fof(f1352,plain,
! [X0] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0))
=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X0)) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
inference(rectify,[],[f507]) ).
fof(f507,axiom,
! [X48] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X48))
=> c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_Osucc(X48)) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48)) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X48))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__nat__number__of) ).
fof(f9913,plain,
spl104_646,
inference(avatar_split_clause,[],[f5387,f9911]) ).
fof(f9911,plain,
( spl104_646
<=> ! [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,[spl104_646])]) ).
fof(f5387,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,[],[f2104]) ).
fof(f2104,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,[],[f927]) ).
fof(f927,axiom,
! [X9,X89,X90,X4] : hAPP(hAPP(c_Power_Opower_Opower(X4,X90,X89),X9),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X90,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_power_Opower_Opower__0) ).
fof(f9909,plain,
spl104_645,
inference(avatar_split_clause,[],[f5339,f9907]) ).
fof(f9907,plain,
( spl104_645
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP18(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_645])]) ).
fof(f5339,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP18(X2,X1,X0) ),
inference(cnf_transformation,[],[f3799]) ).
fof(f3799,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP18(X2,X1,X0) )
& ( sP18(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(nnf_transformation,[],[f3373]) ).
fof(f3373,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> sP18(X2,X1,X0) ),
inference(definition_folding,[],[f3045,f3372]) ).
fof(f3045,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,[],[f2086]) ).
fof(f2086,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,[],[f185]) ).
fof(f185,axiom,
! [X7,X9,X41] :
( hBOOL(hAPP(X41,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,X7)))
<=> ~ ( ? [X43] :
( ~ hBOOL(hAPP(X41,X43))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X43) = X9 )
| ( ~ hBOOL(hAPP(X41,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X7) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__diff__split__asm) ).
fof(f9905,plain,
spl104_644,
inference(avatar_split_clause,[],[f5338,f9903]) ).
fof(f9903,plain,
( spl104_644
<=> ! [X2,X0,X1] :
( sP18(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_644])]) ).
fof(f5338,plain,
! [X2,X0,X1] :
( sP18(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3799]) ).
fof(f9901,plain,
spl104_643,
inference(avatar_split_clause,[],[f5331,f9899]) ).
fof(f9899,plain,
( spl104_643
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP17(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_643])]) ).
fof(f5331,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP17(X2,X1,X0) ),
inference(cnf_transformation,[],[f3793]) ).
fof(f3793,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
| ~ sP17(X2,X1,X0) )
& ( sP17(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
inference(nnf_transformation,[],[f3371]) ).
fof(f3371,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0)))
<=> sP17(X2,X1,X0) ),
inference(definition_folding,[],[f3044,f3370]) ).
fof(f3044,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,[],[f2085]) ).
fof(f2085,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,[],[f184]) ).
fof(f184,axiom,
! [X7,X9,X41] :
( hBOOL(hAPP(X41,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X9,X7)))
<=> ( ! [X43] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X7,X43) = X9
=> hBOOL(hAPP(X41,X43)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X9,X7)
=> hBOOL(hAPP(X41,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__diff__split) ).
fof(f9897,plain,
spl104_642,
inference(avatar_split_clause,[],[f5330,f9895]) ).
fof(f9895,plain,
( spl104_642
<=> ! [X2,X0,X1] :
( sP17(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_642])]) ).
fof(f5330,plain,
! [X2,X0,X1] :
( sP17(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3793]) ).
fof(f9893,plain,
spl104_641,
inference(avatar_split_clause,[],[f5323,f9891]) ).
fof(f9891,plain,
( spl104_641
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ sP16(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_641])]) ).
fof(f5323,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ sP16(X2,X0,X1) ),
inference(cnf_transformation,[],[f3787]) ).
fof(f3787,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ( ~ sP16(X2,X0,X1)
& ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) )
& ( sP16(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,[],[f3786]) ).
fof(f3786,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ( ~ sP16(X2,X0,X1)
& ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) )
& ( sP16(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,[],[f3369]) ).
fof(f3369,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
<=> ( sP16(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,[],[f2084,f3368]) ).
fof(f3368,plain,
! [X2,X0,X1] :
( sP16(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,[sP16])]) ).
fof(f2084,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,[],[f989]) ).
fof(f989,axiom,
! [X18,X17,X41] :
( hBOOL(hAPP(X41,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X17,X18)))
<=> ( ? [X95] :
( hBOOL(hAPP(X41,X95))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),c_Nat_OSuc(X95)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X18),X95),X17) )
| ( hBOOL(hAPP(X41,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_split__div_H) ).
fof(f9889,plain,
spl104_640,
inference(avatar_split_clause,[],[f5318,f9887]) ).
fof(f9887,plain,
( spl104_640
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK97(X0,X1,X2)))
| ~ sP16(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_640])]) ).
fof(f5318,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK97(X0,X1,X2)))
| ~ sP16(X0,X1,X2) ),
inference(cnf_transformation,[],[f3785]) ).
fof(f3785,plain,
! [X0,X1,X2] :
( ( sP16(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,sK97(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(sK97(X0,X1,X2))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),sK97(X0,X1,X2)),X2) )
| ~ sP16(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK97])],[f3783,f3784]) ).
fof(f3784,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,sK97(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(sK97(X0,X1,X2))))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),sK97(X0,X1,X2)),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f3783,plain,
! [X0,X1,X2] :
( ( sP16(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) )
| ~ sP16(X0,X1,X2) ) ),
inference(rectify,[],[f3782]) ).
fof(f3782,plain,
! [X2,X0,X1] :
( ( sP16(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) )
| ~ sP16(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f3368]) ).
fof(f9885,plain,
spl104_639,
inference(avatar_split_clause,[],[f5313,f9883]) ).
fof(f9883,plain,
( spl104_639
<=> ! [X2,X0,X1] :
( sP15(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_639])]) ).
fof(f5313,plain,
! [X2,X0,X1] :
( sP15(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f3781]) ).
fof(f3781,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ sP15(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP15(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,[],[f3780]) ).
fof(f3780,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
| ~ sP15(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP15(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,[],[f3367]) ).
fof(f3367,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X1,X0)))
<=> ( sP15(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,[],[f3043,f3366]) ).
fof(f3366,plain,
! [X2,X1,X0] :
( sP15(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,[sP15])]) ).
fof(f3043,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,[],[f3042]) ).
fof(f3042,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,[],[f2083]) ).
fof(f2083,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,[],[f987]) ).
fof(f987,axiom,
! [X20,X18,X41] :
( hBOOL(hAPP(X41,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X18,X20)))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X20
=> ! [X47,X37] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X37,X20)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X20),X47),X37) = X18
=> hBOOL(hAPP(X41,X47)) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X20
=> hBOOL(hAPP(X41,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_split__div) ).
fof(f9881,plain,
( spl104_638
| ~ spl104_416
| spl104_418
| ~ spl104_419 ),
inference(avatar_split_clause,[],[f8062,f7990,f7942,f7925,f9879]) ).
fof(f9879,plain,
( spl104_638
<=> ! [X6,X7] : sP13(X6,X7,c_Int_Osucc(c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_638])]) ).
fof(f7942,plain,
( spl104_418
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_418])]) ).
fof(f8062,plain,
( ! [X6,X7] : sP13(X6,X7,c_Int_Osucc(c_Int_OPls))
| ~ spl104_416
| spl104_418
| ~ spl104_419 ),
inference(forward_demodulation,[],[f8058,f7992]) ).
fof(f8058,plain,
( ! [X6,X7] : sP13(X6,X7,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl104_416
| spl104_418 ),
inference(resolution,[],[f7926,f7944]) ).
fof(f7944,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)
| spl104_418 ),
inference(avatar_component_clause,[],[f7942]) ).
fof(f9877,plain,
spl104_637,
inference(avatar_split_clause,[],[f5311,f9875]) ).
fof(f9875,plain,
( spl104_637
<=> ! [X2,X0,X1] :
( sP15(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK95(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_637])]) ).
fof(f5311,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK95(X0,X1,X2))) ),
inference(cnf_transformation,[],[f3779]) ).
fof(f3779,plain,
! [X0,X1,X2] :
( ( sP15(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK95(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK95(X0,X1,X2)),sK96(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK96(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
| ~ sP15(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK95,sK96])],[f3777,f3778]) ).
fof(f3778,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,sK95(X0,X1,X2)))
& c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK95(X0,X1,X2)),sK96(X0,X1,X2)) = X1
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK96(X0,X1,X2),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f3777,plain,
! [X0,X1,X2] :
( ( sP15(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
| ~ sP15(X0,X1,X2) ) ),
inference(rectify,[],[f3776]) ).
fof(f3776,plain,
! [X2,X1,X0] :
( ( sP15(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
| ~ sP15(X2,X1,X0) ) ),
inference(flattening,[],[f3775]) ).
fof(f3775,plain,
! [X2,X1,X0] :
( ( sP15(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
| ~ sP15(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f3366]) ).
fof(f9873,plain,
spl104_636,
inference(avatar_split_clause,[],[f5309,f9871]) ).
fof(f9871,plain,
( spl104_636
<=> ! [X2,X0,X1] :
( sP15(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK96(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_636])]) ).
fof(f5309,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK96(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f3779]) ).
fof(f9869,plain,
spl104_635,
inference(avatar_split_clause,[],[f5306,f9867]) ).
fof(f9867,plain,
( spl104_635
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_635])]) ).
fof(f5306,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f3774]) ).
fof(f3774,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
| ~ sP14(X0,X1,X2) )
& ( sP14(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0))) ) ),
inference(nnf_transformation,[],[f3365]) ).
fof(f3365,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
<=> sP14(X0,X1,X2) ),
inference(definition_folding,[],[f3041,f3364,f3363,f3362]) ).
fof(f3041,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,[],[f2082]) ).
fof(f2082,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X3] :
( ? [X4] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3),X4) = X1
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X4,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X4) )
=> hBOOL(hAPP(X2,X3)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
=> ! [X5] :
( ? [X6] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5),X6) = X1
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X6,X0)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X6) )
=> hBOOL(hAPP(X2,X5)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
=> hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
inference(rectify,[],[f966]) ).
fof(f966,axiom,
! [X20,X18,X41] :
( hBOOL(hAPP(X41,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X18,X20)))
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ! [X47] :
( ? [X37] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X47),X37) = X18
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X37,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,X37) )
=> hBOOL(hAPP(X41,X47)) ) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X20)
=> ! [X47] :
( ? [X37] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X20),X47),X37) = X18
& c_Orderings_Oord__class_Oless(tc_Int_Oint,X37,X20)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X37) )
=> hBOOL(hAPP(X41,X47)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X20
=> hBOOL(hAPP(X41,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_split__zdiv) ).
fof(f9865,plain,
spl104_634,
inference(avatar_split_clause,[],[f5305,f9863]) ).
fof(f9863,plain,
( spl104_634
<=> ! [X2,X0,X1] :
( sP14(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_634])]) ).
fof(f5305,plain,
! [X2,X0,X1] :
( sP14(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0))) ),
inference(cnf_transformation,[],[f3774]) ).
fof(f9861,plain,
spl104_633,
inference(avatar_split_clause,[],[f5304,f9859]) ).
fof(f9859,plain,
( spl104_633
<=> ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK93(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_633])]) ).
fof(f5304,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK93(X0,X1,X2))) ),
inference(cnf_transformation,[],[f3773]) ).
fof(f9857,plain,
spl104_632,
inference(avatar_split_clause,[],[f5302,f9855]) ).
fof(f9855,plain,
( spl104_632
<=> ! [X2,X0,X1] :
( sP12(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,sK94(X0,X1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_632])]) ).
fof(f5302,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,sK94(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f3773]) ).
fof(f9853,plain,
spl104_631,
inference(avatar_split_clause,[],[f5298,f9851]) ).
fof(f9851,plain,
( spl104_631
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK91(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_631])]) ).
fof(f5298,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK91(X0,X1,X2))) ),
inference(cnf_transformation,[],[f3767]) ).
fof(f9849,plain,
spl104_630,
inference(avatar_split_clause,[],[f5295,f9847]) ).
fof(f9847,plain,
( spl104_630
<=> ! [X2,X0,X1] :
( sP13(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK92(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_630])]) ).
fof(f5295,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,sK92(X0,X1,X2)) ),
inference(cnf_transformation,[],[f3767]) ).
fof(f9845,plain,
spl104_629,
inference(avatar_split_clause,[],[f5263,f9843]) ).
fof(f9843,plain,
( spl104_629
<=> ! [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,[spl104_629])]) ).
fof(f5263,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,[],[f3021]) ).
fof(f3021,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,[],[f2071]) ).
fof(f2071,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,[],[f29]) ).
fof(f29,axiom,
! [X5,X14,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X14),X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X14,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__leD2) ).
fof(f9841,plain,
spl104_628,
inference(avatar_split_clause,[],[f5262,f9839]) ).
fof(f9839,plain,
( spl104_628
<=> ! [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,[spl104_628])]) ).
fof(f5262,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,[],[f3020]) ).
fof(f3020,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,[],[f2070]) ).
fof(f2070,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,[],[f28]) ).
fof(f28,axiom,
! [X5,X14,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X14),X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__leD1) ).
fof(f9826,plain,
spl104_627,
inference(avatar_split_clause,[],[f5261,f9824]) ).
fof(f9824,plain,
( spl104_627
<=> ! [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,[spl104_627])]) ).
fof(f5261,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,[],[f3019]) ).
fof(f3019,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,[],[f2069]) ).
fof(f2069,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,[],[f264]) ).
fof(f264,axiom,
! [X14,X15,X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X15),X14)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X14) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__lessD1) ).
fof(f9822,plain,
spl104_626,
inference(avatar_split_clause,[],[f5201,f9820]) ).
fof(f9820,plain,
( spl104_626
<=> ! [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,[spl104_626])]) ).
fof(f5201,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,[],[f2959]) ).
fof(f2959,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,[],[f2024]) ).
fof(f2024,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,[],[f72]) ).
fof(f72,axiom,
! [X22,X25,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X25)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_termination__basic__simps_I4_J) ).
fof(f9818,plain,
spl104_625,
inference(avatar_split_clause,[],[f5200,f9816]) ).
fof(f9816,plain,
( spl104_625
<=> ! [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,[spl104_625])]) ).
fof(f5200,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,[],[f2958]) ).
fof(f2958,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,[],[f2023]) ).
fof(f2023,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,[],[f73]) ).
fof(f73,axiom,
! [X25,X22,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X22)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X22,X25)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_termination__basic__simps_I3_J) ).
fof(f9814,plain,
spl104_624,
inference(avatar_split_clause,[],[f5186,f9812]) ).
fof(f9812,plain,
( spl104_624
<=> ! [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,[spl104_624])]) ).
fof(f5186,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,[],[f2934]) ).
fof(f2934,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,[],[f2009]) ).
fof(f2009,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,[],[f157]) ).
fof(f157,axiom,
! [X5,X14,X15] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X15,X14)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X15,X5),X14) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__imp__diff__less) ).
fof(f9810,plain,
spl104_623,
inference(avatar_split_clause,[],[f5183,f9808]) ).
fof(f9808,plain,
( spl104_623
<=> ! [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,[spl104_623])]) ).
fof(f5183,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,[],[f2931]) ).
fof(f2931,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,[],[f2006]) ).
fof(f2006,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,[],[f259]) ).
fof(f259,axiom,
! [X6,X15,X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X15)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_trans__less__add1) ).
fof(f9806,plain,
spl104_622,
inference(avatar_split_clause,[],[f5182,f9804]) ).
fof(f9804,plain,
( spl104_622
<=> ! [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,[spl104_622])]) ).
fof(f5182,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,[],[f2930]) ).
fof(f2930,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,[],[f2005]) ).
fof(f2005,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,[],[f260]) ).
fof(f260,axiom,
! [X6,X15,X16] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,X15)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X15)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_trans__less__add2) ).
fof(f9802,plain,
spl104_621,
inference(avatar_split_clause,[],[f5134,f9800]) ).
fof(f9800,plain,
( spl104_621
<=> ! [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,[spl104_621])]) ).
fof(f5134,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,[],[f2874]) ).
fof(f2874,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,[],[f1970]) ).
fof(f1970,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,[],[f87]) ).
fof(f87,axiom,
! [X10,X12,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> c_Groups_Oplus__class_Oplus(X4,X12,X10) = c_Groups_Oplus__class_Oplus(X4,X10,X12) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f9798,plain,
spl104_620,
inference(avatar_split_clause,[],[f5040,f9796]) ).
fof(f9796,plain,
( spl104_620
<=> ! [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,[spl104_620])]) ).
fof(f5040,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,[],[f2752]) ).
fof(f2752,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,[],[f1896]) ).
fof(f1896,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,[],[f197]) ).
fof(f197,axiom,
! [X11,X12,X4] :
( class_Groups_Ogroup__add(X4)
=> c_Groups_Oplus__class_Oplus(X4,c_Groups_Ominus__class_Ominus(X4,X12,X11),X11) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__add__cancel) ).
fof(f9794,plain,
spl104_619,
inference(avatar_split_clause,[],[f5039,f9792]) ).
fof(f9792,plain,
( spl104_619
<=> ! [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,[spl104_619])]) ).
fof(f5039,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,[],[f2751]) ).
fof(f2751,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,[],[f1895]) ).
fof(f1895,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,[],[f198]) ).
fof(f198,axiom,
! [X11,X12,X4] :
( class_Groups_Ogroup__add(X4)
=> c_Groups_Ominus__class_Ominus(X4,c_Groups_Oplus__class_Oplus(X4,X12,X11),X11) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__diff__cancel) ).
fof(f9790,plain,
spl104_618,
inference(avatar_split_clause,[],[f4844,f9788]) ).
fof(f9788,plain,
( spl104_618
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_618])]) ).
fof(f4844,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f3629]) ).
fof(f9781,plain,
spl104_617,
inference(avatar_split_clause,[],[f4836,f9779]) ).
fof(f9779,plain,
( spl104_617
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_617])]) ).
fof(f4836,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f3626]) ).
fof(f9777,plain,
spl104_616,
inference(avatar_split_clause,[],[f4819,f9775]) ).
fof(f9775,plain,
( spl104_616
<=> ! [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,[spl104_616])]) ).
fof(f4819,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,[],[f3618]) ).
fof(f3618,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,[],[f3617]) ).
fof(f3617,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,[],[f1785]) ).
fof(f1785,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,[],[f287]) ).
fof(f287,axiom,
! [X18,X17] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X18)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X17 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__is__0) ).
fof(f9773,plain,
spl104_615,
inference(avatar_split_clause,[],[f4818,f9771]) ).
fof(f9771,plain,
( spl104_615
<=> ! [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,[spl104_615])]) ).
fof(f4818,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,[],[f3618]) ).
fof(f9769,plain,
spl104_614,
inference(avatar_split_clause,[],[f4816,f9767]) ).
fof(f9767,plain,
( spl104_614
<=> ! [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,[spl104_614])]) ).
fof(f4816,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,[],[f3616]) ).
fof(f3616,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,[],[f1784]) ).
fof(f1784,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,[],[f116]) ).
fof(f116,axiom,
! [X18,X17] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X17,X18)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X18) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__is__0__eq) ).
fof(f9765,plain,
spl104_613,
inference(avatar_split_clause,[],[f4768,f9763]) ).
fof(f9763,plain,
( spl104_613
<=> ! [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 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_613])]) ).
fof(f4768,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,[],[f3578]) ).
fof(f9761,plain,
spl104_612,
inference(avatar_split_clause,[],[f4757,f9759]) ).
fof(f9759,plain,
( spl104_612
<=> ! [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,[spl104_612])]) ).
fof(f4757,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,[],[f3566]) ).
fof(f3566,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,[],[f3565]) ).
fof(f3565,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,[],[f1761]) ).
fof(f1761,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,[],[f431]) ).
fof(f431,axiom,
! [X50,X55] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X55,X50)
<=> ( X50 != X55
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X55,X50) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zless__le) ).
fof(f9757,plain,
spl104_611,
inference(avatar_split_clause,[],[f4752,f9755]) ).
fof(f9755,plain,
( spl104_611
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_611])]) ).
fof(f4752,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(cnf_transformation,[],[f3563]) ).
fof(f3563,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,[],[f3562]) ).
fof(f3562,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,[],[f1759]) ).
fof(f1759,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,[],[f252]) ).
fof(f252,axiom,
! [X26,X23] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,X26)
<=> ( X23 != X26
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X26) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__less__def) ).
fof(f9753,plain,
spl104_610,
inference(avatar_split_clause,[],[f4642,f9751]) ).
fof(f9751,plain,
( spl104_610
<=> ! [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,[spl104_610])]) ).
fof(f4642,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,[],[f2568]) ).
fof(f2568,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,[],[f2567]) ).
fof(f2567,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,[],[f1682]) ).
fof(f1682,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,[],[f19]) ).
fof(f19,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X6)
=> X5 = X6 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__antisym) ).
fof(f9749,plain,
spl104_609,
inference(avatar_split_clause,[],[f4641,f9747]) ).
fof(f9747,plain,
( spl104_609
<=> ! [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,[spl104_609])]) ).
fof(f4641,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,[],[f2566]) ).
fof(f2566,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,[],[f2565]) ).
fof(f2565,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,[],[f1681]) ).
fof(f1681,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,[],[f267]) ).
fof(f267,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5)
=> ( X5 != X6
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X5) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__neq__implies__less) ).
fof(f9745,plain,
spl104_608,
inference(avatar_split_clause,[],[f4634,f9743]) ).
fof(f9743,plain,
( spl104_608
<=> ! [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,[spl104_608])]) ).
fof(f4634,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,[],[f2558]) ).
fof(f2558,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,[],[f1674]) ).
fof(f1674,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,[],[f117]) ).
fof(f117,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__is__0__eq_H) ).
fof(f9735,plain,
spl104_607,
inference(avatar_split_clause,[],[f4631,f9733]) ).
fof(f9733,plain,
( spl104_607
<=> ! [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,[spl104_607])]) ).
fof(f4631,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,[],[f2555]) ).
fof(f2555,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,[],[f2554]) ).
fof(f2554,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,[],[f1671]) ).
fof(f1671,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,[],[f437]) ).
fof(f437,axiom,
! [X32,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X32)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,X25)
=> X25 = X32 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zle__antisym) ).
fof(f9731,plain,
spl104_606,
inference(avatar_split_clause,[],[f4629,f9729]) ).
fof(f9729,plain,
( spl104_606
<=> ! [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,[spl104_606])]) ).
fof(f4629,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f2552]) ).
fof(f2552,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(flattening,[],[f2551]) ).
fof(f2551,plain,
! [X0,X1] :
( X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(ennf_transformation,[],[f1669]) ).
fof(f1669,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,[],[f78]) ).
fof(f78,axiom,
! [X32,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X32)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X32,X25)
=> X25 = X32 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__le__antisym) ).
fof(f9727,plain,
spl104_605,
inference(avatar_split_clause,[],[f4625,f9725]) ).
fof(f9725,plain,
( spl104_605
<=> ! [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,[spl104_605])]) ).
fof(f4625,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,[],[f2546]) ).
fof(f2546,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,[],[f1665]) ).
fof(f1665,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,[],[f971]) ).
fof(f971,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X5)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X6,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_div__less) ).
fof(f9723,plain,
spl104_604,
inference(avatar_split_clause,[],[f4602,f9721]) ).
fof(f9721,plain,
( spl104_604
<=> ! [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,[spl104_604])]) ).
fof(f4602,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,[],[f2520]) ).
fof(f2520,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,[],[f2519]) ).
fof(f2519,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| X0 = X1 ),
inference(ennf_transformation,[],[f1645]) ).
fof(f1645,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,[],[f144]) ).
fof(f144,axiom,
! [X22,X3] :
( X3 != X22
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X22)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X22,X3) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_linorder__neqE__nat) ).
fof(f9719,plain,
spl104_603,
inference(avatar_split_clause,[],[f4599,f9717]) ).
fof(f9717,plain,
( spl104_603
<=> ! [X0,X1] :
( sP0(X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK71(X0,X1),sK72(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_603])]) ).
fof(f4599,plain,
! [X0,X1] :
( sP0(X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK71(X0,X1),sK72(X0,X1)) ),
inference(cnf_transformation,[],[f3526]) ).
fof(f3526,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK72(X0,X1)),hAPP(X0,sK71(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK71(X0,X1),sK72(X0,X1))
& ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK73(X0,X1)),hAPP(X0,sK74(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK73(X0,X1),sK74(X0,X1)) ) )
& ( ! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X7),hAPP(X0,X6))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7) )
| ! [X8,X9] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X8),hAPP(X0,X9))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8,X9) )
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK71,sK72,sK73,sK74])],[f3523,f3525,f3524]) ).
fof(f3524,plain,
! [X0,X1] :
( ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
=> ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK72(X0,X1)),hAPP(X0,sK71(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK71(X0,X1),sK72(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3525,plain,
! [X0,X1] :
( ? [X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X0,X5))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) )
=> ( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,sK73(X0,X1)),hAPP(X0,sK74(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK73(X0,X1),sK74(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f3523,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
& ? [X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X0,X5))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) ) ) )
& ( ! [X6,X7] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X7),hAPP(X0,X6))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X7) )
| ! [X8,X9] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X8),hAPP(X0,X9))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X8,X9) )
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f3522]) ).
fof(f3522,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
& ? [X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X0,X5))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) ) ) )
& ( ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
| ! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X0,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) )
| ~ sP0(X0,X1) ) ),
inference(flattening,[],[f3521]) ).
fof(f3521,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ? [X2,X3] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
& ? [X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X0,X5))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) ) ) )
& ( ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
| ! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X0,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) )
| ~ sP0(X0,X1) ) ),
inference(nnf_transformation,[],[f3342]) ).
fof(f3342,plain,
! [X0,X1] :
( sP0(X0,X1)
<=> ( ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
| ! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X0,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f9715,plain,
spl104_602,
inference(avatar_split_clause,[],[f4597,f9713]) ).
fof(f9713,plain,
( spl104_602
<=> ! [X0,X1] :
( sP0(X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK73(X0,X1),sK74(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_602])]) ).
fof(f4597,plain,
! [X0,X1] :
( sP0(X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK73(X0,X1),sK74(X0,X1)) ),
inference(cnf_transformation,[],[f3526]) ).
fof(f9711,plain,
spl104_601,
inference(avatar_split_clause,[],[f4566,f9709]) ).
fof(f9709,plain,
( spl104_601
<=> ! [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,[spl104_601])]) ).
fof(f4566,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,[],[f2491]) ).
fof(f2491,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,[],[f1624]) ).
fof(f1624,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,[],[f627]) ).
fof(f627,axiom,
! [X12,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oone__class_Oone(X4)),X12) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(f9707,plain,
spl104_600,
inference(avatar_split_clause,[],[f4565,f9705]) ).
fof(f9705,plain,
( spl104_600
<=> ! [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,[spl104_600])]) ).
fof(f4565,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,[],[f2490]) ).
fof(f2490,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,[],[f1623]) ).
fof(f1623,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,[],[f626]) ).
fof(f626,axiom,
! [X12,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),c_Groups_Oone__class_Oone(X4)) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(f9703,plain,
spl104_599,
inference(avatar_split_clause,[],[f4564,f9701]) ).
fof(f9701,plain,
( spl104_599
<=> ! [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,[spl104_599])]) ).
fof(f4564,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,[],[f2489]) ).
fof(f2489,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,[],[f1622]) ).
fof(f1622,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,[],[f849]) ).
fof(f849,axiom,
! [X3,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X4),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X3 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(f9699,plain,
spl104_598,
inference(avatar_split_clause,[],[f4560,f9697]) ).
fof(f9697,plain,
( spl104_598
<=> ! [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,[spl104_598])]) ).
fof(f4560,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(cnf_transformation,[],[f2485]) ).
fof(f2485,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(ennf_transformation,[],[f1618]) ).
fof(f1618,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,[],[f622]) ).
fof(f622,axiom,
! [X12,X4] :
( class_Groups_Omonoid__mult(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oone__class_Oone(X4)),X12) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__1__left) ).
fof(f9683,plain,
spl104_597,
inference(avatar_split_clause,[],[f4559,f9681]) ).
fof(f9681,plain,
( spl104_597
<=> ! [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,[spl104_597])]) ).
fof(f4559,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(cnf_transformation,[],[f2484]) ).
fof(f2484,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(ennf_transformation,[],[f1617]) ).
fof(f1617,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,[],[f624]) ).
fof(f624,axiom,
! [X12,X4] :
( class_Groups_Omonoid__mult(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),c_Groups_Oone__class_Oone(X4)) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__1__right) ).
fof(f9679,plain,
spl104_596,
inference(avatar_split_clause,[],[f4558,f9677]) ).
fof(f9677,plain,
( spl104_596
<=> ! [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,[spl104_596])]) ).
fof(f4558,plain,
! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(cnf_transformation,[],[f2483]) ).
fof(f2483,plain,
! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(ennf_transformation,[],[f1616]) ).
fof(f1616,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,[],[f892]) ).
fof(f892,axiom,
! [X12,X4] :
( class_Groups_Omonoid__mult(X4)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X4),X12),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_power__one__right) ).
fof(f9675,plain,
spl104_595,
inference(avatar_split_clause,[],[f4547,f9673]) ).
fof(f9673,plain,
( spl104_595
<=> ! [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,[spl104_595])]) ).
fof(f4547,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,[],[f2474]) ).
fof(f2474,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,[],[f1607]) ).
fof(f1607,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,[],[f623]) ).
fof(f623,axiom,
! [X12,X4] :
( class_Groups_Ocomm__monoid__mult(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),c_Groups_Oone__class_Oone(X4)),X12) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__1) ).
fof(f9671,plain,
spl104_594,
inference(avatar_split_clause,[],[f4546,f9669]) ).
fof(f9669,plain,
( spl104_594
<=> ! [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,[spl104_594])]) ).
fof(f4546,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,[],[f2473]) ).
fof(f2473,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,[],[f1606]) ).
fof(f1606,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,[],[f625]) ).
fof(f625,axiom,
! [X12,X4] :
( class_Groups_Ocomm__monoid__mult(X4)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),c_Groups_Oone__class_Oone(X4)) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult_Ocomm__neutral) ).
fof(f9667,plain,
spl104_593,
inference(avatar_split_clause,[],[f4513,f9665]) ).
fof(f9665,plain,
( spl104_593
<=> ! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_593])]) ).
fof(f4513,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f2446]) ).
fof(f2446,plain,
! [X0,X1] :
( c_Groups_Oabs__class_Oabs(X1,X0) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1581]) ).
fof(f1581,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> c_Groups_Oabs__class_Oabs(X1,X0) = c_Groups_Oabs__class_Oabs(X1,c_Groups_Oabs__class_Oabs(X1,X0)) ),
inference(rectify,[],[f373]) ).
fof(f373,axiom,
! [X12,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> c_Groups_Oabs__class_Oabs(X4,X12) = c_Groups_Oabs__class_Oabs(X4,c_Groups_Oabs__class_Oabs(X4,X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__idempotent) ).
fof(f9663,plain,
spl104_592,
inference(avatar_split_clause,[],[f4470,f9661]) ).
fof(f9661,plain,
( spl104_592
<=> ! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_592])]) ).
fof(f4470,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(cnf_transformation,[],[f2419]) ).
fof(f2419,plain,
! [X0,X1] :
( c_RealVector_Onorm__class_Onorm(X1,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0))
| ~ class_RealVector_Oreal__normed__vector(X1) ),
inference(ennf_transformation,[],[f1556]) ).
fof(f1556,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__vector(X1)
=> c_RealVector_Onorm__class_Onorm(X1,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,X0)) ),
inference(rectify,[],[f476]) ).
fof(f476,axiom,
! [X12,X4] :
( class_RealVector_Oreal__normed__vector(X4)
=> c_RealVector_Onorm__class_Onorm(X4,X12) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__norm__cancel) ).
fof(f9659,plain,
spl104_591,
inference(avatar_split_clause,[],[f4450,f9657]) ).
fof(f9657,plain,
( spl104_591
<=> ! [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,[spl104_591])]) ).
fof(f4450,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,[],[f1540]) ).
fof(f1540,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,[],[f427]) ).
fof(f427,axiom,
! [X22,X3] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X22,X3)
| X3 = X22
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X3,X22) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zless__linear) ).
fof(f9655,plain,
spl104_590,
inference(avatar_split_clause,[],[f4402,f9653]) ).
fof(f9653,plain,
( spl104_590
<=> ! [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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_590])]) ).
fof(f4402,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,[],[f1500]) ).
fof(f1500,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,[],[f5]) ).
fof(f5,axiom,
! [X5,X6] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Nat_OSuc(X5)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X5)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__Suc__right) ).
fof(f9651,plain,
spl104_589,
inference(avatar_split_clause,[],[f4401,f9649]) ).
fof(f9649,plain,
( spl104_589
<=> ! [X0,X1] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_589])]) ).
fof(f4401,plain,
! [X0,X1] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X0),
inference(cnf_transformation,[],[f1499]) ).
fof(f1499,plain,
! [X0,X1] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X1),X0),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X5,X6] : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X5)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(X6),X5),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__Suc) ).
fof(f9647,plain,
spl104_588,
inference(avatar_split_clause,[],[f4400,f9645]) ).
fof(f9645,plain,
( spl104_588
<=> ! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_588])]) ).
fof(f4400,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)),
inference(cnf_transformation,[],[f1498]) ).
fof(f1498,plain,
! [X0,X1] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)),
inference(rectify,[],[f227]) ).
fof(f227,axiom,
! [X5,X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X5) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X6),c_Nat_OSuc(X5)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__Suc__Suc) ).
fof(f9639,plain,
spl104_587,
inference(avatar_split_clause,[],[f4366,f9637]) ).
fof(f9637,plain,
( spl104_587
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_587])]) ).
fof(f4366,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0) ),
inference(cnf_transformation,[],[f3422]) ).
fof(f3422,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
inference(nnf_transformation,[],[f1474]) ).
fof(f1474,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0) ),
inference(rectify,[],[f548]) ).
fof(f548,axiom,
! [X52] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X52))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X52) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__0__number__of) ).
fof(f9635,plain,
spl104_586,
inference(avatar_split_clause,[],[f4365,f9633]) ).
fof(f9633,plain,
( spl104_586
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_586])]) ).
fof(f4365,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ),
inference(cnf_transformation,[],[f3422]) ).
fof(f9631,plain,
spl104_585,
inference(avatar_split_clause,[],[f4362,f9629]) ).
fof(f9629,plain,
( spl104_585
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_585])]) ).
fof(f4362,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f3420]) ).
fof(f3420,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) ) ),
inference(nnf_transformation,[],[f1472]) ).
fof(f1472,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f346]) ).
fof(f346,axiom,
! [X18] :
( hAPP(c_RealDef_Oreal(tc_Nat_Onat),X18) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__of__nat__zero__iff) ).
fof(f9627,plain,
spl104_584,
inference(avatar_split_clause,[],[f4361,f9625]) ).
fof(f9625,plain,
( spl104_584
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_584])]) ).
fof(f4361,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f3420]) ).
fof(f9623,plain,
spl104_583,
inference(avatar_split_clause,[],[f4358,f9621]) ).
fof(f9621,plain,
( spl104_583
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_583])]) ).
fof(f4358,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f3418]) ).
fof(f3418,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(nnf_transformation,[],[f1470]) ).
fof(f1470,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(rectify,[],[f406]) ).
fof(f406,axiom,
! [X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X23),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_natceiling__le__eq__one) ).
fof(f9619,plain,
spl104_582,
inference(avatar_split_clause,[],[f4357,f9617]) ).
fof(f9617,plain,
( spl104_582
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_582])]) ).
fof(f4357,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(cnf_transformation,[],[f3418]) ).
fof(f9615,plain,
spl104_581,
inference(avatar_split_clause,[],[f4356,f9613]) ).
fof(f9613,plain,
( spl104_581
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_581])]) ).
fof(f4356,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
inference(cnf_transformation,[],[f3417]) ).
fof(f3417,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0)) ) ),
inference(nnf_transformation,[],[f1469]) ).
fof(f1469,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
inference(rectify,[],[f458]) ).
fof(f458,axiom,
! [X23] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X23))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X23) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__natfloor__eq__one) ).
fof(f9611,plain,
spl104_580,
inference(avatar_split_clause,[],[f4355,f9609]) ).
fof(f9609,plain,
( spl104_580
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_580])]) ).
fof(f4355,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(X0)) ),
inference(cnf_transformation,[],[f3417]) ).
fof(f9607,plain,
spl104_579,
inference(avatar_split_clause,[],[f4332,f9605]) ).
fof(f9605,plain,
( spl104_579
<=> ! [X2,X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X2),hAPP(X0,c_Nat_OSuc(X2)))
| ~ c_SEQ_Osubseq(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_579])]) ).
fof(f4332,plain,
! [X2,X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(X0,X2),hAPP(X0,c_Nat_OSuc(X2)))
| ~ c_SEQ_Osubseq(X0) ),
inference(cnf_transformation,[],[f3400]) ).
fof(f9603,plain,
spl104_578,
inference(avatar_split_clause,[],[f4299,f9601]) ).
fof(f9601,plain,
( spl104_578
<=> ! [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,[spl104_578])]) ).
fof(f4299,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,[],[f2368]) ).
fof(f2368,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,[],[f1429]) ).
fof(f1429,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,[],[f926]) ).
fof(f926,axiom,
! [X4] :
( class_Power_Opower(X4)
=> c_Power_Opower__class_Opower(X4) = c_Power_Opower_Opower(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Otimes__class_Otimes(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_power__power__power) ).
fof(f9599,plain,
( spl104_577
| ~ spl104_222
| ~ spl104_501 ),
inference(avatar_split_clause,[],[f8764,f8405,f7087,f9597]) ).
fof(f8405,plain,
( spl104_501
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_Opred(X0))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_501])]) ).
fof(f8764,plain,
( ! [X2] : c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X2),X2)
| ~ spl104_222
| ~ spl104_501 ),
inference(resolution,[],[f8406,f7088]) ).
fof(f8406,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_Opred(X0))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
| ~ spl104_501 ),
inference(avatar_component_clause,[],[f8405]) ).
fof(f9595,plain,
spl104_576,
inference(avatar_split_clause,[],[f4207,f9593]) ).
fof(f9593,plain,
( spl104_576
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_576])]) ).
fof(f4207,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))),
inference(cnf_transformation,[],[f1345]) ).
fof(f1345,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0))),
inference(rectify,[],[f405]) ).
fof(f405,axiom,
! [X3] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3))),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__add__one__gt__zero) ).
fof(f9591,plain,
spl104_575,
inference(avatar_split_clause,[],[f4206,f9589]) ).
fof(f9589,plain,
( spl104_575
<=> ! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_575])]) ).
fof(f4206,plain,
! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f1344]) ).
fof(f1344,plain,
! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(rectify,[],[f578]) ).
fof(f578,axiom,
! [X6] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__int__eq) ).
fof(f9587,plain,
spl104_574,
inference(avatar_split_clause,[],[f4205,f9585]) ).
fof(f9585,plain,
( spl104_574
<=> ! [X0] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_574])]) ).
fof(f4205,plain,
! [X0] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)),
inference(cnf_transformation,[],[f1343]) ).
fof(f1343,plain,
! [X0] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)),
inference(rectify,[],[f380]) ).
fof(f380,axiom,
! [X3] : hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X3)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__real__of__nat__cancel) ).
fof(f9563,plain,
( spl104_573
| ~ spl104_222
| ~ spl104_493 ),
inference(avatar_split_clause,[],[f8739,f8372,f7087,f9561]) ).
fof(f9561,plain,
( spl104_573
<=> ! [X0] :
( ~ c_Nat__Numeral_Oneg(X0)
| sP4(c_Int_OPls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_573])]) ).
fof(f8372,plain,
( spl104_493
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Nat__Numeral_Oneg(X1)
| sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_493])]) ).
fof(f8739,plain,
( ! [X0] :
( ~ c_Nat__Numeral_Oneg(X0)
| sP4(c_Int_OPls,X0) )
| ~ spl104_222
| ~ spl104_493 ),
inference(resolution,[],[f8373,f7088]) ).
fof(f8373,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Nat__Numeral_Oneg(X1)
| sP4(X0,X1) )
| ~ spl104_493 ),
inference(avatar_component_clause,[],[f8372]) ).
fof(f9550,plain,
( spl104_572
| ~ spl104_419
| ~ spl104_563 ),
inference(avatar_split_clause,[],[f9017,f9014,f7990,f9548]) ).
fof(f9548,plain,
( spl104_572
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Int_Osucc(c_Int_OPls))
| c_Int_OPls = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_572])]) ).
fof(f9014,plain,
( spl104_563
<=> ! [X0] :
( c_Int_OPls = X0
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_563])]) ).
fof(f9017,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Int_Osucc(c_Int_OPls))
| c_Int_OPls = X0 )
| ~ spl104_419
| ~ spl104_563 ),
inference(forward_demodulation,[],[f9015,f7992]) ).
fof(f9015,plain,
( ! [X0] :
( c_Int_OPls = X0
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
| ~ spl104_563 ),
inference(avatar_component_clause,[],[f9014]) ).
fof(f9546,plain,
( spl104_571
| ~ spl104_419
| ~ spl104_562 ),
inference(avatar_split_clause,[],[f9012,f9009,f7990,f9544]) ).
fof(f9544,plain,
( spl104_571
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Int_Osucc(c_Int_OPls))
| c_Int_OPls != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_571])]) ).
fof(f9009,plain,
( spl104_562
<=> ! [X0] :
( c_Int_OPls != X0
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_562])]) ).
fof(f9012,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Int_Osucc(c_Int_OPls))
| c_Int_OPls != X0 )
| ~ spl104_419
| ~ spl104_562 ),
inference(forward_demodulation,[],[f9010,f7992]) ).
fof(f9010,plain,
( ! [X0] :
( c_Int_OPls != X0
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
| ~ spl104_562 ),
inference(avatar_component_clause,[],[f9009]) ).
fof(f9530,plain,
( spl104_570
| ~ spl104_419
| ~ spl104_557 ),
inference(avatar_split_clause,[],[f8990,f8987,f7990,f9528]) ).
fof(f9528,plain,
( spl104_570
<=> ! [X0] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X0) = c_Int_Osucc(c_Int_OPls)
| c_Int_OPls = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_570])]) ).
fof(f8987,plain,
( spl104_557
<=> ! [X0] :
( c_Int_OPls = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_557])]) ).
fof(f8990,plain,
( ! [X0] :
( c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X0) = c_Int_Osucc(c_Int_OPls)
| c_Int_OPls = X0 )
| ~ spl104_419
| ~ spl104_557 ),
inference(forward_demodulation,[],[f8988,f7992]) ).
fof(f8988,plain,
( ! [X0] :
( c_Int_OPls = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X0) )
| ~ spl104_557 ),
inference(avatar_component_clause,[],[f8987]) ).
fof(f9256,plain,
( spl104_569
| ~ spl104_538 ),
inference(avatar_split_clause,[],[f9224,f8903,f9254]) ).
fof(f9254,plain,
( spl104_569
<=> ! [X0] : sP4(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_569])]) ).
fof(f8903,plain,
( spl104_538
<=> ! [X0,X1] :
( sP4(X0,X1)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_538])]) ).
fof(f9224,plain,
( ! [X0] : sP4(X0,X0)
| ~ spl104_538 ),
inference(equality_resolution,[],[f8904]) ).
fof(f8904,plain,
( ! [X0,X1] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
| sP4(X0,X1) )
| ~ spl104_538 ),
inference(avatar_component_clause,[],[f8903]) ).
fof(f9037,plain,
spl104_568,
inference(avatar_split_clause,[],[f5864,f9035]) ).
fof(f9035,plain,
( spl104_568
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_568])]) ).
fof(f5864,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| sP6(X0,X1) ),
inference(forward_demodulation,[],[f4849,f4119]) ).
fof(f4849,plain,
! [X0,X1] :
( sP6(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3630]) ).
fof(f3630,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP6(X0,X1) )
& ( sP6(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f3353]) ).
fof(f3353,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
<=> sP6(X0,X1) ),
inference(definition_folding,[],[f1788,f3352]) ).
fof(f1788,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,[],[f326]) ).
fof(f326,axiom,
! [X18,X17] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X18)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X18
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X17 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X17 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_one__is__add) ).
fof(f9033,plain,
spl104_567,
inference(avatar_split_clause,[],[f5863,f9031]) ).
fof(f9031,plain,
( spl104_567
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_567])]) ).
fof(f5863,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f4850,f4119]) ).
fof(f4850,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f3630]) ).
fof(f9029,plain,
spl104_566,
inference(avatar_split_clause,[],[f5856,f9027]) ).
fof(f9027,plain,
( spl104_566
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_566])]) ).
fof(f5856,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| sP5(X0,X1) ),
inference(forward_demodulation,[],[f4841,f4119]) ).
fof(f4841,plain,
! [X0,X1] :
( sP5(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3627]) ).
fof(f3627,plain,
! [X0,X1] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP5(X0,X1) )
& ( sP5(X0,X1)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f3351]) ).
fof(f3351,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
<=> sP5(X0,X1) ),
inference(definition_folding,[],[f1787,f3350]) ).
fof(f1787,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,[],[f327]) ).
fof(f327,axiom,
! [X18,X17] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X17,X18)
<=> ( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X18
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X17 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18
& c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X17 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__is__1) ).
fof(f9025,plain,
spl104_565,
inference(avatar_split_clause,[],[f5855,f9023]) ).
fof(f9023,plain,
( spl104_565
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_565])]) ).
fof(f5855,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f4842,f4119]) ).
fof(f4842,plain,
! [X0,X1] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f3627]) ).
fof(f9021,plain,
spl104_564,
inference(avatar_split_clause,[],[f5830,f9019]) ).
fof(f5830,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| sP4(X0,X1)
| ~ sP3(X1,X0) ),
inference(forward_demodulation,[],[f5829,f4155]) ).
fof(f5829,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0),c_Int_OPls)
| sP4(X0,X1)
| ~ sP3(X1,X0) ),
inference(forward_demodulation,[],[f4826,f4101]) ).
fof(f4826,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ sP3(X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3620]) ).
fof(f3620,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ( ~ sP3(X1,X0)
& ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ) )
& ( ( ( sP3(X1,X0)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ) )
| ~ sP4(X0,X1) ) ),
inference(flattening,[],[f3619]) ).
fof(f3619,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ( ~ sP3(X1,X0)
& ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
& c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ) )
& ( ( ( sP3(X1,X0)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ) )
| ~ sP4(X0,X1) ) ),
inference(nnf_transformation,[],[f3348]) ).
fof(f3348,plain,
! [X0,X1] :
( sP4(X0,X1)
<=> ( ( sP3(X1,X0)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f9016,plain,
spl104_563,
inference(avatar_split_clause,[],[f5689,f9014]) ).
fof(f5689,plain,
! [X0] :
( c_Int_OPls = X0
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(forward_demodulation,[],[f4363,f4101]) ).
fof(f4363,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3421]) ).
fof(f3421,plain,
! [X0] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(nnf_transformation,[],[f1473]) ).
fof(f1473,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ),
inference(rectify,[],[f425]) ).
fof(f425,axiom,
! [X55] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X55),c_Groups_Oone__class_Oone(tc_Int_Oint))
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X55 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zabs__less__one__iff) ).
fof(f9011,plain,
spl104_562,
inference(avatar_split_clause,[],[f5688,f9009]) ).
fof(f5688,plain,
! [X0] :
( c_Int_OPls != X0
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(forward_demodulation,[],[f4364,f4101]) ).
fof(f4364,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ),
inference(cnf_transformation,[],[f3421]) ).
fof(f9007,plain,
spl104_561,
inference(avatar_split_clause,[],[f5687,f9005]) ).
fof(f9005,plain,
( spl104_561
<=> ! [X0] :
( c_Int_OPls != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_561])]) ).
fof(f5687,plain,
! [X0] :
( c_Int_OPls != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(forward_demodulation,[],[f4359,f4101]) ).
fof(f4359,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f3419]) ).
fof(f3419,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) ) ),
inference(nnf_transformation,[],[f1471]) ).
fof(f1471,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f641]) ).
fof(f641,axiom,
! [X18] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X18)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_int__eq__0__conv) ).
fof(f9003,plain,
spl104_560,
inference(avatar_split_clause,[],[f5686,f9001]) ).
fof(f9001,plain,
( spl104_560
<=> ! [X0] :
( c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_560])]) ).
fof(f5686,plain,
! [X0] :
( c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(forward_demodulation,[],[f4360,f4101]) ).
fof(f4360,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f3419]) ).
fof(f8999,plain,
spl104_559,
inference(avatar_split_clause,[],[f5668,f8997]) ).
fof(f8997,plain,
( spl104_559
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK28(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_559])]) ).
fof(f5668,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK28(X0)) ),
inference(forward_demodulation,[],[f4312,f4101]) ).
fof(f4312,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK28(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f3391]) ).
fof(f8995,plain,
( spl104_558
| ~ spl104_31
| ~ spl104_218
| ~ spl104_432 ),
inference(avatar_split_clause,[],[f8435,f8110,f7070,f6133,f8992]) ).
fof(f8992,plain,
( spl104_558
<=> c_Int_OPls = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_558])]) ).
fof(f8110,plain,
( spl104_432
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_432])]) ).
fof(f8435,plain,
( c_Int_OPls = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Int_OPls)
| ~ spl104_31
| ~ spl104_218
| ~ spl104_432 ),
inference(forward_demodulation,[],[f8433,f7072]) ).
fof(f8433,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl104_31
| ~ spl104_432 ),
inference(resolution,[],[f8111,f6135]) ).
fof(f6135,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint)
| ~ spl104_31 ),
inference(avatar_component_clause,[],[f6133]) ).
fof(f8111,plain,
( ! [X0] :
( ~ class_Groups_Oordered__ab__group__add__abs(X0)
| c_Groups_Ozero__class_Ozero(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Ozero__class_Ozero(X0)) )
| ~ spl104_432 ),
inference(avatar_component_clause,[],[f8110]) ).
fof(f8989,plain,
spl104_557,
inference(avatar_split_clause,[],[f5665,f8987]) ).
fof(f5665,plain,
! [X0] :
( c_Int_OPls = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X0,X0) ),
inference(forward_demodulation,[],[f4307,f4101]) ).
fof(f4307,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,[],[f2376]) ).
fof(f2376,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,[],[f1437]) ).
fof(f1437,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,[],[f955]) ).
fof(f955,axiom,
! [X12] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X12
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X12,X12) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zdiv__self) ).
fof(f8985,plain,
spl104_556,
inference(avatar_split_clause,[],[f5660,f8983]) ).
fof(f8983,plain,
( spl104_556
<=> ! [X0] :
( ~ c_Nat__Numeral_Oneg(X0)
| c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_556])]) ).
fof(f5660,plain,
! [X0] :
( ~ c_Nat__Numeral_Oneg(X0)
| c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ),
inference(forward_demodulation,[],[f5659,f4155]) ).
fof(f5659,plain,
! [X0] :
( c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ),
inference(forward_demodulation,[],[f4218,f4101]) ).
fof(f4218,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ),
inference(cnf_transformation,[],[f2293]) ).
fof(f2293,plain,
! [X0] :
( ( c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ) ),
inference(ennf_transformation,[],[f1354]) ).
fof(f1354,plain,
! [X0] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0))
=> c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
inference(rectify,[],[f746]) ).
fof(f746,axiom,
! [X48] :
( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X48))
=> c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X48) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48)) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X48))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_int__nat__number__of) ).
fof(f8981,plain,
spl104_555,
inference(avatar_split_clause,[],[f5658,f8979]) ).
fof(f8979,plain,
( spl104_555
<=> ! [X0] :
( c_Nat__Numeral_Oneg(X0)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_555])]) ).
fof(f5658,plain,
! [X0] :
( c_Nat__Numeral_Oneg(X0)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) = X0 ),
inference(forward_demodulation,[],[f5657,f4155]) ).
fof(f5657,plain,
! [X0] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) = X0
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ),
inference(forward_demodulation,[],[f4219,f4155]) ).
fof(f4219,plain,
! [X0] :
( c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ),
inference(cnf_transformation,[],[f2293]) ).
fof(f8977,plain,
spl104_554,
inference(avatar_split_clause,[],[f5652,f8975]) ).
fof(f8975,plain,
( spl104_554
<=> ! [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,[spl104_554])]) ).
fof(f5652,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,[],[f4208,f4119]) ).
fof(f4208,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,[],[f1346]) ).
fof(f1346,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,[],[f873]) ).
fof(f873,axiom,
! [X5] : 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))),X5),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_power__Suc__0) ).
fof(f8967,plain,
( spl104_553
| ~ spl104_370
| ~ spl104_419
| ~ spl104_439
| ~ spl104_552 ),
inference(avatar_split_clause,[],[f8963,f8959,f8138,f7990,f7740,f8965]) ).
fof(f8959,plain,
( spl104_552
<=> ! [X0] : c_Int_OPls != 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,[spl104_552])]) ).
fof(f8963,plain,
( ! [X0] : c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Osucc(X0),X0)
| ~ spl104_370
| ~ spl104_419
| ~ spl104_439
| ~ spl104_552 ),
inference(forward_demodulation,[],[f8962,f8470]) ).
fof(f8962,plain,
( ! [X0] : c_Int_OPls != c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Osucc(c_Int_OPls),X0),X0)
| ~ spl104_419
| ~ spl104_552 ),
inference(forward_demodulation,[],[f8960,f7992]) ).
fof(f8960,plain,
( ! [X0] : c_Int_OPls != 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)
| ~ spl104_552 ),
inference(avatar_component_clause,[],[f8959]) ).
fof(f8961,plain,
spl104_552,
inference(avatar_split_clause,[],[f5651,f8959]) ).
fof(f5651,plain,
! [X0] : c_Int_OPls != 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(forward_demodulation,[],[f4204,f4101]) ).
fof(f4204,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,[],[f1342]) ).
fof(f1342,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,[],[f415]) ).
fof(f415,axiom,
! [X25] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X25),X25) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_odd__nonzero) ).
fof(f8957,plain,
spl104_551,
inference(avatar_split_clause,[],[f5283,f8955]) ).
fof(f8955,plain,
( spl104_551
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_551])]) ).
fof(f5283,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f3759]) ).
fof(f3759,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1) )
| ~ sP11(X0,X1,X2) ),
inference(rectify,[],[f3758]) ).
fof(f3758,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
| ~ sP11(X2,X1,X0) ),
inference(nnf_transformation,[],[f3360]) ).
fof(f3360,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,X2,X1) )
| ~ sP11(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f8953,plain,
spl104_550,
inference(avatar_split_clause,[],[f5166,f8951]) ).
fof(f8951,plain,
( spl104_550
<=> ! [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,[spl104_550])]) ).
fof(f5166,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,[],[f3724]) ).
fof(f3724,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f3723]) ).
fof(f3723,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
| X0 = X1
| ~ c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
& ( ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) )
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0) ) )
| ~ class_Orderings_Oorder(X2) ),
inference(nnf_transformation,[],[f2919]) ).
fof(f2919,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) )
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f1997]) ).
fof(f1997,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
<=> ( X0 != X1
& c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ) ),
inference(rectify,[],[f202]) ).
fof(f202,axiom,
! [X26,X23,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X23,X26)
<=> ( X23 != X26
& c_Orderings_Oord__class_Oless__eq(X4,X23,X26) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_order__less__le) ).
fof(f8949,plain,
spl104_549,
inference(avatar_split_clause,[],[f5155,f8947]) ).
fof(f8947,plain,
( spl104_549
<=> ! [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,[spl104_549])]) ).
fof(f5155,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,[],[f2905]) ).
fof(f2905,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,[],[f2904]) ).
fof(f2904,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,[],[f1989]) ).
fof(f1989,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,[],[f159]) ).
fof(f159,axiom,
! [X12,X11,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X11,X12)
=> ~ c_Orderings_Oord__class_Oless(X4,X12,X11) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_xt1_I9_J) ).
fof(f8945,plain,
( spl104_548
| ~ spl104_415 ),
inference(avatar_split_clause,[],[f8055,f7921,f8943]) ).
fof(f7921,plain,
( spl104_415
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Osucc(X0))
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_415])]) ).
fof(f8055,plain,
( ! [X0] : c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_Osucc(X0))
| ~ spl104_415 ),
inference(equality_resolution,[],[f7922]) ).
fof(f7922,plain,
( ! [X0,X1] :
( X0 != X1
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Osucc(X0)) )
| ~ spl104_415 ),
inference(avatar_component_clause,[],[f7921]) ).
fof(f8941,plain,
spl104_547,
inference(avatar_split_clause,[],[f5148,f8939]) ).
fof(f8939,plain,
( spl104_547
<=> ! [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,[spl104_547])]) ).
fof(f5148,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,[],[f3719]) ).
fof(f8937,plain,
spl104_546,
inference(avatar_split_clause,[],[f5146,f8935]) ).
fof(f8935,plain,
( spl104_546
<=> ! [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,[spl104_546])]) ).
fof(f5146,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,[],[f2892]) ).
fof(f2892,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,[],[f2891]) ).
fof(f2891,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,[],[f1982]) ).
fof(f1982,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,[],[f211]) ).
fof(f211,axiom,
! [X22,X3,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X22)
=> c_Orderings_Oord__class_Oless__eq(X4,X3,X22) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_order__less__imp__le) ).
fof(f8933,plain,
spl104_545,
inference(avatar_split_clause,[],[f5142,f8931]) ).
fof(f8931,plain,
( spl104_545
<=> ! [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,[spl104_545])]) ).
fof(f5142,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,[],[f2884]) ).
fof(f2884,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,[],[f2883]) ).
fof(f2883,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,[],[f1978]) ).
fof(f1978,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,[],[f153]) ).
fof(f153,axiom,
! [X22,X3,X4] :
( class_Orderings_Opreorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X22)
=> ~ c_Orderings_Oord__class_Oless(X4,X22,X3) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_order__less__not__sym) ).
fof(f8929,plain,
spl104_544,
inference(avatar_split_clause,[],[f5124,f8927]) ).
fof(f8927,plain,
( spl104_544
<=> ! [X2,X0,X1] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0
| ~ class_Rings_Osemiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_544])]) ).
fof(f5124,plain,
! [X2,X0,X1] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0
| ~ class_Rings_Osemiring__1(X2) ),
inference(cnf_transformation,[],[f2864]) ).
fof(f2864,plain,
! [X0,X1,X2] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0
| ~ class_Rings_Osemiring__1(X2) ),
inference(ennf_transformation,[],[f1961]) ).
fof(f1961,plain,
! [X0,X1,X2] :
( class_Rings_Osemiring__1(X2)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0 ),
inference(rectify,[],[f141]) ).
fof(f141,axiom,
! [X35,X36,X4] :
( class_Rings_Osemiring__1(X4)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X4,X36,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X35) = X35 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_of__nat__aux_Osimps_I1_J) ).
fof(f8925,plain,
spl104_543,
inference(avatar_split_clause,[],[f5090,f8923]) ).
fof(f8923,plain,
( spl104_543
<=> ! [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,[spl104_543])]) ).
fof(f5090,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,[],[f3711]) ).
fof(f3711,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,[],[f3710]) ).
fof(f3710,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,[],[f2822]) ).
fof(f2822,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,[],[f1934]) ).
fof(f1934,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,[],[f127]) ).
fof(f127,axiom,
! [X26,X23,X4] :
( class_Orderings_Olinorder(X4)
=> ( ~ c_Orderings_Oord__class_Oless(X4,X23,X26)
<=> ( X23 = X26
| c_Orderings_Oord__class_Oless(X4,X26,X23) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__less__iff__gr__or__eq) ).
fof(f8921,plain,
spl104_542,
inference(avatar_split_clause,[],[f5081,f8919]) ).
fof(f8919,plain,
( spl104_542
<=> ! [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,[spl104_542])]) ).
fof(f5081,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,[],[f2817]) ).
fof(f2817,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,[],[f2816]) ).
fof(f2816,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,[],[f1930]) ).
fof(f1930,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,[],[f210]) ).
fof(f210,axiom,
! [X3,X22,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X22,X3)
=> ~ c_Orderings_Oord__class_Oless(X4,X3,X22) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_leD) ).
fof(f8917,plain,
spl104_541,
inference(avatar_split_clause,[],[f5071,f8915]) ).
fof(f5071,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,[],[f2801]) ).
fof(f2801,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,[],[f2800]) ).
fof(f2800,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,[],[f1922]) ).
fof(f1922,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,[],[f52]) ).
fof(f52,axiom,
! [X22,X3,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,X22,X3)
| c_Orderings_Oord__class_Oless__eq(X4,X3,X22) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_linorder__linear) ).
fof(f8913,plain,
spl104_540,
inference(avatar_split_clause,[],[f5070,f8911]) ).
fof(f8911,plain,
( spl104_540
<=> ! [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,[spl104_540])]) ).
fof(f5070,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,[],[f2799]) ).
fof(f2799,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,[],[f2798]) ).
fof(f2798,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,[],[f1921]) ).
fof(f1921,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X0,X1)
| c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
inference(rectify,[],[f201]) ).
fof(f201,axiom,
! [X22,X3,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X22,X3)
| c_Orderings_Oord__class_Oless__eq(X4,X3,X22) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_linorder__le__less__linear) ).
fof(f8909,plain,
spl104_539,
inference(avatar_split_clause,[],[f4834,f8907]) ).
fof(f8907,plain,
( spl104_539
<=> ! [X0,X1] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_539])]) ).
fof(f4834,plain,
! [X0,X1] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f3624]) ).
fof(f3624,plain,
! [X0,X1] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
| ~ sP4(X0,X1) )
& ( sP4(X0,X1)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) ) ),
inference(nnf_transformation,[],[f3349]) ).
fof(f3349,plain,
! [X0,X1] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
<=> sP4(X0,X1) ),
inference(definition_folding,[],[f2683,f3348,f3347]) ).
fof(f3347,plain,
! [X1,X0] :
( sP3(X1,X0)
<=> ( ( X0 = X1
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f2683,plain,
! [X0,X1] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
<=> ( ( ( ( X0 = X1
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ) )
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ) ) ),
inference(ennf_transformation,[],[f1786]) ).
fof(f1786,plain,
! [X0,X1] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1)
<=> ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
=> ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0))
=> X0 = X1 )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1) ) ) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
inference(rectify,[],[f501]) ).
fof(f501,axiom,
! [X66,X52] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X52) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X66)
<=> ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X52))
=> ( ( ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X66))
=> X52 = X66 )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X66))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X52) ) ) )
& ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X52))
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X66),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_eq__nat__number__of) ).
fof(f8905,plain,
spl104_538,
inference(avatar_split_clause,[],[f4833,f8903]) ).
fof(f4833,plain,
! [X0,X1] :
( sP4(X0,X1)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X1) ),
inference(cnf_transformation,[],[f3624]) ).
fof(f8901,plain,
( spl104_537
| ~ spl104_412 ),
inference(avatar_split_clause,[],[f8054,f7909,f8899]) ).
fof(f8899,plain,
( spl104_537
<=> ! [X0] :
( ~ c_Nat__Numeral_Oneg(X0)
| sP3(c_Int_OPls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_537])]) ).
fof(f7909,plain,
( spl104_412
<=> ! [X0,X1] :
( c_Int_OPls != X0
| ~ c_Nat__Numeral_Oneg(X1)
| sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_412])]) ).
fof(f8054,plain,
( ! [X0] :
( ~ c_Nat__Numeral_Oneg(X0)
| sP3(c_Int_OPls,X0) )
| ~ spl104_412 ),
inference(equality_resolution,[],[f7910]) ).
fof(f7910,plain,
( ! [X0,X1] :
( c_Int_OPls != X0
| ~ c_Nat__Numeral_Oneg(X1)
| sP3(X0,X1) )
| ~ spl104_412 ),
inference(avatar_component_clause,[],[f7909]) ).
fof(f8897,plain,
spl104_536,
inference(avatar_split_clause,[],[f4806,f8895]) ).
fof(f4806,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f3611]) ).
fof(f3611,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ) ),
inference(nnf_transformation,[],[f1782]) ).
fof(f1782,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f23]) ).
fof(f23,axiom,
! [X17,X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X18),c_Nat_OSuc(X17))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,X17) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__le__mono) ).
fof(f8893,plain,
spl104_535,
inference(avatar_split_clause,[],[f4805,f8891]) ).
fof(f8891,plain,
( spl104_535
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_535])]) ).
fof(f4805,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f3611]) ).
fof(f8889,plain,
spl104_534,
inference(avatar_split_clause,[],[f4784,f8887]) ).
fof(f8887,plain,
( spl104_534
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_534])]) ).
fof(f4784,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X2) != X0 ),
inference(cnf_transformation,[],[f3593]) ).
fof(f8885,plain,
spl104_533,
inference(avatar_split_clause,[],[f4714,f8883]) ).
fof(f8883,plain,
( spl104_533
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_533])]) ).
fof(f4714,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ),
inference(cnf_transformation,[],[f2649]) ).
fof(f2649,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ),
inference(ennf_transformation,[],[f1735]) ).
fof(f1735,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f251]) ).
fof(f251,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X6),c_Nat_OSuc(X5))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__less__SucD) ).
fof(f8881,plain,
spl104_532,
inference(avatar_split_clause,[],[f4709,f8879]) ).
fof(f8879,plain,
( spl104_532
<=> ! [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,[spl104_532])]) ).
fof(f4709,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,[],[f2641]) ).
fof(f2641,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,[],[f1730]) ).
fof(f1730,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,[],[f288]) ).
fof(f288,axiom,
! [X5,X6] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X5) = X6
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X5 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__eq__self__zero) ).
fof(f8877,plain,
spl104_531,
inference(avatar_split_clause,[],[f4628,f8875]) ).
fof(f8875,plain,
( spl104_531
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_531])]) ).
fof(f4628,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f2550]) ).
fof(f2550,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(ennf_transformation,[],[f1668]) ).
fof(f1668,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X1),c_RComplete_Onatfloor(X0)) ),
inference(rectify,[],[f450]) ).
fof(f450,axiom,
! [X22,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X22)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(X3),c_RComplete_Onatfloor(X22)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_natfloor__mono) ).
fof(f8873,plain,
spl104_530,
inference(avatar_split_clause,[],[f4627,f8871]) ).
fof(f8871,plain,
( spl104_530
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_RComplete_Onatceiling(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_530])]) ).
fof(f4627,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_RComplete_Onatceiling(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f2549]) ).
fof(f2549,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_RComplete_Onatceiling(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) ),
inference(ennf_transformation,[],[f1667]) ).
fof(f1667,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X1),c_RComplete_Onatceiling(X0)) ),
inference(rectify,[],[f383]) ).
fof(f383,axiom,
! [X22,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,X22)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(X3),c_RComplete_Onatceiling(X22)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_natceiling__mono) ).
fof(f8869,plain,
spl104_529,
inference(avatar_split_clause,[],[f4624,f8867]) ).
fof(f8867,plain,
( spl104_529
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_529])]) ).
fof(f4624,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2545]) ).
fof(f2545,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1664]) ).
fof(f1664,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),c_Nat_OSuc(X0)) ),
inference(rectify,[],[f108]) ).
fof(f108,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X6),c_Nat_OSuc(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__mono) ).
fof(f8865,plain,
spl104_528,
inference(avatar_split_clause,[],[f4539,f8863]) ).
fof(f8863,plain,
( spl104_528
<=> ! [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,[spl104_528])]) ).
fof(f4539,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,[],[f2468]) ).
fof(f2468,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,[],[f1601]) ).
fof(f1601,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,[],[f332]) ).
fof(f332,axiom,
! [X12,X4] :
( class_Rings_Olinordered__semidom(X4)
=> c_Orderings_Oord__class_Oless(X4,X12,c_Groups_Oplus__class_Oplus(X4,X12,c_Groups_Oone__class_Oone(X4))) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__add__one) ).
fof(f8861,plain,
spl104_527,
inference(avatar_split_clause,[],[f4537,f8859]) ).
fof(f8859,plain,
( spl104_527
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0))
| ~ class_Rings_Olinordered__semidom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_527])]) ).
fof(f4537,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(cnf_transformation,[],[f2466]) ).
fof(f2466,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(ennf_transformation,[],[f1599]) ).
fof(f1599,plain,
! [X0,X1] :
( class_Rings_Olinordered__semidom(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)) ),
inference(rectify,[],[f630]) ).
fof(f630,axiom,
! [X6,X4] :
( class_Rings_Olinordered__semidom(X4)
=> c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X6)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__le__imp__of__nat) ).
fof(f8856,plain,
spl104_526,
inference(avatar_split_clause,[],[f4536,f8854]) ).
fof(f8854,plain,
( spl104_526
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semidom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_526])]) ).
fof(f4536,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(cnf_transformation,[],[f2465]) ).
fof(f2465,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(ennf_transformation,[],[f1598]) ).
fof(f1598,plain,
! [X0,X1] :
( class_Rings_Olinordered__semidom(X1)
=> ~ c_Orderings_Oord__class_Oless(X1,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(rectify,[],[f631]) ).
fof(f631,axiom,
! [X6,X4] :
( class_Rings_Olinordered__semidom(X4)
=> ~ c_Orderings_Oord__class_Oless(X4,hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X6),c_Groups_Ozero__class_Ozero(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_of__nat__less__0__iff) ).
fof(f8852,plain,
spl104_525,
inference(avatar_split_clause,[],[f4530,f8850]) ).
fof(f8850,plain,
( spl104_525
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),X0) = X0
| ~ class_Int_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_525])]) ).
fof(f4530,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),X0) = X0
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f2461]) ).
fof(f2461,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),X0) = X0
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f1594]) ).
fof(f1594,plain,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls),X0) = X0 ),
inference(rectify,[],[f533]) ).
fof(f533,axiom,
! [X12,X4] :
( class_Int_Onumber__ring(X4)
=> c_Groups_Oplus__class_Oplus(X4,c_Int_Onumber__class_Onumber__of(X4,c_Int_OPls),X12) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__numeral__0) ).
fof(f8848,plain,
spl104_524,
inference(avatar_split_clause,[],[f4529,f8846]) ).
fof(f8846,plain,
( spl104_524
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)) = X0
| ~ class_Int_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_524])]) ).
fof(f4529,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)) = X0
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f2460]) ).
fof(f2460,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)) = X0
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f1593]) ).
fof(f1593,plain,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,c_Int_Onumber__class_Onumber__of(X1,c_Int_OPls)) = X0 ),
inference(rectify,[],[f534]) ).
fof(f534,axiom,
! [X12,X4] :
( class_Int_Onumber__ring(X4)
=> c_Groups_Oplus__class_Oplus(X4,X12,c_Int_Onumber__class_Onumber__of(X4,c_Int_OPls)) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__numeral__0__right) ).
fof(f8844,plain,
spl104_523,
inference(avatar_split_clause,[],[f4508,f8842]) ).
fof(f8842,plain,
( spl104_523
<=> ! [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,[spl104_523])]) ).
fof(f4508,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,[],[f2440]) ).
fof(f2440,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,[],[f1576]) ).
fof(f1576,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,[],[f958]) ).
fof(f958,axiom,
! [X12,X4] :
( class_Divides_Osemiring__div(X4)
=> c_Groups_Ozero__class_Ozero(X4) = c_Divides_Odiv__class_Odiv(X4,c_Groups_Ozero__class_Ozero(X4),X12) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_div__0) ).
fof(f8840,plain,
spl104_522,
inference(avatar_split_clause,[],[f4507,f8838]) ).
fof(f8838,plain,
( spl104_522
<=> ! [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,[spl104_522])]) ).
fof(f4507,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,[],[f2439]) ).
fof(f2439,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,[],[f1575]) ).
fof(f1575,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,[],[f959]) ).
fof(f959,axiom,
! [X12,X4] :
( class_Divides_Osemiring__div(X4)
=> c_Groups_Ozero__class_Ozero(X4) = c_Divides_Odiv__class_Odiv(X4,X12,c_Groups_Ozero__class_Ozero(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_div__by__0) ).
fof(f8836,plain,
spl104_521,
inference(avatar_split_clause,[],[f4435,f8834]) ).
fof(f8834,plain,
( spl104_521
<=> ! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_521])]) ).
fof(f4435,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f2400]) ).
fof(f2400,plain,
! [X0,X1] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(ennf_transformation,[],[f1533]) ).
fof(f1533,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0) = X0 ) ),
inference(rectify,[],[f189]) ).
fof(f189,axiom,
! [X5,X6] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X6
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X5) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X6
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X5) = X5 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__eq__if) ).
fof(f8832,plain,
spl104_520,
inference(avatar_split_clause,[],[f4399,f8830]) ).
fof(f8830,plain,
( spl104_520
<=> ! [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,[spl104_520])]) ).
fof(f4399,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,[],[f1497]) ).
fof(f1497,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,[],[f115]) ).
fof(f115,axiom,
! [X6,X5] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X6)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__add__0) ).
fof(f8828,plain,
spl104_519,
inference(avatar_split_clause,[],[f4350,f8826]) ).
fof(f8826,plain,
( spl104_519
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_519])]) ).
fof(f4350,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls) ),
inference(cnf_transformation,[],[f3414]) ).
fof(f3414,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ) ),
inference(nnf_transformation,[],[f1466]) ).
fof(f1466,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls) ),
inference(rectify,[],[f541]) ).
fof(f541,axiom,
! [X52] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X52)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X52,c_Int_OPls) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_eq__number__of__0) ).
fof(f8824,plain,
spl104_518,
inference(avatar_split_clause,[],[f4349,f8822]) ).
fof(f8822,plain,
( spl104_518
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_518])]) ).
fof(f4349,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ),
inference(cnf_transformation,[],[f3414]) ).
fof(f8820,plain,
spl104_517,
inference(avatar_split_clause,[],[f4343,f8818]) ).
fof(f8818,plain,
( spl104_517
<=> ! [X0] :
( c_Nat_OSuc(sK34(X0)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_517])]) ).
fof(f4343,plain,
! [X0] :
( c_Nat_OSuc(sK34(X0)) = X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f3411]) ).
fof(f3411,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(sK34(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,[sK34])],[f3409,f3410]) ).
fof(f3410,plain,
! [X0] :
( ? [X2] : c_Nat_OSuc(X2) = X0
=> c_Nat_OSuc(sK34(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f3409,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,[],[f3408]) ).
fof(f3408,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,[],[f1463]) ).
fof(f1463,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,[],[f118]) ).
fof(f118,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X18)
<=> ? [X34] : c_Nat_OSuc(X34) = X18 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_gr0__conv__Suc) ).
fof(f8816,plain,
( spl104_516
| ~ spl104_324
| ~ spl104_492 ),
inference(avatar_split_clause,[],[f8738,f8368,f7514,f8814]) ).
fof(f8814,plain,
( spl104_516
<=> ! [X0] : sP2(c_Int_OPls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_516])]) ).
fof(f7514,plain,
( spl104_324
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_OPls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_324])]) ).
fof(f8368,plain,
( spl104_492
<=> ! [X0,X1] :
( c_Int_OPls != c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| sP2(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_492])]) ).
fof(f8738,plain,
( ! [X0] : sP2(c_Int_OPls,X0)
| ~ spl104_324
| ~ spl104_492 ),
inference(trivial_inequality_removal,[],[f8737]) ).
fof(f8737,plain,
( ! [X0] :
( c_Int_OPls != c_Int_OPls
| sP2(c_Int_OPls,X0) )
| ~ spl104_324
| ~ spl104_492 ),
inference(superposition,[],[f8369,f7515]) ).
fof(f7515,plain,
( ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_OPls,X0)
| ~ spl104_324 ),
inference(avatar_component_clause,[],[f7514]) ).
fof(f8369,plain,
( ! [X0,X1] :
( c_Int_OPls != c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| sP2(X1,X0) )
| ~ spl104_492 ),
inference(avatar_component_clause,[],[f8368]) ).
fof(f8812,plain,
spl104_515,
inference(avatar_split_clause,[],[f4318,f8810]) ).
fof(f8810,plain,
( spl104_515
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_515])]) ).
fof(f4318,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f2386]) ).
fof(f2386,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(ennf_transformation,[],[f1447]) ).
fof(f1447,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X0) ),
inference(rectify,[],[f452]) ).
fof(f452,axiom,
! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(X3) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_natfloor__neg) ).
fof(f8808,plain,
spl104_514,
inference(avatar_split_clause,[],[f4317,f8806]) ).
fof(f8806,plain,
( spl104_514
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_514])]) ).
fof(f4317,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(cnf_transformation,[],[f2385]) ).
fof(f2385,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(ennf_transformation,[],[f1446]) ).
fof(f1446,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X0) ),
inference(rectify,[],[f381]) ).
fof(f381,axiom,
! [X3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(X3) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_natceiling__neg) ).
fof(f8804,plain,
spl104_513,
inference(avatar_split_clause,[],[f4298,f8802]) ).
fof(f8802,plain,
( spl104_513
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_513])]) ).
fof(f4298,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f2367]) ).
fof(f2367,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f1428]) ).
fof(f1428,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(rectify,[],[f632]) ).
fof(f632,axiom,
! [X4] :
( class_Rings_Osemiring__1(X4)
=> c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_of__nat__0) ).
fof(f8800,plain,
spl104_512,
inference(avatar_split_clause,[],[f4297,f8798]) ).
fof(f8798,plain,
( spl104_512
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_512])]) ).
fof(f4297,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f2366]) ).
fof(f2366,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f1427]) ).
fof(f1427,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> c_Groups_Oone__class_Oone(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rectify,[],[f638]) ).
fof(f638,axiom,
! [X4] :
( class_Rings_Osemiring__1(X4)
=> c_Groups_Oone__class_Oone(X4) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_of__nat__1) ).
fof(f8796,plain,
spl104_511,
inference(avatar_split_clause,[],[f4203,f8794]) ).
fof(f8794,plain,
( spl104_511
<=> ! [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,[spl104_511])]) ).
fof(f4203,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,[],[f1341]) ).
fof(f1341,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,[],[f755]) ).
fof(f755,axiom,
! [X5] : 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)),X5),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__0) ).
fof(f8792,plain,
spl104_510,
inference(avatar_split_clause,[],[f4202,f8790]) ).
fof(f8790,plain,
( spl104_510
<=> ! [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,[spl104_510])]) ).
fof(f4202,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,[],[f1340]) ).
fof(f1340,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,[],[f756]) ).
fof(f756,axiom,
! [X6] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__0__right) ).
fof(f8788,plain,
spl104_509,
inference(avatar_split_clause,[],[f4201,f8786]) ).
fof(f8786,plain,
( spl104_509
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_509])]) ).
fof(f4201,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0),
inference(cnf_transformation,[],[f1339]) ).
fof(f1339,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0),
inference(rectify,[],[f404]) ).
fof(f404,axiom,
! [X3] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X3),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X3),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__add__one__not__less__self) ).
fof(f8735,plain,
( spl104_508
| ~ spl104_310
| ~ spl104_483 ),
inference(avatar_split_clause,[],[f8721,f8330,f7455,f8732]) ).
fof(f8732,plain,
( spl104_508
<=> c_Nat__Numeral_Oneg(c_Int_Opred(c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_508])]) ).
fof(f7455,plain,
( spl104_310
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_310])]) ).
fof(f8330,plain,
( spl104_483
<=> ! [X0] :
( c_Nat__Numeral_Oneg(c_Int_Opred(X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_483])]) ).
fof(f8721,plain,
( c_Nat__Numeral_Oneg(c_Int_Opred(c_Int_OPls))
| ~ spl104_310
| ~ spl104_483 ),
inference(trivial_inequality_removal,[],[f8720]) ).
fof(f8720,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Nat__Numeral_Oneg(c_Int_Opred(c_Int_OPls))
| ~ spl104_310
| ~ spl104_483 ),
inference(superposition,[],[f8331,f7457]) ).
fof(f7457,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls)
| ~ spl104_310 ),
inference(avatar_component_clause,[],[f7455]) ).
fof(f8331,plain,
( ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)
| c_Nat__Numeral_Oneg(c_Int_Opred(X0)) )
| ~ spl104_483 ),
inference(avatar_component_clause,[],[f8330]) ).
fof(f8716,plain,
( spl104_507
| ~ spl104_411 ),
inference(avatar_split_clause,[],[f8053,f7905,f8714]) ).
fof(f8714,plain,
( spl104_507
<=> ! [X0] :
( sP3(X0,X0)
| c_Nat__Numeral_Oneg(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_507])]) ).
fof(f7905,plain,
( spl104_411
<=> ! [X0,X1] :
( c_Nat__Numeral_Oneg(X1)
| sP3(X0,X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_411])]) ).
fof(f8053,plain,
( ! [X0] :
( sP3(X0,X0)
| c_Nat__Numeral_Oneg(X0) )
| ~ spl104_411 ),
inference(equality_resolution,[],[f7906]) ).
fof(f7906,plain,
( ! [X0,X1] :
( X0 != X1
| sP3(X0,X1)
| c_Nat__Numeral_Oneg(X1) )
| ~ spl104_411 ),
inference(avatar_component_clause,[],[f7905]) ).
fof(f8576,plain,
( spl104_506
| ~ spl104_407 ),
inference(avatar_split_clause,[],[f8048,f7889,f8574]) ).
fof(f8574,plain,
( spl104_506
<=> ! [X0,X1] : sP15(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_506])]) ).
fof(f7889,plain,
( spl104_407
<=> ! [X2,X0,X1] :
( sP15(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_407])]) ).
fof(f8048,plain,
( ! [X0,X1] : sP15(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl104_407 ),
inference(equality_resolution,[],[f7890]) ).
fof(f7890,plain,
( ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
| sP15(X0,X1,X2) )
| ~ spl104_407 ),
inference(avatar_component_clause,[],[f7889]) ).
fof(f8530,plain,
( spl104_505
| ~ spl104_229
| ~ spl104_400 ),
inference(avatar_split_clause,[],[f8040,f7861,f7121,f8527]) ).
fof(f8527,plain,
( spl104_505
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_505])]) ).
fof(f7121,plain,
( spl104_229
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_229])]) ).
fof(f7861,plain,
( spl104_400
<=> ! [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,[spl104_400])]) ).
fof(f8040,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____)
| ~ spl104_229
| ~ spl104_400 ),
inference(resolution,[],[f7862,f7123]) ).
fof(f7123,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____)
| ~ spl104_229 ),
inference(avatar_component_clause,[],[f7121]) ).
fof(f7862,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0) )
| ~ spl104_400 ),
inference(avatar_component_clause,[],[f7861]) ).
fof(f8421,plain,
( spl104_504
| ~ spl104_419
| ~ spl104_426 ),
inference(avatar_split_clause,[],[f8088,f8085,f7990,f8419]) ).
fof(f8419,plain,
( spl104_504
<=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Osucc(c_Int_OPls)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_504])]) ).
fof(f8085,plain,
( spl104_426
<=> ! [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,[spl104_426])]) ).
fof(f8088,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Osucc(c_Int_OPls)),X0) = X0
| ~ spl104_419
| ~ spl104_426 ),
inference(forward_demodulation,[],[f8086,f7992]) ).
fof(f8086,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0
| ~ spl104_426 ),
inference(avatar_component_clause,[],[f8085]) ).
fof(f8415,plain,
( spl104_503
| ~ spl104_419
| ~ spl104_422 ),
inference(avatar_split_clause,[],[f8071,f8068,f7990,f8413]) ).
fof(f8413,plain,
( spl104_503
<=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Int_Osucc(c_Int_OPls)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_503])]) ).
fof(f8068,plain,
( spl104_422
<=> ! [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,[spl104_422])]) ).
fof(f8071,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Int_Osucc(c_Int_OPls)) = X0
| ~ spl104_419
| ~ spl104_422 ),
inference(forward_demodulation,[],[f8069,f7992]) ).
fof(f8069,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0
| ~ spl104_422 ),
inference(avatar_component_clause,[],[f8068]) ).
fof(f8411,plain,
spl104_502,
inference(avatar_split_clause,[],[f5881,f8409]) ).
fof(f8409,plain,
( spl104_502
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Osucc(X1),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_502])]) ).
fof(f5881,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Osucc(X1),X0)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f4871,f4183]) ).
fof(f4871,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,[],[f3642]) ).
fof(f3642,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,[],[f1797]) ).
fof(f1797,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,[],[f420]) ).
fof(f420,axiom,
! [X55,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X50,c_Groups_Oone__class_Oone(tc_Int_Oint)),X55)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X55) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add1__zle__eq) ).
fof(f8407,plain,
spl104_501,
inference(avatar_split_clause,[],[f5875,f8405]) ).
fof(f5875,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_Opred(X0))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f4867,f4182]) ).
fof(f4182,plain,
! [X0] : c_Int_Opred(X0) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f1320]) ).
fof(f1320,plain,
! [X0] : c_Int_Opred(X0) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(rectify,[],[f556]) ).
fof(f556,axiom,
! [X14] : c_Int_Opred(X14) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X14,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_pred__def) ).
fof(f4867,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,[],[f3640]) ).
fof(f3640,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,[],[f1795]) ).
fof(f1795,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,[],[f418]) ).
fof(f418,axiom,
! [X55,X50] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,c_Groups_Ominus__class_Ominus(tc_Int_Oint,X55,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,X55) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zle__diff1__eq) ).
fof(f8403,plain,
spl104_500,
inference(avatar_split_clause,[],[f5874,f8401]) ).
fof(f8401,plain,
( spl104_500
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_Opred(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_500])]) ).
fof(f5874,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,c_Int_Opred(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f4868,f4182]) ).
fof(f4868,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,[],[f3640]) ).
fof(f8399,plain,
spl104_499,
inference(avatar_split_clause,[],[f5868,f8397]) ).
fof(f5868,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Osucc(X0))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f4854,f4183]) ).
fof(f4854,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,[],[f3633]) ).
fof(f8395,plain,
spl104_498,
inference(avatar_split_clause,[],[f5866,f8393]) ).
fof(f8393,plain,
( spl104_498
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Osucc(X0))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_498])]) ).
fof(f5866,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Osucc(X0))
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f4851,f4183]) ).
fof(f4851,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,[],[f3631]) ).
fof(f3631,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,[],[f1789]) ).
fof(f1789,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,[],[f417]) ).
fof(f417,axiom,
! [X55,X50] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X50,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X55,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X50,X55) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zle__add1__eq__le) ).
fof(f8391,plain,
spl104_497,
inference(avatar_split_clause,[],[f5865,f8389]) ).
fof(f5865,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Osucc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f4852,f4183]) ).
fof(f4852,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,[],[f3631]) ).
fof(f8387,plain,
( ~ spl104_496
| spl104_224
| ~ spl104_419 ),
inference(avatar_split_clause,[],[f8242,f7990,f7095,f8384]) ).
fof(f8384,plain,
( spl104_496
<=> c_Int_OPls = c_Int_Osucc(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_496])]) ).
fof(f7095,plain,
( spl104_224
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl104_224])]) ).
fof(f8242,plain,
( c_Int_OPls != c_Int_Osucc(c_Int_OPls)
| spl104_224
| ~ spl104_419 ),
inference(superposition,[],[f7097,f7992]) ).
fof(f7097,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Int_OPls
| spl104_224 ),
inference(avatar_component_clause,[],[f7095]) ).
fof(f8382,plain,
spl104_495,
inference(avatar_split_clause,[],[f5840,f8380]) ).
fof(f5840,plain,
! [X0,X1] :
( c_Int_OPls != X0
| sP3(X0,X1)
| X0 != X1 ),
inference(forward_demodulation,[],[f5839,f4101]) ).
fof(f5839,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| sP3(X0,X1)
| X0 != X1 ),
inference(forward_demodulation,[],[f4832,f4155]) ).
fof(f4832,plain,
! [X0,X1] :
( sP3(X0,X1)
| X0 != X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) ),
inference(cnf_transformation,[],[f3623]) ).
fof(f3623,plain,
! [X0,X1] :
( ( sP3(X0,X1)
| ( X0 != X1
& ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) )
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)
& c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ) )
& ( ( ( X0 = X1
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ) )
| ~ sP3(X0,X1) ) ),
inference(rectify,[],[f3622]) ).
fof(f3622,plain,
! [X1,X0] :
( ( sP3(X1,X0)
| ( X0 != X1
& ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) )
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)
& c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ) )
& ( ( ( X0 = X1
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ) )
| ~ sP3(X1,X0) ) ),
inference(flattening,[],[f3621]) ).
fof(f3621,plain,
! [X1,X0] :
( ( sP3(X1,X0)
| ( X0 != X1
& ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) )
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)
& c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ) )
& ( ( ( X0 = X1
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ) )
| ~ sP3(X1,X0) ) ),
inference(nnf_transformation,[],[f3347]) ).
fof(f8378,plain,
spl104_494,
inference(avatar_split_clause,[],[f5838,f8376]) ).
fof(f8376,plain,
( spl104_494
<=> ! [X0,X1] :
( ~ c_Nat__Numeral_Oneg(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_494])]) ).
fof(f5838,plain,
! [X0,X1] :
( ~ c_Nat__Numeral_Oneg(X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| ~ sP4(X0,X1) ),
inference(forward_demodulation,[],[f5837,f4155]) ).
fof(f5837,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ sP4(X0,X1) ),
inference(forward_demodulation,[],[f5836,f4155]) ).
fof(f5836,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0),c_Int_OPls)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ sP4(X0,X1) ),
inference(forward_demodulation,[],[f4821,f4101]) ).
fof(f4821,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f3620]) ).
fof(f8374,plain,
spl104_493,
inference(avatar_split_clause,[],[f5834,f8372]) ).
fof(f5834,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Nat__Numeral_Oneg(X1)
| sP4(X0,X1) ),
inference(forward_demodulation,[],[f5833,f4155]) ).
fof(f5833,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0),c_Int_OPls)
| ~ c_Nat__Numeral_Oneg(X1)
| sP4(X0,X1) ),
inference(forward_demodulation,[],[f5832,f4101]) ).
fof(f5832,plain,
! [X0,X1] :
( ~ c_Nat__Numeral_Oneg(X1)
| sP4(X0,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_demodulation,[],[f4824,f4155]) ).
fof(f4824,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3620]) ).
fof(f8370,plain,
spl104_492,
inference(avatar_split_clause,[],[f5828,f8368]) ).
fof(f5828,plain,
! [X0,X1] :
( c_Int_OPls != c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| sP2(X1,X0) ),
inference(forward_demodulation,[],[f4814,f4101]) ).
fof(f4814,plain,
! [X0,X1] :
( sP2(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3615]) ).
fof(f3615,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0) ) ),
inference(nnf_transformation,[],[f3346]) ).
fof(f3346,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
<=> sP2(X1,X0) ),
inference(definition_folding,[],[f1783,f3345]) ).
fof(f1783,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,[],[f943]) ).
fof(f943,axiom,
! [X20,X35] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X35,X20)
<=> ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X20,X35)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X35,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
| ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X35,X20)
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X35) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X20 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zdiv__eq__0__iff) ).
fof(f8366,plain,
spl104_491,
inference(avatar_split_clause,[],[f5827,f8364]) ).
fof(f8364,plain,
( spl104_491
<=> ! [X0,X1] :
( c_Int_OPls = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| ~ sP2(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_491])]) ).
fof(f5827,plain,
! [X0,X1] :
( c_Int_OPls = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| ~ sP2(X1,X0) ),
inference(forward_demodulation,[],[f4815,f4101]) ).
fof(f4815,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,X1,X0)
| ~ sP2(X1,X0) ),
inference(cnf_transformation,[],[f3615]) ).
fof(f8362,plain,
spl104_490,
inference(avatar_split_clause,[],[f5727,f8360]) ).
fof(f8360,plain,
( spl104_490
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Osucc(X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_490])]) ).
fof(f5727,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Osucc(X1),X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f4615,f4183]) ).
fof(f4615,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,[],[f2536]) ).
fof(f2536,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,[],[f1655]) ).
fof(f1655,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,[],[f423]) ).
fof(f423,axiom,
! [X25,X32] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X32,X25)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,X32,c_Groups_Oone__class_Oone(tc_Int_Oint)),X25) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zless__imp__add1__zle) ).
fof(f8358,plain,
spl104_489,
inference(avatar_split_clause,[],[f5713,f8356]) ).
fof(f8356,plain,
( spl104_489
<=> ! [X0,X1] :
( c_Int_OPls = c_Nat__Transfer_Otsub(X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_489])]) ).
fof(f5713,plain,
! [X0,X1] :
( c_Int_OPls = c_Nat__Transfer_Otsub(X0,X1)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(forward_demodulation,[],[f4449,f4101]) ).
fof(f4449,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,[],[f2406]) ).
fof(f8354,plain,
spl104_488,
inference(avatar_split_clause,[],[f5685,f8352]) ).
fof(f8352,plain,
( spl104_488
<=> ! [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,[spl104_488])]) ).
fof(f5685,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,[],[f4353,f4119]) ).
fof(f4353,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,[],[f3416]) ).
fof(f3416,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,[],[f1468]) ).
fof(f1468,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,[],[f119]) ).
fof(f119,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__Suc0) ).
fof(f8350,plain,
spl104_487,
inference(avatar_split_clause,[],[f5684,f8348]) ).
fof(f8348,plain,
( spl104_487
<=> ! [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,[spl104_487])]) ).
fof(f5684,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,[],[f4354,f4119]) ).
fof(f4354,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(cnf_transformation,[],[f3416]) ).
fof(f8345,plain,
spl104_486,
inference(avatar_split_clause,[],[f5683,f8343]) ).
fof(f8343,plain,
( spl104_486
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,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,[spl104_486])]) ).
fof(f5683,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(forward_demodulation,[],[f4345,f4101]) ).
fof(f4345,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,[],[f3412]) ).
fof(f3412,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,[],[f1464]) ).
fof(f1464,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,[],[f416]) ).
fof(f416,axiom,
! [X55] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X55)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X55) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_int__one__le__iff__zero__less) ).
fof(f8340,plain,
spl104_485,
inference(avatar_split_clause,[],[f5682,f8338]) ).
fof(f8338,plain,
( spl104_485
<=> ! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,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,[spl104_485])]) ).
fof(f5682,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X0)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0) ),
inference(forward_demodulation,[],[f4346,f4101]) ).
fof(f4346,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,[],[f3412]) ).
fof(f8336,plain,
spl104_484,
inference(avatar_split_clause,[],[f5681,f8334]) ).
fof(f8334,plain,
( spl104_484
<=> ! [X0] :
( ~ c_Nat__Numeral_Oneg(c_Int_Opred(X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_484])]) ).
fof(f5681,plain,
! [X0] :
( ~ c_Nat__Numeral_Oneg(c_Int_Opred(X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ),
inference(forward_demodulation,[],[f4341,f4155]) ).
fof(f4341,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(X0))) ),
inference(cnf_transformation,[],[f3407]) ).
fof(f3407,plain,
! [X0] :
( ( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(X0))) ) ),
inference(nnf_transformation,[],[f1462]) ).
fof(f1462,plain,
! [X0] :
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(X0)))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ),
inference(rectify,[],[f557]) ).
fof(f557,axiom,
! [X52] :
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(X52)))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X52) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_neg__number__of__pred__iff__0) ).
fof(f8332,plain,
spl104_483,
inference(avatar_split_clause,[],[f5680,f8330]) ).
fof(f5680,plain,
! [X0] :
( c_Nat__Numeral_Oneg(c_Int_Opred(X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ),
inference(forward_demodulation,[],[f4342,f4155]) ).
fof(f4342,plain,
! [X0] :
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_Opred(X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ),
inference(cnf_transformation,[],[f3407]) ).
fof(f8328,plain,
spl104_482,
inference(avatar_split_clause,[],[f5654,f8326]) ).
fof(f8326,plain,
( spl104_482
<=> ! [X0] :
( ~ c_Nat__Numeral_Oneg(X0)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_482])]) ).
fof(f5654,plain,
! [X0] :
( ~ c_Nat__Numeral_Oneg(X0)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)) ),
inference(forward_demodulation,[],[f4214,f4155]) ).
fof(f4214,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0))
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ),
inference(cnf_transformation,[],[f2291]) ).
fof(f8324,plain,
spl104_481,
inference(avatar_split_clause,[],[f5164,f8322]) ).
fof(f5164,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X0,X1)
| X0 != X1
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f3722]) ).
fof(f3722,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,[],[f3721]) ).
fof(f3721,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,[],[f2918]) ).
fof(f2918,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,[],[f1996]) ).
fof(f1996,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,[],[f51]) ).
fof(f51,axiom,
! [X26,X23,X4] :
( class_Orderings_Oorder(X4)
=> ( X23 = X26
<=> ( c_Orderings_Oord__class_Oless__eq(X4,X26,X23)
& c_Orderings_Oord__class_Oless__eq(X4,X23,X26) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_order__eq__iff) ).
fof(f8320,plain,
spl104_480,
inference(avatar_split_clause,[],[f5152,f8318]) ).
fof(f5152,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f2899]) ).
fof(f2899,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f2898]) ).
fof(f2898,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X1,X0)
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f1986]) ).
fof(f1986,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( c_Orderings_Oord__class_Oless(X2,X1,X0)
=> X0 != X1 ) ),
inference(rectify,[],[f152]) ).
fof(f152,axiom,
! [X22,X3,X4] :
( class_Orderings_Oorder(X4)
=> ( c_Orderings_Oord__class_Oless(X4,X3,X22)
=> X3 != X22 ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__imp__neq) ).
fof(f8316,plain,
spl104_479,
inference(avatar_split_clause,[],[f5141,f8314]) ).
fof(f8314,plain,
( spl104_479
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 != X1
| ~ class_Orderings_Opreorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_479])]) ).
fof(f5141,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 != X1
| ~ class_Orderings_Opreorder(X2) ),
inference(cnf_transformation,[],[f2882]) ).
fof(f2882,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 != X1
| ~ class_Orderings_Opreorder(X2) ),
inference(flattening,[],[f2881]) ).
fof(f2881,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,X0)
| X0 != X1
| ~ class_Orderings_Opreorder(X2) ),
inference(ennf_transformation,[],[f1977]) ).
fof(f1977,plain,
! [X0,X1,X2] :
( class_Orderings_Opreorder(X2)
=> ( X0 = X1
=> c_Orderings_Oord__class_Oless__eq(X2,X1,X0) ) ),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X22,X3,X4] :
( class_Orderings_Opreorder(X4)
=> ( X3 = X22
=> c_Orderings_Oord__class_Oless__eq(X4,X3,X22) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_order__eq__refl) ).
fof(f8312,plain,
spl104_478,
inference(avatar_split_clause,[],[f5086,f8310]) ).
fof(f5086,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(X2,X0,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f3708]) ).
fof(f3708,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,[],[f3707]) ).
fof(f3707,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,[],[f2820]) ).
fof(f2820,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,[],[f1932]) ).
fof(f1932,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,[],[f126]) ).
fof(f126,axiom,
! [X26,X23,X4] :
( class_Orderings_Olinorder(X4)
=> ( X23 != X26
<=> ( c_Orderings_Oord__class_Oless(X4,X26,X23)
| c_Orderings_Oord__class_Oless(X4,X23,X26) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_linorder__neq__iff) ).
fof(f8308,plain,
spl104_477,
inference(avatar_split_clause,[],[f4793,f8306]) ).
fof(f8306,plain,
( spl104_477
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_477])]) ).
fof(f4793,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f3604]) ).
fof(f8304,plain,
spl104_476,
inference(avatar_split_clause,[],[f4789,f8302]) ).
fof(f8302,plain,
( spl104_476
<=> ! [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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_476])]) ).
fof(f4789,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,[],[f3599]) ).
fof(f3599,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,[],[f1776]) ).
fof(f1776,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,[],[f314]) ).
fof(f314,axiom,
! [X18,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X18) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__Suc__eq__le) ).
fof(f8300,plain,
( ~ spl104_475
| spl104_211
| ~ spl104_419 ),
inference(avatar_split_clause,[],[f8241,f7990,f7033,f8297]) ).
fof(f8297,plain,
( spl104_475
<=> c_Nat__Numeral_Oneg(c_Int_Osucc(c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_475])]) ).
fof(f7033,plain,
( spl104_211
<=> c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_211])]) ).
fof(f8241,plain,
( ~ c_Nat__Numeral_Oneg(c_Int_Osucc(c_Int_OPls))
| spl104_211
| ~ spl104_419 ),
inference(superposition,[],[f7035,f7992]) ).
fof(f7035,plain,
( ~ c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint))
| spl104_211 ),
inference(avatar_component_clause,[],[f7033]) ).
fof(f8295,plain,
spl104_474,
inference(avatar_split_clause,[],[f4775,f8293]) ).
fof(f8293,plain,
( spl104_474
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_474])]) ).
fof(f4775,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X1),X0) ),
inference(cnf_transformation,[],[f3582]) ).
fof(f3582,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X1),X0) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ) ),
inference(nnf_transformation,[],[f1769]) ).
fof(f1769,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X1),X0) ),
inference(rectify,[],[f555]) ).
fof(f555,axiom,
! [X29,X20] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X20,X29)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X20),X29) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__iff__pred__less) ).
fof(f8291,plain,
spl104_473,
inference(avatar_split_clause,[],[f4774,f8289]) ).
fof(f4774,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Opred(X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3582]) ).
fof(f8287,plain,
spl104_472,
inference(avatar_split_clause,[],[f4749,f8285]) ).
fof(f8285,plain,
( spl104_472
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_472])]) ).
fof(f4749,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,[],[f3561]) ).
fof(f3561,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,[],[f1758]) ).
fof(f1758,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,[],[f25]) ).
fof(f25,axiom,
! [X18,X17] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X17,X18)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X18),X17) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__less__eq__eq) ).
fof(f8283,plain,
spl104_471,
inference(avatar_split_clause,[],[f4748,f8281]) ).
fof(f8281,plain,
( spl104_471
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_471])]) ).
fof(f4748,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,[],[f3561]) ).
fof(f8279,plain,
spl104_470,
inference(avatar_split_clause,[],[f4747,f8277]) ).
fof(f8277,plain,
( spl104_470
<=> ! [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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_470])]) ).
fof(f4747,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,[],[f3560]) ).
fof(f3560,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,[],[f1757]) ).
fof(f1757,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,[],[f241]) ).
fof(f241,axiom,
! [X18,X17] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X18,c_Nat_OSuc(X17)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__less__eq) ).
fof(f8275,plain,
spl104_469,
inference(avatar_split_clause,[],[f4746,f8273]) ).
fof(f8273,plain,
( spl104_469
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_469])]) ).
fof(f4746,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,[],[f3560]) ).
fof(f8271,plain,
spl104_468,
inference(avatar_split_clause,[],[f4708,f8269]) ).
fof(f8269,plain,
( spl104_468
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_468])]) ).
fof(f4708,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(cnf_transformation,[],[f2640]) ).
fof(f2640,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(ennf_transformation,[],[f1729]) ).
fof(f1729,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f20]) ).
fof(f20,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X6),X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__leD) ).
fof(f8267,plain,
spl104_467,
inference(avatar_split_clause,[],[f4707,f8265]) ).
fof(f8265,plain,
( spl104_467
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_467])]) ).
fof(f4707,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,[],[f2639]) ).
fof(f2639,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,[],[f1728]) ).
fof(f1728,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,[],[f309]) ).
fof(f309,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X6),X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__le__lessD) ).
fof(f8263,plain,
spl104_466,
inference(avatar_split_clause,[],[f4705,f8261]) ).
fof(f8261,plain,
( spl104_466
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_466])]) ).
fof(f4705,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(cnf_transformation,[],[f2636]) ).
fof(f2636,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0) ),
inference(ennf_transformation,[],[f1726]) ).
fof(f1726,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X1),X0)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f250]) ).
fof(f250,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X6),X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__lessD) ).
fof(f8259,plain,
spl104_465,
inference(avatar_split_clause,[],[f4633,f8257]) ).
fof(f4633,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2557]) ).
fof(f2557,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1673]) ).
fof(f1673,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X0)) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,c_Nat_OSuc(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__SucI) ).
fof(f8240,plain,
spl104_464,
inference(avatar_split_clause,[],[f4632,f8238]) ).
fof(f8238,plain,
( spl104_464
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_464])]) ).
fof(f4632,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,[],[f2556]) ).
fof(f2556,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,[],[f1672]) ).
fof(f1672,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,[],[f312]) ).
fof(f312,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Nat_OSuc(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__imp__less__Suc) ).
fof(f8236,plain,
spl104_463,
inference(avatar_split_clause,[],[f4623,f8234]) ).
fof(f8234,plain,
( spl104_463
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_463])]) ).
fof(f4623,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,[],[f2544]) ).
fof(f2544,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,[],[f1663]) ).
fof(f1663,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,[],[f311]) ).
fof(f311,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X5)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X6),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__leI) ).
fof(f8232,plain,
spl104_462,
inference(avatar_split_clause,[],[f4622,f8230]) ).
fof(f8230,plain,
( spl104_462
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_462])]) ).
fof(f4622,plain,
! [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,[],[f2543]) ).
fof(f2543,plain,
! [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,[],[f1662]) ).
fof(f1662,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)) ),
inference(rectify,[],[f246]) ).
fof(f246,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X5)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,c_Nat_OSuc(X5)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__SucI) ).
fof(f8228,plain,
spl104_461,
inference(avatar_split_clause,[],[f4595,f8226]) ).
fof(f8226,plain,
( spl104_461
<=> ! [X0,X1] :
( c_SEQ_Omonoseq(X0,X1)
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_461])]) ).
fof(f4595,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X0,X1)
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f3520]) ).
fof(f3520,plain,
! [X0,X1] :
( ( ( c_SEQ_Omonoseq(X0,X1)
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| ~ c_SEQ_Omonoseq(X0,X1) ) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f3519]) ).
fof(f3519,plain,
! [X1,X0] :
( ( ( c_SEQ_Omonoseq(X1,X0)
| ~ sP0(X0,X1) )
& ( sP0(X0,X1)
| ~ c_SEQ_Omonoseq(X1,X0) ) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f3343]) ).
fof(f3343,plain,
! [X1,X0] :
( ( c_SEQ_Omonoseq(X1,X0)
<=> sP0(X0,X1) )
| ~ sP1(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f8224,plain,
spl104_460,
inference(avatar_split_clause,[],[f4594,f8222]) ).
fof(f8222,plain,
( spl104_460
<=> ! [X0,X1] :
( sP0(X1,X0)
| ~ c_SEQ_Omonoseq(X0,X1)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_460])]) ).
fof(f4594,plain,
! [X0,X1] :
( sP0(X1,X0)
| ~ c_SEQ_Omonoseq(X0,X1)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f3520]) ).
fof(f8220,plain,
spl104_459,
inference(avatar_split_clause,[],[f4563,f8218]) ).
fof(f8218,plain,
( spl104_459
<=> ! [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,[spl104_459])]) ).
fof(f4563,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2488]) ).
fof(f2488,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1621]) ).
fof(f1621,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,[],[f276]) ).
fof(f276,axiom,
! [X12,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> c_Groups_Oplus__class_Oplus(X4,c_Groups_Ozero__class_Ozero(X4),X12) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(f8216,plain,
spl104_458,
inference(avatar_split_clause,[],[f4562,f8214]) ).
fof(f8214,plain,
( spl104_458
<=> ! [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,[spl104_458])]) ).
fof(f4562,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f2487]) ).
fof(f2487,plain,
! [X0,X1] :
( c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f1620]) ).
fof(f1620,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,
! [X12,X4] :
( class_Rings_Ocomm__semiring__1(X4)
=> c_Groups_Oplus__class_Oplus(X4,X12,c_Groups_Ozero__class_Ozero(X4)) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(f8212,plain,
spl104_457,
inference(avatar_split_clause,[],[f4555,f8210]) ).
fof(f8210,plain,
( spl104_457
<=> ! [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,[spl104_457])]) ).
fof(f4555,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,[],[f2480]) ).
fof(f2480,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,[],[f1613]) ).
fof(f1613,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,[],[f272]) ).
fof(f272,axiom,
! [X12,X4] :
( class_Groups_Ocomm__monoid__add(X4)
=> c_Groups_Oplus__class_Oplus(X4,c_Groups_Ozero__class_Ozero(X4),X12) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__0) ).
fof(f8208,plain,
spl104_456,
inference(avatar_split_clause,[],[f4554,f8206]) ).
fof(f8206,plain,
( spl104_456
<=> ! [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,[spl104_456])]) ).
fof(f4554,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,[],[f2479]) ).
fof(f2479,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,[],[f1612]) ).
fof(f1612,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,[],[f275]) ).
fof(f275,axiom,
! [X12,X4] :
( class_Groups_Ocomm__monoid__add(X4)
=> c_Groups_Oplus__class_Oplus(X4,X12,c_Groups_Ozero__class_Ozero(X4)) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add_Ocomm__neutral) ).
fof(f8204,plain,
spl104_455,
inference(avatar_split_clause,[],[f4545,f8202]) ).
fof(f8202,plain,
( spl104_455
<=> ! [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,[spl104_455])]) ).
fof(f4545,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,[],[f2472]) ).
fof(f2472,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,[],[f1605]) ).
fof(f1605,plain,
! [X0,X1] :
( class_Groups_Omonoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,c_Groups_Ozero__class_Ozero(X1),X0) = X0 ),
inference(rectify,[],[f271]) ).
fof(f271,axiom,
! [X12,X4] :
( class_Groups_Omonoid__add(X4)
=> c_Groups_Oplus__class_Oplus(X4,c_Groups_Ozero__class_Ozero(X4),X12) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__0__left) ).
fof(f8200,plain,
spl104_454,
inference(avatar_split_clause,[],[f4544,f8198]) ).
fof(f8198,plain,
( spl104_454
<=> ! [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,[spl104_454])]) ).
fof(f4544,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,[],[f2471]) ).
fof(f2471,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,[],[f1604]) ).
fof(f1604,plain,
! [X0,X1] :
( class_Groups_Omonoid__add(X1)
=> c_Groups_Oplus__class_Oplus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f274]) ).
fof(f274,axiom,
! [X12,X4] :
( class_Groups_Omonoid__add(X4)
=> c_Groups_Oplus__class_Oplus(X4,X12,c_Groups_Ozero__class_Ozero(X4)) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__0__right) ).
fof(f8196,plain,
spl104_453,
inference(avatar_split_clause,[],[f4528,f8194]) ).
fof(f8194,plain,
( spl104_453
<=> ! [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,[spl104_453])]) ).
fof(f4528,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,[],[f2459]) ).
fof(f2459,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,[],[f1592]) ).
fof(f1592,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ominus__class_Ominus(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f132]) ).
fof(f132,axiom,
! [X12,X4] :
( class_Groups_Ogroup__add(X4)
=> c_Groups_Ominus__class_Ominus(X4,X12,c_Groups_Ozero__class_Ozero(X4)) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__0__right) ).
fof(f8192,plain,
spl104_452,
inference(avatar_split_clause,[],[f4527,f8190]) ).
fof(f4527,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,[],[f2458]) ).
fof(f2458,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,[],[f1591]) ).
fof(f1591,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Groups_Ominus__class_Ominus(X1,X0,X0) ),
inference(rectify,[],[f134]) ).
fof(f134,axiom,
! [X12,X4] :
( class_Groups_Ogroup__add(X4)
=> c_Groups_Ozero__class_Ozero(X4) = c_Groups_Ominus__class_Ominus(X4,X12,X12) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__self) ).
fof(f8188,plain,
spl104_451,
inference(avatar_split_clause,[],[f4512,f8186]) ).
fof(f8186,plain,
( spl104_451
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_451])]) ).
fof(f4512,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f2445]) ).
fof(f2445,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1580]) ).
fof(f1580,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,c_Groups_Ozero__class_Ozero(X1),c_Groups_Oabs__class_Oabs(X1,X0)) ),
inference(rectify,[],[f386]) ).
fof(f386,axiom,
! [X12,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Oabs__class_Oabs(X4,X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__ge__zero) ).
fof(f8184,plain,
spl104_450,
inference(avatar_split_clause,[],[f4511,f8182]) ).
fof(f8182,plain,
( spl104_450
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_450])]) ).
fof(f4511,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f2444]) ).
fof(f2444,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1579]) ).
fof(f1579,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ~ c_Orderings_Oord__class_Oless(X1,c_Groups_Oabs__class_Oabs(X1,X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(rectify,[],[f389]) ).
fof(f389,axiom,
! [X12,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Oabs__class_Oabs(X4,X12),c_Groups_Ozero__class_Ozero(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__not__less__zero) ).
fof(f8180,plain,
spl104_449,
inference(avatar_split_clause,[],[f4506,f8178]) ).
fof(f8178,plain,
( spl104_449
<=> ! [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,[spl104_449])]) ).
fof(f4506,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,[],[f2438]) ).
fof(f2438,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,[],[f1574]) ).
fof(f1574,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Divides_Odiv__class_Odiv(X1,X0,c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(rectify,[],[f964]) ).
fof(f964,axiom,
! [X12,X4] :
( class_Divides_Osemiring__div(X4)
=> c_Divides_Odiv__class_Odiv(X4,X12,c_Groups_Oone__class_Oone(X4)) = X12 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_div__by__1) ).
fof(f8176,plain,
spl104_448,
inference(avatar_split_clause,[],[f4469,f8174]) ).
fof(f8174,plain,
( spl104_448
<=> ! [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,[spl104_448])]) ).
fof(f4469,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,[],[f2418]) ).
fof(f2418,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,[],[f1555]) ).
fof(f1555,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,[],[f479]) ).
fof(f479,axiom,
! [X3,X4] :
( class_RealVector_Oreal__normed__vector(X4)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,X3)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_norm__ge__zero) ).
fof(f8172,plain,
spl104_447,
inference(avatar_split_clause,[],[f4468,f8170]) ).
fof(f8170,plain,
( spl104_447
<=> ! [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,[spl104_447])]) ).
fof(f4468,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,[],[f2417]) ).
fof(f2417,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,[],[f1554]) ).
fof(f1554,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,[],[f480]) ).
fof(f480,axiom,
! [X3,X4] :
( class_RealVector_Oreal__normed__vector(X4)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,X3),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_norm__not__less__zero) ).
fof(f8168,plain,
spl104_446,
inference(avatar_split_clause,[],[f4466,f8166]) ).
fof(f8166,plain,
( spl104_446
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK42(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_446])]) ).
fof(f4466,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK42(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(cnf_transformation,[],[f3446]) ).
fof(f3446,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)),sK42(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK42(X0,X1)) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42])],[f2416,f3445]) ).
fof(f3445,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
=> ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK42(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK42(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2416,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(ennf_transformation,[],[f1553]) ).
fof(f1553,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__algebra(X1)
=> ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X3),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ),
inference(rectify,[],[f842]) ).
fof(f842,axiom,
! [X22,X4] :
( class_RealVector_Oreal__normed__algebra(X4)
=> ? [X61] :
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X22)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,X2)),X61))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__left_Ononneg__bounded) ).
fof(f8164,plain,
spl104_445,
inference(avatar_split_clause,[],[f4464,f8162]) ).
fof(f8162,plain,
( spl104_445
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK41(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_445])]) ).
fof(f4464,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK41(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(cnf_transformation,[],[f3444]) ).
fof(f3444,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)),sK41(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK41(X0,X1)) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK41])],[f2415,f3443]) ).
fof(f3443,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
=> ( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),sK41(X0,X1)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK41(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2415,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(ennf_transformation,[],[f1552]) ).
fof(f1552,plain,
! [X0,X1] :
( class_RealVector_Oreal__normed__algebra(X1)
=> ? [X2] :
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X1,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X1,X3)),X2))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X2) ) ),
inference(rectify,[],[f843]) ).
fof(f843,axiom,
! [X3,X4] :
( class_RealVector_Oreal__normed__algebra(X4)
=> ? [X61] :
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,X2)),X61))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__right_Ononneg__bounded) ).
fof(f8160,plain,
spl104_444,
inference(avatar_split_clause,[],[f4462,f8158]) ).
fof(f8158,plain,
( spl104_444
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK40(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_444])]) ).
fof(f4462,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK40(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(cnf_transformation,[],[f3442]) ).
fof(f3442,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)),sK40(X0,X1)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK40(X0,X1)) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40])],[f2414,f3441]) ).
fof(f3441,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)),sK40(X0,X1)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK40(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2414,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,[],[f1551]) ).
fof(f1551,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,[],[f837]) ).
fof(f837,axiom,
! [X3,X4] :
( class_RealVector_Oreal__normed__algebra(X4)
=> ? [X61] :
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X3),X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,X2)),X61))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__right_Opos__bounded) ).
fof(f8156,plain,
spl104_443,
inference(avatar_split_clause,[],[f4460,f8154]) ).
fof(f8154,plain,
( spl104_443
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK39(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_443])]) ).
fof(f4460,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK39(X0,X1))
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(cnf_transformation,[],[f3440]) ).
fof(f3440,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)),sK39(X0,X1)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK39(X0,X1)) )
| ~ class_RealVector_Oreal__normed__algebra(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39])],[f2413,f3439]) ).
fof(f3439,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)),sK39(X0,X1)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK39(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2413,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,[],[f1550]) ).
fof(f1550,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,[],[f835]) ).
fof(f835,axiom,
! [X22,X4] :
( class_RealVector_Oreal__normed__algebra(X4)
=> ? [X61] :
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X2),X22)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X4,X2)),X61))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__left_Opos__bounded) ).
fof(f8152,plain,
spl104_442,
inference(avatar_split_clause,[],[f4398,f8150]) ).
fof(f8150,plain,
( spl104_442
<=> ! [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,[spl104_442])]) ).
fof(f4398,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,[],[f1496]) ).
fof(f1496,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,[],[f230]) ).
fof(f230,axiom,
! [X6,X5] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X6),X5) = X6,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__add__inverse) ).
fof(f8148,plain,
spl104_441,
inference(avatar_split_clause,[],[f4397,f8146]) ).
fof(f8146,plain,
( spl104_441
<=> ! [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,[spl104_441])]) ).
fof(f4397,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,[],[f1495]) ).
fof(f1495,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,[],[f229]) ).
fof(f229,axiom,
! [X5,X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X5),X5) = X6,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__add__inverse2) ).
fof(f8144,plain,
spl104_440,
inference(avatar_split_clause,[],[f4396,f8142]) ).
fof(f4396,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,[],[f1494]) ).
fof(f1494,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,[],[f68]) ).
fof(f68,axiom,
! [X5,X6] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X5) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X6),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__add__commute) ).
fof(f8140,plain,
spl104_439,
inference(avatar_split_clause,[],[f4395,f8138]) ).
fof(f4395,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0),
inference(cnf_transformation,[],[f1493]) ).
fof(f1493,plain,
! [X0,X1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,X1) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X1,X0),
inference(rectify,[],[f443]) ).
fof(f443,axiom,
! [X32,X25] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X32,X25) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,X25,X32),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zadd__commute) ).
fof(f8136,plain,
spl104_438,
inference(avatar_split_clause,[],[f4394,f8134]) ).
fof(f8134,plain,
( spl104_438
<=> ! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_438])]) ).
fof(f4394,plain,
! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X0)),
inference(cnf_transformation,[],[f1492]) ).
fof(f1492,plain,
! [X0,X1] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X1) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X1,X0)),
inference(rectify,[],[f982]) ).
fof(f982,axiom,
! [X12,X53] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X53) = c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Orcis(X53,X12)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_complex__mod__rcis) ).
fof(f8132,plain,
spl104_437,
inference(avatar_split_clause,[],[f4347,f8130]) ).
fof(f8130,plain,
( spl104_437
<=> ! [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,[spl104_437])]) ).
fof(f4347,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,[],[f3413]) ).
fof(f3413,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,[],[f1465]) ).
fof(f1465,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,[],[f289]) ).
fof(f289,axiom,
! [X18] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X18 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__0__eq) ).
fof(f8128,plain,
spl104_436,
inference(avatar_split_clause,[],[f4344,f8126]) ).
fof(f8126,plain,
( spl104_436
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Nat_OSuc(X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_436])]) ).
fof(f4344,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)
| c_Nat_OSuc(X1) != X0 ),
inference(cnf_transformation,[],[f3411]) ).
fof(f8124,plain,
spl104_435,
inference(avatar_split_clause,[],[f4308,f8122]) ).
fof(f8122,plain,
( spl104_435
<=> ! [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,[spl104_435])]) ).
fof(f4308,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,[],[f2377]) ).
fof(f2377,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,[],[f1438]) ).
fof(f1438,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,[],[f171]) ).
fof(f171,axiom,
! [X5] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X5
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_gr0I) ).
fof(f8120,plain,
( spl104_434
| ~ spl104_371
| ~ spl104_417 ),
inference(avatar_split_clause,[],[f8064,f7929,f7744,f8118]) ).
fof(f8118,plain,
( spl104_434
<=> ! [X2,X3] : sP12(X2,X3,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_434])]) ).
fof(f8064,plain,
( ! [X2,X3] : sP12(X2,X3,c_Int_OPls)
| ~ spl104_371
| ~ spl104_417 ),
inference(resolution,[],[f7930,f7745]) ).
fof(f8116,plain,
spl104_433,
inference(avatar_split_clause,[],[f4261,f8114]) ).
fof(f8114,plain,
( spl104_433
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_433])]) ).
fof(f4261,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2330]) ).
fof(f2330,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1391]) ).
fof(f1391,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> c_Groups_Oone__class_Oone(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f362]) ).
fof(f362,axiom,
! [X4] :
( class_Rings_Olinordered__idom(X4)
=> c_Groups_Oone__class_Oone(X4) = c_Groups_Oabs__class_Oabs(X4,c_Groups_Oone__class_Oone(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__one) ).
fof(f8112,plain,
spl104_432,
inference(avatar_split_clause,[],[f4233,f8110]) ).
fof(f4233,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[],[f2302]) ).
fof(f2302,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(ennf_transformation,[],[f1363]) ).
fof(f1363,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add__abs(X0)
=> c_Groups_Ozero__class_Ozero(X0) = c_Groups_Oabs__class_Oabs(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f368]) ).
fof(f368,axiom,
! [X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> c_Groups_Ozero__class_Ozero(X4) = c_Groups_Oabs__class_Oabs(X4,c_Groups_Ozero__class_Ozero(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__zero) ).
fof(f8108,plain,
spl104_431,
inference(avatar_split_clause,[],[f4232,f8106]) ).
fof(f8106,plain,
( spl104_431
<=> ! [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,[spl104_431])]) ).
fof(f4232,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,[],[f2301]) ).
fof(f2301,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,[],[f1362]) ).
fof(f1362,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,[],[f478]) ).
fof(f478,axiom,
! [X4] :
( class_RealVector_Oreal__normed__vector(X4)
=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X4,c_Groups_Ozero__class_Ozero(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_norm__zero) ).
fof(f8104,plain,
spl104_430,
inference(avatar_split_clause,[],[f4227,f8102]) ).
fof(f8102,plain,
( spl104_430
<=> ! [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,[spl104_430])]) ).
fof(f4227,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,[],[f2298]) ).
fof(f2298,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,[],[f1359]) ).
fof(f1359,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,[],[f481]) ).
fof(f481,axiom,
! [X4] :
( class_RealVector_Oreal__normed__algebra__1(X4)
=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(X4,c_Groups_Oone__class_Oone(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_norm__one) ).
fof(f8100,plain,
spl104_429,
inference(avatar_split_clause,[],[f4200,f8098]) ).
fof(f8098,plain,
( spl104_429
<=> ! [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,[spl104_429])]) ).
fof(f4200,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,[],[f1338]) ).
fof(f1338,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,[],[f775]) ).
fof(f775,axiom,
! [X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X6),X6)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__square) ).
fof(f8096,plain,
spl104_428,
inference(avatar_split_clause,[],[f4199,f8094]) ).
fof(f4199,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X0))),
inference(cnf_transformation,[],[f1337]) ).
fof(f1337,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X0))),
inference(rectify,[],[f351]) ).
fof(f351,axiom,
! [X5] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(X5))),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__of__nat__Suc__gt__zero) ).
fof(f8092,plain,
spl104_427,
inference(avatar_split_clause,[],[f4198,f8090]) ).
fof(f8090,plain,
( spl104_427
<=> ! [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,[spl104_427])]) ).
fof(f4198,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,[],[f1336]) ).
fof(f1336,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f782]) ).
fof(f782,axiom,
! [X5] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X5) = X5,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__mult__1) ).
fof(f8087,plain,
spl104_426,
inference(avatar_split_clause,[],[f4197,f8085]) ).
fof(f4197,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,[],[f1335]) ).
fof(f1335,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
inference(rectify,[],[f621]) ).
fof(f621,axiom,
! [X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X25) = X25,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zmult__1) ).
fof(f8083,plain,
spl104_425,
inference(avatar_split_clause,[],[f4196,f8081]) ).
fof(f8081,plain,
( spl104_425
<=> ! [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,[spl104_425])]) ).
fof(f4196,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,[],[f1334]) ).
fof(f1334,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X0) = X0,
inference(rectify,[],[f781]) ).
fof(f781,axiom,
! [X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),X25) = X25,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__mult__1) ).
fof(f8079,plain,
spl104_424,
inference(avatar_split_clause,[],[f4195,f8077]) ).
fof(f8077,plain,
( spl104_424
<=> ! [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,[spl104_424])]) ).
fof(f4195,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,[],[f1333]) ).
fof(f1333,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(rectify,[],[f784]) ).
fof(f784,axiom,
! [X5] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X5),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X5,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__mult__1__right) ).
fof(f8075,plain,
( spl104_423
| ~ spl104_371
| ~ spl104_416 ),
inference(avatar_split_clause,[],[f8059,f7925,f7744,f8073]) ).
fof(f8073,plain,
( spl104_423
<=> ! [X9,X8] : sP13(X8,X9,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_423])]) ).
fof(f8059,plain,
( ! [X8,X9] : sP13(X8,X9,c_Int_OPls)
| ~ spl104_371
| ~ spl104_416 ),
inference(resolution,[],[f7926,f7745]) ).
fof(f8070,plain,
spl104_422,
inference(avatar_split_clause,[],[f4194,f8068]) ).
fof(f4194,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,[],[f1332]) ).
fof(f1332,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
inference(rectify,[],[f620]) ).
fof(f620,axiom,
! [X25] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X25),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X25,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zmult__1__right) ).
fof(f8052,plain,
( spl104_421
| ~ spl104_343
| ~ spl104_372 ),
inference(avatar_split_clause,[],[f7953,f7748,f7604,f8050]) ).
fof(f8050,plain,
( spl104_421
<=> ! [X3] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_421])]) ).
fof(f7604,plain,
( spl104_343
<=> ! [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,[spl104_343])]) ).
fof(f7953,plain,
( ! [X3] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(X3),X3)
| ~ spl104_343
| ~ spl104_372 ),
inference(superposition,[],[f7605,f7749]) ).
fof(f7605,plain,
( ! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1)
| ~ spl104_343 ),
inference(avatar_component_clause,[],[f7604]) ).
fof(f8036,plain,
( spl104_420
| ~ spl104_345
| ~ spl104_372 ),
inference(avatar_split_clause,[],[f7951,f7748,f7612,f8034]) ).
fof(f8034,plain,
( spl104_420
<=> ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_420])]) ).
fof(f7612,plain,
( spl104_345
<=> ! [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,[spl104_345])]) ).
fof(f7951,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Nat_OSuc(X1))
| ~ spl104_345
| ~ spl104_372 ),
inference(superposition,[],[f7613,f7749]) ).
fof(f7613,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))
| ~ spl104_345 ),
inference(avatar_component_clause,[],[f7612]) ).
fof(f7993,plain,
( spl104_419
| ~ spl104_315
| ~ spl104_370 ),
inference(avatar_split_clause,[],[f7947,f7740,f7478,f7990]) ).
fof(f7478,plain,
( spl104_315
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_315])]) ).
fof(f7947,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Osucc(c_Int_OPls)
| ~ spl104_315
| ~ spl104_370 ),
inference(superposition,[],[f7741,f7479]) ).
fof(f7479,plain,
( ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0
| ~ spl104_315 ),
inference(avatar_component_clause,[],[f7478]) ).
fof(f7945,plain,
( ~ spl104_418
| ~ spl104_358
| ~ spl104_364 ),
inference(avatar_split_clause,[],[f7935,f7714,f7666,f7942]) ).
fof(f7666,plain,
( spl104_358
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_358])]) ).
fof(f7714,plain,
( spl104_364
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_364])]) ).
fof(f7935,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls)
| ~ spl104_358
| ~ spl104_364 ),
inference(superposition,[],[f7667,f7716]) ).
fof(f7716,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl104_364 ),
inference(avatar_component_clause,[],[f7714]) ).
fof(f7667,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Int_OPls)
| ~ spl104_358 ),
inference(avatar_component_clause,[],[f7666]) ).
fof(f7931,plain,
spl104_417,
inference(avatar_split_clause,[],[f5958,f7929]) ).
fof(f5958,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,X2)
| sP12(X0,X1,X2) ),
inference(forward_demodulation,[],[f5300,f4101]) ).
fof(f5300,plain,
! [X2,X0,X1] :
( sP12(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X2) ),
inference(cnf_transformation,[],[f3773]) ).
fof(f7927,plain,
spl104_416,
inference(avatar_split_clause,[],[f5953,f7925]) ).
fof(f5953,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Int_OPls)
| sP13(X0,X1,X2) ),
inference(forward_demodulation,[],[f5294,f4101]) ).
fof(f5294,plain,
! [X2,X0,X1] :
( sP13(X0,X1,X2)
| c_Orderings_Oord__class_Oless(tc_Int_Oint,X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3767]) ).
fof(f7923,plain,
spl104_415,
inference(avatar_split_clause,[],[f5867,f7921]) ).
fof(f5867,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,c_Int_Osucc(X0))
| X0 != X1 ),
inference(forward_demodulation,[],[f4855,f4183]) ).
fof(f4855,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,[],[f3633]) ).
fof(f7919,plain,
spl104_414,
inference(avatar_split_clause,[],[f5848,f7917]) ).
fof(f7917,plain,
( spl104_414
<=> ! [X0,X1] :
( ~ c_Nat__Numeral_Oneg(X1)
| c_Int_OPls = X0
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_414])]) ).
fof(f5848,plain,
! [X0,X1] :
( ~ c_Nat__Numeral_Oneg(X1)
| c_Int_OPls = X0
| ~ sP3(X0,X1) ),
inference(forward_demodulation,[],[f5847,f4155]) ).
fof(f5847,plain,
! [X0,X1] :
( c_Int_OPls = X0
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ sP3(X0,X1) ),
inference(forward_demodulation,[],[f5846,f4101]) ).
fof(f5846,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ sP3(X0,X1) ),
inference(forward_demodulation,[],[f4827,f4155]) ).
fof(f4827,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f3623]) ).
fof(f7915,plain,
spl104_413,
inference(avatar_split_clause,[],[f5845,f7913]) ).
fof(f7913,plain,
( spl104_413
<=> ! [X0,X1] :
( c_Nat__Numeral_Oneg(X1)
| X0 = X1
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_413])]) ).
fof(f5845,plain,
! [X0,X1] :
( c_Nat__Numeral_Oneg(X1)
| X0 = X1
| ~ sP3(X0,X1) ),
inference(forward_demodulation,[],[f4828,f4155]) ).
fof(f4828,plain,
! [X0,X1] :
( X0 = X1
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f3623]) ).
fof(f7911,plain,
spl104_412,
inference(avatar_split_clause,[],[f5844,f7909]) ).
fof(f5844,plain,
! [X0,X1] :
( c_Int_OPls != X0
| ~ c_Nat__Numeral_Oneg(X1)
| sP3(X0,X1) ),
inference(forward_demodulation,[],[f5843,f4101]) ).
fof(f5843,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ c_Nat__Numeral_Oneg(X1)
| sP3(X0,X1) ),
inference(forward_demodulation,[],[f5842,f4155]) ).
fof(f5842,plain,
! [X0,X1] :
( ~ c_Nat__Numeral_Oneg(X1)
| sP3(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) ),
inference(forward_demodulation,[],[f4830,f4155]) ).
fof(f4830,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) ),
inference(cnf_transformation,[],[f3623]) ).
fof(f7907,plain,
spl104_411,
inference(avatar_split_clause,[],[f5841,f7905]) ).
fof(f5841,plain,
! [X0,X1] :
( c_Nat__Numeral_Oneg(X1)
| sP3(X0,X1)
| X0 != X1 ),
inference(forward_demodulation,[],[f4831,f4155]) ).
fof(f4831,plain,
! [X0,X1] :
( sP3(X0,X1)
| X0 != X1
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(cnf_transformation,[],[f3623]) ).
fof(f7903,plain,
spl104_410,
inference(avatar_split_clause,[],[f5835,f7901]) ).
fof(f7901,plain,
( spl104_410
<=> ! [X0,X1] :
( c_Nat__Numeral_Oneg(X1)
| sP3(X1,X0)
| ~ sP4(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_410])]) ).
fof(f5835,plain,
! [X0,X1] :
( c_Nat__Numeral_Oneg(X1)
| sP3(X1,X0)
| ~ sP4(X0,X1) ),
inference(forward_demodulation,[],[f4822,f4155]) ).
fof(f4822,plain,
! [X0,X1] :
( sP3(X1,X0)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1))
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f3620]) ).
fof(f7899,plain,
spl104_409,
inference(avatar_split_clause,[],[f5831,f7897]) ).
fof(f7897,plain,
( spl104_409
<=> ! [X0,X1] :
( c_Nat__Numeral_Oneg(X1)
| sP4(X0,X1)
| ~ sP3(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_409])]) ).
fof(f5831,plain,
! [X0,X1] :
( c_Nat__Numeral_Oneg(X1)
| sP4(X0,X1)
| ~ sP3(X1,X0) ),
inference(forward_demodulation,[],[f4825,f4155]) ).
fof(f4825,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ sP3(X1,X0)
| c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X1)) ),
inference(cnf_transformation,[],[f3620]) ).
fof(f7895,plain,
spl104_408,
inference(avatar_split_clause,[],[f5666,f7893]) ).
fof(f7893,plain,
( spl104_408
<=> ! [X0] :
( ~ c_Nat__Numeral_Oneg(X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_408])]) ).
fof(f5666,plain,
! [X0] :
( ~ c_Nat__Numeral_Oneg(X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ),
inference(forward_demodulation,[],[f4309,f4155]) ).
fof(f4309,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ),
inference(cnf_transformation,[],[f2378]) ).
fof(f2378,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0)
| ~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0)) ),
inference(ennf_transformation,[],[f1439]) ).
fof(f1439,plain,
! [X0] :
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) ),
inference(rectify,[],[f500]) ).
fof(f500,axiom,
! [X48] :
( c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X48))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X48) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_neg__imp__number__of__eq__0) ).
fof(f7891,plain,
spl104_407,
inference(avatar_split_clause,[],[f5308,f7889]) ).
fof(f5308,plain,
! [X2,X0,X1] :
( sP15(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f3779]) ).
fof(f7887,plain,
spl104_406,
inference(avatar_split_clause,[],[f5290,f7885]) ).
fof(f7885,plain,
( spl104_406
<=> ! [X2,X0,X1] :
( sP13(X2,X1,X0)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_406])]) ).
fof(f5290,plain,
! [X2,X0,X1] :
( sP13(X2,X1,X0)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f3761]) ).
fof(f7883,plain,
spl104_405,
inference(avatar_split_clause,[],[f5289,f7881]) ).
fof(f7881,plain,
( spl104_405
<=> ! [X2,X0,X1] :
( sP12(X2,X1,X0)
| ~ sP14(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_405])]) ).
fof(f5289,plain,
! [X2,X0,X1] :
( sP12(X2,X1,X0)
| ~ sP14(X0,X1,X2) ),
inference(cnf_transformation,[],[f3761]) ).
fof(f7879,plain,
spl104_404,
inference(avatar_split_clause,[],[f5282,f7877]) ).
fof(f7877,plain,
( spl104_404
<=> ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ sP11(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_404])]) ).
fof(f5282,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X1)
| ~ sP11(X0,X1,X2) ),
inference(cnf_transformation,[],[f3759]) ).
fof(f7875,plain,
spl104_403,
inference(avatar_split_clause,[],[f4797,f7873]) ).
fof(f7873,plain,
( spl104_403
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_403])]) ).
fof(f4797,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f3606]) ).
fof(f3606,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
& ( 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)) ) ),
inference(flattening,[],[f3605]) ).
fof(f3605,plain,
! [X0,X1] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
| ( X0 != X1
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) )
& ( 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)) ) ),
inference(nnf_transformation,[],[f1778]) ).
fof(f1778,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(X0))
<=> ( X0 = X1
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f242]) ).
fof(f242,axiom,
! [X18,X17] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,c_Nat_OSuc(X18))
<=> ( X17 = X18
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,X17,X18) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__Suc__eq) ).
fof(f7871,plain,
spl104_402,
inference(avatar_split_clause,[],[f4788,f7869]) ).
fof(f7869,plain,
( spl104_402
<=> ! [X0,X1] :
( c_Nat_OSuc(X0) = c_Nat_OSuc(X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_402])]) ).
fof(f4788,plain,
! [X0,X1] :
( c_Nat_OSuc(X0) = c_Nat_OSuc(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f3598]) ).
fof(f3598,plain,
! [X0,X1] :
( ( c_Nat_OSuc(X0) = c_Nat_OSuc(X1)
| X0 != X1 )
& ( X0 = X1
| c_Nat_OSuc(X0) != c_Nat_OSuc(X1) ) ),
inference(nnf_transformation,[],[f1775]) ).
fof(f1775,plain,
! [X0,X1] :
( c_Nat_OSuc(X0) = c_Nat_OSuc(X1)
<=> X0 = X1 ),
inference(rectify,[],[f61]) ).
fof(f61,axiom,
! [X27,X28] :
( c_Nat_OSuc(X28) = c_Nat_OSuc(X27)
<=> X27 = X28 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat_Oinject) ).
fof(f7867,plain,
spl104_401,
inference(avatar_split_clause,[],[f4755,f7865]) ).
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,X0) ),
inference(cnf_transformation,[],[f3566]) ).
fof(f7863,plain,
spl104_400,
inference(avatar_split_clause,[],[f4750,f7861]) ).
fof(f4750,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,[],[f3563]) ).
fof(f7859,plain,
spl104_399,
inference(avatar_split_clause,[],[f4648,f7857]) ).
fof(f7857,plain,
( spl104_399
<=> ! [X0,X1] :
( X0 = X1
| c_Nat_OSuc(X0) != c_Nat_OSuc(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_399])]) ).
fof(f4648,plain,
! [X0,X1] :
( X0 = X1
| c_Nat_OSuc(X0) != c_Nat_OSuc(X1) ),
inference(cnf_transformation,[],[f2572]) ).
fof(f2572,plain,
! [X0,X1] :
( X0 = X1
| c_Nat_OSuc(X0) != c_Nat_OSuc(X1) ),
inference(ennf_transformation,[],[f1685]) ).
fof(f1685,plain,
! [X0,X1] :
( c_Nat_OSuc(X0) = c_Nat_OSuc(X1)
=> X0 = X1 ),
inference(rectify,[],[f60]) ).
fof(f60,axiom,
! [X22,X3] :
( c_Nat_OSuc(X3) = c_Nat_OSuc(X22)
=> X3 = X22 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__inject) ).
fof(f7855,plain,
spl104_398,
inference(avatar_split_clause,[],[f4620,f7853]) ).
fof(f7853,plain,
( spl104_398
<=> ! [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,[spl104_398])]) ).
fof(f4620,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,[],[f2541]) ).
fof(f2541,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,[],[f1660]) ).
fof(f1660,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,[],[f265]) ).
fof(f265,axiom,
! [X22,X3] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X3,X22)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X3,X22) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_termination__basic__simps_I5_J) ).
fof(f7851,plain,
spl104_397,
inference(avatar_split_clause,[],[f4619,f7849]) ).
fof(f7849,plain,
( spl104_397
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_397])]) ).
fof(f4619,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2540]) ).
fof(f2540,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1659]) ).
fof(f1659,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(rectify,[],[f149]) ).
fof(f149,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X6,X5)
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X5 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_gr__implies__not0) ).
fof(f7847,plain,
spl104_396,
inference(avatar_split_clause,[],[f4577,f7845]) ).
fof(f7845,plain,
( spl104_396
<=> ! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| ~ c_SEQ_Oincseq(X1,X0)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_396])]) ).
fof(f4577,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| ~ c_SEQ_Oincseq(X1,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f2504]) ).
fof(f2504,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| ~ c_SEQ_Oincseq(X1,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(flattening,[],[f2503]) ).
fof(f2503,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| ~ c_SEQ_Oincseq(X1,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f1635]) ).
fof(f1635,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> ( c_SEQ_Oincseq(X1,X0)
=> c_SEQ_Omonoseq(X1,X0) ) ),
inference(rectify,[],[f92]) ).
fof(f92,axiom,
! [X33,X4] :
( class_Orderings_Oorder(X4)
=> ( c_SEQ_Oincseq(X4,X33)
=> c_SEQ_Omonoseq(X4,X33) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_incseq__imp__monoseq) ).
fof(f7843,plain,
spl104_395,
inference(avatar_split_clause,[],[f4576,f7841]) ).
fof(f7841,plain,
( spl104_395
<=> ! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| ~ c_SEQ_Odecseq(X1,X0)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_395])]) ).
fof(f4576,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| ~ c_SEQ_Odecseq(X1,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f2502]) ).
fof(f2502,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| ~ c_SEQ_Odecseq(X1,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(flattening,[],[f2501]) ).
fof(f2501,plain,
! [X0,X1] :
( c_SEQ_Omonoseq(X1,X0)
| ~ c_SEQ_Odecseq(X1,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f1634]) ).
fof(f1634,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> ( c_SEQ_Odecseq(X1,X0)
=> c_SEQ_Omonoseq(X1,X0) ) ),
inference(rectify,[],[f93]) ).
fof(f93,axiom,
! [X33,X4] :
( class_Orderings_Oorder(X4)
=> ( c_SEQ_Odecseq(X4,X33)
=> c_SEQ_Omonoseq(X4,X33) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_decseq__imp__monoseq) ).
fof(f7839,plain,
spl104_394,
inference(avatar_split_clause,[],[f4510,f7837]) ).
fof(f4510,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f2443]) ).
fof(f2443,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oabs__class_Oabs(X1,X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f1578]) ).
fof(f1578,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,X0,c_Groups_Oabs__class_Oabs(X1,X0)) ),
inference(rectify,[],[f370]) ).
fof(f370,axiom,
! [X12,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> c_Orderings_Oord__class_Oless__eq(X4,X12,c_Groups_Oabs__class_Oabs(X4,X12)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_abs__ge__self) ).
fof(f7835,plain,
spl104_393,
inference(avatar_split_clause,[],[f4454,f7833]) ).
fof(f7833,plain,
( spl104_393
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(X1,X0))
| ~ c_SEQ_Osubseq(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_393])]) ).
fof(f4454,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(X1,X0))
| ~ c_SEQ_Osubseq(X1) ),
inference(cnf_transformation,[],[f2407]) ).
fof(f2407,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(X1,X0))
| ~ c_SEQ_Osubseq(X1) ),
inference(ennf_transformation,[],[f1544]) ).
fof(f1544,plain,
! [X0,X1] :
( c_SEQ_Osubseq(X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(X1,X0)) ),
inference(rectify,[],[f70]) ).
fof(f70,axiom,
! [X18,X1] :
( c_SEQ_Osubseq(X1)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X18,hAPP(X1,X18)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_seq__suble) ).
fof(f7831,plain,
spl104_392,
inference(avatar_split_clause,[],[f4453,f7829]) ).
fof(f7829,plain,
( spl104_392
<=> ! [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,[spl104_392])]) ).
fof(f4453,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,[],[f1543]) ).
fof(f1543,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,[],[f16]) ).
fof(f16,axiom,
! [X5,X6] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X6)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat__le__linear) ).
fof(f7826,plain,
spl104_391,
inference(avatar_split_clause,[],[f4452,f7824]) ).
fof(f4452,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,[],[f1542]) ).
fof(f1542,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,[],[f442]) ).
fof(f442,axiom,
! [X32,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,X25)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X25,X32) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zle__linear) ).
fof(f7822,plain,
spl104_390,
inference(avatar_split_clause,[],[f4451,f7820]) ).
fof(f7820,plain,
( spl104_390
<=> ! [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,[spl104_390])]) ).
fof(f4451,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,[],[f1541]) ).
fof(f1541,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,[],[f80]) ).
fof(f80,axiom,
! [X32,X25] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X32,X25)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X25,X32) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__le__linear) ).
fof(f7818,plain,
spl104_389,
inference(avatar_split_clause,[],[f4393,f7816]) ).
fof(f7816,plain,
( spl104_389
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X1,X0),c_Nat_OSuc(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_389])]) ).
fof(f4393,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,[],[f1491]) ).
fof(f1491,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,[],[f182]) ).
fof(f182,axiom,
! [X5,X6] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X5),c_Nat_OSuc(X6)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__less__Suc) ).
fof(f7814,plain,
spl104_388,
inference(avatar_split_clause,[],[f4392,f7812]) ).
fof(f7812,plain,
( spl104_388
<=> ! [X0,X1] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_388])]) ).
fof(f4392,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,[],[f1490]) ).
fof(f1490,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,[],[f306]) ).
fof(f306,axiom,
! [X6,X16] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X6))),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__add__Suc1) ).
fof(f7810,plain,
spl104_387,
inference(avatar_split_clause,[],[f4391,f7808]) ).
fof(f4391,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,[],[f1489]) ).
fof(f1489,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,[],[f307]) ).
fof(f307,axiom,
! [X6,X16] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X16,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X16))),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__add__Suc2) ).
fof(f7806,plain,
spl104_386,
inference(avatar_split_clause,[],[f4335,f7804]) ).
fof(f7804,plain,
( spl104_386
<=> ! [X0] :
( c_SEQ_Osubseq(X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK32(X0),sK33(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_386])]) ).
fof(f4335,plain,
! [X0] :
( c_SEQ_Osubseq(X0)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK32(X0),sK33(X0)) ),
inference(cnf_transformation,[],[f3404]) ).
fof(f7802,plain,
spl104_385,
inference(avatar_split_clause,[],[f4280,f7800]) ).
fof(f7800,plain,
( spl104_385
<=> ! [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,[spl104_385])]) ).
fof(f4280,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,[],[f2349]) ).
fof(f2349,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,[],[f1410]) ).
fof(f1410,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,[],[f335]) ).
fof(f335,axiom,
! [X4] :
( class_Rings_Olinordered__semidom(X4)
=> c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Oone__class_Oone(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__le__one) ).
fof(f7798,plain,
spl104_384,
inference(avatar_split_clause,[],[f4279,f7796]) ).
fof(f7796,plain,
( spl104_384
<=> ! [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,[spl104_384])]) ).
fof(f4279,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,[],[f2348]) ).
fof(f2348,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,[],[f1409]) ).
fof(f1409,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,[],[f334]) ).
fof(f334,axiom,
! [X4] :
( class_Rings_Olinordered__semidom(X4)
=> c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),c_Groups_Oone__class_Oone(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__less__one) ).
fof(f7794,plain,
spl104_383,
inference(avatar_split_clause,[],[f4278,f7792]) ).
fof(f7792,plain,
( spl104_383
<=> ! [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,[spl104_383])]) ).
fof(f4278,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,[],[f2347]) ).
fof(f2347,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,[],[f1408]) ).
fof(f1408,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,[],[f336]) ).
fof(f336,axiom,
! [X4] :
( class_Rings_Olinordered__semidom(X4)
=> ~ c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Ozero__class_Ozero(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__one__le__zero) ).
fof(f7790,plain,
spl104_382,
inference(avatar_split_clause,[],[f4277,f7788]) ).
fof(f7788,plain,
( spl104_382
<=> ! [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,[spl104_382])]) ).
fof(f4277,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,[],[f2346]) ).
fof(f2346,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,[],[f1407]) ).
fof(f1407,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,[],[f333]) ).
fof(f333,axiom,
! [X4] :
( class_Rings_Olinordered__semidom(X4)
=> ~ c_Orderings_Oord__class_Oless(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Ozero__class_Ozero(X4)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__one__less__zero) ).
fof(f7786,plain,
spl104_381,
inference(avatar_split_clause,[],[f4275,f7784]) ).
fof(f4275,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OPls)
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f2344]) ).
fof(f2344,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OPls)
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f1405]) ).
fof(f1405,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> c_Groups_Ozero__class_Ozero(X0) = c_Int_Onumber__class_Onumber__of(X0,c_Int_OPls) ),
inference(rectify,[],[f531]) ).
fof(f531,axiom,
! [X4] :
( class_Int_Onumber__ring(X4)
=> c_Groups_Ozero__class_Ozero(X4) = c_Int_Onumber__class_Onumber__of(X4,c_Int_OPls) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_number__of__Pls) ).
fof(f7782,plain,
spl104_380,
inference(avatar_split_clause,[],[f4230,f7780]) ).
fof(f7780,plain,
( spl104_380
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK26(X0))
| ~ class_RealVector_Oreal__normed__algebra(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_380])]) ).
fof(f4230,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK26(X0))
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(cnf_transformation,[],[f3387]) ).
fof(f3387,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))),sK26(X0)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK26(X0)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK26])],[f2300,f3386]) ).
fof(f3386,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),X1))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
=> ( ! [X3,X2] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),sK26(X0)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK26(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f2300,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),X1))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(ennf_transformation,[],[f1361]) ).
fof(f1361,plain,
! [X0] :
( class_RealVector_Oreal__normed__algebra(X0)
=> ? [X1] :
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X0,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X0),X2),X3)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(X0,X2)),c_RealVector_Onorm__class_Onorm(X0,X3))),X1))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X1) ) ),
inference(rectify,[],[f841]) ).
fof(f841,axiom,
! [X4] :
( class_RealVector_Oreal__normed__algebra(X4)
=> ? [X61] :
( ! [X84,X85] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X84),X85)),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(X4,X84)),c_RealVector_Onorm__class_Onorm(X4,X85))),X61))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult_Ononneg__bounded) ).
fof(f7778,plain,
spl104_379,
inference(avatar_split_clause,[],[f4228,f7776]) ).
fof(f7776,plain,
( spl104_379
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK25(X0))
| ~ class_RealVector_Oreal__normed__algebra(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_379])]) ).
fof(f4228,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK25(X0))
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(cnf_transformation,[],[f3385]) ).
fof(f3385,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))),sK25(X0)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK25(X0)) )
| ~ class_RealVector_Oreal__normed__algebra(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25])],[f2299,f3384]) ).
fof(f3384,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))),sK25(X0)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK25(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f2299,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,[],[f1360]) ).
fof(f1360,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,[],[f836]) ).
fof(f836,axiom,
! [X4] :
( class_RealVector_Oreal__normed__algebra(X4)
=> ? [X61] :
( ! [X84,X85] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X84),X85)),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(X4,X84)),c_RealVector_Onorm__class_Onorm(X4,X85))),X61))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X61) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult_Opos__bounded) ).
fof(f7774,plain,
spl104_378,
inference(avatar_split_clause,[],[f4191,f7772]) ).
fof(f4191,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)),
inference(cnf_transformation,[],[f1329]) ).
fof(f1329,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)),
inference(rectify,[],[f341]) ).
fof(f341,axiom,
! [X5] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__of__nat__ge__zero) ).
fof(f7770,plain,
spl104_377,
inference(avatar_split_clause,[],[f4190,f7768]) ).
fof(f7768,plain,
( spl104_377
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_377])]) ).
fof(f4190,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(X0))),
inference(cnf_transformation,[],[f1328]) ).
fof(f1328,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(X0))),
inference(rectify,[],[f384]) ).
fof(f384,axiom,
! [X3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X3,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_RComplete_Onatceiling(X3))),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__natceiling__ge) ).
fof(f7766,plain,
spl104_376,
inference(avatar_split_clause,[],[f4189,f7764]) ).
fof(f7764,plain,
( spl104_376
<=> ! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_376])]) ).
fof(f4189,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f1327]) ).
fof(f1327,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(rectify,[],[f111]) ).
fof(f111,axiom,
! [X5] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(X5),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X5,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__Suc__1) ).
fof(f7762,plain,
spl104_375,
inference(avatar_split_clause,[],[f4187,f7760]) ).
fof(f7760,plain,
( spl104_375
<=> ! [X0] : c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_375])]) ).
fof(f4187,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0)),
inference(cnf_transformation,[],[f1325]) ).
fof(f1325,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0)),
inference(rectify,[],[f436]) ).
fof(f436,axiom,
! [X5] : c_RComplete_Onatfloor(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X5)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X5),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_natfloor__number__of__eq) ).
fof(f7758,plain,
spl104_374,
inference(avatar_split_clause,[],[f4186,f7756]) ).
fof(f7756,plain,
( spl104_374
<=> ! [X0] : c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_374])]) ).
fof(f4186,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0)),
inference(cnf_transformation,[],[f1324]) ).
fof(f1324,plain,
! [X0] : c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X0) = c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X0)),
inference(rectify,[],[f447]) ).
fof(f447,axiom,
! [X5] : c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,X5) = c_RComplete_Onatceiling(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,X5)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_natceiling__number__of__eq) ).
fof(f7754,plain,
spl104_373,
inference(avatar_split_clause,[],[f4185,f7752]) ).
fof(f7750,plain,
spl104_372,
inference(avatar_split_clause,[],[f4184,f7748]) ).
fof(f7746,plain,
( spl104_371
| ~ spl104_352 ),
inference(avatar_split_clause,[],[f7696,f7640,f7744]) ).
fof(f7640,plain,
( spl104_352
<=> ! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_352])]) ).
fof(f7696,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,X0)
| ~ spl104_352 ),
inference(equality_resolution,[],[f7641]) ).
fof(f7641,plain,
( ! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) )
| ~ spl104_352 ),
inference(avatar_component_clause,[],[f7640]) ).
fof(f7742,plain,
spl104_370,
inference(avatar_split_clause,[],[f4183,f7740]) ).
fof(f7738,plain,
spl104_369,
inference(avatar_split_clause,[],[f4182,f7736]) ).
fof(f7736,plain,
( spl104_369
<=> ! [X0] : c_Int_Opred(X0) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_369])]) ).
fof(f7734,plain,
spl104_368,
inference(avatar_split_clause,[],[f4181,f7732]) ).
fof(f4181,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,[],[f1319]) ).
fof(f1319,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,[],[f128]) ).
fof(f128,axiom,
! [X5] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__0__eq__0) ).
fof(f7730,plain,
spl104_367,
inference(avatar_split_clause,[],[f4179,f7728]) ).
fof(f7728,plain,
( spl104_367
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_367])]) ).
fof(f4179,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0),
inference(cnf_transformation,[],[f1317]) ).
fof(f1317,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0),
inference(rectify,[],[f628]) ).
fof(f628,axiom,
! [X32] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X32),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__Pls) ).
fof(f7726,plain,
spl104_366,
inference(avatar_split_clause,[],[f4177,f7724]) ).
fof(f4177,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f1315]) ).
fof(f1315,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(rectify,[],[f347]) ).
fof(f347,axiom,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__real__of__nat__less__zero) ).
fof(f7722,plain,
spl104_365,
inference(avatar_split_clause,[],[f4128,f7719]) ).
fof(f7719,plain,
( spl104_365
<=> c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_365])]) ).
fof(f4128,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f345]) ).
fof(f345,axiom,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__of__nat__zero) ).
fof(f7717,plain,
spl104_364,
inference(avatar_split_clause,[],[f4126,f7714]) ).
fof(f4126,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f703]) ).
fof(f703,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_transfer__int__nat__numerals_I2_J) ).
fof(f7712,plain,
spl104_363,
inference(avatar_split_clause,[],[f4125,f7709]) ).
fof(f4125,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f325]) ).
fof(f325,axiom,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__of__nat__1) ).
fof(f7704,plain,
( spl104_362
| ~ spl104_351 ),
inference(avatar_split_clause,[],[f7695,f7636,f7702]) ).
fof(f7702,plain,
( spl104_362
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_362])]) ).
fof(f7636,plain,
( spl104_351
<=> ! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_351])]) ).
fof(f7695,plain,
( ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X0,X0)
| ~ spl104_351 ),
inference(equality_resolution,[],[f7637]) ).
fof(f7637,plain,
( ! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) )
| ~ spl104_351 ),
inference(avatar_component_clause,[],[f7636]) ).
fof(f7681,plain,
( ~ spl104_361
| ~ spl104_235
| ~ spl104_311 ),
inference(avatar_split_clause,[],[f7538,f7460,f7147,f7678]) ).
fof(f7678,plain,
( spl104_361
<=> 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,[spl104_361])]) ).
fof(f7538,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))
| ~ spl104_235
| ~ spl104_311 ),
inference(superposition,[],[f7148,f7462]) ).
fof(f7676,plain,
spl104_360,
inference(avatar_split_clause,[],[f5649,f7674]) ).
fof(f7674,plain,
( spl104_360
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_360])]) ).
fof(f5649,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(forward_demodulation,[],[f4192,f4101]) ).
fof(f4192,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f1330]) ).
fof(f1330,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(rectify,[],[f679]) ).
fof(f679,axiom,
! [X5] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__zle__int) ).
fof(f7672,plain,
spl104_359,
inference(avatar_split_clause,[],[f5648,f7670]) ).
fof(f7670,plain,
( spl104_359
<=> ! [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,[spl104_359])]) ).
fof(f5648,plain,
! [X0] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(forward_demodulation,[],[f4188,f4119]) ).
fof(f4188,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,[],[f1326]) ).
fof(f1326,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,[],[f972]) ).
fof(f972,axiom,
! [X6] : c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X6,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X6,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_div__1) ).
fof(f7668,plain,
spl104_358,
inference(avatar_split_clause,[],[f5646,f7666]) ).
fof(f5646,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Int_OPls),
inference(forward_demodulation,[],[f4178,f4101]) ).
fof(f4178,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f1316]) ).
fof(f1316,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(rectify,[],[f680]) ).
fof(f680,axiom,
! [X14] : ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_int__less__0__conv) ).
fof(f7664,plain,
spl104_357,
inference(avatar_split_clause,[],[f5640,f7661]) ).
fof(f7661,plain,
( spl104_357
<=> c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_357])]) ).
fof(f5640,plain,
c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f4129,f4101]) ).
fof(f4129,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f639]) ).
fof(f639,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_transfer__int__nat__numerals_I1_J) ).
fof(f7659,plain,
( spl104_356
| ~ spl104_239
| ~ spl104_311 ),
inference(avatar_split_clause,[],[f7537,f7460,f7163,f7656]) ).
fof(f7656,plain,
( spl104_356
<=> 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,[spl104_356])]) ).
fof(f7163,plain,
( spl104_239
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_239])]) ).
fof(f7537,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))
| ~ spl104_239
| ~ spl104_311 ),
inference(superposition,[],[f7164,f7462]) ).
fof(f7164,plain,
( ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0))
| ~ spl104_239 ),
inference(avatar_component_clause,[],[f7163]) ).
fof(f7654,plain,
spl104_355,
inference(avatar_split_clause,[],[f5435,f7652]) ).
fof(f7652,plain,
( spl104_355
<=> ! [X0,X3,X2,X1] :
( sP23(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_355])]) ).
fof(f5435,plain,
! [X2,X3,X0,X1] :
( sP23(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3381]) ).
fof(f3381,plain,
! [X0,X1,X2,X3] :
( sP23(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f3087,f3380,f3379]) ).
fof(f3380,plain,
! [X1,X3,X0,X2] :
( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))
<=> sP22(X2,X0,X3,X1) )
| ~ sP23(X1,X3,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).
fof(f3087,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,[],[f2131]) ).
fof(f2131,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,[],[f660]) ).
fof(f660,axiom,
! [X7,X8,X9,X4] :
( class_Rings_Olinordered__ring__strict(X4)
=> ( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X9),X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X7),X8))
<=> ( ( c_Orderings_Oord__class_Oless(X4,X7,X9)
& c_Orderings_Oord__class_Oless(X4,X8,c_Groups_Ozero__class_Ozero(X4)) )
| ( c_Orderings_Oord__class_Oless(X4,X9,X7)
& c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X8) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__less__cancel__right__disj) ).
fof(f7650,plain,
spl104_354,
inference(avatar_split_clause,[],[f5426,f7648]) ).
fof(f7648,plain,
( spl104_354
<=> ! [X0,X3,X2,X1] :
( sP21(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_354])]) ).
fof(f5426,plain,
! [X2,X3,X0,X1] :
( sP21(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f3378]) ).
fof(f3378,plain,
! [X0,X1,X2,X3] :
( sP21(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f3086,f3377,f3376]) ).
fof(f3377,plain,
! [X2,X3,X0,X1] :
( ( c_Orderings_Oord__class_Oless(X3,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))
<=> sP20(X1,X0,X3,X2) )
| ~ sP21(X2,X3,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
fof(f3086,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,[],[f2130]) ).
fof(f2130,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,[],[f661]) ).
fof(f661,axiom,
! [X7,X9,X8,X4] :
( class_Rings_Olinordered__ring__strict(X4)
=> ( c_Orderings_Oord__class_Oless(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X8),X9),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X8),X7))
<=> ( ( c_Orderings_Oord__class_Oless(X4,X7,X9)
& c_Orderings_Oord__class_Oless(X4,X8,c_Groups_Ozero__class_Ozero(X4)) )
| ( c_Orderings_Oord__class_Oless(X4,X9,X7)
& c_Orderings_Oord__class_Oless(X4,c_Groups_Ozero__class_Ozero(X4),X8) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__less__cancel__left__disj) ).
fof(f7646,plain,
spl104_353,
inference(avatar_split_clause,[],[f4773,f7644]) ).
fof(f7644,plain,
( spl104_353
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_353])]) ).
fof(f4773,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f3581]) ).
fof(f3581,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,[],[f3580]) ).
fof(f3580,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,[],[f1768]) ).
fof(f1768,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,[],[f253]) ).
fof(f253,axiom,
! [X26,X23] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X23,X26)
<=> ( X23 = X26
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X23,X26) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__eq__real__def) ).
fof(f7642,plain,
spl104_352,
inference(avatar_split_clause,[],[f4756,f7640]) ).
fof(f4756,plain,
! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X1,X0) ),
inference(cnf_transformation,[],[f3566]) ).
fof(f7638,plain,
spl104_351,
inference(avatar_split_clause,[],[f4751,f7636]) ).
fof(f4751,plain,
! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,X1,X0) ),
inference(cnf_transformation,[],[f3563]) ).
fof(f7634,plain,
spl104_350,
inference(avatar_split_clause,[],[f4617,f7632]) ).
fof(f7632,plain,
( spl104_350
<=> ! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_350])]) ).
fof(f4617,plain,
! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(cnf_transformation,[],[f2538]) ).
fof(f2538,plain,
! [X0,X1] :
( X0 != X1
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0) ),
inference(ennf_transformation,[],[f1657]) ).
fof(f1657,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X1,X0)
=> X0 != X1 ),
inference(rectify,[],[f150]) ).
fof(f150,axiom,
! [X6,X5] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X6)
=> X5 != X6 ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__not__refl2) ).
fof(f7630,plain,
spl104_349,
inference(avatar_split_clause,[],[f4603,f7628]) ).
fof(f7628,plain,
( spl104_349
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_349])]) ).
fof(f4603,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f2521]) ).
fof(f2521,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0)
| X0 != X1 ),
inference(ennf_transformation,[],[f1646]) ).
fof(f1646,plain,
! [X0,X1] :
( X0 = X1
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,X0) ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X5,X6] :
( X5 = X6
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X6,X5) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_eq__imp__le) ).
fof(f7626,plain,
spl104_348,
inference(avatar_split_clause,[],[f4390,f7624]) ).
fof(f7624,plain,
( spl104_348
<=> ! [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,[spl104_348])]) ).
fof(f4390,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,[],[f1488]) ).
fof(f1488,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,[],[f240]) ).
fof(f240,axiom,
! [X5,X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X5),X6),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__le__self) ).
fof(f7622,plain,
spl104_347,
inference(avatar_split_clause,[],[f4389,f7620]) ).
fof(f7620,plain,
( spl104_347
<=> ! [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,[spl104_347])]) ).
fof(f4389,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,[],[f1487]) ).
fof(f1487,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,[],[f973]) ).
fof(f973,axiom,
! [X5,X6] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Divides_Odiv__class_Odiv(tc_Nat_Onat,X6,X5),X6),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_div__le__dividend) ).
fof(f7618,plain,
spl104_346,
inference(avatar_split_clause,[],[f4388,f7616]) ).
fof(f4388,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,[],[f1486]) ).
fof(f1486,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,[],[f37]) ).
fof(f37,axiom,
! [X6,X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,X5)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__add2) ).
fof(f7614,plain,
spl104_345,
inference(avatar_split_clause,[],[f4387,f7612]) ).
fof(f4387,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,[],[f1485]) ).
fof(f1485,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,[],[f36]) ).
fof(f36,axiom,
! [X6,X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X5,X6)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__add1) ).
fof(f7610,plain,
spl104_344,
inference(avatar_split_clause,[],[f4386,f7608]) ).
fof(f4386,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,[],[f1484]) ).
fof(f1484,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X0),
inference(rectify,[],[f257]) ).
fof(f257,axiom,
! [X16,X15] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X15,X16),X16),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__add__less2) ).
fof(f7606,plain,
spl104_343,
inference(avatar_split_clause,[],[f4385,f7604]) ).
fof(f4385,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,[],[f1483]) ).
fof(f1483,plain,
! [X0,X1] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X1,X0),X1),
inference(rectify,[],[f256]) ).
fof(f256,axiom,
! [X15,X16] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X16,X15),X16),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__add__less1) ).
fof(f7602,plain,
spl104_342,
inference(avatar_split_clause,[],[f4286,f7600]) ).
fof(f7600,plain,
( spl104_342
<=> ! [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,[spl104_342])]) ).
fof(f4286,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(cnf_transformation,[],[f2355]) ).
fof(f2355,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(ennf_transformation,[],[f1416]) ).
fof(f1416,plain,
! [X0] :
( class_Rings_Ozero__neq__one(X0)
=> c_Groups_Oone__class_Oone(X0) != c_Groups_Ozero__class_Ozero(X0) ),
inference(rectify,[],[f355]) ).
fof(f355,axiom,
! [X4] :
( class_Rings_Ozero__neq__one(X4)
=> c_Groups_Oone__class_Oone(X4) != c_Groups_Ozero__class_Ozero(X4) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__neq__one) ).
fof(f7598,plain,
spl104_341,
inference(avatar_split_clause,[],[f4176,f7596]) ).
fof(f7596,plain,
( spl104_341
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(X0)),v_r) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_341])]) ).
fof(f4176,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(X0)),v_r),
inference(cnf_transformation,[],[f1314]) ).
fof(f1314,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(X0)),v_r),
inference(rectify,[],[f414]) ).
fof(f414,axiom,
! [X30] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_g____(X30)),v_r),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_g_I1_J) ).
fof(f7594,plain,
spl104_340,
inference(avatar_split_clause,[],[f4175,f7592]) ).
fof(f7592,plain,
( spl104_340
<=> ! [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,[spl104_340])]) ).
fof(f4175,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f1313]) ).
fof(f1313,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0,
inference(rectify,[],[f285]) ).
fof(f285,axiom,
! [X5] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5) = X5,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_plus__nat_Oadd__0) ).
fof(f7590,plain,
spl104_339,
inference(avatar_split_clause,[],[f4174,f7588]) ).
fof(f7588,plain,
( spl104_339
<=> ! [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,[spl104_339])]) ).
fof(f4174,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f1312]) ).
fof(f1312,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f286]) ).
fof(f286,axiom,
! [X6] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X6,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Nat_Oadd__0__right) ).
fof(f7586,plain,
spl104_338,
inference(avatar_split_clause,[],[f4171,f7584]) ).
fof(f7584,plain,
( spl104_338
<=> ! [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,[spl104_338])]) ).
fof(f4171,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f1309]) ).
fof(f1309,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f133]) ).
fof(f133,axiom,
! [X6] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X6,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_minus__nat_Odiff__0) ).
fof(f7582,plain,
spl104_337,
inference(avatar_split_clause,[],[f4170,f7580]) ).
fof(f7580,plain,
( spl104_337
<=> ! [X0] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_337])]) ).
fof(f4170,plain,
! [X0] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0,
inference(cnf_transformation,[],[f1308]) ).
fof(f1308,plain,
! [X0] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0,
inference(rectify,[],[f445]) ).
fof(f445,axiom,
! [X5] : c_RComplete_Onatfloor(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5)) = X5,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_natfloor__real__of__nat) ).
fof(f7578,plain,
spl104_336,
inference(avatar_split_clause,[],[f4169,f7576]) ).
fof(f7576,plain,
( spl104_336
<=> ! [X0] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_336])]) ).
fof(f4169,plain,
! [X0] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0,
inference(cnf_transformation,[],[f1307]) ).
fof(f1307,plain,
! [X0] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X0)) = X0,
inference(rectify,[],[f366]) ).
fof(f366,axiom,
! [X5] : c_RComplete_Onatceiling(hAPP(c_RealDef_Oreal(tc_Nat_Onat),X5)) = X5,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_natceiling__real__of__nat) ).
fof(f7574,plain,
( spl104_335
| ~ spl104_329 ),
inference(avatar_split_clause,[],[f7554,f7534,f7572]) ).
fof(f7572,plain,
( spl104_335
<=> ! [X0] : sP2(X0,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_335])]) ).
fof(f7534,plain,
( spl104_329
<=> ! [X0,X1] :
( c_Int_OPls != X1
| sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_329])]) ).
fof(f7554,plain,
( ! [X0] : sP2(X0,c_Int_OPls)
| ~ spl104_329 ),
inference(equality_resolution,[],[f7535]) ).
fof(f7535,plain,
( ! [X0,X1] :
( c_Int_OPls != X1
| sP2(X0,X1) )
| ~ spl104_329 ),
inference(avatar_component_clause,[],[f7534]) ).
fof(f7570,plain,
spl104_334,
inference(avatar_split_clause,[],[f4168,f7568]) ).
fof(f7568,plain,
( spl104_334
<=> ! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_334])]) ).
fof(f4168,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(cnf_transformation,[],[f1306]) ).
fof(f1306,plain,
! [X0] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X0) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X0),
inference(rectify,[],[f473]) ).
fof(f473,axiom,
! [X53] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,X53) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,X53),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__norm__def) ).
fof(f7566,plain,
spl104_333,
inference(avatar_split_clause,[],[f4167,f7564]) ).
fof(f7564,plain,
( spl104_333
<=> ! [X0] : c_Complex_Ocis(X0) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_333])]) ).
fof(f4167,plain,
! [X0] : c_Complex_Ocis(X0) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0),
inference(cnf_transformation,[],[f1305]) ).
fof(f1305,plain,
! [X0] : c_Complex_Ocis(X0) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X0),
inference(rectify,[],[f984]) ).
fof(f984,axiom,
! [X12] : c_Complex_Ocis(X12) = c_Complex_Orcis(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),X12),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_cis__rcis__eq) ).
fof(f7562,plain,
spl104_332,
inference(avatar_split_clause,[],[f4166,f7560]) ).
fof(f7560,plain,
( spl104_332
<=> ! [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,[spl104_332])]) ).
fof(f4166,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1304]) ).
fof(f1304,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f135]) ).
fof(f135,axiom,
! [X6] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,X6,X6),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__self__eq__0) ).
fof(f7558,plain,
spl104_331,
inference(avatar_split_clause,[],[f4165,f7556]) ).
fof(f7556,plain,
( spl104_331
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_331])]) ).
fof(f4165,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0),
inference(cnf_transformation,[],[f1303]) ).
fof(f1303,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X0),
inference(rectify,[],[f983]) ).
fof(f983,axiom,
! [X12] : c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),X12),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_rcis__zero__mod) ).
fof(f7545,plain,
( ~ spl104_330
| ~ spl104_232
| ~ spl104_311 ),
inference(avatar_split_clause,[],[f7539,f7460,f7135,f7542]) ).
fof(f7542,plain,
( spl104_330
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_330])]) ).
fof(f7135,plain,
( spl104_232
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_232])]) ).
fof(f7539,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ spl104_232
| ~ spl104_311 ),
inference(superposition,[],[f7136,f7462]) ).
fof(f7136,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0)
| ~ spl104_232 ),
inference(avatar_component_clause,[],[f7135]) ).
fof(f7536,plain,
spl104_329,
inference(avatar_split_clause,[],[f5821,f7534]) ).
fof(f5821,plain,
! [X0,X1] :
( c_Int_OPls != X1
| sP2(X0,X1) ),
inference(forward_demodulation,[],[f4811,f4101]) ).
fof(f4811,plain,
! [X0,X1] :
( sP2(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ),
inference(cnf_transformation,[],[f3614]) ).
fof(f7532,plain,
spl104_328,
inference(avatar_split_clause,[],[f5679,f7530]) ).
fof(f7530,plain,
( spl104_328
<=> ! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Nat__Numeral_Oneg(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_328])]) ).
fof(f5679,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| ~ c_Nat__Numeral_Oneg(X0) ),
inference(forward_demodulation,[],[f4337,f4101]) ).
fof(f4337,plain,
! [X0] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Nat__Numeral_Oneg(X0) ),
inference(cnf_transformation,[],[f3405]) ).
fof(f3405,plain,
! [X0] :
( ( c_Nat__Numeral_Oneg(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Nat__Numeral_Oneg(X0) ) ),
inference(nnf_transformation,[],[f1460]) ).
fof(f1460,plain,
! [X0] :
( c_Nat__Numeral_Oneg(X0)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rectify,[],[f499]) ).
fof(f499,axiom,
! [X65] :
( c_Nat__Numeral_Oneg(X65)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,X65,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_neg__def) ).
fof(f7528,plain,
spl104_327,
inference(avatar_split_clause,[],[f5678,f7526]) ).
fof(f5678,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Int_OPls)
| c_Nat__Numeral_Oneg(X0) ),
inference(forward_demodulation,[],[f4338,f4101]) ).
fof(f4338,plain,
! [X0] :
( c_Nat__Numeral_Oneg(X0)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(cnf_transformation,[],[f3405]) ).
fof(f7524,plain,
spl104_326,
inference(avatar_split_clause,[],[f5677,f7522]) ).
fof(f7522,plain,
( spl104_326
<=> ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| c_Nat__Numeral_Oneg(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_326])]) ).
fof(f5677,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| c_Nat__Numeral_Oneg(X0) ),
inference(forward_demodulation,[],[f4330,f4101]) ).
fof(f4330,plain,
! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Nat__Numeral_Oneg(X0) ),
inference(cnf_transformation,[],[f3396]) ).
fof(f3396,plain,
! [X0] :
( ( ~ c_Nat__Numeral_Oneg(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0)
| c_Nat__Numeral_Oneg(X0) ) ),
inference(nnf_transformation,[],[f1457]) ).
fof(f1457,plain,
! [X0] :
( ~ c_Nat__Numeral_Oneg(X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(rectify,[],[f498]) ).
fof(f498,axiom,
! [X23] :
( ~ c_Nat__Numeral_Oneg(X23)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X23) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__neg__eq__ge__0) ).
fof(f7520,plain,
spl104_325,
inference(avatar_split_clause,[],[f5676,f7518]) ).
fof(f5676,plain,
! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,X0)
| ~ c_Nat__Numeral_Oneg(X0) ),
inference(forward_demodulation,[],[f4331,f4101]) ).
fof(f4331,plain,
! [X0] :
( ~ c_Nat__Numeral_Oneg(X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f3396]) ).
fof(f7516,plain,
spl104_324,
inference(avatar_split_clause,[],[f5647,f7514]) ).
fof(f5647,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Int_OPls,X0),
inference(forward_demodulation,[],[f4180,f4101]) ).
fof(f4180,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,[],[f1318]) ).
fof(f1318,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,[],[f957]) ).
fof(f957,axiom,
! [X11] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Odiv(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X11),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zdiv__zero) ).
fof(f7512,plain,
spl104_323,
inference(avatar_split_clause,[],[f5009,f7510]) ).
fof(f7510,plain,
( spl104_323
<=> ! [X2,X0,X1] :
( sP10(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_323])]) ).
fof(f5009,plain,
! [X2,X0,X1] :
( sP10(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3359]) ).
fof(f3359,plain,
! [X0,X1,X2] :
( sP10(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f2722,f3358,f3357]) ).
fof(f3358,plain,
! [X1,X2,X0] :
( ( c_Orderings_Oord__class_Oless__eq(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),c_Groups_Ozero__class_Ozero(X2))
<=> sP9(X0,X2,X1) )
| ~ sP10(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f2722,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,[],[f1873]) ).
fof(f1873,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,[],[f644]) ).
fof(f644,axiom,
! [X7,X9,X4] :
( class_Rings_Olinordered__ring__strict(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X9),X7),c_Groups_Ozero__class_Ozero(X4))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X7)
& c_Orderings_Oord__class_Oless__eq(X4,X9,c_Groups_Ozero__class_Ozero(X4)) )
| ( c_Orderings_Oord__class_Oless__eq(X4,X7,c_Groups_Ozero__class_Ozero(X4))
& c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X9) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_mult__le__0__iff) ).
fof(f7508,plain,
spl104_322,
inference(avatar_split_clause,[],[f5000,f7506]) ).
fof(f7506,plain,
( spl104_322
<=> ! [X2,X0,X1] :
( sP8(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_322])]) ).
fof(f5000,plain,
! [X2,X0,X1] :
( sP8(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f3356]) ).
fof(f3356,plain,
! [X0,X1,X2] :
( sP8(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f2721,f3355,f3354]) ).
fof(f3355,plain,
! [X1,X0,X2] :
( ( c_Orderings_Oord__class_Oless__eq(X2,c_Groups_Ozero__class_Ozero(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))
<=> sP7(X2,X0,X1) )
| ~ sP8(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f2721,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,[],[f1872]) ).
fof(f1872,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,[],[f643]) ).
fof(f643,axiom,
! [X7,X9,X4] :
( class_Rings_Olinordered__ring__strict(X4)
=> ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X9),X7))
<=> ( ( c_Orderings_Oord__class_Oless__eq(X4,X7,c_Groups_Ozero__class_Ozero(X4))
& c_Orderings_Oord__class_Oless__eq(X4,X9,c_Groups_Ozero__class_Ozero(X4)) )
| ( c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X7)
& c_Orderings_Oord__class_Oless__eq(X4,c_Groups_Ozero__class_Ozero(X4),X9) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__le__mult__iff) ).
fof(f7504,plain,
spl104_321,
inference(avatar_split_clause,[],[f4575,f7502]) ).
fof(f7502,plain,
( spl104_321
<=> ! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_321])]) ).
fof(f4575,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f2500]) ).
fof(f2500,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f1633]) ).
fof(f1633,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> class_Orderings_Oorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f1015]) ).
fof(f1015,axiom,
! [X100,X99] :
( class_Orderings_Oorder(X99)
=> class_Orderings_Oorder(tc_fun(X100,X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_fun__Orderings_Oorder) ).
fof(f7500,plain,
spl104_320,
inference(avatar_split_clause,[],[f4574,f7498]) ).
fof(f7498,plain,
( spl104_320
<=> ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_320])]) ).
fof(f4574,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f2499]) ).
fof(f2499,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f1632]) ).
fof(f1632,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,X0,X0) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X3,X4] :
( class_Orderings_Opreorder(X4)
=> c_Orderings_Oord__class_Oless__eq(X4,X3,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_order__refl) ).
fof(f7496,plain,
spl104_319,
inference(avatar_split_clause,[],[f4573,f7494]) ).
fof(f7494,plain,
( spl104_319
<=> ! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_319])]) ).
fof(f4573,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f2498]) ).
fof(f2498,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f1631]) ).
fof(f1631,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> class_Orderings_Opreorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f1014]) ).
fof(f1014,axiom,
! [X100,X99] :
( class_Orderings_Opreorder(X99)
=> class_Orderings_Opreorder(tc_fun(X100,X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_fun__Orderings_Opreorder) ).
fof(f7492,plain,
spl104_318,
inference(avatar_split_clause,[],[f4572,f7490]) ).
fof(f7490,plain,
( spl104_318
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_318])]) ).
fof(f4572,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f2497]) ).
fof(f2497,plain,
! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless(X1,X0,X0)
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f1630]) ).
fof(f1630,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> ~ c_Orderings_Oord__class_Oless(X1,X0,X0) ),
inference(rectify,[],[f123]) ).
fof(f123,axiom,
! [X3,X4] :
( class_Orderings_Opreorder(X4)
=> ~ c_Orderings_Oord__class_Oless(X4,X3,X3) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_order__less__irrefl) ).
fof(f7488,plain,
spl104_317,
inference(avatar_split_clause,[],[f4571,f7486]) ).
fof(f7486,plain,
( spl104_317
<=> ! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_317])]) ).
fof(f4571,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(cnf_transformation,[],[f2496]) ).
fof(f2496,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(ennf_transformation,[],[f1629]) ).
fof(f1629,plain,
! [X0,X1] :
( class_Orderings_Oord(X1)
=> class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(rectify,[],[f1016]) ).
fof(f1016,axiom,
! [X100,X99] :
( class_Orderings_Oord(X99)
=> class_Orderings_Oord(tc_fun(X100,X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_fun__Orderings_Oord) ).
fof(f7484,plain,
spl104_316,
inference(avatar_split_clause,[],[f4162,f7482]) ).
fof(f7482,plain,
( spl104_316
<=> ! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_316])]) ).
fof(f4162,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,[],[f1300]) ).
fof(f1300,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X0)),
inference(rectify,[],[f110]) ).
fof(f110,axiom,
! [X5] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(X5)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zero__less__Suc) ).
fof(f7480,plain,
spl104_315,
inference(avatar_split_clause,[],[f4161,f7478]) ).
fof(f4161,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(cnf_transformation,[],[f1299]) ).
fof(f1299,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X0) = X0,
inference(rectify,[],[f526]) ).
fof(f526,axiom,
! [X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,X14) = X14,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__Pls) ).
fof(f7476,plain,
spl104_314,
inference(avatar_split_clause,[],[f4160,f7474]) ).
fof(f7474,plain,
( spl104_314
<=> ! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_314])]) ).
fof(f4160,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(cnf_transformation,[],[f1298]) ).
fof(f1298,plain,
! [X0] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(rectify,[],[f527]) ).
fof(f527,axiom,
! [X14] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,X14,c_Int_OPls) = X14,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_add__Pls__right) ).
fof(f7472,plain,
spl104_313,
inference(avatar_split_clause,[],[f4159,f7470]) ).
fof(f7470,plain,
( spl104_313
<=> ! [X0] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_313])]) ).
fof(f4159,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(cnf_transformation,[],[f1297]) ).
fof(f1297,plain,
! [X0] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(rectify,[],[f530]) ).
fof(f530,axiom,
! [X14] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,X14,c_Int_OPls) = X14,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_diff__bin__simps_I1_J) ).
fof(f7468,plain,
spl104_312,
inference(avatar_split_clause,[],[f4121,f7465]) ).
fof(f7465,plain,
( spl104_312
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_312])]) ).
fof(f4121,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
inference(cnf_transformation,[],[f409]) ).
fof(f409,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_w____),v_r),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_wr) ).
fof(f7463,plain,
spl104_311,
inference(avatar_split_clause,[],[f4119,f7460]) ).
fof(f7458,plain,
spl104_310,
inference(avatar_split_clause,[],[f4117,f7455]) ).
fof(f4117,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
inference(cnf_transformation,[],[f536]) ).
fof(f536,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_semiring__norm_I113_J) ).
fof(f7453,plain,
spl104_309,
inference(avatar_split_clause,[],[f4116,f7450]) ).
fof(f7450,plain,
( spl104_309
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_309])]) ).
fof(f4116,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f448]) ).
fof(f448,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_natfloor__zero) ).
fof(f7448,plain,
spl104_308,
inference(avatar_split_clause,[],[f4115,f7445]) ).
fof(f7445,plain,
( spl104_308
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_308])]) ).
fof(f4115,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f363]) ).
fof(f363,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_natceiling__zero) ).
fof(f7443,plain,
spl104_307,
inference(avatar_split_clause,[],[f4113,f7440]) ).
fof(f7440,plain,
( spl104_307
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_307])]) ).
fof(f4113,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f451]) ).
fof(f451,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_natfloor__one) ).
fof(f7438,plain,
spl104_306,
inference(avatar_split_clause,[],[f4112,f7435]) ).
fof(f7435,plain,
( spl104_306
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_306])]) ).
fof(f4112,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f385]) ).
fof(f385,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_natceiling__one) ).
fof(f7433,plain,
spl104_305,
inference(avatar_split_clause,[],[f4111,f7430]) ).
fof(f7430,plain,
( spl104_305
<=> c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_305])]) ).
fof(f4111,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(cnf_transformation,[],[f858]) ).
fof(f858,axiom,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_cis__zero) ).
fof(f7428,plain,
spl104_304,
inference(avatar_split_clause,[],[f4110,f7425]) ).
fof(f7425,plain,
( spl104_304
<=> c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_304])]) ).
fof(f4110,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(cnf_transformation,[],[f553]) ).
fof(f553,axiom,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_expi__zero) ).
fof(f7423,plain,
spl104_303,
inference(avatar_split_clause,[],[f5636,f7420]) ).
fof(f7420,plain,
( spl104_303
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_303])]) ).
fof(f5636,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(forward_demodulation,[],[f4122,f4101]) ).
fof(f4122,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,[],[f489]) ).
fof(f489,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(f7418,plain,
spl104_302,
inference(avatar_split_clause,[],[f5635,f7415]) ).
fof(f7415,plain,
( spl104_302
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_302])]) ).
fof(f5635,plain,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(forward_demodulation,[],[f4120,f4101]) ).
fof(f4120,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,[],[f424]) ).
fof(f424,axiom,
c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_int__0__less__1) ).
fof(f7413,plain,
spl104_301,
inference(avatar_split_clause,[],[f4601,f7411]) ).
fof(f7411,plain,
( spl104_301
<=> ! [X0,X1] :
( sP1(X1,X0)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_301])]) ).
fof(f4601,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f3344]) ).
fof(f3344,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(definition_folding,[],[f2518,f3343,f3342]) ).
fof(f2518,plain,
! [X0,X1] :
( ( c_SEQ_Omonoseq(X1,X0)
<=> ( ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3) )
| ! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X0,X5))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5) ) ) )
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f1644]) ).
fof(f1644,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> ( c_SEQ_Omonoseq(X1,X0)
<=> ( ! [X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X2,X3)
=> c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X3),hAPP(X0,X2)) )
| ! [X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X4,X5)
=> c_Orderings_Oord__class_Oless__eq(X1,hAPP(X0,X4),hAPP(X0,X5)) ) ) ) ),
inference(rectify,[],[f84]) ).
fof(f84,axiom,
! [X33,X4] :
( class_Orderings_Oorder(X4)
=> ( c_SEQ_Omonoseq(X4,X33)
<=> ( ! [X34,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X30)
=> c_Orderings_Oord__class_Oless__eq(X4,hAPP(X33,X30),hAPP(X33,X34)) )
| ! [X34,X30] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X34,X30)
=> c_Orderings_Oord__class_Oless__eq(X4,hAPP(X33,X34),hAPP(X33,X30)) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_monoseq__def) ).
fof(f7409,plain,
spl104_300,
inference(avatar_split_clause,[],[f4306,f7407]) ).
fof(f7407,plain,
( spl104_300
<=> ! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_300])]) ).
fof(f4306,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2375]) ).
fof(f2375,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1436]) ).
fof(f1436,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1242]) ).
fof(f1242,axiom,
! [X99] :
( class_Rings_Ocomm__semiring__1(X99)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(f7405,plain,
spl104_299,
inference(avatar_split_clause,[],[f4305,f7403]) ).
fof(f7403,plain,
( spl104_299
<=> ! [X0] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_299])]) ).
fof(f4305,plain,
! [X0] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2374]) ).
fof(f2374,plain,
! [X0] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1435]) ).
fof(f1435,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1251]) ).
fof(f1251,axiom,
! [X99] :
( class_Rings_Ocomm__semiring__1(X99)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(f7401,plain,
spl104_298,
inference(avatar_split_clause,[],[f4304,f7399]) ).
fof(f7399,plain,
( spl104_298
<=> ! [X0] :
( class_Power_Opower(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_298])]) ).
fof(f4304,plain,
! [X0] :
( class_Power_Opower(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2373]) ).
fof(f2373,plain,
! [X0] :
( class_Power_Opower(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1434]) ).
fof(f1434,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Power_Opower(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1264]) ).
fof(f1264,axiom,
! [X99] :
( class_Rings_Ocomm__semiring__1(X99)
=> class_Power_Opower(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Power_Opower) ).
fof(f7397,plain,
spl104_297,
inference(avatar_split_clause,[],[f4303,f7395]) ).
fof(f7395,plain,
( spl104_297
<=> ! [X0] :
( class_Rings_Osemiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_297])]) ).
fof(f4303,plain,
! [X0] :
( class_Rings_Osemiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2372]) ).
fof(f2372,plain,
! [X0] :
( class_Rings_Osemiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1433]) ).
fof(f1433,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Osemiring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1254]) ).
fof(f1254,axiom,
! [X99] :
( class_Rings_Ocomm__semiring__1(X99)
=> class_Rings_Osemiring__1(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Osemiring__1) ).
fof(f7393,plain,
spl104_296,
inference(avatar_split_clause,[],[f4302,f7391]) ).
fof(f7391,plain,
( spl104_296
<=> ! [X0] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_296])]) ).
fof(f4302,plain,
! [X0] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2371]) ).
fof(f2371,plain,
! [X0] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1432]) ).
fof(f1432,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1247]) ).
fof(f1247,axiom,
! [X99] :
( class_Rings_Ocomm__semiring__1(X99)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(f7389,plain,
spl104_295,
inference(avatar_split_clause,[],[f4301,f7387]) ).
fof(f7387,plain,
( spl104_295
<=> ! [X0] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_295])]) ).
fof(f4301,plain,
! [X0] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2370]) ).
fof(f2370,plain,
! [X0] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1431]) ).
fof(f1431,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1234]) ).
fof(f1234,axiom,
! [X99] :
( class_Rings_Ocomm__semiring__1(X99)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(f7385,plain,
spl104_294,
inference(avatar_split_clause,[],[f4300,f7383]) ).
fof(f7383,plain,
( spl104_294
<=> ! [X0] :
( class_Groups_Oone(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_294])]) ).
fof(f4300,plain,
! [X0] :
( class_Groups_Oone(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(cnf_transformation,[],[f2369]) ).
fof(f2369,plain,
! [X0] :
( class_Groups_Oone(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__1(X0) ),
inference(ennf_transformation,[],[f1430]) ).
fof(f1430,plain,
! [X0] :
( class_Rings_Ocomm__semiring__1(X0)
=> class_Groups_Oone(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1268]) ).
fof(f1268,axiom,
! [X99] :
( class_Rings_Ocomm__semiring__1(X99)
=> class_Groups_Oone(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Oone) ).
fof(f7381,plain,
spl104_293,
inference(avatar_split_clause,[],[f4296,f7379]) ).
fof(f7379,plain,
( spl104_293
<=> ! [X0] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_293])]) ).
fof(f4296,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2365]) ).
fof(f2365,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1426]) ).
fof(f1426,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f998]) ).
fof(f998,axiom,
! [X99] :
( class_Rings_Ocomm__semiring__0(X99)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(f7377,plain,
spl104_292,
inference(avatar_split_clause,[],[f4295,f7375]) ).
fof(f7375,plain,
( spl104_292
<=> ! [X0] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_292])]) ).
fof(f4295,plain,
! [X0] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2364]) ).
fof(f2364,plain,
! [X0] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1425]) ).
fof(f1425,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1257]) ).
fof(f1257,axiom,
! [X99] :
( class_Rings_Ocomm__semiring__0(X99)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(f7373,plain,
spl104_291,
inference(avatar_split_clause,[],[f4294,f7371]) ).
fof(f7371,plain,
( spl104_291
<=> ! [X0] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_291])]) ).
fof(f4294,plain,
! [X0] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2363]) ).
fof(f2363,plain,
! [X0] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1424]) ).
fof(f1424,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1255]) ).
fof(f1255,axiom,
! [X99] :
( class_Rings_Ocomm__semiring__0(X99)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(f7369,plain,
spl104_290,
inference(avatar_split_clause,[],[f4293,f7367]) ).
fof(f7367,plain,
( spl104_290
<=> ! [X0] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_290])]) ).
fof(f4293,plain,
! [X0] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2362]) ).
fof(f2362,plain,
! [X0] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1423]) ).
fof(f1423,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1261]) ).
fof(f1261,axiom,
! [X99] :
( class_Rings_Ocomm__semiring__0(X99)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(f7365,plain,
spl104_289,
inference(avatar_split_clause,[],[f4292,f7363]) ).
fof(f7363,plain,
( spl104_289
<=> ! [X0] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_289])]) ).
fof(f4292,plain,
! [X0] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2361]) ).
fof(f2361,plain,
! [X0] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1422]) ).
fof(f1422,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1233]) ).
fof(f1233,axiom,
! [X99] :
( class_Rings_Ocomm__semiring__0(X99)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(f7361,plain,
spl104_288,
inference(avatar_split_clause,[],[f4291,f7359]) ).
fof(f7359,plain,
( spl104_288
<=> ! [X0] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_288])]) ).
fof(f4291,plain,
! [X0] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(cnf_transformation,[],[f2360]) ).
fof(f2360,plain,
! [X0] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__semiring__0(X0) ),
inference(ennf_transformation,[],[f1421]) ).
fof(f1421,plain,
! [X0] :
( class_Rings_Ocomm__semiring__0(X0)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1244]) ).
fof(f1244,axiom,
! [X99] :
( class_Rings_Ocomm__semiring__0(X99)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(f7357,plain,
spl104_287,
inference(avatar_split_clause,[],[f4290,f7355]) ).
fof(f7355,plain,
( spl104_287
<=> ! [X0] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_287])]) ).
fof(f4290,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2359]) ).
fof(f2359,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1420]) ).
fof(f1420,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1239]) ).
fof(f1239,axiom,
! [X99] :
( class_Groups_Ocomm__monoid__add(X99)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(f7353,plain,
spl104_286,
inference(avatar_split_clause,[],[f4289,f7351]) ).
fof(f7351,plain,
( spl104_286
<=> ! [X0] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_286])]) ).
fof(f4289,plain,
! [X0] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2358]) ).
fof(f2358,plain,
! [X0] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1419]) ).
fof(f1419,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1253]) ).
fof(f1253,axiom,
! [X99] :
( class_Groups_Ocomm__monoid__add(X99)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(f7349,plain,
spl104_285,
inference(avatar_split_clause,[],[f4288,f7347]) ).
fof(f7347,plain,
( spl104_285
<=> ! [X0] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_285])]) ).
fof(f4288,plain,
! [X0] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2357]) ).
fof(f2357,plain,
! [X0] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocomm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1418]) ).
fof(f1418,plain,
! [X0] :
( class_Groups_Ocomm__monoid__add(X0)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1235]) ).
fof(f1235,axiom,
! [X99] :
( class_Groups_Ocomm__monoid__add(X99)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(f7345,plain,
spl104_284,
inference(avatar_split_clause,[],[f4285,f7343]) ).
fof(f7343,plain,
( spl104_284
<=> ! [X0] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_284])]) ).
fof(f4285,plain,
! [X0] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2354]) ).
fof(f2354,plain,
! [X0] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1415]) ).
fof(f1415,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(X0)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1230]) ).
fof(f1230,axiom,
! [X99] :
( class_Groups_Ocancel__comm__monoid__add(X99)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(f7341,plain,
spl104_283,
inference(avatar_split_clause,[],[f4284,f7339]) ).
fof(f7339,plain,
( spl104_283
<=> ! [X0] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_283])]) ).
fof(f4284,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2353]) ).
fof(f2353,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1414]) ).
fof(f1414,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,
! [X99] :
( class_Groups_Ocancel__comm__monoid__add(X99)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(f7337,plain,
spl104_282,
inference(avatar_split_clause,[],[f4283,f7335]) ).
fof(f7335,plain,
( spl104_282
<=> ! [X0] :
( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_282])]) ).
fof(f4283,plain,
! [X0] :
( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0) ),
inference(cnf_transformation,[],[f2352]) ).
fof(f2352,plain,
! [X0] :
( class_Groups_Ozero(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ozero(X0) ),
inference(ennf_transformation,[],[f1413]) ).
fof(f1413,plain,
! [X0] :
( class_Groups_Ozero(X0)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1265]) ).
fof(f1265,axiom,
! [X99] :
( class_Groups_Ozero(X99)
=> class_Groups_Ozero(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(f7333,plain,
spl104_281,
inference(avatar_split_clause,[],[f4282,f7331]) ).
fof(f7331,plain,
( spl104_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,[spl104_281])]) ).
fof(f4282,plain,
! [X0] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(cnf_transformation,[],[f2351]) ).
fof(f2351,plain,
! [X0] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Ocancel__comm__monoid__add(X0) ),
inference(ennf_transformation,[],[f1412]) ).
fof(f1412,plain,
! [X0] :
( class_Groups_Ocancel__comm__monoid__add(X0)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1222]) ).
fof(f1222,axiom,
! [X99] :
( class_Groups_Ocancel__comm__monoid__add(X99)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(f7329,plain,
spl104_280,
inference(avatar_split_clause,[],[f4274,f7327]) ).
fof(f7327,plain,
( spl104_280
<=> ! [X0] :
( class_Int_Onumber(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_280])]) ).
fof(f4274,plain,
! [X0] :
( class_Int_Onumber(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f2343]) ).
fof(f2343,plain,
! [X0] :
( class_Int_Onumber(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(ennf_transformation,[],[f1404]) ).
fof(f1404,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(X0)
=> class_Int_Onumber(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1267]) ).
fof(f1267,axiom,
! [X99] :
( class_Rings_Ocomm__ring__1(X99)
=> class_Int_Onumber(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Int_Onumber) ).
fof(f7325,plain,
spl104_279,
inference(avatar_split_clause,[],[f4273,f7323]) ).
fof(f7323,plain,
( spl104_279
<=> ! [X0] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_279])]) ).
fof(f4273,plain,
! [X0] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2342]) ).
fof(f2342,plain,
! [X0] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1403]) ).
fof(f1403,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1238]) ).
fof(f1238,axiom,
! [X99] :
( class_Rings_Oidom(X99)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(f7321,plain,
spl104_278,
inference(avatar_split_clause,[],[f4272,f7319]) ).
fof(f7319,plain,
( spl104_278
<=> ! [X0] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_278])]) ).
fof(f4272,plain,
! [X0] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2341]) ).
fof(f2341,plain,
! [X0] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1402]) ).
fof(f1402,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1212]) ).
fof(f1212,axiom,
! [X99] :
( class_Rings_Oidom(X99)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f7317,plain,
spl104_277,
inference(avatar_split_clause,[],[f4271,f7315]) ).
fof(f7315,plain,
( spl104_277
<=> ! [X0] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_277])]) ).
fof(f4271,plain,
! [X0] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f2340]) ).
fof(f2340,plain,
! [X0] :
( class_Int_Onumber__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(ennf_transformation,[],[f1401]) ).
fof(f1401,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(X0)
=> class_Int_Onumber__ring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1260]) ).
fof(f1260,axiom,
! [X99] :
( class_Rings_Ocomm__ring__1(X99)
=> class_Int_Onumber__ring(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Int_Onumber__ring) ).
fof(f7313,plain,
spl104_276,
inference(avatar_split_clause,[],[f4270,f7311]) ).
fof(f7311,plain,
( spl104_276
<=> ! [X0] :
( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_276])]) ).
fof(f4270,plain,
! [X0] :
( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2339]) ).
fof(f2339,plain,
! [X0] :
( class_Rings_Oidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1400]) ).
fof(f1400,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f996]) ).
fof(f996,axiom,
! [X99] :
( class_Rings_Oidom(X99)
=> class_Rings_Oidom(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(f7309,plain,
spl104_275,
inference(avatar_split_clause,[],[f4269,f7307]) ).
fof(f7307,plain,
( spl104_275
<=> ! [X0] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_275])]) ).
fof(f4269,plain,
! [X0] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2338]) ).
fof(f2338,plain,
! [X0] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1399]) ).
fof(f1399,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1246]) ).
fof(f1246,axiom,
! [X99] :
( class_Groups_Oab__group__add(X99)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(f7305,plain,
spl104_274,
inference(avatar_split_clause,[],[f4268,f7303]) ).
fof(f7303,plain,
( spl104_274
<=> ! [X0] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_274])]) ).
fof(f4268,plain,
! [X0] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(cnf_transformation,[],[f2337]) ).
fof(f2337,plain,
! [X0] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Groups_Oab__group__add(X0) ),
inference(ennf_transformation,[],[f1398]) ).
fof(f1398,plain,
! [X0] :
( class_Groups_Oab__group__add(X0)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1256]) ).
fof(f1256,axiom,
! [X99] :
( class_Groups_Oab__group__add(X99)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(f7301,plain,
spl104_273,
inference(avatar_split_clause,[],[f4267,f7299]) ).
fof(f7299,plain,
( spl104_273
<=> ! [X0] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_273])]) ).
fof(f4267,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f2336]) ).
fof(f2336,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(ennf_transformation,[],[f1397]) ).
fof(f1397,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(X0)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1252]) ).
fof(f1252,axiom,
! [X99] :
( class_Rings_Ocomm__ring__1(X99)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(f7297,plain,
spl104_272,
inference(avatar_split_clause,[],[f4266,f7295]) ).
fof(f7295,plain,
( spl104_272
<=> ! [X0] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_272])]) ).
fof(f4266,plain,
! [X0] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(cnf_transformation,[],[f2335]) ).
fof(f2335,plain,
! [X0] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring__1(X0) ),
inference(ennf_transformation,[],[f1396]) ).
fof(f1396,plain,
! [X0] :
( class_Rings_Ocomm__ring__1(X0)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1263]) ).
fof(f1263,axiom,
! [X99] :
( class_Rings_Ocomm__ring__1(X99)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(f7293,plain,
spl104_271,
inference(avatar_split_clause,[],[f4265,f7291]) ).
fof(f7291,plain,
( spl104_271
<=> ! [X0] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_271])]) ).
fof(f4265,plain,
! [X0] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2334]) ).
fof(f2334,plain,
! [X0] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1395]) ).
fof(f1395,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1226]) ).
fof(f1226,axiom,
! [X99] :
( class_Rings_Oidom(X99)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(f7289,plain,
spl104_270,
inference(avatar_split_clause,[],[f4264,f7287]) ).
fof(f7287,plain,
( spl104_270
<=> ! [X0] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_270])]) ).
fof(f4264,plain,
! [X0] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(cnf_transformation,[],[f2333]) ).
fof(f2333,plain,
! [X0] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Oidom(X0) ),
inference(ennf_transformation,[],[f1394]) ).
fof(f1394,plain,
! [X0] :
( class_Rings_Oidom(X0)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1223]) ).
fof(f1223,axiom,
! [X99] :
( class_Rings_Oidom(X99)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(f7285,plain,
spl104_269,
inference(avatar_split_clause,[],[f4263,f7283]) ).
fof(f7283,plain,
( spl104_269
<=> ! [X0] :
( class_Rings_Oring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_269])]) ).
fof(f4263,plain,
! [X0] :
( class_Rings_Oring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f2332]) ).
fof(f2332,plain,
! [X0] :
( class_Rings_Oring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(ennf_transformation,[],[f1393]) ).
fof(f1393,plain,
! [X0] :
( class_Rings_Ocomm__ring(X0)
=> class_Rings_Oring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1266]) ).
fof(f1266,axiom,
! [X99] :
( class_Rings_Ocomm__ring(X99)
=> class_Rings_Oring(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Oring) ).
fof(f7281,plain,
spl104_268,
inference(avatar_split_clause,[],[f4262,f7279]) ).
fof(f7279,plain,
( spl104_268
<=> ! [X0] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_268])]) ).
fof(f4262,plain,
! [X0] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(cnf_transformation,[],[f2331]) ).
fof(f2331,plain,
! [X0] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Ocomm__ring(X0) ),
inference(ennf_transformation,[],[f1392]) ).
fof(f1392,plain,
! [X0] :
( class_Rings_Ocomm__ring(X0)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f999]) ).
fof(f999,axiom,
! [X99] :
( class_Rings_Ocomm__ring(X99)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(f7277,plain,
spl104_267,
inference(avatar_split_clause,[],[f4260,f7275]) ).
fof(f7275,plain,
( spl104_267
<=> ! [X0] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_267])]) ).
fof(f4260,plain,
! [X0] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2329]) ).
fof(f2329,plain,
! [X0] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1390]) ).
fof(f1390,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1258]) ).
fof(f1258,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(f7273,plain,
spl104_266,
inference(avatar_split_clause,[],[f4259,f7271]) ).
fof(f7271,plain,
( spl104_266
<=> ! [X0] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_266])]) ).
fof(f4259,plain,
! [X0] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2328]) ).
fof(f2328,plain,
! [X0] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1389]) ).
fof(f1389,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1249]) ).
fof(f1249,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(f7269,plain,
spl104_265,
inference(avatar_split_clause,[],[f4258,f7267]) ).
fof(f7267,plain,
( spl104_265
<=> ! [X0] :
( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_265])]) ).
fof(f4258,plain,
! [X0] :
( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2327]) ).
fof(f2327,plain,
! [X0] :
( class_Orderings_Oord(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1388]) ).
fof(f1388,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1262]) ).
fof(f1262,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Orderings_Oord(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(f7265,plain,
spl104_264,
inference(avatar_split_clause,[],[f4257,f7263]) ).
fof(f7263,plain,
( spl104_264
<=> ! [X0] :
( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_264])]) ).
fof(f4257,plain,
! [X0] :
( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2326]) ).
fof(f2326,plain,
! [X0] :
( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1387]) ).
fof(f1387,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1245]) ).
fof(f1245,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Nat_Osemiring__char__0) ).
fof(f7261,plain,
spl104_263,
inference(avatar_split_clause,[],[f4256,f7259]) ).
fof(f7259,plain,
( spl104_263
<=> ! [X0] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_263])]) ).
fof(f4256,plain,
! [X0] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2325]) ).
fof(f2325,plain,
! [X0] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1386]) ).
fof(f1386,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1232]) ).
fof(f1232,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(f7257,plain,
spl104_262,
inference(avatar_split_clause,[],[f4255,f7255]) ).
fof(f7255,plain,
( spl104_262
<=> ! [X0] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_262])]) ).
fof(f4255,plain,
! [X0] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2324]) ).
fof(f2324,plain,
! [X0] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1385]) ).
fof(f1385,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1250]) ).
fof(f1250,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(f7253,plain,
spl104_261,
inference(avatar_split_clause,[],[f4254,f7251]) ).
fof(f7251,plain,
( spl104_261
<=> ! [X0] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_261])]) ).
fof(f4254,plain,
! [X0] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2323]) ).
fof(f2323,plain,
! [X0] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1384]) ).
fof(f1384,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1217]) ).
fof(f1217,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(f7249,plain,
spl104_260,
inference(avatar_split_clause,[],[f4253,f7247]) ).
fof(f7247,plain,
( spl104_260
<=> ! [X0] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_260])]) ).
fof(f4253,plain,
! [X0] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2322]) ).
fof(f2322,plain,
! [X0] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1383]) ).
fof(f1383,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1220]) ).
fof(f1220,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(f7245,plain,
spl104_259,
inference(avatar_split_clause,[],[f4252,f7243]) ).
fof(f7243,plain,
( spl104_259
<=> ! [X0] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_259])]) ).
fof(f4252,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2321]) ).
fof(f2321,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1382]) ).
fof(f1382,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1214]) ).
fof(f1214,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f7241,plain,
spl104_258,
inference(avatar_split_clause,[],[f4251,f7239]) ).
fof(f7239,plain,
( spl104_258
<=> ! [X0] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_258])]) ).
fof(f4251,plain,
! [X0] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2320]) ).
fof(f2320,plain,
! [X0] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1381]) ).
fof(f1381,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1224]) ).
fof(f1224,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(f7237,plain,
spl104_257,
inference(avatar_split_clause,[],[f4250,f7235]) ).
fof(f7235,plain,
( spl104_257
<=> ! [X0] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_257])]) ).
fof(f4250,plain,
! [X0] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2319]) ).
fof(f2319,plain,
! [X0] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1380]) ).
fof(f1380,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1213]) ).
fof(f1213,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f7233,plain,
spl104_256,
inference(avatar_split_clause,[],[f4249,f7231]) ).
fof(f7231,plain,
( spl104_256
<=> ! [X0] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_256])]) ).
fof(f4249,plain,
! [X0] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2318]) ).
fof(f2318,plain,
! [X0] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1379]) ).
fof(f1379,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1236]) ).
fof(f1236,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(f7229,plain,
spl104_255,
inference(avatar_split_clause,[],[f4248,f7227]) ).
fof(f7227,plain,
( spl104_255
<=> ! [X0] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_255])]) ).
fof(f4248,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2317]) ).
fof(f2317,plain,
! [X0] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1378]) ).
fof(f1378,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1218]) ).
fof(f1218,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
fof(f7225,plain,
spl104_254,
inference(avatar_split_clause,[],[f4247,f7223]) ).
fof(f7223,plain,
( spl104_254
<=> ! [X0] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_254])]) ).
fof(f4247,plain,
! [X0] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2316]) ).
fof(f2316,plain,
! [X0] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1377]) ).
fof(f1377,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1231]) ).
fof(f1231,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
fof(f7221,plain,
spl104_253,
inference(avatar_split_clause,[],[f4246,f7219]) ).
fof(f7219,plain,
( spl104_253
<=> ! [X0] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_253])]) ).
fof(f4246,plain,
! [X0] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2315]) ).
fof(f2315,plain,
! [X0] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1376]) ).
fof(f1376,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1215]) ).
fof(f1215,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(f7217,plain,
spl104_252,
inference(avatar_split_clause,[],[f4245,f7215]) ).
fof(f7215,plain,
( spl104_252
<=> ! [X0] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_252])]) ).
fof(f4245,plain,
! [X0] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2314]) ).
fof(f2314,plain,
! [X0] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1375]) ).
fof(f1375,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1227]) ).
fof(f1227,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(f7213,plain,
spl104_251,
inference(avatar_split_clause,[],[f4244,f7211]) ).
fof(f7211,plain,
( spl104_251
<=> ! [X0] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_251])]) ).
fof(f4244,plain,
! [X0] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2313]) ).
fof(f2313,plain,
! [X0] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1374]) ).
fof(f1374,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1259]) ).
fof(f1259,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(f7209,plain,
spl104_250,
inference(avatar_split_clause,[],[f4243,f7207]) ).
fof(f7207,plain,
( spl104_250
<=> ! [X0] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_250])]) ).
fof(f4243,plain,
! [X0] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2312]) ).
fof(f2312,plain,
! [X0] :
( class_Rings_Olinordered__idom(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__idom(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1241]) ).
fof(f1241,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(f7205,plain,
spl104_249,
inference(avatar_split_clause,[],[f4242,f7203]) ).
fof(f7203,plain,
( spl104_249
<=> ! [X0] :
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_249])]) ).
fof(f4242,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2311]) ).
fof(f2311,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add__abs(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__ab__group__add__abs(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1219]) ).
fof(f1219,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).
fof(f7201,plain,
spl104_248,
inference(avatar_split_clause,[],[f4241,f7199]) ).
fof(f7199,plain,
( spl104_248
<=> ! [X0] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_248])]) ).
fof(f4241,plain,
! [X0] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2310]) ).
fof(f2310,plain,
! [X0] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1371]) ).
fof(f1371,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1225]) ).
fof(f1225,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(f7197,plain,
spl104_247,
inference(avatar_split_clause,[],[f4240,f7195]) ).
fof(f7195,plain,
( spl104_247
<=> ! [X0] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_247])]) ).
fof(f4240,plain,
! [X0] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2309]) ).
fof(f2309,plain,
! [X0] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1370]) ).
fof(f1370,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1248]) ).
fof(f1248,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(f7193,plain,
spl104_246,
inference(avatar_split_clause,[],[f4239,f7191]) ).
fof(f7191,plain,
( spl104_246
<=> ! [X0] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_246])]) ).
fof(f4239,plain,
! [X0] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2308]) ).
fof(f2308,plain,
! [X0] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1369]) ).
fof(f1369,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1221]) ).
fof(f1221,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(f7189,plain,
spl104_245,
inference(avatar_split_clause,[],[f4238,f7187]) ).
fof(f7187,plain,
( spl104_245
<=> ! [X0] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_245])]) ).
fof(f4238,plain,
! [X0] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2307]) ).
fof(f2307,plain,
! [X0] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1368]) ).
fof(f1368,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1240]) ).
fof(f1240,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(f7185,plain,
spl104_244,
inference(avatar_split_clause,[],[f4237,f7183]) ).
fof(f7183,plain,
( spl104_244
<=> ! [X0] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_244])]) ).
fof(f4237,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2306]) ).
fof(f2306,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1367]) ).
fof(f1367,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1229]) ).
fof(f1229,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(f7181,plain,
spl104_243,
inference(avatar_split_clause,[],[f4236,f7179]) ).
fof(f7179,plain,
( spl104_243
<=> ! [X0] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_243])]) ).
fof(f4236,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2305]) ).
fof(f2305,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f1366]) ).
fof(f1366,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1228]) ).
fof(f1228,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
fof(f7177,plain,
spl104_242,
inference(avatar_split_clause,[],[f4235,f7175]) ).
fof(f7175,plain,
( spl104_242
<=> ! [X0] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_242])]) ).
fof(f4235,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2304]) ).
fof(f2304,plain,
! [X0] :
( class_Rings_Olinordered__semiring__1__strict(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__1__strict(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1216]) ).
fof(f1216,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
fof(f7173,plain,
spl104_241,
inference(avatar_split_clause,[],[f4234,f7171]) ).
fof(f7171,plain,
( spl104_241
<=> ! [X0] :
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_241])]) ).
fof(f4234,plain,
! [X0] :
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f2303]) ).
fof(f2303,plain,
! [X0] :
( class_Rings_Oordered__ring__abs(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__ring__abs(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1237]) ).
fof(f1237,axiom,
! [X99] :
( class_Rings_Olinordered__idom(X99)
=> class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).
fof(f7169,plain,
spl104_240,
inference(avatar_split_clause,[],[f4226,f7167]) ).
fof(f7167,plain,
( spl104_240
<=> ! [X0] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_240])]) ).
fof(f4226,plain,
! [X0] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(cnf_transformation,[],[f2297]) ).
fof(f2297,plain,
! [X0] :
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0))
| ~ class_Fields_Ofield(X0) ),
inference(ennf_transformation,[],[f1358]) ).
fof(f1358,plain,
! [X0] :
( class_Fields_Ofield(X0)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X0)) ),
inference(rectify,[],[f1243]) ).
fof(f1243,axiom,
! [X99] :
( class_Fields_Ofield(X99)
=> class_Divides_Osemiring__div(tc_Polynomial_Opoly(X99)) ),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Polynomial__Opoly__Divides_Osemiring__div) ).
fof(f7165,plain,
spl104_239,
inference(avatar_split_clause,[],[f4158,f7163]) ).
fof(f4158,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)),
inference(cnf_transformation,[],[f1296]) ).
fof(f1296,plain,
! [X0] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Nat_OSuc(X0)),
inference(rectify,[],[f107]) ).
fof(f107,axiom,
! [X5] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,c_Nat_OSuc(X5)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_lessI) ).
fof(f7161,plain,
spl104_238,
inference(avatar_split_clause,[],[f4156,f7159]) ).
fof(f7159,plain,
( spl104_238
<=> ! [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,[spl104_238])]) ).
fof(f4156,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f1294]) ).
fof(f1294,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(rectify,[],[f290]) ).
fof(f290,axiom,
! [X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X5),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__eq__nat_Osimps_I1_J) ).
fof(f7157,plain,
spl104_237,
inference(avatar_split_clause,[],[f4155,f7155]) ).
fof(f7155,plain,
( spl104_237
<=> ! [X0] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_237])]) ).
fof(f7153,plain,
spl104_236,
inference(avatar_split_clause,[],[f4154,f7151]) ).
fof(f4154,plain,
! [X0] : c_Int_Osucc(c_Int_Opred(X0)) = X0,
inference(cnf_transformation,[],[f1292]) ).
fof(f1292,plain,
! [X0] : c_Int_Osucc(c_Int_Opred(X0)) = X0,
inference(rectify,[],[f554]) ).
fof(f554,axiom,
! [X3] : c_Int_Osucc(c_Int_Opred(X3)) = X3,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_succ__pred) ).
fof(f7149,plain,
spl104_235,
inference(avatar_split_clause,[],[f4153,f7147]) ).
fof(f4153,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
inference(cnf_transformation,[],[f1291]) ).
fof(f1291,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X0),X0),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X5] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(X5),X5),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_Suc__n__not__le__n) ).
fof(f7145,plain,
spl104_234,
inference(avatar_split_clause,[],[f4150,f7143]) ).
fof(f7143,plain,
( spl104_234
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_234])]) ).
fof(f4150,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1288]) ).
fof(f1288,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f131]) ).
fof(f131,axiom,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__nat__zero__code) ).
fof(f7141,plain,
spl104_233,
inference(avatar_split_clause,[],[f4149,f7139]) ).
fof(f7139,plain,
( spl104_233
<=> ! [X0] : ~ c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_233])]) ).
fof(f4149,plain,
! [X0] : ~ c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f1287]) ).
fof(f1287,plain,
! [X0] : ~ c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(rectify,[],[f577]) ).
fof(f577,axiom,
! [X5] : ~ c_Nat__Numeral_Oneg(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X5)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__neg__int) ).
fof(f7137,plain,
spl104_232,
inference(avatar_split_clause,[],[f4143,f7135]) ).
fof(f4143,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
inference(cnf_transformation,[],[f1281]) ).
fof(f1281,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X0),
inference(rectify,[],[f282]) ).
fof(f282,axiom,
! [X45] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(X45),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_nat_Osimps_I3_J) ).
fof(f7133,plain,
spl104_231,
inference(avatar_split_clause,[],[f4142,f7131]) ).
fof(f7131,plain,
( spl104_231
<=> ! [X0] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_231])]) ).
fof(f4142,plain,
! [X0] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X0),
inference(cnf_transformation,[],[f1280]) ).
fof(f1280,plain,
! [X0] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X0),
inference(rectify,[],[f512]) ).
fof(f512,axiom,
! [X32] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,X32),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_complex__i__not__number__of) ).
fof(f7129,plain,
spl104_230,
inference(avatar_split_clause,[],[f4109,f7126]) ).
fof(f7126,plain,
( spl104_230
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_230])]) ).
fof(f4109,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
inference(cnf_transformation,[],[f340]) ).
fof(f340,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_r),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_rp) ).
fof(f7124,plain,
spl104_229,
inference(avatar_split_clause,[],[f4108,f7121]) ).
fof(f4108,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
inference(cnf_transformation,[],[f339]) ).
fof(f339,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),v_d____),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_d_I1_J) ).
fof(f7119,plain,
spl104_228,
inference(avatar_split_clause,[],[f4106,f7116]) ).
fof(f7116,plain,
( spl104_228
<=> c_RealDef_Oreal(tc_Nat_Onat) = c_Nat_Osemiring__1__class_Oof__nat(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_228])]) ).
fof(f7114,plain,
~ spl104_227,
inference(avatar_split_clause,[],[f4103,f7111]) ).
fof(f7111,plain,
( spl104_227
<=> c_Groups_Oone__class_Oone(tc_RealDef_Oreal) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_227])]) ).
fof(f4103,plain,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f344]) ).
fof(f344,axiom,
c_Groups_Oone__class_Oone(tc_RealDef_Oreal) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__zero__not__eq__one) ).
fof(f7109,plain,
( ~ spl104_226
| spl104_225 ),
inference(avatar_split_clause,[],[f7104,f7100,f7106]) ).
fof(f7100,plain,
( spl104_225
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_225])]) ).
fof(f7104,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N2____,v_N1____)))))
| spl104_225 ),
inference(forward_demodulation,[],[f7102,f4396]) ).
fof(f7102,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))))
| spl104_225 ),
inference(avatar_component_clause,[],[f7100]) ).
fof(f7103,plain,
~ spl104_225,
inference(avatar_split_clause,[],[f3884,f7100]) ).
fof(f3884,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(cnf_transformation,[],[f1271]) ).
fof(f1271,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(flattening,[],[f1270]) ).
fof(f1270,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
inference(negated_conjecture,[],[f1269]) ).
fof(f1269,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))),hAPP(c_RealDef_Oreal(tc_Nat_Onat),c_Nat_OSuc(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',conj_0) ).
fof(f7098,plain,
~ spl104_224,
inference(avatar_split_clause,[],[f5632,f7095]) ).
fof(f5632,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Int_OPls,
inference(forward_demodulation,[],[f4104,f4101]) ).
fof(f4104,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f474]) ).
fof(f474,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_int__0__neq__1) ).
fof(f7093,plain,
spl104_223,
inference(avatar_split_clause,[],[f4141,f7091]) ).
fof(f7091,plain,
( spl104_223
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_223])]) ).
fof(f4141,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1279]) ).
fof(f1279,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X5,X5),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_le__refl) ).
fof(f7089,plain,
spl104_222,
inference(avatar_split_clause,[],[f4140,f7087]) ).
fof(f4140,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f1278]) ).
fof(f1278,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X0,X0),
inference(rectify,[],[f444]) ).
fof(f444,axiom,
! [X32] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,X32,X32),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_zle__refl) ).
fof(f7085,plain,
spl104_221,
inference(avatar_split_clause,[],[f4139,f7083]) ).
fof(f7083,plain,
( spl104_221
<=> ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_221])]) ).
fof(f4139,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
inference(cnf_transformation,[],[f1277]) ).
fof(f1277,plain,
! [X0] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X0,X0),
inference(rectify,[],[f81]) ).
fof(f81,axiom,
! [X32] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,X32,X32),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_real__le__refl) ).
fof(f7081,plain,
spl104_220,
inference(avatar_split_clause,[],[f4137,f7079]) ).
fof(f7079,plain,
( spl104_220
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_220])]) ).
fof(f4137,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
inference(cnf_transformation,[],[f1275]) ).
fof(f1275,plain,
! [X0] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X0,X0),
inference(rectify,[],[f122]) ).
fof(f122,axiom,
! [X5] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,X5,X5),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_less__not__refl) ).
fof(f7077,plain,
spl104_219,
inference(avatar_split_clause,[],[f4135,f7075]) ).
fof(f7075,plain,
( spl104_219
<=> ! [X0] : c_Nat_OSuc(X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl104_219])]) ).
fof(f4135,plain,
! [X0] : c_Nat_OSuc(X0) != X0,
inference(cnf_transformation,[],[f1273]) ).
fof(f1273,plain,
! [X0] : c_Nat_OSuc(X0) != X0,
inference(rectify,[],[f63]) ).
fof(f63,axiom,
! [X5] : c_Nat_OSuc(X5) != X5,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_n__not__Suc__n) ).
fof(f7073,plain,
spl104_218,
inference(avatar_split_clause,[],[f4101,f7070]) ).
fof(f7068,plain,
~ spl104_217,
inference(avatar_split_clause,[],[f4100,f7065]) ).
fof(f7065,plain,
( spl104_217
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_217])]) ).
fof(f4100,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(cnf_transformation,[],[f529]) ).
fof(f529,axiom,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_rel__simps_I2_J) ).
fof(f7062,plain,
~ spl104_216,
inference(avatar_split_clause,[],[f4099,f7059]) ).
fof(f7059,plain,
( spl104_216
<=> c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_216])]) ).
fof(f4099,plain,
~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
inference(cnf_transformation,[],[f539]) ).
fof(f539,axiom,
~ c_Nat__Numeral_Oneg(c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__neg__number__of__Pls) ).
fof(f7057,plain,
~ spl104_215,
inference(avatar_split_clause,[],[f4098,f7054]) ).
fof(f7054,plain,
( spl104_215
<=> c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Oii ),
introduced(avatar_definition,[new_symbols(naming,[spl104_215])]) ).
fof(f4098,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Oii,
inference(cnf_transformation,[],[f511]) ).
fof(f511,axiom,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) != c_Complex_Oii,
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_complex__i__not__one) ).
fof(f7052,plain,
~ spl104_214,
inference(avatar_split_clause,[],[f4097,f7049]) ).
fof(f7049,plain,
( spl104_214
<=> c_Complex_Oii = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_214])]) ).
fof(f4097,plain,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f510]) ).
fof(f510,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_complex__i__not__zero) ).
fof(f7047,plain,
( ~ spl104_213
| spl104_212 ),
inference(avatar_split_clause,[],[f7042,f7038,f7044]) ).
fof(f7044,plain,
( spl104_213
<=> c_Nat__Numeral_Oneg(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_213])]) ).
fof(f7038,plain,
( spl104_212
<=> c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_212])]) ).
fof(f7042,plain,
( ~ c_Nat__Numeral_Oneg(c_Int_OPls)
| spl104_212 ),
inference(forward_demodulation,[],[f7040,f4101]) ).
fof(f7040,plain,
( ~ c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| spl104_212 ),
inference(avatar_component_clause,[],[f7038]) ).
fof(f7041,plain,
~ spl104_212,
inference(avatar_split_clause,[],[f4096,f7038]) ).
fof(f4096,plain,
~ c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f496]) ).
fof(f496,axiom,
~ c_Nat__Numeral_Oneg(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__neg__0) ).
fof(f7036,plain,
~ spl104_211,
inference(avatar_split_clause,[],[f4095,f7033]) ).
fof(f4095,plain,
~ c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f497]) ).
fof(f497,axiom,
~ c_Nat__Numeral_Oneg(c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_not__neg__1) ).
fof(f7031,plain,
spl104_210,
inference(avatar_split_clause,[],[f4094,f7028]) ).
fof(f7028,plain,
( spl104_210
<=> class_Orderings_Oorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_210])]) ).
fof(f4094,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1105]) ).
fof(f1105,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Orderings_Oorder) ).
fof(f7026,plain,
spl104_209,
inference(avatar_split_clause,[],[f4093,f7023]) ).
fof(f7023,plain,
( spl104_209
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_209])]) ).
fof(f4093,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(cnf_transformation,[],[f1063]) ).
fof(f1063,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Orderings_Oorder) ).
fof(f7021,plain,
spl104_208,
inference(avatar_split_clause,[],[f4092,f7018]) ).
fof(f7018,plain,
( spl104_208
<=> class_Orderings_Oorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_208])]) ).
fof(f4092,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1164]) ).
fof(f1164,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(f7016,plain,
spl104_207,
inference(avatar_split_clause,[],[f4091,f7013]) ).
fof(f7013,plain,
( spl104_207
<=> class_Orderings_Oorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_207])]) ).
fof(f4091,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f1113]) ).
fof(f1113,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_HOL__Obool__Orderings_Oorder) ).
fof(f7011,plain,
spl104_206,
inference(avatar_split_clause,[],[f4090,f7008]) ).
fof(f7008,plain,
( spl104_206
<=> class_Orderings_Opreorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_206])]) ).
fof(f4090,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1098]) ).
fof(f1098,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Orderings_Opreorder) ).
fof(f7006,plain,
spl104_205,
inference(avatar_split_clause,[],[f4089,f7003]) ).
fof(f7003,plain,
( spl104_205
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_205])]) ).
fof(f4089,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(cnf_transformation,[],[f1054]) ).
fof(f1054,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Orderings_Opreorder) ).
fof(f7001,plain,
spl104_204,
inference(avatar_split_clause,[],[f4088,f6998]) ).
fof(f6998,plain,
( spl104_204
<=> class_Orderings_Opreorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_204])]) ).
fof(f4088,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1155]) ).
fof(f1155,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Orderings_Opreorder) ).
fof(f6996,plain,
spl104_203,
inference(avatar_split_clause,[],[f4087,f6993]) ).
fof(f6993,plain,
( spl104_203
<=> class_Orderings_Opreorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_203])]) ).
fof(f4087,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f1112]) ).
fof(f1112,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_HOL__Obool__Orderings_Opreorder) ).
fof(f6991,plain,
spl104_202,
inference(avatar_split_clause,[],[f4086,f6988]) ).
fof(f6988,plain,
( spl104_202
<=> class_Orderings_Oord(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_202])]) ).
fof(f4086,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f1107]) ).
fof(f1107,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Orderings_Oord) ).
fof(f6986,plain,
spl104_201,
inference(avatar_split_clause,[],[f4085,f6983]) ).
fof(f6983,plain,
( spl104_201
<=> class_Orderings_Oord(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_201])]) ).
fof(f4085,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(cnf_transformation,[],[f1067]) ).
fof(f1067,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Orderings_Oord) ).
fof(f6981,plain,
spl104_200,
inference(avatar_split_clause,[],[f4084,f6978]) ).
fof(f6978,plain,
( spl104_200
<=> class_Orderings_Oord(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_200])]) ).
fof(f4084,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1168]) ).
fof(f1168,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Orderings_Oord) ).
fof(f6976,plain,
spl104_199,
inference(avatar_split_clause,[],[f4083,f6973]) ).
fof(f6973,plain,
( spl104_199
<=> class_Orderings_Oord(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_199])]) ).
fof(f4083,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f1114]) ).
fof(f1114,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_HOL__Obool__Orderings_Oord) ).
fof(f6971,plain,
spl104_198,
inference(avatar_split_clause,[],[f4082,f6968]) ).
fof(f6968,plain,
( spl104_198
<=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_198])]) ).
fof(f4082,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f1093]) ).
fof(f1093,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(f6966,plain,
spl104_197,
inference(avatar_split_clause,[],[f4081,f6963]) ).
fof(f6963,plain,
( spl104_197
<=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_197])]) ).
fof(f4081,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1047]) ).
fof(f1047,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(f6961,plain,
spl104_196,
inference(avatar_split_clause,[],[f4080,f6958]) ).
fof(f6958,plain,
( spl104_196
<=> class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_196])]) ).
fof(f4080,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/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Ocomm__semiring__1) ).
fof(f6956,plain,
spl104_195,
inference(avatar_split_clause,[],[f4079,f6953]) ).
fof(f6953,plain,
( spl104_195
<=> class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_195])]) ).
fof(f4079,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1190]) ).
fof(f1190,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(f6951,plain,
spl104_194,
inference(avatar_split_clause,[],[f4078,f6948]) ).
fof(f6948,plain,
( spl104_194
<=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_194])]) ).
fof(f4078,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1100]) ).
fof(f1100,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(f6946,plain,
spl104_193,
inference(avatar_split_clause,[],[f4077,f6943]) ).
fof(f6943,plain,
( spl104_193
<=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_193])]) ).
fof(f4077,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1056]) ).
fof(f1056,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(f6941,plain,
spl104_192,
inference(avatar_split_clause,[],[f4076,f6938]) ).
fof(f6938,plain,
( spl104_192
<=> class_Groups_Omonoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_192])]) ).
fof(f4076,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1157]) ).
fof(f1157,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Omonoid__mult) ).
fof(f6936,plain,
spl104_191,
inference(avatar_split_clause,[],[f4075,f6933]) ).
fof(f6933,plain,
( spl104_191
<=> class_Groups_Omonoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_191])]) ).
fof(f4075,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1195]) ).
fof(f1195,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Groups_Omonoid__mult) ).
fof(f6931,plain,
spl104_190,
inference(avatar_split_clause,[],[f4074,f6928]) ).
fof(f6928,plain,
( spl104_190
<=> class_Power_Opower(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_190])]) ).
fof(f4074,plain,
class_Power_Opower(tc_Nat_Onat),
inference(cnf_transformation,[],[f1108]) ).
fof(f1108,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Power_Opower) ).
fof(f6926,plain,
spl104_189,
inference(avatar_split_clause,[],[f4073,f6923]) ).
fof(f6923,plain,
( spl104_189
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_189])]) ).
fof(f4073,plain,
class_Power_Opower(tc_Int_Oint),
inference(cnf_transformation,[],[f1069]) ).
fof(f1069,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Power_Opower) ).
fof(f6921,plain,
spl104_188,
inference(avatar_split_clause,[],[f4072,f6918]) ).
fof(f6918,plain,
( spl104_188
<=> class_Power_Opower(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_188])]) ).
fof(f4072,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1171]) ).
fof(f1171,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Power_Opower) ).
fof(f6916,plain,
spl104_187,
inference(avatar_split_clause,[],[f4071,f6913]) ).
fof(f6913,plain,
( spl104_187
<=> class_Power_Opower(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_187])]) ).
fof(f4071,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1207]) ).
fof(f1207,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Power_Opower) ).
fof(f6911,plain,
spl104_186,
inference(avatar_split_clause,[],[f4070,f6908]) ).
fof(f6908,plain,
( spl104_186
<=> class_Rings_Osemiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_186])]) ).
fof(f4070,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f1102]) ).
fof(f1102,axiom,
class_Rings_Osemiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Osemiring__1) ).
fof(f6906,plain,
spl104_185,
inference(avatar_split_clause,[],[f4069,f6903]) ).
fof(f6903,plain,
( spl104_185
<=> class_Rings_Osemiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_185])]) ).
fof(f4069,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1059]) ).
fof(f1059,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Osemiring__1) ).
fof(f6901,plain,
spl104_184,
inference(avatar_split_clause,[],[f4068,f6898]) ).
fof(f6898,plain,
( spl104_184
<=> class_Rings_Osemiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_184])]) ).
fof(f4068,plain,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1160]) ).
fof(f1160,axiom,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Osemiring__1) ).
fof(f6896,plain,
spl104_183,
inference(avatar_split_clause,[],[f4067,f6893]) ).
fof(f6893,plain,
( spl104_183
<=> class_Rings_Osemiring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_183])]) ).
fof(f4067,plain,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1198]) ).
fof(f1198,axiom,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Osemiring__1) ).
fof(f6891,plain,
spl104_182,
inference(avatar_split_clause,[],[f4066,f6888]) ).
fof(f6888,plain,
( spl104_182
<=> class_Int_Onumber(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_182])]) ).
fof(f4066,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(cnf_transformation,[],[f1110]) ).
fof(f1110,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Int_Onumber) ).
fof(f6886,plain,
spl104_181,
inference(avatar_split_clause,[],[f4065,f6883]) ).
fof(f6883,plain,
( spl104_181
<=> class_Rings_Ocomm__semiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_181])]) ).
fof(f4065,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f1009]) ).
fof(f1009,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
fof(f6881,plain,
spl104_180,
inference(avatar_split_clause,[],[f4064,f6878]) ).
fof(f6878,plain,
( spl104_180
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_180])]) ).
fof(f4064,plain,
class_Int_Onumber(tc_Int_Oint),
inference(cnf_transformation,[],[f1072]) ).
fof(f1072,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Int_Onumber) ).
fof(f6876,plain,
spl104_179,
inference(avatar_split_clause,[],[f4063,f6873]) ).
fof(f6873,plain,
( spl104_179
<=> class_Rings_Ocomm__semiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_179])]) ).
fof(f4063,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f1012]) ).
fof(f1012,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
fof(f6871,plain,
spl104_178,
inference(avatar_split_clause,[],[f4062,f6868]) ).
fof(f6868,plain,
( spl104_178
<=> class_Int_Onumber(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_178])]) ).
fof(f4062,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1174]) ).
fof(f1174,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Int_Onumber) ).
fof(f6866,plain,
spl104_177,
inference(avatar_split_clause,[],[f4061,f6863]) ).
fof(f6863,plain,
( spl104_177
<=> class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_177])]) ).
fof(f4061,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1006]) ).
fof(f1006,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).
fof(f6861,plain,
spl104_176,
inference(avatar_split_clause,[],[f4060,f6858]) ).
fof(f6858,plain,
( spl104_176
<=> class_Int_Onumber(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_176])]) ).
fof(f4060,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1210]) ).
fof(f1210,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Int_Onumber) ).
fof(f6856,plain,
spl104_175,
inference(avatar_split_clause,[],[f4059,f6853]) ).
fof(f6853,plain,
( spl104_175
<=> class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_175])]) ).
fof(f4059,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1002]) ).
fof(f1002,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(f6851,plain,
spl104_174,
inference(avatar_split_clause,[],[f4058,f6848]) ).
fof(f6848,plain,
( spl104_174
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_174])]) ).
fof(f4058,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1092]) ).
fof(f1092,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(f6846,plain,
spl104_173,
inference(avatar_split_clause,[],[f4057,f6843]) ).
fof(f6843,plain,
( spl104_173
<=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_173])]) ).
fof(f4057,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1044]) ).
fof(f1044,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(f6841,plain,
spl104_172,
inference(avatar_split_clause,[],[f4056,f6838]) ).
fof(f6838,plain,
( spl104_172
<=> class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_172])]) ).
fof(f4056,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/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Ocomm__monoid__add) ).
fof(f6836,plain,
spl104_171,
inference(avatar_split_clause,[],[f4055,f6833]) ).
fof(f6833,plain,
( spl104_171
<=> class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_171])]) ).
fof(f4055,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1189]) ).
fof(f1189,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(f6831,plain,
spl104_170,
inference(avatar_split_clause,[],[f4054,f6828]) ).
fof(f6828,plain,
( spl104_170
<=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_170])]) ).
fof(f4054,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(cnf_transformation,[],[f1097]) ).
fof(f1097,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(f6826,plain,
spl104_169,
inference(avatar_split_clause,[],[f4053,f6823]) ).
fof(f6823,plain,
( spl104_169
<=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_169])]) ).
fof(f4053,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(cnf_transformation,[],[f1091]) ).
fof(f1091,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(f6821,plain,
spl104_168,
inference(avatar_split_clause,[],[f4052,f6818]) ).
fof(f6818,plain,
( spl104_168
<=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_168])]) ).
fof(f4052,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1084]) ).
fof(f1084,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(f6816,plain,
spl104_167,
inference(avatar_split_clause,[],[f4051,f6813]) ).
fof(f6813,plain,
( spl104_167
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_167])]) ).
fof(f4051,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(cnf_transformation,[],[f1074]) ).
fof(f1074,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f6811,plain,
spl104_166,
inference(avatar_split_clause,[],[f4050,f6808]) ).
fof(f6808,plain,
( spl104_166
<=> class_Rings_Omult__zero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_166])]) ).
fof(f4050,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(cnf_transformation,[],[f1104]) ).
fof(f1104,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Omult__zero) ).
fof(f6806,plain,
spl104_165,
inference(avatar_split_clause,[],[f4049,f6803]) ).
fof(f6803,plain,
( spl104_165
<=> class_Rings_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_165])]) ).
fof(f4049,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(cnf_transformation,[],[f1062]) ).
fof(f1062,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Omult__zero) ).
fof(f6801,plain,
spl104_164,
inference(avatar_split_clause,[],[f4048,f6798]) ).
fof(f6798,plain,
( spl104_164
<=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_164])]) ).
fof(f4048,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(cnf_transformation,[],[f1052]) ).
fof(f1052,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(f6796,plain,
spl104_163,
inference(avatar_split_clause,[],[f4047,f6793]) ).
fof(f6793,plain,
( spl104_163
<=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_163])]) ).
fof(f4047,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1043]) ).
fof(f1043,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(f6791,plain,
spl104_162,
inference(avatar_split_clause,[],[f4046,f6788]) ).
fof(f6788,plain,
( spl104_162
<=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_162])]) ).
fof(f4046,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1035]) ).
fof(f1035,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(f6786,plain,
spl104_161,
inference(avatar_split_clause,[],[f4045,f6783]) ).
fof(f6783,plain,
( spl104_161
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_161])]) ).
fof(f4045,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(cnf_transformation,[],[f1017]) ).
fof(f1017,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f6781,plain,
spl104_160,
inference(avatar_split_clause,[],[f4044,f6778]) ).
fof(f6778,plain,
( spl104_160
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_160])]) ).
fof(f4044,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1115]) ).
fof(f1115,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f6776,plain,
spl104_159,
inference(avatar_split_clause,[],[f4043,f6773]) ).
fof(f6773,plain,
( spl104_159
<=> class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_159])]) ).
fof(f4043,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1137]) ).
fof(f1137,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Ocancel__semigroup__add) ).
fof(f6771,plain,
spl104_158,
inference(avatar_split_clause,[],[f4042,f6768]) ).
fof(f6768,plain,
( spl104_158
<=> class_Rings_Ozero__neq__one(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_158])]) ).
fof(f4042,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1153]) ).
fof(f1153,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Ozero__neq__one) ).
fof(f6766,plain,
spl104_157,
inference(avatar_split_clause,[],[f4041,f6763]) ).
fof(f6763,plain,
( spl104_157
<=> class_Rings_Omult__zero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_157])]) ).
fof(f4041,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/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Omult__zero) ).
fof(f6761,plain,
spl104_156,
inference(avatar_split_clause,[],[f4040,f6758]) ).
fof(f6758,plain,
( spl104_156
<=> class_Rings_Ono__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_156])]) ).
fof(f4040,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/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Ono__zero__divisors) ).
fof(f6756,plain,
spl104_155,
inference(avatar_split_clause,[],[f4039,f6753]) ).
fof(f6753,plain,
( spl104_155
<=> class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_155])]) ).
fof(f4039,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1188]) ).
fof(f1188,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(f6751,plain,
spl104_154,
inference(avatar_split_clause,[],[f4038,f6748]) ).
fof(f6748,plain,
( spl104_154
<=> class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_154])]) ).
fof(f4038,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1184]) ).
fof(f1184,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add) ).
fof(f6746,plain,
spl104_153,
inference(avatar_split_clause,[],[f4037,f6743]) ).
fof(f6743,plain,
( spl104_153
<=> class_Rings_Omult__zero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_153])]) ).
fof(f4037,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1201]) ).
fof(f1201,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(f6741,plain,
spl104_152,
inference(avatar_split_clause,[],[f4036,f6738]) ).
fof(f6738,plain,
( spl104_152
<=> class_Rings_Ozero__neq__one(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_152])]) ).
fof(f4036,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1194]) ).
fof(f1194,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Ozero__neq__one) ).
fof(f6736,plain,
spl104_151,
inference(avatar_split_clause,[],[f4035,f6733]) ).
fof(f6733,plain,
( spl104_151
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_151])]) ).
fof(f4035,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1176]) ).
fof(f1176,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f6731,plain,
spl104_150,
inference(avatar_split_clause,[],[f4034,f6728]) ).
fof(f6728,plain,
( spl104_150
<=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_150])]) ).
fof(f4034,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f1103]) ).
fof(f1103,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(f6726,plain,
spl104_149,
inference(avatar_split_clause,[],[f4033,f6723]) ).
fof(f6723,plain,
( spl104_149
<=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_149])]) ).
fof(f4033,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1088]) ).
fof(f1088,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(f6721,plain,
spl104_148,
inference(avatar_split_clause,[],[f4032,f6718]) ).
fof(f6718,plain,
( spl104_148
<=> class_Groups_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_148])]) ).
fof(f4032,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f1109]) ).
fof(f1109,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Ozero) ).
fof(f6716,plain,
spl104_147,
inference(avatar_split_clause,[],[f4031,f6713]) ).
fof(f6713,plain,
( spl104_147
<=> class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_147])]) ).
fof(f4031,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1008]) ).
fof(f1008,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
fof(f6711,plain,
spl104_146,
inference(avatar_split_clause,[],[f4030,f6708]) ).
fof(f6708,plain,
( spl104_146
<=> class_Rings_Osemiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_146])]) ).
fof(f4030,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1106]) ).
fof(f1106,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Osemiring) ).
fof(f6706,plain,
spl104_145,
inference(avatar_split_clause,[],[f4029,f6703]) ).
fof(f6703,plain,
( spl104_145
<=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_145])]) ).
fof(f4029,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1039]) ).
fof(f1039,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(f6701,plain,
spl104_144,
inference(avatar_split_clause,[],[f4028,f6698]) ).
fof(f6698,plain,
( spl104_144
<=> class_Rings_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_144])]) ).
fof(f4028,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f1060]) ).
fof(f1060,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Osemiring__0) ).
fof(f6696,plain,
spl104_143,
inference(avatar_split_clause,[],[f4027,f6693]) ).
fof(f6693,plain,
( spl104_143
<=> class_Groups_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_143])]) ).
fof(f4027,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f1070]) ).
fof(f1070,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Ozero) ).
fof(f6691,plain,
spl104_142,
inference(avatar_split_clause,[],[f4026,f6688]) ).
fof(f6688,plain,
( spl104_142
<=> class_Rings_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_142])]) ).
fof(f4026,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1066]) ).
fof(f1066,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Osemiring) ).
fof(f6686,plain,
spl104_141,
inference(avatar_split_clause,[],[f4025,f6683]) ).
fof(f6683,plain,
( spl104_141
<=> class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_141])]) ).
fof(f4025,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1011]) ).
fof(f1011,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
fof(f6681,plain,
spl104_140,
inference(avatar_split_clause,[],[f4024,f6678]) ).
fof(f6678,plain,
( spl104_140
<=> class_Rings_Osemiring__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_140])]) ).
fof(f4024,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/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Osemiring__0) ).
fof(f6676,plain,
spl104_139,
inference(avatar_split_clause,[],[f4023,f6673]) ).
fof(f6673,plain,
( spl104_139
<=> class_Groups_Ozero(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_139])]) ).
fof(f4023,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1172]) ).
fof(f1172,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Ozero) ).
fof(f6671,plain,
spl104_138,
inference(avatar_split_clause,[],[f4022,f6668]) ).
fof(f6668,plain,
( spl104_138
<=> class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_138])]) ).
fof(f4022,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1005]) ).
fof(f1005,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).
fof(f6666,plain,
spl104_137,
inference(avatar_split_clause,[],[f4021,f6663]) ).
fof(f6663,plain,
( spl104_137
<=> class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_137])]) ).
fof(f4021,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/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Ocomm__monoid__mult) ).
fof(f6661,plain,
spl104_136,
inference(avatar_split_clause,[],[f4020,f6658]) ).
fof(f6658,plain,
( spl104_136
<=> class_Rings_Osemiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_136])]) ).
fof(f4020,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1167]) ).
fof(f1167,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Osemiring) ).
fof(f6656,plain,
spl104_135,
inference(avatar_split_clause,[],[f4019,f6653]) ).
fof(f6653,plain,
( spl104_135
<=> class_Rings_Osemiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_135])]) ).
fof(f4019,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1204]) ).
fof(f1204,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(f6651,plain,
spl104_134,
inference(avatar_split_clause,[],[f4018,f6648]) ).
fof(f6648,plain,
( spl104_134
<=> class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_134])]) ).
fof(f4018,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1186]) ).
fof(f1186,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(f6646,plain,
spl104_133,
inference(avatar_split_clause,[],[f4017,f6643]) ).
fof(f6643,plain,
( spl104_133
<=> class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_133])]) ).
fof(f4017,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1001]) ).
fof(f1001,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
fof(f6641,plain,
spl104_132,
inference(avatar_split_clause,[],[f4016,f6638]) ).
fof(f6638,plain,
( spl104_132
<=> class_Rings_Osemiring__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_132])]) ).
fof(f4016,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1199]) ).
fof(f1199,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(f6636,plain,
spl104_131,
inference(avatar_split_clause,[],[f4015,f6633]) ).
fof(f6633,plain,
( spl104_131
<=> class_Groups_Ozero(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_131])]) ).
fof(f4015,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1208]) ).
fof(f1208,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(f6631,plain,
spl104_130,
inference(avatar_split_clause,[],[f4014,f6628]) ).
fof(f6628,plain,
( spl104_130
<=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_130])]) ).
fof(f4014,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1101]) ).
fof(f1101,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(f6626,plain,
spl104_129,
inference(avatar_split_clause,[],[f4013,f6623]) ).
fof(f6623,plain,
( spl104_129
<=> class_Groups_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_129])]) ).
fof(f4013,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1058]) ).
fof(f1058,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Omonoid__add) ).
fof(f6621,plain,
spl104_128,
inference(avatar_split_clause,[],[f4012,f6618]) ).
fof(f6618,plain,
( spl104_128
<=> class_Groups_Omonoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_128])]) ).
fof(f4012,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1159]) ).
fof(f1159,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Omonoid__add) ).
fof(f6616,plain,
spl104_127,
inference(avatar_split_clause,[],[f4011,f6613]) ).
fof(f6613,plain,
( spl104_127
<=> class_Groups_Omonoid__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_127])]) ).
fof(f4011,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1197]) ).
fof(f1197,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Groups_Omonoid__add) ).
fof(f6611,plain,
spl104_126,
inference(avatar_split_clause,[],[f4010,f6608]) ).
fof(f6608,plain,
( spl104_126
<=> class_Groups_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_126])]) ).
fof(f4010,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f1111]) ).
fof(f1111,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Oone) ).
fof(f6606,plain,
spl104_125,
inference(avatar_split_clause,[],[f4009,f6603]) ).
fof(f6603,plain,
( spl104_125
<=> class_Nat_Osemiring__char__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_125])]) ).
fof(f4009,plain,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f1096]) ).
fof(f1096,axiom,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Nat_Osemiring__char__0) ).
fof(f6601,plain,
spl104_124,
inference(avatar_split_clause,[],[f4008,f6598]) ).
fof(f6598,plain,
( spl104_124
<=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_124])]) ).
fof(f4008,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1089]) ).
fof(f1089,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(f6596,plain,
spl104_123,
inference(avatar_split_clause,[],[f4007,f6593]) ).
fof(f6593,plain,
( spl104_123
<=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_123])]) ).
fof(f4007,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1095]) ).
fof(f1095,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(f6591,plain,
spl104_122,
inference(avatar_split_clause,[],[f4006,f6588]) ).
fof(f6588,plain,
( spl104_122
<=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_122])]) ).
fof(f4006,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f1087]) ).
fof(f1087,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(f6586,plain,
spl104_121,
inference(avatar_split_clause,[],[f4005,f6583]) ).
fof(f6583,plain,
( spl104_121
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_121])]) ).
fof(f4005,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1081]) ).
fof(f1081,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(f6581,plain,
spl104_120,
inference(avatar_split_clause,[],[f4004,f6578]) ).
fof(f6578,plain,
( spl104_120
<=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_120])]) ).
fof(f4004,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1049]) ).
fof(f1049,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(f6576,plain,
spl104_119,
inference(avatar_split_clause,[],[f4003,f6573]) ).
fof(f6573,plain,
( spl104_119
<=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_119])]) ).
fof(f4003,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f1038]) ).
fof(f1038,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(f6571,plain,
spl104_118,
inference(avatar_split_clause,[],[f4002,f6568]) ).
fof(f6568,plain,
( spl104_118
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_118])]) ).
fof(f4002,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1027]) ).
fof(f1027,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(f6566,plain,
spl104_117,
inference(avatar_split_clause,[],[f4001,f6563]) ).
fof(f6563,plain,
( spl104_117
<=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_117])]) ).
fof(f4001,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1040]) ).
fof(f1040,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(f6561,plain,
spl104_116,
inference(avatar_split_clause,[],[f4000,f6558]) ).
fof(f6558,plain,
( spl104_116
<=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_116])]) ).
fof(f4000,plain,
class_Nat_Osemiring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f1050]) ).
fof(f1050,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Nat_Osemiring__char__0) ).
fof(f6556,plain,
spl104_115,
inference(avatar_split_clause,[],[f3999,f6553]) ).
fof(f6553,plain,
( spl104_115
<=> class_Groups_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_115])]) ).
fof(f3999,plain,
class_Groups_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f1073]) ).
fof(f1073,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Oone) ).
fof(f6551,plain,
spl104_114,
inference(avatar_split_clause,[],[f3998,f6548]) ).
fof(f6548,plain,
( spl104_114
<=> class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_114])]) ).
fof(f3998,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1128]) ).
fof(f1128,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add) ).
fof(f6546,plain,
spl104_113,
inference(avatar_split_clause,[],[f3997,f6543]) ).
fof(f6543,plain,
( spl104_113
<=> class_Nat_Osemiring__char__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_113])]) ).
fof(f3997,plain,
class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1151]) ).
fof(f1151,axiom,
class_Nat_Osemiring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Nat_Osemiring__char__0) ).
fof(f6541,plain,
spl104_112,
inference(avatar_split_clause,[],[f3996,f6538]) ).
fof(f6538,plain,
( spl104_112
<=> class_Rings_Ocomm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_112])]) ).
fof(f3996,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1150]) ).
fof(f1150,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Ocomm__semiring) ).
fof(f6536,plain,
spl104_111,
inference(avatar_split_clause,[],[f3995,f6533]) ).
fof(f6533,plain,
( spl104_111
<=> class_Groups_Oone(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_111])]) ).
fof(f3995,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1175]) ).
fof(f1175,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Oone) ).
fof(f6531,plain,
spl104_110,
inference(avatar_split_clause,[],[f3994,f6528]) ).
fof(f6528,plain,
( spl104_110
<=> class_Groups_Oab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_110])]) ).
fof(f3994,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/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Oab__semigroup__add) ).
fof(f6526,plain,
spl104_109,
inference(avatar_split_clause,[],[f3993,f6523]) ).
fof(f6523,plain,
( spl104_109
<=> class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_109])]) ).
fof(f3993,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/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Oab__semigroup__mult) ).
fof(f6521,plain,
spl104_108,
inference(avatar_split_clause,[],[f3992,f6518]) ).
fof(f6518,plain,
( spl104_108
<=> class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_108])]) ).
fof(f3992,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1187]) ).
fof(f1187,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(f6516,plain,
spl104_107,
inference(avatar_split_clause,[],[f3991,f6513]) ).
fof(f6513,plain,
( spl104_107
<=> class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_107])]) ).
fof(f3991,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1185]) ).
fof(f1185,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(f6511,plain,
spl104_106,
inference(avatar_split_clause,[],[f3990,f6508]) ).
fof(f6508,plain,
( spl104_106
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_106])]) ).
fof(f3990,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1180]) ).
fof(f1180,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add) ).
fof(f6506,plain,
spl104_105,
inference(avatar_split_clause,[],[f3989,f6503]) ).
fof(f6503,plain,
( spl104_105
<=> class_Groups_Oone(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_105])]) ).
fof(f3989,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1211]) ).
fof(f1211,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Groups_Oone) ).
fof(f6501,plain,
spl104_104,
inference(avatar_split_clause,[],[f3988,f6498]) ).
fof(f6498,plain,
( spl104_104
<=> class_Rings_Ocomm__semiring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_104])]) ).
fof(f3988,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1191]) ).
fof(f1191,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Ocomm__semiring) ).
fof(f6496,plain,
spl104_103,
inference(avatar_split_clause,[],[f3987,f6493]) ).
fof(f6493,plain,
( spl104_103
<=> class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_103])]) ).
fof(f3987,plain,
class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1192]) ).
fof(f1192,axiom,
class_Nat_Osemiring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Nat_Osemiring__char__0) ).
fof(f6491,plain,
spl104_102,
inference(avatar_split_clause,[],[f3986,f6488]) ).
fof(f6488,plain,
( spl104_102
<=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_102])]) ).
fof(f3986,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f1086]) ).
fof(f1086,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(f6486,plain,
spl104_101,
inference(avatar_split_clause,[],[f3985,f6483]) ).
fof(f6483,plain,
( spl104_101
<=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_101])]) ).
fof(f3985,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(cnf_transformation,[],[f1037]) ).
fof(f1037,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(f6481,plain,
spl104_100,
inference(avatar_split_clause,[],[f3984,f6478]) ).
fof(f6478,plain,
( spl104_100
<=> class_Rings_Olinordered__semidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_100])]) ).
fof(f3984,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/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Olinordered__semidom) ).
fof(f6476,plain,
spl104_99,
inference(avatar_split_clause,[],[f3983,f6473]) ).
fof(f6473,plain,
( spl104_99
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_99])]) ).
fof(f3983,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1065]) ).
fof(f1065,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Int_Onumber__ring) ).
fof(f6471,plain,
spl104_98,
inference(avatar_split_clause,[],[f3982,f6468]) ).
fof(f3982,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1166]) ).
fof(f1166,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Int_Onumber__ring) ).
fof(f6466,plain,
spl104_97,
inference(avatar_split_clause,[],[f3981,f6463]) ).
fof(f3981,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1203]) ).
fof(f1203,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Int_Onumber__ring) ).
fof(f6461,plain,
spl104_96,
inference(avatar_split_clause,[],[f3980,f6458]) ).
fof(f6458,plain,
( spl104_96
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_96])]) ).
fof(f3980,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f1099]) ).
fof(f1099,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Orderings_Olinorder) ).
fof(f6456,plain,
spl104_95,
inference(avatar_split_clause,[],[f3979,f6453]) ).
fof(f6453,plain,
( spl104_95
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_95])]) ).
fof(f3979,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(cnf_transformation,[],[f1055]) ).
fof(f1055,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Orderings_Olinorder) ).
fof(f6451,plain,
spl104_94,
inference(avatar_split_clause,[],[f3978,f6448]) ).
fof(f6448,plain,
( spl104_94
<=> class_Orderings_Olinorder(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_94])]) ).
fof(f3978,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1156]) ).
fof(f1156,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Orderings_Olinorder) ).
fof(f6446,plain,
spl104_93,
inference(avatar_split_clause,[],[f3977,f6443]) ).
fof(f6443,plain,
( spl104_93
<=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_93])]) ).
fof(f3977,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f1078]) ).
fof(f1078,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(f6441,plain,
spl104_92,
inference(avatar_split_clause,[],[f3976,f6438]) ).
fof(f6438,plain,
( spl104_92
<=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_92])]) ).
fof(f3976,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1022]) ).
fof(f1022,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(f6436,plain,
spl104_91,
inference(avatar_split_clause,[],[f3975,f6433]) ).
fof(f6433,plain,
( spl104_91
<=> class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_91])]) ).
fof(f3975,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1121]) ).
fof(f1121,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Olinordered__semiring__strict) ).
fof(f6431,plain,
spl104_90,
inference(avatar_split_clause,[],[f3974,f6428]) ).
fof(f6428,plain,
( spl104_90
<=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_90])]) ).
fof(f3974,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1080]) ).
fof(f1080,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(f6426,plain,
spl104_89,
inference(avatar_split_clause,[],[f3973,f6423]) ).
fof(f6423,plain,
( spl104_89
<=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_89])]) ).
fof(f3973,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1025]) ).
fof(f1025,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(f6421,plain,
spl104_88,
inference(avatar_split_clause,[],[f3972,f6418]) ).
fof(f6418,plain,
( spl104_88
<=> class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_88])]) ).
fof(f3972,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1126]) ).
fof(f1126,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add) ).
fof(f6416,plain,
spl104_87,
inference(avatar_split_clause,[],[f3971,f6413]) ).
fof(f6413,plain,
( spl104_87
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_87])]) ).
fof(f3971,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[],[f1076]) ).
fof(f1076,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f6411,plain,
spl104_86,
inference(avatar_split_clause,[],[f3970,f6408]) ).
fof(f6408,plain,
( spl104_86
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_86])]) ).
fof(f3970,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[],[f1019]) ).
fof(f1019,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f6406,plain,
spl104_85,
inference(avatar_split_clause,[],[f3969,f6403]) ).
fof(f6403,plain,
( spl104_85
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_85])]) ).
fof(f3969,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1117]) ).
fof(f1117,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f6401,plain,
spl104_84,
inference(avatar_split_clause,[],[f3968,f6398]) ).
fof(f6398,plain,
( spl104_84
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_84])]) ).
fof(f3968,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1075]) ).
fof(f1075,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f6396,plain,
spl104_83,
inference(avatar_split_clause,[],[f3967,f6393]) ).
fof(f6393,plain,
( spl104_83
<=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_83])]) ).
fof(f3967,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1082]) ).
fof(f1082,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(f6391,plain,
spl104_82,
inference(avatar_split_clause,[],[f3966,f6388]) ).
fof(f6388,plain,
( spl104_82
<=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_82])]) ).
fof(f3966,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1057]) ).
fof(f1057,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(f6386,plain,
spl104_81,
inference(avatar_split_clause,[],[f3965,f6383]) ).
fof(f6383,plain,
( spl104_81
<=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_81])]) ).
fof(f3965,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1029]) ).
fof(f1029,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(f6381,plain,
spl104_80,
inference(avatar_split_clause,[],[f3964,f6378]) ).
fof(f6378,plain,
( spl104_80
<=> class_Rings_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_80])]) ).
fof(f3964,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(cnf_transformation,[],[f1010]) ).
fof(f1010,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Oidom) ).
fof(f6376,plain,
spl104_79,
inference(avatar_split_clause,[],[f3963,f6373]) ).
fof(f6373,plain,
( spl104_79
<=> class_Groups_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_79])]) ).
fof(f3963,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1051]) ).
fof(f1051,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Oab__group__add) ).
fof(f6371,plain,
spl104_78,
inference(avatar_split_clause,[],[f3962,f6368]) ).
fof(f3962,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1061]) ).
fof(f1061,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Ogroup__add) ).
fof(f6366,plain,
spl104_77,
inference(avatar_split_clause,[],[f3961,f6363]) ).
fof(f6363,plain,
( spl104_77
<=> class_Rings_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_77])]) ).
fof(f3961,plain,
class_Rings_Oring(tc_Int_Oint),
inference(cnf_transformation,[],[f1071]) ).
fof(f1071,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Oring) ).
fof(f6361,plain,
spl104_76,
inference(avatar_split_clause,[],[f3960,f6358]) ).
fof(f6358,plain,
( spl104_76
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_76])]) ).
fof(f3960,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1018]) ).
fof(f1018,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f6356,plain,
spl104_75,
inference(avatar_split_clause,[],[f3959,f6353]) ).
fof(f6353,plain,
( spl104_75
<=> class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_75])]) ).
fof(f3959,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1130]) ).
fof(f1130,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Oordered__cancel__semiring) ).
fof(f6351,plain,
spl104_74,
inference(avatar_split_clause,[],[f3958,f6348]) ).
fof(f6348,plain,
( spl104_74
<=> class_Rings_Ocomm__ring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_74])]) ).
fof(f3958,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1158]) ).
fof(f1158,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Ocomm__ring__1) ).
fof(f6346,plain,
spl104_73,
inference(avatar_split_clause,[],[f3957,f6343]) ).
fof(f6343,plain,
( spl104_73
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_73])]) ).
fof(f3957,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1116]) ).
fof(f1116,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f6341,plain,
spl104_72,
inference(avatar_split_clause,[],[f3956,f6338]) ).
fof(f6338,plain,
( spl104_72
<=> class_Rings_Oidom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_72])]) ).
fof(f3956,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1004]) ).
fof(f1004,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Oidom) ).
fof(f6336,plain,
spl104_71,
inference(avatar_split_clause,[],[f3955,f6333]) ).
fof(f6333,plain,
( spl104_71
<=> class_Groups_Ogroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_71])]) ).
fof(f3955,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/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(f6331,plain,
spl104_70,
inference(avatar_split_clause,[],[f3954,f6328]) ).
fof(f6328,plain,
( spl104_70
<=> class_Rings_Oring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_70])]) ).
fof(f3954,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1173]) ).
fof(f1173,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Oring) ).
fof(f6326,plain,
spl104_69,
inference(avatar_split_clause,[],[f3953,f6323]) ).
fof(f6323,plain,
( spl104_69
<=> class_Groups_Oab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_69])]) ).
fof(f3953,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1152]) ).
fof(f1152,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Oab__group__add) ).
fof(f6321,plain,
spl104_68,
inference(avatar_split_clause,[],[f3952,f6318]) ).
fof(f6318,plain,
( spl104_68
<=> class_Rings_Oring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_68])]) ).
fof(f3952,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1209]) ).
fof(f1209,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Oring) ).
fof(f6316,plain,
spl104_67,
inference(avatar_split_clause,[],[f3951,f6313]) ).
fof(f6313,plain,
( spl104_67
<=> class_Rings_Oidom(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_67])]) ).
fof(f3951,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1000]) ).
fof(f1000,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(f6311,plain,
spl104_66,
inference(avatar_split_clause,[],[f3950,f6308]) ).
fof(f6308,plain,
( spl104_66
<=> class_Groups_Ogroup__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_66])]) ).
fof(f3950,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1200]) ).
fof(f1200,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(f6306,plain,
spl104_65,
inference(avatar_split_clause,[],[f3949,f6303]) ).
fof(f6303,plain,
( spl104_65
<=> class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_65])]) ).
fof(f3949,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1196]) ).
fof(f1196,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Ocomm__ring__1) ).
fof(f6301,plain,
spl104_64,
inference(avatar_split_clause,[],[f3948,f6298]) ).
fof(f6298,plain,
( spl104_64
<=> class_Groups_Oab__group__add(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_64])]) ).
fof(f3948,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1193]) ).
fof(f1193,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Groups_Oab__group__add) ).
fof(f6296,plain,
spl104_63,
inference(avatar_split_clause,[],[f3947,f6293]) ).
fof(f6293,plain,
( spl104_63
<=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_63])]) ).
fof(f3947,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1090]) ).
fof(f1090,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(f6291,plain,
spl104_62,
inference(avatar_split_clause,[],[f3946,f6288]) ).
fof(f6288,plain,
( spl104_62
<=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_62])]) ).
fof(f3946,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1041]) ).
fof(f1041,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(f6286,plain,
spl104_61,
inference(avatar_split_clause,[],[f3945,f6283]) ).
fof(f6283,plain,
( spl104_61
<=> class_Rings_Oordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_61])]) ).
fof(f3945,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1143]) ).
fof(f1143,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Oordered__semiring) ).
fof(f6281,plain,
spl104_60,
inference(avatar_split_clause,[],[f3944,f6278]) ).
fof(f6278,plain,
( spl104_60
<=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_60])]) ).
fof(f3944,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f1079]) ).
fof(f1079,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(f6276,plain,
spl104_59,
inference(avatar_split_clause,[],[f3943,f6273]) ).
fof(f6273,plain,
( spl104_59
<=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_59])]) ).
fof(f3943,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1023]) ).
fof(f1023,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(f6271,plain,
spl104_58,
inference(avatar_split_clause,[],[f3942,f6268]) ).
fof(f6268,plain,
( spl104_58
<=> class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_58])]) ).
fof(f3942,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/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add) ).
fof(f6266,plain,
spl104_57,
inference(avatar_split_clause,[],[f3941,f6263]) ).
fof(f6263,plain,
( spl104_57
<=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_57])]) ).
fof(f3941,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1085]) ).
fof(f1085,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(f6261,plain,
spl104_56,
inference(avatar_split_clause,[],[f3940,f6258]) ).
fof(f6258,plain,
( spl104_56
<=> class_Rings_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_56])]) ).
fof(f3940,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1068]) ).
fof(f1068,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Oring__1) ).
fof(f6256,plain,
spl104_55,
inference(avatar_split_clause,[],[f3939,f6253]) ).
fof(f6253,plain,
( spl104_55
<=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_55])]) ).
fof(f3939,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1036]) ).
fof(f1036,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(f6251,plain,
spl104_54,
inference(avatar_split_clause,[],[f3938,f6248]) ).
fof(f6248,plain,
( spl104_54
<=> class_Rings_Ocomm__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_54])]) ).
fof(f3938,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1013]) ).
fof(f1013,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(f6246,plain,
spl104_53,
inference(avatar_split_clause,[],[f3937,f6243]) ).
fof(f6243,plain,
( spl104_53
<=> class_Rings_Ocomm__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_53])]) ).
fof(f3937,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1007]) ).
fof(f1007,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
fof(f6241,plain,
spl104_52,
inference(avatar_split_clause,[],[f3936,f6238]) ).
fof(f6238,plain,
( spl104_52
<=> class_Rings_Olinordered__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_52])]) ).
fof(f3936,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1138]) ).
fof(f1138,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
fof(f6236,plain,
spl104_51,
inference(avatar_split_clause,[],[f3935,f6233]) ).
fof(f6233,plain,
( spl104_51
<=> class_Rings_Oring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_51])]) ).
fof(f3935,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1169]) ).
fof(f1169,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Oring__1) ).
fof(f6231,plain,
spl104_50,
inference(avatar_split_clause,[],[f3934,f6228]) ).
fof(f6228,plain,
( spl104_50
<=> class_Rings_Oring__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_50])]) ).
fof(f3934,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1205]) ).
fof(f1205,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(f6226,plain,
spl104_49,
inference(avatar_split_clause,[],[f3933,f6223]) ).
fof(f6223,plain,
( spl104_49
<=> class_Rings_Ocomm__ring(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_49])]) ).
fof(f3933,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1003]) ).
fof(f1003,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(f6221,plain,
spl104_48,
inference(avatar_split_clause,[],[f3932,f6218]) ).
fof(f6218,plain,
( spl104_48
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_48])]) ).
fof(f3932,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f1077]) ).
fof(f1077,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(f6216,plain,
spl104_47,
inference(avatar_split_clause,[],[f3931,f6213]) ).
fof(f6213,plain,
( spl104_47
<=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_47])]) ).
fof(f3931,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f1083]) ).
fof(f1083,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(f6211,plain,
spl104_46,
inference(avatar_split_clause,[],[f3930,f6208]) ).
fof(f6208,plain,
( spl104_46
<=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_46])]) ).
fof(f3930,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f1032]) ).
fof(f1032,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(f6206,plain,
spl104_45,
inference(avatar_split_clause,[],[f3929,f6203]) ).
fof(f6203,plain,
( spl104_45
<=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_45])]) ).
fof(f3929,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1028]) ).
fof(f1028,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(f6201,plain,
spl104_44,
inference(avatar_split_clause,[],[f3928,f6198]) ).
fof(f6198,plain,
( spl104_44
<=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_44])]) ).
fof(f3928,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f1031]) ).
fof(f1031,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(f6196,plain,
spl104_43,
inference(avatar_split_clause,[],[f3927,f6193]) ).
fof(f6193,plain,
( spl104_43
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_43])]) ).
fof(f3927,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1020]) ).
fof(f1020,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(f6191,plain,
spl104_42,
inference(avatar_split_clause,[],[f3926,f6188]) ).
fof(f6188,plain,
( spl104_42
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_42])]) ).
fof(f3926,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f1064]) ).
fof(f1064,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Int_Oring__char__0) ).
fof(f6186,plain,
spl104_41,
inference(avatar_split_clause,[],[f3925,f6183]) ).
fof(f6183,plain,
( spl104_41
<=> class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_41])]) ).
fof(f3925,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1118]) ).
fof(f1118,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
fof(f6181,plain,
spl104_40,
inference(avatar_split_clause,[],[f3924,f6178]) ).
fof(f6178,plain,
( spl104_40
<=> class_Int_Oring__char__0(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_40])]) ).
fof(f3924,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1165]) ).
fof(f1165,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Int_Oring__char__0) ).
fof(f6176,plain,
spl104_39,
inference(avatar_split_clause,[],[f3923,f6173]) ).
fof(f6173,plain,
( spl104_39
<=> class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_39])]) ).
fof(f3923,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1129]) ).
fof(f1129,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors) ).
fof(f6171,plain,
spl104_38,
inference(avatar_split_clause,[],[f3922,f6168]) ).
fof(f6168,plain,
( spl104_38
<=> class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_38])]) ).
fof(f3922,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1133]) ).
fof(f1133,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Oring__no__zero__divisors) ).
fof(f6166,plain,
spl104_37,
inference(avatar_split_clause,[],[f3921,f6163]) ).
fof(f6163,plain,
( spl104_37
<=> class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_37])]) ).
fof(f3921,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1134]) ).
fof(f1134,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Oordered__comm__semiring) ).
fof(f6161,plain,
spl104_36,
inference(avatar_split_clause,[],[f3920,f6158]) ).
fof(f6158,plain,
( spl104_36
<=> class_Int_Oring__char__0(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_36])]) ).
fof(f3920,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1202]) ).
fof(f1202,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(f6156,plain,
spl104_35,
inference(avatar_split_clause,[],[f3919,f6153]) ).
fof(f6153,plain,
( spl104_35
<=> class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_35])]) ).
fof(f3919,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1183]) ).
fof(f1183,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors) ).
fof(f6151,plain,
spl104_34,
inference(avatar_split_clause,[],[f3918,f6148]) ).
fof(f6148,plain,
( spl104_34
<=> class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_34])]) ).
fof(f3918,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1181]) ).
fof(f1181,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors) ).
fof(f6146,plain,
spl104_33,
inference(avatar_split_clause,[],[f3917,f6143]) ).
fof(f6143,plain,
( spl104_33
<=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_33])]) ).
fof(f3917,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(cnf_transformation,[],[f1046]) ).
fof(f1046,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(f6141,plain,
spl104_32,
inference(avatar_split_clause,[],[f3916,f6138]) ).
fof(f6138,plain,
( spl104_32
<=> class_Rings_Olinordered__idom(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_32])]) ).
fof(f3916,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/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Olinordered__idom) ).
fof(f6136,plain,
spl104_31,
inference(avatar_split_clause,[],[f3915,f6133]) ).
fof(f3915,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f1024]) ).
fof(f1024,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(f6131,plain,
spl104_30,
inference(avatar_split_clause,[],[f3914,f6128]) ).
fof(f6128,plain,
( spl104_30
<=> class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_30])]) ).
fof(f3914,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1124]) ).
fof(f1124,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs) ).
fof(f6126,plain,
spl104_29,
inference(avatar_split_clause,[],[f3913,f6123]) ).
fof(f6123,plain,
( spl104_29
<=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_29])]) ).
fof(f3913,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1030]) ).
fof(f1030,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(f6121,plain,
spl104_28,
inference(avatar_split_clause,[],[f3912,f6118]) ).
fof(f6118,plain,
( spl104_28
<=> class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_28])]) ).
fof(f3912,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1132]) ).
fof(f1132,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Olinordered__ring__strict) ).
fof(f6116,plain,
spl104_27,
inference(avatar_split_clause,[],[f3911,f6113]) ).
fof(f6113,plain,
( spl104_27
<=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_27])]) ).
fof(f3911,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(cnf_transformation,[],[f1094]) ).
fof(f1094,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(f6111,plain,
spl104_26,
inference(avatar_split_clause,[],[f3910,f6108]) ).
fof(f6108,plain,
( spl104_26
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_26])]) ).
fof(f3910,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f1048]) ).
fof(f1048,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Divides_Osemiring__div) ).
fof(f6106,plain,
spl104_25,
inference(avatar_split_clause,[],[f3909,f6103]) ).
fof(f6103,plain,
( spl104_25
<=> class_Rings_Oordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_25])]) ).
fof(f3909,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1053]) ).
fof(f1053,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Oordered__ring) ).
fof(f6101,plain,
spl104_24,
inference(avatar_split_clause,[],[f3908,f6098]) ).
fof(f6098,plain,
( spl104_24
<=> class_Rings_Oordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_24])]) ).
fof(f3908,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1154]) ).
fof(f1154,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Oordered__ring) ).
fof(f6096,plain,
spl104_23,
inference(avatar_split_clause,[],[f3907,f6093]) ).
fof(f6093,plain,
( spl104_23
<=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_23])]) ).
fof(f3907,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1026]) ).
fof(f1026,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(f6091,plain,
spl104_22,
inference(avatar_split_clause,[],[f3906,f6088]) ).
fof(f6088,plain,
( spl104_22
<=> class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_22])]) ).
fof(f3906,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1127]) ).
fof(f1127,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Olinordered__ab__group__add) ).
fof(f6086,plain,
spl104_21,
inference(avatar_split_clause,[],[f3905,f6083]) ).
fof(f6083,plain,
( spl104_21
<=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_21])]) ).
fof(f3905,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f1045]) ).
fof(f1045,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(f6081,plain,
spl104_20,
inference(avatar_split_clause,[],[f3904,f6078]) ).
fof(f6078,plain,
( spl104_20
<=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_20])]) ).
fof(f3904,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f1034]) ).
fof(f1034,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(f6076,plain,
spl104_19,
inference(avatar_split_clause,[],[f3903,f6073]) ).
fof(f6073,plain,
( spl104_19
<=> class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_19])]) ).
fof(f3903,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1136]) ).
fof(f1136,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Groups_Oordered__ab__group__add) ).
fof(f6071,plain,
spl104_18,
inference(avatar_split_clause,[],[f3902,f6068]) ).
fof(f6068,plain,
( spl104_18
<=> class_Rings_Olinordered__ring(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_18])]) ).
fof(f3902,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/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Olinordered__ring) ).
fof(f6066,plain,
spl104_17,
inference(avatar_split_clause,[],[f3901,f6063]) ).
fof(f6063,plain,
( spl104_17
<=> class_Rings_Oordered__ring__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_17])]) ).
fof(f3901,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f1042]) ).
fof(f1042,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(f6061,plain,
spl104_16,
inference(avatar_split_clause,[],[f3900,f6058]) ).
fof(f6058,plain,
( spl104_16
<=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_16])]) ).
fof(f3900,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f1033]) ).
fof(f1033,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(f6056,plain,
spl104_15,
inference(avatar_split_clause,[],[f3899,f6053]) ).
fof(f6053,plain,
( spl104_15
<=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_15])]) ).
fof(f3899,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f1021]) ).
fof(f1021,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(f6051,plain,
spl104_14,
inference(avatar_split_clause,[],[f3898,f6048]) ).
fof(f6048,plain,
( spl104_14
<=> class_Rings_Oordered__ring__abs(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_14])]) ).
fof(f3898,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1144]) ).
fof(f1144,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
fof(f6046,plain,
spl104_13,
inference(avatar_split_clause,[],[f3897,f6043]) ).
fof(f6043,plain,
( spl104_13
<=> class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_13])]) ).
fof(f3897,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1135]) ).
fof(f1135,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
fof(f6041,plain,
spl104_12,
inference(avatar_split_clause,[],[f3896,f6038]) ).
fof(f6038,plain,
( spl104_12
<=> class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_12])]) ).
fof(f3896,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1119]) ).
fof(f1119,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
fof(f6036,plain,
spl104_11,
inference(avatar_split_clause,[],[f3895,f6033]) ).
fof(f6033,plain,
( spl104_11
<=> class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_11])]) ).
fof(f3895,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1131]) ).
fof(f1131,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).
fof(f6031,plain,
spl104_10,
inference(avatar_split_clause,[],[f3894,f6028]) ).
fof(f6028,plain,
( spl104_10
<=> class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_10])]) ).
fof(f3894,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1182]) ).
fof(f1182,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).
fof(f6026,plain,
spl104_9,
inference(avatar_split_clause,[],[f3893,f6023]) ).
fof(f6023,plain,
( spl104_9
<=> class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_9])]) ).
fof(f3893,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1125]) ).
fof(f1125,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).
fof(f6021,plain,
spl104_8,
inference(avatar_split_clause,[],[f3892,f6018]) ).
fof(f6018,plain,
( spl104_8
<=> class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_8])]) ).
fof(f3892,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1179]) ).
fof(f1179,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).
fof(f6016,plain,
spl104_7,
inference(avatar_split_clause,[],[f3891,f6013]) ).
fof(f6013,plain,
( spl104_7
<=> class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_7])]) ).
fof(f3891,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/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).
fof(f6011,plain,
spl104_6,
inference(avatar_split_clause,[],[f3890,f6008]) ).
fof(f6008,plain,
( spl104_6
<=> class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_6])]) ).
fof(f3890,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1178]) ).
fof(f1178,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).
fof(f6006,plain,
spl104_5,
inference(avatar_split_clause,[],[f3889,f6003]) ).
fof(f6003,plain,
( spl104_5
<=> class_Fields_Ofield(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_5])]) ).
fof(f3889,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1170]) ).
fof(f1170,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__Fields_Ofield) ).
fof(f6001,plain,
spl104_4,
inference(avatar_split_clause,[],[f3888,f5998]) ).
fof(f5998,plain,
( spl104_4
<=> class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_4])]) ).
fof(f3888,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(cnf_transformation,[],[f1120]) ).
fof(f1120,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).
fof(f5996,plain,
spl104_3,
inference(avatar_split_clause,[],[f3887,f5993]) ).
fof(f5993,plain,
( spl104_3
<=> class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_3])]) ).
fof(f3887,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1177]) ).
fof(f1177,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).
fof(f5991,plain,
spl104_2,
inference(avatar_split_clause,[],[f3886,f5988]) ).
fof(f5988,plain,
( spl104_2
<=> class_Fields_Ofield(tc_Complex_Ocomplex) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_2])]) ).
fof(f3886,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(cnf_transformation,[],[f1206]) ).
fof(f1206,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',arity_Complex__Ocomplex__Fields_Ofield) ).
fof(f5986,plain,
spl104_1,
inference(avatar_split_clause,[],[f3885,f5983]) ).
fof(f5983,plain,
( spl104_1
<=> c_SEQ_Osubseq(v_f____) ),
introduced(avatar_definition,[new_symbols(naming,[spl104_1])]) ).
fof(f3885,plain,
c_SEQ_Osubseq(v_f____),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
c_SEQ_Osubseq(v_f____),
file('/export/starexec/sandbox2/tmp/tmp.HWViB2P9q3/Vampire---4.8_16678',fact_fz_I1_J) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.15/0.24 % Problem : SWW225+1 : TPTP v8.1.2. Released v5.2.0.
% 0.15/0.25 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.25/0.44 % Computer : n004.cluster.edu
% 0.25/0.44 % Model : x86_64 x86_64
% 0.25/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.44 % Memory : 8042.1875MB
% 0.25/0.44 % OS : Linux 3.10.0-693.el7.x86_64
% 0.25/0.44 % CPULimit : 300
% 0.25/0.44 % WCLimit : 300
% 0.25/0.44 % DateTime : Wed Aug 30 16:35:22 EDT 2023
% 0.25/0.45 % CPUTime :
% 0.29/0.50 % (16871)Running in auto input_syntax mode. Trying TPTP
% 0.29/0.54 % (16875)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.29/0.54 % (16883)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.29/0.54 % (16876)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.29/0.54 % (16886)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 Vampire---4 for (531ds/0Mi)
% 0.29/0.54 % (16880)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 Vampire---4 for (569ds/0Mi)
% 0.29/0.54 % (16888)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 Vampire---4 for (522ds/0Mi)
% 0.29/0.54 % (16889)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 Vampire---4 for (497ds/0Mi)
% 2.14/0.81 TRYING [1]
% 2.14/0.85 % (16886)First to succeed.
% 2.14/0.86 TRYING [2]
% 2.83/0.91 % (16886)Refutation found. Thanks to Tanya!
% 2.83/0.91 % SZS status Theorem for Vampire---4
% 2.83/0.91 % SZS output start Proof for Vampire---4
% See solution above
% 2.83/0.95 % (16886)------------------------------
% 2.83/0.95 % (16886)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 2.83/0.95 % (16886)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 2.83/0.95 % (16886)Termination reason: Refutation
% 2.83/0.95
% 2.83/0.95 % (16886)Memory used [KB]: 15863
% 2.83/0.95 % (16886)Time elapsed: 0.363 s
% 2.83/0.95 % (16886)------------------------------
% 2.83/0.95 % (16886)------------------------------
% 2.83/0.95 % (16871)Success in time 0.484 s
% 2.83/0.95 % Vampire---4.8 exiting
%------------------------------------------------------------------------------