TSTP Solution File: SWW317+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW317+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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 2 14:07:09 EDT 2023
% Result : Theorem 8.07s 2.58s
% Output : Refutation 8.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1784
% Syntax : Number of formulae : 4683 (2282 unt; 0 def)
% Number of atoms : 9514 (2366 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 7355 (2524 ~;2248 |; 837 &)
% (1218 <=>; 528 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 1133 (1131 usr; 905 prp; 0-6 aty)
% Number of functors : 251 ( 251 usr; 39 con; 0-5 aty)
% Number of variables : 6055 (;5885 !; 170 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33087,plain,
$false,
inference(avatar_sat_refutation,[],[f28024,f28029,f28034,f28039,f28044,f28049,f28054,f28059,f28064,f28069,f28074,f28079,f28084,f28089,f28094,f28099,f28104,f28109,f28114,f28119,f28124,f28129,f28134,f28139,f28144,f28149,f28154,f28159,f28164,f28169,f28174,f28179,f28184,f28189,f28194,f28199,f28204,f28209,f28214,f28219,f28224,f28229,f28234,f28239,f28244,f28249,f28254,f28259,f28264,f28269,f28274,f28279,f28284,f28289,f28294,f28299,f28304,f28309,f28314,f28319,f28324,f28329,f28334,f28339,f28344,f28349,f28354,f28359,f28364,f28369,f28374,f28379,f28384,f28389,f28394,f28399,f28404,f28409,f28414,f28419,f28424,f28429,f28434,f28439,f28444,f28449,f28454,f28459,f28464,f28469,f28474,f28479,f28484,f28489,f28494,f28499,f28504,f28509,f28514,f28519,f28524,f28529,f28534,f28539,f28544,f28549,f28554,f28559,f28564,f28569,f28574,f28579,f28584,f28589,f28594,f28599,f28604,f28609,f28614,f28619,f28624,f28629,f28634,f28639,f28644,f28649,f28654,f28659,f28664,f28669,f28674,f28679,f28684,f28689,f28694,f28699,f28704,f28709,f28714,f28719,f28724,f28729,f28734,f28739,f28744,f28749,f28754,f28759,f28764,f28769,f28774,f28779,f28784,f28789,f28794,f28799,f28804,f28809,f28814,f28819,f28824,f28829,f28834,f28839,f28844,f28849,f28854,f28859,f28864,f28869,f28874,f28879,f28884,f28889,f28894,f28899,f28904,f28909,f28914,f28919,f28924,f28929,f28934,f28939,f28944,f28949,f28954,f28959,f28964,f28969,f28974,f28979,f28984,f28989,f28994,f28999,f29004,f29009,f29014,f29019,f29025,f29030,f29035,f29039,f29043,f29047,f29051,f29055,f29059,f29063,f29067,f29071,f29075,f29080,f29085,f29090,f29095,f29100,f29105,f29110,f29115,f29119,f29123,f29127,f29131,f29135,f29139,f29143,f29147,f29152,f29157,f29164,f29170,f29175,f29180,f29185,f29190,f29195,f29200,f29205,f29210,f29215,f29221,f29225,f29229,f29233,f29237,f29241,f29245,f29249,f29253,f29257,f29261,f29265,f29269,f29273,f29277,f29281,f29285,f29289,f29293,f29297,f29301,f29305,f29310,f29315,f29320,f29327,f29332,f29338,f29345,f29350,f29354,f29358,f29362,f29366,f29370,f29374,f29378,f29382,f29386,f29390,f29394,f29398,f29402,f29406,f29410,f29414,f29418,f29422,f29426,f29430,f29434,f29438,f29442,f29448,f29452,f29456,f29460,f29464,f29468,f29472,f29476,f29480,f29484,f29489,f29493,f29497,f29501,f29505,f29509,f29513,f29517,f29521,f29525,f29529,f29533,f29537,f29541,f29545,f29549,f29553,f29557,f29561,f29565,f29569,f29574,f29579,f29584,f29589,f29594,f29598,f29602,f29606,f29610,f29614,f29618,f29622,f29634,f29657,f29662,f29667,f29688,f29693,f29699,f29705,f29711,f29716,f29722,f29727,f29732,f29737,f29742,f29747,f29752,f29757,f29762,f29767,f29772,f29777,f29782,f29787,f29792,f29798,f29803,f29808,f29812,f29816,f29820,f29824,f29828,f29832,f29836,f29840,f29844,f29848,f29853,f29857,f29861,f29865,f29869,f29873,f29877,f29881,f29885,f29889,f29893,f29897,f29901,f29905,f29909,f29913,f29917,f29921,f29925,f29929,f29933,f29937,f29942,f29946,f29950,f29954,f29958,f29962,f29966,f29970,f29974,f29978,f29983,f29987,f29991,f29995,f29999,f30003,f30007,f30011,f30015,f30019,f30023,f30027,f30031,f30035,f30039,f30043,f30048,f30053,f30058,f30063,f30068,f30073,f30078,f30083,f30088,f30096,f30101,f30107,f30112,f30117,f30121,f30125,f30130,f30145,f30158,f30172,f30191,f30196,f30201,f30206,f30211,f30215,f30220,f30227,f30232,f30239,f30243,f30248,f30255,f30260,f30267,f30271,f30275,f30279,f30283,f30287,f30291,f30295,f30299,f30303,f30307,f30311,f30315,f30319,f30323,f30328,f30332,f30336,f30340,f30344,f30348,f30352,f30356,f30360,f30364,f30368,f30372,f30376,f30380,f30384,f30388,f30392,f30396,f30400,f30404,f30408,f30412,f30416,f30420,f30424,f30428,f30432,f30436,f30440,f30444,f30448,f30452,f30456,f30460,f30464,f30468,f30476,f30480,f30484,f30488,f30492,f30496,f30500,f30504,f30508,f30512,f30516,f30520,f30524,f30528,f30532,f30536,f30540,f30544,f30548,f30552,f30556,f30560,f30564,f30568,f30572,f30576,f30580,f30584,f30588,f30592,f30596,f30600,f30604,f30608,f30612,f30616,f30620,f30624,f30628,f30633,f30638,f30644,f30655,f30660,f30665,f30670,f30676,f30682,f30686,f30690,f30694,f30698,f30702,f30706,f30710,f30714,f30718,f30722,f30726,f30730,f30734,f30738,f30742,f30746,f30752,f30761,f30770,f30775,f30822,f30827,f30847,f30852,f30856,f30860,f30865,f30869,f30874,f30878,f30882,f30886,f30890,f30894,f30898,f30902,f30906,f30910,f30914,f30919,f30923,f30928,f30932,f30936,f30940,f30944,f30948,f30952,f30956,f30960,f30964,f30969,f30979,f30984,f30994,f30998,f31002,f31006,f31010,f31014,f31018,f31022,f31026,f31030,f31034,f31038,f31042,f31046,f31050,f31054,f31058,f31062,f31066,f31070,f31075,f31079,f31083,f31087,f31091,f31095,f31099,f31103,f31107,f31111,f31115,f31119,f31123,f31127,f31131,f31135,f31139,f31143,f31147,f31151,f31155,f31159,f31163,f31167,f31171,f31175,f31179,f31183,f31188,f31192,f31196,f31200,f31204,f31208,f31212,f31216,f31220,f31224,f31228,f31232,f31236,f31240,f31244,f31248,f31252,f31256,f31260,f31264,f31268,f31272,f31277,f31281,f31285,f31289,f31293,f31297,f31301,f31305,f31309,f31313,f31317,f31321,f31325,f31329,f31333,f31337,f31341,f31345,f31349,f31353,f31357,f31361,f31365,f31369,f31373,f31377,f31381,f31385,f31389,f31393,f31397,f31401,f31405,f31410,f31414,f31418,f31422,f31426,f31430,f31434,f31438,f31442,f31446,f31450,f31455,f31459,f31463,f31470,f31493,f31497,f31527,f31538,f31548,f31573,f31662,f31698,f31744,f31772,f31777,f31782,f31787,f31792,f31798,f31802,f31806,f31810,f31814,f31819,f31824,f31828,f31832,f31836,f31840,f31844,f31848,f31853,f31857,f31861,f31865,f31869,f31873,f31877,f31881,f31885,f31889,f31893,f31897,f31901,f31905,f31909,f31913,f31917,f31922,f31926,f31930,f31934,f31938,f31942,f31946,f31950,f31954,f31958,f31963,f31967,f31971,f31975,f31979,f31983,f31987,f31991,f31995,f31999,f32006,f32010,f32014,f32018,f32022,f32026,f32030,f32034,f32038,f32042,f32047,f32051,f32055,f32059,f32063,f32067,f32071,f32075,f32079,f32083,f32087,f32092,f32096,f32100,f32104,f32108,f32112,f32116,f32120,f32124,f32128,f32136,f32140,f32144,f32148,f32152,f32156,f32160,f32164,f32168,f32172,f32176,f32180,f32184,f32188,f32192,f32196,f32200,f32204,f32208,f32213,f32218,f32224,f32228,f32232,f32236,f32240,f32244,f32248,f32252,f32256,f32265,f32269,f32273,f32277,f32281,f32285,f32289,f32293,f32297,f32301,f32306,f32310,f32314,f32318,f32322,f32326,f32330,f32334,f32338,f32343,f32348,f32354,f32359,f32363,f32367,f32371,f32375,f32379,f32383,f32387,f32391,f32400,f32404,f32408,f32412,f32417,f32425,f32429,f32440,f32466,f32927,f32943,f32955,f33051,f33055,f33059,f33063,f33069,f33086]) ).
fof(f33086,plain,
( spl698_233
| ~ spl698_888 ),
inference(avatar_contradiction_clause,[],[f33085]) ).
fof(f33085,plain,
( $false
| spl698_233
| ~ spl698_888 ),
inference(resolution,[],[f32403,f29169]) ).
fof(f29169,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)))
| spl698_233 ),
inference(avatar_component_clause,[],[f29167]) ).
fof(f29167,plain,
( spl698_233
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_233])]) ).
fof(f32403,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(X2,X0,c_Com_Ocom_OSKIP,X0)))
| ~ spl698_888 ),
inference(avatar_component_clause,[],[f32402]) ).
fof(f32402,plain,
( spl698_888
<=> ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(X2,X0,c_Com_Ocom_OSKIP,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_888])]) ).
fof(f33069,plain,
( spl698_904
| ~ spl698_378
| ~ spl698_818 ),
inference(avatar_split_clause,[],[f32755,f32098,f29855,f33067]) ).
fof(f33067,plain,
( spl698_904
<=> ! [X1] : ~ sP37(X1,X1,c_Natural_Oevalc(c_Com_Ocom_OSKIP)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_904])]) ).
fof(f29855,plain,
( spl698_378
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_378])]) ).
fof(f32098,plain,
( spl698_818
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP37(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_818])]) ).
fof(f32755,plain,
( ! [X1] : ~ sP37(X1,X1,c_Natural_Oevalc(c_Com_Ocom_OSKIP))
| ~ spl698_378
| ~ spl698_818 ),
inference(resolution,[],[f32099,f29856]) ).
fof(f29856,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X0),X0))
| ~ spl698_378 ),
inference(avatar_component_clause,[],[f29855]) ).
fof(f32099,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP37(X0,X1,X2) )
| ~ spl698_818 ),
inference(avatar_component_clause,[],[f32098]) ).
fof(f33063,plain,
( spl698_903
| ~ spl698_552
| ~ spl698_877 ),
inference(avatar_split_clause,[],[f32355,f32352,f30641,f33061]) ).
fof(f33061,plain,
( spl698_903
<=> ! [X0,X1] :
( c_Int_Osucc(c_Int_OPls) = X1
| c_Int_OMin = X1
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_903])]) ).
fof(f30641,plain,
( spl698_552
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Osucc(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_552])]) ).
fof(f32352,plain,
( spl698_877
<=> ! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_877])]) ).
fof(f32355,plain,
( ! [X0,X1] :
( c_Int_Osucc(c_Int_OPls) = X1
| c_Int_OMin = X1
| ~ sP8(X0,X1) )
| ~ spl698_552
| ~ spl698_877 ),
inference(forward_demodulation,[],[f32353,f30643]) ).
fof(f30643,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Osucc(c_Int_OPls)
| ~ spl698_552 ),
inference(avatar_component_clause,[],[f30641]) ).
fof(f32353,plain,
( ! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP8(X0,X1) )
| ~ spl698_877 ),
inference(avatar_component_clause,[],[f32352]) ).
fof(f33059,plain,
( spl698_902
| ~ spl698_552
| ~ spl698_876 ),
inference(avatar_split_clause,[],[f32349,f32346,f30641,f33057]) ).
fof(f33057,plain,
( spl698_902
<=> ! [X0,X1] :
( c_Int_Osucc(c_Int_OPls) = X0
| c_Int_OMin = X1
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_902])]) ).
fof(f32346,plain,
( spl698_876
<=> ! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_876])]) ).
fof(f32349,plain,
( ! [X0,X1] :
( c_Int_Osucc(c_Int_OPls) = X0
| c_Int_OMin = X1
| ~ sP8(X0,X1) )
| ~ spl698_552
| ~ spl698_876 ),
inference(forward_demodulation,[],[f32347,f30643]) ).
fof(f32347,plain,
( ! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP8(X0,X1) )
| ~ spl698_876 ),
inference(avatar_component_clause,[],[f32346]) ).
fof(f33055,plain,
( spl698_901
| ~ spl698_552
| ~ spl698_875 ),
inference(avatar_split_clause,[],[f32344,f32341,f30641,f33053]) ).
fof(f33053,plain,
( spl698_901
<=> ! [X0,X1] :
( c_Int_Osucc(c_Int_OPls) = X1
| c_Int_OMin = X0
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_901])]) ).
fof(f32341,plain,
( spl698_875
<=> ! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_875])]) ).
fof(f32344,plain,
( ! [X0,X1] :
( c_Int_Osucc(c_Int_OPls) = X1
| c_Int_OMin = X0
| ~ sP8(X0,X1) )
| ~ spl698_552
| ~ spl698_875 ),
inference(forward_demodulation,[],[f32342,f30643]) ).
fof(f32342,plain,
( ! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP8(X0,X1) )
| ~ spl698_875 ),
inference(avatar_component_clause,[],[f32341]) ).
fof(f33051,plain,
( spl698_900
| ~ spl698_552
| ~ spl698_874 ),
inference(avatar_split_clause,[],[f32339,f32336,f30641,f33049]) ).
fof(f33049,plain,
( spl698_900
<=> ! [X0,X1] :
( c_Int_Osucc(c_Int_OPls) = X0
| c_Int_OMin = X0
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_900])]) ).
fof(f32336,plain,
( spl698_874
<=> ! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_874])]) ).
fof(f32339,plain,
( ! [X0,X1] :
( c_Int_Osucc(c_Int_OPls) = X0
| c_Int_OMin = X0
| ~ sP8(X0,X1) )
| ~ spl698_552
| ~ spl698_874 ),
inference(forward_demodulation,[],[f32337,f30643]) ).
fof(f32337,plain,
( ! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP8(X0,X1) )
| ~ spl698_874 ),
inference(avatar_component_clause,[],[f32336]) ).
fof(f32955,plain,
( spl698_898
| ~ spl698_899
| ~ spl698_708
| ~ spl698_777 ),
inference(avatar_split_clause,[],[f32483,f31928,f31375,f32952,f32948]) ).
fof(f32948,plain,
( spl698_898
<=> c_Nat__Transfer_Ois__nat(c_Orderings_Otop__class_Otop(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_898])]) ).
fof(f32952,plain,
( spl698_899
<=> class_Orderings_Otop(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_899])]) ).
fof(f31375,plain,
( spl698_708
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| c_Nat__Transfer_Ois__nat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_708])]) ).
fof(f31928,plain,
( spl698_777
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_777])]) ).
fof(f32483,plain,
( ~ class_Orderings_Otop(tc_Int_Oint)
| c_Nat__Transfer_Ois__nat(c_Orderings_Otop__class_Otop(tc_Int_Oint))
| ~ spl698_708
| ~ spl698_777 ),
inference(resolution,[],[f31929,f31376]) ).
fof(f31376,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| c_Nat__Transfer_Ois__nat(X0) )
| ~ spl698_708 ),
inference(avatar_component_clause,[],[f31375]) ).
fof(f31929,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) )
| ~ spl698_777 ),
inference(avatar_component_clause,[],[f31928]) ).
fof(f32943,plain,
( spl698_897
| ~ spl698_594
| ~ spl698_846 ),
inference(avatar_split_clause,[],[f32219,f32215,f30900,f32940]) ).
fof(f32940,plain,
( spl698_897
<=> hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) = c_Option_Oset(tc_Nat_Onat,c_Option_Ooption_ONone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_897])]) ).
fof(f30900,plain,
( spl698_594
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Option_Oset(X0,c_Option_Ooption_ONone(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_594])]) ).
fof(f32215,plain,
( spl698_846
<=> c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_846])]) ).
fof(f32219,plain,
( hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) = c_Option_Oset(tc_Nat_Onat,c_Option_Ooption_ONone(tc_Nat_Onat))
| ~ spl698_594
| ~ spl698_846 ),
inference(forward_demodulation,[],[f32217,f30901]) ).
fof(f30901,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Option_Oset(X0,c_Option_Ooption_ONone(X0))
| ~ spl698_594 ),
inference(avatar_component_clause,[],[f30900]) ).
fof(f32217,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue))
| ~ spl698_846 ),
inference(avatar_component_clause,[],[f32215]) ).
fof(f32927,plain,
( spl698_896
| ~ spl698_377
| ~ spl698_818 ),
inference(avatar_split_clause,[],[f32754,f32098,f29851,f32925]) ).
fof(f32925,plain,
( spl698_896
<=> ! [X0] : ~ sP37(X0,X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_896])]) ).
fof(f29851,plain,
( spl698_377
<=> ! [X0] : hBOOL(hAPP(hAPP(c_fequal,X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_377])]) ).
fof(f32754,plain,
( ! [X0] : ~ sP37(X0,X0,c_fequal)
| ~ spl698_377
| ~ spl698_818 ),
inference(resolution,[],[f32099,f29852]) ).
fof(f29852,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_fequal,X0),X0))
| ~ spl698_377 ),
inference(avatar_component_clause,[],[f29851]) ).
fof(f32466,plain,
( spl698_895
| ~ spl698_329
| ~ spl698_734 ),
inference(avatar_split_clause,[],[f32393,f31536,f29581,f32463]) ).
fof(f32463,plain,
( spl698_895
<=> sP6(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_895])]) ).
fof(f29581,plain,
( spl698_329
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_329])]) ).
fof(f31536,plain,
( spl698_734
<=> ! [X0] : sP6(hAPP(c_Int_Onat,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_734])]) ).
fof(f32393,plain,
( sP6(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls)
| ~ spl698_329
| ~ spl698_734 ),
inference(superposition,[],[f31537,f29583]) ).
fof(f29583,plain,
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OPls)
| ~ spl698_329 ),
inference(avatar_component_clause,[],[f29581]) ).
fof(f31537,plain,
( ! [X0] : sP6(hAPP(c_Int_Onat,X0),X0)
| ~ spl698_734 ),
inference(avatar_component_clause,[],[f31536]) ).
fof(f32440,plain,
( spl698_894
| ~ spl698_552
| ~ spl698_757 ),
inference(avatar_split_clause,[],[f31849,f31846,f30641,f32438]) ).
fof(f32438,plain,
( spl698_894
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Int_Osucc(c_Int_OPls))
| ~ class_Rings_Oring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_894])]) ).
fof(f31846,plain,
( spl698_757
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Rings_Oring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_757])]) ).
fof(f31849,plain,
( ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Int_Osucc(c_Int_OPls))
| ~ class_Rings_Oring__1(X0) )
| ~ spl698_552
| ~ spl698_757 ),
inference(forward_demodulation,[],[f31847,f30643]) ).
fof(f31847,plain,
( ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Rings_Oring__1(X0) )
| ~ spl698_757 ),
inference(avatar_component_clause,[],[f31846]) ).
fof(f32429,plain,
( spl698_893
| ~ spl698_552
| ~ spl698_750 ),
inference(avatar_split_clause,[],[f31820,f31817,f30641,f32427]) ).
fof(f32427,plain,
( spl698_893
<=> ! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_Osucc(c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_893])]) ).
fof(f31817,plain,
( spl698_750
<=> ! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_750])]) ).
fof(f31820,plain,
( ! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_Osucc(c_Int_OPls))
| ~ spl698_552
| ~ spl698_750 ),
inference(forward_demodulation,[],[f31818,f30643]) ).
fof(f31818,plain,
( ! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl698_750 ),
inference(avatar_component_clause,[],[f31817]) ).
fof(f32425,plain,
( spl698_892
| ~ spl698_552
| ~ spl698_749 ),
inference(avatar_split_clause,[],[f31815,f31812,f30641,f32423]) ).
fof(f32423,plain,
( spl698_892
<=> ! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_Osucc(c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_892])]) ).
fof(f31812,plain,
( spl698_749
<=> ! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_749])]) ).
fof(f31815,plain,
( ! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_Osucc(c_Int_OPls))
| ~ spl698_552
| ~ spl698_749 ),
inference(forward_demodulation,[],[f31813,f30643]) ).
fof(f31813,plain,
( ! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl698_749 ),
inference(avatar_component_clause,[],[f31812]) ).
fof(f32417,plain,
( spl698_891
| ~ spl698_410
| ~ spl698_746 ),
inference(avatar_split_clause,[],[f32413,f31800,f29985,f32415]) ).
fof(f32415,plain,
( spl698_891
<=> ! [X0] : ~ class_Finite__Set_Ofinite(tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_891])]) ).
fof(f29985,plain,
( spl698_410
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_410])]) ).
fof(f31800,plain,
( spl698_746
<=> ! [X0] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X0)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X0),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_746])]) ).
fof(f32413,plain,
( ! [X0] : ~ class_Finite__Set_Ofinite(tc_List_Olist(X0))
| ~ spl698_410
| ~ spl698_746 ),
inference(resolution,[],[f31801,f29986]) ).
fof(f29986,plain,
( ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) )
| ~ spl698_410 ),
inference(avatar_component_clause,[],[f29985]) ).
fof(f31801,plain,
( ! [X0] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X0)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X0),tc_HOL_Obool))))
| ~ spl698_746 ),
inference(avatar_component_clause,[],[f31800]) ).
fof(f32412,plain,
spl698_890,
inference(avatar_split_clause,[],[f27008,f32410]) ).
fof(f32410,plain,
( spl698_890
<=> ! [X2,X0,X1] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_HOL_Obool_Obool__size(c_fTrue),X0) = X0
| ~ class_Rings_Osemiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_890])]) ).
fof(f27008,plain,
! [X2,X0,X1] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_HOL_Obool_Obool__size(c_fTrue),X0) = X0
| ~ class_Rings_Osemiring__1(X2) ),
inference(forward_demodulation,[],[f20469,f17447]) ).
fof(f17447,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
inference(cnf_transformation,[],[f4934]) ).
fof(f4934,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_bool_Osize_I1_J) ).
fof(f20469,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,[],[f11435]) ).
fof(f11435,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,[],[f7429]) ).
fof(f7429,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,[],[f1834]) ).
fof(f1834,axiom,
! [X147,X202,X4] :
( class_Rings_Osemiring__1(X4)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X4,X202,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X147) = X147 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_of__nat__aux_Osimps_I1_J) ).
fof(f32408,plain,
spl698_889,
inference(avatar_split_clause,[],[f26771,f32406]) ).
fof(f32406,plain,
( spl698_889
<=> ! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_889])]) ).
fof(f26771,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)),
inference(forward_demodulation,[],[f26770,f25487]) ).
fof(f25487,plain,
! [X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f25486,f24883]) ).
fof(f24883,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17470,f17447]) ).
fof(f17470,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1609]) ).
fof(f1609,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_One__nat__def) ).
fof(f25486,plain,
! [X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f18405,f17447]) ).
fof(f18405,plain,
! [X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f6002]) ).
fof(f6002,plain,
! [X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rectify,[],[f1723]) ).
fof(f1723,axiom,
! [X193,X194] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X194,X193)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X194)),c_Com_Ocom_Ocom__size(X193))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osize_I4_J) ).
fof(f26770,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f26769,f24883]) ).
fof(f26769,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f19953,f17447]) ).
fof(f19953,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)),
inference(cnf_transformation,[],[f7044]) ).
fof(f7044,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)),
inference(rectify,[],[f1778]) ).
fof(f1778,axiom,
! [X57,X58,X53] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X53,X58,X57)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X58)),c_Com_Ocom_Ocom__size(X57))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osize_I5_J) ).
fof(f32404,plain,
spl698_888,
inference(avatar_split_clause,[],[f26755,f32402]) ).
fof(f26755,plain,
! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(X2,X0,c_Com_Ocom_OSKIP,X0))),
inference(forward_demodulation,[],[f19922,f25465]) ).
fof(f25465,plain,
! [X0,X1] : hAPP(c_fequal,X0) = hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(forward_demodulation,[],[f18324,f18121]) ).
fof(f18121,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(cnf_transformation,[],[f5718]) ).
fof(f5718,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(rectify,[],[f202]) ).
fof(f202,axiom,
! [X5,X4] : hAPP(c_Set_OCollect(X4),X5) = X5,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Collect__def) ).
fof(f18324,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X0)),
inference(cnf_transformation,[],[f5921]) ).
fof(f5921,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X0)),
inference(rectify,[],[f201]) ).
fof(f201,axiom,
! [X6,X4] : hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X4),hAPP(c_fequal,X6)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_singleton__conv2) ).
fof(f19922,plain,
! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X0,c_Com_Ocom_OSKIP,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f7013]) ).
fof(f7013,plain,
! [X0,X1,X2] : c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X0,c_Com_Ocom_OSKIP,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)))),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X7,X8,X4] : c_Hoare__Mirabelle_Ohoare__derivs(X4,X8,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),c_Hoare__Mirabelle_Otriple_Otriple(X4,X7,c_Com_Ocom_OSKIP,X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_hoare__derivs_Oequations_I7_J) ).
fof(f32400,plain,
spl698_887,
inference(avatar_split_clause,[],[f26750,f32398]) ).
fof(f32398,plain,
( spl698_887
<=> ! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)) = hAPP(c_Nat_OSuc,c_Com_Ocom_Ocom__size(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_887])]) ).
fof(f26750,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)) = hAPP(c_Nat_OSuc,c_Com_Ocom_Ocom__size(X0)),
inference(forward_demodulation,[],[f26749,f17703]) ).
fof(f17703,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f5389]) ).
fof(f5389,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rectify,[],[f1400]) ).
fof(f1400,axiom,
! [X88] : hAPP(c_Nat_OSuc,X88) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X88),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Suc__eq__plus1) ).
fof(f26749,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X0)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f26748,f24883]) ).
fof(f26748,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X0)),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f19880,f17447]) ).
fof(f19880,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X0)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)),
inference(cnf_transformation,[],[f6971]) ).
fof(f6971,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X0)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)),
inference(rectify,[],[f1722]) ).
fof(f1722,axiom,
! [X13,X53,X70] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X70,X53,X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X13)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osize_I3_J) ).
fof(f32391,plain,
spl698_886,
inference(avatar_split_clause,[],[f26507,f32389]) ).
fof(f32389,plain,
( spl698_886
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) != hAPP(c_Int_Onat,X1)
| sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_886])]) ).
fof(f26507,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) != hAPP(c_Int_Onat,X1)
| sP11(X0,X1) ),
inference(forward_demodulation,[],[f26506,f25011]) ).
fof(f25011,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X0),
inference(forward_demodulation,[],[f17711,f17595]) ).
fof(f17595,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(cnf_transformation,[],[f5281]) ).
fof(f5281,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(rectify,[],[f2379]) ).
fof(f2379,axiom,
! [X112] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X112) = X112,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_number__of__is__id) ).
fof(f17711,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f5397]) ).
fof(f5397,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),
inference(rectify,[],[f2421]) ).
fof(f2421,axiom,
! [X190] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X190) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X190)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__number__of__def) ).
fof(f26506,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) != hAPP(c_Int_Onat,X1)
| sP11(X0,X1) ),
inference(forward_demodulation,[],[f19608,f25011]) ).
fof(f19608,plain,
! [X0,X1] :
( sP11(X0,X1)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f15259]) ).
fof(f15259,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
| ~ sP11(X0,X1) )
& ( sP11(X0,X1)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) ) ),
inference(nnf_transformation,[],[f14556]) ).
fof(f14556,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
<=> sP11(X0,X1) ),
inference(definition_folding,[],[f11110,f14555,f14554]) ).
fof(f14554,plain,
! [X1,X0] :
( sP10(X1,X0)
<=> ( ( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f14555,plain,
! [X0,X1] :
( sP11(X0,X1)
<=> ( ( sP10(X1,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f11110,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
<=> ( ( ( ( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) ) ),
inference(ennf_transformation,[],[f6826]) ).
fof(f6826,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
<=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> X0 = X1 )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ) ) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
inference(rectify,[],[f2546]) ).
fof(f2546,axiom,
! [X235,X102] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X102) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X235)
<=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X102)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X235)))
=> X102 = X235 )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X235)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X102) ) ) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X102)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X235)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__nat__number__of) ).
fof(f32387,plain,
spl698_885,
inference(avatar_split_clause,[],[f26505,f32385]) ).
fof(f32385,plain,
( spl698_885
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) = hAPP(c_Int_Onat,X1)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_885])]) ).
fof(f26505,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = hAPP(c_Int_Onat,X1)
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f26504,f25011]) ).
fof(f26504,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X1)
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f19609,f25011]) ).
fof(f19609,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f15259]) ).
fof(f32383,plain,
spl698_884,
inference(avatar_split_clause,[],[f26503,f32381]) ).
fof(f32381,plain,
( spl698_884
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Int_OPls = X0
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_884])]) ).
fof(f26503,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Int_OPls = X0
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f26502,f17595]) ).
fof(f26502,plain,
! [X0,X1] :
( c_Int_OPls = X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f26501,f17436]) ).
fof(f17436,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
inference(cnf_transformation,[],[f2565]) ).
fof(f2565,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Pls__def) ).
fof(f26501,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f19602,f17595]) ).
fof(f19602,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f15258]) ).
fof(f15258,plain,
! [X0,X1] :
( ( sP10(X0,X1)
| ( X0 != X1
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
& ( ( ( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
| ~ sP10(X0,X1) ) ),
inference(rectify,[],[f15257]) ).
fof(f15257,plain,
! [X1,X0] :
( ( sP10(X1,X0)
| ( X0 != X1
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
& ( ( ( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
| ~ sP10(X1,X0) ) ),
inference(flattening,[],[f15256]) ).
fof(f15256,plain,
! [X1,X0] :
( ( sP10(X1,X0)
| ( X0 != X1
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
& ( ( ( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
| ~ sP10(X1,X0) ) ),
inference(nnf_transformation,[],[f14554]) ).
fof(f32379,plain,
spl698_883,
inference(avatar_split_clause,[],[f26500,f32377]) ).
fof(f32377,plain,
( spl698_883
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| X0 = X1
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_883])]) ).
fof(f26500,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| X0 = X1
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f19603,f17595]) ).
fof(f19603,plain,
! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f15258]) ).
fof(f32375,plain,
spl698_882,
inference(avatar_split_clause,[],[f26499,f32373]) ).
fof(f32373,plain,
( spl698_882
<=> ! [X0,X1] :
( c_Int_OPls != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_882])]) ).
fof(f26499,plain,
! [X0,X1] :
( c_Int_OPls != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X0,X1) ),
inference(forward_demodulation,[],[f26498,f17436]) ).
fof(f26498,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X0,X1) ),
inference(forward_demodulation,[],[f26497,f17595]) ).
fof(f26497,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ),
inference(forward_demodulation,[],[f19605,f17595]) ).
fof(f19605,plain,
! [X0,X1] :
( sP10(X0,X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f15258]) ).
fof(f32371,plain,
spl698_881,
inference(avatar_split_clause,[],[f26496,f32369]) ).
fof(f32369,plain,
( spl698_881
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X0,X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_881])]) ).
fof(f26496,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X0,X1)
| X0 != X1 ),
inference(forward_demodulation,[],[f19606,f17595]) ).
fof(f19606,plain,
! [X0,X1] :
( sP10(X0,X1)
| X0 != X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(cnf_transformation,[],[f15258]) ).
fof(f32367,plain,
spl698_880,
inference(avatar_split_clause,[],[f26490,f32365]) ).
fof(f32365,plain,
( spl698_880
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X1,X0)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_880])]) ).
fof(f26490,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X1,X0)
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f19597,f17595]) ).
fof(f19597,plain,
! [X0,X1] :
( sP10(X1,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f15255]) ).
fof(f15255,plain,
! [X0,X1] :
( ( sP11(X0,X1)
| ( ~ sP10(X1,X0)
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
& ( ( ( sP10(X1,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
| ~ sP11(X0,X1) ) ),
inference(flattening,[],[f15254]) ).
fof(f15254,plain,
! [X0,X1] :
( ( sP11(X0,X1)
| ( ~ sP10(X1,X0)
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
& ( ( ( sP10(X1,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
| ~ sP11(X0,X1) ) ),
inference(nnf_transformation,[],[f14555]) ).
fof(f32363,plain,
spl698_879,
inference(avatar_split_clause,[],[f26486,f32361]) ).
fof(f32361,plain,
( spl698_879
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X0,X1)
| ~ sP10(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_879])]) ).
fof(f26486,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X0,X1)
| ~ sP10(X1,X0) ),
inference(forward_demodulation,[],[f19600,f17595]) ).
fof(f19600,plain,
! [X0,X1] :
( sP11(X0,X1)
| ~ sP10(X1,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(cnf_transformation,[],[f15255]) ).
fof(f32359,plain,
spl698_878,
inference(avatar_split_clause,[],[f26474,f32357]) ).
fof(f32357,plain,
( spl698_878
<=> ! [X0,X1,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0
| ~ hBOOL(hAPP(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_878])]) ).
fof(f26474,plain,
! [X3,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0
| ~ hBOOL(hAPP(X0,X3)) ),
inference(forward_demodulation,[],[f19581,f18121]) ).
fof(f19581,plain,
! [X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X3))
| hAPP(c_Set_OCollect(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(cnf_transformation,[],[f15243]) ).
fof(f15243,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK245(X0))) )
& ( ! [X3] : ~ hBOOL(hAPP(X0,X3))
| hAPP(c_Set_OCollect(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK245])],[f15241,f15242]) ).
fof(f15242,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X0,sK245(X0))) ),
introduced(choice_axiom,[]) ).
fof(f15241,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ? [X2] : hBOOL(hAPP(X0,X2)) )
& ( ! [X3] : ~ hBOOL(hAPP(X0,X3))
| hAPP(c_Set_OCollect(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ) ),
inference(rectify,[],[f15240]) ).
fof(f15240,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ? [X2] : hBOOL(hAPP(X0,X2)) )
& ( ! [X2] : ~ hBOOL(hAPP(X0,X2))
| hAPP(c_Set_OCollect(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ) ),
inference(nnf_transformation,[],[f6819]) ).
fof(f6819,plain,
! [X0,X1] :
( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
<=> ! [X2] : ~ hBOOL(hAPP(X0,X2)) ),
inference(rectify,[],[f206]) ).
fof(f206,axiom,
! [X5,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X4),X5)
<=> ! [X2] : ~ hBOOL(hAPP(X5,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_empty__Collect__eq) ).
fof(f32354,plain,
spl698_877,
inference(avatar_split_clause,[],[f26453,f32352]) ).
fof(f26453,plain,
! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP8(X0,X1) ),
inference(forward_demodulation,[],[f19553,f17595]) ).
fof(f19553,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f15227]) ).
fof(f15227,plain,
! [X0,X1] :
( ( sP8(X0,X1)
| ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ) ) )
& ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 )
| ~ sP8(X0,X1) ) ),
inference(flattening,[],[f15226]) ).
fof(f15226,plain,
! [X0,X1] :
( ( sP8(X0,X1)
| ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ) ) )
& ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 )
| ~ sP8(X0,X1) ) ),
inference(nnf_transformation,[],[f14550]) ).
fof(f14550,plain,
! [X0,X1] :
( sP8(X0,X1)
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f32348,plain,
spl698_876,
inference(avatar_split_clause,[],[f26452,f32346]) ).
fof(f26452,plain,
! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP8(X0,X1) ),
inference(forward_demodulation,[],[f19554,f17595]) ).
fof(f19554,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f15227]) ).
fof(f32343,plain,
spl698_875,
inference(avatar_split_clause,[],[f26451,f32341]) ).
fof(f26451,plain,
! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP8(X0,X1) ),
inference(forward_demodulation,[],[f19555,f17595]) ).
fof(f19555,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f15227]) ).
fof(f32338,plain,
spl698_874,
inference(avatar_split_clause,[],[f26450,f32336]) ).
fof(f26450,plain,
! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP8(X0,X1) ),
inference(forward_demodulation,[],[f19556,f17595]) ).
fof(f19556,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f15227]) ).
fof(f32334,plain,
spl698_873,
inference(avatar_split_clause,[],[f26413,f32332]) ).
fof(f32332,plain,
( spl698_873
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != X0
| c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_873])]) ).
fof(f26413,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != X0
| c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X1,X0) ),
inference(forward_demodulation,[],[f19449,f17447]) ).
fof(f19449,plain,
! [X0,X1] :
( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f15141]) ).
fof(f15141,plain,
! [X0,X1] :
( ( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X1,X0)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_List_Olist_ONil(tc_Nat_Onat) != c_List_Oupt(X1,X0) ) ),
inference(flattening,[],[f15140]) ).
fof(f15140,plain,
! [X0,X1] :
( ( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X1,X0)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_List_Olist_ONil(tc_Nat_Onat) != c_List_Oupt(X1,X0) ) ),
inference(nnf_transformation,[],[f6768]) ).
fof(f6768,plain,
! [X0,X1] :
( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X1,X0)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f4008]) ).
fof(f4008,axiom,
! [X172,X147] :
( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X147,X172)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X172),X147))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X172 ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_upt__eq__Nil__conv) ).
fof(f32330,plain,
spl698_872,
inference(avatar_split_clause,[],[f25967,f32328]) ).
fof(f32328,plain,
( spl698_872
<=> ! [X0,X1] :
( hAPP(c_fequal,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_872])]) ).
fof(f25967,plain,
! [X0,X1] :
( hAPP(c_fequal,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(forward_demodulation,[],[f18982,f25465]) ).
fof(f18982,plain,
! [X0,X1] :
( hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f10675]) ).
fof(f10675,plain,
! [X0,X1] :
( hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f6446]) ).
fof(f6446,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0) ),
inference(rectify,[],[f3118]) ).
fof(f3118,axiom,
! [X6,X4] :
( class_Orderings_Oorder(X4)
=> hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X4,X6,X6) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_atLeastAtMost__singleton) ).
fof(f32326,plain,
spl698_871,
inference(avatar_split_clause,[],[f25466,f32324]) ).
fof(f32324,plain,
( spl698_871
<=> ! [X0,X1] : hAPP(c_fequal,X0) = c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_871])]) ).
fof(f25466,plain,
! [X0,X1] : hAPP(c_fequal,X0) = c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(forward_demodulation,[],[f18325,f25465]) ).
fof(f18325,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(cnf_transformation,[],[f5922]) ).
fof(f5922,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(rectify,[],[f837]) ).
fof(f837,axiom,
! [X20,X4] : hAPP(hAPP(c_Set_Oinsert(X4),X20),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = c_Option_Oset(X4,hAPP(c_Option_Ooption_OSome(X4),X20)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Option_Oset_Osimps_I2_J) ).
fof(f32322,plain,
spl698_870,
inference(avatar_split_clause,[],[f25458,f32320]) ).
fof(f32320,plain,
( spl698_870
<=> ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_Osucc(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_870])]) ).
fof(f25458,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_Osucc(X1),X0),
inference(forward_demodulation,[],[f18285,f17688]) ).
fof(f17688,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f5374]) ).
fof(f5374,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(rectify,[],[f2604]) ).
fof(f2604,axiom,
! [X112] : c_Int_Osucc(X112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X112),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_succ__def) ).
fof(f18285,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0),
inference(cnf_transformation,[],[f5882]) ).
fof(f5882,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0),
inference(rectify,[],[f3158]) ).
fof(f3158,axiom,
! [X152,X153] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X153,X152) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X153),c_Groups_Oone__class_Oone(tc_Int_Oint)),X152),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).
fof(f32318,plain,
spl698_869,
inference(avatar_split_clause,[],[f25453,f32316]) ).
fof(f32316,plain,
( spl698_869
<=> ! [X0,X1] : c_Fun_Oid(X1) = hAPP(hAPP(c_Nat_Ofunpow(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_869])]) ).
fof(f25453,plain,
! [X0,X1] : c_Fun_Oid(X1) = hAPP(hAPP(c_Nat_Ofunpow(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0),
inference(forward_demodulation,[],[f25452,f17593]) ).
fof(f17593,plain,
! [X0] : c_Nat_Ocompow(X0,X0) = c_Nat_Ofunpow(X0),
inference(cnf_transformation,[],[f5279]) ).
fof(f5279,plain,
! [X0] : c_Nat_Ocompow(X0,X0) = c_Nat_Ofunpow(X0),
inference(rectify,[],[f4818]) ).
fof(f4818,axiom,
! [X4] : c_Nat_Ocompow(X4,X4) = c_Nat_Ofunpow(X4),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_funpow__code__def) ).
fof(f25452,plain,
! [X0,X1] : c_Fun_Oid(X1) = hAPP(hAPP(c_Nat_Ocompow(X1,X1),c_HOL_Obool_Obool__size(c_fTrue)),X0),
inference(forward_demodulation,[],[f18200,f17447]) ).
fof(f18200,plain,
! [X0,X1] : c_Fun_Oid(X1) = hAPP(hAPP(c_Nat_Ocompow(X1,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f5797]) ).
fof(f5797,plain,
! [X0,X1] : c_Fun_Oid(X1) = hAPP(hAPP(c_Nat_Ocompow(X1,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(rectify,[],[f4815]) ).
fof(f4815,axiom,
! [X1,X4] : c_Fun_Oid(X4) = hAPP(hAPP(c_Nat_Ocompow(X4,X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_funpow_Osimps_I1_J) ).
fof(f32314,plain,
spl698_868,
inference(avatar_split_clause,[],[f25449,f32312]) ).
fof(f32312,plain,
( spl698_868
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Osublist(X1,X0,c_Option_Oset(tc_Nat_Onat,c_Option_Ooption_ONone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_868])]) ).
fof(f25449,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Osublist(X1,X0,c_Option_Oset(tc_Nat_Onat,c_Option_Ooption_ONone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f18188,f17660]) ).
fof(f17660,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Option_Oset(X0,c_Option_Ooption_ONone(X0)),
inference(cnf_transformation,[],[f5346]) ).
fof(f5346,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Option_Oset(X0,c_Option_Ooption_ONone(X0)),
inference(rectify,[],[f847]) ).
fof(f847,axiom,
! [X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = c_Option_Oset(X4,c_Option_Ooption_ONone(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Option_Oset_Osimps_I1_J) ).
fof(f18188,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Osublist(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(cnf_transformation,[],[f5785]) ).
fof(f5785,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Osublist(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(rectify,[],[f3982]) ).
fof(f3982,axiom,
! [X258,X4] : c_List_Olist_ONil(X4) = c_List_Osublist(X4,X258,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_sublist__empty) ).
fof(f32310,plain,
spl698_867,
inference(avatar_split_clause,[],[f25448,f32308]) ).
fof(f32308,plain,
( spl698_867
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_867])]) ).
fof(f25448,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0),
inference(forward_demodulation,[],[f18187,f17447]) ).
fof(f18187,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f5784]) ).
fof(f5784,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(rectify,[],[f3955]) ).
fof(f3955,axiom,
! [X263,X23] : c_List_Olist_ONil(X23) = hAPP(hAPP(c_List_Otake(X23),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X263),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_take__0) ).
fof(f32306,plain,
( spl698_866
| ~ spl698_329
| ~ spl698_733 ),
inference(avatar_split_clause,[],[f32258,f31525,f29581,f32303]) ).
fof(f32303,plain,
( spl698_866
<=> sP5(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_866])]) ).
fof(f31525,plain,
( spl698_733
<=> ! [X0] : sP5(hAPP(c_Int_Onat,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_733])]) ).
fof(f32258,plain,
( sP5(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls)
| ~ spl698_329
| ~ spl698_733 ),
inference(superposition,[],[f31526,f29583]) ).
fof(f31526,plain,
( ! [X0] : sP5(hAPP(c_Int_Onat,X0),X0)
| ~ spl698_733 ),
inference(avatar_component_clause,[],[f31525]) ).
fof(f32301,plain,
spl698_865,
inference(avatar_split_clause,[],[f25336,f32299]) ).
fof(f32299,plain,
( spl698_865
<=> ! [X0] :
( c_Int_OPls != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_HOL_Obool_Obool__size(c_fTrue) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_865])]) ).
fof(f25336,plain,
! [X0] :
( c_Int_OPls != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_HOL_Obool_Obool__size(c_fTrue) = X0 ),
inference(forward_demodulation,[],[f25335,f17436]) ).
fof(f25335,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) ),
inference(forward_demodulation,[],[f17993,f17447]) ).
fof(f17993,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,[],[f14809]) ).
fof(f14809,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,[],[f5642]) ).
fof(f5642,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,[],[f1728]) ).
fof(f1728,axiom,
! [X78] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X78)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X78 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_int__eq__0__conv) ).
fof(f32297,plain,
spl698_864,
inference(avatar_split_clause,[],[f25334,f32295]) ).
fof(f32295,plain,
( spl698_864
<=> ! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) != X0
| c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_864])]) ).
fof(f25334,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) != X0
| c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) ),
inference(forward_demodulation,[],[f25333,f17447]) ).
fof(f25333,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,[],[f17994,f17436]) ).
fof(f17994,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,[],[f14809]) ).
fof(f32293,plain,
spl698_863,
inference(avatar_split_clause,[],[f25313,f32291]) ).
fof(f32291,plain,
( spl698_863
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK150(X0)))
| c_Nat__Transfer_Onat__set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_863])]) ).
fof(f25313,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK150(X0)))
| c_Nat__Transfer_Onat__set(X0) ),
inference(forward_demodulation,[],[f17964,f17436]) ).
fof(f17964,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK150(X0))) ),
inference(cnf_transformation,[],[f14787]) ).
fof(f14787,plain,
! [X0] :
( ( c_Nat__Transfer_Onat__set(X0)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK150(X0)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK150(X0)),X0)) ) )
& ( ! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X0)) )
| ~ c_Nat__Transfer_Onat__set(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK150])],[f14785,f14786]) ).
fof(f14786,plain,
! [X0] :
( ? [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X0)) )
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK150(X0)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK150(X0)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14785,plain,
! [X0] :
( ( c_Nat__Transfer_Onat__set(X0)
| ? [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X0)) ) )
& ( ! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X0)) )
| ~ c_Nat__Transfer_Onat__set(X0) ) ),
inference(rectify,[],[f14784]) ).
fof(f14784,plain,
! [X0] :
( ( c_Nat__Transfer_Onat__set(X0)
| ? [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X0)) ) )
& ( ! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X0)) )
| ~ c_Nat__Transfer_Onat__set(X0) ) ),
inference(nnf_transformation,[],[f10281]) ).
fof(f10281,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(X0)
<=> ! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X0)) ) ),
inference(ennf_transformation,[],[f5628]) ).
fof(f5628,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(X0)
<=> ! [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ),
inference(rectify,[],[f2587]) ).
fof(f2587,axiom,
! [X117] :
( c_Nat__Transfer_Onat__set(X117)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X117))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__set__def) ).
fof(f32289,plain,
spl698_862,
inference(avatar_split_clause,[],[f25200,f32287]) ).
fof(f32287,plain,
( spl698_862
<=> ! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_862])]) ).
fof(f25200,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f17920,f17447]) ).
fof(f17920,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(cnf_transformation,[],[f10240]) ).
fof(f10240,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(ennf_transformation,[],[f5591]) ).
fof(f5591,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0) ),
inference(rectify,[],[f2541]) ).
fof(f2541,axiom,
! [X30] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X30))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X30) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_neg__nat) ).
fof(f32285,plain,
spl698_861,
inference(avatar_split_clause,[],[f25186,f32283]) ).
fof(f32283,plain,
( spl698_861
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_HOL_Obool_Obool__size(c_fTrue))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_861])]) ).
fof(f25186,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_HOL_Obool_Obool__size(c_fTrue))
| ~ class_Rings_Osemiring__1(X0) ),
inference(forward_demodulation,[],[f17880,f17447]) ).
fof(f17880,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,[],[f10201]) ).
fof(f10201,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,[],[f5552]) ).
fof(f5552,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,[],[f1752]) ).
fof(f1752,axiom,
! [X23] :
( class_Rings_Osemiring__1(X23)
=> c_Groups_Ozero__class_Ozero(X23) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X23),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_of__nat__0) ).
fof(f32281,plain,
spl698_860,
inference(avatar_split_clause,[],[f25180,f32279]) ).
fof(f32279,plain,
( spl698_860
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_Osucc(c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_860])]) ).
fof(f25180,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_Osucc(c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f17858,f17442]) ).
fof(f17442,plain,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
inference(cnf_transformation,[],[f2568]) ).
fof(f2568,axiom,
c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_succ__Pls) ).
fof(f17858,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f10179]) ).
fof(f10179,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f5530]) ).
fof(f5530,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OBit1(c_Int_OPls)) ),
inference(rectify,[],[f2593]) ).
fof(f2593,axiom,
! [X23] :
( class_Int_Onumber__ring(X23)
=> c_Groups_Oone__class_Oone(X23) = hAPP(c_Int_Onumber__class_Onumber__of(X23),c_Int_OBit1(c_Int_OPls)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_numeral__1__eq__1) ).
fof(f32277,plain,
spl698_859,
inference(avatar_split_clause,[],[f25028,f32275]) ).
fof(f32275,plain,
( spl698_859
<=> ! [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,[spl698_859])]) ).
fof(f25028,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,[],[f25027,f24883]) ).
fof(f25027,plain,
! [X0] : hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),X0),
inference(forward_demodulation,[],[f17742,f17447]) ).
fof(f17742,plain,
! [X0] : hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
inference(cnf_transformation,[],[f5428]) ).
fof(f5428,plain,
! [X0] : hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
inference(rectify,[],[f1965]) ).
fof(f1965,axiom,
! [X88] : hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X88),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_power__Suc__0) ).
fof(f32273,plain,
spl698_858,
inference(avatar_split_clause,[],[f25016,f32271]) ).
fof(f32271,plain,
( spl698_858
<=> ! [X0] : hBOOL(hAPP(hAPP(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,[spl698_858])]) ).
fof(f25016,plain,
! [X0] : hBOOL(hAPP(hAPP(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,[],[f17719,f17436]) ).
fof(f17719,plain,
! [X0] : hBOOL(hAPP(hAPP(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,[],[f5405]) ).
fof(f5405,plain,
! [X0] : hBOOL(hAPP(hAPP(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,[],[f1864]) ).
fof(f1864,axiom,
! [X30] : hBOOL(hAPP(hAPP(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),X30))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
fof(f32269,plain,
spl698_857,
inference(avatar_split_clause,[],[f25012,f32267]) ).
fof(f32267,plain,
( spl698_857
<=> ! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X0)) = hAPP(c_Int_Onat,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_857])]) ).
fof(f25012,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X0)) = hAPP(c_Int_Onat,X0),
inference(forward_demodulation,[],[f17714,f25011]) ).
fof(f17714,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X0)),
inference(cnf_transformation,[],[f5400]) ).
fof(f5400,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X0)),
inference(rectify,[],[f4644]) ).
fof(f4644,axiom,
! [X112] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X112)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X112),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__of__number) ).
fof(f32265,plain,
spl698_856,
inference(avatar_split_clause,[],[f25007,f32263]) ).
fof(f32263,plain,
( spl698_856
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(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,[spl698_856])]) ).
fof(f25007,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(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,[],[f17699,f17436]) ).
fof(f17699,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(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,[],[f5385]) ).
fof(f5385,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(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,[],[f1787]) ).
fof(f1787,axiom,
! [X112] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X112)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_int__less__0__conv) ).
fof(f32256,plain,
spl698_855,
inference(avatar_split_clause,[],[f25006,f32254]) ).
fof(f32254,plain,
( spl698_855
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),hAPP(c_Nat_OSuc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_855])]) ).
fof(f25006,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),hAPP(c_Nat_OSuc,X0))),
inference(forward_demodulation,[],[f17698,f17447]) ).
fof(f17698,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X0))),
inference(cnf_transformation,[],[f5384]) ).
fof(f5384,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X0))),
inference(rectify,[],[f1418]) ).
fof(f1418,axiom,
! [X88] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X88))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zero__less__Suc) ).
fof(f32252,plain,
spl698_854,
inference(avatar_split_clause,[],[f25003,f32250]) ).
fof(f32250,plain,
( spl698_854
<=> ! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_854])]) ).
fof(f25003,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue),X0),
inference(forward_demodulation,[],[f17692,f17447]) ).
fof(f17692,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f5378]) ).
fof(f5378,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(rectify,[],[f3184]) ).
fof(f3184,axiom,
! [X78] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X78) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X78),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_atLeast0AtMost) ).
fof(f32248,plain,
spl698_853,
inference(avatar_split_clause,[],[f25002,f32246]) ).
fof(f32246,plain,
( spl698_853
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Finite__Set_Ocard(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_853])]) ).
fof(f25002,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Finite__Set_Ocard(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(forward_demodulation,[],[f17685,f17447]) ).
fof(f17685,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(cnf_transformation,[],[f5371]) ).
fof(f5371,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(rectify,[],[f1594]) ).
fof(f1594,axiom,
! [X4] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X4),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_card_Oempty) ).
fof(f32244,plain,
spl698_852,
inference(avatar_split_clause,[],[f24999,f32242]) ).
fof(f32242,plain,
( spl698_852
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_852])]) ).
fof(f24999,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0),
inference(forward_demodulation,[],[f17683,f17447]) ).
fof(f17683,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,[],[f5369]) ).
fof(f5369,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,[],[f1508]) ).
fof(f1508,axiom,
! [X88] : 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)),X88),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_mult__0) ).
fof(f32240,plain,
spl698_851,
inference(avatar_split_clause,[],[f24998,f32238]) ).
fof(f32238,plain,
( spl698_851
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_851])]) ).
fof(f24998,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0),
inference(forward_demodulation,[],[f17682,f17447]) ).
fof(f17682,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f5368]) ).
fof(f5368,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(rectify,[],[f1499]) ).
fof(f1499,axiom,
! [X88] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X88),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_diff__0__eq__0) ).
fof(f32236,plain,
spl698_850,
inference(avatar_split_clause,[],[f24997,f32234]) ).
fof(f32234,plain,
( spl698_850
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_850])]) ).
fof(f24997,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0),
inference(forward_demodulation,[],[f17681,f17447]) ).
fof(f17681,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f5367]) ).
fof(f5367,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(rectify,[],[f1430]) ).
fof(f1430,axiom,
! [X88] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X88),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_min__0L) ).
fof(f32232,plain,
spl698_849,
inference(avatar_split_clause,[],[f24996,f32230]) ).
fof(f32230,plain,
( spl698_849
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_849])]) ).
fof(f24996,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17680,f17447]) ).
fof(f17680,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,[],[f5366]) ).
fof(f5366,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,[],[f1507]) ).
fof(f1507,axiom,
! [X93] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_mult__0__right) ).
fof(f32228,plain,
spl698_848,
inference(avatar_split_clause,[],[f24995,f32226]) ).
fof(f32226,plain,
( spl698_848
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_848])]) ).
fof(f24995,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17679,f17447]) ).
fof(f17679,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f5365]) ).
fof(f5365,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f1431]) ).
fof(f1431,axiom,
! [X88] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X88),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_min__0R) ).
fof(f32224,plain,
spl698_847,
inference(avatar_split_clause,[],[f24924,f32221]) ).
fof(f32221,plain,
( spl698_847
<=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_847])]) ).
fof(f24924,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),
inference(forward_demodulation,[],[f17525,f17435]) ).
fof(f17435,plain,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
inference(cnf_transformation,[],[f4654]) ).
fof(f4654,axiom,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_subtract__code__numeral__def) ).
fof(f17525,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),
inference(cnf_transformation,[],[f2855]) ).
fof(f2855,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_code__numeral__zero__minus__one) ).
fof(f32218,plain,
spl698_846,
inference(avatar_split_clause,[],[f24923,f32215]) ).
fof(f24923,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17521,f17447]) ).
fof(f17521,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(cnf_transformation,[],[f1709]) ).
fof(f1709,axiom,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_lessThan__0) ).
fof(f32213,plain,
spl698_845,
inference(avatar_split_clause,[],[f24919,f32210]) ).
fof(f32210,plain,
( spl698_845
<=> c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_845])]) ).
fof(f24919,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17519,f17447]) ).
fof(f17519,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f3063]) ).
fof(f3063,axiom,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_atLeast__0) ).
fof(f32208,plain,
spl698_844,
inference(avatar_split_clause,[],[f24164,f32206]) ).
fof(f32206,plain,
( spl698_844
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,X3))
| ~ sP133(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_844])]) ).
fof(f24164,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X1,X3))
| ~ sP133(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16957]) ).
fof(f16957,plain,
! [X0,X1,X2,X3,X4] :
( ( sP133(X0,X1,X2,X3,X4)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X2,X1),X6) != X0
| ~ hBOOL(hAPP(X1,X3))
| ( hBOOL(hAPP(X1,sK625(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK625(X1,X2,X5)),hAPP(c_List_Oset(X2),X5))) )
| hAPP(hAPP(c_List_Oappend(X2),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X6)) != X4 ) )
& ( ( hAPP(c_List_Ofilter(X2,X1),sK627(X0,X1,X2,X3,X4)) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),sK626(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK626(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK627(X0,X1,X2,X3,X4))) = X4 )
| ~ sP133(X0,X1,X2,X3,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK625,sK626,sK627])],[f16954,f16956,f16955]) ).
fof(f16955,plain,
! [X1,X2,X5] :
( ? [X7] :
( hBOOL(hAPP(X1,X7))
& hBOOL(hAPP(hAPP(c_member(X2),X7),hAPP(c_List_Oset(X2),X5))) )
=> ( hBOOL(hAPP(X1,sK625(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK625(X1,X2,X5)),hAPP(c_List_Oset(X2),X5))) ) ),
introduced(choice_axiom,[]) ).
fof(f16956,plain,
! [X0,X1,X2,X3,X4] :
( ? [X8,X9] :
( hAPP(c_List_Ofilter(X2,X1),X9) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),X8))) )
& hAPP(hAPP(c_List_Oappend(X2),X8),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X9)) = X4 )
=> ( hAPP(c_List_Ofilter(X2,X1),sK627(X0,X1,X2,X3,X4)) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),sK626(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK626(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK627(X0,X1,X2,X3,X4))) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f16954,plain,
! [X0,X1,X2,X3,X4] :
( ( sP133(X0,X1,X2,X3,X4)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X2,X1),X6) != X0
| ~ hBOOL(hAPP(X1,X3))
| ? [X7] :
( hBOOL(hAPP(X1,X7))
& hBOOL(hAPP(hAPP(c_member(X2),X7),hAPP(c_List_Oset(X2),X5))) )
| hAPP(hAPP(c_List_Oappend(X2),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X6)) != X4 ) )
& ( ? [X8,X9] :
( hAPP(c_List_Ofilter(X2,X1),X9) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),X8))) )
& hAPP(hAPP(c_List_Oappend(X2),X8),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X9)) = X4 )
| ~ sP133(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16953]) ).
fof(f16953,plain,
! [X0,X3,X4,X1,X2] :
( ( sP133(X0,X3,X4,X1,X2)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X4,X3),X6) != X0
| ~ hBOOL(hAPP(X3,X1))
| ? [X7] :
( hBOOL(hAPP(X3,X7))
& hBOOL(hAPP(hAPP(c_member(X4),X7),hAPP(c_List_Oset(X4),X5))) )
| hAPP(hAPP(c_List_Oappend(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X1),X6)) != X2 ) )
& ( ? [X5,X6] :
( hAPP(c_List_Ofilter(X4,X3),X6) = X0
& hBOOL(hAPP(X3,X1))
& ! [X7] :
( ~ hBOOL(hAPP(X3,X7))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X7),hAPP(c_List_Oset(X4),X5))) )
& hAPP(hAPP(c_List_Oappend(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X1),X6)) = X2 )
| ~ sP133(X0,X3,X4,X1,X2) ) ),
inference(nnf_transformation,[],[f14748]) ).
fof(f14748,plain,
! [X0,X3,X4,X1,X2] :
( sP133(X0,X3,X4,X1,X2)
<=> ? [X5,X6] :
( hAPP(c_List_Ofilter(X4,X3),X6) = X0
& hBOOL(hAPP(X3,X1))
& ! [X7] :
( ~ hBOOL(hAPP(X3,X7))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X7),hAPP(c_List_Oset(X4),X5))) )
& hAPP(hAPP(c_List_Oappend(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X1),X6)) = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP133])]) ).
fof(f32204,plain,
spl698_843,
inference(avatar_split_clause,[],[f24156,f32202]) ).
fof(f32202,plain,
( spl698_843
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,X3))
| ~ sP132(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_843])]) ).
fof(f24156,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X1,X3))
| ~ sP132(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16951]) ).
fof(f16951,plain,
! [X0,X1,X2,X3,X4] :
( ( sP132(X0,X1,X2,X3,X4)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X2,X1),X6) != X0
| ~ hBOOL(hAPP(X1,X3))
| ( hBOOL(hAPP(X1,sK622(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK622(X1,X2,X5)),hAPP(c_List_Oset(X2),X5))) )
| hAPP(hAPP(c_List_Oappend(X2),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X6)) != X4 ) )
& ( ( hAPP(c_List_Ofilter(X2,X1),sK624(X0,X1,X2,X3,X4)) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),sK623(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK623(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK624(X0,X1,X2,X3,X4))) = X4 )
| ~ sP132(X0,X1,X2,X3,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK622,sK623,sK624])],[f16948,f16950,f16949]) ).
fof(f16949,plain,
! [X1,X2,X5] :
( ? [X7] :
( hBOOL(hAPP(X1,X7))
& hBOOL(hAPP(hAPP(c_member(X2),X7),hAPP(c_List_Oset(X2),X5))) )
=> ( hBOOL(hAPP(X1,sK622(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK622(X1,X2,X5)),hAPP(c_List_Oset(X2),X5))) ) ),
introduced(choice_axiom,[]) ).
fof(f16950,plain,
! [X0,X1,X2,X3,X4] :
( ? [X8,X9] :
( hAPP(c_List_Ofilter(X2,X1),X9) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),X8))) )
& hAPP(hAPP(c_List_Oappend(X2),X8),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X9)) = X4 )
=> ( hAPP(c_List_Ofilter(X2,X1),sK624(X0,X1,X2,X3,X4)) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),sK623(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK623(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK624(X0,X1,X2,X3,X4))) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f16948,plain,
! [X0,X1,X2,X3,X4] :
( ( sP132(X0,X1,X2,X3,X4)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X2,X1),X6) != X0
| ~ hBOOL(hAPP(X1,X3))
| ? [X7] :
( hBOOL(hAPP(X1,X7))
& hBOOL(hAPP(hAPP(c_member(X2),X7),hAPP(c_List_Oset(X2),X5))) )
| hAPP(hAPP(c_List_Oappend(X2),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X6)) != X4 ) )
& ( ? [X8,X9] :
( hAPP(c_List_Ofilter(X2,X1),X9) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),X8))) )
& hAPP(hAPP(c_List_Oappend(X2),X8),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X9)) = X4 )
| ~ sP132(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16947]) ).
fof(f16947,plain,
! [X2,X1,X4,X3,X0] :
( ( sP132(X2,X1,X4,X3,X0)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X4,X1),X6) != X2
| ~ hBOOL(hAPP(X1,X3))
| ? [X7] :
( hBOOL(hAPP(X1,X7))
& hBOOL(hAPP(hAPP(c_member(X4),X7),hAPP(c_List_Oset(X4),X5))) )
| hAPP(hAPP(c_List_Oappend(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6)) != X0 ) )
& ( ? [X5,X6] :
( hAPP(c_List_Ofilter(X4,X1),X6) = X2
& hBOOL(hAPP(X1,X3))
& ! [X7] :
( ~ hBOOL(hAPP(X1,X7))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X7),hAPP(c_List_Oset(X4),X5))) )
& hAPP(hAPP(c_List_Oappend(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6)) = X0 )
| ~ sP132(X2,X1,X4,X3,X0) ) ),
inference(nnf_transformation,[],[f14746]) ).
fof(f14746,plain,
! [X2,X1,X4,X3,X0] :
( sP132(X2,X1,X4,X3,X0)
<=> ? [X5,X6] :
( hAPP(c_List_Ofilter(X4,X1),X6) = X2
& hBOOL(hAPP(X1,X3))
& ! [X7] :
( ~ hBOOL(hAPP(X1,X7))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X7),hAPP(c_List_Oset(X4),X5))) )
& hAPP(hAPP(c_List_Oappend(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6)) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP132])]) ).
fof(f32200,plain,
spl698_842,
inference(avatar_split_clause,[],[f24094,f32198]) ).
fof(f32198,plain,
( spl698_842
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,X4))
| ~ sP129(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_842])]) ).
fof(f24094,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,X4))
| ~ sP129(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16909]) ).
fof(f16909,plain,
! [X0,X1,X2,X3,X4] :
( ( sP129(X0,X1,X2,X3,X4)
| ! [X5] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X5,X1,X0)
| ~ c_Natural_Oevaln(X2,X4,X1,X5) )
| ~ hBOOL(hAPP(X3,X4)) )
& ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),sK617(X0,X1,X2,X3,X4),X1,X0)
& c_Natural_Oevaln(X2,X4,X1,sK617(X0,X1,X2,X3,X4))
& hBOOL(hAPP(X3,X4)) )
| ~ sP129(X0,X1,X2,X3,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK617])],[f16907,f16908]) ).
fof(f16908,plain,
! [X0,X1,X2,X3,X4] :
( ? [X6] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X6,X1,X0)
& c_Natural_Oevaln(X2,X4,X1,X6) )
=> ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),sK617(X0,X1,X2,X3,X4),X1,X0)
& c_Natural_Oevaln(X2,X4,X1,sK617(X0,X1,X2,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f16907,plain,
! [X0,X1,X2,X3,X4] :
( ( sP129(X0,X1,X2,X3,X4)
| ! [X5] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X5,X1,X0)
| ~ c_Natural_Oevaln(X2,X4,X1,X5) )
| ~ hBOOL(hAPP(X3,X4)) )
& ( ( ? [X6] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X6,X1,X0)
& c_Natural_Oevaln(X2,X4,X1,X6) )
& hBOOL(hAPP(X3,X4)) )
| ~ sP129(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16906]) ).
fof(f16906,plain,
! [X0,X1,X3,X4,X2] :
( ( sP129(X0,X1,X3,X4,X2)
| ! [X5] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
| ~ c_Natural_Oevaln(X3,X2,X1,X5) )
| ~ hBOOL(hAPP(X4,X2)) )
& ( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) )
| ~ sP129(X0,X1,X3,X4,X2) ) ),
inference(flattening,[],[f16905]) ).
fof(f16905,plain,
! [X0,X1,X3,X4,X2] :
( ( sP129(X0,X1,X3,X4,X2)
| ! [X5] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
| ~ c_Natural_Oevaln(X3,X2,X1,X5) )
| ~ hBOOL(hAPP(X4,X2)) )
& ( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) )
| ~ sP129(X0,X1,X3,X4,X2) ) ),
inference(nnf_transformation,[],[f14740]) ).
fof(f14740,plain,
! [X0,X1,X3,X4,X2] :
( sP129(X0,X1,X3,X4,X2)
<=> ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP129])]) ).
fof(f32196,plain,
spl698_841,
inference(avatar_split_clause,[],[f23865,f32194]) ).
fof(f32194,plain,
( spl698_841
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,X4))
| ~ sP126(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_841])]) ).
fof(f23865,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,X4))
| ~ sP126(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16796]) ).
fof(f16796,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),sK571(X0,X1,X2,X3,X4),X1,X0)
& c_Natural_Oevaln(X2,X4,X1,sK571(X0,X1,X2,X3,X4))
& hBOOL(hAPP(X3,X4)) )
| ~ sP126(X0,X1,X2,X3,X4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK571])],[f16794,f16795]) ).
fof(f16795,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X5,X1,X0)
& c_Natural_Oevaln(X2,X4,X1,X5) )
=> ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),sK571(X0,X1,X2,X3,X4),X1,X0)
& c_Natural_Oevaln(X2,X4,X1,sK571(X0,X1,X2,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f16794,plain,
! [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X5,X1,X0)
& c_Natural_Oevaln(X2,X4,X1,X5) )
& hBOOL(hAPP(X3,X4)) )
| ~ sP126(X0,X1,X2,X3,X4) ),
inference(rectify,[],[f16793]) ).
fof(f16793,plain,
! [X0,X1,X3,X4,X2] :
( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) )
| ~ sP126(X0,X1,X3,X4,X2) ),
inference(nnf_transformation,[],[f14734]) ).
fof(f14734,plain,
! [X0,X1,X3,X4,X2] :
( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) )
| ~ sP126(X0,X1,X3,X4,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP126])]) ).
fof(f32192,plain,
spl698_840,
inference(avatar_split_clause,[],[f23390,f32190]) ).
fof(f32190,plain,
( spl698_840
<=> ! [X0,X3,X2,X1] :
( sP122(X0,X1,X2,X3)
| ~ sP123(X0,X1,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_840])]) ).
fof(f23390,plain,
! [X2,X3,X0,X1] :
( sP122(X0,X1,X2,X3)
| ~ sP123(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f16718]) ).
fof(f16718,plain,
! [X0,X1,X2,X3] :
( ( sP122(X0,X1,X2,X3)
| ~ sP123(X0,X1,X3,X2) )
& ( sP123(X0,X1,X3,X2)
| ~ sP122(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f14730]) ).
fof(f14730,plain,
! [X0,X1,X2,X3] :
( sP122(X0,X1,X2,X3)
<=> sP123(X0,X1,X3,X2) ),
inference(definition_folding,[],[f9160,f14729,f14728]) ).
fof(f14728,plain,
! [X0,X1,X2,X3] :
( sP122(X0,X1,X2,X3)
<=> ? [X4] :
( hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP122])]) ).
fof(f14729,plain,
! [X0,X1,X3,X2] :
( sP123(X0,X1,X3,X2)
<=> ( ? [X5] :
( hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X1)) )
| ? [X6] :
( hBOOL(hAPP(X0,X6))
& hBOOL(hAPP(hAPP(c_member(X3),X6),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP123])]) ).
fof(f9160,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) )
<=> ( ? [X5] :
( hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X1)) )
| ? [X6] :
( hBOOL(hAPP(X0,X6))
& hBOOL(hAPP(hAPP(c_member(X3),X6),X2)) ) ) ),
inference(rectify,[],[f244]) ).
fof(f244,axiom,
! [X5,X21,X19,X4] :
( ? [X2] :
( hBOOL(hAPP(X5,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X19),X21))) )
<=> ( ? [X2] :
( hBOOL(hAPP(X5,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),X21)) )
| ? [X2] :
( hBOOL(hAPP(X5,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),X19)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_bex__Un) ).
fof(f32188,plain,
spl698_839,
inference(avatar_split_clause,[],[f23389,f32186]) ).
fof(f32186,plain,
( spl698_839
<=> ! [X0,X3,X2,X1] :
( sP123(X0,X1,X3,X2)
| ~ sP122(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_839])]) ).
fof(f23389,plain,
! [X2,X3,X0,X1] :
( sP123(X0,X1,X3,X2)
| ~ sP122(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16718]) ).
fof(f32184,plain,
spl698_838,
inference(avatar_split_clause,[],[f23105,f32182]) ).
fof(f32182,plain,
( spl698_838
<=> ! [X2,X0,X1,X3] :
( X0 = X2
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_838])]) ).
fof(f23105,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ),
inference(cnf_transformation,[],[f16506]) ).
fof(f16506,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OWhile(X1,X0) = c_Com_Ocom_OWhile(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ) ),
inference(flattening,[],[f16505]) ).
fof(f16505,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OWhile(X1,X0) = c_Com_Ocom_OWhile(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ) ),
inference(nnf_transformation,[],[f9070]) ).
fof(f9070,plain,
! [X0,X1,X2,X3] :
( c_Com_Ocom_OWhile(X1,X0) = c_Com_Ocom_OWhile(X3,X2)
<=> ( X0 = X2
& X1 = X3 ) ),
inference(rectify,[],[f79]) ).
fof(f79,axiom,
! [X10,X51,X13,X53] :
( c_Com_Ocom_OWhile(X51,X10) = c_Com_Ocom_OWhile(X53,X13)
<=> ( X10 = X13
& X51 = X53 ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I5_J) ).
fof(f32180,plain,
spl698_837,
inference(avatar_split_clause,[],[f23104,f32178]) ).
fof(f32178,plain,
( spl698_837
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_837])]) ).
fof(f23104,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ),
inference(cnf_transformation,[],[f16506]) ).
fof(f32176,plain,
spl698_836,
inference(avatar_split_clause,[],[f23102,f32174]) ).
fof(f32174,plain,
( spl698_836
<=> ! [X2,X0,X1,X3] :
( X0 = X2
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_836])]) ).
fof(f23102,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ),
inference(cnf_transformation,[],[f16504]) ).
fof(f16504,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OAss(X1,X0) = c_Com_Ocom_OAss(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ) ),
inference(flattening,[],[f16503]) ).
fof(f16503,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OAss(X1,X0) = c_Com_Ocom_OAss(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ) ),
inference(nnf_transformation,[],[f9069]) ).
fof(f9069,plain,
! [X0,X1,X2,X3] :
( c_Com_Ocom_OAss(X1,X0) = c_Com_Ocom_OAss(X3,X2)
<=> ( X0 = X2
& X1 = X3 ) ),
inference(rectify,[],[f80]) ).
fof(f80,axiom,
! [X51,X52,X53,X54] :
( c_Com_Ocom_OAss(X52,X51) = c_Com_Ocom_OAss(X54,X53)
<=> ( X51 = X53
& X52 = X54 ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I1_J) ).
fof(f32172,plain,
spl698_835,
inference(avatar_split_clause,[],[f23101,f32170]) ).
fof(f32170,plain,
( spl698_835
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_835])]) ).
fof(f23101,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ),
inference(cnf_transformation,[],[f16504]) ).
fof(f32168,plain,
spl698_834,
inference(avatar_split_clause,[],[f23099,f32166]) ).
fof(f32166,plain,
( spl698_834
<=> ! [X2,X0,X1,X3] :
( X0 = X2
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_834])]) ).
fof(f23099,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ),
inference(cnf_transformation,[],[f16502]) ).
fof(f16502,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OSemi(X1,X0) = c_Com_Ocom_OSemi(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ) ),
inference(flattening,[],[f16501]) ).
fof(f16501,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OSemi(X1,X0) = c_Com_Ocom_OSemi(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ) ),
inference(nnf_transformation,[],[f9068]) ).
fof(f9068,plain,
! [X0,X1,X2,X3] :
( c_Com_Ocom_OSemi(X1,X0) = c_Com_Ocom_OSemi(X3,X2)
<=> ( X0 = X2
& X1 = X3 ) ),
inference(rectify,[],[f81]) ).
fof(f81,axiom,
! [X55,X56,X57,X58] :
( c_Com_Ocom_OSemi(X56,X55) = c_Com_Ocom_OSemi(X58,X57)
<=> ( X55 = X57
& X56 = X58 ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I3_J) ).
fof(f32164,plain,
spl698_833,
inference(avatar_split_clause,[],[f23098,f32162]) ).
fof(f32162,plain,
( spl698_833
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_833])]) ).
fof(f23098,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ),
inference(cnf_transformation,[],[f16502]) ).
fof(f32160,plain,
spl698_832,
inference(avatar_split_clause,[],[f23088,f32158]) ).
fof(f32158,plain,
( spl698_832
<=> ! [X0,X3,X2,X1] :
( sP113(X2,X0,X3,X1)
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_832])]) ).
fof(f23088,plain,
! [X2,X3,X0,X1] :
( sP113(X2,X0,X3,X1)
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16491]) ).
fof(f16491,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
| ~ sP113(X2,X0,X3,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = X0
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)) )
& ( ( sP113(X2,X0,X3,X1)
& c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) != X0
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)) )
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
inference(flattening,[],[f16490]) ).
fof(f16490,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
| ~ sP113(X2,X0,X3,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = X0
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)) )
& ( ( sP113(X2,X0,X3,X1)
& c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) != X0
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)) )
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14712]) ).
fof(f14712,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
<=> ( sP113(X2,X0,X3,X1)
& c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) != X0
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)) ) ),
inference(definition_folding,[],[f13456,f14711]) ).
fof(f14711,plain,
! [X2,X0,X3,X1] :
( sP113(X2,X0,X3,X1)
<=> ! [X4] :
( ? [X5] :
( hBOOL(hAPP(hAPP(X2,X4),X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP113])]) ).
fof(f13456,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
<=> ( ! [X4] :
( ? [X5] :
( hBOOL(hAPP(hAPP(X2,X4),X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X1)) )
& c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) != X0
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)) ) ),
inference(ennf_transformation,[],[f9065]) ).
fof(f9065,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
<=> ( ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X3),X4),X1))
=> ? [X5] :
( hBOOL(hAPP(hAPP(X2,X4),X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) ) )
& c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) != X0
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)) ) ),
inference(rectify,[],[f3342]) ).
fof(f3342,axiom,
! [X7,X8,X42,X4] :
( c_Wellfounded_Omax__extp(X4,X42,X8,X7)
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),X8))
=> ? [X118] :
( hBOOL(hAPP(hAPP(X42,X2),X118))
& hBOOL(hAPP(hAPP(c_member(X4),X118),X7)) ) )
& c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) != X7
& hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X7))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X8)) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_max__extp_Oequations) ).
fof(f32156,plain,
spl698_831,
inference(avatar_split_clause,[],[f23086,f32154]) ).
fof(f32154,plain,
( spl698_831
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_831])]) ).
fof(f23086,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16491]) ).
fof(f32152,plain,
spl698_830,
inference(avatar_split_clause,[],[f23085,f32150]) ).
fof(f32150,plain,
( spl698_830
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_830])]) ).
fof(f23085,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16491]) ).
fof(f32148,plain,
spl698_829,
inference(avatar_split_clause,[],[f21821,f32146]) ).
fof(f32146,plain,
( spl698_829
<=> ! [X0,X3,X2,X1] : c_Nitpick_Ofold__graph_H(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_829])]) ).
fof(f21821,plain,
! [X2,X3,X0,X1] : c_Nitpick_Ofold__graph_H(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),X0),
inference(cnf_transformation,[],[f8237]) ).
fof(f8237,plain,
! [X0,X1,X2,X3] : c_Nitpick_Ofold__graph_H(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),X0),
inference(rectify,[],[f538]) ).
fof(f538,axiom,
! [X116,X1,X24,X4] : c_Nitpick_Ofold__graph_H(X4,X24,X1,X116,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X116),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_fold__graph_H_Ointros_I1_J) ).
fof(f32144,plain,
spl698_828,
inference(avatar_split_clause,[],[f21820,f32142]) ).
fof(f32142,plain,
( spl698_828
<=> ! [X2,X0,X1,X3] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_828])]) ).
fof(f21820,plain,
! [X2,X3,X0,X1] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0,
inference(cnf_transformation,[],[f8236]) ).
fof(f8236,plain,
! [X0,X1,X2,X3] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0,
inference(rectify,[],[f4209]) ).
fof(f4209,axiom,
! [X6,X1,X24,X4] : hAPP(c_List_Ofoldl(X4,X24,X1,X6),c_List_Olist_ONil(X24)) = X6,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_foldl__Nil) ).
fof(f32140,plain,
spl698_827,
inference(avatar_split_clause,[],[f21819,f32138]) ).
fof(f32138,plain,
( spl698_827
<=> ! [X2,X0,X1,X3] : hAPP(c_Option_Ooption_Ooption__case(X3,X2,X1,X0),c_Option_Ooption_ONone(X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_827])]) ).
fof(f21819,plain,
! [X2,X3,X0,X1] : hAPP(c_Option_Ooption_Ooption__case(X3,X2,X1,X0),c_Option_Ooption_ONone(X2)) = X1,
inference(cnf_transformation,[],[f8235]) ).
fof(f8235,plain,
! [X0,X1,X2,X3] : hAPP(c_Option_Ooption_Ooption__case(X3,X2,X1,X0),c_Option_Ooption_ONone(X2)) = X1,
inference(rectify,[],[f1179]) ).
fof(f1179,axiom,
! [X67,X25,X24,X4] : hAPP(c_Option_Ooption_Ooption__case(X4,X24,X25,X67),c_Option_Ooption_ONone(X24)) = X25,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_option_Osimps_I4_J) ).
fof(f32136,plain,
spl698_826,
inference(avatar_split_clause,[],[f21818,f32134]) ).
fof(f32134,plain,
( spl698_826
<=> ! [X2,X0,X1,X3] : hAPP(c_List_Olist_Olist__case(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_826])]) ).
fof(f21818,plain,
! [X2,X3,X0,X1] : hAPP(c_List_Olist_Olist__case(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X1,
inference(cnf_transformation,[],[f8234]) ).
fof(f8234,plain,
! [X0,X1,X2,X3] : hAPP(c_List_Olist_Olist__case(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X1,
inference(rectify,[],[f4034]) ).
fof(f4034,axiom,
! [X67,X25,X24,X4] : hAPP(c_List_Olist_Olist__case(X4,X24,X25,X67),c_List_Olist_ONil(X24)) = X25,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_list_Osimps_I4_J) ).
fof(f32128,plain,
spl698_825,
inference(avatar_split_clause,[],[f21817,f32126]) ).
fof(f32126,plain,
( spl698_825
<=> ! [X0,X3,X2,X1] : hAPP(X1,X0) = c_Com_Ovname_Ovname__rec(X3,X2,X1,c_Com_Ovname_OLoc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_825])]) ).
fof(f21817,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0) = c_Com_Ovname_Ovname__rec(X3,X2,X1,c_Com_Ovname_OLoc(X0)),
inference(cnf_transformation,[],[f8233]) ).
fof(f8233,plain,
! [X0,X1,X2,X3] : hAPP(X1,X0) = c_Com_Ovname_Ovname__rec(X3,X2,X1,c_Com_Ovname_OLoc(X0)),
inference(rectify,[],[f114]) ).
fof(f114,axiom,
! [X70,X67,X25,X4] : c_Com_Ovname_Ovname__rec(X4,X25,X67,c_Com_Ovname_OLoc(X70)) = hAPP(X67,X70),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_vname_Orecs_I2_J) ).
fof(f32124,plain,
spl698_824,
inference(avatar_split_clause,[],[f21816,f32122]) ).
fof(f32122,plain,
( spl698_824
<=> ! [X0,X3,X2,X1] : hAPP(X1,X0) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X2,X1,c_Code__Numeral_OSuc__code__numeral(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_824])]) ).
fof(f21816,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X2,X1,c_Code__Numeral_OSuc__code__numeral(X0)),
inference(cnf_transformation,[],[f8232]) ).
fof(f8232,plain,
! [X0,X1,X2,X3] : hAPP(X1,X0) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X3,X2,X1,c_Code__Numeral_OSuc__code__numeral(X0)),
inference(rectify,[],[f3233]) ).
fof(f3233,axiom,
! [X238,X67,X25,X4] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X4,X25,X67,c_Code__Numeral_OSuc__code__numeral(X238)) = hAPP(X67,X238),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_code__numeral_Osimps_I5_J) ).
fof(f32120,plain,
spl698_823,
inference(avatar_split_clause,[],[f21815,f32118]) ).
fof(f32118,plain,
( spl698_823
<=> ! [X0,X3,X2,X1] : hAPP(X2,X0) = c_Com_Ovname_Ovname__case(X3,X2,X1,c_Com_Ovname_OGlb(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_823])]) ).
fof(f21815,plain,
! [X2,X3,X0,X1] : hAPP(X2,X0) = c_Com_Ovname_Ovname__case(X3,X2,X1,c_Com_Ovname_OGlb(X0)),
inference(cnf_transformation,[],[f8231]) ).
fof(f8231,plain,
! [X0,X1,X2,X3] : hAPP(X2,X0) = c_Com_Ovname_Ovname__case(X3,X2,X1,c_Com_Ovname_OGlb(X0)),
inference(rectify,[],[f180]) ).
fof(f180,axiom,
! [X103,X67,X25,X4] : c_Com_Ovname_Ovname__case(X4,X25,X67,c_Com_Ovname_OGlb(X103)) = hAPP(X25,X103),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_vname_Osimps_I5_J) ).
fof(f32116,plain,
spl698_822,
inference(avatar_split_clause,[],[f21814,f32114]) ).
fof(f32114,plain,
( spl698_822
<=> ! [X0,X3,X2,X1] : hAPP(X1,X0) = c_Com_Ovname_Ovname__case(X3,X2,X1,c_Com_Ovname_OLoc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_822])]) ).
fof(f21814,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0) = c_Com_Ovname_Ovname__case(X3,X2,X1,c_Com_Ovname_OLoc(X0)),
inference(cnf_transformation,[],[f8230]) ).
fof(f8230,plain,
! [X0,X1,X2,X3] : hAPP(X1,X0) = c_Com_Ovname_Ovname__case(X3,X2,X1,c_Com_Ovname_OLoc(X0)),
inference(rectify,[],[f115]) ).
fof(f115,axiom,
! [X70,X67,X25,X4] : hAPP(X67,X70) = c_Com_Ovname_Ovname__case(X4,X25,X67,c_Com_Ovname_OLoc(X70)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_vname_Osimps_I6_J) ).
fof(f32112,plain,
spl698_821,
inference(avatar_split_clause,[],[f21813,f32110]) ).
fof(f32110,plain,
( spl698_821
<=> ! [X0,X3,X2,X1] : hAPP(X2,X0) = c_Com_Ovname_Ovname__rec(X3,X2,X1,c_Com_Ovname_OGlb(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_821])]) ).
fof(f21813,plain,
! [X2,X3,X0,X1] : hAPP(X2,X0) = c_Com_Ovname_Ovname__rec(X3,X2,X1,c_Com_Ovname_OGlb(X0)),
inference(cnf_transformation,[],[f8229]) ).
fof(f8229,plain,
! [X0,X1,X2,X3] : hAPP(X2,X0) = c_Com_Ovname_Ovname__rec(X3,X2,X1,c_Com_Ovname_OGlb(X0)),
inference(rectify,[],[f181]) ).
fof(f181,axiom,
! [X103,X67,X25,X4] : hAPP(X25,X103) = c_Com_Ovname_Ovname__rec(X4,X25,X67,c_Com_Ovname_OGlb(X103)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_vname_Orecs_I1_J) ).
fof(f32108,plain,
spl698_820,
inference(avatar_split_clause,[],[f21477,f32106]) ).
fof(f32106,plain,
( spl698_820
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP42(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_820])]) ).
fof(f21477,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP42(X1,X0,X2) ),
inference(cnf_transformation,[],[f15890]) ).
fof(f15890,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP42(X1,X0,X2) )
& ( sP42(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ) ),
inference(nnf_transformation,[],[f14606]) ).
fof(f14606,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
<=> sP42(X1,X0,X2) ),
inference(definition_folding,[],[f12437,f14605,f14604]) ).
fof(f14604,plain,
! [X0,X1] :
( sP41(X0,X1)
<=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP41])]) ).
fof(f14605,plain,
! [X1,X0,X2] :
( sP42(X1,X0,X2)
<=> ( ( sP41(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X0)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)) = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP42])]) ).
fof(f12437,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
<=> ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0))) )
| ~ hBOOL(hAPP(hAPP(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) = X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X0)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)) = X2 ) ),
inference(ennf_transformation,[],[f8116]) ).
fof(f8116,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0))) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0))) ) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X0) )
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X0)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)) = X2 ) ),
inference(rectify,[],[f2409]) ).
fof(f2409,axiom,
! [X230,X78,X123] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X123,X78),X230))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X78
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X78))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X230)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X78),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X230))) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X78))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X230)),X78))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X230))) ) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X78
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X230) )
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X230)),X78)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X230)) = X123 ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_divmod__nat__rel__def) ).
fof(f32104,plain,
spl698_819,
inference(avatar_split_clause,[],[f21476,f32102]) ).
fof(f32102,plain,
( spl698_819
<=> ! [X2,X0,X1] :
( sP42(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_819])]) ).
fof(f21476,plain,
! [X2,X0,X1] :
( sP42(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ),
inference(cnf_transformation,[],[f15890]) ).
fof(f32100,plain,
spl698_818,
inference(avatar_split_clause,[],[f21342,f32098]) ).
fof(f21342,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP37(X0,X1,X2) ),
inference(cnf_transformation,[],[f15765]) ).
fof(f15765,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1)) )
| ~ sP37(X0,X1,X2) ),
inference(rectify,[],[f15764]) ).
fof(f15764,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) )
| ~ sP37(X2,X1,X0) ),
inference(nnf_transformation,[],[f14596]) ).
fof(f14596,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) )
| ~ sP37(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP37])]) ).
fof(f32096,plain,
spl698_817,
inference(avatar_split_clause,[],[f21024,f32094]) ).
fof(f32094,plain,
( spl698_817
<=> ! [X0,X1] :
( sK308(X0,X1) != sK309(X0,X1)
| ~ sP32(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_817])]) ).
fof(f21024,plain,
! [X0,X1] :
( sK308(X0,X1) != sK309(X0,X1)
| ~ sP32(X0,X1) ),
inference(cnf_transformation,[],[f15646]) ).
fof(f15646,plain,
! [X0,X1] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),sK308(X0,X1)),sK309(X0,X1))
& sK308(X0,X1) != sK309(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK309(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK308(X0,X1)),X1)) )
| ~ sP32(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK308,sK309])],[f15643,f15645,f15644]) ).
fof(f15644,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X2),X3)
& X2 != X3
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),X3),X1)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),X2),X1)) )
=> ( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),sK308(X0,X1)),X3)
& sK308(X0,X1) != X3
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),X3),X1)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK308(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15645,plain,
! [X0,X1] :
( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),sK308(X0,X1)),X3)
& sK308(X0,X1) != X3
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),X3),X1)) )
=> ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),sK308(X0,X1)),sK309(X0,X1))
& sK308(X0,X1) != sK309(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK309(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15643,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X2),X3)
& X2 != X3
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),X3),X1)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),X2),X1)) )
| ~ sP32(X0,X1) ),
inference(rectify,[],[f15642]) ).
fof(f15642,plain,
! [X2,X1] :
( ? [X4] :
( ? [X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)
& X4 != X5
& hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X5),X1)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X4),X1)) )
| ~ sP32(X2,X1) ),
inference(nnf_transformation,[],[f14588]) ).
fof(f14588,plain,
! [X2,X1] :
( ? [X4] :
( ? [X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)
& X4 != X5
& hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X5),X1)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X4),X1)) )
| ~ sP32(X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP32])]) ).
fof(f32092,plain,
spl698_816,
inference(avatar_split_clause,[],[f21016,f32090]) ).
fof(f32090,plain,
( spl698_816
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_816])]) ).
fof(f21016,plain,
! [X2,X0,X1] :
( c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0) ),
inference(cnf_transformation,[],[f12084]) ).
fof(f12084,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0) ),
inference(ennf_transformation,[],[f7851]) ).
fof(f7851,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0)
=> c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0) ),
inference(rectify,[],[f1335]) ).
fof(f1335,axiom,
! [X91,X88,X23] :
( c_Hoare__Mirabelle_Otriple__valid(X23,hAPP(c_Nat_OSuc,X88),X91)
=> c_Hoare__Mirabelle_Otriple__valid(X23,X88,X91) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_triple__valid__Suc) ).
fof(f32087,plain,
spl698_815,
inference(avatar_split_clause,[],[f19837,f32085]) ).
fof(f32085,plain,
( spl698_815
<=> ! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_815])]) ).
fof(f19837,plain,
! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0,
inference(cnf_transformation,[],[f6928]) ).
fof(f6928,plain,
! [X0,X1,X2] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0,
inference(rectify,[],[f3479]) ).
fof(f3479,axiom,
! [X0,X4,X24] : hAPP(c_Fun_Ocomp(X24,X24,X4,c_Fun_Oid(X24)),X0) = X0,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_id__o) ).
fof(f32083,plain,
spl698_814,
inference(avatar_split_clause,[],[f19836,f32081]) ).
fof(f32081,plain,
( spl698_814
<=> ! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_814])]) ).
fof(f19836,plain,
! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0,
inference(cnf_transformation,[],[f6927]) ).
fof(f6927,plain,
! [X0,X1,X2] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0,
inference(rectify,[],[f3480]) ).
fof(f3480,axiom,
! [X1,X24,X4] : hAPP(c_Fun_Ocomp(X4,X24,X4,X1),c_Fun_Oid(X4)) = X1,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_o__id) ).
fof(f32079,plain,
spl698_813,
inference(avatar_split_clause,[],[f19835,f32077]) ).
fof(f32077,plain,
( spl698_813
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_813])]) ).
fof(f19835,plain,
! [X2,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X0)),
inference(cnf_transformation,[],[f6926]) ).
fof(f6926,plain,
! [X0,X1,X2] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X0)),
inference(rectify,[],[f1697]) ).
fof(f1697,axiom,
! [X20,X1,X4] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X20)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_empty__fold1SetE) ).
fof(f32075,plain,
spl698_812,
inference(avatar_split_clause,[],[f19538,f32073]) ).
fof(f32073,plain,
( spl698_812
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_812])]) ).
fof(f19538,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ),
inference(cnf_transformation,[],[f15218]) ).
fof(f15218,plain,
! [X0,X1] :
( ( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) )
& ( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
inference(nnf_transformation,[],[f6805]) ).
fof(f6805,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
<=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f4762]) ).
fof(f4762,axiom,
! [X60,X4] :
( c_Wellfounded_Oacyclic(X4,hAPP(c_Relation_Oconverse(X4,X4),X60))
<=> c_Wellfounded_Oacyclic(X4,X60) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_acyclic__converse) ).
fof(f32071,plain,
spl698_811,
inference(avatar_split_clause,[],[f19537,f32069]) ).
fof(f32069,plain,
( spl698_811
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_811])]) ).
fof(f19537,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ),
inference(cnf_transformation,[],[f15218]) ).
fof(f32067,plain,
spl698_810,
inference(avatar_split_clause,[],[f19513,f32065]) ).
fof(f32065,plain,
( spl698_810
<=> ! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_810])]) ).
fof(f19513,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f15193]) ).
fof(f15193,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) )
& ( ( X0 != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ) ),
inference(flattening,[],[f15192]) ).
fof(f15192,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) )
& ( ( X0 != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ) ),
inference(nnf_transformation,[],[f6794]) ).
fof(f6794,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
<=> ( X0 != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) ) ),
inference(rectify,[],[f1809]) ).
fof(f1809,axiom,
! [X180,X116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X116),X180))
<=> ( X116 != X180
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X116),X180)) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zless__le) ).
fof(f32063,plain,
spl698_809,
inference(avatar_split_clause,[],[f19497,f32061]) ).
fof(f32061,plain,
( spl698_809
<=> ! [X0,X1] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Nat_OSuc,X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_809])]) ).
fof(f19497,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Nat_OSuc,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f15181]) ).
fof(f15181,plain,
! [X0,X1] :
( ( hAPP(c_Nat_OSuc,X0) = hAPP(c_Nat_OSuc,X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ) ),
inference(nnf_transformation,[],[f6787]) ).
fof(f6787,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Nat_OSuc,X1)
<=> X0 = X1 ),
inference(rectify,[],[f1264]) ).
fof(f1264,axiom,
! [X178,X179] :
( hAPP(c_Nat_OSuc,X179) = hAPP(c_Nat_OSuc,X178)
<=> X178 = X179 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat_Oinject) ).
fof(f32059,plain,
spl698_808,
inference(avatar_split_clause,[],[f19495,f32057]) ).
fof(f32057,plain,
( spl698_808
<=> ! [X0,X1] :
( hAPP(c_Code__Numeral_Oof__nat,X0) = hAPP(c_Code__Numeral_Oof__nat,X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_808])]) ).
fof(f19495,plain,
! [X0,X1] :
( hAPP(c_Code__Numeral_Oof__nat,X0) = hAPP(c_Code__Numeral_Oof__nat,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f15180]) ).
fof(f15180,plain,
! [X0,X1] :
( ( hAPP(c_Code__Numeral_Oof__nat,X0) = hAPP(c_Code__Numeral_Oof__nat,X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Code__Numeral_Oof__nat,X0) != hAPP(c_Code__Numeral_Oof__nat,X1) ) ),
inference(nnf_transformation,[],[f6786]) ).
fof(f6786,plain,
! [X0,X1] :
( hAPP(c_Code__Numeral_Oof__nat,X0) = hAPP(c_Code__Numeral_Oof__nat,X1)
<=> X0 = X1 ),
inference(rectify,[],[f4623]) ).
fof(f4623,axiom,
! [X123,X78] :
( hAPP(c_Code__Numeral_Oof__nat,X78) = hAPP(c_Code__Numeral_Oof__nat,X123)
<=> X78 = X123 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Code__Numeral_Oof__nat__inject) ).
fof(f32055,plain,
spl698_807,
inference(avatar_split_clause,[],[f19494,f32053]) ).
fof(f32053,plain,
( spl698_807
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Oof__nat,X0) != hAPP(c_Code__Numeral_Oof__nat,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_807])]) ).
fof(f19494,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Oof__nat,X0) != hAPP(c_Code__Numeral_Oof__nat,X1) ),
inference(cnf_transformation,[],[f15180]) ).
fof(f32051,plain,
spl698_806,
inference(avatar_split_clause,[],[f19491,f32049]) ).
fof(f32049,plain,
( spl698_806
<=> ! [X0,X1] :
( hAPP(c_Code__Numeral_Onat__of,X0) = hAPP(c_Code__Numeral_Onat__of,X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_806])]) ).
fof(f19491,plain,
! [X0,X1] :
( hAPP(c_Code__Numeral_Onat__of,X0) = hAPP(c_Code__Numeral_Onat__of,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f15178]) ).
fof(f15178,plain,
! [X0,X1] :
( ( hAPP(c_Code__Numeral_Onat__of,X0) = hAPP(c_Code__Numeral_Onat__of,X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Code__Numeral_Onat__of,X0) != hAPP(c_Code__Numeral_Onat__of,X1) ) ),
inference(nnf_transformation,[],[f6784]) ).
fof(f6784,plain,
! [X0,X1] :
( hAPP(c_Code__Numeral_Onat__of,X0) = hAPP(c_Code__Numeral_Onat__of,X1)
<=> X0 = X1 ),
inference(rectify,[],[f4642]) ).
fof(f4642,axiom,
! [X153,X59] :
( hAPP(c_Code__Numeral_Onat__of,X59) = hAPP(c_Code__Numeral_Onat__of,X153)
<=> X59 = X153 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Code__Numeral_Onat__of__inject) ).
fof(f32047,plain,
( ~ spl698_805
| ~ spl698_216
| ~ spl698_694 ),
inference(avatar_split_clause,[],[f32000,f31319,f29087,f32044]) ).
fof(f32044,plain,
( spl698_805
<=> c_Int_OMin = c_Int_Osucc(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_805])]) ).
fof(f29087,plain,
( spl698_216
<=> c_Int_OMin = c_Int_OBit1(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_216])]) ).
fof(f31319,plain,
( spl698_694
<=> ! [X4] : c_Int_OMin != c_Int_Osucc(c_Int_OBit1(X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_694])]) ).
fof(f32000,plain,
( c_Int_OMin != c_Int_Osucc(c_Int_OMin)
| ~ spl698_216
| ~ spl698_694 ),
inference(superposition,[],[f31320,f29089]) ).
fof(f29089,plain,
( c_Int_OMin = c_Int_OBit1(c_Int_OMin)
| ~ spl698_216 ),
inference(avatar_component_clause,[],[f29087]) ).
fof(f31320,plain,
( ! [X4] : c_Int_OMin != c_Int_Osucc(c_Int_OBit1(X4))
| ~ spl698_694 ),
inference(avatar_component_clause,[],[f31319]) ).
fof(f32042,plain,
spl698_804,
inference(avatar_split_clause,[],[f19490,f32040]) ).
fof(f32040,plain,
( spl698_804
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Onat__of,X0) != hAPP(c_Code__Numeral_Onat__of,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_804])]) ).
fof(f19490,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Onat__of,X0) != hAPP(c_Code__Numeral_Onat__of,X1) ),
inference(cnf_transformation,[],[f15178]) ).
fof(f32038,plain,
spl698_803,
inference(avatar_split_clause,[],[f19489,f32036]) ).
fof(f32036,plain,
( spl698_803
<=> ! [X0,X1] :
( hAPP(c_Int_ORep__Integ,X0) = hAPP(c_Int_ORep__Integ,X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_803])]) ).
fof(f19489,plain,
! [X0,X1] :
( hAPP(c_Int_ORep__Integ,X0) = hAPP(c_Int_ORep__Integ,X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f15177]) ).
fof(f15177,plain,
! [X0,X1] :
( ( hAPP(c_Int_ORep__Integ,X0) = hAPP(c_Int_ORep__Integ,X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Int_ORep__Integ,X0) != hAPP(c_Int_ORep__Integ,X1) ) ),
inference(nnf_transformation,[],[f6783]) ).
fof(f6783,plain,
! [X0,X1] :
( hAPP(c_Int_ORep__Integ,X0) = hAPP(c_Int_ORep__Integ,X1)
<=> X0 = X1 ),
inference(rectify,[],[f2536]) ).
fof(f2536,axiom,
! [X34,X20] :
( hAPP(c_Int_ORep__Integ,X20) = hAPP(c_Int_ORep__Integ,X34)
<=> X20 = X34 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Rep__Integ__inject) ).
fof(f32034,plain,
spl698_802,
inference(avatar_split_clause,[],[f19488,f32032]) ).
fof(f32032,plain,
( spl698_802
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Int_ORep__Integ,X0) != hAPP(c_Int_ORep__Integ,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_802])]) ).
fof(f19488,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Int_ORep__Integ,X0) != hAPP(c_Int_ORep__Integ,X1) ),
inference(cnf_transformation,[],[f15177]) ).
fof(f32030,plain,
spl698_801,
inference(avatar_split_clause,[],[f19452,f32028]) ).
fof(f32028,plain,
( spl698_801
<=> ! [X0,X1] :
( c_List_Olist_ONil(X1) = c_List_Oremdups(X1,X0)
| c_List_Olist_ONil(X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_801])]) ).
fof(f19452,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = c_List_Oremdups(X1,X0)
| c_List_Olist_ONil(X1) != X0 ),
inference(cnf_transformation,[],[f15142]) ).
fof(f15142,plain,
! [X0,X1] :
( ( c_List_Olist_ONil(X1) = c_List_Oremdups(X1,X0)
| c_List_Olist_ONil(X1) != X0 )
& ( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != c_List_Oremdups(X1,X0) ) ),
inference(nnf_transformation,[],[f6769]) ).
fof(f6769,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = c_List_Oremdups(X1,X0)
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f4210]) ).
fof(f4210,axiom,
! [X20,X4] :
( c_List_Olist_ONil(X4) = c_List_Oremdups(X4,X20)
<=> c_List_Olist_ONil(X4) = X20 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_remdups__eq__nil__iff) ).
fof(f32026,plain,
spl698_800,
inference(avatar_split_clause,[],[f19451,f32024]) ).
fof(f32024,plain,
( spl698_800
<=> ! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != c_List_Oremdups(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_800])]) ).
fof(f19451,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != c_List_Oremdups(X1,X0) ),
inference(cnf_transformation,[],[f15142]) ).
fof(f32022,plain,
spl698_799,
inference(avatar_split_clause,[],[f19439,f32020]) ).
fof(f32020,plain,
( spl698_799
<=> ! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| c_List_Oremdups(X1,X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_799])]) ).
fof(f19439,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| c_List_Oremdups(X1,X0) != X0 ),
inference(cnf_transformation,[],[f15130]) ).
fof(f15130,plain,
! [X0,X1] :
( ( c_List_Oremdups(X1,X0) = X0
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) )
& ( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| c_List_Oremdups(X1,X0) != X0 ) ),
inference(nnf_transformation,[],[f6765]) ).
fof(f6765,plain,
! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
<=> hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(rectify,[],[f4201]) ).
fof(f4201,axiom,
! [X258,X4] :
( c_List_Oremdups(X4,X258) = X258
<=> hBOOL(hAPP(c_List_Odistinct(X4),X258)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_remdups__id__iff__distinct) ).
fof(f32018,plain,
spl698_798,
inference(avatar_split_clause,[],[f19412,f32016]) ).
fof(f32016,plain,
( spl698_798
<=> ! [X2,X0,X1] :
( c_Option_Ooption_ONone(X0) != X1
| hAPP(c_Option_Ooption_OSome(X0),X2) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_798])]) ).
fof(f19412,plain,
! [X2,X0,X1] :
( c_Option_Ooption_ONone(X0) != X1
| hAPP(c_Option_Ooption_OSome(X0),X2) != X1 ),
inference(cnf_transformation,[],[f15117]) ).
fof(f15117,plain,
! [X0,X1] :
( ( c_Option_Ooption_ONone(X0) != X1
| ! [X2] : hAPP(c_Option_Ooption_OSome(X0),X2) != X1 )
& ( hAPP(c_Option_Ooption_OSome(X0),sK229(X0,X1)) = X1
| c_Option_Ooption_ONone(X0) = X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK229])],[f15115,f15116]) ).
fof(f15116,plain,
! [X0,X1] :
( ? [X3] : hAPP(c_Option_Ooption_OSome(X0),X3) = X1
=> hAPP(c_Option_Ooption_OSome(X0),sK229(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f15115,plain,
! [X0,X1] :
( ( c_Option_Ooption_ONone(X0) != X1
| ! [X2] : hAPP(c_Option_Ooption_OSome(X0),X2) != X1 )
& ( ? [X3] : hAPP(c_Option_Ooption_OSome(X0),X3) = X1
| c_Option_Ooption_ONone(X0) = X1 ) ),
inference(rectify,[],[f15114]) ).
fof(f15114,plain,
! [X0,X1] :
( ( c_Option_Ooption_ONone(X0) != X1
| ! [X2] : hAPP(c_Option_Ooption_OSome(X0),X2) != X1 )
& ( ? [X2] : hAPP(c_Option_Ooption_OSome(X0),X2) = X1
| c_Option_Ooption_ONone(X0) = X1 ) ),
inference(nnf_transformation,[],[f6757]) ).
fof(f6757,plain,
! [X0,X1] :
( c_Option_Ooption_ONone(X0) != X1
<=> ? [X2] : hAPP(c_Option_Ooption_OSome(X0),X2) = X1 ),
inference(rectify,[],[f831]) ).
fof(f831,axiom,
! [X4,X20] :
( c_Option_Ooption_ONone(X4) != X20
<=> ? [X115] : hAPP(c_Option_Ooption_OSome(X4),X115) = X20 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_not__None__eq) ).
fof(f32014,plain,
spl698_797,
inference(avatar_split_clause,[],[f19367,f32012]) ).
fof(f32012,plain,
( spl698_797
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ~ hBOOL(hAPP(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_797])]) ).
fof(f19367,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(cnf_transformation,[],[f11097]) ).
fof(f11097,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ! [X2] : ~ hBOOL(hAPP(X1,X2)) ),
inference(ennf_transformation,[],[f6739]) ).
fof(f6739,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(X1,X2))
=> hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ),
inference(rectify,[],[f3885]) ).
fof(f3885,axiom,
! [X4,X5] :
( ? [X48] : hBOOL(hAPP(X5,X48))
=> hBOOL(hAPP(X5,c_Hilbert__Choice_OEps(X4,X5))) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_someI__ex) ).
fof(f32010,plain,
spl698_796,
inference(avatar_split_clause,[],[f19093,f32008]) ).
fof(f32008,plain,
( spl698_796
<=> ! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_796])]) ).
fof(f19093,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f10782]) ).
fof(f10782,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ),
inference(ennf_transformation,[],[f6528]) ).
fof(f6528,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
=> X0 != X1 ),
inference(rectify,[],[f653]) ).
fof(f653,axiom,
! [X93,X88] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),X93))
=> X88 != X93 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_less__not__refl2) ).
fof(f32006,plain,
spl698_795,
inference(avatar_split_clause,[],[f19090,f32004]) ).
fof(f32004,plain,
( spl698_795
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_795])]) ).
fof(f19090,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X0)) ),
inference(cnf_transformation,[],[f10779]) ).
fof(f10779,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X0)) ),
inference(ennf_transformation,[],[f6525]) ).
fof(f6525,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X0))
=> X0 = X1 ),
inference(rectify,[],[f135]) ).
fof(f135,axiom,
! [X91,X92] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X92),X91))
=> X91 = X92 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_evalc__elim__cases_I1_J) ).
fof(f31999,plain,
spl698_794,
inference(avatar_split_clause,[],[f19086,f31997]) ).
fof(f31997,plain,
( spl698_794
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_794])]) ).
fof(f19086,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ),
inference(cnf_transformation,[],[f10775]) ).
fof(f10775,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ),
inference(ennf_transformation,[],[f6522]) ).
fof(f6522,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Nat_OSuc,X1)
=> X0 = X1 ),
inference(rectify,[],[f1266]) ).
fof(f1266,axiom,
! [X29,X22] :
( hAPP(c_Nat_OSuc,X22) = hAPP(c_Nat_OSuc,X29)
=> X22 = X29 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Suc__inject) ).
fof(f31995,plain,
spl698_793,
inference(avatar_split_clause,[],[f19076,f31993]) ).
fof(f31993,plain,
( spl698_793
<=> ! [X0,X1] :
( sK199(X0,X1) != sK200(X0,X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_793])]) ).
fof(f19076,plain,
! [X0,X1] :
( sK199(X0,X1) != sK200(X0,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f15002]) ).
fof(f15002,plain,
! [X0,X1] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(c_List_Oset(X0),sK199(X0,X1))),hAPP(c_List_Oset(X0),sK200(X0,X1)))
& sK199(X0,X1) != sK200(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),sK200(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1)))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),sK199(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK199,sK200])],[f14999,f15001,f15000]) ).
fof(f15000,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(c_List_Oset(X0),X2)),hAPP(c_List_Oset(X0),X3))
& X2 != X3
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),X3),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),X2),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
=> ( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(c_List_Oset(X0),sK199(X0,X1))),hAPP(c_List_Oset(X0),X3))
& sK199(X0,X1) != X3
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),X3),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),sK199(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15001,plain,
! [X0,X1] :
( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(c_List_Oset(X0),sK199(X0,X1))),hAPP(c_List_Oset(X0),X3))
& sK199(X0,X1) != X3
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),X3),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
=> ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(c_List_Oset(X0),sK199(X0,X1))),hAPP(c_List_Oset(X0),sK200(X0,X1)))
& sK199(X0,X1) != sK200(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),sK200(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f14999,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(c_List_Oset(X0),X2)),hAPP(c_List_Oset(X0),X3))
& X2 != X3
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),X3),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),X2),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f14998]) ).
fof(f14998,plain,
! [X1,X0] :
( ? [X3] :
( ? [X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),hAPP(c_List_Oset(X1),X4))
& X3 != X4
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) )
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) )
| ~ sP2(X1,X0) ),
inference(nnf_transformation,[],[f14538]) ).
fof(f14538,plain,
! [X1,X0] :
( ? [X3] :
( ? [X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),hAPP(c_List_Oset(X1),X4))
& X3 != X4
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) )
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) )
| ~ sP2(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f31991,plain,
spl698_792,
inference(avatar_split_clause,[],[f19063,f31989]) ).
fof(f31989,plain,
( spl698_792
<=> ! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_792])]) ).
fof(f19063,plain,
! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(cnf_transformation,[],[f10757]) ).
fof(f10757,plain,
! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(ennf_transformation,[],[f6507]) ).
fof(f6507,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
=> c_List_Oremdups(X1,X0) = X0 ),
inference(rectify,[],[f4200]) ).
fof(f4200,axiom,
! [X263,X23] :
( hBOOL(hAPP(c_List_Odistinct(X23),X263))
=> c_List_Oremdups(X23,X263) = X263 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_distinct__remdups__id) ).
fof(f31987,plain,
spl698_791,
inference(avatar_split_clause,[],[f19040,f31985]) ).
fof(f31985,plain,
( spl698_791
<=> ! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_791])]) ).
fof(f19040,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10734]) ).
fof(f10734,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6488]) ).
fof(f6488,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X0)) ),
inference(rectify,[],[f3358]) ).
fof(f3358,axiom,
! [X60,X4] :
( c_Wellfounded_Owf(X4,X60)
=> c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Omax__ext(X4,X60)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_max__ext__wf) ).
fof(f31983,plain,
spl698_790,
inference(avatar_split_clause,[],[f19039,f31981]) ).
fof(f31981,plain,
( spl698_790
<=> ! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_790])]) ).
fof(f19039,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10733]) ).
fof(f10733,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6487]) ).
fof(f6487,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X0)) ),
inference(rectify,[],[f3350]) ).
fof(f3350,axiom,
! [X60,X4] :
( c_Wellfounded_Owf(X4,X60)
=> c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Omin__ext(X4,X60)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_min__ext__wf) ).
fof(f31979,plain,
spl698_789,
inference(avatar_split_clause,[],[f19032,f31977]) ).
fof(f31977,plain,
( spl698_789
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_789])]) ).
fof(f19032,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f10726]) ).
fof(f10726,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| X0 != X1 ),
inference(ennf_transformation,[],[f6480]) ).
fof(f6480,plain,
! [X0,X1] :
( X0 = X1
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ),
inference(rectify,[],[f193]) ).
fof(f193,axiom,
! [X88,X93] :
( X88 = X93
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X93),X88)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__imp__le) ).
fof(f31975,plain,
spl698_788,
inference(avatar_split_clause,[],[f18968,f31973]) ).
fof(f31973,plain,
( spl698_788
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_788])]) ).
fof(f18968,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10656]) ).
fof(f10656,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6432]) ).
fof(f6432,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0 ),
inference(rectify,[],[f361]) ).
fof(f361,axiom,
! [X22,X23] :
( class_Lattices_Olattice(X23)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23),X22),X22) = X22 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Sup__fin_Oidem) ).
fof(f31971,plain,
spl698_787,
inference(avatar_split_clause,[],[f18967,f31969]) ).
fof(f31969,plain,
( spl698_787
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_787])]) ).
fof(f18967,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10655]) ).
fof(f10655,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6431]) ).
fof(f6431,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0 ),
inference(rectify,[],[f398]) ).
fof(f398,axiom,
! [X22,X23] :
( class_Lattices_Olattice(X23)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23),X22),X22) = X22 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Inf__fin_Oidem) ).
fof(f31967,plain,
spl698_786,
inference(avatar_split_clause,[],[f18962,f31965]) ).
fof(f31965,plain,
( spl698_786
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__inf(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_786])]) ).
fof(f18962,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(cnf_transformation,[],[f10650]) ).
fof(f10650,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(ennf_transformation,[],[f6426]) ).
fof(f6426,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0 ),
inference(rectify,[],[f369]) ).
fof(f369,axiom,
! [X22,X23] :
( class_Lattices_Osemilattice__inf(X23)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23),X22),X22) = X22 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_inf__idem) ).
fof(f31963,plain,
spl698_785,
inference(avatar_split_clause,[],[f18960,f31961]) ).
fof(f31961,plain,
( spl698_785
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_785])]) ).
fof(f18960,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(cnf_transformation,[],[f10648]) ).
fof(f10648,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(ennf_transformation,[],[f6424]) ).
fof(f6424,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0 ),
inference(rectify,[],[f329]) ).
fof(f329,axiom,
! [X32,X23] :
( class_Lattices_Osemilattice__sup(X23)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23),X32),X32) = X32 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_sup_Oidem) ).
fof(f31958,plain,
spl698_784,
inference(avatar_split_clause,[],[f18922,f31956]) ).
fof(f31956,plain,
( spl698_784
<=> ! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X0))
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_784])]) ).
fof(f18922,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X0))
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10612]) ).
fof(f10612,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X0))
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ class_Orderings_Olinorder(X1) ),
inference(flattening,[],[f10611]) ).
fof(f10611,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X0))
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6404]) ).
fof(f6404,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> ( c_List_Olinorder__class_Osorted(X1,X0)
=> c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X0)) ) ),
inference(rectify,[],[f4266]) ).
fof(f4266,axiom,
! [X124,X23] :
( class_Orderings_Olinorder(X23)
=> ( c_List_Olinorder__class_Osorted(X23,X124)
=> c_List_Olinorder__class_Osorted(X23,c_List_Oremdups(X23,X124)) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_sorted__remdups) ).
fof(f31954,plain,
spl698_783,
inference(avatar_split_clause,[],[f18908,f31952]) ).
fof(f31952,plain,
( spl698_783
<=> ! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X0))
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_783])]) ).
fof(f18908,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X0))
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10597]) ).
fof(f10597,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X0))
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6390]) ).
fof(f6390,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X0)) ),
inference(rectify,[],[f4369]) ).
fof(f4369,axiom,
! [X258,X4] :
( class_Orderings_Olinorder(X4)
=> c_List_Olinorder__class_Osorted(X4,c_List_Olinorder__class_Osort__key(X4,X4,c_COMBI(X4),X258)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_sorted__sort) ).
fof(f31950,plain,
spl698_782,
inference(avatar_split_clause,[],[f18906,f31948]) ).
fof(f31948,plain,
( spl698_782
<=> ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_782])]) ).
fof(f18906,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10595]) ).
fof(f10595,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6388]) ).
fof(f6388,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0 ),
inference(rectify,[],[f1432]) ).
fof(f1432,axiom,
! [X22,X23] :
( class_Orderings_Olinorder(X23)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X23),X22),X22) = X22 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Min_Oidem) ).
fof(f31946,plain,
spl698_781,
inference(avatar_split_clause,[],[f18904,f31944]) ).
fof(f31944,plain,
( spl698_781
<=> ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_781])]) ).
fof(f18904,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10593]) ).
fof(f10593,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6386]) ).
fof(f6386,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0 ),
inference(rectify,[],[f2100]) ).
fof(f2100,axiom,
! [X22,X23] :
( class_Orderings_Olinorder(X23)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X23),X22),X22) = X22 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Max_Oidem) ).
fof(f31942,plain,
spl698_780,
inference(avatar_split_clause,[],[f18886,f31940]) ).
fof(f31940,plain,
( spl698_780
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_780])]) ).
fof(f18886,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f10574]) ).
fof(f10574,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f6369]) ).
fof(f6369,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(rectify,[],[f2107]) ).
fof(f2107,axiom,
! [X32,X23] :
( class_Divides_Osemiring__div(X23)
=> c_Groups_Ozero__class_Ozero(X23) = c_Divides_Odiv__class_Omod(X23,c_Groups_Ozero__class_Ozero(X23),X32) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_mod__0) ).
fof(f31938,plain,
spl698_779,
inference(avatar_split_clause,[],[f18885,f31936]) ).
fof(f31936,plain,
( spl698_779
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_779])]) ).
fof(f18885,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f10573]) ).
fof(f10573,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f6368]) ).
fof(f6368,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1)) ),
inference(rectify,[],[f2161]) ).
fof(f2161,axiom,
! [X32,X23] :
( class_Divides_Osemiring__div(X23)
=> c_Groups_Ozero__class_Ozero(X23) = c_Divides_Odiv__class_Omod(X23,X32,c_Groups_Oone__class_Oone(X23)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_mod__by__1) ).
fof(f31934,plain,
spl698_778,
inference(avatar_split_clause,[],[f18854,f31932]) ).
fof(f31932,plain,
( spl698_778
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Obot__class_Obot(X1)),X0))
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_778])]) ).
fof(f18854,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Obot__class_Obot(X1)),X0))
| ~ class_Orderings_Obot(X1) ),
inference(cnf_transformation,[],[f10541]) ).
fof(f10541,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Obot__class_Obot(X1)),X0))
| ~ class_Orderings_Obot(X1) ),
inference(ennf_transformation,[],[f6338]) ).
fof(f6338,plain,
! [X0,X1] :
( class_Orderings_Obot(X1)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Obot__class_Obot(X1)),X0)) ),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X22,X23] :
( class_Orderings_Obot(X23)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23),c_Orderings_Obot__class_Obot(X23)),X22)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_bot__least) ).
fof(f31930,plain,
spl698_777,
inference(avatar_split_clause,[],[f18813,f31928]) ).
fof(f18813,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ),
inference(cnf_transformation,[],[f10492]) ).
fof(f10492,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ),
inference(ennf_transformation,[],[f6299]) ).
fof(f6299,plain,
! [X0,X1] :
( class_Orderings_Otop(X1)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),c_Orderings_Otop__class_Otop(X1))) ),
inference(rectify,[],[f1092]) ).
fof(f1092,axiom,
! [X22,X23] :
( class_Orderings_Otop(X23)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23),X22),c_Orderings_Otop__class_Otop(X23))) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_top__greatest) ).
fof(f31926,plain,
spl698_776,
inference(avatar_split_clause,[],[f18625,f31924]) ).
fof(f31924,plain,
( spl698_776
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = X0
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_776])]) ).
fof(f18625,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = X0
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(cnf_transformation,[],[f10340]) ).
fof(f10340,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = X0
| ~ class_Lattices_Oab__semigroup__idem__mult(X1) ),
inference(ennf_transformation,[],[f6164]) ).
fof(f6164,plain,
! [X0,X1] :
( class_Lattices_Oab__semigroup__idem__mult(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) = X0 ),
inference(rectify,[],[f1260]) ).
fof(f1260,axiom,
! [X22,X23] :
( class_Lattices_Oab__semigroup__idem__mult(X23)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X23),X22),X22) = X22 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_mult__idem) ).
fof(f31922,plain,
spl698_775,
inference(avatar_split_clause,[],[f18615,f31920]) ).
fof(f31920,plain,
( spl698_775
<=> ! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_775])]) ).
fof(f18615,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ),
inference(cnf_transformation,[],[f6155]) ).
fof(f6155,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ),
inference(rectify,[],[f5240]) ).
fof(f5240,axiom,
! [X37,X5] :
( hBOOL(X37)
| ~ hBOOL(X5)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X5),X37)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fimplies__3) ).
fof(f31917,plain,
spl698_774,
inference(avatar_split_clause,[],[f18614,f31915]) ).
fof(f31915,plain,
( spl698_774
<=> ! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_774])]) ).
fof(f18614,plain,
! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ),
inference(cnf_transformation,[],[f6154]) ).
fof(f6154,plain,
! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ),
inference(rectify,[],[f5237]) ).
fof(f5237,axiom,
! [X37,X5] :
( hBOOL(X37)
| hBOOL(X5)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X5),X37)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fdisj__3) ).
fof(f31913,plain,
spl698_773,
inference(avatar_split_clause,[],[f18608,f31911]) ).
fof(f31911,plain,
( spl698_773
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_773])]) ).
fof(f18608,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6148]) ).
fof(f6148,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(rectify,[],[f5232]) ).
fof(f5232,axiom,
! [X37,X5] :
( hBOOL(hAPP(hAPP(c_fconj,X5),X37))
| ~ hBOOL(X37)
| ~ hBOOL(X5) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fconj__1) ).
fof(f31909,plain,
spl698_772,
inference(avatar_split_clause,[],[f18197,f31907]) ).
fof(f31907,plain,
( spl698_772
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_772])]) ).
fof(f18197,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)),X1)),
inference(cnf_transformation,[],[f5794]) ).
fof(f5794,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)),X1)),
inference(rectify,[],[f2255]) ).
fof(f2255,axiom,
! [X88,X93] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X93,X88)),X93)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_mod__less__eq__dividend) ).
fof(f31905,plain,
spl698_771,
inference(avatar_split_clause,[],[f18195,f31903]) ).
fof(f31903,plain,
( spl698_771
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_771])]) ).
fof(f18195,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5792]) ).
fof(f5792,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f1012]) ).
fof(f1012,axiom,
! [X20,X4] : hBOOL(hAPP(hAPP(c_member(X4),X20),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_UNIV__I) ).
fof(f31901,plain,
spl698_770,
inference(avatar_split_clause,[],[f18193,f31899]) ).
fof(f31899,plain,
( spl698_770
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_770])]) ).
fof(f18193,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(cnf_transformation,[],[f5790]) ).
fof(f5790,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(rectify,[],[f235]) ).
fof(f235,axiom,
! [X19,X4] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X19),X19) = X19,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Un__absorb) ).
fof(f31897,plain,
spl698_769,
inference(avatar_split_clause,[],[f18192,f31895]) ).
fof(f31895,plain,
( spl698_769
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_769])]) ).
fof(f18192,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(cnf_transformation,[],[f5789]) ).
fof(f5789,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(rectify,[],[f388]) ).
fof(f388,axiom,
! [X19,X4] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X19),X19) = X19,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Int__absorb) ).
fof(f31893,plain,
spl698_768,
inference(avatar_split_clause,[],[f18191,f31891]) ).
fof(f31891,plain,
( spl698_768
<=> ! [X0,X1] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_768])]) ).
fof(f18191,plain,
! [X0,X1] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X0)) = X0,
inference(cnf_transformation,[],[f5788]) ).
fof(f5788,plain,
! [X0,X1] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X0)) = X0,
inference(rectify,[],[f3834]) ).
fof(f3834,axiom,
! [X19,X4] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_OPow(X4),X19)) = X19,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Union__Pow__eq) ).
fof(f31889,plain,
spl698_767,
inference(avatar_split_clause,[],[f18190,f31887]) ).
fof(f31887,plain,
( spl698_767
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),X0),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_767])]) ).
fof(f18190,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5787]) ).
fof(f5787,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f3957]) ).
fof(f3957,axiom,
! [X88,X23] : c_List_Olist_ONil(X23) = hAPP(hAPP(c_List_Otake(X23),X88),c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_take__Nil) ).
fof(f31885,plain,
spl698_766,
inference(avatar_split_clause,[],[f18189,f31883]) ).
fof(f31883,plain,
( spl698_766
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Odrop(X1),X0),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_766])]) ).
fof(f18189,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Odrop(X1),X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5786]) ).
fof(f5786,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Odrop(X1),X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f4135]) ).
fof(f4135,axiom,
! [X88,X23] : c_List_Olist_ONil(X23) = hAPP(hAPP(c_List_Odrop(X23),X88),c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_drop__Nil) ).
fof(f31881,plain,
spl698_765,
inference(avatar_split_clause,[],[f18185,f31879]) ).
fof(f31879,plain,
( spl698_765
<=> ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_765])]) ).
fof(f18185,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5782]) ).
fof(f5782,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f227]) ).
fof(f227,axiom,
! [X6,X4] : ~ hBOOL(hAPP(hAPP(c_member(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_emptyE) ).
fof(f31877,plain,
spl698_764,
inference(avatar_split_clause,[],[f17963,f31875]) ).
fof(f31875,plain,
( spl698_764
<=> ! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK150(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_764])]) ).
fof(f17963,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK150(X0)),X0)) ),
inference(cnf_transformation,[],[f14787]) ).
fof(f31873,plain,
spl698_763,
inference(avatar_split_clause,[],[f17879,f31871]) ).
fof(f31871,plain,
( spl698_763
<=> ! [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,[spl698_763])]) ).
fof(f17879,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,[],[f10200]) ).
fof(f10200,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,[],[f5551]) ).
fof(f5551,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,[],[f1759]) ).
fof(f1759,axiom,
! [X23] :
( class_Rings_Osemiring__1(X23)
=> c_Groups_Oone__class_Oone(X23) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X23),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_of__nat__1) ).
fof(f31869,plain,
spl698_762,
inference(avatar_split_clause,[],[f17875,f31867]) ).
fof(f31867,plain,
( spl698_762
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_List_Omonoid__add__class_Olistsum(X0),c_List_Olist_ONil(X0))
| ~ class_Groups_Omonoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_762])]) ).
fof(f17875,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_List_Omonoid__add__class_Olistsum(X0),c_List_Olist_ONil(X0))
| ~ class_Groups_Omonoid__add(X0) ),
inference(cnf_transformation,[],[f10196]) ).
fof(f10196,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_List_Omonoid__add__class_Olistsum(X0),c_List_Olist_ONil(X0))
| ~ class_Groups_Omonoid__add(X0) ),
inference(ennf_transformation,[],[f5547]) ).
fof(f5547,plain,
! [X0] :
( class_Groups_Omonoid__add(X0)
=> c_Groups_Ozero__class_Ozero(X0) = hAPP(c_List_Omonoid__add__class_Olistsum(X0),c_List_Olist_ONil(X0)) ),
inference(rectify,[],[f3945]) ).
fof(f3945,axiom,
! [X23] :
( class_Groups_Omonoid__add(X23)
=> c_Groups_Ozero__class_Ozero(X23) = hAPP(c_List_Omonoid__add__class_Olistsum(X23),c_List_Olist_ONil(X23)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_listsum__simps_I1_J) ).
fof(f31865,plain,
spl698_761,
inference(avatar_split_clause,[],[f17865,f31863]) ).
fof(f31863,plain,
( spl698_761
<=> ! [X0] :
( c_Orderings_Obot__class_Obot(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0))
| ~ class_Lattices_Oboolean__algebra(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_761])]) ).
fof(f17865,plain,
! [X0] :
( c_Orderings_Obot__class_Obot(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0))
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[],[f10186]) ).
fof(f10186,plain,
! [X0] :
( c_Orderings_Obot__class_Obot(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0))
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(ennf_transformation,[],[f5537]) ).
fof(f5537,plain,
! [X0] :
( class_Lattices_Oboolean__algebra(X0)
=> c_Orderings_Obot__class_Obot(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0)) ),
inference(rectify,[],[f1150]) ).
fof(f1150,axiom,
! [X23] :
( class_Lattices_Oboolean__algebra(X23)
=> c_Orderings_Obot__class_Obot(X23) = hAPP(c_Groups_Ouminus__class_Ouminus(X23),c_Orderings_Otop__class_Otop(X23)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_compl__top__eq) ).
fof(f31861,plain,
spl698_760,
inference(avatar_split_clause,[],[f17864,f31859]) ).
fof(f31859,plain,
( spl698_760
<=> ! [X0] :
( c_Orderings_Otop__class_Otop(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0))
| ~ class_Lattices_Oboolean__algebra(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_760])]) ).
fof(f17864,plain,
! [X0] :
( c_Orderings_Otop__class_Otop(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0))
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[],[f10185]) ).
fof(f10185,plain,
! [X0] :
( c_Orderings_Otop__class_Otop(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0))
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(ennf_transformation,[],[f5536]) ).
fof(f5536,plain,
! [X0] :
( class_Lattices_Oboolean__algebra(X0)
=> c_Orderings_Otop__class_Otop(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0)) ),
inference(rectify,[],[f1149]) ).
fof(f1149,axiom,
! [X23] :
( class_Lattices_Oboolean__algebra(X23)
=> c_Orderings_Otop__class_Otop(X23) = hAPP(c_Groups_Ouminus__class_Ouminus(X23),c_Orderings_Obot__class_Obot(X23)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_compl__bot__eq) ).
fof(f31857,plain,
spl698_759,
inference(avatar_split_clause,[],[f17852,f31855]) ).
fof(f31855,plain,
( spl698_759
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_759])]) ).
fof(f17852,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f10173]) ).
fof(f10173,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f5524]) ).
fof(f5524,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> c_Groups_Oone__class_Oone(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f3264]) ).
fof(f3264,axiom,
! [X23] :
( class_Rings_Olinordered__idom(X23)
=> c_Groups_Oone__class_Oone(X23) = hAPP(c_Groups_Oabs__class_Oabs(X23),c_Groups_Oone__class_Oone(X23)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_abs__one) ).
fof(f31853,plain,
spl698_758,
inference(avatar_split_clause,[],[f17851,f31851]) ).
fof(f31851,plain,
( spl698_758
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(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,[spl698_758])]) ).
fof(f17851,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[],[f10172]) ).
fof(f10172,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(ennf_transformation,[],[f5523]) ).
fof(f5523,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add__abs(X0)
=> c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f3251]) ).
fof(f3251,axiom,
! [X23] :
( class_Groups_Oordered__ab__group__add__abs(X23)
=> c_Groups_Ozero__class_Ozero(X23) = hAPP(c_Groups_Oabs__class_Oabs(X23),c_Groups_Ozero__class_Ozero(X23)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_abs__zero) ).
fof(f31848,plain,
spl698_757,
inference(avatar_split_clause,[],[f17847,f31846]) ).
fof(f17847,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Rings_Oring__1(X0) ),
inference(cnf_transformation,[],[f10168]) ).
fof(f10168,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Rings_Oring__1(X0) ),
inference(ennf_transformation,[],[f5519]) ).
fof(f5519,plain,
! [X0] :
( class_Rings_Oring__1(X0)
=> c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(rectify,[],[f2814]) ).
fof(f2814,axiom,
! [X23] :
( class_Rings_Oring__1(X23)
=> c_Groups_Oone__class_Oone(X23) = hAPP(c_Int_Oring__1__class_Oof__int(X23),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_of__int__1) ).
fof(f31844,plain,
spl698_756,
inference(avatar_split_clause,[],[f17846,f31842]) ).
fof(f31842,plain,
( spl698_756
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Ogroup__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_756])]) ).
fof(f17846,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f10167]) ).
fof(f10167,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Ogroup__add(X0) ),
inference(ennf_transformation,[],[f5518]) ).
fof(f5518,plain,
! [X0] :
( class_Groups_Ogroup__add(X0)
=> c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f1477]) ).
fof(f1477,axiom,
! [X23] :
( class_Groups_Ogroup__add(X23)
=> c_Groups_Ozero__class_Ozero(X23) = hAPP(c_Groups_Ouminus__class_Ouminus(X23),c_Groups_Ozero__class_Ozero(X23)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_minus__zero) ).
fof(f31840,plain,
spl698_755,
inference(avatar_split_clause,[],[f17695,f31838]) ).
fof(f31838,plain,
( spl698_755
<=> ! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_755])]) ).
fof(f17695,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)),
inference(cnf_transformation,[],[f5381]) ).
fof(f5381,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)),
inference(rectify,[],[f3612]) ).
fof(f3612,axiom,
! [X4] : hAPP(c_List_Omap(X4,X4),c_COMBI(X4)) = c_Fun_Oid(tc_List_Olist(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_List_Omap_Oidentity) ).
fof(f31836,plain,
spl698_754,
inference(avatar_split_clause,[],[f17694,f31834]) ).
fof(f31834,plain,
( spl698_754
<=> ! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_754])]) ).
fof(f17694,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)),
inference(cnf_transformation,[],[f5380]) ).
fof(f5380,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)),
inference(rectify,[],[f3611]) ).
fof(f3611,axiom,
! [X4] : hAPP(c_List_Omap(X4,X4),c_Fun_Oid(X4)) = c_Fun_Oid(tc_List_Olist(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_List_Omap_Oid) ).
fof(f31832,plain,
spl698_753,
inference(avatar_split_clause,[],[f17693,f31830]) ).
fof(f31830,plain,
( spl698_753
<=> ! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_Fun_Oid(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_753])]) ).
fof(f17693,plain,
! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_Fun_Oid(X0)),
inference(cnf_transformation,[],[f5379]) ).
fof(f5379,plain,
! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_Fun_Oid(X0)),
inference(rectify,[],[f3562]) ).
fof(f3562,axiom,
! [X4] : hAPP(c_Option_Omap(X4,X4),c_Fun_Oid(X4)) = c_Fun_Oid(tc_Option_Ooption(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Option_Omap_Oid) ).
fof(f31828,plain,
spl698_752,
inference(avatar_split_clause,[],[f17691,f31826]) ).
fof(f31826,plain,
( spl698_752
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_List_Oset(X0),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_752])]) ).
fof(f17691,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_List_Oset(X0),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5377]) ).
fof(f5377,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_List_Oset(X0),c_List_Olist_ONil(X0)),
inference(rectify,[],[f3950]) ).
fof(f3950,axiom,
! [X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_List_Oset(X4),c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_List_Oset_Osimps_I1_J) ).
fof(f31824,plain,
spl698_751,
inference(avatar_split_clause,[],[f17690,f31822]) ).
fof(f31822,plain,
( spl698_751
<=> ! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_COMBI(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_751])]) ).
fof(f17690,plain,
! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_COMBI(X0)),
inference(cnf_transformation,[],[f5376]) ).
fof(f5376,plain,
! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_COMBI(X0)),
inference(rectify,[],[f3563]) ).
fof(f3563,axiom,
! [X4] : c_Fun_Oid(tc_Option_Ooption(X4)) = hAPP(c_Option_Omap(X4,X4),c_COMBI(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Option_Omap_Oidentity) ).
fof(f31819,plain,
spl698_750,
inference(avatar_split_clause,[],[f17689,f31817]) ).
fof(f17689,plain,
! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f5375]) ).
fof(f5375,plain,
! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(rectify,[],[f2871]) ).
fof(f2871,axiom,
! [X112] : c_Int_Opred(X112) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X112),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_pred__def) ).
fof(f31814,plain,
spl698_749,
inference(avatar_split_clause,[],[f17688,f31812]) ).
fof(f31810,plain,
spl698_748,
inference(avatar_split_clause,[],[f17687,f31808]) ).
fof(f31808,plain,
( spl698_748
<=> ! [X0] : c_Code__Numeral_OSuc__code__numeral(X0) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_748])]) ).
fof(f17687,plain,
! [X0] : c_Code__Numeral_OSuc__code__numeral(X0) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0))),
inference(cnf_transformation,[],[f5373]) ).
fof(f5373,plain,
! [X0] : c_Code__Numeral_OSuc__code__numeral(X0) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0))),
inference(rectify,[],[f4649]) ).
fof(f4649,axiom,
! [X112] : c_Code__Numeral_OSuc__code__numeral(X112) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X112))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Suc__code__numeral__def) ).
fof(f31806,plain,
spl698_747,
inference(avatar_split_clause,[],[f17686,f31804]) ).
fof(f31804,plain,
( spl698_747
<=> ! [X0] : c_List_Oreturn__list(X0) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_747])]) ).
fof(f17686,plain,
! [X0] : c_List_Oreturn__list(X0) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X0),
inference(cnf_transformation,[],[f5372]) ).
fof(f5372,plain,
! [X0] : c_List_Oreturn__list(X0) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X0),
inference(rectify,[],[f4084]) ).
fof(f4084,axiom,
! [X153] : c_List_Oreturn__list(X153) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),X153),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_return__list__def) ).
fof(f31802,plain,
spl698_746,
inference(avatar_split_clause,[],[f17676,f31800]) ).
fof(f17676,plain,
! [X0] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X0)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X0),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5362]) ).
fof(f5362,plain,
! [X0] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X0)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X0),tc_HOL_Obool)))),
inference(rectify,[],[f3620]) ).
fof(f3620,axiom,
! [X4] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X4)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_infinite__UNIV__listI) ).
fof(f31798,plain,
spl698_745,
inference(avatar_split_clause,[],[f17524,f31795]) ).
fof(f31795,plain,
( spl698_745
<=> c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_745])]) ).
fof(f17524,plain,
c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
inference(cnf_transformation,[],[f3107]) ).
fof(f3107,axiom,
c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_type__definition__Integ) ).
fof(f31792,plain,
spl698_744,
inference(avatar_split_clause,[],[f17523,f31789]) ).
fof(f31789,plain,
( spl698_744
<=> c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_744])]) ).
fof(f17523,plain,
c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
inference(cnf_transformation,[],[f4950]) ).
fof(f4950,axiom,
c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_COMBK(tc_HOL_Obool,tc_Nat_Onat),c_fTrue)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_transfer__morphism__int__nat) ).
fof(f31787,plain,
spl698_743,
inference(avatar_split_clause,[],[f17518,f31784]) ).
fof(f31784,plain,
( spl698_743
<=> c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_743])]) ).
fof(f17518,plain,
c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
inference(cnf_transformation,[],[f4621]) ).
fof(f4621,axiom,
c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_number__of__code__numeral__def) ).
fof(f31782,plain,
spl698_742,
inference(avatar_split_clause,[],[f17517,f31779]) ).
fof(f31779,plain,
( spl698_742
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_742])]) ).
fof(f17517,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))),
inference(cnf_transformation,[],[f1192]) ).
fof(f1192,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_card__UNIV__unit) ).
fof(f31777,plain,
spl698_741,
inference(avatar_split_clause,[],[f17515,f31774]) ).
fof(f31774,plain,
( spl698_741
<=> c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_741])]) ).
fof(f17515,plain,
c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
inference(cnf_transformation,[],[f4645]) ).
fof(f4645,axiom,
c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_int__of__def) ).
fof(f31772,plain,
spl698_740,
inference(avatar_split_clause,[],[f17226,f31769]) ).
fof(f31769,plain,
( spl698_740
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_740])]) ).
fof(f17226,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)),
inference(cnf_transformation,[],[f5241]) ).
fof(f5241,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',conj_0) ).
fof(f31744,plain,
( ~ spl698_739
| spl698_354
| ~ spl698_709 ),
inference(avatar_split_clause,[],[f31721,f31379,f29744,f31741]) ).
fof(f31741,plain,
( spl698_739
<=> c_Nat__Transfer_Ois__nat(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_739])]) ).
fof(f29744,plain,
( spl698_354
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_354])]) ).
fof(f31379,plain,
( spl698_709
<=> ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| ~ c_Nat__Transfer_Ois__nat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_709])]) ).
fof(f31721,plain,
( ~ c_Nat__Transfer_Ois__nat(c_Int_OMin)
| spl698_354
| ~ spl698_709 ),
inference(resolution,[],[f31380,f29746]) ).
fof(f29746,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| spl698_354 ),
inference(avatar_component_clause,[],[f29744]) ).
fof(f31380,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| ~ c_Nat__Transfer_Ois__nat(X0) )
| ~ spl698_709 ),
inference(avatar_component_clause,[],[f31379]) ).
fof(f31698,plain,
( spl698_738
| ~ spl698_574 ),
inference(avatar_split_clause,[],[f30840,f30744,f31696]) ).
fof(f31696,plain,
( spl698_738
<=> ! [X0,X1] : sP51(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_738])]) ).
fof(f30744,plain,
( spl698_574
<=> ! [X2,X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != X2
| sP51(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_574])]) ).
fof(f30840,plain,
( ! [X0,X1] : sP51(X0,X1,c_HOL_Obool_Obool__size(c_fTrue))
| ~ spl698_574 ),
inference(equality_resolution,[],[f30745]) ).
fof(f30745,plain,
( ! [X2,X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != X2
| sP51(X0,X1,X2) )
| ~ spl698_574 ),
inference(avatar_component_clause,[],[f30744]) ).
fof(f31662,plain,
( spl698_737
| ~ spl698_573 ),
inference(avatar_split_clause,[],[f30836,f30740,f31660]) ).
fof(f31660,plain,
( spl698_737
<=> ! [X0,X1] : sP46(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_737])]) ).
fof(f30740,plain,
( spl698_573
<=> ! [X2,X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != X2
| sP46(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_573])]) ).
fof(f30836,plain,
( ! [X0,X1] : sP46(X0,X1,c_HOL_Obool_Obool__size(c_fTrue))
| ~ spl698_573 ),
inference(equality_resolution,[],[f30741]) ).
fof(f30741,plain,
( ! [X2,X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != X2
| sP46(X0,X1,X2) )
| ~ spl698_573 ),
inference(avatar_component_clause,[],[f30740]) ).
fof(f31573,plain,
( spl698_736
| ~ spl698_569 ),
inference(avatar_split_clause,[],[f30835,f30724,f31570]) ).
fof(f31570,plain,
( spl698_736
<=> c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_736])]) ).
fof(f30724,plain,
( spl698_569
<=> ! [X0] :
( c_Int_OPls != X0
| c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_569])]) ).
fof(f30835,plain,
( c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls)
| ~ spl698_569 ),
inference(equality_resolution,[],[f30725]) ).
fof(f30725,plain,
( ! [X0] :
( c_Int_OPls != X0
| c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) )
| ~ spl698_569 ),
inference(avatar_component_clause,[],[f30724]) ).
fof(f31548,plain,
( spl698_735
| ~ spl698_540 ),
inference(avatar_split_clause,[],[f30817,f30590,f31546]) ).
fof(f31546,plain,
( spl698_735
<=> ! [X0,X1] : sP55(X0,X1,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_735])]) ).
fof(f30590,plain,
( spl698_540
<=> ! [X2,X0,X1] :
( sP55(X0,X1,X2)
| c_List_Olist_ONil(X1) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_540])]) ).
fof(f30817,plain,
( ! [X0,X1] : sP55(X0,X1,c_List_Olist_ONil(X1))
| ~ spl698_540 ),
inference(equality_resolution,[],[f30591]) ).
fof(f30591,plain,
( ! [X2,X0,X1] :
( c_List_Olist_ONil(X1) != X2
| sP55(X0,X1,X2) )
| ~ spl698_540 ),
inference(avatar_component_clause,[],[f30590]) ).
fof(f31538,plain,
( spl698_734
| ~ spl698_524 ),
inference(avatar_split_clause,[],[f30810,f30526,f31536]) ).
fof(f30526,plain,
( spl698_524
<=> ! [X0,X1] :
( sP6(X0,X1)
| hAPP(c_Int_Onat,X1) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_524])]) ).
fof(f30810,plain,
( ! [X0] : sP6(hAPP(c_Int_Onat,X0),X0)
| ~ spl698_524 ),
inference(equality_resolution,[],[f30527]) ).
fof(f30527,plain,
( ! [X0,X1] :
( hAPP(c_Int_Onat,X1) != X0
| sP6(X0,X1) )
| ~ spl698_524 ),
inference(avatar_component_clause,[],[f30526]) ).
fof(f31527,plain,
( spl698_733
| ~ spl698_522 ),
inference(avatar_split_clause,[],[f30805,f30518,f31525]) ).
fof(f30518,plain,
( spl698_522
<=> ! [X0,X1] :
( sP5(X1,X0)
| hAPP(c_Int_Onat,X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_522])]) ).
fof(f30805,plain,
( ! [X0] : sP5(hAPP(c_Int_Onat,X0),X0)
| ~ spl698_522 ),
inference(equality_resolution,[],[f30519]) ).
fof(f30519,plain,
( ! [X0,X1] :
( hAPP(c_Int_Onat,X0) != X1
| sP5(X1,X0) )
| ~ spl698_522 ),
inference(avatar_component_clause,[],[f30518]) ).
fof(f31497,plain,
( spl698_732
| ~ spl698_552
| ~ spl698_599 ),
inference(avatar_split_clause,[],[f30924,f30921,f30641,f31495]) ).
fof(f31495,plain,
( spl698_732
<=> ! [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,[spl698_732])]) ).
fof(f30921,plain,
( spl698_599
<=> ! [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,[spl698_599])]) ).
fof(f30924,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Osucc(c_Int_OPls)),X0) = X0
| ~ spl698_552
| ~ spl698_599 ),
inference(forward_demodulation,[],[f30922,f30643]) ).
fof(f30922,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0
| ~ spl698_599 ),
inference(avatar_component_clause,[],[f30921]) ).
fof(f31493,plain,
( spl698_731
| ~ spl698_552
| ~ spl698_597 ),
inference(avatar_split_clause,[],[f30915,f30912,f30641,f31491]) ).
fof(f31491,plain,
( spl698_731
<=> ! [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,[spl698_731])]) ).
fof(f30912,plain,
( spl698_597
<=> ! [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,[spl698_597])]) ).
fof(f30915,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Int_Osucc(c_Int_OPls)) = X0
| ~ spl698_552
| ~ spl698_597 ),
inference(forward_demodulation,[],[f30913,f30643]) ).
fof(f30913,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0
| ~ spl698_597 ),
inference(avatar_component_clause,[],[f30912]) ).
fof(f31470,plain,
( ~ spl698_25
| ~ spl698_730
| ~ spl698_278
| ~ spl698_476 ),
inference(avatar_split_clause,[],[f30762,f30334,f29372,f31467,f28141]) ).
fof(f28141,plain,
( spl698_25
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_25])]) ).
fof(f31467,plain,
( spl698_730
<=> c_Int_Oiszero(tc_Int_Oint,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_730])]) ).
fof(f29372,plain,
( spl698_278
<=> ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_278])]) ).
fof(f30334,plain,
( spl698_476
<=> ! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_476])]) ).
fof(f30762,plain,
( ~ c_Int_Oiszero(tc_Int_Oint,c_Int_OMin)
| ~ class_Int_Onumber__ring(tc_Int_Oint)
| ~ spl698_278
| ~ spl698_476 ),
inference(superposition,[],[f30335,f29373]) ).
fof(f29373,plain,
( ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0
| ~ spl698_278 ),
inference(avatar_component_clause,[],[f29372]) ).
fof(f30335,plain,
( ! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) )
| ~ spl698_476 ),
inference(avatar_component_clause,[],[f30334]) ).
fof(f31463,plain,
spl698_729,
inference(avatar_split_clause,[],[f26747,f31461]) ).
fof(f31461,plain,
( spl698_729
<=> ! [X2,X0,X1] : hAPP(c_Finite__Set_Ofold1(X2,X1),hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_729])]) ).
fof(f26747,plain,
! [X2,X0,X1] : hAPP(c_Finite__Set_Ofold1(X2,X1),hAPP(c_fequal,X0)) = X0,
inference(forward_demodulation,[],[f19879,f25465]) ).
fof(f19879,plain,
! [X2,X0,X1] : hAPP(c_Finite__Set_Ofold1(X2,X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = X0,
inference(cnf_transformation,[],[f6970]) ).
fof(f6970,plain,
! [X0,X1,X2] : hAPP(c_Finite__Set_Ofold1(X2,X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = X0,
inference(rectify,[],[f3531]) ).
fof(f3531,axiom,
! [X6,X1,X4] : hAPP(c_Finite__Set_Ofold1(X4,X1),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X6,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_fold1__singleton) ).
fof(f31459,plain,
spl698_728,
inference(avatar_split_clause,[],[f26744,f31457]) ).
fof(f31457,plain,
( spl698_728
<=> ! [X2,X0,X1] : hAPP(c_Nat_Onat_Onat__rec(X2,X1,X0),c_HOL_Obool_Obool__size(c_fTrue)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_728])]) ).
fof(f26744,plain,
! [X2,X0,X1] : hAPP(c_Nat_Onat_Onat__rec(X2,X1,X0),c_HOL_Obool_Obool__size(c_fTrue)) = X1,
inference(forward_demodulation,[],[f19834,f17447]) ).
fof(f19834,plain,
! [X2,X0,X1] : hAPP(c_Nat_Onat_Onat__rec(X2,X1,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(cnf_transformation,[],[f6925]) ).
fof(f6925,plain,
! [X0,X1,X2] : hAPP(c_Nat_Onat_Onat__rec(X2,X1,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rectify,[],[f2891]) ).
fof(f2891,axiom,
! [X67,X25,X4] : hAPP(c_Nat_Onat_Onat__rec(X4,X25,X67),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X25,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__rec__0) ).
fof(f31455,plain,
( ~ spl698_727
| spl698_234
| ~ spl698_552 ),
inference(avatar_split_clause,[],[f30647,f30641,f29172,f31452]) ).
fof(f31452,plain,
( spl698_727
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_Osucc(c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_727])]) ).
fof(f29172,plain,
( spl698_234
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_234])]) ).
fof(f30647,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_Osucc(c_Int_OPls)))
| spl698_234
| ~ spl698_552 ),
inference(superposition,[],[f29174,f30643]) ).
fof(f29174,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| spl698_234 ),
inference(avatar_component_clause,[],[f29172]) ).
fof(f31450,plain,
spl698_726,
inference(avatar_split_clause,[],[f26495,f31448]) ).
fof(f31448,plain,
( spl698_726
<=> ! [X0,X1] :
( c_Int_OPls != X0
| sP10(X0,X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_726])]) ).
fof(f26495,plain,
! [X0,X1] :
( c_Int_OPls != X0
| sP10(X0,X1)
| X0 != X1 ),
inference(forward_demodulation,[],[f26494,f17436]) ).
fof(f26494,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| sP10(X0,X1)
| X0 != X1 ),
inference(forward_demodulation,[],[f19607,f17595]) ).
fof(f19607,plain,
! [X0,X1] :
( sP10(X0,X1)
| X0 != X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f15258]) ).
fof(f31446,plain,
spl698_725,
inference(avatar_split_clause,[],[f26449,f31444]) ).
fof(f31444,plain,
( spl698_725
<=> ! [X0,X1] :
( c_Int_OMin != X1
| c_Int_OMin != X0
| sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_725])]) ).
fof(f26449,plain,
! [X0,X1] :
( c_Int_OMin != X1
| c_Int_OMin != X0
| sP8(X0,X1) ),
inference(forward_demodulation,[],[f26448,f17595]) ).
fof(f26448,plain,
! [X0,X1] :
( c_Int_OMin != X0
| sP8(X0,X1)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 ),
inference(forward_demodulation,[],[f19558,f17595]) ).
fof(f19558,plain,
! [X0,X1] :
( sP8(X0,X1)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 ),
inference(cnf_transformation,[],[f15227]) ).
fof(f31442,plain,
spl698_724,
inference(avatar_split_clause,[],[f25964,f31440]) ).
fof(f31440,plain,
( spl698_724
<=> ! [X0,X1] :
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_724])]) ).
fof(f25964,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(forward_demodulation,[],[f18970,f25465]) ).
fof(f18970,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10658]) ).
fof(f10658,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6434]) ).
fof(f6434,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f859]) ).
fof(f859,axiom,
! [X20,X4] :
( class_Lattices_Olattice(X4)
=> c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X20),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X20 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Inf__fin_Osingleton) ).
fof(f31438,plain,
spl698_723,
inference(avatar_split_clause,[],[f25963,f31436]) ).
fof(f31436,plain,
( spl698_723
<=> ! [X0,X1] :
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_723])]) ).
fof(f25963,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(forward_demodulation,[],[f18969,f25465]) ).
fof(f18969,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10657]) ).
fof(f10657,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6433]) ).
fof(f6433,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f858]) ).
fof(f858,axiom,
! [X20,X4] :
( class_Lattices_Olattice(X4)
=> c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X20),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X20 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Sup__fin_Osingleton) ).
fof(f31434,plain,
spl698_722,
inference(avatar_split_clause,[],[f25956,f31432]) ).
fof(f31432,plain,
( spl698_722
<=> ! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_722])]) ).
fof(f25956,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(forward_demodulation,[],[f18911,f25465]) ).
fof(f18911,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10600]) ).
fof(f10600,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6393]) ).
fof(f6393,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f1203]) ).
fof(f1203,axiom,
! [X20,X4] :
( class_Orderings_Olinorder(X4)
=> c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Set_Oinsert(X4),X20),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X20 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Max_Osingleton) ).
fof(f31430,plain,
spl698_721,
inference(avatar_split_clause,[],[f25955,f31428]) ).
fof(f31428,plain,
( spl698_721
<=> ! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_721])]) ).
fof(f25955,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(forward_demodulation,[],[f18910,f25465]) ).
fof(f18910,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10599]) ).
fof(f10599,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6392]) ).
fof(f6392,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f1202]) ).
fof(f1202,axiom,
! [X20,X4] :
( class_Orderings_Olinorder(X4)
=> c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X20),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X20 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Min_Osingleton) ).
fof(f31426,plain,
spl698_720,
inference(avatar_split_clause,[],[f25954,f31424]) ).
fof(f31424,plain,
( spl698_720
<=> ! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Oinsert(X1,X0,c_List_Olist_ONil(X1)))
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_720])]) ).
fof(f25954,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Oinsert(X1,X0,c_List_Olist_ONil(X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(forward_demodulation,[],[f18909,f18250]) ).
fof(f18250,plain,
! [X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1)) = c_List_Oinsert(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5847]) ).
fof(f5847,plain,
! [X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1)) = c_List_Oinsert(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4546]) ).
fof(f4546,axiom,
! [X22,X23] : hAPP(hAPP(c_List_Olist_OCons(X23),X22),c_List_Olist_ONil(X23)) = c_List_Oinsert(X23,X22,c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_insert__Nil) ).
fof(f18909,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10598]) ).
fof(f10598,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6391]) ).
fof(f6391,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1))) ),
inference(rectify,[],[f4263]) ).
fof(f4263,axiom,
! [X22,X23] :
( class_Orderings_Olinorder(X23)
=> c_List_Olinorder__class_Osorted(X23,hAPP(hAPP(c_List_Olist_OCons(X23),X22),c_List_Olist_ONil(X23))) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_sorted__single) ).
fof(f31422,plain,
spl698_719,
inference(avatar_split_clause,[],[f25930,f31420]) ).
fof(f31420,plain,
( spl698_719
<=> ! [X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_719])]) ).
fof(f25930,plain,
! [X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(forward_demodulation,[],[f18831,f25465]) ).
fof(f18831,plain,
! [X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(cnf_transformation,[],[f10510]) ).
fof(f10510,plain,
! [X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(ennf_transformation,[],[f6317]) ).
fof(f6317,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(X1)
=> c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f3849]) ).
fof(f3849,axiom,
! [X6,X4] :
( class_Complete__Lattice_Ocomplete__lattice(X4)
=> c_Complete__Lattice_OSup__class_OSup(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X6 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Sup__singleton) ).
fof(f31418,plain,
spl698_718,
inference(avatar_split_clause,[],[f25929,f31416]) ).
fof(f31416,plain,
( spl698_718
<=> ! [X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_718])]) ).
fof(f25929,plain,
! [X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(forward_demodulation,[],[f18830,f25465]) ).
fof(f18830,plain,
! [X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(cnf_transformation,[],[f10509]) ).
fof(f10509,plain,
! [X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(ennf_transformation,[],[f6316]) ).
fof(f6316,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(X1)
=> c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f4486]) ).
fof(f4486,axiom,
! [X6,X4] :
( class_Complete__Lattice_Ocomplete__lattice(X4)
=> c_Complete__Lattice_OInf__class_OInf(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X6 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Inf__singleton) ).
fof(f31414,plain,
spl698_717,
inference(avatar_split_clause,[],[f25606,f31412]) ).
fof(f31412,plain,
( spl698_717
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != X1
| c_Nitpick_Onat__gcd(X0,X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_717])]) ).
fof(f25606,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != X1
| c_Nitpick_Onat__gcd(X0,X1) = X0 ),
inference(forward_demodulation,[],[f18519,f17447]) ).
fof(f18519,plain,
! [X0,X1] :
( c_Nitpick_Onat__gcd(X0,X1) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f10294]) ).
fof(f10294,plain,
! [X0,X1] :
( ( c_Nitpick_Onat__gcd(X0,X1) = c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Nitpick_Onat__gcd(X0,X1) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(ennf_transformation,[],[f6109]) ).
fof(f6109,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> c_Nitpick_Onat__gcd(X0,X1) = c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Nitpick_Onat__gcd(X0,X1) = X0 ) ),
inference(rectify,[],[f3306]) ).
fof(f3306,axiom,
! [X22,X29] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X29
=> c_Nitpick_Onat__gcd(X22,X29) = c_Nitpick_Onat__gcd(X29,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22,X29)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X29
=> c_Nitpick_Onat__gcd(X22,X29) = X22 ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__gcd_Osimps) ).
fof(f31410,plain,
( ~ spl698_716
| ~ spl698_331
| ~ spl698_426 ),
inference(avatar_split_clause,[],[f30181,f30050,f29592,f31407]) ).
fof(f31407,plain,
( spl698_716
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_716])]) ).
fof(f29592,plain,
( spl698_331
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_331])]) ).
fof(f30050,plain,
( spl698_426
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_426])]) ).
fof(f30181,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_HOL_Obool_Obool__size(c_fTrue)
| ~ spl698_331
| ~ spl698_426 ),
inference(superposition,[],[f29593,f30052]) ).
fof(f30052,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))
| ~ spl698_426 ),
inference(avatar_component_clause,[],[f30050]) ).
fof(f29593,plain,
( ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0)
| ~ spl698_331 ),
inference(avatar_component_clause,[],[f29592]) ).
fof(f31405,plain,
spl698_715,
inference(avatar_split_clause,[],[f25447,f31403]) ).
fof(f31403,plain,
( spl698_715
<=> ! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_715])]) ).
fof(f25447,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f18169,f17447]) ).
fof(f18169,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f5766]) ).
fof(f5766,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f4130]) ).
fof(f4130,axiom,
! [X263,X23] : hAPP(hAPP(c_List_Odrop(X23),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X263) = X263,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_drop__0) ).
fof(f31401,plain,
spl698_714,
inference(avatar_split_clause,[],[f25446,f31399]) ).
fof(f31399,plain,
( spl698_714
<=> ! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_714])]) ).
fof(f25446,plain,
! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X1,X0)),
inference(forward_demodulation,[],[f18162,f17447]) ).
fof(f18162,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X1,X0)),
inference(cnf_transformation,[],[f5759]) ).
fof(f5759,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X1,X0)),
inference(rectify,[],[f2055]) ).
fof(f2055,axiom,
! [X53,X54] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X54,X53)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osize_I10_J) ).
fof(f31397,plain,
spl698_713,
inference(avatar_split_clause,[],[f25363,f31395]) ).
fof(f31395,plain,
( spl698_713
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit1(X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_713])]) ).
fof(f25363,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit1(X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f25362,f17595]) ).
fof(f25362,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X0)))) ),
inference(forward_demodulation,[],[f18006,f17595]) ).
fof(f18006,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X0)))) ),
inference(cnf_transformation,[],[f14818]) ).
fof(f14818,plain,
! [X0] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X0))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X0)))) ) ),
inference(nnf_transformation,[],[f5648]) ).
fof(f5648,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X0))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(rectify,[],[f2542]) ).
fof(f2542,axiom,
! [X180] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X180))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X180))) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_neg__number__of__Bit1) ).
fof(f31393,plain,
spl698_712,
inference(avatar_split_clause,[],[f25361,f31391]) ).
fof(f31391,plain,
( spl698_712
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit1(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_712])]) ).
fof(f25361,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit1(X0))) ),
inference(forward_demodulation,[],[f25360,f17595]) ).
fof(f25360,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit1(X0)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f18007,f17595]) ).
fof(f18007,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X0))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f14818]) ).
fof(f31389,plain,
spl698_711,
inference(avatar_split_clause,[],[f25359,f31387]) ).
fof(f31387,plain,
( spl698_711
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_711])]) ).
fof(f25359,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f25358,f17595]) ).
fof(f25358,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X0)))) ),
inference(forward_demodulation,[],[f18004,f17595]) ).
fof(f18004,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X0)))) ),
inference(cnf_transformation,[],[f14817]) ).
fof(f14817,plain,
! [X0] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X0))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X0)))) ) ),
inference(nnf_transformation,[],[f5647]) ).
fof(f5647,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X0))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(rectify,[],[f2684]) ).
fof(f2684,axiom,
! [X180] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X180))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X180))) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_neg__number__of__Bit0) ).
fof(f31385,plain,
spl698_710,
inference(avatar_split_clause,[],[f25357,f31383]) ).
fof(f31383,plain,
( spl698_710
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_710])]) ).
fof(f25357,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0))) ),
inference(forward_demodulation,[],[f25356,f17595]) ).
fof(f25356,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f18005,f17595]) ).
fof(f18005,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X0))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f14817]) ).
fof(f31381,plain,
spl698_709,
inference(avatar_split_clause,[],[f25316,f31379]) ).
fof(f25316,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| ~ c_Nat__Transfer_Ois__nat(X0) ),
inference(forward_demodulation,[],[f17965,f17436]) ).
fof(f17965,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ c_Nat__Transfer_Ois__nat(X0) ),
inference(cnf_transformation,[],[f14788]) ).
fof(f14788,plain,
! [X0] :
( ( c_Nat__Transfer_Ois__nat(X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ c_Nat__Transfer_Ois__nat(X0) ) ),
inference(nnf_transformation,[],[f5629]) ).
fof(f5629,plain,
! [X0] :
( c_Nat__Transfer_Ois__nat(X0)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ),
inference(rectify,[],[f2914]) ).
fof(f2914,axiom,
! [X20] :
( c_Nat__Transfer_Ois__nat(X20)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_is__nat__def) ).
fof(f31377,plain,
spl698_708,
inference(avatar_split_clause,[],[f25315,f31375]) ).
fof(f25315,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| c_Nat__Transfer_Ois__nat(X0) ),
inference(forward_demodulation,[],[f17966,f17436]) ).
fof(f17966,plain,
! [X0] :
( c_Nat__Transfer_Ois__nat(X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ),
inference(cnf_transformation,[],[f14788]) ).
fof(f31373,plain,
spl698_707,
inference(avatar_split_clause,[],[f25179,f31371]) ).
fof(f31371,plain,
( spl698_707
<=> ! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_Osucc(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_707])]) ).
fof(f25179,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_Osucc(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f17855,f17442]) ).
fof(f17855,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f10176]) ).
fof(f10176,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f5527]) ).
fof(f5527,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OBit1(c_Int_OPls))) ),
inference(rectify,[],[f2727]) ).
fof(f2727,axiom,
! [X23] :
( class_Int_Onumber__ring(X23)
=> ~ c_Int_Oiszero(X23,hAPP(c_Int_Onumber__class_Onumber__of(X23),c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_not__iszero__Numeral1) ).
fof(f31369,plain,
spl698_706,
inference(avatar_split_clause,[],[f25178,f31367]) ).
fof(f31367,plain,
( spl698_706
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Int_OPls)
| ~ class_Rings_Oring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_706])]) ).
fof(f25178,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Int_OPls)
| ~ class_Rings_Oring__1(X0) ),
inference(forward_demodulation,[],[f17848,f17436]) ).
fof(f17848,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Rings_Oring__1(X0) ),
inference(cnf_transformation,[],[f10169]) ).
fof(f10169,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Rings_Oring__1(X0) ),
inference(ennf_transformation,[],[f5520]) ).
fof(f5520,plain,
! [X0] :
( class_Rings_Oring__1(X0)
=> c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rectify,[],[f2804]) ).
fof(f2804,axiom,
! [X23] :
( class_Rings_Oring__1(X23)
=> c_Groups_Ozero__class_Ozero(X23) = hAPP(c_Int_Oring__1__class_Oof__int(X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_of__int__0) ).
fof(f31365,plain,
( spl698_705
| ~ spl698_222
| ~ spl698_372 ),
inference(avatar_split_clause,[],[f30150,f29830,f29117,f31363]) ).
fof(f31363,plain,
( spl698_705
<=> ! [X3] : c_Int_OPls != c_Int_Opred(c_Int_OBit0(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_705])]) ).
fof(f29117,plain,
( spl698_222
<=> ! [X0] : c_Int_OPls != c_Int_OBit1(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_222])]) ).
fof(f29830,plain,
( spl698_372
<=> ! [X0] : c_Int_Opred(c_Int_OBit0(X0)) = c_Int_OBit1(c_Int_Opred(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_372])]) ).
fof(f30150,plain,
( ! [X3] : c_Int_OPls != c_Int_Opred(c_Int_OBit0(X3))
| ~ spl698_222
| ~ spl698_372 ),
inference(superposition,[],[f29118,f29831]) ).
fof(f29831,plain,
( ! [X0] : c_Int_Opred(c_Int_OBit0(X0)) = c_Int_OBit1(c_Int_Opred(X0))
| ~ spl698_372 ),
inference(avatar_component_clause,[],[f29830]) ).
fof(f29118,plain,
( ! [X0] : c_Int_OPls != c_Int_OBit1(X0)
| ~ spl698_222 ),
inference(avatar_component_clause,[],[f29117]) ).
fof(f31361,plain,
spl698_704,
inference(avatar_split_clause,[],[f25125,f31359]) ).
fof(f31359,plain,
( spl698_704
<=> ! [X0] :
( c_Int_OPls = hAPP(c_Code__Numeral_Oint__of,X0)
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_704])]) ).
fof(f25125,plain,
! [X0] :
( c_Int_OPls = hAPP(c_Code__Numeral_Oint__of,X0)
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X0 ),
inference(forward_demodulation,[],[f17816,f17436]) ).
fof(f17816,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X0)
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X0 ),
inference(cnf_transformation,[],[f10152]) ).
fof(f10152,plain,
! [X0] :
( ( ( ( hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) )
& ( hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) )
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X0)
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X0 ) ),
inference(ennf_transformation,[],[f5501]) ).
fof(f5501,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X0
=> ( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X0
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X0) ) ),
inference(rectify,[],[f2854]) ).
fof(f2854,axiom,
! [X112] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X112
=> ( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X112,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X112),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X112,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X112) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X112),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X112
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X112) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_int__of__code) ).
fof(f31357,plain,
spl698_703,
inference(avatar_split_clause,[],[f25015,f31355]) ).
fof(f31355,plain,
( spl698_703
<=> ! [X0] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_703])]) ).
fof(f25015,plain,
! [X0] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(forward_demodulation,[],[f25014,f24883]) ).
fof(f25014,plain,
! [X0] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))) = X0,
inference(forward_demodulation,[],[f17717,f17447]) ).
fof(f17717,plain,
! [X0] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X0,
inference(cnf_transformation,[],[f5403]) ).
fof(f5403,plain,
! [X0] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X0,
inference(rectify,[],[f2163]) ).
fof(f2163,axiom,
! [X93] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X93),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X93,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_div__1) ).
fof(f31353,plain,
spl698_702,
inference(avatar_split_clause,[],[f25004,f31351]) ).
fof(f31351,plain,
( spl698_702
<=> ! [X0] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,c_Code__Numeral_OSuc__code__numeral(X0)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_702])]) ).
fof(f25004,plain,
! [X0] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,c_Code__Numeral_OSuc__code__numeral(X0)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X0,
inference(forward_demodulation,[],[f17696,f17435]) ).
fof(f17696,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X0)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X0,
inference(cnf_transformation,[],[f5382]) ).
fof(f5382,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X0)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X0,
inference(rectify,[],[f3034]) ).
fof(f3034,axiom,
! [X88] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X88)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X88,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Suc__code__numeral__minus__one) ).
fof(f31349,plain,
spl698_701,
inference(avatar_split_clause,[],[f24991,f31347]) ).
fof(f31347,plain,
( spl698_701
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_701])]) ).
fof(f24991,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f17674,f17447]) ).
fof(f17674,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f5360]) ).
fof(f5360,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f1496]) ).
fof(f1496,axiom,
! [X88] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X88) = X88,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_plus__nat_Oadd__0) ).
fof(f31345,plain,
spl698_700,
inference(avatar_split_clause,[],[f24989,f31343]) ).
fof(f31343,plain,
( spl698_700
<=> ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_700])]) ).
fof(f24989,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f17670,f17447]) ).
fof(f17670,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f5356]) ).
fof(f5356,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f2090]) ).
fof(f2090,axiom,
! [X88] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X88) = X88,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_max__0L) ).
fof(f31341,plain,
spl698_699,
inference(avatar_split_clause,[],[f24988,f31339]) ).
fof(f31339,plain,
( spl698_699
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_699])]) ).
fof(f24988,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17669,f17447]) ).
fof(f17669,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f5355]) ).
fof(f5355,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f1495]) ).
fof(f1495,axiom,
! [X93] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X93),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X93,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Nat_Oadd__0__right) ).
fof(f31337,plain,
spl698_698,
inference(avatar_split_clause,[],[f24986,f31335]) ).
fof(f31335,plain,
( spl698_698
<=> ! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_698])]) ).
fof(f24986,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17665,f17447]) ).
fof(f17665,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f5351]) ).
fof(f5351,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f1500]) ).
fof(f1500,axiom,
! [X93] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X93),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X93,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_minus__nat_Odiff__0) ).
fof(f31333,plain,
spl698_697,
inference(avatar_split_clause,[],[f24985,f31331]) ).
fof(f31331,plain,
( spl698_697
<=> ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_697])]) ).
fof(f24985,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17664,f17447]) ).
fof(f17664,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f5350]) ).
fof(f5350,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f2089]) ).
fof(f2089,axiom,
! [X88] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X88),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X88,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_max__0R) ).
fof(f31329,plain,
spl698_696,
inference(avatar_split_clause,[],[f24982,f31327]) ).
fof(f31327,plain,
( spl698_696
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_696])]) ).
fof(f24982,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0),
inference(forward_demodulation,[],[f17651,f17447]) ).
fof(f17651,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0),
inference(cnf_transformation,[],[f5337]) ).
fof(f5337,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0),
inference(rectify,[],[f1501]) ).
fof(f1501,axiom,
! [X93] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X93),X93),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_diff__self__eq__0) ).
fof(f31325,plain,
spl698_695,
inference(avatar_split_clause,[],[f24981,f31323]) ).
fof(f31323,plain,
( spl698_695
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_695])]) ).
fof(f24981,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),c_List_Olist_ONil(X0)),
inference(forward_demodulation,[],[f17650,f17447]) ).
fof(f17650,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5336]) ).
fof(f5336,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),c_List_Olist_ONil(X0)),
inference(rectify,[],[f3946]) ).
fof(f3946,axiom,
! [X23] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X23)),c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_list_Osize_I3_J) ).
fof(f31321,plain,
( spl698_694
| ~ spl698_223
| ~ spl698_371 ),
inference(avatar_split_clause,[],[f30137,f29826,f29121,f31319]) ).
fof(f29121,plain,
( spl698_223
<=> ! [X0] : c_Int_OMin != c_Int_OBit0(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_223])]) ).
fof(f29826,plain,
( spl698_371
<=> ! [X0] : c_Int_Osucc(c_Int_OBit1(X0)) = c_Int_OBit0(c_Int_Osucc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_371])]) ).
fof(f30137,plain,
( ! [X4] : c_Int_OMin != c_Int_Osucc(c_Int_OBit1(X4))
| ~ spl698_223
| ~ spl698_371 ),
inference(superposition,[],[f29122,f29827]) ).
fof(f29827,plain,
( ! [X0] : c_Int_Osucc(c_Int_OBit1(X0)) = c_Int_OBit0(c_Int_Osucc(X0))
| ~ spl698_371 ),
inference(avatar_component_clause,[],[f29826]) ).
fof(f29122,plain,
( ! [X0] : c_Int_OMin != c_Int_OBit0(X0)
| ~ spl698_223 ),
inference(avatar_component_clause,[],[f29121]) ).
fof(f31317,plain,
spl698_693,
inference(avatar_split_clause,[],[f24980,f31315]) ).
fof(f31315,plain,
( spl698_693
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X0)),c_Option_Ooption_ONone(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_693])]) ).
fof(f24980,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X0)),c_Option_Ooption_ONone(X0)),
inference(forward_demodulation,[],[f17649,f17447]) ).
fof(f17649,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X0)),c_Option_Ooption_ONone(X0)),
inference(cnf_transformation,[],[f5335]) ).
fof(f5335,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X0)),c_Option_Ooption_ONone(X0)),
inference(rectify,[],[f1879]) ).
fof(f1879,axiom,
! [X23] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X23)),c_Option_Ooption_ONone(X23)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_option_Osize_I3_J) ).
fof(f31313,plain,
spl698_692,
inference(avatar_split_clause,[],[f24280,f31311]) ).
fof(f31311,plain,
( spl698_692
<=> ! [X2,X4,X0,X5,X3,X1] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OCond(X5,X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_692])]) ).
fof(f24280,plain,
! [X2,X3,X0,X1,X4,X5] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OCond(X5,X4,X3),
inference(cnf_transformation,[],[f9741]) ).
fof(f9741,plain,
! [X0,X1,X2,X3,X4,X5] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OCond(X5,X4,X3),
inference(rectify,[],[f166]) ).
fof(f166,axiom,
! [X13,X53,X70,X55,X56,X51] : c_Com_Ocom_OLocal(X70,X53,X13) != c_Com_Ocom_OCond(X51,X56,X55),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I37_J) ).
fof(f31309,plain,
spl698_691,
inference(avatar_split_clause,[],[f23125,f31307]) ).
fof(f31307,plain,
( spl698_691
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP(X2,X3))
| ~ sP114(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_691])]) ).
fof(f23125,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X2,X3))
| ~ sP114(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16532]) ).
fof(f16532,plain,
! [X0,X1,X2,X3] :
( ( sP114(X0,X1,X2,X3)
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X4),X0))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X4)) )
| ~ hBOOL(hAPP(X2,X3)) )
& ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),sK529(X0,X1,X2,X3)),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),sK529(X0,X1,X2,X3)))
& hBOOL(hAPP(X2,X3)) )
| ~ sP114(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK529])],[f16530,f16531]) ).
fof(f16531,plain,
! [X0,X1,X2,X3] :
( ? [X5] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X5),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X5)) )
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),sK529(X0,X1,X2,X3)),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),sK529(X0,X1,X2,X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f16530,plain,
! [X0,X1,X2,X3] :
( ( sP114(X0,X1,X2,X3)
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X4),X0))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X4)) )
| ~ hBOOL(hAPP(X2,X3)) )
& ( ( ? [X5] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X5),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X5)) )
& hBOOL(hAPP(X2,X3)) )
| ~ sP114(X0,X1,X2,X3) ) ),
inference(rectify,[],[f16529]) ).
fof(f16529,plain,
! [X0,X2,X3,X1] :
( ( sP114(X0,X2,X3,X1)
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
| ~ hBOOL(hAPP(X3,X1)) )
& ( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) )
| ~ sP114(X0,X2,X3,X1) ) ),
inference(flattening,[],[f16528]) ).
fof(f16528,plain,
! [X0,X2,X3,X1] :
( ( sP114(X0,X2,X3,X1)
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
| ~ hBOOL(hAPP(X3,X1)) )
& ( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) )
| ~ sP114(X0,X2,X3,X1) ) ),
inference(nnf_transformation,[],[f14713]) ).
fof(f14713,plain,
! [X0,X2,X3,X1] :
( sP114(X0,X2,X3,X1)
<=> ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP114])]) ).
fof(f31305,plain,
spl698_690,
inference(avatar_split_clause,[],[f23010,f31303]) ).
fof(f31303,plain,
( spl698_690
<=> ! [X0,X3,X2,X1] :
( sP110(X0,X3,X1,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_690])]) ).
fof(f23010,plain,
! [X2,X3,X0,X1] :
( sP110(X0,X3,X1,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14706]) ).
fof(f14706,plain,
! [X0,X1,X2,X3] :
( sP110(X0,X3,X1,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f13403,f14705,f14704,f14703]) ).
fof(f14703,plain,
! [X0,X3,X1,X2] :
( sP108(X0,X3,X1,X2)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP108])]) ).
fof(f14704,plain,
! [X2,X1,X3,X0] :
( sP109(X2,X1,X3,X0)
<=> ( ( sP108(X0,X3,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP109])]) ).
fof(f14705,plain,
! [X0,X3,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X0))
<=> sP109(X2,X1,X3,X0) )
| ~ sP110(X0,X3,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP110])]) ).
fof(f13403,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X0))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(flattening,[],[f13402]) ).
fof(f13402,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X0))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f9029]) ).
fof(f9029,plain,
! [X0,X1,X2,X3] :
( ( class_Int_Onumber(X3)
& class_Fields_Olinordered__field__inverse__zero(X3) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X0))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)))) ) ) ) ),
inference(rectify,[],[f2964]) ).
fof(f2964,axiom,
! [X6,X180,X26,X4] :
( ( class_Int_Onumber(X4)
& class_Fields_Olinordered__field__inverse__zero(X4) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180))),X6))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X6)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180))),X26)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)))) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_divide__le__eq__number__of1) ).
fof(f31301,plain,
spl698_689,
inference(avatar_split_clause,[],[f22995,f31299]) ).
fof(f31299,plain,
( spl698_689
<=> ! [X0,X3,X2,X1] :
( sP107(X0,X3,X1,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_689])]) ).
fof(f22995,plain,
! [X2,X3,X0,X1] :
( sP107(X0,X3,X1,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14702]) ).
fof(f14702,plain,
! [X0,X1,X2,X3] :
( sP107(X0,X3,X1,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f13401,f14701,f14700,f14699]) ).
fof(f14699,plain,
! [X0,X3,X1,X2] :
( sP105(X0,X3,X1,X2)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP105])]) ).
fof(f14700,plain,
! [X2,X1,X3,X0] :
( sP106(X2,X1,X3,X0)
<=> ( ( sP105(X0,X3,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP106])]) ).
fof(f14701,plain,
! [X0,X3,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X0))
<=> sP106(X2,X1,X3,X0) )
| ~ sP107(X0,X3,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP107])]) ).
fof(f13401,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X0))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(flattening,[],[f13400]) ).
fof(f13400,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X0))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f9028]) ).
fof(f9028,plain,
! [X0,X1,X2,X3] :
( ( class_Int_Onumber(X3)
& class_Fields_Olinordered__field__inverse__zero(X3) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X0))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1))),X2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)))) ) ) ) ),
inference(rectify,[],[f2959]) ).
fof(f2959,axiom,
! [X6,X180,X26,X4] :
( ( class_Int_Onumber(X4)
& class_Fields_Olinordered__field__inverse__zero(X4) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180))),X6))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X6)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180))),X26)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)))) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_divide__less__eq__number__of1) ).
fof(f31297,plain,
spl698_688,
inference(avatar_split_clause,[],[f22980,f31295]) ).
fof(f31295,plain,
( spl698_688
<=> ! [X0,X3,X2,X1] :
( sP104(X0,X3,X1,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_688])]) ).
fof(f22980,plain,
! [X2,X3,X0,X1] :
( sP104(X0,X3,X1,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14698]) ).
fof(f14698,plain,
! [X0,X1,X2,X3] :
( sP104(X0,X3,X1,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f13399,f14697,f14696,f14695]) ).
fof(f14695,plain,
! [X0,X3,X1,X2] :
( sP102(X0,X3,X1,X2)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP102])]) ).
fof(f14696,plain,
! [X2,X1,X3,X0] :
( sP103(X2,X1,X3,X0)
<=> ( ( sP102(X0,X3,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP103])]) ).
fof(f14697,plain,
! [X0,X3,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
<=> sP103(X2,X1,X3,X0) )
| ~ sP104(X0,X3,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP104])]) ).
fof(f13399,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(flattening,[],[f13398]) ).
fof(f13398,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f9027]) ).
fof(f9027,plain,
! [X0,X1,X2,X3] :
( ( class_Int_Onumber(X3)
& class_Fields_Olinordered__field__inverse__zero(X3) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1)),X2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1))) ) ) ) ),
inference(rectify,[],[f2965]) ).
fof(f2965,axiom,
! [X180,X36,X26,X4] :
( ( class_Int_Onumber(X4)
& class_Fields_Olinordered__field__inverse__zero(X4) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X36)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),X36)),X26)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),X36))) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_divide__le__eq__number__of) ).
fof(f31293,plain,
spl698_687,
inference(avatar_split_clause,[],[f22965,f31291]) ).
fof(f31291,plain,
( spl698_687
<=> ! [X0,X3,X2,X1] :
( sP101(X0,X3,X1,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_687])]) ).
fof(f22965,plain,
! [X2,X3,X0,X1] :
( sP101(X0,X3,X1,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14694]) ).
fof(f14694,plain,
! [X0,X1,X2,X3] :
( sP101(X0,X3,X1,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f13397,f14693,f14692,f14691]) ).
fof(f14691,plain,
! [X0,X3,X1,X2] :
( sP99(X0,X3,X1,X2)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP99])]) ).
fof(f14692,plain,
! [X2,X1,X3,X0] :
( sP100(X2,X1,X3,X0)
<=> ( ( sP99(X0,X3,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP100])]) ).
fof(f14693,plain,
! [X0,X3,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
<=> sP100(X2,X1,X3,X0) )
| ~ sP101(X0,X3,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP101])]) ).
fof(f13397,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(flattening,[],[f13396]) ).
fof(f13396,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f9026]) ).
fof(f9026,plain,
! [X0,X1,X2,X3] :
( ( class_Int_Onumber(X3)
& class_Fields_Olinordered__field__inverse__zero(X3) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1)),X2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1))) ) ) ) ),
inference(rectify,[],[f2958]) ).
fof(f2958,axiom,
! [X180,X36,X26,X4] :
( ( class_Int_Onumber(X4)
& class_Fields_Olinordered__field__inverse__zero(X4) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X36)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),X36)),X26)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),X36))) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_divide__less__eq__number__of) ).
fof(f31289,plain,
spl698_686,
inference(avatar_split_clause,[],[f22950,f31287]) ).
fof(f31287,plain,
( spl698_686
<=> ! [X0,X3,X2,X1] :
( sP98(X3,X2,X0,X1)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_686])]) ).
fof(f22950,plain,
! [X2,X3,X0,X1] :
( sP98(X3,X2,X0,X1)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14690]) ).
fof(f14690,plain,
! [X0,X1,X2,X3] :
( sP98(X3,X2,X0,X1)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f13395,f14689,f14688,f14687]) ).
fof(f14687,plain,
! [X3,X2,X0,X1] :
( sP96(X3,X2,X0,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP96])]) ).
fof(f14688,plain,
! [X1,X0,X2,X3] :
( sP97(X1,X0,X2,X3)
<=> ( ( sP96(X3,X2,X0,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP97])]) ).
fof(f14689,plain,
! [X3,X2,X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0)))
<=> sP97(X1,X0,X2,X3) )
| ~ sP98(X3,X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP98])]) ).
fof(f13395,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0)))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(flattening,[],[f13394]) ).
fof(f13394,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0)))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f9025]) ).
fof(f9025,plain,
! [X0,X1,X2,X3] :
( ( class_Int_Onumber(X3)
& class_Fields_Olinordered__field__inverse__zero(X3) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0)),X1)) ) ) ) ),
inference(rectify,[],[f2966]) ).
fof(f2966,axiom,
! [X36,X26,X180,X4] :
( ( class_Int_Onumber(X4)
& class_Fields_Olinordered__field__inverse__zero(X4) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X36)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),c_Groups_Ozero__class_Ozero(X4))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),X36))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),X36)),X26)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_le__divide__eq__number__of) ).
fof(f31285,plain,
spl698_685,
inference(avatar_split_clause,[],[f22935,f31283]) ).
fof(f31283,plain,
( spl698_685
<=> ! [X0,X3,X2,X1] :
( sP95(X3,X2,X0,X1)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_685])]) ).
fof(f22935,plain,
! [X2,X3,X0,X1] :
( sP95(X3,X2,X0,X1)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14686]) ).
fof(f14686,plain,
! [X0,X1,X2,X3] :
( sP95(X3,X2,X0,X1)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f13393,f14685,f14684,f14683]) ).
fof(f14683,plain,
! [X3,X2,X0,X1] :
( sP93(X3,X2,X0,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP93])]) ).
fof(f14684,plain,
! [X1,X0,X2,X3] :
( sP94(X1,X0,X2,X3)
<=> ( ( sP93(X3,X2,X0,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP94])]) ).
fof(f14685,plain,
! [X3,X2,X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0)))
<=> sP94(X1,X0,X2,X3) )
| ~ sP95(X3,X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP95])]) ).
fof(f13393,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0)))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(flattening,[],[f13392]) ).
fof(f13392,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0)))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f9024]) ).
fof(f9024,plain,
! [X0,X1,X2,X3] :
( ( class_Int_Onumber(X3)
& class_Fields_Olinordered__field__inverse__zero(X3) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0)),X1)) ) ) ) ),
inference(rectify,[],[f2957]) ).
fof(f2957,axiom,
! [X36,X26,X180,X4] :
( ( class_Int_Onumber(X4)
& class_Fields_Olinordered__field__inverse__zero(X4) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X36)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),c_Groups_Ozero__class_Ozero(X4))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),X36))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),X36)),X26)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_less__divide__eq__number__of) ).
fof(f31281,plain,
spl698_684,
inference(avatar_split_clause,[],[f22920,f31279]) ).
fof(f31279,plain,
( spl698_684
<=> ! [X0,X3,X2,X1] :
( sP92(X3,X2,X0,X1)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_684])]) ).
fof(f22920,plain,
! [X2,X3,X0,X1] :
( sP92(X3,X2,X0,X1)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14682]) ).
fof(f14682,plain,
! [X0,X1,X2,X3] :
( sP92(X3,X2,X0,X1)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f13391,f14681,f14680,f14679]) ).
fof(f14679,plain,
! [X3,X2,X0,X1] :
( sP90(X3,X2,X0,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP90])]) ).
fof(f14680,plain,
! [X1,X0,X2,X3] :
( sP91(X1,X0,X2,X3)
<=> ( ( sP90(X3,X2,X0,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP91])]) ).
fof(f14681,plain,
! [X3,X2,X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))))
<=> sP91(X1,X0,X2,X3) )
| ~ sP92(X3,X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP92])]) ).
fof(f13391,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(flattening,[],[f13390]) ).
fof(f13390,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f9023]) ).
fof(f9023,plain,
! [X0,X1,X2,X3] :
( ( class_Int_Onumber(X3)
& class_Fields_Olinordered__field__inverse__zero(X3) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))),X1)) ) ) ) ),
inference(rectify,[],[f2967]) ).
fof(f2967,axiom,
! [X180,X26,X6,X4] :
( ( class_Int_Onumber(X4)
& class_Fields_Olinordered__field__inverse__zero(X4) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180))))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),c_Groups_Ozero__class_Ozero(X4))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180))),X26)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_le__divide__eq__number__of1) ).
fof(f31277,plain,
( spl698_683
| ~ spl698_243
| ~ spl698_316 ),
inference(avatar_split_clause,[],[f29681,f29527,f29218,f31274]) ).
fof(f31274,plain,
( spl698_683
<=> sP4(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_683])]) ).
fof(f29218,plain,
( spl698_243
<=> c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_243])]) ).
fof(f29527,plain,
( spl698_316
<=> ! [X0,X1] :
( sP4(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_316])]) ).
fof(f29681,plain,
( sP4(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl698_243
| ~ spl698_316 ),
inference(resolution,[],[f29528,f29220]) ).
fof(f29220,plain,
( c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl698_243 ),
inference(avatar_component_clause,[],[f29218]) ).
fof(f29528,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,X0)
| sP4(X1,X0) )
| ~ spl698_316 ),
inference(avatar_component_clause,[],[f29527]) ).
fof(f31272,plain,
spl698_682,
inference(avatar_split_clause,[],[f22905,f31270]) ).
fof(f31270,plain,
( spl698_682
<=> ! [X0,X3,X2,X1] :
( sP89(X3,X2,X0,X1)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_682])]) ).
fof(f22905,plain,
! [X2,X3,X0,X1] :
( sP89(X3,X2,X0,X1)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14678]) ).
fof(f14678,plain,
! [X0,X1,X2,X3] :
( sP89(X3,X2,X0,X1)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f13389,f14677,f14676,f14675]) ).
fof(f14675,plain,
! [X3,X2,X0,X1] :
( sP87(X3,X2,X0,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP87])]) ).
fof(f14676,plain,
! [X1,X0,X2,X3] :
( sP88(X1,X0,X2,X3)
<=> ( ( sP87(X3,X2,X0,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP88])]) ).
fof(f14677,plain,
! [X3,X2,X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))))
<=> sP88(X1,X0,X2,X3) )
| ~ sP89(X3,X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP89])]) ).
fof(f13389,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(flattening,[],[f13388]) ).
fof(f13388,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f9022]) ).
fof(f9022,plain,
! [X0,X1,X2,X3] :
( ( class_Int_Onumber(X3)
& class_Fields_Olinordered__field__inverse__zero(X3) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0))),X1)) ) ) ) ),
inference(rectify,[],[f2956]) ).
fof(f2956,axiom,
! [X180,X26,X6,X4] :
( ( class_Int_Onumber(X4)
& class_Fields_Olinordered__field__inverse__zero(X4) )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180))))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),c_Groups_Ozero__class_Ozero(X4))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180))),X26)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_less__divide__eq__number__of1) ).
fof(f31268,plain,
spl698_681,
inference(avatar_split_clause,[],[f22890,f31266]) ).
fof(f31266,plain,
( spl698_681
<=> ! [X0,X3,X2,X1] :
( sP86(X2,X1,X3,X0)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_681])]) ).
fof(f22890,plain,
! [X2,X3,X0,X1] :
( sP86(X2,X1,X3,X0)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14674]) ).
fof(f14674,plain,
! [X0,X1,X2,X3] :
( sP86(X2,X1,X3,X0)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(definition_folding,[],[f13387,f14673,f14672]) ).
fof(f14672,plain,
! [X0,X3,X1,X2] :
( sP85(X0,X3,X1,X2)
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X0
| c_Groups_Ozero__class_Ozero(X3) != hAPP(c_Int_Onumber__class_Onumber__of(X3),X1) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)) = X2
| c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X1) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP85])]) ).
fof(f14673,plain,
! [X2,X1,X3,X0] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)) = X0
<=> sP85(X0,X3,X1,X2) )
| ~ sP86(X2,X1,X3,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP86])]) ).
fof(f13387,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)) = X0
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X0
| c_Groups_Ozero__class_Ozero(X3) != hAPP(c_Int_Onumber__class_Onumber__of(X3),X1) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)) = X2
| c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X1) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(flattening,[],[f13386]) ).
fof(f13386,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)) = X0
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X0
| c_Groups_Ozero__class_Ozero(X3) != hAPP(c_Int_Onumber__class_Onumber__of(X3),X1) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)) = X2
| c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X1) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(ennf_transformation,[],[f9021]) ).
fof(f9021,plain,
! [X0,X1,X2,X3] :
( ( class_Int_Onumber(X3)
& class_Fields_Ofield__inverse__zero(X3) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)) = X0
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)
=> c_Groups_Ozero__class_Ozero(X3) = X0 )
& ( c_Groups_Ozero__class_Ozero(X3) != hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),hAPP(c_Int_Onumber__class_Onumber__of(X3),X1)) = X2 ) ) ) ),
inference(rectify,[],[f2945]) ).
fof(f2945,axiom,
! [X6,X180,X26,X4] :
( ( class_Int_Onumber(X4)
& class_Fields_Ofield__inverse__zero(X4) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)) = X6
<=> ( ( c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)
=> c_Groups_Ozero__class_Ozero(X4) = X6 )
& ( c_Groups_Ozero__class_Ozero(X4) != hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)) = X26 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_divide__eq__eq__number__of1) ).
fof(f31264,plain,
spl698_680,
inference(avatar_split_clause,[],[f22881,f31262]) ).
fof(f31262,plain,
( spl698_680
<=> ! [X0,X3,X2,X1] :
( sP84(X1,X0,X3,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_680])]) ).
fof(f22881,plain,
! [X2,X3,X0,X1] :
( sP84(X1,X0,X3,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14671]) ).
fof(f14671,plain,
! [X0,X1,X2,X3] :
( sP84(X1,X0,X3,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(definition_folding,[],[f13385,f14670,f14669]) ).
fof(f14669,plain,
! [X2,X3,X0,X1] :
( sP83(X2,X3,X0,X1)
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ozero__class_Ozero(X3) != hAPP(c_Int_Onumber__class_Onumber__of(X3),X0) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)) = X1
| c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X0) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP83])]) ).
fof(f14670,plain,
! [X1,X0,X3,X2] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)) = X2
<=> sP83(X2,X3,X0,X1) )
| ~ sP84(X1,X0,X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP84])]) ).
fof(f13385,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)) = X2
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ozero__class_Ozero(X3) != hAPP(c_Int_Onumber__class_Onumber__of(X3),X0) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)) = X1
| c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X0) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(flattening,[],[f13384]) ).
fof(f13384,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)) = X2
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ozero__class_Ozero(X3) != hAPP(c_Int_Onumber__class_Onumber__of(X3),X0) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)) = X1
| c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X0) ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(ennf_transformation,[],[f9020]) ).
fof(f9020,plain,
! [X0,X1,X2,X3] :
( ( class_Int_Onumber(X3)
& class_Fields_Ofield__inverse__zero(X3) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)) = X2
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)
=> c_Groups_Ozero__class_Ozero(X3) = X2 )
& ( c_Groups_Ozero__class_Ozero(X3) != hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)) = X1 ) ) ) ),
inference(rectify,[],[f2948]) ).
fof(f2948,axiom,
! [X180,X26,X6,X4] :
( ( class_Int_Onumber(X4)
& class_Fields_Ofield__inverse__zero(X4) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)) = X6
<=> ( ( c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)
=> c_Groups_Ozero__class_Ozero(X4) = X6 )
& ( c_Groups_Ozero__class_Ozero(X4) != hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)) = X26 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__divide__eq__number__of1) ).
fof(f31260,plain,
spl698_679,
inference(avatar_split_clause,[],[f22872,f31258]) ).
fof(f31258,plain,
( spl698_679
<=> ! [X0,X3,X2,X1] :
( sP82(X2,X1,X3,X0)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_679])]) ).
fof(f22872,plain,
! [X2,X3,X0,X1] :
( sP82(X2,X1,X3,X0)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14668]) ).
fof(f14668,plain,
! [X0,X1,X2,X3] :
( sP82(X2,X1,X3,X0)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(definition_folding,[],[f13383,f14667,f14666]) ).
fof(f14666,plain,
! [X0,X3,X1,X2] :
( sP81(X0,X3,X1,X2)
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)
| c_Groups_Ozero__class_Ozero(X3) != X1 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1) = X2
| c_Groups_Ozero__class_Ozero(X3) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP81])]) ).
fof(f14667,plain,
! [X2,X1,X3,X0] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)
<=> sP81(X0,X3,X1,X2) )
| ~ sP82(X2,X1,X3,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP82])]) ).
fof(f13383,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)
| c_Groups_Ozero__class_Ozero(X3) != X1 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1) = X2
| c_Groups_Ozero__class_Ozero(X3) = X1 ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(flattening,[],[f13382]) ).
fof(f13382,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)
| c_Groups_Ozero__class_Ozero(X3) != X1 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1) = X2
| c_Groups_Ozero__class_Ozero(X3) = X1 ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(ennf_transformation,[],[f9019]) ).
fof(f9019,plain,
! [X0,X1,X2,X3] :
( ( class_Int_Onumber(X3)
& class_Fields_Ofield__inverse__zero(X3) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X1
=> c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X0) )
& ( c_Groups_Ozero__class_Ozero(X3) != X1
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X0)),X1) = X2 ) ) ) ),
inference(rectify,[],[f2946]) ).
fof(f2946,axiom,
! [X180,X36,X26,X4] :
( ( class_Int_Onumber(X4)
& class_Fields_Ofield__inverse__zero(X4) )
=> ( hAPP(c_Int_Onumber__class_Onumber__of(X4),X180) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X36)
<=> ( ( c_Groups_Ozero__class_Ozero(X4) = X36
=> c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Int_Onumber__class_Onumber__of(X4),X180) )
& ( c_Groups_Ozero__class_Ozero(X4) != X36
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),X36) = X26 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_divide__eq__eq__number__of) ).
fof(f31256,plain,
spl698_678,
inference(avatar_split_clause,[],[f22863,f31254]) ).
fof(f31254,plain,
( spl698_678
<=> ! [X0,X3,X2,X1] :
( sP80(X1,X0,X3,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_678])]) ).
fof(f22863,plain,
! [X2,X3,X0,X1] :
( sP80(X1,X0,X3,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14665]) ).
fof(f14665,plain,
! [X0,X1,X2,X3] :
( sP80(X1,X0,X3,X2)
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(definition_folding,[],[f13381,f14664,f14663]) ).
fof(f14663,plain,
! [X2,X3,X0,X1] :
( sP79(X2,X3,X0,X1)
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)
| c_Groups_Ozero__class_Ozero(X3) != X0 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0) = X1
| c_Groups_Ozero__class_Ozero(X3) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP79])]) ).
fof(f14664,plain,
! [X1,X0,X3,X2] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)
<=> sP79(X2,X3,X0,X1) )
| ~ sP80(X1,X0,X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP80])]) ).
fof(f13381,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)
| c_Groups_Ozero__class_Ozero(X3) != X0 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0) = X1
| c_Groups_Ozero__class_Ozero(X3) = X0 ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(flattening,[],[f13380]) ).
fof(f13380,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)
| c_Groups_Ozero__class_Ozero(X3) != X0 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0) = X1
| c_Groups_Ozero__class_Ozero(X3) = X0 ) ) )
| ~ class_Int_Onumber(X3)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(ennf_transformation,[],[f9018]) ).
fof(f9018,plain,
! [X0,X1,X2,X3] :
( ( class_Int_Onumber(X3)
& class_Fields_Ofield__inverse__zero(X3) )
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X0
=> c_Groups_Ozero__class_Ozero(X3) = hAPP(c_Int_Onumber__class_Onumber__of(X3),X2) )
& ( c_Groups_Ozero__class_Ozero(X3) != X0
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),hAPP(c_Int_Onumber__class_Onumber__of(X3),X2)),X0) = X1 ) ) ) ),
inference(rectify,[],[f2947]) ).
fof(f2947,axiom,
! [X36,X26,X180,X4] :
( ( class_Int_Onumber(X4)
& class_Fields_Ofield__inverse__zero(X4) )
=> ( hAPP(c_Int_Onumber__class_Onumber__of(X4),X180) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X36)
<=> ( ( c_Groups_Ozero__class_Ozero(X4) = X36
=> c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Int_Onumber__class_Onumber__of(X4),X180) )
& ( c_Groups_Ozero__class_Ozero(X4) != X36
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X180)),X36) = X26 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__divide__eq__number__of) ).
fof(f31252,plain,
spl698_677,
inference(avatar_split_clause,[],[f22718,f31250]) ).
fof(f31250,plain,
( spl698_677
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP(X2,X3))
| ~ sP78(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_677])]) ).
fof(f22718,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X2,X3))
| ~ sP78(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16322]) ).
fof(f16322,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),sK483(X0,X1,X2,X3)),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),sK483(X0,X1,X2,X3)))
& hBOOL(hAPP(X2,X3)) )
| ~ sP78(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK483])],[f16320,f16321]) ).
fof(f16321,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X4)) )
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),sK483(X0,X1,X2,X3)),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),sK483(X0,X1,X2,X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f16320,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X4)) )
& hBOOL(hAPP(X2,X3)) )
| ~ sP78(X0,X1,X2,X3) ),
inference(rectify,[],[f16319]) ).
fof(f16319,plain,
! [X0,X2,X3,X1] :
( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) )
| ~ sP78(X0,X2,X3,X1) ),
inference(nnf_transformation,[],[f14661]) ).
fof(f14661,plain,
! [X0,X2,X3,X1] :
( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) )
| ~ sP78(X0,X2,X3,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP78])]) ).
fof(f31248,plain,
spl698_676,
inference(avatar_split_clause,[],[f21812,f31246]) ).
fof(f31246,plain,
( spl698_676
<=> ! [X0,X3,X2,X1] : c_Map_Omap__upds(X3,X2,X1,c_List_Olist_ONil(X3),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_676])]) ).
fof(f21812,plain,
! [X2,X3,X0,X1] : c_Map_Omap__upds(X3,X2,X1,c_List_Olist_ONil(X3),X0) = X1,
inference(cnf_transformation,[],[f8228]) ).
fof(f8228,plain,
! [X0,X1,X2,X3] : c_Map_Omap__upds(X3,X2,X1,c_List_Olist_ONil(X3),X0) = X1,
inference(rectify,[],[f3959]) ).
fof(f3959,axiom,
! [X274,X123,X24,X4] : c_Map_Omap__upds(X4,X24,X123,c_List_Olist_ONil(X4),X274) = X123,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_map__upds__Nil1) ).
fof(f31244,plain,
spl698_675,
inference(avatar_split_clause,[],[f21811,f31242]) ).
fof(f31242,plain,
( spl698_675
<=> ! [X2,X0,X1,X3] : c_Map_Omap__upds(X3,X2,X1,X0,c_List_Olist_ONil(X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_675])]) ).
fof(f21811,plain,
! [X2,X3,X0,X1] : c_Map_Omap__upds(X3,X2,X1,X0,c_List_Olist_ONil(X2)) = X1,
inference(cnf_transformation,[],[f8227]) ).
fof(f8227,plain,
! [X0,X1,X2,X3] : c_Map_Omap__upds(X3,X2,X1,X0,c_List_Olist_ONil(X2)) = X1,
inference(rectify,[],[f3958]) ).
fof(f3958,axiom,
! [X275,X123,X24,X4] : c_Map_Omap__upds(X4,X24,X123,X275,c_List_Olist_ONil(X24)) = X123,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_map__upds__Nil2) ).
fof(f31240,plain,
spl698_674,
inference(avatar_split_clause,[],[f21810,f31238]) ).
fof(f31238,plain,
( spl698_674
<=> ! [X0,X3,X2,X1] : c_List_Ofoldr(X3,X2,X1,c_List_Olist_ONil(X3),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_674])]) ).
fof(f21810,plain,
! [X2,X3,X0,X1] : c_List_Ofoldr(X3,X2,X1,c_List_Olist_ONil(X3),X0) = X0,
inference(cnf_transformation,[],[f8226]) ).
fof(f8226,plain,
! [X0,X1,X2,X3] : c_List_Ofoldr(X3,X2,X1,c_List_Olist_ONil(X3),X0) = X0,
inference(rectify,[],[f3942]) ).
fof(f3942,axiom,
! [X6,X1,X4,X24] : c_List_Ofoldr(X24,X4,X1,c_List_Olist_ONil(X24),X6) = X6,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_foldr_Osimps_I1_J) ).
fof(f31236,plain,
spl698_673,
inference(avatar_split_clause,[],[f21809,f31234]) ).
fof(f31234,plain,
( spl698_673
<=> ! [X2,X0,X1,X3] : c_Option_Ooption_Ooption__rec(X3,X2,X1,X0,c_Option_Ooption_ONone(X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_673])]) ).
fof(f21809,plain,
! [X2,X3,X0,X1] : c_Option_Ooption_Ooption__rec(X3,X2,X1,X0,c_Option_Ooption_ONone(X2)) = X1,
inference(cnf_transformation,[],[f8225]) ).
fof(f8225,plain,
! [X0,X1,X2,X3] : c_Option_Ooption_Ooption__rec(X3,X2,X1,X0,c_Option_Ooption_ONone(X2)) = X1,
inference(rectify,[],[f4906]) ).
fof(f4906,axiom,
! [X67,X25,X24,X4] : c_Option_Ooption_Ooption__rec(X4,X24,X25,X67,c_Option_Ooption_ONone(X24)) = X25,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_option_Orecs_I1_J) ).
fof(f31232,plain,
( spl698_672
| ~ spl698_261
| ~ spl698_316 ),
inference(avatar_split_clause,[],[f29676,f29527,f29291,f31230]) ).
fof(f31230,plain,
( spl698_672
<=> ! [X0,X1] : sP4(X0,c_List_Omeasures(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_672])]) ).
fof(f29291,plain,
( spl698_261
<=> ! [X0,X1] : c_Wellfounded_Owf(X1,c_List_Omeasures(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_261])]) ).
fof(f29676,plain,
( ! [X0,X1] : sP4(X0,c_List_Omeasures(X0,X1))
| ~ spl698_261
| ~ spl698_316 ),
inference(resolution,[],[f29528,f29292]) ).
fof(f29292,plain,
( ! [X0,X1] : c_Wellfounded_Owf(X1,c_List_Omeasures(X1,X0))
| ~ spl698_261 ),
inference(avatar_component_clause,[],[f29291]) ).
fof(f31228,plain,
spl698_671,
inference(avatar_split_clause,[],[f21808,f31226]) ).
fof(f31226,plain,
( spl698_671
<=> ! [X2,X0,X1,X3] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_671])]) ).
fof(f21808,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1,
inference(cnf_transformation,[],[f8224]) ).
fof(f8224,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1,
inference(rectify,[],[f5222]) ).
fof(f5222,axiom,
! [X326,X325,X4,X23] : hAPP(hAPP(c_COMBK(X23,X4),X325),X326) = X325,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__COMBK__1) ).
fof(f31224,plain,
spl698_670,
inference(avatar_split_clause,[],[f21385,f31222]) ).
fof(f31222,plain,
( spl698_670
<=> ! [X2,X0,X1] :
( X1 = X2
| ~ c_List_Olist__all2(X0,X0,c_fequal,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_670])]) ).
fof(f21385,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ c_List_Olist__all2(X0,X0,c_fequal,X2,X1) ),
inference(cnf_transformation,[],[f15806]) ).
fof(f15806,plain,
! [X0,X1,X2] :
( ( X1 = X2
| ~ c_List_Olist__all2(X0,X0,c_fequal,X2,X1) )
& ( c_List_Olist__all2(X0,X0,c_fequal,X2,X1)
| X1 != X2 ) ),
inference(nnf_transformation,[],[f8096]) ).
fof(f8096,plain,
! [X0,X1,X2] :
( X1 = X2
<=> c_List_Olist__all2(X0,X0,c_fequal,X2,X1) ),
inference(rectify,[],[f4513]) ).
fof(f4513,axiom,
! [X4,X259,X258] :
( X258 = X259
<=> c_List_Olist__all2(X4,X4,c_fequal,X258,X259) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_list__all2__eq) ).
fof(f31220,plain,
spl698_669,
inference(avatar_split_clause,[],[f21384,f31218]) ).
fof(f31218,plain,
( spl698_669
<=> ! [X2,X0,X1] :
( c_List_Olist__all2(X0,X0,c_fequal,X2,X1)
| X1 != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_669])]) ).
fof(f21384,plain,
! [X2,X0,X1] :
( c_List_Olist__all2(X0,X0,c_fequal,X2,X1)
| X1 != X2 ),
inference(cnf_transformation,[],[f15806]) ).
fof(f31216,plain,
spl698_668,
inference(avatar_split_clause,[],[f21007,f31214]) ).
fof(f31214,plain,
( spl698_668
<=> ! [X2,X0,X1] :
( sP31(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_668])]) ).
fof(f21007,plain,
! [X2,X0,X1] :
( sP31(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(cnf_transformation,[],[f14587]) ).
fof(f14587,plain,
! [X0,X1,X2] :
( sP31(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(definition_folding,[],[f12078,f14586,f14585]) ).
fof(f14585,plain,
! [X0,X1,X2] :
( sP30(X0,X1,X2)
<=> ? [X3] :
( ! [X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP30])]) ).
fof(f14586,plain,
! [X2,X1,X0] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> sP30(X0,X1,X2) )
| ~ sP31(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP31])]) ).
fof(f12078,plain,
! [X0,X1,X2] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> ? [X3] :
( ! [X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(flattening,[],[f12077]) ).
fof(f12077,plain,
! [X0,X1,X2] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> ? [X3] :
( ! [X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(ennf_transformation,[],[f7845]) ).
fof(f7845,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
=> ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> ? [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
=> ( X3 != X4
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4) ) )
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) ) ),
inference(rectify,[],[f1653]) ).
fof(f1653,axiom,
! [X1,X19,X4] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X19))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X19) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ? [X2] :
( ! [X118] :
( hBOOL(hAPP(hAPP(c_member(X4),X118),X19))
=> ( X2 != X118
=> hAPP(X1,X118) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& hAPP(X1,X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(X4),X2),X19)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_setsum__eq__Suc0__iff) ).
fof(f31212,plain,
spl698_667,
inference(avatar_split_clause,[],[f20998,f31210]) ).
fof(f31210,plain,
( spl698_667
<=> ! [X2,X0,X1] :
( sP29(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_667])]) ).
fof(f20998,plain,
! [X2,X0,X1] :
( sP29(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(cnf_transformation,[],[f14584]) ).
fof(f14584,plain,
! [X0,X1,X2] :
( sP29(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(definition_folding,[],[f12076,f14583,f14582]) ).
fof(f14582,plain,
! [X0,X1,X2] :
( sP28(X0,X1,X2)
<=> ? [X3] :
( ! [X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP28])]) ).
fof(f14583,plain,
! [X2,X1,X0] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> sP28(X0,X1,X2) )
| ~ sP29(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP29])]) ).
fof(f12076,plain,
! [X0,X1,X2] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> ? [X3] :
( ! [X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(flattening,[],[f12075]) ).
fof(f12075,plain,
! [X0,X1,X2] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> ? [X3] :
( ! [X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(ennf_transformation,[],[f7844]) ).
fof(f7844,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> ? [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
=> ( X3 != X4
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4) ) )
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) ) ),
inference(rectify,[],[f1655]) ).
fof(f1655,axiom,
! [X1,X19,X4] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X19))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X19) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ? [X2] :
( ! [X118] :
( hBOOL(hAPP(hAPP(c_member(X4),X118),X19))
=> ( X2 != X118
=> hAPP(X1,X118) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& hAPP(X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(X4),X2),X19)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_setsum__eq__1__iff) ).
fof(f31208,plain,
spl698_666,
inference(avatar_split_clause,[],[f20886,f31206]) ).
fof(f31206,plain,
( spl698_666
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(X2,c_Wellfounded_Omlex__prod(X2,X0,X1))
| ~ c_Wellfounded_Owf(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_666])]) ).
fof(f20886,plain,
! [X2,X0,X1] :
( c_Wellfounded_Owf(X2,c_Wellfounded_Omlex__prod(X2,X0,X1))
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(cnf_transformation,[],[f11953]) ).
fof(f11953,plain,
! [X0,X1,X2] :
( c_Wellfounded_Owf(X2,c_Wellfounded_Omlex__prod(X2,X0,X1))
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(ennf_transformation,[],[f7755]) ).
fof(f7755,plain,
! [X0,X1,X2] :
( c_Wellfounded_Owf(X2,X1)
=> c_Wellfounded_Owf(X2,c_Wellfounded_Omlex__prod(X2,X0,X1)) ),
inference(rectify,[],[f3356]) ).
fof(f3356,axiom,
! [X1,X42,X4] :
( c_Wellfounded_Owf(X4,X42)
=> c_Wellfounded_Owf(X4,c_Wellfounded_Omlex__prod(X4,X1,X42)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__mlex) ).
fof(f31204,plain,
spl698_665,
inference(avatar_split_clause,[],[f20880,f31202]) ).
fof(f31202,plain,
( spl698_665
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_665])]) ).
fof(f20880,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(cnf_transformation,[],[f11945]) ).
fof(f11945,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(ennf_transformation,[],[f7749]) ).
fof(f7749,plain,
! [X0,X1,X2] :
( c_Equiv__Relations_Oequivp(X2,X1)
=> hBOOL(hAPP(hAPP(X1,X0),X0)) ),
inference(rectify,[],[f1254]) ).
fof(f1254,axiom,
! [X20,X42,X4] :
( c_Equiv__Relations_Oequivp(X4,X42)
=> hBOOL(hAPP(hAPP(X42,X20),X20)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_equivp__reflp) ).
fof(f31200,plain,
spl698_664,
inference(avatar_split_clause,[],[f20879,f31198]) ).
fof(f31198,plain,
( spl698_664
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_664])]) ).
fof(f20879,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ),
inference(cnf_transformation,[],[f11944]) ).
fof(f11944,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ),
inference(ennf_transformation,[],[f7748]) ).
fof(f7748,plain,
! [X0,X1,X2] :
( c_Predicate_Oreflp(X2,X1)
=> hBOOL(hAPP(hAPP(X1,X0),X0)) ),
inference(rectify,[],[f3529]) ).
fof(f3529,axiom,
! [X20,X60,X4] :
( c_Predicate_Oreflp(X4,X60)
=> hBOOL(hAPP(hAPP(X60,X20),X20)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_reflpE) ).
fof(f31196,plain,
spl698_663,
inference(avatar_split_clause,[],[f19833,f31194]) ).
fof(f31194,plain,
( spl698_663
<=> ! [X2,X0,X1] : c_Product__Type_Oprod_Oprod__case(X2,X1,X0) = c_Product__Type_Ointernal__split(X2,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_663])]) ).
fof(f19833,plain,
! [X2,X0,X1] : c_Product__Type_Oprod_Oprod__case(X2,X1,X0) = c_Product__Type_Ointernal__split(X2,X1,X0),
inference(cnf_transformation,[],[f6924]) ).
fof(f6924,plain,
! [X0,X1,X2] : c_Product__Type_Oprod_Oprod__case(X2,X1,X0) = c_Product__Type_Ointernal__split(X2,X1,X0),
inference(rectify,[],[f4920]) ).
fof(f4920,axiom,
! [X74,X24,X4] : c_Product__Type_Oprod_Oprod__case(X4,X24,X74) = c_Product__Type_Ointernal__split(X4,X24,X74),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_internal__split__def) ).
fof(f31192,plain,
spl698_662,
inference(avatar_split_clause,[],[f19832,f31190]) ).
fof(f31190,plain,
( spl698_662
<=> ! [X2,X0,X1] : c_List_Olist_ONil(X1) = c_List_Omap__filter(X2,X1,X0,c_List_Olist_ONil(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_662])]) ).
fof(f19832,plain,
! [X2,X0,X1] : c_List_Olist_ONil(X1) = c_List_Omap__filter(X2,X1,X0,c_List_Olist_ONil(X2)),
inference(cnf_transformation,[],[f6923]) ).
fof(f6923,plain,
! [X0,X1,X2] : c_List_Olist_ONil(X1) = c_List_Omap__filter(X2,X1,X0,c_List_Olist_ONil(X2)),
inference(rectify,[],[f3940]) ).
fof(f3940,axiom,
! [X1,X4,X24] : c_List_Olist_ONil(X4) = c_List_Omap__filter(X24,X4,X1,c_List_Olist_ONil(X24)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_map__filter__simps_I2_J) ).
fof(f31188,plain,
( spl698_661
| ~ spl698_243
| ~ spl698_314 ),
inference(avatar_split_clause,[],[f29673,f29519,f29218,f31185]) ).
fof(f31185,plain,
( spl698_661
<=> c_Wellfounded_Oacyclic(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_661])]) ).
fof(f29519,plain,
( spl698_314
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_314])]) ).
fof(f29673,plain,
( c_Wellfounded_Oacyclic(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl698_243
| ~ spl698_314 ),
inference(resolution,[],[f29520,f29220]) ).
fof(f29520,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,X0)
| c_Wellfounded_Oacyclic(X1,X0) )
| ~ spl698_314 ),
inference(avatar_component_clause,[],[f29519]) ).
fof(f31183,plain,
spl698_660,
inference(avatar_split_clause,[],[f19831,f31181]) ).
fof(f31181,plain,
( spl698_660
<=> ! [X2,X0,X1] : c_List_Olist_ONil(X1) = c_List_Omaps(X2,X1,X0,c_List_Olist_ONil(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_660])]) ).
fof(f19831,plain,
! [X2,X0,X1] : c_List_Olist_ONil(X1) = c_List_Omaps(X2,X1,X0,c_List_Olist_ONil(X2)),
inference(cnf_transformation,[],[f6922]) ).
fof(f6922,plain,
! [X0,X1,X2] : c_List_Olist_ONil(X1) = c_List_Omaps(X2,X1,X0,c_List_Olist_ONil(X2)),
inference(rectify,[],[f4549]) ).
fof(f4549,axiom,
! [X1,X4,X24] : c_List_Olist_ONil(X4) = c_List_Omaps(X24,X4,X1,c_List_Olist_ONil(X24)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_maps__simps_I2_J) ).
fof(f31179,plain,
spl698_659,
inference(avatar_split_clause,[],[f19829,f31177]) ).
fof(f31177,plain,
( spl698_659
<=> ! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_659])]) ).
fof(f19829,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[],[f6920]) ).
fof(f6920,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2),
inference(rectify,[],[f3962]) ).
fof(f3962,axiom,
! [X283,X149,X23] : c_List_Olist_ONil(X23) != hAPP(hAPP(c_List_Olist_OCons(X23),X149),X283),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_list_Osimps_I3_J) ).
fof(f31175,plain,
spl698_658,
inference(avatar_split_clause,[],[f19471,f31173]) ).
fof(f31173,plain,
( spl698_658
<=> ! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP7(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_658])]) ).
fof(f19471,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP7(X1,X0) ),
inference(cnf_transformation,[],[f15159]) ).
fof(f15159,plain,
! [X0,X1] :
( ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP7(X1,X0) )
& ( sP7(X1,X0)
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ) ),
inference(nnf_transformation,[],[f14549]) ).
fof(f14549,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
<=> sP7(X1,X0) ),
inference(definition_folding,[],[f11108,f14548]) ).
fof(f14548,plain,
! [X1,X0] :
( sP7(X1,X0)
<=> ( ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [X2] :
( hBOOL(hAPP(X1,X2))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) != X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f11108,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
<=> ( ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [X2] :
( hBOOL(hAPP(X1,X2))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) != X0 ) ) ),
inference(ennf_transformation,[],[f6774]) ).
fof(f6774,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X2] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X0
=> hBOOL(hAPP(X1,X2)) ) ) ),
inference(rectify,[],[f2499]) ).
fof(f2499,axiom,
! [X147,X5] :
( hBOOL(hAPP(X5,hAPP(c_Int_Onat,X147)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X147),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X94] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X94) = X147
=> hBOOL(hAPP(X5,X94)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_split__nat) ).
fof(f31171,plain,
spl698_657,
inference(avatar_split_clause,[],[f19470,f31169]) ).
fof(f31169,plain,
( spl698_657
<=> ! [X0,X1] :
( sP7(X1,X0)
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_657])]) ).
fof(f19470,plain,
! [X0,X1] :
( sP7(X1,X0)
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ),
inference(cnf_transformation,[],[f15159]) ).
fof(f31167,plain,
spl698_656,
inference(avatar_split_clause,[],[f19396,f31165]) ).
fof(f31165,plain,
( spl698_656
<=> ! [X0,X1,X3] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_656])]) ).
fof(f19396,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ),
inference(cnf_transformation,[],[f15095]) ).
fof(f15095,plain,
! [X0,X1] :
( ( c_Wellfounded_OwfP(X1,X0)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK221(X0,X1))) )
& ( ! [X3] : hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK221])],[f15093,f15094]) ).
fof(f15094,plain,
! [X0,X1] :
( ? [X2] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2))
=> ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK221(X0,X1))) ),
introduced(choice_axiom,[]) ).
fof(f15093,plain,
! [X0,X1] :
( ( c_Wellfounded_OwfP(X1,X0)
| ? [X2] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) )
& ( ! [X3] : hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
inference(rectify,[],[f15092]) ).
fof(f15092,plain,
! [X0,X1] :
( ( c_Wellfounded_OwfP(X1,X0)
| ? [X2] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) )
& ( ! [X2] : hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
inference(nnf_transformation,[],[f6752]) ).
fof(f6752,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
<=> ! [X2] : hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) ),
inference(rectify,[],[f3566]) ).
fof(f3566,axiom,
! [X60,X4] :
( c_Wellfounded_OwfP(X4,X60)
<=> ! [X48] : hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X60),X48)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wfP__accp__iff) ).
fof(f31163,plain,
spl698_655,
inference(avatar_split_clause,[],[f19038,f31161]) ).
fof(f31161,plain,
( spl698_655
<=> ! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_655])]) ).
fof(f19038,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10732]) ).
fof(f10732,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6486]) ).
fof(f6486,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0)) ),
inference(rectify,[],[f3573]) ).
fof(f3573,axiom,
! [X42,X4] :
( c_Wellfounded_Owf(X4,X42)
=> c_Wellfounded_OwfP(X4,c_FunDef_Oin__rel(X4,X4,X42)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__in__rel) ).
fof(f31159,plain,
spl698_654,
inference(avatar_split_clause,[],[f19037,f31157]) ).
fof(f31157,plain,
( spl698_654
<=> ! [X0,X1] :
( c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olex(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_654])]) ).
fof(f19037,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olex(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10731]) ).
fof(f10731,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olex(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6485]) ).
fof(f6485,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olex(X1,X0)) ),
inference(rectify,[],[f3380]) ).
fof(f3380,axiom,
! [X60,X4] :
( c_Wellfounded_Owf(X4,X60)
=> c_Wellfounded_Owf(tc_List_Olist(X4),c_List_Olex(X4,X60)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__lex) ).
fof(f31155,plain,
spl698_653,
inference(avatar_split_clause,[],[f19036,f31153]) ).
fof(f31153,plain,
( spl698_653
<=> ! [X0,X1] :
( c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olenlex(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_653])]) ).
fof(f19036,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olenlex(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10730]) ).
fof(f10730,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olenlex(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6484]) ).
fof(f6484,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Owf(tc_List_Olist(X1),c_List_Olenlex(X1,X0)) ),
inference(rectify,[],[f3376]) ).
fof(f3376,axiom,
! [X60,X4] :
( c_Wellfounded_Owf(X4,X60)
=> c_Wellfounded_Owf(tc_List_Olist(X4),c_List_Olenlex(X4,X60)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__lenlex) ).
fof(f31151,plain,
spl698_652,
inference(avatar_split_clause,[],[f19030,f31149]) ).
fof(f31149,plain,
( spl698_652
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X0),X0))
| ~ class_HOL_Oequal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_652])]) ).
fof(f19030,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X0),X0))
| ~ class_HOL_Oequal(X1) ),
inference(cnf_transformation,[],[f10723]) ).
fof(f10723,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X0),X0))
| ~ class_HOL_Oequal(X1) ),
inference(ennf_transformation,[],[f6478]) ).
fof(f6478,plain,
! [X0,X1] :
( class_HOL_Oequal(X1)
=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X0),X0)) ),
inference(rectify,[],[f4945]) ).
fof(f4945,axiom,
! [X22,X23] :
( class_HOL_Oequal(X23)
=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X23),X22),X22)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_equal__refl) ).
fof(f31147,plain,
spl698_651,
inference(avatar_split_clause,[],[f19025,f31145]) ).
fof(f31145,plain,
( spl698_651
<=> ! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_651])]) ).
fof(f19025,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(cnf_transformation,[],[f10714]) ).
fof(f10714,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(flattening,[],[f10713]) ).
fof(f10713,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(ennf_transformation,[],[f6473]) ).
fof(f6473,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X1)
=> ( c_Nat__Transfer_Ois__nat(X0)
=> c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)) ) ),
inference(rectify,[],[f2909]) ).
fof(f2909,axiom,
! [X29,X22] :
( c_Nat__Transfer_Ois__nat(X22)
=> ( c_Nat__Transfer_Ois__nat(X29)
=> c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X29)) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).
fof(f31143,plain,
( spl698_650
| ~ spl698_261
| ~ spl698_314 ),
inference(avatar_split_clause,[],[f29668,f29519,f29291,f31141]) ).
fof(f31141,plain,
( spl698_650
<=> ! [X0,X1] : c_Wellfounded_Oacyclic(X0,c_List_Omeasures(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_650])]) ).
fof(f29668,plain,
( ! [X0,X1] : c_Wellfounded_Oacyclic(X0,c_List_Omeasures(X0,X1))
| ~ spl698_261
| ~ spl698_314 ),
inference(resolution,[],[f29520,f29292]) ).
fof(f31139,plain,
spl698_649,
inference(avatar_split_clause,[],[f19021,f31137]) ).
fof(f31137,plain,
( spl698_649
<=> ! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_649])]) ).
fof(f19021,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(cnf_transformation,[],[f10708]) ).
fof(f10708,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(ennf_transformation,[],[f6470]) ).
fof(f6470,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X1)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0)) ),
inference(rectify,[],[f2912]) ).
fof(f2912,axiom,
! [X88,X22] :
( c_Nat__Transfer_Ois__nat(X22)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X22),X88)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).
fof(f31135,plain,
spl698_648,
inference(avatar_split_clause,[],[f18979,f31133]) ).
fof(f31133,plain,
( spl698_648
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_648])]) ).
fof(f18979,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10672]) ).
fof(f10672,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6443]) ).
fof(f6443,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0)) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X22,X23] :
( class_Orderings_Opreorder(X23)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23),X22),X22)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_order__refl) ).
fof(f31131,plain,
spl698_647,
inference(avatar_split_clause,[],[f18978,f31129]) ).
fof(f31129,plain,
( spl698_647
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_647])]) ).
fof(f18978,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10671]) ).
fof(f10671,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6442]) ).
fof(f6442,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0)) ),
inference(rectify,[],[f527]) ).
fof(f527,axiom,
! [X22,X23] :
( class_Orderings_Opreorder(X23)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23),X22),X22)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_order__less__irrefl) ).
fof(f31127,plain,
spl698_646,
inference(avatar_split_clause,[],[f18947,f31125]) ).
fof(f31125,plain,
( spl698_646
<=> ! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_646])]) ).
fof(f18947,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f14944]) ).
fof(f14944,plain,
! [X0,X1] :
( ( ( c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| ~ c_List_Olinorder__class_Osorted(X1,X0) ) )
| ~ sP1(X0,X1) ),
inference(nnf_transformation,[],[f14536]) ).
fof(f14536,plain,
! [X0,X1] :
( ( c_List_Olinorder__class_Osorted(X1,X0)
<=> sP0(X1,X0) )
| ~ sP1(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f31123,plain,
spl698_645,
inference(avatar_split_clause,[],[f18946,f31121]) ).
fof(f31121,plain,
( spl698_645
<=> ! [X0,X1] :
( sP0(X1,X0)
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_645])]) ).
fof(f18946,plain,
! [X0,X1] :
( sP0(X1,X0)
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f14944]) ).
fof(f31119,plain,
spl698_644,
inference(avatar_split_clause,[],[f18884,f31117]) ).
fof(f31117,plain,
( spl698_644
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_644])]) ).
fof(f18884,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f10572]) ).
fof(f10572,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f6367]) ).
fof(f6367,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f2105]) ).
fof(f2105,axiom,
! [X32,X23] :
( class_Divides_Osemiring__div(X23)
=> c_Divides_Odiv__class_Omod(X23,X32,c_Groups_Ozero__class_Ozero(X23)) = X32 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_mod__by__0) ).
fof(f31115,plain,
spl698_643,
inference(avatar_split_clause,[],[f18883,f31113]) ).
fof(f31113,plain,
( spl698_643
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0)
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_643])]) ).
fof(f18883,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f10571]) ).
fof(f10571,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f6366]) ).
fof(f6366,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0) ),
inference(rectify,[],[f2104]) ).
fof(f2104,axiom,
! [X32,X23] :
( class_Divides_Osemiring__div(X23)
=> c_Groups_Ozero__class_Ozero(X23) = c_Divides_Odiv__class_Omod(X23,X32,X32) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_mod__self) ).
fof(f31111,plain,
spl698_642,
inference(avatar_split_clause,[],[f18871,f31109]) ).
fof(f31109,plain,
( spl698_642
<=> ! [X0,X1] :
( c_Int_Oiszero(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Rings_Osemiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_642])]) ).
fof(f18871,plain,
! [X0,X1] :
( c_Int_Oiszero(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Rings_Osemiring__1(X1) ),
inference(cnf_transformation,[],[f14930]) ).
fof(f14930,plain,
! [X0,X1] :
( ( ( c_Int_Oiszero(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Int_Oiszero(X1,X0) ) )
| ~ class_Rings_Osemiring__1(X1) ),
inference(nnf_transformation,[],[f10559]) ).
fof(f10559,plain,
! [X0,X1] :
( ( c_Int_Oiszero(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Rings_Osemiring__1(X1) ),
inference(ennf_transformation,[],[f6354]) ).
fof(f6354,plain,
! [X0,X1] :
( class_Rings_Osemiring__1(X1)
=> ( c_Int_Oiszero(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f2667]) ).
fof(f2667,axiom,
! [X116,X4] :
( class_Rings_Osemiring__1(X4)
=> ( c_Int_Oiszero(X4,X116)
<=> c_Groups_Ozero__class_Ozero(X4) = X116 ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_iszero__def) ).
fof(f31107,plain,
spl698_641,
inference(avatar_split_clause,[],[f18870,f31105]) ).
fof(f31105,plain,
( spl698_641
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Int_Oiszero(X1,X0)
| ~ class_Rings_Osemiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_641])]) ).
fof(f18870,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Int_Oiszero(X1,X0)
| ~ class_Rings_Osemiring__1(X1) ),
inference(cnf_transformation,[],[f14930]) ).
fof(f31103,plain,
spl698_640,
inference(avatar_split_clause,[],[f18618,f31101]) ).
fof(f31101,plain,
( spl698_640
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_640])]) ).
fof(f18618,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ),
inference(cnf_transformation,[],[f6158]) ).
fof(f6158,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ),
inference(rectify,[],[f5226]) ).
fof(f5226,axiom,
! [X34,X20] :
( X20 = X34
| ~ hBOOL(hAPP(hAPP(c_fequal,X20),X34)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fequal__1) ).
fof(f31099,plain,
( spl698_639
| ~ spl698_208
| ~ spl698_287 ),
inference(avatar_split_clause,[],[f29652,f29408,f29053,f31097]) ).
fof(f31097,plain,
( spl698_639
<=> ! [X7] : c_fequal = c_HOL_Oequal__class_Oequal(tc_Lazy__Sequence_Olazy__sequence(X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_639])]) ).
fof(f29053,plain,
( spl698_208
<=> ! [X0] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_208])]) ).
fof(f29408,plain,
( spl698_287
<=> ! [X0] :
( c_fequal = c_HOL_Oequal__class_Oequal(X0)
| ~ class_HOL_Oequal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_287])]) ).
fof(f29652,plain,
( ! [X7] : c_fequal = c_HOL_Oequal__class_Oequal(tc_Lazy__Sequence_Olazy__sequence(X7))
| ~ spl698_208
| ~ spl698_287 ),
inference(resolution,[],[f29409,f29054]) ).
fof(f29054,plain,
( ! [X0] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X0))
| ~ spl698_208 ),
inference(avatar_component_clause,[],[f29053]) ).
fof(f29409,plain,
( ! [X0] :
( ~ class_HOL_Oequal(X0)
| c_fequal = c_HOL_Oequal__class_Oequal(X0) )
| ~ spl698_287 ),
inference(avatar_component_clause,[],[f29408]) ).
fof(f31095,plain,
spl698_638,
inference(avatar_split_clause,[],[f18613,f31093]) ).
fof(f31093,plain,
( spl698_638
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_638])]) ).
fof(f18613,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f6153]) ).
fof(f6153,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
| X0 != X1 ),
inference(rectify,[],[f5227]) ).
fof(f5227,axiom,
! [X34,X20] :
( hBOOL(hAPP(hAPP(c_fequal,X20),X34))
| X20 != X34 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fequal__2) ).
fof(f31091,plain,
spl698_637,
inference(avatar_split_clause,[],[f18509,f31089]) ).
fof(f31089,plain,
( spl698_637
<=> ! [X0,X1] :
( c_Code__Numeral_Onat__of__aux(X1,X0) = X0
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_637])]) ).
fof(f18509,plain,
! [X0,X1] :
( c_Code__Numeral_Onat__of__aux(X1,X0) = X0
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X1 ),
inference(cnf_transformation,[],[f10290]) ).
fof(f10290,plain,
! [X0,X1] :
( ( c_Code__Numeral_Onat__of__aux(X1,X0) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X0))
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X1 )
& ( c_Code__Numeral_Onat__of__aux(X1,X0) = X0
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X1 ) ),
inference(ennf_transformation,[],[f6105]) ).
fof(f6105,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X1
=> c_Code__Numeral_Onat__of__aux(X1,X0) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X1
=> c_Code__Numeral_Onat__of__aux(X1,X0) = X0 ) ),
inference(rectify,[],[f2862]) ).
fof(f2862,axiom,
! [X88,X114] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X114
=> c_Code__Numeral_Onat__of__aux(X114,X88) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X114),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X88)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X114
=> c_Code__Numeral_Onat__of__aux(X114,X88) = X88 ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__of__aux__code) ).
fof(f31087,plain,
spl698_636,
inference(avatar_split_clause,[],[f18507,f31085]) ).
fof(f31085,plain,
( spl698_636
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X0)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_636])]) ).
fof(f18507,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f10289]) ).
fof(f10289,plain,
! [X0,X1] :
( ( c_Random_Oinc__shift(X1,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X0),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| X0 = X1 )
& ( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X0)
| X0 != X1 ) ),
inference(ennf_transformation,[],[f6104]) ).
fof(f6104,plain,
! [X0,X1] :
( ( X0 != X1
=> c_Random_Oinc__shift(X1,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X0),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) )
& ( X0 = X1
=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X0) ) ),
inference(rectify,[],[f4610]) ).
fof(f4610,axiom,
! [X112,X190] :
( ( X112 != X190
=> c_Random_Oinc__shift(X190,X112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X112),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) )
& ( X112 = X190
=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X190,X112) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_inc__shift__def) ).
fof(f31083,plain,
spl698_635,
inference(avatar_split_clause,[],[f18184,f31081]) ).
fof(f31081,plain,
( spl698_635
<=> ! [X0,X1] : c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_635])]) ).
fof(f18184,plain,
! [X0,X1] : c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X0)),
inference(cnf_transformation,[],[f5781]) ).
fof(f5781,plain,
! [X0,X1] : c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X0)),
inference(rectify,[],[f4706]) ).
fof(f4706,axiom,
! [X60,X4] : c_Relation_Orefl__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X60)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_refl__rtrancl) ).
fof(f31079,plain,
spl698_634,
inference(avatar_split_clause,[],[f18183,f31077]) ).
fof(f31077,plain,
( spl698_634
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_634])]) ).
fof(f18183,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X0)),
inference(cnf_transformation,[],[f5780]) ).
fof(f5780,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X0)),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X19,X4] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X19),X19)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_subset__refl) ).
fof(f31075,plain,
spl698_633,
inference(avatar_split_clause,[],[f18182,f31073]) ).
fof(f31073,plain,
( spl698_633
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_633])]) ).
fof(f18182,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))),
inference(cnf_transformation,[],[f5779]) ).
fof(f5779,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))),
inference(rectify,[],[f1885]) ).
fof(f1885,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X153),X152))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_finite__atLeastLessThan) ).
fof(f31070,plain,
spl698_632,
inference(avatar_split_clause,[],[f18181,f31068]) ).
fof(f31068,plain,
( spl698_632
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_632])]) ).
fof(f18181,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X0))),
inference(cnf_transformation,[],[f5778]) ).
fof(f5778,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X0))),
inference(rectify,[],[f1939]) ).
fof(f1939,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X153),X152))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_finite__atLeastLessThan__int) ).
fof(f31066,plain,
spl698_631,
inference(avatar_split_clause,[],[f18180,f31064]) ).
fof(f31064,plain,
( spl698_631
<=> ! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_631])]) ).
fof(f18180,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(cnf_transformation,[],[f5777]) ).
fof(f5777,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(rectify,[],[f259]) ).
fof(f259,axiom,
! [X76,X4] : hAPP(c_Set_Oimage(X4,X4,c_COMBI(X4)),X76) = X76,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_image__ident) ).
fof(f31062,plain,
spl698_630,
inference(avatar_split_clause,[],[f18179,f31060]) ).
fof(f31060,plain,
( spl698_630
<=> ! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_630])]) ).
fof(f18179,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(cnf_transformation,[],[f5776]) ).
fof(f5776,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(rectify,[],[f3476]) ).
fof(f3476,axiom,
! [X76,X4] : hAPP(c_Set_Oimage(X4,X4,c_Fun_Oid(X4)),X76) = X76,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_image__id) ).
fof(f31058,plain,
spl698_629,
inference(avatar_split_clause,[],[f18178,f31056]) ).
fof(f31056,plain,
( spl698_629
<=> ! [X0,X1] : hAPP(c_Relation_OImage(X1,X1,c_Relation_OId(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_629])]) ).
fof(f18178,plain,
! [X0,X1] : hAPP(c_Relation_OImage(X1,X1,c_Relation_OId(X1)),X0) = X0,
inference(cnf_transformation,[],[f5775]) ).
fof(f5775,plain,
! [X0,X1] : hAPP(c_Relation_OImage(X1,X1,c_Relation_OId(X1)),X0) = X0,
inference(rectify,[],[f4721]) ).
fof(f4721,axiom,
! [X19,X4] : hAPP(c_Relation_OImage(X4,X4,c_Relation_OId(X4)),X19) = X19,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Image__Id) ).
fof(f31054,plain,
( spl698_628
| ~ spl698_211
| ~ spl698_287 ),
inference(avatar_split_clause,[],[f29649,f29408,f29065,f31052]) ).
fof(f31052,plain,
( spl698_628
<=> ! [X6] : c_fequal = c_HOL_Oequal__class_Oequal(tc_List_Olist(X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_628])]) ).
fof(f29065,plain,
( spl698_211
<=> ! [X0] : class_HOL_Oequal(tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_211])]) ).
fof(f29649,plain,
( ! [X6] : c_fequal = c_HOL_Oequal__class_Oequal(tc_List_Olist(X6))
| ~ spl698_211
| ~ spl698_287 ),
inference(resolution,[],[f29409,f29066]) ).
fof(f29066,plain,
( ! [X0] : class_HOL_Oequal(tc_List_Olist(X0))
| ~ spl698_211 ),
inference(avatar_component_clause,[],[f29065]) ).
fof(f31050,plain,
spl698_627,
inference(avatar_split_clause,[],[f18177,f31048]) ).
fof(f31048,plain,
( spl698_627
<=> ! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_627])]) ).
fof(f18177,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(cnf_transformation,[],[f5774]) ).
fof(f5774,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(rectify,[],[f1258]) ).
fof(f1258,axiom,
! [X76,X4] : hAPP(c_Set_Ovimage(X4,X4,c_COMBI(X4)),X76) = X76,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_vimage__ident) ).
fof(f31046,plain,
spl698_626,
inference(avatar_split_clause,[],[f18176,f31044]) ).
fof(f31044,plain,
( spl698_626
<=> ! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_626])]) ).
fof(f18176,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(cnf_transformation,[],[f5773]) ).
fof(f5773,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(rectify,[],[f3482]) ).
fof(f3482,axiom,
! [X19,X4] : hAPP(c_Set_Ovimage(X4,X4,c_Fun_Oid(X4)),X19) = X19,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_vimage__id) ).
fof(f31042,plain,
spl698_625,
inference(avatar_split_clause,[],[f18175,f31040]) ).
fof(f31040,plain,
( spl698_625
<=> ! [X0,X1] : hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId__on(X1,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_625])]) ).
fof(f18175,plain,
! [X0,X1] : hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId__on(X1,X0)) = X0,
inference(cnf_transformation,[],[f5772]) ).
fof(f5772,plain,
! [X0,X1] : hAPP(c_Relation_ODomain(X1,X1),c_Relation_OId__on(X1,X0)) = X0,
inference(rectify,[],[f3408]) ).
fof(f3408,axiom,
! [X19,X4] : hAPP(c_Relation_ODomain(X4,X4),c_Relation_OId__on(X4,X19)) = X19,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Domain__Id__on) ).
fof(f31038,plain,
spl698_624,
inference(avatar_split_clause,[],[f18174,f31036]) ).
fof(f31036,plain,
( spl698_624
<=> ! [X0,X1] : hAPP(c_Relation_ORange(X1,X1),c_Relation_OId__on(X1,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_624])]) ).
fof(f18174,plain,
! [X0,X1] : hAPP(c_Relation_ORange(X1,X1),c_Relation_OId__on(X1,X0)) = X0,
inference(cnf_transformation,[],[f5771]) ).
fof(f5771,plain,
! [X0,X1] : hAPP(c_Relation_ORange(X1,X1),c_Relation_OId__on(X1,X0)) = X0,
inference(rectify,[],[f3389]) ).
fof(f3389,axiom,
! [X19,X4] : hAPP(c_Relation_ORange(X4,X4),c_Relation_OId__on(X4,X19)) = X19,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Range__Id__on) ).
fof(f31034,plain,
spl698_623,
inference(avatar_split_clause,[],[f18173,f31032]) ).
fof(f31032,plain,
( spl698_623
<=> ! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_623])]) ).
fof(f18173,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0,
inference(cnf_transformation,[],[f5770]) ).
fof(f5770,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0,
inference(rectify,[],[f4072]) ).
fof(f4072,axiom,
! [X266,X23] : hAPP(hAPP(c_List_Oappend(X23),c_List_Olist_ONil(X23)),X266) = X266,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_append__Nil) ).
fof(f31030,plain,
spl698_622,
inference(avatar_split_clause,[],[f18172,f31028]) ).
fof(f31028,plain,
( spl698_622
<=> ! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_622])]) ).
fof(f18172,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0,
inference(cnf_transformation,[],[f5769]) ).
fof(f5769,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0,
inference(rectify,[],[f4070]) ).
fof(f4070,axiom,
! [X263,X23] : hAPP(hAPP(c_List_Oappend(X23),X263),c_List_Olist_ONil(X23)) = X263,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_append__Nil2) ).
fof(f31026,plain,
spl698_621,
inference(avatar_split_clause,[],[f18171,f31024]) ).
fof(f31024,plain,
( spl698_621
<=> ! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_621])]) ).
fof(f18171,plain,
! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0,
inference(cnf_transformation,[],[f5768]) ).
fof(f5768,plain,
! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0,
inference(rectify,[],[f4311]) ).
fof(f4311,axiom,
! [X263,X23] : hAPP(c_List_Orev(X23),hAPP(c_List_Orev(X23),X263)) = X263,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rev__rev__ident) ).
fof(f31022,plain,
spl698_620,
inference(avatar_split_clause,[],[f18170,f31020]) ).
fof(f31020,plain,
( spl698_620
<=> ! [X0,X1] : hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_620])]) ).
fof(f18170,plain,
! [X0,X1] : hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X0)) = X0,
inference(cnf_transformation,[],[f5767]) ).
fof(f5767,plain,
! [X0,X1] : hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X0)) = X0,
inference(rectify,[],[f3638]) ).
fof(f3638,axiom,
! [X22,X23] : hAPP(c_Option_Othe(X23),hAPP(c_Option_Ooption_OSome(X23),X22)) = X22,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_the_Osimps) ).
fof(f31018,plain,
spl698_619,
inference(avatar_split_clause,[],[f18168,f31016]) ).
fof(f31016,plain,
( spl698_619
<=> ! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_619])]) ).
fof(f18168,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X1,X0)),
inference(cnf_transformation,[],[f5765]) ).
fof(f5765,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Otrancl(X1,X0)),
inference(rectify,[],[f4689]) ).
fof(f4689,axiom,
! [X42,X4] : c_Transitive__Closure_Ortrancl(X4,c_Transitive__Closure_Otrancl(X4,X42)) = c_Transitive__Closure_Ortrancl(X4,X42),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_trancl__rtrancl__absorb) ).
fof(f31014,plain,
spl698_618,
inference(avatar_split_clause,[],[f18167,f31012]) ).
fof(f31012,plain,
( spl698_618
<=> ! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_618])]) ).
fof(f18167,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(cnf_transformation,[],[f5764]) ).
fof(f5764,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(rectify,[],[f4707]) ).
fof(f4707,axiom,
! [X60,X4] : c_Transitive__Closure_Ortrancl(X4,X60) = c_Transitive__Closure_Ortrancl(X4,c_Transitive__Closure_Ortrancl(X4,X60)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rtrancl__idemp) ).
fof(f31010,plain,
( spl698_617
| ~ spl698_210
| ~ spl698_287 ),
inference(avatar_split_clause,[],[f29643,f29408,f29061,f31008]) ).
fof(f31008,plain,
( spl698_617
<=> ! [X1] : c_fequal = c_HOL_Oequal__class_Oequal(tc_Option_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_617])]) ).
fof(f29061,plain,
( spl698_210
<=> ! [X0] : class_HOL_Oequal(tc_Option_Ooption(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_210])]) ).
fof(f29643,plain,
( ! [X1] : c_fequal = c_HOL_Oequal__class_Oequal(tc_Option_Ooption(X1))
| ~ spl698_210
| ~ spl698_287 ),
inference(resolution,[],[f29409,f29062]) ).
fof(f29062,plain,
( ! [X0] : class_HOL_Oequal(tc_Option_Ooption(X0))
| ~ spl698_210 ),
inference(avatar_component_clause,[],[f29061]) ).
fof(f31006,plain,
spl698_616,
inference(avatar_split_clause,[],[f18166,f31004]) ).
fof(f31004,plain,
( spl698_616
<=> ! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Otrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_616])]) ).
fof(f18166,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Otrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(cnf_transformation,[],[f5763]) ).
fof(f5763,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Otrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(rectify,[],[f4690]) ).
fof(f4690,axiom,
! [X42,X4] : c_Transitive__Closure_Ortrancl(X4,X42) = c_Transitive__Closure_Otrancl(X4,c_Transitive__Closure_Ortrancl(X4,X42)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rtrancl__trancl__absorb) ).
fof(f31002,plain,
spl698_615,
inference(avatar_split_clause,[],[f18165,f31000]) ).
fof(f31000,plain,
( spl698_615
<=> ! [X0,X1] : c_List_Oremdups(X1,X0) = c_List_Oremdups(X1,c_List_Oremdups(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_615])]) ).
fof(f18165,plain,
! [X0,X1] : c_List_Oremdups(X1,X0) = c_List_Oremdups(X1,c_List_Oremdups(X1,X0)),
inference(cnf_transformation,[],[f5762]) ).
fof(f5762,plain,
! [X0,X1] : c_List_Oremdups(X1,X0) = c_List_Oremdups(X1,c_List_Oremdups(X1,X0)),
inference(rectify,[],[f4207]) ).
fof(f4207,axiom,
! [X263,X23] : c_List_Oremdups(X23,X263) = c_List_Oremdups(X23,c_List_Oremdups(X23,X263)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_remdups__remdups) ).
fof(f30998,plain,
spl698_614,
inference(avatar_split_clause,[],[f18164,f30996]) ).
fof(f30996,plain,
( spl698_614
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_614])]) ).
fof(f18164,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5761]) ).
fof(f5761,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f3939]) ).
fof(f3939,axiom,
! [X5,X4] : c_List_Olist_ONil(X4) = hAPP(c_List_Ofilter(X4,X5),c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_filter_Osimps_I1_J) ).
fof(f30994,plain,
spl698_613,
inference(avatar_split_clause,[],[f18163,f30992]) ).
fof(f30992,plain,
( spl698_613
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_OremoveAll(X1,X0),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_613])]) ).
fof(f18163,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_OremoveAll(X1,X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5760]) ).
fof(f5760,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_OremoveAll(X1,X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f4531]) ).
fof(f4531,axiom,
! [X22,X23] : c_List_Olist_ONil(X23) = hAPP(c_List_OremoveAll(X23,X22),c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_removeAll_Osimps_I1_J) ).
fof(f30984,plain,
( spl698_612
| ~ spl698_441
| ~ spl698_611 ),
inference(avatar_split_clause,[],[f30980,f30977,f30127,f30982]) ).
fof(f30982,plain,
( spl698_612
<=> ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OBit1(X1)),c_Int_OBit0(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_612])]) ).
fof(f30127,plain,
( spl698_441
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_441])]) ).
fof(f30977,plain,
( spl698_611
<=> ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_611])]) ).
fof(f30980,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OBit1(X1)),c_Int_OBit0(X0)))
| ~ spl698_441
| ~ spl698_611 ),
inference(forward_demodulation,[],[f30978,f30129]) ).
fof(f30129,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Int_Oint)
| ~ spl698_441 ),
inference(avatar_component_clause,[],[f30127]) ).
fof(f30978,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X0)))
| ~ spl698_611 ),
inference(avatar_component_clause,[],[f30977]) ).
fof(f30979,plain,
spl698_611,
inference(avatar_split_clause,[],[f18161,f30977]) ).
fof(f18161,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X0))),
inference(cnf_transformation,[],[f5758]) ).
fof(f5758,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X1)),c_Int_OBit0(X0))),
inference(rectify,[],[f4963]) ).
fof(f4963,axiom,
! [X317,X318] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X318)),c_Int_OBit0(X317))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__int__code_I15_J) ).
fof(f30969,plain,
( spl698_610
| ~ spl698_441
| ~ spl698_609 ),
inference(avatar_split_clause,[],[f30965,f30962,f30127,f30967]) ).
fof(f30967,plain,
( spl698_610
<=> ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OBit0(X1)),c_Int_OBit1(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_610])]) ).
fof(f30962,plain,
( spl698_609
<=> ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_609])]) ).
fof(f30965,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OBit0(X1)),c_Int_OBit1(X0)))
| ~ spl698_441
| ~ spl698_609 ),
inference(forward_demodulation,[],[f30963,f30129]) ).
fof(f30963,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X0)))
| ~ spl698_609 ),
inference(avatar_component_clause,[],[f30962]) ).
fof(f30964,plain,
spl698_609,
inference(avatar_split_clause,[],[f18160,f30962]) ).
fof(f18160,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X0))),
inference(cnf_transformation,[],[f5757]) ).
fof(f5757,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OBit1(X0))),
inference(rectify,[],[f4962]) ).
fof(f4962,axiom,
! [X317,X318] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X318)),c_Int_OBit1(X317))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__int__code_I14_J) ).
fof(f30960,plain,
( spl698_608
| ~ spl698_209
| ~ spl698_287 ),
inference(avatar_split_clause,[],[f29638,f29408,f29057,f30958]) ).
fof(f30958,plain,
( spl698_608
<=> ! [X0] : c_fequal = c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_608])]) ).
fof(f29057,plain,
( spl698_209
<=> ! [X0] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_209])]) ).
fof(f29638,plain,
( ! [X0] : c_fequal = c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(X0))
| ~ spl698_209
| ~ spl698_287 ),
inference(resolution,[],[f29409,f29058]) ).
fof(f29058,plain,
( ! [X0] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X0))
| ~ spl698_209 ),
inference(avatar_component_clause,[],[f29057]) ).
fof(f30956,plain,
spl698_607,
inference(avatar_split_clause,[],[f17959,f30954]) ).
fof(f30954,plain,
( spl698_607
<=> ! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Lattices_Osemilattice__inf__class_Oinf(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__inf(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_607])]) ).
fof(f17959,plain,
! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Lattices_Osemilattice__inf__class_Oinf(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__inf(X0) ),
inference(cnf_transformation,[],[f10280]) ).
fof(f10280,plain,
! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Lattices_Osemilattice__inf__class_Oinf(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__inf(X0) ),
inference(flattening,[],[f10279]) ).
fof(f10279,plain,
! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Lattices_Osemilattice__inf__class_Oinf(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__inf(X0) ),
inference(ennf_transformation,[],[f5626]) ).
fof(f5626,plain,
! [X0] :
( ( class_Orderings_Olinorder(X0)
& class_Lattices_Osemilattice__inf(X0) )
=> c_Orderings_Oord__class_Omin(X0) = c_Lattices_Osemilattice__inf__class_Oinf(X0) ),
inference(rectify,[],[f1452]) ).
fof(f1452,axiom,
! [X4] :
( ( class_Orderings_Olinorder(X4)
& class_Lattices_Osemilattice__inf(X4) )
=> c_Lattices_Osemilattice__inf__class_Oinf(X4) = c_Orderings_Oord__class_Omin(X4) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_inf__min) ).
fof(f30952,plain,
spl698_606,
inference(avatar_split_clause,[],[f17958,f30950]) ).
fof(f30950,plain,
( spl698_606
<=> ! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Lattices_Osemilattice__sup__class_Osup(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_606])]) ).
fof(f17958,plain,
! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Lattices_Osemilattice__sup__class_Osup(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) ),
inference(cnf_transformation,[],[f10278]) ).
fof(f10278,plain,
! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Lattices_Osemilattice__sup__class_Osup(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) ),
inference(flattening,[],[f10277]) ).
fof(f10277,plain,
! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Lattices_Osemilattice__sup__class_Osup(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) ),
inference(ennf_transformation,[],[f5625]) ).
fof(f5625,plain,
! [X0] :
( ( class_Orderings_Olinorder(X0)
& class_Lattices_Osemilattice__sup(X0) )
=> c_Orderings_Oord__class_Omax(X0) = c_Lattices_Osemilattice__sup__class_Osup(X0) ),
inference(rectify,[],[f2153]) ).
fof(f2153,axiom,
! [X4] :
( ( class_Orderings_Olinorder(X4)
& class_Lattices_Osemilattice__sup(X4) )
=> c_Lattices_Osemilattice__sup__class_Osup(X4) = c_Orderings_Oord__class_Omax(X4) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_sup__max) ).
fof(f30948,plain,
spl698_605,
inference(avatar_split_clause,[],[f17901,f30946]) ).
fof(f30946,plain,
( spl698_605
<=> ! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Orderings_Oord_Omin(X0,c_Orderings_Oord__class_Oless__eq(X0))
| ~ class_Orderings_Oord(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_605])]) ).
fof(f17901,plain,
! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Orderings_Oord_Omin(X0,c_Orderings_Oord__class_Oless__eq(X0))
| ~ class_Orderings_Oord(X0) ),
inference(cnf_transformation,[],[f10222]) ).
fof(f10222,plain,
! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Orderings_Oord_Omin(X0,c_Orderings_Oord__class_Oless__eq(X0))
| ~ class_Orderings_Oord(X0) ),
inference(ennf_transformation,[],[f5573]) ).
fof(f5573,plain,
! [X0] :
( class_Orderings_Oord(X0)
=> c_Orderings_Oord__class_Omin(X0) = c_Orderings_Oord_Omin(X0,c_Orderings_Oord__class_Oless__eq(X0)) ),
inference(rectify,[],[f1693]) ).
fof(f1693,axiom,
! [X4] :
( class_Orderings_Oord(X4)
=> c_Orderings_Oord__class_Omin(X4) = c_Orderings_Oord_Omin(X4,c_Orderings_Oord__class_Oless__eq(X4)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_min__ord__min) ).
fof(f30944,plain,
spl698_604,
inference(avatar_split_clause,[],[f17900,f30942]) ).
fof(f30942,plain,
( spl698_604
<=> ! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Orderings_Oord_Omax(X0,c_Orderings_Oord__class_Oless__eq(X0))
| ~ class_Orderings_Oord(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_604])]) ).
fof(f17900,plain,
! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Orderings_Oord_Omax(X0,c_Orderings_Oord__class_Oless__eq(X0))
| ~ class_Orderings_Oord(X0) ),
inference(cnf_transformation,[],[f10221]) ).
fof(f10221,plain,
! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Orderings_Oord_Omax(X0,c_Orderings_Oord__class_Oless__eq(X0))
| ~ class_Orderings_Oord(X0) ),
inference(ennf_transformation,[],[f5572]) ).
fof(f5572,plain,
! [X0] :
( class_Orderings_Oord(X0)
=> c_Orderings_Oord__class_Omax(X0) = c_Orderings_Oord_Omax(X0,c_Orderings_Oord__class_Oless__eq(X0)) ),
inference(rectify,[],[f2199]) ).
fof(f2199,axiom,
! [X4] :
( class_Orderings_Oord(X4)
=> c_Orderings_Oord__class_Omax(X4) = c_Orderings_Oord_Omax(X4,c_Orderings_Oord__class_Oless__eq(X4)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_max__ord__max) ).
fof(f30940,plain,
spl698_603,
inference(avatar_split_clause,[],[f17856,f30938]) ).
fof(f30938,plain,
( spl698_603
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls)
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_603])]) ).
fof(f17856,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls)
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f10177]) ).
fof(f10177,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls)
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f5528]) ).
fof(f5528,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls) ),
inference(rectify,[],[f2571]) ).
fof(f2571,axiom,
! [X23] :
( class_Int_Onumber__ring(X23)
=> c_Groups_Ozero__class_Ozero(X23) = hAPP(c_Int_Onumber__class_Onumber__of(X23),c_Int_OPls) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_semiring__norm_I112_J) ).
fof(f30936,plain,
spl698_602,
inference(avatar_split_clause,[],[f17844,f30934]) ).
fof(f30934,plain,
( spl698_602
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Osgn__if(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_602])]) ).
fof(f17844,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Osgn__if(X0) ),
inference(cnf_transformation,[],[f10165]) ).
fof(f10165,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Osgn__if(X0) ),
inference(ennf_transformation,[],[f5516]) ).
fof(f5516,plain,
! [X0] :
( class_Groups_Osgn__if(X0)
=> c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f3224]) ).
fof(f3224,axiom,
! [X23] :
( class_Groups_Osgn__if(X23)
=> c_Groups_Ozero__class_Ozero(X23) = c_Groups_Osgn__class_Osgn(X23,c_Groups_Ozero__class_Ozero(X23)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_sgn0) ).
fof(f30932,plain,
spl698_601,
inference(avatar_split_clause,[],[f17675,f30930]) ).
fof(f30930,plain,
( spl698_601
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_601])]) ).
fof(f17675,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))),
inference(cnf_transformation,[],[f5361]) ).
fof(f5361,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))),
inference(rectify,[],[f1229]) ).
fof(f1229,axiom,
! [X88] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),hAPP(c_Nat_OSuc,X88))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_lessI) ).
fof(f30928,plain,
spl698_600,
inference(avatar_split_clause,[],[f17672,f30926]) ).
fof(f30926,plain,
( spl698_600
<=> ! [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,[spl698_600])]) ).
fof(f17672,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,[],[f5358]) ).
fof(f5358,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f1324]) ).
fof(f1324,axiom,
! [X88] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X88) = X88,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__mult__1) ).
fof(f30923,plain,
spl698_599,
inference(avatar_split_clause,[],[f17671,f30921]) ).
fof(f17671,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,[],[f5357]) ).
fof(f5357,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
inference(rectify,[],[f1793]) ).
fof(f1793,axiom,
! [X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X30) = X30,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zmult__1) ).
fof(f30919,plain,
spl698_598,
inference(avatar_split_clause,[],[f17667,f30917]) ).
fof(f30917,plain,
( spl698_598
<=> ! [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,[spl698_598])]) ).
fof(f17667,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,[],[f5353]) ).
fof(f5353,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(rectify,[],[f1326]) ).
fof(f1326,axiom,
! [X88] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X88),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X88,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__mult__1__right) ).
fof(f30914,plain,
spl698_597,
inference(avatar_split_clause,[],[f17666,f30912]) ).
fof(f17666,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,[],[f5352]) ).
fof(f5352,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
inference(rectify,[],[f1794]) ).
fof(f1794,axiom,
! [X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X30,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zmult__1__right) ).
fof(f30910,plain,
spl698_596,
inference(avatar_split_clause,[],[f17663,f30908]) ).
fof(f30908,plain,
( spl698_596
<=> ! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_596])]) ).
fof(f17663,plain,
! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = X0,
inference(cnf_transformation,[],[f5349]) ).
fof(f5349,plain,
! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = X0,
inference(rectify,[],[f1814]) ).
fof(f1814,axiom,
! [X30] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30)) = X30,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zminus__zminus) ).
fof(f30906,plain,
spl698_595,
inference(avatar_split_clause,[],[f17662,f30904]) ).
fof(f30904,plain,
( spl698_595
<=> ! [X0] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_595])]) ).
fof(f17662,plain,
! [X0] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)) = X0,
inference(cnf_transformation,[],[f5348]) ).
fof(f5348,plain,
! [X0] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)) = X0,
inference(rectify,[],[f1711]) ).
fof(f1711,axiom,
! [X152] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X152)) = X152,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_card__lessThan) ).
fof(f30902,plain,
spl698_594,
inference(avatar_split_clause,[],[f17660,f30900]) ).
fof(f30898,plain,
spl698_593,
inference(avatar_split_clause,[],[f17659,f30896]) ).
fof(f30896,plain,
( spl698_593
<=> ! [X0] : c_List_Olist_ONil(tc_List_Olist(X0)) = c_List_Otranspose(X0,c_List_Olist_ONil(tc_List_Olist(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_593])]) ).
fof(f17659,plain,
! [X0] : c_List_Olist_ONil(tc_List_Olist(X0)) = c_List_Otranspose(X0,c_List_Olist_ONil(tc_List_Olist(X0))),
inference(cnf_transformation,[],[f5345]) ).
fof(f5345,plain,
! [X0] : c_List_Olist_ONil(tc_List_Olist(X0)) = c_List_Otranspose(X0,c_List_Olist_ONil(tc_List_Olist(X0))),
inference(rectify,[],[f3941]) ).
fof(f3941,axiom,
! [X23] : c_List_Olist_ONil(tc_List_Olist(X23)) = c_List_Otranspose(X23,c_List_Olist_ONil(tc_List_Olist(X23))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_transpose_Osimps_I1_J) ).
fof(f30894,plain,
spl698_592,
inference(avatar_split_clause,[],[f17658,f30892]) ).
fof(f30892,plain,
( spl698_592
<=> ! [X0] : c_Int_OBit0(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_592])]) ).
fof(f17658,plain,
! [X0] : c_Int_OBit0(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0),
inference(cnf_transformation,[],[f5344]) ).
fof(f5344,plain,
! [X0] : c_Int_OBit0(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0),
inference(rectify,[],[f2658]) ).
fof(f2658,axiom,
! [X112] : c_Int_OBit0(X112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X112),X112),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Bit0__def) ).
fof(f30890,plain,
spl698_591,
inference(avatar_split_clause,[],[f17657,f30888]) ).
fof(f30888,plain,
( spl698_591
<=> ! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_591])]) ).
fof(f17657,plain,
! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OMin),
inference(cnf_transformation,[],[f5343]) ).
fof(f5343,plain,
! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OMin),
inference(rectify,[],[f2873]) ).
fof(f2873,axiom,
! [X112] : c_Int_Opred(X112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X112),c_Int_OMin),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_add__Min__right) ).
fof(f30886,plain,
spl698_590,
inference(avatar_split_clause,[],[f17656,f30884]) ).
fof(f30884,plain,
( spl698_590
<=> ! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_590])]) ).
fof(f17656,plain,
! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X0),
inference(cnf_transformation,[],[f5342]) ).
fof(f5342,plain,
! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X0),
inference(rectify,[],[f2872]) ).
fof(f2872,axiom,
! [X112] : c_Int_Opred(X112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X112),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_add__Min) ).
fof(f30882,plain,
spl698_589,
inference(avatar_split_clause,[],[f17655,f30880]) ).
fof(f30880,plain,
( spl698_589
<=> ! [X0] : c_Relation_OId(X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_589])]) ).
fof(f17655,plain,
! [X0] : c_Relation_OId(X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Relation_OId(X0)),
inference(cnf_transformation,[],[f5341]) ).
fof(f5341,plain,
! [X0] : c_Relation_OId(X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Relation_OId(X0)),
inference(rectify,[],[f4751]) ).
fof(f4751,axiom,
! [X4] : c_Relation_OId(X4) = hAPP(c_Relation_Oconverse(X4,X4),c_Relation_OId(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_converse__Id) ).
fof(f30878,plain,
spl698_588,
inference(avatar_split_clause,[],[f17654,f30876]) ).
fof(f30876,plain,
( spl698_588
<=> ! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_588])]) ).
fof(f17654,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(cnf_transformation,[],[f5340]) ).
fof(f5340,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(rectify,[],[f2816]) ).
fof(f2816,axiom,
! [X112] : c_Int_Osucc(X112) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X112),c_Int_OMin),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_diff__bin__simps_I2_J) ).
fof(f30874,plain,
( ~ spl698_128
| spl698_587
| ~ spl698_220
| ~ spl698_284 ),
inference(avatar_split_clause,[],[f29636,f29396,f29107,f30871,f28656]) ).
fof(f28656,plain,
( spl698_128
<=> class_Rings_Osemiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_128])]) ).
fof(f30871,plain,
( spl698_587
<=> c_Int_Oiszero(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_587])]) ).
fof(f29107,plain,
( spl698_220
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl698_220])]) ).
fof(f29396,plain,
( spl698_284
<=> ! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_284])]) ).
fof(f29636,plain,
( c_Int_Oiszero(tc_Int_Oint,c_Int_OPls)
| ~ class_Rings_Osemiring__1(tc_Int_Oint)
| ~ spl698_220
| ~ spl698_284 ),
inference(superposition,[],[f29397,f29109]) ).
fof(f29109,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls
| ~ spl698_220 ),
inference(avatar_component_clause,[],[f29107]) ).
fof(f29397,plain,
( ! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) )
| ~ spl698_284 ),
inference(avatar_component_clause,[],[f29396]) ).
fof(f30869,plain,
spl698_586,
inference(avatar_split_clause,[],[f17653,f30867]) ).
fof(f30867,plain,
( spl698_586
<=> ! [X0] : c_Lazy__Sequence_Oyieldn(X0) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(X0),X0,c_Lazy__Sequence_Oyield(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_586])]) ).
fof(f17653,plain,
! [X0] : c_Lazy__Sequence_Oyieldn(X0) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(X0),X0,c_Lazy__Sequence_Oyield(X0)),
inference(cnf_transformation,[],[f5339]) ).
fof(f5339,plain,
! [X0] : c_Lazy__Sequence_Oyieldn(X0) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(X0),X0,c_Lazy__Sequence_Oyield(X0)),
inference(rectify,[],[f4979]) ).
fof(f4979,axiom,
! [X4] : c_Lazy__Sequence_Oyieldn(X4) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(X4),X4,c_Lazy__Sequence_Oyield(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_yieldn__def) ).
fof(f30865,plain,
spl698_585,
inference(avatar_split_clause,[],[f17652,f30863]) ).
fof(f30863,plain,
( spl698_585
<=> ! [X0] : c_Hoare__Mirabelle_OMGT(X0) = c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate,c_fequal,X0,c_Natural_Oevalc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_585])]) ).
fof(f17652,plain,
! [X0] : c_Hoare__Mirabelle_OMGT(X0) = c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate,c_fequal,X0,c_Natural_Oevalc(X0)),
inference(cnf_transformation,[],[f5338]) ).
fof(f5338,plain,
! [X0] : c_Hoare__Mirabelle_OMGT(X0) = c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate,c_fequal,X0,c_Natural_Oevalc(X0)),
inference(rectify,[],[f177]) ).
fof(f177,axiom,
! [X36] : c_Hoare__Mirabelle_OMGT(X36) = c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate,c_fequal,X36,c_Natural_Oevalc(X36)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_MGT__def) ).
fof(f30860,plain,
spl698_584,
inference(avatar_split_clause,[],[f17648,f30858]) ).
fof(f30858,plain,
( spl698_584
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_584])]) ).
fof(f17648,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X0)),
inference(cnf_transformation,[],[f5334]) ).
fof(f5334,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X0)),
inference(rectify,[],[f1305]) ).
fof(f1305,axiom,
! [X88] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X88)),X88)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Suc__n__not__le__n) ).
fof(f30856,plain,
spl698_583,
inference(avatar_split_clause,[],[f17647,f30854]) ).
fof(f30854,plain,
( spl698_583
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_583])]) ).
fof(f17647,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),
inference(cnf_transformation,[],[f5333]) ).
fof(f5333,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),
inference(rectify,[],[f1058]) ).
fof(f1058,axiom,
! [X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) != c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_UNIV__not__empty) ).
fof(f30852,plain,
spl698_582,
inference(avatar_split_clause,[],[f17514,f30849]) ).
fof(f30849,plain,
( spl698_582
<=> c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_582])]) ).
fof(f17514,plain,
c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(cnf_transformation,[],[f4635]) ).
fof(f4635,axiom,
c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_type__definition__code__numeral) ).
fof(f30847,plain,
spl698_581,
inference(avatar_split_clause,[],[f17513,f30844]) ).
fof(f30844,plain,
( spl698_581
<=> c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_581])]) ).
fof(f17513,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(cnf_transformation,[],[f1743]) ).
fof(f1743,axiom,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_inj__int) ).
fof(f30827,plain,
( spl698_580
| ~ spl698_552
| ~ spl698_557 ),
inference(avatar_split_clause,[],[f30677,f30673,f30641,f30824]) ).
fof(f30824,plain,
( spl698_580
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_Osucc(c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_580])]) ).
fof(f30673,plain,
( spl698_557
<=> hBOOL(hAPP(hAPP(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,[spl698_557])]) ).
fof(f30677,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_Osucc(c_Int_OPls)))
| ~ spl698_552
| ~ spl698_557 ),
inference(forward_demodulation,[],[f30675,f30643]) ).
fof(f30675,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl698_557 ),
inference(avatar_component_clause,[],[f30673]) ).
fof(f30822,plain,
( spl698_579
| ~ spl698_552
| ~ spl698_556 ),
inference(avatar_split_clause,[],[f30671,f30667,f30641,f30819]) ).
fof(f30819,plain,
( spl698_579
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_Osucc(c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_579])]) ).
fof(f30667,plain,
( spl698_556
<=> hBOOL(hAPP(hAPP(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,[spl698_556])]) ).
fof(f30671,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_Osucc(c_Int_OPls)))
| ~ spl698_552
| ~ spl698_556 ),
inference(forward_demodulation,[],[f30669,f30643]) ).
fof(f30669,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl698_556 ),
inference(avatar_component_clause,[],[f30667]) ).
fof(f30775,plain,
( spl698_578
| ~ spl698_260
| ~ spl698_439 ),
inference(avatar_split_clause,[],[f30187,f30119,f29287,f30772]) ).
fof(f30772,plain,
( spl698_578
<=> c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olist_ONil(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_578])]) ).
fof(f29287,plain,
( spl698_260
<=> ! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_260])]) ).
fof(f30119,plain,
( spl698_439
<=> ! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_439])]) ).
fof(f30187,plain,
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olist_ONil(tc_Nat_Onat))
| ~ spl698_260
| ~ spl698_439 ),
inference(superposition,[],[f29288,f30120]) ).
fof(f30120,plain,
( ! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_HOL_Obool_Obool__size(c_fTrue))
| ~ spl698_439 ),
inference(avatar_component_clause,[],[f30119]) ).
fof(f29288,plain,
( ! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X0))
| ~ spl698_260 ),
inference(avatar_component_clause,[],[f29287]) ).
fof(f30770,plain,
( ~ spl698_577
| ~ spl698_410
| spl698_447 ),
inference(avatar_split_clause,[],[f30753,f30198,f29985,f30767]) ).
fof(f30767,plain,
( spl698_577
<=> class_Finite__Set_Ofinite(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_577])]) ).
fof(f30198,plain,
( spl698_447
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_447])]) ).
fof(f30753,plain,
( ~ class_Finite__Set_Ofinite(tc_Nat_Onat)
| ~ spl698_410
| spl698_447 ),
inference(resolution,[],[f30200,f29986]) ).
fof(f30200,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| spl698_447 ),
inference(avatar_component_clause,[],[f30198]) ).
fof(f30761,plain,
( spl698_576
| ~ spl698_473 ),
inference(avatar_split_clause,[],[f30324,f30321,f30759]) ).
fof(f30759,plain,
( spl698_576
<=> ! [X0] : c_Wellfounded_Owf(X0,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_576])]) ).
fof(f30321,plain,
( spl698_473
<=> ! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_473])]) ).
fof(f30324,plain,
( ! [X0] : c_Wellfounded_Owf(X0,c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))
| ~ spl698_473 ),
inference(forward_demodulation,[],[f30322,f17736]) ).
fof(f17736,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)) = c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(cnf_transformation,[],[f5422]) ).
fof(f5422,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)) = c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(rectify,[],[f1380]) ).
fof(f1380,axiom,
! [X4] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)) = c_Relation_OId__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Id__on__empty) ).
fof(f30322,plain,
( ! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))
| ~ spl698_473 ),
inference(avatar_component_clause,[],[f30321]) ).
fof(f30752,plain,
( ~ spl698_575
| ~ spl698_410
| spl698_446 ),
inference(avatar_split_clause,[],[f30747,f30193,f29985,f30749]) ).
fof(f30749,plain,
( spl698_575
<=> class_Finite__Set_Ofinite(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_575])]) ).
fof(f30193,plain,
( spl698_446
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_446])]) ).
fof(f30747,plain,
( ~ class_Finite__Set_Ofinite(tc_Int_Oint)
| ~ spl698_410
| spl698_446 ),
inference(resolution,[],[f30195,f29986]) ).
fof(f30195,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool))))
| spl698_446 ),
inference(avatar_component_clause,[],[f30193]) ).
fof(f30746,plain,
spl698_574,
inference(avatar_split_clause,[],[f27421,f30744]) ).
fof(f27421,plain,
! [X2,X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != X2
| sP51(X0,X1,X2) ),
inference(forward_demodulation,[],[f21591,f17447]) ).
fof(f21591,plain,
! [X2,X0,X1] :
( sP51(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f15983]) ).
fof(f15983,plain,
! [X0,X1,X2] :
( ( sP51(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK425(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK425(X0,X1,X2))),sK426(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK426(X0,X1,X2)),X2))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X5))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X2)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP51(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK425,sK426])],[f15981,f15982]) ).
fof(f15982,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)) )
=> ( ~ hBOOL(hAPP(X0,sK425(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK425(X0,X1,X2))),sK426(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK426(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15981,plain,
! [X0,X1,X2] :
( ( sP51(X0,X1,X2)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(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))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X2)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP51(X0,X1,X2) ) ),
inference(rectify,[],[f15980]) ).
fof(f15980,plain,
! [X2,X1,X0] :
( ( sP51(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(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))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP51(X2,X1,X0) ) ),
inference(flattening,[],[f15979]) ).
fof(f15979,plain,
! [X2,X1,X0] :
( ( sP51(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(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))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP51(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14619]) ).
fof(f14619,plain,
! [X2,X1,X0] :
( sP51(X2,X1,X0)
<=> ( ! [X3,X4] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(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,[sP51])]) ).
fof(f30742,plain,
spl698_573,
inference(avatar_split_clause,[],[f27398,f30740]) ).
fof(f27398,plain,
! [X2,X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != X2
| sP46(X0,X1,X2) ),
inference(forward_demodulation,[],[f21513,f17447]) ).
fof(f21513,plain,
! [X2,X0,X1] :
( sP46(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f15928]) ).
fof(f15928,plain,
! [X0,X1,X2] :
( ( sP46(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK416(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK415(X0,X1,X2))),sK416(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK416(X0,X1,X2)),X2))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X2)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP46(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK415,sK416])],[f15926,f15927]) ).
fof(f15927,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)) )
=> ( ~ hBOOL(hAPP(X0,sK416(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK415(X0,X1,X2))),sK416(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK416(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15926,plain,
! [X0,X1,X2] :
( ( sP46(X0,X1,X2)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X2)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP46(X0,X1,X2) ) ),
inference(rectify,[],[f15925]) ).
fof(f15925,plain,
! [X2,X1,X0] :
( ( sP46(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP46(X2,X1,X0) ) ),
inference(flattening,[],[f15924]) ).
fof(f15924,plain,
! [X2,X1,X0] :
( ( sP46(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP46(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14611]) ).
fof(f14611,plain,
! [X2,X1,X0] :
( sP46(X2,X1,X0)
<=> ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(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,[sP46])]) ).
fof(f30738,plain,
spl698_572,
inference(avatar_split_clause,[],[f26743,f30736]) ).
fof(f30736,plain,
( spl698_572
<=> ! [X2,X0,X1] : c_Nat_Onat_Onat__case(X2,X1,X0,c_HOL_Obool_Obool__size(c_fTrue)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_572])]) ).
fof(f26743,plain,
! [X2,X0,X1] : c_Nat_Onat_Onat__case(X2,X1,X0,c_HOL_Obool_Obool__size(c_fTrue)) = X1,
inference(forward_demodulation,[],[f19827,f17447]) ).
fof(f19827,plain,
! [X2,X0,X1] : c_Nat_Onat_Onat__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(cnf_transformation,[],[f6918]) ).
fof(f6918,plain,
! [X0,X1,X2] : c_Nat_Onat_Onat__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rectify,[],[f2893]) ).
fof(f2893,axiom,
! [X67,X25,X4] : c_Nat_Onat_Onat__case(X4,X25,X67,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X25,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__case__0) ).
fof(f30734,plain,
spl698_571,
inference(avatar_split_clause,[],[f25445,f30732]) ).
fof(f30732,plain,
( spl698_571
<=> ! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_List_Olist_Olist__size(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_571])]) ).
fof(f25445,plain,
! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_List_Olist_Olist__size(X1,X0,c_List_Olist_ONil(X1)),
inference(forward_demodulation,[],[f18144,f17447]) ).
fof(f18144,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_List_Olist_Olist__size(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5741]) ).
fof(f5741,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_List_Olist_Olist__size(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f3954]) ).
fof(f3954,axiom,
! [X143,X4] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_List_Olist_Olist__size(X4,X143,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_list_Osize_I1_J) ).
fof(f30730,plain,
spl698_570,
inference(avatar_split_clause,[],[f25444,f30728]) ).
fof(f30728,plain,
( spl698_570
<=> ! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_Option_Ooption_Ooption__size(X1,X0,c_Option_Ooption_ONone(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_570])]) ).
fof(f25444,plain,
! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_Option_Ooption_Ooption__size(X1,X0,c_Option_Ooption_ONone(X1)),
inference(forward_demodulation,[],[f18143,f17447]) ).
fof(f18143,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Option_Ooption_Ooption__size(X1,X0,c_Option_Ooption_ONone(X1)),
inference(cnf_transformation,[],[f5740]) ).
fof(f5740,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Option_Ooption_Ooption__size(X1,X0,c_Option_Ooption_ONone(X1)),
inference(rectify,[],[f1770]) ).
fof(f1770,axiom,
! [X143,X4] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Option_Ooption_Ooption__size(X4,X143,c_Option_Ooption_ONone(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_option_Osize_I1_J) ).
fof(f30726,plain,
spl698_569,
inference(avatar_split_clause,[],[f25132,f30724]) ).
fof(f25132,plain,
! [X0] :
( c_Int_OPls != X0
| c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) ),
inference(forward_demodulation,[],[f25131,f17436]) ).
fof(f25131,plain,
! [X0] :
( c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ),
inference(forward_demodulation,[],[f17819,f17436]) ).
fof(f17819,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ),
inference(cnf_transformation,[],[f10153]) ).
fof(f10153,plain,
! [X0] :
( ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ),
inference(ennf_transformation,[],[f5502]) ).
fof(f5502,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) ) ),
inference(rectify,[],[f3230]) ).
fof(f3230,axiom,
! [X114] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X114
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X114))
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X114) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X114))
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X114) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X114
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X114) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zsgn__def) ).
fof(f30722,plain,
spl698_568,
inference(avatar_split_clause,[],[f25110,f30720]) ).
fof(f30720,plain,
( spl698_568
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_568])]) ).
fof(f25110,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Int_OPls),
inference(forward_demodulation,[],[f17814,f17436]) ).
fof(f17814,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f5500]) ).
fof(f5500,plain,
! [X0] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rectify,[],[f2181]) ).
fof(f2181,axiom,
! [X32] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X32,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X32
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X32),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_DIVISION__BY__ZERO) ).
fof(f30718,plain,
spl698_567,
inference(avatar_split_clause,[],[f25011,f30716]) ).
fof(f30716,plain,
( spl698_567
<=> ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_567])]) ).
fof(f30714,plain,
spl698_566,
inference(avatar_split_clause,[],[f25001,f30712]) ).
fof(f30712,plain,
( spl698_566
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_566])]) ).
fof(f25001,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f25000,f24883]) ).
fof(f25000,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f17684,f17447]) ).
fof(f17684,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f5370]) ).
fof(f5370,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rectify,[],[f2258]) ).
fof(f2258,axiom,
! [X93] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X93,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_mod__1) ).
fof(f30710,plain,
spl698_565,
inference(avatar_split_clause,[],[f24992,f30708]) ).
fof(f30708,plain,
( spl698_565
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OPls),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_565])]) ).
fof(f24992,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OPls),X0),
inference(forward_demodulation,[],[f17677,f17436]) ).
fof(f17677,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0),
inference(cnf_transformation,[],[f5363]) ).
fof(f5363,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0),
inference(rectify,[],[f2013]) ).
fof(f2013,axiom,
! [X33] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zdiv__zero) ).
fof(f30706,plain,
spl698_564,
inference(avatar_split_clause,[],[f24978,f30704]) ).
fof(f30704,plain,
( spl698_564
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_564])]) ).
fof(f24978,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0)),
inference(forward_demodulation,[],[f17641,f17447]) ).
fof(f17641,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),
inference(cnf_transformation,[],[f5327]) ).
fof(f5327,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),
inference(rectify,[],[f1497]) ).
fof(f1497,axiom,
! [X88] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X88)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_less__eq__nat_Osimps_I1_J) ).
fof(f30702,plain,
spl698_563,
inference(avatar_split_clause,[],[f24977,f30700]) ).
fof(f30700,plain,
( spl698_563
<=> ! [X0] : hAPP(c_Code__Numeral_Onat__of,X0) = c_Code__Numeral_Onat__of__aux(X0,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_563])]) ).
fof(f24977,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,X0) = c_Code__Numeral_Onat__of__aux(X0,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17633,f17447]) ).
fof(f17633,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,X0) = c_Code__Numeral_Onat__of__aux(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f5319]) ).
fof(f5319,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,X0) = c_Code__Numeral_Onat__of__aux(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f4647]) ).
fof(f4647,axiom,
! [X114] : hAPP(c_Code__Numeral_Onat__of,X114) = c_Code__Numeral_Onat__of__aux(X114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__of__code) ).
fof(f30698,plain,
spl698_562,
inference(avatar_split_clause,[],[f24976,f30696]) ).
fof(f30696,plain,
( spl698_562
<=> ! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = c_List_Orotate(X0,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_562])]) ).
fof(f24976,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = c_List_Orotate(X0,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17632,f17447]) ).
fof(f17632,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = c_List_Orotate(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f5318]) ).
fof(f5318,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = c_List_Orotate(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f4244]) ).
fof(f4244,axiom,
! [X4] : c_Fun_Oid(tc_List_Olist(X4)) = c_List_Orotate(X4,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rotate0) ).
fof(f30694,plain,
spl698_561,
inference(avatar_split_clause,[],[f24975,f30692]) ).
fof(f30692,plain,
( spl698_561
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_561])]) ).
fof(f24975,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X0)),
inference(forward_demodulation,[],[f17627,f17447]) ).
fof(f17627,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X0)),
inference(cnf_transformation,[],[f5313]) ).
fof(f5313,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X0)),
inference(rectify,[],[f1700]) ).
fof(f1700,axiom,
! [X191] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X191)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_vname_Osize_I4_J) ).
fof(f30690,plain,
spl698_560,
inference(avatar_split_clause,[],[f24974,f30688]) ).
fof(f30688,plain,
( spl698_560
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_560])]) ).
fof(f24974,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X0)),
inference(forward_demodulation,[],[f17626,f17447]) ).
fof(f17626,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X0)),
inference(cnf_transformation,[],[f5312]) ).
fof(f5312,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X0)),
inference(rectify,[],[f1695]) ).
fof(f1695,axiom,
! [X111] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X111)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_vname_Osize_I3_J) ).
fof(f30686,plain,
spl698_559,
inference(avatar_split_clause,[],[f24970,f30684]) ).
fof(f30684,plain,
( spl698_559
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_559])]) ).
fof(f24970,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f17619,f17447]) ).
fof(f17619,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f5305]) ).
fof(f5305,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rectify,[],[f1416]) ).
fof(f1416,axiom,
! [X88] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_less__zeroE) ).
fof(f30682,plain,
spl698_558,
inference(avatar_split_clause,[],[f24916,f30679]) ).
fof(f30679,plain,
( spl698_558
<=> c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_558])]) ).
fof(f24916,plain,
c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls)),
inference(forward_demodulation,[],[f17512,f17436]) ).
fof(f17512,plain,
c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(cnf_transformation,[],[f2532]) ).
fof(f2532,axiom,
c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_transfer__morphism__nat__int) ).
fof(f30676,plain,
spl698_557,
inference(avatar_split_clause,[],[f24914,f30673]) ).
fof(f24914,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f17510,f17436]) ).
fof(f17510,plain,
hBOOL(hAPP(hAPP(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,[],[f1865]) ).
fof(f1865,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(f30670,plain,
spl698_556,
inference(avatar_split_clause,[],[f24913,f30667]) ).
fof(f24913,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f17509,f17436]) ).
fof(f17509,plain,
hBOOL(hAPP(hAPP(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,[],[f1825]) ).
fof(f1825,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_int__0__less__1) ).
fof(f30665,plain,
( spl698_555
| ~ spl698_199
| ~ spl698_552 ),
inference(avatar_split_clause,[],[f30649,f30641,f29011,f30662]) ).
fof(f30662,plain,
( spl698_555
<=> c_Nat__Transfer_Ois__nat(c_Int_Osucc(c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_555])]) ).
fof(f29011,plain,
( spl698_199
<=> c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_199])]) ).
fof(f30649,plain,
( c_Nat__Transfer_Ois__nat(c_Int_Osucc(c_Int_OPls))
| ~ spl698_199
| ~ spl698_552 ),
inference(superposition,[],[f29013,f30643]) ).
fof(f29013,plain,
( c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl698_199 ),
inference(avatar_component_clause,[],[f29011]) ).
fof(f30660,plain,
spl698_554,
inference(avatar_split_clause,[],[f24903,f30657]) ).
fof(f30657,plain,
( spl698_554
<=> hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_554])]) ).
fof(f24903,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17502,f17447]) ).
fof(f17502,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(cnf_transformation,[],[f3046]) ).
fof(f3046,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_code__numeral_Osize_I3_J) ).
fof(f30655,plain,
spl698_553,
inference(avatar_split_clause,[],[f24900,f30652]) ).
fof(f30652,plain,
( spl698_553
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_553])]) ).
fof(f24900,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(c_Int_OPls)),
inference(forward_demodulation,[],[f17499,f17442]) ).
fof(f17499,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f2603]) ).
fof(f2603,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Numeral1__eq1__nat) ).
fof(f30644,plain,
( spl698_552
| ~ spl698_278
| ~ spl698_551 ),
inference(avatar_split_clause,[],[f30639,f30635,f29372,f30641]) ).
fof(f30635,plain,
( spl698_551
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Osucc(c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_551])]) ).
fof(f30639,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_Osucc(c_Int_OPls)
| ~ spl698_278
| ~ spl698_551 ),
inference(forward_demodulation,[],[f30637,f29373]) ).
fof(f30637,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Osucc(c_Int_OPls))
| ~ spl698_551 ),
inference(avatar_component_clause,[],[f30635]) ).
fof(f30638,plain,
spl698_551,
inference(avatar_split_clause,[],[f24899,f30635]) ).
fof(f24899,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Osucc(c_Int_OPls)),
inference(forward_demodulation,[],[f17498,f17442]) ).
fof(f17498,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f2601]) ).
fof(f2601,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_one__is__num__one) ).
fof(f30633,plain,
spl698_550,
inference(avatar_split_clause,[],[f24898,f30630]) ).
fof(f30630,plain,
( spl698_550
<=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_Osucc(c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_550])]) ).
fof(f24898,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_Osucc(c_Int_OPls)),
inference(forward_demodulation,[],[f17495,f17442]) ).
fof(f17495,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f2857]) ).
fof(f2857,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_one__code__numeral__code) ).
fof(f30628,plain,
spl698_549,
inference(avatar_split_clause,[],[f23762,f30626]) ).
fof(f30626,plain,
( spl698_549
<=> ! [X2,X4,X0,X3,X1] :
( sP125(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_549])]) ).
fof(f23762,plain,
! [X2,X3,X0,X1,X4] :
( sP125(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ),
inference(cnf_transformation,[],[f14733]) ).
fof(f14733,plain,
! [X0,X1,X2,X3,X4] :
( sP125(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ),
inference(definition_folding,[],[f13736,f14732,f14731]) ).
fof(f14731,plain,
! [X0,X1,X4,X2,X3] :
( sP124(X0,X1,X4,X2,X3)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X1),X0))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X2),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X1),X3)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X1),X3)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X3),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP124])]) ).
fof(f14732,plain,
! [X3,X2,X4,X1,X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X3,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X1,X0)))
<=> sP124(X0,X1,X4,X2,X3) )
| ~ sP125(X3,X2,X4,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP125])]) ).
fof(f13736,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X3,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X1,X0)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X1),X0))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X2),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X1),X3)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X1),X3)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X3),X2)) ) ) )
| ~ class_Orderings_Oorder(X4) ),
inference(ennf_transformation,[],[f9460]) ).
fof(f9460,plain,
! [X0,X1,X2,X3,X4] :
( class_Orderings_Oorder(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X3,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X1,X0)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X1),X0))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X2),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X1),X3)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X1),X3)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X3),X2)) ) ) ) ),
inference(rectify,[],[f3133]) ).
fof(f3133,axiom,
! [X35,X36,X26,X6,X4] :
( class_Orderings_Oorder(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X6,X26)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X36,X35)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X36),X35))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X35))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),X6)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),X35))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X36),X6)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X26)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_atLeastatMost__psubset__iff) ).
fof(f30624,plain,
spl698_548,
inference(avatar_split_clause,[],[f23403,f30622]) ).
fof(f30622,plain,
( spl698_548
<=> ! [X2,X4,X0,X3,X1] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_548])]) ).
fof(f23403,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3),
inference(cnf_transformation,[],[f9172]) ).
fof(f9172,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3),
inference(rectify,[],[f158]) ).
fof(f158,axiom,
! [X57,X58,X53,X10,X51] : c_Com_Ocom_OWhile(X51,X10) != c_Com_Ocom_OCond(X53,X58,X57),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I53_J) ).
fof(f30620,plain,
spl698_547,
inference(avatar_split_clause,[],[f23401,f30618]) ).
fof(f30618,plain,
( spl698_547
<=> ! [X2,X4,X0,X3,X1] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_547])]) ).
fof(f23401,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3),
inference(cnf_transformation,[],[f9170]) ).
fof(f9170,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3),
inference(rectify,[],[f103]) ).
fof(f103,axiom,
! [X13,X53,X70,X10,X51] : c_Com_Ocom_OWhile(X51,X10) != c_Com_Ocom_OLocal(X70,X53,X13),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I39_J) ).
fof(f30616,plain,
spl698_546,
inference(avatar_split_clause,[],[f23399,f30614]) ).
fof(f30614,plain,
( spl698_546
<=> ! [X4,X0,X3,X2,X1] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OCond(X4,X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_546])]) ).
fof(f23399,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OCond(X4,X3,X2),
inference(cnf_transformation,[],[f9168]) ).
fof(f9168,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OCond(X4,X3,X2),
inference(rectify,[],[f162]) ).
fof(f162,axiom,
! [X53,X54,X55,X56,X51] : c_Com_Ocom_OAss(X54,X53) != c_Com_Ocom_OCond(X51,X56,X55),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I27_J) ).
fof(f30612,plain,
( spl698_545
| ~ spl698_409 ),
inference(avatar_split_clause,[],[f30180,f29981,f30610]) ).
fof(f30610,plain,
( spl698_545
<=> ! [X0] : sP0(X0,c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_545])]) ).
fof(f29981,plain,
( spl698_409
<=> ! [X0,X1] :
( sP0(X0,X1)
| c_List_Olist_ONil(X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_409])]) ).
fof(f30180,plain,
( ! [X0] : sP0(X0,c_List_Olist_ONil(X0))
| ~ spl698_409 ),
inference(equality_resolution,[],[f29982]) ).
fof(f29982,plain,
( ! [X0,X1] :
( c_List_Olist_ONil(X0) != X1
| sP0(X0,X1) )
| ~ spl698_409 ),
inference(avatar_component_clause,[],[f29981]) ).
fof(f30608,plain,
spl698_544,
inference(avatar_split_clause,[],[f23397,f30606]) ).
fof(f30606,plain,
( spl698_544
<=> ! [X2,X4,X0,X3,X1] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OAss(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_544])]) ).
fof(f23397,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OAss(X4,X3),
inference(cnf_transformation,[],[f9166]) ).
fof(f9166,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OAss(X4,X3),
inference(rectify,[],[f105]) ).
fof(f105,axiom,
! [X10,X51,X69,X53,X54] : c_Com_Ocom_OAss(X54,X53) != c_Com_Ocom_OLocal(X69,X51,X10),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I22_J) ).
fof(f30604,plain,
spl698_543,
inference(avatar_split_clause,[],[f23395,f30602]) ).
fof(f30602,plain,
( spl698_543
<=> ! [X2,X4,X0,X3,X1] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OSemi(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_543])]) ).
fof(f23395,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OSemi(X4,X3),
inference(cnf_transformation,[],[f9164]) ).
fof(f9164,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OSemi(X4,X3),
inference(rectify,[],[f163]) ).
fof(f163,axiom,
! [X55,X56,X51,X57,X58] : c_Com_Ocom_OSemi(X58,X57) != c_Com_Ocom_OCond(X51,X56,X55),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I44_J) ).
fof(f30600,plain,
spl698_542,
inference(avatar_split_clause,[],[f23393,f30598]) ).
fof(f30598,plain,
( spl698_542
<=> ! [X4,X0,X3,X2,X1] : c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OLocal(X4,X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_542])]) ).
fof(f23393,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OLocal(X4,X3,X2),
inference(cnf_transformation,[],[f9162]) ).
fof(f9162,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OLocal(X4,X3,X2),
inference(rectify,[],[f106]) ).
fof(f106,axiom,
! [X55,X56,X13,X53,X70] : c_Com_Ocom_OSemi(X56,X55) != c_Com_Ocom_OLocal(X70,X53,X13),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I34_J) ).
fof(f30596,plain,
spl698_541,
inference(avatar_split_clause,[],[f21988,f30594]) ).
fof(f30594,plain,
( spl698_541
<=> ! [X3] : c_List_Olist_ONil(X3) = hAPP(c_List_Orotate1(X3),c_List_Olist_ONil(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_541])]) ).
fof(f21988,plain,
! [X3] : c_List_Olist_ONil(X3) = hAPP(c_List_Orotate1(X3),c_List_Olist_ONil(X3)),
inference(cnf_transformation,[],[f8404]) ).
fof(f8404,plain,
! [X0,X1,X2,X3] :
( hAPP(c_List_Orotate1(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = hAPP(hAPP(c_List_Oappend(X2),X0),hAPP(hAPP(c_List_Olist_OCons(X2),X1),c_List_Olist_ONil(X2)))
& c_List_Olist_ONil(X3) = hAPP(c_List_Orotate1(X3),c_List_Olist_ONil(X3)) ),
inference(rectify,[],[f4108]) ).
fof(f4108,axiom,
! [X263,X22,X4,X23] :
( hAPP(c_List_Orotate1(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X22),X263)) = hAPP(hAPP(c_List_Oappend(X4),X263),hAPP(hAPP(c_List_Olist_OCons(X4),X22),c_List_Olist_ONil(X4)))
& c_List_Olist_ONil(X23) = hAPP(c_List_Orotate1(X23),c_List_Olist_ONil(X23)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rotate__simps) ).
fof(f30592,plain,
spl698_540,
inference(avatar_split_clause,[],[f21673,f30590]) ).
fof(f21673,plain,
! [X2,X0,X1] :
( sP55(X0,X1,X2)
| c_List_Olist_ONil(X1) != X2 ),
inference(cnf_transformation,[],[f16050]) ).
fof(f16050,plain,
! [X0,X1,X2] :
( ( sP55(X0,X1,X2)
| ( ! [X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X0))
| hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4) != X2 )
& c_List_Olist_ONil(X1) != X2 ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),sK440(X0,X1,X2)),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),sK439(X0,X1,X2)),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),sK439(X0,X1,X2)),sK440(X0,X1,X2)) = X2 )
| c_List_Olist_ONil(X1) = X2
| ~ sP55(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK439,sK440])],[f16048,f16049]) ).
fof(f16049,plain,
! [X0,X1,X2] :
( ? [X5,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X6),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),X5),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6) = X2 )
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),sK440(X0,X1,X2)),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),sK439(X0,X1,X2)),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),sK439(X0,X1,X2)),sK440(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f16048,plain,
! [X0,X1,X2] :
( ( sP55(X0,X1,X2)
| ( ! [X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X0))
| hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4) != X2 )
& c_List_Olist_ONil(X1) != X2 ) )
& ( ? [X5,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X6),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),X5),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6) = X2 )
| c_List_Olist_ONil(X1) = X2
| ~ sP55(X0,X1,X2) ) ),
inference(rectify,[],[f16047]) ).
fof(f16047,plain,
! [X0,X2,X1] :
( ( sP55(X0,X2,X1)
| ( ! [X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
| hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) != X1 )
& c_List_Olist_ONil(X2) != X1 ) )
& ( ? [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
& hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) = X1 )
| c_List_Olist_ONil(X2) = X1
| ~ sP55(X0,X2,X1) ) ),
inference(flattening,[],[f16046]) ).
fof(f16046,plain,
! [X0,X2,X1] :
( ( sP55(X0,X2,X1)
| ( ! [X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
| hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) != X1 )
& c_List_Olist_ONil(X2) != X1 ) )
& ( ? [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
& hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) = X1 )
| c_List_Olist_ONil(X2) = X1
| ~ sP55(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f14627]) ).
fof(f14627,plain,
! [X0,X2,X1] :
( sP55(X0,X2,X1)
<=> ( ? [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
& hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) = X1 )
| c_List_Olist_ONil(X2) = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP55])]) ).
fof(f30588,plain,
spl698_539,
inference(avatar_split_clause,[],[f21573,f30586]) ).
fof(f30586,plain,
( spl698_539
<=> ! [X2,X0,X1] :
( sP49(X2,X1,X0)
| ~ sP50(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_539])]) ).
fof(f21573,plain,
! [X2,X0,X1] :
( sP49(X2,X1,X0)
| ~ sP50(X0,X1,X2) ),
inference(cnf_transformation,[],[f15965]) ).
fof(f15965,plain,
! [X0,X1,X2] :
( ( sP50(X0,X1,X2)
| ~ sP49(X2,X1,X0)
| ~ sP48(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP49(X2,X1,X0)
& sP48(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP50(X0,X1,X2) ) ),
inference(flattening,[],[f15964]) ).
fof(f15964,plain,
! [X0,X1,X2] :
( ( sP50(X0,X1,X2)
| ~ sP49(X2,X1,X0)
| ~ sP48(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP49(X2,X1,X0)
& sP48(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP50(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14617]) ).
fof(f14617,plain,
! [X0,X1,X2] :
( sP50(X0,X1,X2)
<=> ( sP49(X2,X1,X0)
& sP48(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,[sP50])]) ).
fof(f30584,plain,
spl698_538,
inference(avatar_split_clause,[],[f21572,f30582]) ).
fof(f30582,plain,
( spl698_538
<=> ! [X2,X0,X1] :
( sP48(X2,X1,X0)
| ~ sP50(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_538])]) ).
fof(f21572,plain,
! [X2,X0,X1] :
( sP48(X2,X1,X0)
| ~ sP50(X0,X1,X2) ),
inference(cnf_transformation,[],[f15965]) ).
fof(f30580,plain,
spl698_537,
inference(avatar_split_clause,[],[f21495,f30578]) ).
fof(f30578,plain,
( spl698_537
<=> ! [X2,X0,X1] :
( sP44(X2,X1,X0)
| ~ sP45(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_537])]) ).
fof(f21495,plain,
! [X2,X0,X1] :
( sP44(X2,X1,X0)
| ~ sP45(X0,X1,X2) ),
inference(cnf_transformation,[],[f15912]) ).
fof(f15912,plain,
! [X0,X1,X2] :
( ( sP45(X0,X1,X2)
| ~ sP44(X2,X1,X0)
| ~ sP43(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP44(X2,X1,X0)
& sP43(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP45(X0,X1,X2) ) ),
inference(flattening,[],[f15911]) ).
fof(f15911,plain,
! [X0,X1,X2] :
( ( sP45(X0,X1,X2)
| ~ sP44(X2,X1,X0)
| ~ sP43(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP44(X2,X1,X0)
& sP43(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP45(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14609]) ).
fof(f14609,plain,
! [X0,X1,X2] :
( sP45(X0,X1,X2)
<=> ( sP44(X2,X1,X0)
& sP43(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP45])]) ).
fof(f30576,plain,
spl698_536,
inference(avatar_split_clause,[],[f21494,f30574]) ).
fof(f30574,plain,
( spl698_536
<=> ! [X2,X0,X1] :
( sP43(X2,X1,X0)
| ~ sP45(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_536])]) ).
fof(f21494,plain,
! [X2,X0,X1] :
( sP43(X2,X1,X0)
| ~ sP45(X0,X1,X2) ),
inference(cnf_transformation,[],[f15912]) ).
fof(f30572,plain,
spl698_535,
inference(avatar_split_clause,[],[f21452,f30570]) ).
fof(f30570,plain,
( spl698_535
<=> ! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP40(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_535])]) ).
fof(f21452,plain,
! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP40(X0,X2,X1) ),
inference(cnf_transformation,[],[f15875]) ).
fof(f15875,plain,
! [X0,X1,X2] :
( ( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP40(X0,X2,X1) )
& ( sP40(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14603]) ).
fof(f14603,plain,
! [X0,X1,X2] :
( c_Relation_Orefl__on(X2,X1,X0)
<=> sP40(X0,X2,X1) ),
inference(definition_folding,[],[f12434,f14602]) ).
fof(f14602,plain,
! [X0,X2,X1] :
( sP40(X0,X2,X1)
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X3)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) )
& ! [X4] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X2),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1)))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X4),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP40])]) ).
fof(f12434,plain,
! [X0,X1,X2] :
( c_Relation_Orefl__on(X2,X1,X0)
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X3)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) )
& ! [X4] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X2),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1)))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X4),X0)) ) ) ),
inference(ennf_transformation,[],[f8112]) ).
fof(f8112,plain,
! [X0,X1,X2] :
( c_Relation_Orefl__on(X2,X1,X0)
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X3)),X0)) )
& ! [X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X4),X0))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X2),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1)))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1))),X4)) ) ) ),
inference(rectify,[],[f3586]) ).
fof(f3586,axiom,
! [X60,X19,X4] :
( c_Relation_Orefl__on(X4,X19,X60)
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),X19))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X2)),X60)) )
& ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X2),X60))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X19)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X19))),X2)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_refl__on__def_H) ).
fof(f30568,plain,
spl698_534,
inference(avatar_split_clause,[],[f21451,f30566]) ).
fof(f30566,plain,
( spl698_534
<=> ! [X2,X0,X1] :
( sP40(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_534])]) ).
fof(f21451,plain,
! [X2,X0,X1] :
( sP40(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f15875]) ).
fof(f30564,plain,
spl698_533,
inference(avatar_split_clause,[],[f21415,f30562]) ).
fof(f30562,plain,
( spl698_533
<=> ! [X2,X0,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| ~ sP39(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_533])]) ).
fof(f21415,plain,
! [X2,X0,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| ~ sP39(X1,X0,X2) ),
inference(cnf_transformation,[],[f15833]) ).
fof(f15833,plain,
! [X0,X1,X2] :
( ( c_List_Olist__ex1(X2,X1,X0)
| ~ sP39(X1,X0,X2) )
& ( sP39(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14601]) ).
fof(f14601,plain,
! [X0,X1,X2] :
( c_List_Olist__ex1(X2,X1,X0)
<=> sP39(X1,X0,X2) ),
inference(definition_folding,[],[f12426,f14600]) ).
fof(f14600,plain,
! [X1,X0,X2] :
( sP39(X1,X0,X2)
<=> ? [X3] :
( ! [X4] :
( X3 = X4
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
& hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP39])]) ).
fof(f12426,plain,
! [X0,X1,X2] :
( c_List_Olist__ex1(X2,X1,X0)
<=> ? [X3] :
( ! [X4] :
( X3 = X4
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
& hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
inference(flattening,[],[f12425]) ).
fof(f12425,plain,
! [X0,X1,X2] :
( c_List_Olist__ex1(X2,X1,X0)
<=> ? [X3] :
( ! [X4] :
( X3 = X4
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
& hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
inference(ennf_transformation,[],[f8103]) ).
fof(f8103,plain,
! [X0,X1,X2] :
( c_List_Olist__ex1(X2,X1,X0)
<=> ? [X3] :
( ! [X4] :
( ( hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
=> X3 = X4 )
& hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
inference(rectify,[],[f4933]) ).
fof(f4933,axiom,
! [X258,X5,X4] :
( c_List_Olist__ex1(X4,X5,X258)
<=> ? [X2] :
( ! [X115] :
( ( hBOOL(hAPP(X5,X115))
& hBOOL(hAPP(hAPP(c_member(X4),X115),hAPP(c_List_Oset(X4),X258))) )
=> X2 = X115 )
& hBOOL(hAPP(X5,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X258))) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_list__ex1__iff) ).
fof(f30560,plain,
spl698_532,
inference(avatar_split_clause,[],[f21414,f30558]) ).
fof(f30558,plain,
( spl698_532
<=> ! [X2,X0,X1] :
( sP39(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_532])]) ).
fof(f21414,plain,
! [X2,X0,X1] :
( sP39(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ),
inference(cnf_transformation,[],[f15833]) ).
fof(f30556,plain,
spl698_531,
inference(avatar_split_clause,[],[f21407,f30554]) ).
fof(f30554,plain,
( spl698_531
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0)
| ~ sP38(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_531])]) ).
fof(f21407,plain,
! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0)
| ~ sP38(X2,X0,X1) ),
inference(cnf_transformation,[],[f15827]) ).
fof(f15827,plain,
! [X0,X1,X2] :
( ( c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0)
| ~ sP38(X2,X0,X1) )
& ( sP38(X2,X0,X1)
| ~ c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14599]) ).
fof(f14599,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0)
<=> sP38(X2,X0,X1) ),
inference(definition_folding,[],[f12424,f14598]) ).
fof(f14598,plain,
! [X2,X0,X1] :
( sP38(X2,X0,X1)
<=> ! [X3] :
( ! [X5] :
( c_Hoare__Mirabelle_Otriple__valid(X2,X3,X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X2)),X5),X0)) )
| ? [X4] :
( ~ c_Hoare__Mirabelle_Otriple__valid(X2,X3,X4)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X2)),X4),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP38])]) ).
fof(f12424,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0)
<=> ! [X3] :
( ! [X5] :
( c_Hoare__Mirabelle_Otriple__valid(X2,X3,X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X2)),X5),X0)) )
| ? [X4] :
( ~ c_Hoare__Mirabelle_Otriple__valid(X2,X3,X4)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X2)),X4),X1)) ) ) ),
inference(ennf_transformation,[],[f8102]) ).
fof(f8102,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0)
<=> ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X2)),X4),X1))
=> c_Hoare__Mirabelle_Otriple__valid(X2,X3,X4) )
=> ! [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X2)),X5),X0))
=> c_Hoare__Mirabelle_Otriple__valid(X2,X3,X5) ) ) ),
inference(rectify,[],[f3596]) ).
fof(f3596,axiom,
! [X15,X3,X4] :
( c_Hoare__Mirabelle_Ohoare__valids(X4,X3,X15)
<=> ! [X94] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X4)),X2),X3))
=> c_Hoare__Mirabelle_Otriple__valid(X4,X94,X2) )
=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X4)),X2),X15))
=> c_Hoare__Mirabelle_Otriple__valid(X4,X94,X2) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_hoare__valids__def) ).
fof(f30552,plain,
spl698_530,
inference(avatar_split_clause,[],[f21406,f30550]) ).
fof(f30550,plain,
( spl698_530
<=> ! [X2,X0,X1] :
( sP38(X2,X0,X1)
| ~ c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_530])]) ).
fof(f21406,plain,
! [X2,X0,X1] :
( sP38(X2,X0,X1)
| ~ c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0) ),
inference(cnf_transformation,[],[f15827]) ).
fof(f30548,plain,
spl698_529,
inference(avatar_split_clause,[],[f21013,f30546]) ).
fof(f30546,plain,
( spl698_529
<=> ! [X2,X0,X1] :
( X0 = X2
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_529])]) ).
fof(f21013,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X2,X1,X0) ),
inference(cnf_transformation,[],[f12081]) ).
fof(f12081,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X2,X1,X0) ),
inference(ennf_transformation,[],[f7848]) ).
fof(f7848,plain,
! [X0,X1,X2] :
( c_Natural_Oevaln(c_Com_Ocom_OSKIP,X2,X1,X0)
=> X0 = X2 ),
inference(rectify,[],[f132]) ).
fof(f132,axiom,
! [X91,X88,X92] :
( c_Natural_Oevaln(c_Com_Ocom_OSKIP,X92,X88,X91)
=> X91 = X92 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_evaln__elim__cases_I1_J) ).
fof(f30544,plain,
spl698_528,
inference(avatar_split_clause,[],[f19828,f30542]) ).
fof(f30542,plain,
( spl698_528
<=> ! [X2,X0,X1] : c_Fun_Oinj__on(X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_528])]) ).
fof(f19828,plain,
! [X2,X0,X1] : c_Fun_Oinj__on(X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(cnf_transformation,[],[f6919]) ).
fof(f6919,plain,
! [X0,X1,X2] : c_Fun_Oinj__on(X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(rectify,[],[f601]) ).
fof(f601,axiom,
! [X1,X24,X4] : c_Fun_Oinj__on(X4,X24,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_inj__on__empty) ).
fof(f30540,plain,
spl698_527,
inference(avatar_split_clause,[],[f19826,f30538]) ).
fof(f30538,plain,
( spl698_527
<=> ! [X2,X0,X1] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_527])]) ).
fof(f19826,plain,
! [X2,X0,X1] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X1,
inference(cnf_transformation,[],[f6917]) ).
fof(f6917,plain,
! [X0,X1,X2] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X1,
inference(rectify,[],[f3296]) ).
fof(f3296,axiom,
! [X67,X25,X4] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X4,X25,X67,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X25,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_code__numeral_Osimps_I4_J) ).
fof(f30536,plain,
spl698_526,
inference(avatar_split_clause,[],[f19824,f30534]) ).
fof(f30534,plain,
( spl698_526
<=> ! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2) != X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_526])]) ).
fof(f19824,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2) != X2,
inference(cnf_transformation,[],[f6915]) ).
fof(f6915,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2) != X2,
inference(rectify,[],[f3623]) ).
fof(f3623,axiom,
! [X22,X23,X263] : hAPP(hAPP(c_List_Olist_OCons(X23),X22),X263) != X263,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_not__Cons__self) ).
fof(f30532,plain,
spl698_525,
inference(avatar_split_clause,[],[f19438,f30530]) ).
fof(f30530,plain,
( spl698_525
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_525])]) ).
fof(f19438,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f15129]) ).
fof(f15129,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onat,X1) = X0
| ~ sP6(X0,X1) )
& ( sP6(X0,X1)
| hAPP(c_Int_Onat,X1) != X0 ) ),
inference(nnf_transformation,[],[f14547]) ).
fof(f14547,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
<=> sP6(X0,X1) ),
inference(definition_folding,[],[f11103,f14546]) ).
fof(f14546,plain,
! [X0,X1] :
( sP6(X0,X1)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f11103,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ) ),
inference(ennf_transformation,[],[f6764]) ).
fof(f6764,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1 ) ) ),
inference(rectify,[],[f2497]) ).
fof(f2497,axiom,
! [X123,X180] :
( hAPP(c_Int_Onat,X180) = X123
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X180))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X123 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X180))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X123) = X180 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__eq__iff) ).
fof(f30528,plain,
spl698_524,
inference(avatar_split_clause,[],[f19437,f30526]) ).
fof(f19437,plain,
! [X0,X1] :
( sP6(X0,X1)
| hAPP(c_Int_Onat,X1) != X0 ),
inference(cnf_transformation,[],[f15129]) ).
fof(f30524,plain,
spl698_523,
inference(avatar_split_clause,[],[f19430,f30522]) ).
fof(f30522,plain,
( spl698_523
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| ~ sP5(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_523])]) ).
fof(f19430,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| ~ sP5(X1,X0) ),
inference(cnf_transformation,[],[f15126]) ).
fof(f15126,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onat,X0) = X1
| ~ sP5(X1,X0) )
& ( sP5(X1,X0)
| hAPP(c_Int_Onat,X0) != X1 ) ),
inference(nnf_transformation,[],[f14545]) ).
fof(f14545,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
<=> sP5(X1,X0) ),
inference(definition_folding,[],[f11102,f14544]) ).
fof(f14544,plain,
! [X1,X0] :
( sP5(X1,X0)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f11102,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ) ),
inference(ennf_transformation,[],[f6763]) ).
fof(f6763,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0 ) ) ),
inference(rectify,[],[f2496]) ).
fof(f2496,axiom,
! [X180,X123] :
( hAPP(c_Int_Onat,X180) = X123
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X180))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X123 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X180))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X123) = X180 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__eq__iff2) ).
fof(f30520,plain,
spl698_522,
inference(avatar_split_clause,[],[f19429,f30518]) ).
fof(f19429,plain,
! [X0,X1] :
( sP5(X1,X0)
| hAPP(c_Int_Onat,X0) != X1 ),
inference(cnf_transformation,[],[f15126]) ).
fof(f30516,plain,
spl698_521,
inference(avatar_split_clause,[],[f19422,f30514]) ).
fof(f30514,plain,
( spl698_521
<=> ! [X0,X1] :
( c_Int_OBit1(X0) = c_Int_OBit1(X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_521])]) ).
fof(f19422,plain,
! [X0,X1] :
( c_Int_OBit1(X0) = c_Int_OBit1(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f15122]) ).
fof(f15122,plain,
! [X0,X1] :
( ( c_Int_OBit1(X0) = c_Int_OBit1(X1)
| X0 != X1 )
& ( X0 = X1
| c_Int_OBit1(X0) != c_Int_OBit1(X1) ) ),
inference(nnf_transformation,[],[f6762]) ).
fof(f6762,plain,
! [X0,X1] :
( c_Int_OBit1(X0) = c_Int_OBit1(X1)
<=> X0 = X1 ),
inference(rectify,[],[f2429]) ).
fof(f2429,axiom,
! [X153,X59] :
( c_Int_OBit1(X59) = c_Int_OBit1(X153)
<=> X59 = X153 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rel__simps_I51_J) ).
fof(f30512,plain,
spl698_520,
inference(avatar_split_clause,[],[f19421,f30510]) ).
fof(f30510,plain,
( spl698_520
<=> ! [X0,X1] :
( X0 = X1
| c_Int_OBit1(X0) != c_Int_OBit1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_520])]) ).
fof(f19421,plain,
! [X0,X1] :
( X0 = X1
| c_Int_OBit1(X0) != c_Int_OBit1(X1) ),
inference(cnf_transformation,[],[f15122]) ).
fof(f30508,plain,
spl698_519,
inference(avatar_split_clause,[],[f19420,f30506]) ).
fof(f30506,plain,
( spl698_519
<=> ! [X0,X1] :
( c_Int_OBit0(X0) = c_Int_OBit0(X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_519])]) ).
fof(f19420,plain,
! [X0,X1] :
( c_Int_OBit0(X0) = c_Int_OBit0(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f15121]) ).
fof(f15121,plain,
! [X0,X1] :
( ( c_Int_OBit0(X0) = c_Int_OBit0(X1)
| X0 != X1 )
& ( X0 = X1
| c_Int_OBit0(X0) != c_Int_OBit0(X1) ) ),
inference(nnf_transformation,[],[f6761]) ).
fof(f6761,plain,
! [X0,X1] :
( c_Int_OBit0(X0) = c_Int_OBit0(X1)
<=> X0 = X1 ),
inference(rectify,[],[f2659]) ).
fof(f2659,axiom,
! [X153,X59] :
( c_Int_OBit0(X59) = c_Int_OBit0(X153)
<=> X59 = X153 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rel__simps_I48_J) ).
fof(f30504,plain,
spl698_518,
inference(avatar_split_clause,[],[f19419,f30502]) ).
fof(f30502,plain,
( spl698_518
<=> ! [X0,X1] :
( X0 = X1
| c_Int_OBit0(X0) != c_Int_OBit0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_518])]) ).
fof(f19419,plain,
! [X0,X1] :
( X0 = X1
| c_Int_OBit0(X0) != c_Int_OBit0(X1) ),
inference(cnf_transformation,[],[f15121]) ).
fof(f30500,plain,
spl698_517,
inference(avatar_split_clause,[],[f19418,f30498]) ).
fof(f30498,plain,
( spl698_517
<=> ! [X0,X1] :
( c_Com_Ovname_OLoc(X0) = c_Com_Ovname_OLoc(X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_517])]) ).
fof(f19418,plain,
! [X0,X1] :
( c_Com_Ovname_OLoc(X0) = c_Com_Ovname_OLoc(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f15120]) ).
fof(f15120,plain,
! [X0,X1] :
( ( c_Com_Ovname_OLoc(X0) = c_Com_Ovname_OLoc(X1)
| X0 != X1 )
& ( X0 = X1
| c_Com_Ovname_OLoc(X0) != c_Com_Ovname_OLoc(X1) ) ),
inference(nnf_transformation,[],[f6760]) ).
fof(f6760,plain,
! [X0,X1] :
( c_Com_Ovname_OLoc(X0) = c_Com_Ovname_OLoc(X1)
<=> X0 = X1 ),
inference(rectify,[],[f94]) ).
fof(f94,axiom,
! [X69,X70] :
( c_Com_Ovname_OLoc(X70) = c_Com_Ovname_OLoc(X69)
<=> X69 = X70 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_vname_Osimps_I2_J) ).
fof(f30496,plain,
spl698_516,
inference(avatar_split_clause,[],[f19417,f30494]) ).
fof(f30494,plain,
( spl698_516
<=> ! [X0,X1] :
( X0 = X1
| c_Com_Ovname_OLoc(X0) != c_Com_Ovname_OLoc(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_516])]) ).
fof(f19417,plain,
! [X0,X1] :
( X0 = X1
| c_Com_Ovname_OLoc(X0) != c_Com_Ovname_OLoc(X1) ),
inference(cnf_transformation,[],[f15120]) ).
fof(f30492,plain,
spl698_515,
inference(avatar_split_clause,[],[f19416,f30490]) ).
fof(f30490,plain,
( spl698_515
<=> ! [X0,X1] :
( c_Code__Numeral_OSuc__code__numeral(X0) = c_Code__Numeral_OSuc__code__numeral(X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_515])]) ).
fof(f19416,plain,
! [X0,X1] :
( c_Code__Numeral_OSuc__code__numeral(X0) = c_Code__Numeral_OSuc__code__numeral(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f15119]) ).
fof(f15119,plain,
! [X0,X1] :
( ( c_Code__Numeral_OSuc__code__numeral(X0) = c_Code__Numeral_OSuc__code__numeral(X1)
| X0 != X1 )
& ( X0 = X1
| c_Code__Numeral_OSuc__code__numeral(X0) != c_Code__Numeral_OSuc__code__numeral(X1) ) ),
inference(nnf_transformation,[],[f6759]) ).
fof(f6759,plain,
! [X0,X1] :
( c_Code__Numeral_OSuc__code__numeral(X0) = c_Code__Numeral_OSuc__code__numeral(X1)
<=> X0 = X1 ),
inference(rectify,[],[f3031]) ).
fof(f3031,axiom,
! [X237,X238] :
( c_Code__Numeral_OSuc__code__numeral(X238) = c_Code__Numeral_OSuc__code__numeral(X237)
<=> X237 = X238 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_code__numeral_Oinject) ).
fof(f30488,plain,
spl698_514,
inference(avatar_split_clause,[],[f19415,f30486]) ).
fof(f30486,plain,
( spl698_514
<=> ! [X0,X1] :
( X0 = X1
| c_Code__Numeral_OSuc__code__numeral(X0) != c_Code__Numeral_OSuc__code__numeral(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_514])]) ).
fof(f19415,plain,
! [X0,X1] :
( X0 = X1
| c_Code__Numeral_OSuc__code__numeral(X0) != c_Code__Numeral_OSuc__code__numeral(X1) ),
inference(cnf_transformation,[],[f15119]) ).
fof(f30484,plain,
spl698_513,
inference(avatar_split_clause,[],[f19414,f30482]) ).
fof(f30482,plain,
( spl698_513
<=> ! [X0,X1] :
( c_Com_Ovname_OGlb(X0) = c_Com_Ovname_OGlb(X1)
| X0 != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_513])]) ).
fof(f19414,plain,
! [X0,X1] :
( c_Com_Ovname_OGlb(X0) = c_Com_Ovname_OGlb(X1)
| X0 != X1 ),
inference(cnf_transformation,[],[f15118]) ).
fof(f15118,plain,
! [X0,X1] :
( ( c_Com_Ovname_OGlb(X0) = c_Com_Ovname_OGlb(X1)
| X0 != X1 )
& ( X0 = X1
| c_Com_Ovname_OGlb(X0) != c_Com_Ovname_OGlb(X1) ) ),
inference(nnf_transformation,[],[f6758]) ).
fof(f6758,plain,
! [X0,X1] :
( c_Com_Ovname_OGlb(X0) = c_Com_Ovname_OGlb(X1)
<=> X0 = X1 ),
inference(rectify,[],[f188]) ).
fof(f188,axiom,
! [X109,X103] :
( c_Com_Ovname_OGlb(X103) = c_Com_Ovname_OGlb(X109)
<=> X103 = X109 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_vname_Osimps_I1_J) ).
fof(f30480,plain,
spl698_512,
inference(avatar_split_clause,[],[f19413,f30478]) ).
fof(f30478,plain,
( spl698_512
<=> ! [X0,X1] :
( X0 = X1
| c_Com_Ovname_OGlb(X0) != c_Com_Ovname_OGlb(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_512])]) ).
fof(f19413,plain,
! [X0,X1] :
( X0 = X1
| c_Com_Ovname_OGlb(X0) != c_Com_Ovname_OGlb(X1) ),
inference(cnf_transformation,[],[f15118]) ).
fof(f30476,plain,
( ~ spl698_510
| spl698_511 ),
inference(avatar_split_clause,[],[f19378,f30474,f30470]) ).
fof(f30470,plain,
( spl698_510
<=> c_Nitpick_Ounknown(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_510])]) ).
fof(f30474,plain,
( spl698_511
<=> ! [X0,X1] :
( c_Nitpick_Owf_H(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_511])]) ).
fof(f19378,plain,
! [X0,X1] :
( c_Nitpick_Owf_H(X1,X0)
| ~ c_Nitpick_Ounknown(tc_HOL_Obool)
| ~ c_Wellfounded_Oacyclic(X1,X0) ),
inference(cnf_transformation,[],[f15071]) ).
fof(f15071,plain,
! [X0,X1] :
( ( c_Nitpick_Owf_H(X1,X0)
| ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X0)) )
| ~ c_Wellfounded_Oacyclic(X1,X0) )
& ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X0)) )
& c_Wellfounded_Oacyclic(X1,X0) )
| ~ c_Nitpick_Owf_H(X1,X0) ) ),
inference(flattening,[],[f15070]) ).
fof(f15070,plain,
! [X0,X1] :
( ( c_Nitpick_Owf_H(X1,X0)
| ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
& ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X0)) )
| ~ c_Wellfounded_Oacyclic(X1,X0) )
& ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X0)) )
& c_Wellfounded_Oacyclic(X1,X0) )
| ~ c_Nitpick_Owf_H(X1,X0) ) ),
inference(nnf_transformation,[],[f6744]) ).
fof(f6744,plain,
! [X0,X1] :
( c_Nitpick_Owf_H(X1,X0)
<=> ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X0)) )
& c_Wellfounded_Oacyclic(X1,X0) ) ),
inference(rectify,[],[f3582]) ).
fof(f3582,axiom,
! [X60,X4] :
( c_Nitpick_Owf_H(X4,X60)
<=> ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
| hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X4)),X60)) )
& c_Wellfounded_Oacyclic(X4,X60) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Nitpick_Owf_H__def) ).
fof(f30468,plain,
spl698_509,
inference(avatar_split_clause,[],[f19348,f30466]) ).
fof(f30466,plain,
( spl698_509
<=> ! [X0,X1] :
( class_HOL_Oequal(tc_fun(X1,X0))
| ~ class_HOL_Oequal(X0)
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_509])]) ).
fof(f19348,plain,
! [X0,X1] :
( class_HOL_Oequal(tc_fun(X1,X0))
| ~ class_HOL_Oequal(X0)
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f11087]) ).
fof(f11087,plain,
! [X0,X1] :
( class_HOL_Oequal(tc_fun(X1,X0))
| ~ class_HOL_Oequal(X0)
| ~ class_Enum_Oenum(X1) ),
inference(flattening,[],[f11086]) ).
fof(f11086,plain,
! [X0,X1] :
( class_HOL_Oequal(tc_fun(X1,X0))
| ~ class_HOL_Oequal(X0)
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6730]) ).
fof(f6730,plain,
! [X0,X1] :
( ( class_HOL_Oequal(X0)
& class_Enum_Oenum(X1) )
=> class_HOL_Oequal(tc_fun(X1,X0)) ),
inference(rectify,[],[f5006]) ).
fof(f5006,axiom,
! [X324,X323] :
( ( class_HOL_Oequal(X324)
& class_Enum_Oenum(X323) )
=> class_HOL_Oequal(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__HOL_Oequal) ).
fof(f30464,plain,
spl698_508,
inference(avatar_split_clause,[],[f19344,f30462]) ).
fof(f30462,plain,
( spl698_508
<=> ! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_508])]) ).
fof(f19344,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f11079]) ).
fof(f11079,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(flattening,[],[f11078]) ).
fof(f11078,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6726]) ).
fof(f6726,plain,
! [X0,X1] :
( ( class_Enum_Oenum(X0)
& class_Enum_Oenum(X1) )
=> class_Enum_Oenum(tc_fun(X1,X0)) ),
inference(rectify,[],[f5007]) ).
fof(f5007,axiom,
! [X324,X323] :
( ( class_Enum_Oenum(X324)
& class_Enum_Oenum(X323) )
=> class_Enum_Oenum(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Enum_Oenum) ).
fof(f30460,plain,
spl698_507,
inference(avatar_split_clause,[],[f19343,f30458]) ).
fof(f30458,plain,
( spl698_507
<=> ! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_507])]) ).
fof(f19343,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f11077]) ).
fof(f11077,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(flattening,[],[f11076]) ).
fof(f11076,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6725]) ).
fof(f6725,plain,
! [X0,X1] :
( ( class_Enum_Oenum(X0)
& class_Enum_Oenum(X1) )
=> class_Enum_Oenum(tc_prod(X1,X0)) ),
inference(rectify,[],[f5166]) ).
fof(f5166,axiom,
! [X324,X323] :
( ( class_Enum_Oenum(X324)
& class_Enum_Oenum(X323) )
=> class_Enum_Oenum(tc_prod(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_prod__Enum_Oenum) ).
fof(f30456,plain,
spl698_506,
inference(avatar_split_clause,[],[f19342,f30454]) ).
fof(f30454,plain,
( spl698_506
<=> ! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_506])]) ).
fof(f19342,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f11075]) ).
fof(f11075,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(flattening,[],[f11074]) ).
fof(f11074,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6724]) ).
fof(f6724,plain,
! [X0,X1] :
( ( class_Enum_Oenum(X0)
& class_Enum_Oenum(X1) )
=> class_Enum_Oenum(tc_sum(X1,X0)) ),
inference(rectify,[],[f5157]) ).
fof(f5157,axiom,
! [X324,X323] :
( ( class_Enum_Oenum(X324)
& class_Enum_Oenum(X323) )
=> class_Enum_Oenum(tc_sum(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_sum__Enum_Oenum) ).
fof(f30452,plain,
spl698_505,
inference(avatar_split_clause,[],[f19341,f30450]) ).
fof(f30450,plain,
( spl698_505
<=> ! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_505])]) ).
fof(f19341,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11073]) ).
fof(f11073,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11072]) ).
fof(f11072,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6723]) ).
fof(f6723,plain,
! [X0,X1] :
( ( class_Finite__Set_Ofinite(X0)
& class_Finite__Set_Ofinite(X1) )
=> class_Finite__Set_Ofinite(tc_fun(X1,X0)) ),
inference(rectify,[],[f4998]) ).
fof(f4998,axiom,
! [X324,X323] :
( ( class_Finite__Set_Ofinite(X324)
& class_Finite__Set_Ofinite(X323) )
=> class_Finite__Set_Ofinite(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Finite__Set_Ofinite) ).
fof(f30448,plain,
spl698_504,
inference(avatar_split_clause,[],[f19340,f30446]) ).
fof(f30446,plain,
( spl698_504
<=> ! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_504])]) ).
fof(f19340,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11071]) ).
fof(f11071,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11070]) ).
fof(f11070,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6722]) ).
fof(f6722,plain,
! [X0,X1] :
( ( class_Finite__Set_Ofinite(X0)
& class_Finite__Set_Ofinite(X1) )
=> class_Finite__Set_Ofinite(tc_prod(X1,X0)) ),
inference(rectify,[],[f5163]) ).
fof(f5163,axiom,
! [X324,X323] :
( ( class_Finite__Set_Ofinite(X324)
& class_Finite__Set_Ofinite(X323) )
=> class_Finite__Set_Ofinite(tc_prod(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_prod__Finite__Set_Ofinite) ).
fof(f30444,plain,
spl698_503,
inference(avatar_split_clause,[],[f19339,f30442]) ).
fof(f30442,plain,
( spl698_503
<=> ! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_503])]) ).
fof(f19339,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11069]) ).
fof(f11069,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11068]) ).
fof(f11068,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6721]) ).
fof(f6721,plain,
! [X0,X1] :
( ( class_Finite__Set_Ofinite(X0)
& class_Finite__Set_Ofinite(X1) )
=> class_Finite__Set_Ofinite(tc_sum(X1,X0)) ),
inference(rectify,[],[f5155]) ).
fof(f5155,axiom,
! [X324,X323] :
( ( class_Finite__Set_Ofinite(X324)
& class_Finite__Set_Ofinite(X323) )
=> class_Finite__Set_Ofinite(tc_sum(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_sum__Finite__Set_Ofinite) ).
fof(f30440,plain,
spl698_502,
inference(avatar_split_clause,[],[f19334,f30438]) ).
fof(f30438,plain,
( spl698_502
<=> ! [X0,X1] :
( class_Smallcheck_Osmall(tc_prod(X1,X0))
| ~ class_Smallcheck_Osmall(X0)
| ~ class_Smallcheck_Osmall(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_502])]) ).
fof(f19334,plain,
! [X0,X1] :
( class_Smallcheck_Osmall(tc_prod(X1,X0))
| ~ class_Smallcheck_Osmall(X0)
| ~ class_Smallcheck_Osmall(X1) ),
inference(cnf_transformation,[],[f11061]) ).
fof(f11061,plain,
! [X0,X1] :
( class_Smallcheck_Osmall(tc_prod(X1,X0))
| ~ class_Smallcheck_Osmall(X0)
| ~ class_Smallcheck_Osmall(X1) ),
inference(flattening,[],[f11060]) ).
fof(f11060,plain,
! [X0,X1] :
( class_Smallcheck_Osmall(tc_prod(X1,X0))
| ~ class_Smallcheck_Osmall(X0)
| ~ class_Smallcheck_Osmall(X1) ),
inference(ennf_transformation,[],[f6717]) ).
fof(f6717,plain,
! [X0,X1] :
( ( class_Smallcheck_Osmall(X0)
& class_Smallcheck_Osmall(X1) )
=> class_Smallcheck_Osmall(tc_prod(X1,X0)) ),
inference(rectify,[],[f5164]) ).
fof(f5164,axiom,
! [X324,X323] :
( ( class_Smallcheck_Osmall(X324)
& class_Smallcheck_Osmall(X323) )
=> class_Smallcheck_Osmall(tc_prod(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_prod__Smallcheck_Osmall) ).
fof(f30436,plain,
spl698_501,
inference(avatar_split_clause,[],[f19035,f30434]) ).
fof(f30434,plain,
( spl698_501
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_501])]) ).
fof(f19035,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10729]) ).
fof(f10729,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6483]) ).
fof(f6483,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X0)) ),
inference(rectify,[],[f4660]) ).
fof(f4660,axiom,
! [X60,X4] :
( c_Wellfounded_Owf(X4,X60)
=> c_Wellfounded_Owf(X4,c_Transitive__Closure_Otrancl(X4,X60)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__trancl) ).
fof(f30432,plain,
spl698_500,
inference(avatar_split_clause,[],[f19024,f30430]) ).
fof(f30430,plain,
( spl698_500
<=> ! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_500])]) ).
fof(f19024,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(cnf_transformation,[],[f10712]) ).
fof(f10712,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(flattening,[],[f10711]) ).
fof(f10711,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(ennf_transformation,[],[f6472]) ).
fof(f6472,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X1)
=> ( c_Nat__Transfer_Ois__nat(X0)
=> c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X0)) ) ),
inference(rectify,[],[f2913]) ).
fof(f2913,axiom,
! [X29,X22] :
( c_Nat__Transfer_Ois__nat(X22)
=> ( c_Nat__Transfer_Ois__nat(X29)
=> c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X22,X29)) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) ).
fof(f30428,plain,
spl698_499,
inference(avatar_split_clause,[],[f18690,f30426]) ).
fof(f30426,plain,
( spl698_499
<=> ! [X0,X1] :
( c_Fun_Oinj__on(X1,X1,c_Groups_Ouminus__class_Ouminus(X1),X0)
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_499])]) ).
fof(f18690,plain,
! [X0,X1] :
( c_Fun_Oinj__on(X1,X1,c_Groups_Ouminus__class_Ouminus(X1),X0)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f10388]) ).
fof(f10388,plain,
! [X0,X1] :
( c_Fun_Oinj__on(X1,X1,c_Groups_Ouminus__class_Ouminus(X1),X0)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f6205]) ).
fof(f6205,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add(X1)
=> c_Fun_Oinj__on(X1,X1,c_Groups_Ouminus__class_Ouminus(X1),X0) ),
inference(rectify,[],[f709]) ).
fof(f709,axiom,
! [X19,X4] :
( class_Groups_Oordered__ab__group__add(X4)
=> c_Fun_Oinj__on(X4,X4,c_Groups_Ouminus__class_Ouminus(X4),X19) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_inj__uminus) ).
fof(f30424,plain,
spl698_498,
inference(avatar_split_clause,[],[f18617,f30422]) ).
fof(f30422,plain,
( spl698_498
<=> ! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_498])]) ).
fof(f18617,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(cnf_transformation,[],[f6157]) ).
fof(f6157,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(rectify,[],[f5233]) ).
fof(f5233,axiom,
! [X37,X5] :
( hBOOL(X5)
| ~ hBOOL(hAPP(hAPP(c_fconj,X5),X37)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fconj__2) ).
fof(f30420,plain,
spl698_497,
inference(avatar_split_clause,[],[f18616,f30418]) ).
fof(f30418,plain,
( spl698_497
<=> ! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_497])]) ).
fof(f18616,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(cnf_transformation,[],[f6156]) ).
fof(f6156,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(rectify,[],[f5234]) ).
fof(f5234,axiom,
! [X37,X5] :
( hBOOL(X37)
| ~ hBOOL(hAPP(hAPP(c_fconj,X5),X37)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fconj__3) ).
fof(f30416,plain,
spl698_496,
inference(avatar_split_clause,[],[f18612,f30414]) ).
fof(f30414,plain,
( spl698_496
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_496])]) ).
fof(f18612,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ),
inference(cnf_transformation,[],[f6152]) ).
fof(f6152,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ),
inference(rectify,[],[f5238]) ).
fof(f5238,axiom,
! [X37,X5] :
( hBOOL(hAPP(hAPP(c_fimplies,X5),X37))
| hBOOL(X5) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fimplies__1) ).
fof(f30412,plain,
spl698_495,
inference(avatar_split_clause,[],[f18611,f30410]) ).
fof(f30410,plain,
( spl698_495
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_495])]) ).
fof(f18611,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6151]) ).
fof(f6151,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5239]) ).
fof(f5239,axiom,
! [X5,X37] :
( hBOOL(hAPP(hAPP(c_fimplies,X5),X37))
| ~ hBOOL(X37) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fimplies__2) ).
fof(f30408,plain,
spl698_494,
inference(avatar_split_clause,[],[f18610,f30406]) ).
fof(f30406,plain,
( spl698_494
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_494])]) ).
fof(f18610,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6150]) ).
fof(f6150,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5236]) ).
fof(f5236,axiom,
! [X5,X37] :
( hBOOL(hAPP(hAPP(c_fdisj,X5),X37))
| ~ hBOOL(X37) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fdisj__2) ).
fof(f30404,plain,
spl698_493,
inference(avatar_split_clause,[],[f18609,f30402]) ).
fof(f30402,plain,
( spl698_493
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_493])]) ).
fof(f18609,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6149]) ).
fof(f6149,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5235]) ).
fof(f5235,axiom,
! [X37,X5] :
( hBOOL(hAPP(hAPP(c_fdisj,X5),X37))
| ~ hBOOL(X5) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fdisj__1) ).
fof(f30400,plain,
spl698_492,
inference(avatar_split_clause,[],[f18159,f30398]) ).
fof(f30398,plain,
( spl698_492
<=> ! [X0,X1] : c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_492])]) ).
fof(f18159,plain,
! [X0,X1] : c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X0),
inference(cnf_transformation,[],[f5756]) ).
fof(f5756,plain,
! [X0,X1] : c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X0),
inference(rectify,[],[f4300]) ).
fof(f4300,axiom,
! [X19,X4] : c_Fun_Oinj__on(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Orev(X4),X19),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_inj__on__rev) ).
fof(f30396,plain,
spl698_491,
inference(avatar_split_clause,[],[f18157,f30394]) ).
fof(f30394,plain,
( spl698_491
<=> ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_491])]) ).
fof(f18157,plain,
! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))),
inference(cnf_transformation,[],[f5754]) ).
fof(f5754,plain,
! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X3,X4] : c_Hoare__Mirabelle_Ohoare__derivs(X4,X3,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_empty) ).
fof(f30392,plain,
spl698_490,
inference(avatar_split_clause,[],[f18156,f30390]) ).
fof(f30390,plain,
( spl698_490
<=> ! [X0,X1] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),c_Divides_Odivmod__nat(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_490])]) ).
fof(f18156,plain,
! [X0,X1] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),c_Divides_Odivmod__nat(X1,X0))),
inference(cnf_transformation,[],[f5753]) ).
fof(f5753,plain,
! [X0,X1] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),c_Divides_Odivmod__nat(X1,X0))),
inference(rectify,[],[f2295]) ).
fof(f2295,axiom,
! [X88,X93] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X93,X88),c_Divides_Odivmod__nat(X93,X88))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_divmod__nat__rel__divmod__nat) ).
fof(f30388,plain,
spl698_489,
inference(avatar_split_clause,[],[f18155,f30386]) ).
fof(f30386,plain,
( spl698_489
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_489])]) ).
fof(f18155,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X0))),
inference(cnf_transformation,[],[f5752]) ).
fof(f5752,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X0))),
inference(rectify,[],[f3615]) ).
fof(f3615,axiom,
! [X258,X4] : hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_List_Oset(X4),X258))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_finite__set) ).
fof(f30384,plain,
spl698_488,
inference(avatar_split_clause,[],[f18154,f30382]) ).
fof(f30382,plain,
( spl698_488
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_488])]) ).
fof(f18154,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0))),
inference(cnf_transformation,[],[f5751]) ).
fof(f5751,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f3110]) ).
fof(f3110,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X153,X152))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_finite__atLeastAtMost) ).
fof(f30380,plain,
spl698_487,
inference(avatar_split_clause,[],[f18153,f30378]) ).
fof(f30378,plain,
( spl698_487
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_487])]) ).
fof(f18153,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0))),
inference(cnf_transformation,[],[f5750]) ).
fof(f5750,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f2419]) ).
fof(f2419,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X153,X152))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_finite__greaterThanAtMost) ).
fof(f30376,plain,
spl698_486,
inference(avatar_split_clause,[],[f18152,f30374]) ).
fof(f30374,plain,
( spl698_486
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_486])]) ).
fof(f18152,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0))),
inference(cnf_transformation,[],[f5749]) ).
fof(f5749,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f2011]) ).
fof(f2011,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X153,X152))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_finite__greaterThanLessThan) ).
fof(f30372,plain,
spl698_485,
inference(avatar_split_clause,[],[f18151,f30370]) ).
fof(f30370,plain,
( spl698_485
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_485])]) ).
fof(f18151,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))),
inference(cnf_transformation,[],[f5748]) ).
fof(f5748,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f3154]) ).
fof(f3154,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X153,X152))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_finite__atLeastAtMost__int) ).
fof(f30368,plain,
spl698_484,
inference(avatar_split_clause,[],[f18150,f30366]) ).
fof(f30366,plain,
( spl698_484
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_484])]) ).
fof(f18150,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0))),
inference(cnf_transformation,[],[f5747]) ).
fof(f5747,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f2420]) ).
fof(f2420,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X153,X152))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_finite__greaterThanAtMost__int) ).
fof(f30364,plain,
spl698_483,
inference(avatar_split_clause,[],[f18149,f30362]) ).
fof(f30362,plain,
( spl698_483
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_483])]) ).
fof(f18149,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X0))),
inference(cnf_transformation,[],[f5746]) ).
fof(f5746,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f2012]) ).
fof(f2012,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X153,X152))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_finite__greaterThanLessThan__int) ).
fof(f30360,plain,
spl698_482,
inference(avatar_split_clause,[],[f18148,f30358]) ).
fof(f30358,plain,
( spl698_482
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_482])]) ).
fof(f18148,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5745]) ).
fof(f5745,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4337]) ).
fof(f4337,axiom,
! [X5,X4] : c_List_Olist_ONil(X4) = c_List_OtakeWhile(X4,X5,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_takeWhile_Osimps_I1_J) ).
fof(f30356,plain,
spl698_481,
inference(avatar_split_clause,[],[f18147,f30354]) ).
fof(f30354,plain,
( spl698_481
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_481])]) ).
fof(f18147,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5744]) ).
fof(f5744,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f3978]) ).
fof(f3978,axiom,
! [X22,X23] : c_List_Olist_ONil(X23) = c_List_Oremove1(X23,X22,c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_remove1_Osimps_I1_J) ).
fof(f30352,plain,
spl698_480,
inference(avatar_split_clause,[],[f18146,f30350]) ).
fof(f30350,plain,
( spl698_480
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OdropWhile(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_480])]) ).
fof(f18146,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OdropWhile(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5743]) ).
fof(f5743,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OdropWhile(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4357]) ).
fof(f4357,axiom,
! [X5,X4] : c_List_Olist_ONil(X4) = c_List_OdropWhile(X4,X5,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_dropWhile_Osimps_I1_J) ).
fof(f30348,plain,
spl698_479,
inference(avatar_split_clause,[],[f18145,f30346]) ).
fof(f30346,plain,
( spl698_479
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Osublist(X1,c_List_Olist_ONil(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_479])]) ).
fof(f18145,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Osublist(X1,c_List_Olist_ONil(X1),X0),
inference(cnf_transformation,[],[f5742]) ).
fof(f5742,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Osublist(X1,c_List_Olist_ONil(X1),X0),
inference(rectify,[],[f3968]) ).
fof(f3968,axiom,
! [X19,X4] : c_List_Olist_ONil(X4) = c_List_Osublist(X4,c_List_Olist_ONil(X4),X19),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_sublist__nil) ).
fof(f30344,plain,
spl698_478,
inference(avatar_split_clause,[],[f17905,f30342]) ).
fof(f30342,plain,
( spl698_478
<=> ! [X0] :
( hBOOL(hAPP(c_List_Odistinct(X0),c_Enum_Oenum__class_Oenum(X0)))
| ~ class_Enum_Oenum(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_478])]) ).
fof(f17905,plain,
! [X0] :
( hBOOL(hAPP(c_List_Odistinct(X0),c_Enum_Oenum__class_Oenum(X0)))
| ~ class_Enum_Oenum(X0) ),
inference(cnf_transformation,[],[f10226]) ).
fof(f10226,plain,
! [X0] :
( hBOOL(hAPP(c_List_Odistinct(X0),c_Enum_Oenum__class_Oenum(X0)))
| ~ class_Enum_Oenum(X0) ),
inference(ennf_transformation,[],[f5577]) ).
fof(f5577,plain,
! [X0] :
( class_Enum_Oenum(X0)
=> hBOOL(hAPP(c_List_Odistinct(X0),c_Enum_Oenum__class_Oenum(X0))) ),
inference(rectify,[],[f3728]) ).
fof(f3728,axiom,
! [X23] :
( class_Enum_Oenum(X23)
=> hBOOL(hAPP(c_List_Odistinct(X23),c_Enum_Oenum__class_Oenum(X23))) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_enum__distinct) ).
fof(f30340,plain,
spl698_477,
inference(avatar_split_clause,[],[f17854,f30338]) ).
fof(f30338,plain,
( spl698_477
<=> ! [X0] :
( c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_477])]) ).
fof(f17854,plain,
! [X0] :
( c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f10175]) ).
fof(f10175,plain,
! [X0] :
( c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f5526]) ).
fof(f5526,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls)) ),
inference(rectify,[],[f2698]) ).
fof(f2698,axiom,
! [X23] :
( class_Int_Onumber__ring(X23)
=> c_Int_Oiszero(X23,hAPP(c_Int_Onumber__class_Onumber__of(X23),c_Int_OPls)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_iszero__Numeral0) ).
fof(f30336,plain,
spl698_476,
inference(avatar_split_clause,[],[f17853,f30334]) ).
fof(f17853,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f10174]) ).
fof(f10174,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f5525]) ).
fof(f5525,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin)) ),
inference(rectify,[],[f2809]) ).
fof(f2809,axiom,
! [X23] :
( class_Int_Onumber__ring(X23)
=> ~ c_Int_Oiszero(X23,hAPP(c_Int_Onumber__class_Onumber__of(X23),c_Int_OMin)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nonzero__number__of__Min) ).
fof(f30332,plain,
spl698_475,
inference(avatar_split_clause,[],[f17646,f30330]) ).
fof(f30330,plain,
( spl698_475
<=> ! [X0] : c_Relation_Orefl__on(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_475])]) ).
fof(f17646,plain,
! [X0] : c_Relation_Orefl__on(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),c_Relation_OId(X0)),
inference(cnf_transformation,[],[f5332]) ).
fof(f5332,plain,
! [X0] : c_Relation_Orefl__on(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),c_Relation_OId(X0)),
inference(rectify,[],[f4725]) ).
fof(f4725,axiom,
! [X4] : c_Relation_Orefl__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),c_Relation_OId(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_refl__Id) ).
fof(f30328,plain,
( spl698_474
| ~ spl698_225
| ~ spl698_316 ),
inference(avatar_split_clause,[],[f29683,f29527,f29129,f30326]) ).
fof(f30326,plain,
( spl698_474
<=> ! [X6] : sP4(tc_Int_Oint,c_Int_Oint__ge__less__than(X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_474])]) ).
fof(f29129,plain,
( spl698_225
<=> ! [X0] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_225])]) ).
fof(f29683,plain,
( ! [X6] : sP4(tc_Int_Oint,c_Int_Oint__ge__less__than(X6))
| ~ spl698_225
| ~ spl698_316 ),
inference(resolution,[],[f29528,f29130]) ).
fof(f29130,plain,
( ! [X0] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X0))
| ~ spl698_225 ),
inference(avatar_component_clause,[],[f29129]) ).
fof(f30323,plain,
spl698_473,
inference(avatar_split_clause,[],[f17645,f30321]) ).
fof(f17645,plain,
! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f5331]) ).
fof(f5331,plain,
! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f3345]) ).
fof(f3345,axiom,
! [X4] : c_Wellfounded_Owf(X4,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__empty) ).
fof(f30319,plain,
spl698_472,
inference(avatar_split_clause,[],[f17643,f30317]) ).
fof(f30317,plain,
( spl698_472
<=> ! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_472])]) ).
fof(f17643,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5329]) ).
fof(f5329,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(rectify,[],[f704]) ).
fof(f704,axiom,
! [X4] : hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_finite_OemptyI) ).
fof(f30315,plain,
spl698_471,
inference(avatar_split_clause,[],[f17640,f30313]) ).
fof(f30313,plain,
( spl698_471
<=> ! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_471])]) ).
fof(f17640,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0))),
inference(cnf_transformation,[],[f5326]) ).
fof(f5326,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0))),
inference(rectify,[],[f1707]) ).
fof(f1707,axiom,
! [X59] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X59))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_finite__lessThan) ).
fof(f30311,plain,
spl698_470,
inference(avatar_split_clause,[],[f17639,f30309]) ).
fof(f30309,plain,
( spl698_470
<=> ! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_470])]) ).
fof(f17639,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0))),
inference(cnf_transformation,[],[f5325]) ).
fof(f5325,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0))),
inference(rectify,[],[f3182]) ).
fof(f3182,axiom,
! [X59] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X59))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_finite__atMost) ).
fof(f30307,plain,
spl698_469,
inference(avatar_split_clause,[],[f17638,f30305]) ).
fof(f30305,plain,
( spl698_469
<=> ! [X0] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_469])]) ).
fof(f17638,plain,
! [X0] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X0)),
inference(cnf_transformation,[],[f5324]) ).
fof(f5324,plain,
! [X0] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X0)),
inference(rectify,[],[f2588]) ).
fof(f2588,axiom,
! [X28] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X28)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) ).
fof(f30303,plain,
spl698_468,
inference(avatar_split_clause,[],[f17637,f30301]) ).
fof(f30301,plain,
( spl698_468
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_468])]) ).
fof(f17637,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(cnf_transformation,[],[f5323]) ).
fof(f5323,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(rectify,[],[f2567]) ).
fof(f2567,axiom,
! [X112] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X112),c_Int_OPls) = X112,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_add__Pls__right) ).
fof(f30299,plain,
spl698_467,
inference(avatar_split_clause,[],[f17636,f30297]) ).
fof(f30297,plain,
( spl698_467
<=> ! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_467])]) ).
fof(f17636,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(cnf_transformation,[],[f5322]) ).
fof(f5322,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(rectify,[],[f2561]) ).
fof(f2561,axiom,
! [X112] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X112),c_Int_OPls) = X112,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_diff__bin__simps_I1_J) ).
fof(f30295,plain,
spl698_466,
inference(avatar_split_clause,[],[f17635,f30293]) ).
fof(f30293,plain,
( spl698_466
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_466])]) ).
fof(f17635,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0,
inference(cnf_transformation,[],[f5321]) ).
fof(f5321,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0,
inference(rectify,[],[f2566]) ).
fof(f2566,axiom,
! [X112] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X112) = X112,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_add__Pls) ).
fof(f30291,plain,
spl698_465,
inference(avatar_split_clause,[],[f17634,f30289]) ).
fof(f30289,plain,
( spl698_465
<=> ! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_465])]) ).
fof(f17634,plain,
! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0,
inference(cnf_transformation,[],[f5320]) ).
fof(f5320,plain,
! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0,
inference(rectify,[],[f2428]) ).
fof(f2428,axiom,
! [X88] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X88)) = X88,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__int) ).
fof(f30287,plain,
spl698_464,
inference(avatar_split_clause,[],[f17631,f30285]) ).
fof(f30285,plain,
( spl698_464
<=> ! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_464])]) ).
fof(f17631,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5317]) ).
fof(f5317,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)),
inference(rectify,[],[f4316]) ).
fof(f4316,axiom,
! [X23] : c_List_Olist_ONil(X23) = hAPP(c_List_Orev(X23),c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rev_Osimps_I1_J) ).
fof(f30283,plain,
( spl698_463
| ~ spl698_224
| ~ spl698_316 ),
inference(avatar_split_clause,[],[f29682,f29527,f29125,f30281]) ).
fof(f30281,plain,
( spl698_463
<=> ! [X5] : sP4(tc_Int_Oint,c_Int_Oint__ge__less__than2(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_463])]) ).
fof(f29125,plain,
( spl698_224
<=> ! [X0] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_224])]) ).
fof(f29682,plain,
( ! [X5] : sP4(tc_Int_Oint,c_Int_Oint__ge__less__than2(X5))
| ~ spl698_224
| ~ spl698_316 ),
inference(resolution,[],[f29528,f29126]) ).
fof(f29126,plain,
( ! [X0] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X0))
| ~ spl698_224 ),
inference(avatar_component_clause,[],[f29125]) ).
fof(f30279,plain,
spl698_462,
inference(avatar_split_clause,[],[f17630,f30277]) ).
fof(f30277,plain,
( spl698_462
<=> ! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_462])]) ).
fof(f17630,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5316]) ).
fof(f5316,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)),
inference(rectify,[],[f4172]) ).
fof(f4172,axiom,
! [X23] : c_List_Olist_ONil(X23) = hAPP(c_List_Otl(X23),c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_tl_Osimps_I1_J) ).
fof(f30275,plain,
spl698_461,
inference(avatar_split_clause,[],[f17629,f30273]) ).
fof(f30273,plain,
( spl698_461
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Oconcat(X0,c_List_Olist_ONil(tc_List_Olist(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_461])]) ).
fof(f17629,plain,
! [X0] : c_List_Olist_ONil(X0) = c_List_Oconcat(X0,c_List_Olist_ONil(tc_List_Olist(X0))),
inference(cnf_transformation,[],[f5315]) ).
fof(f5315,plain,
! [X0] : c_List_Olist_ONil(X0) = c_List_Oconcat(X0,c_List_Olist_ONil(tc_List_Olist(X0))),
inference(rectify,[],[f4138]) ).
fof(f4138,axiom,
! [X23] : c_List_Olist_ONil(X23) = c_List_Oconcat(X23,c_List_Olist_ONil(tc_List_Olist(X23))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_concat_Osimps_I1_J) ).
fof(f30271,plain,
spl698_460,
inference(avatar_split_clause,[],[f17628,f30269]) ).
fof(f30269,plain,
( spl698_460
<=> ! [X0] : c_Wellfounded_Omeasure(X0) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0),c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_460])]) ).
fof(f17628,plain,
! [X0] : c_Wellfounded_Omeasure(X0) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0),c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f5314]) ).
fof(f5314,plain,
! [X0] : c_Wellfounded_Omeasure(X0) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0),c_Wellfounded_Oless__than),
inference(rectify,[],[f3088]) ).
fof(f3088,axiom,
! [X4] : c_Wellfounded_Omeasure(X4) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X4),c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_measure__def) ).
fof(f30267,plain,
spl698_459,
inference(avatar_split_clause,[],[f17624,f30265]) ).
fof(f30265,plain,
( spl698_459
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_459])]) ).
fof(f17624,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0),
inference(cnf_transformation,[],[f5310]) ).
fof(f5310,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0),
inference(rectify,[],[f2560]) ).
fof(f2560,axiom,
! [X196] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X196),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_mult__Pls) ).
fof(f30260,plain,
( spl698_458
| ~ spl698_441
| ~ spl698_457 ),
inference(avatar_split_clause,[],[f30256,f30253,f30127,f30258]) ).
fof(f30258,plain,
( spl698_458
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OBit1(X0)),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_458])]) ).
fof(f30253,plain,
( spl698_457
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X0)),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_457])]) ).
fof(f30256,plain,
( ! [X0] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OBit1(X0)),c_Int_OPls))
| ~ spl698_441
| ~ spl698_457 ),
inference(forward_demodulation,[],[f30254,f30129]) ).
fof(f30254,plain,
( ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X0)),c_Int_OPls))
| ~ spl698_457 ),
inference(avatar_component_clause,[],[f30253]) ).
fof(f30255,plain,
spl698_457,
inference(avatar_split_clause,[],[f17623,f30253]) ).
fof(f17623,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X0)),c_Int_OPls)),
inference(cnf_transformation,[],[f5309]) ).
fof(f5309,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X0)),c_Int_OPls)),
inference(rectify,[],[f4960]) ).
fof(f4960,axiom,
! [X318] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(X318)),c_Int_OPls)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__int__code_I10_J) ).
fof(f30248,plain,
( spl698_456
| ~ spl698_441
| ~ spl698_455 ),
inference(avatar_split_clause,[],[f30244,f30241,f30127,f30246]) ).
fof(f30246,plain,
( spl698_456
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OBit0(X0)),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_456])]) ).
fof(f30241,plain,
( spl698_455
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_455])]) ).
fof(f30244,plain,
( ! [X0] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OBit0(X0)),c_Int_OMin))
| ~ spl698_441
| ~ spl698_455 ),
inference(forward_demodulation,[],[f30242,f30129]) ).
fof(f30242,plain,
( ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin))
| ~ spl698_455 ),
inference(avatar_component_clause,[],[f30241]) ).
fof(f30243,plain,
spl698_455,
inference(avatar_split_clause,[],[f17622,f30241]) ).
fof(f17622,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin)),
inference(cnf_transformation,[],[f5308]) ).
fof(f5308,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin)),
inference(rectify,[],[f4953]) ).
fof(f4953,axiom,
! [X318] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X318)),c_Int_OMin)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__int__code_I11_J) ).
fof(f30239,plain,
( spl698_454
| ~ spl698_225
| ~ spl698_314 ),
inference(avatar_split_clause,[],[f29675,f29519,f29129,f30237]) ).
fof(f30237,plain,
( spl698_454
<=> ! [X6] : c_Wellfounded_Oacyclic(tc_Int_Oint,c_Int_Oint__ge__less__than(X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_454])]) ).
fof(f29675,plain,
( ! [X6] : c_Wellfounded_Oacyclic(tc_Int_Oint,c_Int_Oint__ge__less__than(X6))
| ~ spl698_225
| ~ spl698_314 ),
inference(resolution,[],[f29520,f29130]) ).
fof(f30232,plain,
( spl698_453
| ~ spl698_441
| ~ spl698_452 ),
inference(avatar_split_clause,[],[f30228,f30225,f30127,f30230]) ).
fof(f30230,plain,
( spl698_453
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OPls),c_Int_OBit1(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_453])]) ).
fof(f30225,plain,
( spl698_452
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_452])]) ).
fof(f30228,plain,
( ! [X0] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OPls),c_Int_OBit1(X0)))
| ~ spl698_441
| ~ spl698_452 ),
inference(forward_demodulation,[],[f30226,f30129]) ).
fof(f30226,plain,
( ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X0)))
| ~ spl698_452 ),
inference(avatar_component_clause,[],[f30225]) ).
fof(f30227,plain,
spl698_452,
inference(avatar_split_clause,[],[f17618,f30225]) ).
fof(f17618,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X0))),
inference(cnf_transformation,[],[f5304]) ).
fof(f5304,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X0))),
inference(rectify,[],[f4959]) ).
fof(f4959,axiom,
! [X317] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(X317))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__int__code_I4_J) ).
fof(f30220,plain,
( spl698_451
| ~ spl698_441
| ~ spl698_450 ),
inference(avatar_split_clause,[],[f30216,f30213,f30127,f30218]) ).
fof(f30218,plain,
( spl698_451
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OMin),c_Int_OBit0(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_451])]) ).
fof(f30213,plain,
( spl698_450
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_450])]) ).
fof(f30216,plain,
( ! [X0] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OMin),c_Int_OBit0(X0)))
| ~ spl698_441
| ~ spl698_450 ),
inference(forward_demodulation,[],[f30214,f30129]) ).
fof(f30214,plain,
( ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X0)))
| ~ spl698_450 ),
inference(avatar_component_clause,[],[f30213]) ).
fof(f30215,plain,
spl698_450,
inference(avatar_split_clause,[],[f17617,f30213]) ).
fof(f17617,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X0))),
inference(cnf_transformation,[],[f5303]) ).
fof(f5303,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X0))),
inference(rectify,[],[f4952]) ).
fof(f4952,axiom,
! [X317] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X317))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__int__code_I7_J) ).
fof(f30211,plain,
spl698_449,
inference(avatar_split_clause,[],[f17496,f30208]) ).
fof(f30208,plain,
( spl698_449
<=> 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,[spl698_449])]) ).
fof(f17496,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,[],[f1847]) ).
fof(f1847,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/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_transfer__int__nat__numerals_I2_J) ).
fof(f30206,plain,
spl698_448,
inference(avatar_split_clause,[],[f17494,f30203]) ).
fof(f30203,plain,
( spl698_448
<=> c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_448])]) ).
fof(f17494,plain,
c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
inference(cnf_transformation,[],[f3305]) ).
fof(f3305,axiom,
c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_negateSnd__def) ).
fof(f30201,plain,
~ spl698_447,
inference(avatar_split_clause,[],[f17492,f30198]) ).
fof(f17492,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f1088]) ).
fof(f1088,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_infinite__UNIV__nat) ).
fof(f30196,plain,
~ spl698_446,
inference(avatar_split_clause,[],[f17491,f30193]) ).
fof(f17491,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f1873]) ).
fof(f1873,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_infinite__UNIV__int) ).
fof(f30191,plain,
( spl698_445
| ~ spl698_224
| ~ spl698_314 ),
inference(avatar_split_clause,[],[f29674,f29519,f29125,f30189]) ).
fof(f30189,plain,
( spl698_445
<=> ! [X5] : c_Wellfounded_Oacyclic(tc_Int_Oint,c_Int_Oint__ge__less__than2(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_445])]) ).
fof(f29674,plain,
( ! [X5] : c_Wellfounded_Oacyclic(tc_Int_Oint,c_Int_Oint__ge__less__than2(X5))
| ~ spl698_224
| ~ spl698_314 ),
inference(resolution,[],[f29520,f29126]) ).
fof(f30172,plain,
( spl698_444
| ~ spl698_193
| ~ spl698_287 ),
inference(avatar_split_clause,[],[f29651,f29408,f28981,f30169]) ).
fof(f30169,plain,
( spl698_444
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_444])]) ).
fof(f28981,plain,
( spl698_193
<=> class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_193])]) ).
fof(f29651,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Code__Numeral_Ocode__numeral)
| ~ spl698_193
| ~ spl698_287 ),
inference(resolution,[],[f29409,f28983]) ).
fof(f28983,plain,
( class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral)
| ~ spl698_193 ),
inference(avatar_component_clause,[],[f28981]) ).
fof(f30158,plain,
( spl698_443
| ~ spl698_190
| ~ spl698_287 ),
inference(avatar_split_clause,[],[f29650,f29408,f28966,f30155]) ).
fof(f30155,plain,
( spl698_443
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Com_Ocom) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_443])]) ).
fof(f28966,plain,
( spl698_190
<=> class_HOL_Oequal(tc_Com_Ocom) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_190])]) ).
fof(f29650,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Com_Ocom)
| ~ spl698_190
| ~ spl698_287 ),
inference(resolution,[],[f29409,f28968]) ).
fof(f28968,plain,
( class_HOL_Oequal(tc_Com_Ocom)
| ~ spl698_190 ),
inference(avatar_component_clause,[],[f28966]) ).
fof(f30145,plain,
( spl698_442
| ~ spl698_191
| ~ spl698_287 ),
inference(avatar_split_clause,[],[f29648,f29408,f28971,f30142]) ).
fof(f30142,plain,
( spl698_442
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Code__Evaluation_Oterm) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_442])]) ).
fof(f28971,plain,
( spl698_191
<=> class_HOL_Oequal(tc_Code__Evaluation_Oterm) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_191])]) ).
fof(f29648,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Code__Evaluation_Oterm)
| ~ spl698_191
| ~ spl698_287 ),
inference(resolution,[],[f29409,f28973]) ).
fof(f28973,plain,
( class_HOL_Oequal(tc_Code__Evaluation_Oterm)
| ~ spl698_191 ),
inference(avatar_component_clause,[],[f28971]) ).
fof(f30130,plain,
( spl698_441
| ~ spl698_194
| ~ spl698_287 ),
inference(avatar_split_clause,[],[f29647,f29408,f28986,f30127]) ).
fof(f28986,plain,
( spl698_194
<=> class_HOL_Oequal(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_194])]) ).
fof(f29647,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Int_Oint)
| ~ spl698_194
| ~ spl698_287 ),
inference(resolution,[],[f29409,f28988]) ).
fof(f28988,plain,
( class_HOL_Oequal(tc_Int_Oint)
| ~ spl698_194 ),
inference(avatar_component_clause,[],[f28986]) ).
fof(f30125,plain,
spl698_440,
inference(avatar_split_clause,[],[f25443,f30123]) ).
fof(f30123,plain,
( spl698_440
<=> ! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_440])]) ).
fof(f25443,plain,
! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X1,X0)),
inference(forward_demodulation,[],[f18129,f17447]) ).
fof(f18129,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X1,X0)),
inference(cnf_transformation,[],[f5726]) ).
fof(f5726,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X1,X0)),
inference(rectify,[],[f1772]) ).
fof(f1772,axiom,
! [X53,X54] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X54,X53)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osize_I2_J) ).
fof(f30121,plain,
spl698_439,
inference(avatar_split_clause,[],[f24968,f30119]) ).
fof(f24968,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17601,f17447]) ).
fof(f17601,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f5287]) ).
fof(f5287,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f4005]) ).
fof(f4005,axiom,
! [X114] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_upt__0) ).
fof(f30117,plain,
( spl698_438
| ~ spl698_188
| ~ spl698_287 ),
inference(avatar_split_clause,[],[f29646,f29408,f28956,f30114]) ).
fof(f30114,plain,
( spl698_438
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_438])]) ).
fof(f28956,plain,
( spl698_188
<=> class_HOL_Oequal(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_188])]) ).
fof(f29646,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Product__Type_Ounit)
| ~ spl698_188
| ~ spl698_287 ),
inference(resolution,[],[f29409,f28958]) ).
fof(f28958,plain,
( class_HOL_Oequal(tc_Product__Type_Ounit)
| ~ spl698_188 ),
inference(avatar_component_clause,[],[f28956]) ).
fof(f30112,plain,
spl698_437,
inference(avatar_split_clause,[],[f24906,f30109]) ).
fof(f30109,plain,
( spl698_437
<=> c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_437])]) ).
fof(f24906,plain,
c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f24905,f17447]) ).
fof(f24905,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Int_OPls,
inference(forward_demodulation,[],[f17504,f17436]) ).
fof(f17504,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f1727]) ).
fof(f1727,axiom,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_int__0) ).
fof(f30107,plain,
( spl698_436
| ~ spl698_278
| ~ spl698_435 ),
inference(avatar_split_clause,[],[f30102,f30098,f29372,f30104]) ).
fof(f30104,plain,
( spl698_436
<=> c_Nat__Transfer_Ois__nat(c_Int_OBit1(c_Int_Osucc(c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_436])]) ).
fof(f30098,plain,
( spl698_435
<=> c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_Osucc(c_Int_OPls)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_435])]) ).
fof(f30102,plain,
( c_Nat__Transfer_Ois__nat(c_Int_OBit1(c_Int_Osucc(c_Int_OPls)))
| ~ spl698_278
| ~ spl698_435 ),
inference(forward_demodulation,[],[f30100,f29373]) ).
fof(f30100,plain,
( c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_Osucc(c_Int_OPls))))
| ~ spl698_435 ),
inference(avatar_component_clause,[],[f30098]) ).
fof(f30101,plain,
spl698_435,
inference(avatar_split_clause,[],[f24896,f30098]) ).
fof(f24896,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_Osucc(c_Int_OPls)))),
inference(forward_demodulation,[],[f17483,f17442]) ).
fof(f17483,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f2916]) ).
fof(f2916,axiom,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J) ).
fof(f30096,plain,
( spl698_434
| ~ spl698_236
| ~ spl698_278
| ~ spl698_371
| ~ spl698_433 ),
inference(avatar_split_clause,[],[f30091,f30085,f29826,f29372,f29182,f30093]) ).
fof(f30093,plain,
( spl698_434
<=> c_Nat__Transfer_Ois__nat(c_Int_Osucc(c_Int_Osucc(c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_434])]) ).
fof(f29182,plain,
( spl698_236
<=> c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_236])]) ).
fof(f30085,plain,
( spl698_433
<=> c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_Osucc(c_Int_OPls)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_433])]) ).
fof(f30091,plain,
( c_Nat__Transfer_Ois__nat(c_Int_Osucc(c_Int_Osucc(c_Int_OPls)))
| ~ spl698_236
| ~ spl698_278
| ~ spl698_371
| ~ spl698_433 ),
inference(forward_demodulation,[],[f30090,f29184]) ).
fof(f29184,plain,
( c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls)
| ~ spl698_236 ),
inference(avatar_component_clause,[],[f29182]) ).
fof(f30090,plain,
( c_Nat__Transfer_Ois__nat(c_Int_Osucc(c_Int_OBit1(c_Int_OPls)))
| ~ spl698_278
| ~ spl698_371
| ~ spl698_433 ),
inference(forward_demodulation,[],[f30089,f29827]) ).
fof(f30089,plain,
( c_Nat__Transfer_Ois__nat(c_Int_OBit0(c_Int_Osucc(c_Int_OPls)))
| ~ spl698_278
| ~ spl698_433 ),
inference(forward_demodulation,[],[f30087,f29373]) ).
fof(f30087,plain,
( c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_Osucc(c_Int_OPls))))
| ~ spl698_433 ),
inference(avatar_component_clause,[],[f30085]) ).
fof(f30088,plain,
spl698_433,
inference(avatar_split_clause,[],[f24895,f30085]) ).
fof(f24895,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_Osucc(c_Int_OPls)))),
inference(forward_demodulation,[],[f17482,f17442]) ).
fof(f17482,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f2917]) ).
fof(f2917,axiom,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J) ).
fof(f30083,plain,
spl698_432,
inference(avatar_split_clause,[],[f24893,f30080]) ).
fof(f30080,plain,
( spl698_432
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_432])]) ).
fof(f24893,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17479,f17447]) ).
fof(f17479,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
inference(cnf_transformation,[],[f2576]) ).
fof(f2576,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__number__of__Pls) ).
fof(f30078,plain,
spl698_431,
inference(avatar_split_clause,[],[f24892,f30075]) ).
fof(f30075,plain,
( spl698_431
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_431])]) ).
fof(f24892,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
inference(forward_demodulation,[],[f17478,f17447]) ).
fof(f17478,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
inference(cnf_transformation,[],[f4971]) ).
fof(f4971,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_bool_Osize_I4_J) ).
fof(f30073,plain,
spl698_430,
inference(avatar_split_clause,[],[f24891,f30070]) ).
fof(f30070,plain,
( spl698_430
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_430])]) ).
fof(f24891,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
inference(forward_demodulation,[],[f17477,f17447]) ).
fof(f17477,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
inference(cnf_transformation,[],[f4970]) ).
fof(f4970,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_bool_Osize_I3_J) ).
fof(f30068,plain,
( spl698_429
| ~ spl698_189
| ~ spl698_287 ),
inference(avatar_split_clause,[],[f29642,f29408,f28961,f30065]) ).
fof(f30065,plain,
( spl698_429
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Com_Ovname) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_429])]) ).
fof(f28961,plain,
( spl698_189
<=> class_HOL_Oequal(tc_Com_Ovname) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_189])]) ).
fof(f29642,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Com_Ovname)
| ~ spl698_189
| ~ spl698_287 ),
inference(resolution,[],[f29409,f28963]) ).
fof(f28963,plain,
( class_HOL_Oequal(tc_Com_Ovname)
| ~ spl698_189 ),
inference(avatar_component_clause,[],[f28961]) ).
fof(f30063,plain,
spl698_428,
inference(avatar_split_clause,[],[f24890,f30060]) ).
fof(f30060,plain,
( spl698_428
<=> hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_428])]) ).
fof(f24890,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17476,f17447]) ).
fof(f17476,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP),
inference(cnf_transformation,[],[f2056]) ).
fof(f2056,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osize_I9_J) ).
fof(f30058,plain,
spl698_427,
inference(avatar_split_clause,[],[f24884,f30055]) ).
fof(f30055,plain,
( spl698_427
<=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_427])]) ).
fof(f24884,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17471,f17447]) ).
fof(f17471,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f4626]) ).
fof(f4626,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zero__code__numeral__def) ).
fof(f30053,plain,
spl698_426,
inference(avatar_split_clause,[],[f24883,f30050]) ).
fof(f30048,plain,
spl698_425,
inference(avatar_split_clause,[],[f24882,f30045]) ).
fof(f30045,plain,
( spl698_425
<=> c_Int_Osucc(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_425])]) ).
fof(f24882,plain,
c_Int_Osucc(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin),
inference(forward_demodulation,[],[f17467,f17442]) ).
fof(f17467,plain,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin),
inference(cnf_transformation,[],[f2829]) ).
fof(f2829,axiom,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_minus__Min) ).
fof(f30043,plain,
spl698_424,
inference(avatar_split_clause,[],[f22203,f30041]) ).
fof(f30041,plain,
( spl698_424
<=> ! [X0,X3,X2,X1] :
( sP76(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_424])]) ).
fof(f22203,plain,
! [X2,X3,X0,X1] :
( sP76(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f14658]) ).
fof(f14658,plain,
! [X0,X1,X2,X3] :
( sP76(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f12592,f14657,f14656]) ).
fof(f14656,plain,
! [X1,X0,X3,X2] :
( sP75(X1,X0,X3,X2)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),c_Groups_Ozero__class_Ozero(X3))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP75])]) ).
fof(f14657,plain,
! [X2,X3,X0,X1] :
( ( hBOOL(hAPP(hAPP(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)))
<=> sP75(X1,X0,X3,X2) )
| ~ sP76(X2,X3,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP76])]) ).
fof(f12592,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(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)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),c_Groups_Ozero__class_Ozero(X3))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X2)) ) ) )
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(ennf_transformation,[],[f8489]) ).
fof(f8489,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( hBOOL(hAPP(hAPP(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)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),c_Groups_Ozero__class_Ozero(X3))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X2)) ) ) ) ),
inference(rectify,[],[f1547]) ).
fof(f1547,axiom,
! [X26,X6,X36,X4] :
( class_Rings_Olinordered__ring__strict(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X36),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X36),X26)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X6))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_mult__less__cancel__left__disj) ).
fof(f30039,plain,
spl698_423,
inference(avatar_split_clause,[],[f22194,f30037]) ).
fof(f30037,plain,
( spl698_423
<=> ! [X0,X3,X2,X1] :
( sP74(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_423])]) ).
fof(f22194,plain,
! [X2,X3,X0,X1] :
( sP74(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f14655]) ).
fof(f14655,plain,
! [X0,X1,X2,X3] :
( sP74(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f12591,f14654,f14653]) ).
fof(f14653,plain,
! [X2,X0,X3,X1] :
( sP73(X2,X0,X3,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP73])]) ).
fof(f14654,plain,
! [X1,X3,X0,X2] :
( ( hBOOL(hAPP(hAPP(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)))
<=> sP73(X2,X0,X3,X1) )
| ~ sP74(X1,X3,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP74])]) ).
fof(f12591,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(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)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) )
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(ennf_transformation,[],[f8488]) ).
fof(f8488,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( hBOOL(hAPP(hAPP(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)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) ) ),
inference(rectify,[],[f1546]) ).
fof(f1546,axiom,
! [X26,X36,X6,X4] :
( class_Rings_Olinordered__ring__strict(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X36)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X6))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_mult__less__cancel__right__disj) ).
fof(f30035,plain,
spl698_422,
inference(avatar_split_clause,[],[f22143,f30033]) ).
fof(f30033,plain,
( spl698_422
<=> ! [X0,X3,X2,X1] :
( sP72(X0,X3,X1,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_422])]) ).
fof(f22143,plain,
! [X2,X3,X0,X1] :
( sP72(X0,X3,X1,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14652]) ).
fof(f14652,plain,
! [X0,X1,X2,X3] :
( sP72(X0,X3,X1,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f12534,f14651,f14650,f14649]) ).
fof(f14649,plain,
! [X0,X3,X1,X2] :
( sP70(X0,X3,X1,X2)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP70])]) ).
fof(f14650,plain,
! [X2,X1,X3,X0] :
( sP71(X2,X1,X3,X0)
<=> ( ( sP70(X0,X3,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP71])]) ).
fof(f14651,plain,
! [X0,X3,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1)),X0))
<=> sP71(X2,X1,X3,X0) )
| ~ sP72(X0,X3,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP72])]) ).
fof(f12534,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1)),X0))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f8457]) ).
fof(f8457,plain,
! [X0,X1,X2,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1)),X0))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)),X2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))) ) ) ) ),
inference(rectify,[],[f3022]) ).
fof(f3022,axiom,
! [X6,X36,X26,X4] :
( class_Fields_Olinordered__field__inverse__zero(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X36)),X6))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X6)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X36)),X26)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X36))) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_divide__le__eq) ).
fof(f30031,plain,
spl698_421,
inference(avatar_split_clause,[],[f22128,f30029]) ).
fof(f30029,plain,
( spl698_421
<=> ! [X0,X3,X2,X1] :
( sP69(X0,X3,X1,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_421])]) ).
fof(f22128,plain,
! [X2,X3,X0,X1] :
( sP69(X0,X3,X1,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14648]) ).
fof(f14648,plain,
! [X0,X1,X2,X3] :
( sP69(X0,X3,X1,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f12533,f14647,f14646,f14645]) ).
fof(f14645,plain,
! [X0,X3,X1,X2] :
( sP67(X0,X3,X1,X2)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP67])]) ).
fof(f14646,plain,
! [X2,X1,X3,X0] :
( sP68(X2,X1,X3,X0)
<=> ( ( sP67(X0,X3,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP68])]) ).
fof(f14647,plain,
! [X0,X3,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1)),X0))
<=> sP68(X2,X1,X3,X0) )
| ~ sP69(X0,X3,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP69])]) ).
fof(f12533,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1)),X0))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f8456]) ).
fof(f8456,plain,
! [X0,X1,X2,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1)),X0))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)),X2)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1))) ) ) ) ),
inference(rectify,[],[f3002]) ).
fof(f3002,axiom,
! [X6,X36,X26,X4] :
( class_Fields_Olinordered__field__inverse__zero(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X36)),X6))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X6)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X36)),X26)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X36))) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_divide__less__eq) ).
fof(f30027,plain,
spl698_420,
inference(avatar_split_clause,[],[f22113,f30025]) ).
fof(f30025,plain,
( spl698_420
<=> ! [X0,X3,X2,X1] :
( sP66(X3,X2,X0,X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_420])]) ).
fof(f22113,plain,
! [X2,X3,X0,X1] :
( sP66(X3,X2,X0,X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14644]) ).
fof(f14644,plain,
! [X0,X1,X2,X3] :
( sP66(X3,X2,X0,X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f12532,f14643,f14642,f14641]) ).
fof(f14641,plain,
! [X3,X2,X0,X1] :
( sP64(X3,X2,X0,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP64])]) ).
fof(f14642,plain,
! [X1,X0,X2,X3] :
( sP65(X1,X0,X2,X3)
<=> ( ( sP64(X3,X2,X0,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP65])]) ).
fof(f14643,plain,
! [X3,X2,X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0)))
<=> sP65(X1,X0,X2,X3) )
| ~ sP66(X3,X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP66])]) ).
fof(f12532,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0)))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) ) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f8455]) ).
fof(f8455,plain,
! [X0,X1,X2,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X2),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X1)) ) ) ) ),
inference(rectify,[],[f3021]) ).
fof(f3021,axiom,
! [X36,X26,X6,X4] :
( class_Fields_Olinordered__field__inverse__zero(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X36)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),c_Groups_Ozero__class_Ozero(X4))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X36))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X36)),X26)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_le__divide__eq) ).
fof(f30023,plain,
spl698_419,
inference(avatar_split_clause,[],[f22098,f30021]) ).
fof(f30021,plain,
( spl698_419
<=> ! [X0,X3,X2,X1] :
( sP63(X3,X2,X0,X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_419])]) ).
fof(f22098,plain,
! [X2,X3,X0,X1] :
( sP63(X3,X2,X0,X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14640]) ).
fof(f14640,plain,
! [X0,X1,X2,X3] :
( sP63(X3,X2,X0,X1)
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(definition_folding,[],[f12531,f14639,f14638,f14637]) ).
fof(f14637,plain,
! [X3,X2,X0,X1] :
( sP61(X3,X2,X0,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP61])]) ).
fof(f14638,plain,
! [X1,X0,X2,X3] :
( sP62(X1,X0,X2,X3)
<=> ( ( sP61(X3,X2,X0,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP62])]) ).
fof(f14639,plain,
! [X3,X2,X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0)))
<=> sP62(X1,X0,X2,X3) )
| ~ sP63(X3,X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP63])]) ).
fof(f12531,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0)))
<=> ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),c_Groups_Ozero__class_Ozero(X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3))) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0)) ) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X3) ),
inference(ennf_transformation,[],[f8454]) ).
fof(f8454,plain,
! [X0,X1,X2,X3] :
( class_Fields_Olinordered__field__inverse__zero(X3)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),c_Groups_Ozero__class_Ozero(X3))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),c_Groups_Ozero__class_Ozero(X3)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)),X1)) ) ) ) ),
inference(rectify,[],[f3001]) ).
fof(f3001,axiom,
! [X36,X26,X6,X4] :
( class_Fields_Olinordered__field__inverse__zero(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X36)))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),c_Groups_Ozero__class_Ozero(X4))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X36))) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X36)),X26)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_less__divide__eq) ).
fof(f30019,plain,
spl698_418,
inference(avatar_split_clause,[],[f22080,f30017]) ).
fof(f30017,plain,
( spl698_418
<=> ! [X0,X3,X2,X1] :
( sP60(X1,X0,X3,X2)
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_418])]) ).
fof(f22080,plain,
! [X2,X3,X0,X1] :
( sP60(X1,X0,X3,X2)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14636]) ).
fof(f14636,plain,
! [X0,X1,X2,X3] :
( sP60(X1,X0,X3,X2)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(definition_folding,[],[f12524,f14635,f14634]) ).
fof(f14634,plain,
! [X2,X3,X0,X1] :
( sP59(X2,X3,X0,X1)
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ozero__class_Ozero(X3) != X0 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0) = X1
| c_Groups_Ozero__class_Ozero(X3) = X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP59])]) ).
fof(f14635,plain,
! [X1,X0,X3,X2] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0) = X2
<=> sP59(X2,X3,X0,X1) )
| ~ sP60(X1,X0,X3,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP60])]) ).
fof(f12524,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0) = X2
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X2
| c_Groups_Ozero__class_Ozero(X3) != X0 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0) = X1
| c_Groups_Ozero__class_Ozero(X3) = X0 ) ) )
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(ennf_transformation,[],[f8450]) ).
fof(f8450,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X1),X0) = X2
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X0
=> c_Groups_Ozero__class_Ozero(X3) = X2 )
& ( c_Groups_Ozero__class_Ozero(X3) != X0
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0) = X1 ) ) ) ),
inference(rectify,[],[f2993]) ).
fof(f2993,axiom,
! [X36,X26,X6,X4] :
( class_Fields_Ofield__inverse__zero(X4)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X36) = X6
<=> ( ( c_Groups_Ozero__class_Ozero(X4) = X36
=> c_Groups_Ozero__class_Ozero(X4) = X6 )
& ( c_Groups_Ozero__class_Ozero(X4) != X36
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X36) = X26 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__divide__eq) ).
fof(f30015,plain,
spl698_417,
inference(avatar_split_clause,[],[f22071,f30013]) ).
fof(f30013,plain,
( spl698_417
<=> ! [X0,X3,X2,X1] :
( sP58(X2,X1,X3,X0)
| ~ class_Fields_Ofield__inverse__zero(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_417])]) ).
fof(f22071,plain,
! [X2,X3,X0,X1] :
( sP58(X2,X1,X3,X0)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(cnf_transformation,[],[f14633]) ).
fof(f14633,plain,
! [X0,X1,X2,X3] :
( sP58(X2,X1,X3,X0)
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(definition_folding,[],[f12523,f14632,f14631]) ).
fof(f14631,plain,
! [X0,X3,X1,X2] :
( sP57(X0,X3,X1,X2)
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X0
| c_Groups_Ozero__class_Ozero(X3) != X1 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1) = X2
| c_Groups_Ozero__class_Ozero(X3) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP57])]) ).
fof(f14632,plain,
! [X2,X1,X3,X0] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1) = X0
<=> sP57(X0,X3,X1,X2) )
| ~ sP58(X2,X1,X3,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP58])]) ).
fof(f12523,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1) = X0
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X0
| c_Groups_Ozero__class_Ozero(X3) != X1 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1) = X2
| c_Groups_Ozero__class_Ozero(X3) = X1 ) ) )
| ~ class_Fields_Ofield__inverse__zero(X3) ),
inference(ennf_transformation,[],[f8449]) ).
fof(f8449,plain,
! [X0,X1,X2,X3] :
( class_Fields_Ofield__inverse__zero(X3)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X3),X2),X1) = X0
<=> ( ( c_Groups_Ozero__class_Ozero(X3) = X1
=> c_Groups_Ozero__class_Ozero(X3) = X0 )
& ( c_Groups_Ozero__class_Ozero(X3) != X1
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1) = X2 ) ) ) ),
inference(rectify,[],[f2992]) ).
fof(f2992,axiom,
! [X6,X36,X26,X4] :
( class_Fields_Ofield__inverse__zero(X4)
=> ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X26),X36) = X6
<=> ( ( c_Groups_Ozero__class_Ozero(X4) = X36
=> c_Groups_Ozero__class_Ozero(X4) = X6 )
& ( c_Groups_Ozero__class_Ozero(X4) != X36
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X36) = X26 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_divide__eq__eq) ).
fof(f30011,plain,
spl698_416,
inference(avatar_split_clause,[],[f21806,f30009]) ).
fof(f30009,plain,
( spl698_416
<=> ! [X2,X0,X1,X3] : c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_416])]) ).
fof(f21806,plain,
! [X2,X3,X0,X1] : c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OSemi(X3,X2),
inference(cnf_transformation,[],[f8222]) ).
fof(f8222,plain,
! [X0,X1,X2,X3] : c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OSemi(X3,X2),
inference(rectify,[],[f76]) ).
fof(f76,axiom,
! [X10,X51,X57,X58] : c_Com_Ocom_OWhile(X51,X10) != c_Com_Ocom_OSemi(X58,X57),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I46_J) ).
fof(f30007,plain,
spl698_415,
inference(avatar_split_clause,[],[f21804,f30005]) ).
fof(f30005,plain,
( spl698_415
<=> ! [X2,X0,X1,X3] : c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OAss(X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_415])]) ).
fof(f21804,plain,
! [X2,X3,X0,X1] : c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OAss(X3,X2),
inference(cnf_transformation,[],[f8220]) ).
fof(f8220,plain,
! [X0,X1,X2,X3] : c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OAss(X3,X2),
inference(rectify,[],[f78]) ).
fof(f78,axiom,
! [X10,X51,X53,X54] : c_Com_Ocom_OAss(X54,X53) != c_Com_Ocom_OWhile(X51,X10),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I28_J) ).
fof(f30003,plain,
spl698_414,
inference(avatar_split_clause,[],[f21802,f30001]) ).
fof(f30001,plain,
( spl698_414
<=> ! [X2,X0,X1,X3] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_414])]) ).
fof(f21802,plain,
! [X2,X3,X0,X1] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OSemi(X3,X2),
inference(cnf_transformation,[],[f8218]) ).
fof(f8218,plain,
! [X0,X1,X2,X3] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OSemi(X3,X2),
inference(rectify,[],[f71]) ).
fof(f71,axiom,
! [X53,X54,X55,X56] : c_Com_Ocom_OSemi(X56,X55) != c_Com_Ocom_OAss(X54,X53),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I25_J) ).
fof(f29999,plain,
spl698_413,
inference(avatar_split_clause,[],[f20696,f29997]) ).
fof(f29997,plain,
( spl698_413
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X1)
| ~ sP26(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_413])]) ).
fof(f20696,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X1)
| ~ sP26(X0,X1,X2) ),
inference(cnf_transformation,[],[f15540]) ).
fof(f15540,plain,
! [X0,X1,X2] :
( ( sP26(X0,X1,X2)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK280(X0,X1,X2)),sK281(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK281(X0,X1,X2)),hAPP(c_List_Oset(X0),X1)))
& hBOOL(hAPP(hAPP(c_member(X0),sK280(X0,X1,X2)),hAPP(c_List_Oset(X0),X2))) )
| ~ c_List_Olinorder__class_Osorted(X0,X1)
| ~ c_List_Olinorder__class_Osorted(X0,X2) )
& ( ( ! [X5] :
( ! [X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X6),hAPP(c_List_Oset(X0),X1))) )
| ~ hBOOL(hAPP(hAPP(c_member(X0),X5),hAPP(c_List_Oset(X0),X2))) )
& c_List_Olinorder__class_Osorted(X0,X1)
& c_List_Olinorder__class_Osorted(X0,X2) )
| ~ sP26(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK280,sK281])],[f15537,f15539,f15538]) ).
fof(f15538,plain,
! [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X1))) )
& hBOOL(hAPP(hAPP(c_member(X0),X3),hAPP(c_List_Oset(X0),X2))) )
=> ( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK280(X0,X1,X2)),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X1))) )
& hBOOL(hAPP(hAPP(c_member(X0),sK280(X0,X1,X2)),hAPP(c_List_Oset(X0),X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15539,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK280(X0,X1,X2)),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X1))) )
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK280(X0,X1,X2)),sK281(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK281(X0,X1,X2)),hAPP(c_List_Oset(X0),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15537,plain,
! [X0,X1,X2] :
( ( sP26(X0,X1,X2)
| ? [X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X1))) )
& hBOOL(hAPP(hAPP(c_member(X0),X3),hAPP(c_List_Oset(X0),X2))) )
| ~ c_List_Olinorder__class_Osorted(X0,X1)
| ~ c_List_Olinorder__class_Osorted(X0,X2) )
& ( ( ! [X5] :
( ! [X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X6),hAPP(c_List_Oset(X0),X1))) )
| ~ hBOOL(hAPP(hAPP(c_member(X0),X5),hAPP(c_List_Oset(X0),X2))) )
& c_List_Olinorder__class_Osorted(X0,X1)
& c_List_Olinorder__class_Osorted(X0,X2) )
| ~ sP26(X0,X1,X2) ) ),
inference(rectify,[],[f15536]) ).
fof(f15536,plain,
! [X2,X0,X1] :
( ( sP26(X2,X0,X1)
| ? [X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
| ~ c_List_Olinorder__class_Osorted(X2,X0)
| ~ c_List_Olinorder__class_Osorted(X2,X1) )
& ( ( ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
& c_List_Olinorder__class_Osorted(X2,X0)
& c_List_Olinorder__class_Osorted(X2,X1) )
| ~ sP26(X2,X0,X1) ) ),
inference(flattening,[],[f15535]) ).
fof(f15535,plain,
! [X2,X0,X1] :
( ( sP26(X2,X0,X1)
| ? [X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
| ~ c_List_Olinorder__class_Osorted(X2,X0)
| ~ c_List_Olinorder__class_Osorted(X2,X1) )
& ( ( ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
& c_List_Olinorder__class_Osorted(X2,X0)
& c_List_Olinorder__class_Osorted(X2,X1) )
| ~ sP26(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f14579]) ).
fof(f14579,plain,
! [X2,X0,X1] :
( sP26(X2,X0,X1)
<=> ( ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
& c_List_Olinorder__class_Osorted(X2,X0)
& c_List_Olinorder__class_Osorted(X2,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP26])]) ).
fof(f29995,plain,
spl698_412,
inference(avatar_split_clause,[],[f20695,f29993]) ).
fof(f29993,plain,
( spl698_412
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X2)
| ~ sP26(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_412])]) ).
fof(f20695,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X2)
| ~ sP26(X0,X1,X2) ),
inference(cnf_transformation,[],[f15540]) ).
fof(f29991,plain,
spl698_411,
inference(avatar_split_clause,[],[f19020,f29989]) ).
fof(f29989,plain,
( spl698_411
<=> ! [X0,X1] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_411])]) ).
fof(f19020,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(cnf_transformation,[],[f10707]) ).
fof(f10707,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(ennf_transformation,[],[f6469]) ).
fof(f6469,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X1)
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0)) ),
inference(rectify,[],[f3155]) ).
fof(f3155,axiom,
! [X34,X20] :
( c_Nat__Transfer_Ois__nat(X20)
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X20,X34)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_SetInterval_Otransfer__int__nat__set__function__closures) ).
fof(f29987,plain,
spl698_410,
inference(avatar_split_clause,[],[f18987,f29985]) ).
fof(f18987,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f10679]) ).
fof(f10679,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6450]) ).
fof(f6450,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(X1)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(rectify,[],[f714]) ).
fof(f714,axiom,
! [X19,X4] :
( class_Finite__Set_Ofinite(X4)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X19)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_finite__code) ).
fof(f29983,plain,
spl698_409,
inference(avatar_split_clause,[],[f18951,f29981]) ).
fof(f18951,plain,
! [X0,X1] :
( sP0(X0,X1)
| c_List_Olist_ONil(X0) != X1 ),
inference(cnf_transformation,[],[f14950]) ).
fof(f14950,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ! [X2,X3] :
( ~ c_List_Olinorder__class_Osorted(X0,X2)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X3),sK181(X0,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X0),sK181(X0,X2,X3)),hAPP(c_List_Oset(X0),X2))) )
| hAPP(hAPP(c_List_Olist_OCons(X0),X3),X2) != X1 )
& c_List_Olist_ONil(X0) != X1 ) )
& ( ( c_List_Olinorder__class_Osorted(X0,sK182(X0,X1))
& ! [X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK183(X0,X1)),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X7),hAPP(c_List_Oset(X0),sK182(X0,X1)))) )
& hAPP(hAPP(c_List_Olist_OCons(X0),sK183(X0,X1)),sK182(X0,X1)) = X1 )
| c_List_Olist_ONil(X0) = X1
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK181,sK182,sK183])],[f14947,f14949,f14948]) ).
fof(f14948,plain,
! [X0,X2,X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X2))) )
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X3),sK181(X0,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X0),sK181(X0,X2,X3)),hAPP(c_List_Oset(X0),X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f14949,plain,
! [X0,X1] :
( ? [X5,X6] :
( c_List_Olinorder__class_Osorted(X0,X5)
& ! [X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X6),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X7),hAPP(c_List_Oset(X0),X5))) )
& hAPP(hAPP(c_List_Olist_OCons(X0),X6),X5) = X1 )
=> ( c_List_Olinorder__class_Osorted(X0,sK182(X0,X1))
& ! [X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK183(X0,X1)),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X7),hAPP(c_List_Oset(X0),sK182(X0,X1)))) )
& hAPP(hAPP(c_List_Olist_OCons(X0),sK183(X0,X1)),sK182(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f14947,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ! [X2,X3] :
( ~ c_List_Olinorder__class_Osorted(X0,X2)
| ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X2))) )
| hAPP(hAPP(c_List_Olist_OCons(X0),X3),X2) != X1 )
& c_List_Olist_ONil(X0) != X1 ) )
& ( ? [X5,X6] :
( c_List_Olinorder__class_Osorted(X0,X5)
& ! [X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X6),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X7),hAPP(c_List_Oset(X0),X5))) )
& hAPP(hAPP(c_List_Olist_OCons(X0),X6),X5) = X1 )
| c_List_Olist_ONil(X0) = X1
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f14946]) ).
fof(f14946,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ! [X2,X3] :
( ~ c_List_Olinorder__class_Osorted(X1,X2)
| ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2))) )
| hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) != X0 )
& c_List_Olist_ONil(X1) != X0 ) )
& ( ? [X2,X3] :
( c_List_Olinorder__class_Osorted(X1,X2)
& ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2))) )
& hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) = X0 )
| c_List_Olist_ONil(X1) = X0
| ~ sP0(X1,X0) ) ),
inference(flattening,[],[f14945]) ).
fof(f14945,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ! [X2,X3] :
( ~ c_List_Olinorder__class_Osorted(X1,X2)
| ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2))) )
| hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) != X0 )
& c_List_Olist_ONil(X1) != X0 ) )
& ( ? [X2,X3] :
( c_List_Olinorder__class_Osorted(X1,X2)
& ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2))) )
& hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) = X0 )
| c_List_Olist_ONil(X1) = X0
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f14535]) ).
fof(f14535,plain,
! [X1,X0] :
( sP0(X1,X0)
<=> ( ? [X2,X3] :
( c_List_Olinorder__class_Osorted(X1,X2)
& ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2))) )
& hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) = X0 )
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f29978,plain,
spl698_408,
inference(avatar_split_clause,[],[f18142,f29976]) ).
fof(f29976,plain,
( spl698_408
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_408])]) ).
fof(f18142,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X0),
inference(cnf_transformation,[],[f5739]) ).
fof(f5739,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X0),
inference(rectify,[],[f797]) ).
fof(f797,axiom,
! [X19,X4] : c_Fun_Oinj__on(X4,tc_Option_Ooption(X4),c_Option_Ooption_OSome(X4),X19),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_inj__Some) ).
fof(f29974,plain,
spl698_407,
inference(avatar_split_clause,[],[f18140,f29972]) ).
fof(f29972,plain,
( spl698_407
<=> ! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_407])]) ).
fof(f18140,plain,
! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5737]) ).
fof(f5737,plain,
! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(rectify,[],[f3970]) ).
fof(f3970,axiom,
! [X60,X4] : c_List_Olistrelp(X4,X60,c_List_Olist_ONil(X4),c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_listrelp_ONil) ).
fof(f29970,plain,
spl698_406,
inference(avatar_split_clause,[],[f18139,f29968]) ).
fof(f29968,plain,
( spl698_406
<=> ! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_406])]) ).
fof(f18139,plain,
! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(cnf_transformation,[],[f5736]) ).
fof(f5736,plain,
! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(rectify,[],[f4788]) ).
fof(f4788,axiom,
! [X60,X4] : c_Relation_Ototal__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X60),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_total__on__empty) ).
fof(f29966,plain,
spl698_405,
inference(avatar_split_clause,[],[f18137,f29964]) ).
fof(f29964,plain,
( spl698_405
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Olistsp(X1,X0),c_List_Olist_ONil(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_405])]) ).
fof(f18137,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Olistsp(X1,X0),c_List_Olist_ONil(X1))),
inference(cnf_transformation,[],[f5734]) ).
fof(f5734,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Olistsp(X1,X0),c_List_Olist_ONil(X1))),
inference(rectify,[],[f4468]) ).
fof(f4468,axiom,
! [X19,X4] : hBOOL(hAPP(c_List_Olistsp(X4,X19),c_List_Olist_ONil(X4))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_listsp_Oequations_I1_J) ).
fof(f29962,plain,
spl698_404,
inference(avatar_split_clause,[],[f18136,f29960]) ).
fof(f29960,plain,
( spl698_404
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_404])]) ).
fof(f18136,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X0))),
inference(cnf_transformation,[],[f5733]) ).
fof(f5733,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X0))),
inference(rectify,[],[f4194]) ).
fof(f4194,axiom,
! [X263,X23] : hBOOL(hAPP(c_List_Odistinct(X23),c_List_Oremdups(X23,X263))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_distinct__remdups) ).
fof(f29958,plain,
spl698_403,
inference(avatar_split_clause,[],[f18135,f29956]) ).
fof(f29956,plain,
( spl698_403
<=> ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_403])]) ).
fof(f18135,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)),
inference(cnf_transformation,[],[f5732]) ).
fof(f5732,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)),
inference(rectify,[],[f1191]) ).
fof(f1191,axiom,
! [X20,X4] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X20)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_top1I) ).
fof(f29954,plain,
spl698_402,
inference(avatar_split_clause,[],[f18134,f29952]) ).
fof(f29952,plain,
( spl698_402
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_402])]) ).
fof(f18134,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X0))),
inference(cnf_transformation,[],[f5731]) ).
fof(f5731,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X0))),
inference(rectify,[],[f4009]) ).
fof(f4009,axiom,
! [X113,X114] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X114,X113))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_distinct__upt) ).
fof(f29950,plain,
spl698_401,
inference(avatar_split_clause,[],[f18133,f29948]) ).
fof(f29948,plain,
( spl698_401
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_401])]) ).
fof(f18133,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))),
inference(cnf_transformation,[],[f5730]) ).
fof(f5730,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))),
inference(rectify,[],[f3687]) ).
fof(f3687,axiom,
! [X113,X114] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X114,X113))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_distinct__upto) ).
fof(f29946,plain,
spl698_400,
inference(avatar_split_clause,[],[f18132,f29944]) ).
fof(f29944,plain,
( spl698_400
<=> ! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_400])]) ).
fof(f18132,plain,
! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0,
inference(cnf_transformation,[],[f5729]) ).
fof(f5729,plain,
! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0,
inference(rectify,[],[f113]) ).
fof(f113,axiom,
! [X20,X4] : c_HOL_OThe(X4,hAPP(c_fequal,X20)) = X20,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_the__sym__eq__trivial) ).
fof(f29942,plain,
spl698_399,
inference(avatar_split_clause,[],[f18131,f29940]) ).
fof(f29940,plain,
( spl698_399
<=> ! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_399])]) ).
fof(f18131,plain,
! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0,
inference(cnf_transformation,[],[f5728]) ).
fof(f5728,plain,
! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0,
inference(rectify,[],[f3882]) ).
fof(f3882,axiom,
! [X20,X4] : c_Hilbert__Choice_OEps(X4,hAPP(c_fequal,X20)) = X20,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_some__sym__eq__trivial) ).
fof(f29937,plain,
spl698_398,
inference(avatar_split_clause,[],[f18130,f29935]) ).
fof(f29935,plain,
( spl698_398
<=> ! [X0,X1] : c_Enum_Oenum__the(X1,X0) = c_HOL_OThe(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_398])]) ).
fof(f18130,plain,
! [X0,X1] : c_Enum_Oenum__the(X1,X0) = c_HOL_OThe(X1,X0),
inference(cnf_transformation,[],[f5727]) ).
fof(f5727,plain,
! [X0,X1] : c_Enum_Oenum__the(X1,X0) = c_HOL_OThe(X1,X0),
inference(rectify,[],[f111]) ).
fof(f111,axiom,
! [X5,X4] : c_Enum_Oenum__the(X4,X5) = c_HOL_OThe(X4,X5),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_enum__the__def) ).
fof(f29933,plain,
spl698_397,
inference(avatar_split_clause,[],[f18127,f29931]) ).
fof(f29931,plain,
( spl698_397
<=> ! [X0,X1] : hAPP(c_Option_Ooption_OSome(X1),X0) != c_Option_Ooption_ONone(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_397])]) ).
fof(f18127,plain,
! [X0,X1] : hAPP(c_Option_Ooption_OSome(X1),X0) != c_Option_Ooption_ONone(X1),
inference(cnf_transformation,[],[f5724]) ).
fof(f5724,plain,
! [X0,X1] : hAPP(c_Option_Ooption_OSome(X1),X0) != c_Option_Ooption_ONone(X1),
inference(rectify,[],[f833]) ).
fof(f833,axiom,
! [X149,X23] : hAPP(c_Option_Ooption_OSome(X23),X149) != c_Option_Ooption_ONone(X23),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_option_Osimps_I3_J) ).
fof(f29929,plain,
spl698_396,
inference(avatar_split_clause,[],[f17976,f29927]) ).
fof(f29927,plain,
( spl698_396
<=> ! [X0] :
( c_Int_OMin = c_Int_OBit1(X0)
| c_Int_OMin != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_396])]) ).
fof(f17976,plain,
! [X0] :
( c_Int_OMin = c_Int_OBit1(X0)
| c_Int_OMin != X0 ),
inference(cnf_transformation,[],[f14793]) ).
fof(f14793,plain,
! [X0] :
( ( c_Int_OMin = c_Int_OBit1(X0)
| c_Int_OMin != X0 )
& ( c_Int_OMin = X0
| c_Int_OMin != c_Int_OBit1(X0) ) ),
inference(nnf_transformation,[],[f5634]) ).
fof(f5634,plain,
! [X0] :
( c_Int_OMin = c_Int_OBit1(X0)
<=> c_Int_OMin = X0 ),
inference(rectify,[],[f2781]) ).
fof(f2781,axiom,
! [X153] :
( c_Int_OBit1(X153) = c_Int_OMin
<=> c_Int_OMin = X153 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rel__simps_I43_J) ).
fof(f29925,plain,
spl698_395,
inference(avatar_split_clause,[],[f17975,f29923]) ).
fof(f29923,plain,
( spl698_395
<=> ! [X0] :
( c_Int_OMin = X0
| c_Int_OMin != c_Int_OBit1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_395])]) ).
fof(f17975,plain,
! [X0] :
( c_Int_OMin = X0
| c_Int_OMin != c_Int_OBit1(X0) ),
inference(cnf_transformation,[],[f14793]) ).
fof(f29921,plain,
spl698_394,
inference(avatar_split_clause,[],[f17972,f29919]) ).
fof(f29919,plain,
( spl698_394
<=> ! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_394])]) ).
fof(f17972,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 ),
inference(cnf_transformation,[],[f14791]) ).
fof(f14791,plain,
! [X0] :
( ( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 )
& ( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) ) ),
inference(nnf_transformation,[],[f5632]) ).
fof(f5632,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
<=> c_Int_OPls = X0 ),
inference(rectify,[],[f2651]) ).
fof(f2651,axiom,
! [X153] :
( c_Int_OPls = c_Int_OBit0(X153)
<=> c_Int_OPls = X153 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rel__simps_I38_J) ).
fof(f29917,plain,
spl698_393,
inference(avatar_split_clause,[],[f17971,f29915]) ).
fof(f29915,plain,
( spl698_393
<=> ! [X0] :
( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_393])]) ).
fof(f17971,plain,
! [X0] :
( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) ),
inference(cnf_transformation,[],[f14791]) ).
fof(f29913,plain,
spl698_392,
inference(avatar_split_clause,[],[f17961,f29911]) ).
fof(f29911,plain,
( spl698_392
<=> ! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_392])]) ).
fof(f17961,plain,
! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ),
inference(cnf_transformation,[],[f14783]) ).
fof(f14783,plain,
! [X0] :
( ( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) )
& ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0))
| ~ c_List_Onat__list(X0) ) ),
inference(nnf_transformation,[],[f5627]) ).
fof(f5627,plain,
! [X0] :
( c_List_Onat__list(X0)
<=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ),
inference(rectify,[],[f3693]) ).
fof(f3693,axiom,
! [X153] :
( c_List_Onat__list(X153)
<=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X153)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__list__def) ).
fof(f29909,plain,
spl698_391,
inference(avatar_split_clause,[],[f17960,f29907]) ).
fof(f29907,plain,
( spl698_391
<=> ! [X0] :
( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0))
| ~ c_List_Onat__list(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_391])]) ).
fof(f17960,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0))
| ~ c_List_Onat__list(X0) ),
inference(cnf_transformation,[],[f14783]) ).
fof(f29905,plain,
spl698_390,
inference(avatar_split_clause,[],[f17899,f29903]) ).
fof(f29903,plain,
( spl698_390
<=> ! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__inf__class_Oinf(X0))
| ~ class_Lattices_Osemilattice__inf(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_390])]) ).
fof(f17899,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__inf__class_Oinf(X0))
| ~ class_Lattices_Osemilattice__inf(X0) ),
inference(cnf_transformation,[],[f10220]) ).
fof(f10220,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__inf__class_Oinf(X0))
| ~ class_Lattices_Osemilattice__inf(X0) ),
inference(ennf_transformation,[],[f5571]) ).
fof(f5571,plain,
! [X0] :
( class_Lattices_Osemilattice__inf(X0)
=> c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__inf__class_Oinf(X0)) ),
inference(rectify,[],[f671]) ).
fof(f671,axiom,
! [X4] :
( class_Lattices_Osemilattice__inf(X4)
=> c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_fun__left__comm__idem__inf) ).
fof(f29901,plain,
spl698_389,
inference(avatar_split_clause,[],[f17898,f29899]) ).
fof(f29899,plain,
( spl698_389
<=> ! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__sup__class_Osup(X0))
| ~ class_Lattices_Osemilattice__sup(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_389])]) ).
fof(f17898,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__sup__class_Osup(X0))
| ~ class_Lattices_Osemilattice__sup(X0) ),
inference(cnf_transformation,[],[f10219]) ).
fof(f10219,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__sup__class_Osup(X0))
| ~ class_Lattices_Osemilattice__sup(X0) ),
inference(ennf_transformation,[],[f5570]) ).
fof(f5570,plain,
! [X0] :
( class_Lattices_Osemilattice__sup(X0)
=> c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__sup__class_Osup(X0)) ),
inference(rectify,[],[f670]) ).
fof(f670,axiom,
! [X4] :
( class_Lattices_Osemilattice__sup(X4)
=> c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_fun__left__comm__idem__sup) ).
fof(f29897,plain,
( spl698_388
| ~ spl698_338 ),
inference(avatar_split_clause,[],[f29694,f29620,f29895]) ).
fof(f29895,plain,
( spl698_388
<=> ! [X0] : sP9(X0,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_388])]) ).
fof(f29620,plain,
( spl698_338
<=> ! [X0,X1] :
( c_Int_OPls != X1
| sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_338])]) ).
fof(f29694,plain,
( ! [X0] : sP9(X0,c_Int_OPls)
| ~ spl698_338 ),
inference(equality_resolution,[],[f29621]) ).
fof(f29621,plain,
( ! [X0,X1] :
( c_Int_OPls != X1
| sP9(X0,X1) )
| ~ spl698_338 ),
inference(avatar_component_clause,[],[f29620]) ).
fof(f29893,plain,
spl698_387,
inference(avatar_split_clause,[],[f17893,f29891]) ).
fof(f29891,plain,
( spl698_387
<=> ! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_387])]) ).
fof(f17893,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10214]) ).
fof(f10214,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5565]) ).
fof(f5565,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0)) ),
inference(rectify,[],[f1513]) ).
fof(f1513,axiom,
! [X4] :
( class_Orderings_Olinorder(X4)
=> c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Orderings_Oord__class_Omin(X4)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_min__max_Ofun__left__comm__idem__inf) ).
fof(f29889,plain,
spl698_386,
inference(avatar_split_clause,[],[f17892,f29887]) ).
fof(f29887,plain,
( spl698_386
<=> ! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_386])]) ).
fof(f17892,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10213]) ).
fof(f10213,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5564]) ).
fof(f5564,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0)) ),
inference(rectify,[],[f2156]) ).
fof(f2156,axiom,
! [X4] :
( class_Orderings_Olinorder(X4)
=> c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Orderings_Oord__class_Omax(X4)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_min__max_Ofun__left__comm__idem__sup) ).
fof(f29885,plain,
spl698_385,
inference(avatar_split_clause,[],[f17874,f29883]) ).
fof(f29883,plain,
( spl698_385
<=> ! [X0] :
( c_Finite__Set_Ofun__left__comm(X0,X0,c_Groups_Otimes__class_Otimes(X0))
| ~ class_Groups_Oab__semigroup__mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_385])]) ).
fof(f17874,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm(X0,X0,c_Groups_Otimes__class_Otimes(X0))
| ~ class_Groups_Oab__semigroup__mult(X0) ),
inference(cnf_transformation,[],[f10195]) ).
fof(f10195,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm(X0,X0,c_Groups_Otimes__class_Otimes(X0))
| ~ class_Groups_Oab__semigroup__mult(X0) ),
inference(ennf_transformation,[],[f5546]) ).
fof(f5546,plain,
! [X0] :
( class_Groups_Oab__semigroup__mult(X0)
=> c_Finite__Set_Ofun__left__comm(X0,X0,c_Groups_Otimes__class_Otimes(X0)) ),
inference(rectify,[],[f4884]) ).
fof(f4884,axiom,
! [X4] :
( class_Groups_Oab__semigroup__mult(X4)
=> c_Finite__Set_Ofun__left__comm(X4,X4,c_Groups_Otimes__class_Otimes(X4)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_fun__left__comm) ).
fof(f29881,plain,
spl698_384,
inference(avatar_split_clause,[],[f17871,f29879]) ).
fof(f29879,plain,
( spl698_384
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_384])]) ).
fof(f17871,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(cnf_transformation,[],[f10192]) ).
fof(f10192,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(ennf_transformation,[],[f5543]) ).
fof(f5543,plain,
! [X0] :
( class_Rings_Ozero__neq__one(X0)
=> c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) ),
inference(rectify,[],[f1475]) ).
fof(f1475,axiom,
! [X23] :
( class_Rings_Ozero__neq__one(X23)
=> c_Groups_Oone__class_Oone(X23) != c_Groups_Ozero__class_Ozero(X23) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zero__neq__one) ).
fof(f29877,plain,
spl698_383,
inference(avatar_split_clause,[],[f17843,f29875]) ).
fof(f29875,plain,
( spl698_383
<=> ! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Groups_Otimes__class_Otimes(X0))
| ~ class_Lattices_Oab__semigroup__idem__mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_383])]) ).
fof(f17843,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Groups_Otimes__class_Otimes(X0))
| ~ class_Lattices_Oab__semigroup__idem__mult(X0) ),
inference(cnf_transformation,[],[f10164]) ).
fof(f10164,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Groups_Otimes__class_Otimes(X0))
| ~ class_Lattices_Oab__semigroup__idem__mult(X0) ),
inference(ennf_transformation,[],[f5515]) ).
fof(f5515,plain,
! [X0] :
( class_Lattices_Oab__semigroup__idem__mult(X0)
=> c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Groups_Otimes__class_Otimes(X0)) ),
inference(rectify,[],[f1333]) ).
fof(f1333,axiom,
! [X4] :
( class_Lattices_Oab__semigroup__idem__mult(X4)
=> c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Groups_Otimes__class_Otimes(X4)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_fun__left__comm__idem) ).
fof(f29873,plain,
spl698_382,
inference(avatar_split_clause,[],[f17842,f29871]) ).
fof(f29871,plain,
( spl698_382
<=> ! [X0] :
( c_List_Oembed__list(c_List_Oreturn__list(X0)) = X0
| ~ c_List_Onat__list(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_382])]) ).
fof(f17842,plain,
! [X0] :
( c_List_Oembed__list(c_List_Oreturn__list(X0)) = X0
| ~ c_List_Onat__list(X0) ),
inference(cnf_transformation,[],[f10163]) ).
fof(f10163,plain,
! [X0] :
( c_List_Oembed__list(c_List_Oreturn__list(X0)) = X0
| ~ c_List_Onat__list(X0) ),
inference(ennf_transformation,[],[f5514]) ).
fof(f5514,plain,
! [X0] :
( c_List_Onat__list(X0)
=> c_List_Oembed__list(c_List_Oreturn__list(X0)) = X0 ),
inference(rectify,[],[f4098]) ).
fof(f4098,axiom,
! [X124] :
( c_List_Onat__list(X124)
=> c_List_Oembed__list(c_List_Oreturn__list(X124)) = X124 ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_transfer__nat__int__list__return__embed) ).
fof(f29869,plain,
spl698_381,
inference(avatar_split_clause,[],[f17616,f29867]) ).
fof(f29867,plain,
( spl698_381
<=> ! [X0] : c_Finite__Set_Ofun__left__comm__idem(X0,tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_381])]) ).
fof(f17616,plain,
! [X0] : c_Finite__Set_Ofun__left__comm__idem(X0,tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0)),
inference(cnf_transformation,[],[f5302]) ).
fof(f5302,plain,
! [X0] : c_Finite__Set_Ofun__left__comm__idem(X0,tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0)),
inference(rectify,[],[f669]) ).
fof(f669,axiom,
! [X4] : c_Finite__Set_Ofun__left__comm__idem(X4,tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_fun__left__comm__idem__insert) ).
fof(f29865,plain,
spl698_380,
inference(avatar_split_clause,[],[f17615,f29863]) ).
fof(f29863,plain,
( spl698_380
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_380])]) ).
fof(f17615,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f5301]) ).
fof(f5301,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f191]) ).
fof(f191,axiom,
! [X88] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X88),X88)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_le__refl) ).
fof(f29861,plain,
spl698_379,
inference(avatar_split_clause,[],[f17614,f29859]) ).
fof(f29859,plain,
( spl698_379
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_379])]) ).
fof(f17614,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)),
inference(cnf_transformation,[],[f5300]) ).
fof(f5300,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)),
inference(rectify,[],[f1813]) ).
fof(f1813,axiom,
! [X196] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X196),X196)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zle__refl) ).
fof(f29857,plain,
spl698_378,
inference(avatar_split_clause,[],[f17612,f29855]) ).
fof(f17612,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X0),X0)),
inference(cnf_transformation,[],[f5298]) ).
fof(f5298,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X0),X0)),
inference(rectify,[],[f157]) ).
fof(f157,axiom,
! [X32] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X32),X32)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_evalc_Oequations_I1_J) ).
fof(f29853,plain,
( spl698_377
| ~ spl698_194
| ~ spl698_287
| ~ spl698_376 ),
inference(avatar_split_clause,[],[f29849,f29846,f29408,f28986,f29851]) ).
fof(f29846,plain,
( spl698_376
<=> ! [X0] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_376])]) ).
fof(f29849,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_fequal,X0),X0))
| ~ spl698_194
| ~ spl698_287
| ~ spl698_376 ),
inference(forward_demodulation,[],[f29847,f29647]) ).
fof(f29847,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X0),X0))
| ~ spl698_376 ),
inference(avatar_component_clause,[],[f29846]) ).
fof(f29848,plain,
spl698_376,
inference(avatar_split_clause,[],[f17611,f29846]) ).
fof(f17611,plain,
! [X0] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X0),X0)),
inference(cnf_transformation,[],[f5297]) ).
fof(f5297,plain,
! [X0] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X0),X0)),
inference(rectify,[],[f4974]) ).
fof(f4974,axiom,
! [X112] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X112),X112)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__int__refl) ).
fof(f29844,plain,
spl698_375,
inference(avatar_split_clause,[],[f17609,f29842]) ).
fof(f29842,plain,
( spl698_375
<=> ! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_375])]) ).
fof(f17609,plain,
! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0,
inference(cnf_transformation,[],[f5295]) ).
fof(f5295,plain,
! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0,
inference(rectify,[],[f4637]) ).
fof(f4637,axiom,
! [X112] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X112)) = X112,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_of__nat__nat__of) ).
fof(f29840,plain,
spl698_374,
inference(avatar_split_clause,[],[f17608,f29838]) ).
fof(f29838,plain,
( spl698_374
<=> ! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_374])]) ).
fof(f17608,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0,
inference(cnf_transformation,[],[f5294]) ).
fof(f5294,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0,
inference(rectify,[],[f4636]) ).
fof(f4636,axiom,
! [X88] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X88)) = X88,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__of__of__nat) ).
fof(f29836,plain,
spl698_373,
inference(avatar_split_clause,[],[f17607,f29834]) ).
fof(f29834,plain,
( spl698_373
<=> ! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_373])]) ).
fof(f17607,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0,
inference(cnf_transformation,[],[f5293]) ).
fof(f5293,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0,
inference(rectify,[],[f3094]) ).
fof(f3094,axiom,
! [X20] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X20)) = X20,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Rep__Integ__inverse) ).
fof(f29832,plain,
spl698_372,
inference(avatar_split_clause,[],[f17606,f29830]) ).
fof(f17606,plain,
! [X0] : c_Int_Opred(c_Int_OBit0(X0)) = c_Int_OBit1(c_Int_Opred(X0)),
inference(cnf_transformation,[],[f5292]) ).
fof(f5292,plain,
! [X0] : c_Int_Opred(c_Int_OBit0(X0)) = c_Int_OBit1(c_Int_Opred(X0)),
inference(rectify,[],[f2868]) ).
fof(f2868,axiom,
! [X112] : c_Int_Opred(c_Int_OBit0(X112)) = c_Int_OBit1(c_Int_Opred(X112)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_pred__Bit0) ).
fof(f29828,plain,
spl698_371,
inference(avatar_split_clause,[],[f17605,f29826]) ).
fof(f17605,plain,
! [X0] : c_Int_Osucc(c_Int_OBit1(X0)) = c_Int_OBit0(c_Int_Osucc(X0)),
inference(cnf_transformation,[],[f5291]) ).
fof(f5291,plain,
! [X0] : c_Int_Osucc(c_Int_OBit1(X0)) = c_Int_OBit0(c_Int_Osucc(X0)),
inference(rectify,[],[f2685]) ).
fof(f2685,axiom,
! [X112] : c_Int_Osucc(c_Int_OBit1(X112)) = c_Int_OBit0(c_Int_Osucc(X112)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_succ__Bit1) ).
fof(f29824,plain,
spl698_370,
inference(avatar_split_clause,[],[f17604,f29822]) ).
fof(f29822,plain,
( spl698_370
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Obutlast(X0,c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_370])]) ).
fof(f17604,plain,
! [X0] : c_List_Olist_ONil(X0) = c_List_Obutlast(X0,c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5290]) ).
fof(f5290,plain,
! [X0] : c_List_Olist_ONil(X0) = c_List_Obutlast(X0,c_List_Olist_ONil(X0)),
inference(rectify,[],[f3976]) ).
fof(f3976,axiom,
! [X23] : c_List_Olist_ONil(X23) = c_List_Obutlast(X23,c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_butlast_Osimps_I1_J) ).
fof(f29820,plain,
spl698_369,
inference(avatar_split_clause,[],[f17603,f29818]) ).
fof(f29818,plain,
( spl698_369
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(X0,c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_369])]) ).
fof(f17603,plain,
! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(X0,c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5289]) ).
fof(f5289,plain,
! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(X0,c_List_Olist_ONil(X0)),
inference(rectify,[],[f4212]) ).
fof(f4212,axiom,
! [X23] : c_List_Olist_ONil(X23) = c_List_Oremdups(X23,c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_remdups_Osimps_I1_J) ).
fof(f29816,plain,
spl698_368,
inference(avatar_split_clause,[],[f17599,f29814]) ).
fof(f29814,plain,
( spl698_368
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_368])]) ).
fof(f17599,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f5285]) ).
fof(f5285,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f657]) ).
fof(f657,axiom,
! [X88] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),X88)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_less__not__refl) ).
fof(f29812,plain,
spl698_367,
inference(avatar_split_clause,[],[f17598,f29810]) ).
fof(f29810,plain,
( spl698_367
<=> ! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_367])]) ).
fof(f17598,plain,
! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(cnf_transformation,[],[f5284]) ).
fof(f5284,plain,
! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(rectify,[],[f2538]) ).
fof(f2538,axiom,
! [X88] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X88))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_not__neg__int) ).
fof(f29808,plain,
spl698_366,
inference(avatar_split_clause,[],[f17489,f29805]) ).
fof(f29805,plain,
( spl698_366
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_366])]) ).
fof(f17489,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f2790]) ).
fof(f2790,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rel__simps_I23_J) ).
fof(f29803,plain,
spl698_365,
inference(avatar_split_clause,[],[f17487,f29800]) ).
fof(f29800,plain,
( spl698_365
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_365])]) ).
fof(f17487,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f2795]) ).
fof(f2795,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rel__simps_I6_J) ).
fof(f29798,plain,
( spl698_364
| ~ spl698_278
| ~ spl698_363 ),
inference(avatar_split_clause,[],[f29793,f29789,f29372,f29795]) ).
fof(f29795,plain,
( spl698_364
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_364])]) ).
fof(f29789,plain,
( spl698_363
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_363])]) ).
fof(f29793,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))
| ~ spl698_278
| ~ spl698_363 ),
inference(forward_demodulation,[],[f29791,f29373]) ).
fof(f29791,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)))
| ~ spl698_363 ),
inference(avatar_component_clause,[],[f29789]) ).
fof(f29792,plain,
spl698_363,
inference(avatar_split_clause,[],[f17484,f29789]) ).
fof(f17484,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
inference(cnf_transformation,[],[f2803]) ).
fof(f2803,axiom,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_neg__number__of__Min) ).
fof(f29787,plain,
spl698_362,
inference(avatar_split_clause,[],[f17481,f29784]) ).
fof(f29784,plain,
( spl698_362
<=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin ),
introduced(avatar_definition,[new_symbols(naming,[spl698_362])]) ).
fof(f17481,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin,
inference(cnf_transformation,[],[f2801]) ).
fof(f2801,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Int_OMin__def) ).
fof(f29782,plain,
spl698_361,
inference(avatar_split_clause,[],[f17472,f29779]) ).
fof(f29779,plain,
( spl698_361
<=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_361])]) ).
fof(f17472,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
inference(cnf_transformation,[],[f2856]) ).
fof(f2856,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zero__code__numeral__code) ).
fof(f29777,plain,
spl698_360,
inference(avatar_split_clause,[],[f17469,f29774]) ).
fof(f29774,plain,
( spl698_360
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_360])]) ).
fof(f17469,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f2450]) ).
fof(f2450,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_transfer__nat__int__numerals_I2_J) ).
fof(f29772,plain,
( spl698_359
| ~ spl698_203
| ~ spl698_316 ),
inference(avatar_split_clause,[],[f29680,f29527,f29032,f29769]) ).
fof(f29769,plain,
( spl698_359
<=> sP4(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_359])]) ).
fof(f29032,plain,
( spl698_203
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_203])]) ).
fof(f29680,plain,
( sP4(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl698_203
| ~ spl698_316 ),
inference(resolution,[],[f29528,f29034]) ).
fof(f29034,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl698_203 ),
inference(avatar_component_clause,[],[f29032]) ).
fof(f29767,plain,
spl698_358,
inference(avatar_split_clause,[],[f17468,f29764]) ).
fof(f29764,plain,
( spl698_358
<=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_358])]) ).
fof(f17468,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f4627]) ).
fof(f4627,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_one__code__numeral__def) ).
fof(f29762,plain,
spl698_357,
inference(avatar_split_clause,[],[f17466,f29759]) ).
fof(f29759,plain,
( spl698_357
<=> c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_357])]) ).
fof(f17466,plain,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f3087]) ).
fof(f3087,axiom,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_pair__less__def) ).
fof(f29757,plain,
spl698_356,
inference(avatar_split_clause,[],[f17465,f29754]) ).
fof(f29754,plain,
( spl698_356
<=> c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_356])]) ).
fof(f17465,plain,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f3078]) ).
fof(f3078,axiom,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_max__strict__def) ).
fof(f29752,plain,
spl698_355,
inference(avatar_split_clause,[],[f17464,f29749]) ).
fof(f29749,plain,
( spl698_355
<=> c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_355])]) ).
fof(f17464,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f3081]) ).
fof(f3081,axiom,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_min__strict__def) ).
fof(f29747,plain,
~ spl698_354,
inference(avatar_split_clause,[],[f17463,f29744]) ).
fof(f17463,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f2791]) ).
fof(f2791,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rel__simps_I20_J) ).
fof(f29742,plain,
~ spl698_353,
inference(avatar_split_clause,[],[f17462,f29739]) ).
fof(f29739,plain,
( spl698_353
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_353])]) ).
fof(f17462,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
inference(cnf_transformation,[],[f2563]) ).
fof(f2563,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rel__simps_I2_J) ).
fof(f29737,plain,
~ spl698_352,
inference(avatar_split_clause,[],[f17461,f29734]) ).
fof(f29734,plain,
( spl698_352
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_352])]) ).
fof(f17461,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f2794]) ).
fof(f2794,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rel__simps_I3_J) ).
fof(f29732,plain,
~ spl698_351,
inference(avatar_split_clause,[],[f17460,f29729]) ).
fof(f29729,plain,
( spl698_351
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_351])]) ).
fof(f17460,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
inference(cnf_transformation,[],[f2785]) ).
fof(f2785,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rel__simps_I7_J) ).
fof(f29727,plain,
( ~ spl698_350
| ~ spl698_194
| ~ spl698_287
| spl698_348 ),
inference(avatar_split_clause,[],[f29717,f29713,f29408,f28986,f29724]) ).
fof(f29724,plain,
( spl698_350
<=> hBOOL(hAPP(hAPP(c_fequal,c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_350])]) ).
fof(f29713,plain,
( spl698_348
<=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_348])]) ).
fof(f29717,plain,
( ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OPls),c_Int_OMin))
| ~ spl698_194
| ~ spl698_287
| spl698_348 ),
inference(forward_demodulation,[],[f29715,f29647]) ).
fof(f29715,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| spl698_348 ),
inference(avatar_component_clause,[],[f29713]) ).
fof(f29722,plain,
( spl698_349
| ~ spl698_202
| ~ spl698_316 ),
inference(avatar_split_clause,[],[f29679,f29527,f29027,f29719]) ).
fof(f29719,plain,
( spl698_349
<=> sP4(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_349])]) ).
fof(f29027,plain,
( spl698_202
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_202])]) ).
fof(f29679,plain,
( sP4(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl698_202
| ~ spl698_316 ),
inference(resolution,[],[f29528,f29029]) ).
fof(f29029,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl698_202 ),
inference(avatar_component_clause,[],[f29027]) ).
fof(f29716,plain,
~ spl698_348,
inference(avatar_split_clause,[],[f17459,f29713]) ).
fof(f17459,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f4969]) ).
fof(f4969,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__int__code_I2_J) ).
fof(f29711,plain,
( ~ spl698_347
| ~ spl698_194
| ~ spl698_287
| spl698_346 ),
inference(avatar_split_clause,[],[f29706,f29702,f29408,f28986,f29708]) ).
fof(f29708,plain,
( spl698_347
<=> hBOOL(hAPP(hAPP(c_fequal,c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_347])]) ).
fof(f29702,plain,
( spl698_346
<=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_346])]) ).
fof(f29706,plain,
( ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OMin),c_Int_OPls))
| ~ spl698_194
| ~ spl698_287
| spl698_346 ),
inference(forward_demodulation,[],[f29704,f29647]) ).
fof(f29704,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls))
| spl698_346 ),
inference(avatar_component_clause,[],[f29702]) ).
fof(f29705,plain,
~ spl698_346,
inference(avatar_split_clause,[],[f17458,f29702]) ).
fof(f17458,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f4968]) ).
fof(f4968,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__int__code_I5_J) ).
fof(f29699,plain,
~ spl698_345,
inference(avatar_split_clause,[],[f17457,f29696]) ).
fof(f29696,plain,
( spl698_345
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_345])]) ).
fof(f17457,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(cnf_transformation,[],[f2582]) ).
fof(f2582,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_not__neg__number__of__Pls) ).
fof(f29693,plain,
( spl698_344
| ~ spl698_203
| ~ spl698_314 ),
inference(avatar_split_clause,[],[f29672,f29519,f29032,f29690]) ).
fof(f29690,plain,
( spl698_344
<=> c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_344])]) ).
fof(f29672,plain,
( c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl698_203
| ~ spl698_314 ),
inference(resolution,[],[f29520,f29034]) ).
fof(f29688,plain,
( spl698_343
| ~ spl698_202
| ~ spl698_314 ),
inference(avatar_split_clause,[],[f29671,f29519,f29027,f29685]) ).
fof(f29685,plain,
( spl698_343
<=> c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_343])]) ).
fof(f29671,plain,
( c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl698_202
| ~ spl698_314 ),
inference(resolution,[],[f29520,f29029]) ).
fof(f29667,plain,
( spl698_342
| ~ spl698_195
| ~ spl698_287 ),
inference(avatar_split_clause,[],[f29641,f29408,f28991,f29664]) ).
fof(f29664,plain,
( spl698_342
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_342])]) ).
fof(f28991,plain,
( spl698_195
<=> class_HOL_Oequal(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_195])]) ).
fof(f29641,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Nat_Onat)
| ~ spl698_195
| ~ spl698_287 ),
inference(resolution,[],[f29409,f28993]) ).
fof(f28993,plain,
( class_HOL_Oequal(tc_Nat_Onat)
| ~ spl698_195 ),
inference(avatar_component_clause,[],[f28991]) ).
fof(f29662,plain,
( spl698_341
| ~ spl698_192
| ~ spl698_287 ),
inference(avatar_split_clause,[],[f29640,f29408,f28976,f29659]) ).
fof(f29659,plain,
( spl698_341
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Com_Ostate) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_341])]) ).
fof(f28976,plain,
( spl698_192
<=> class_HOL_Oequal(tc_Com_Ostate) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_192])]) ).
fof(f29640,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Com_Ostate)
| ~ spl698_192
| ~ spl698_287 ),
inference(resolution,[],[f29409,f28978]) ).
fof(f28978,plain,
( class_HOL_Oequal(tc_Com_Ostate)
| ~ spl698_192 ),
inference(avatar_component_clause,[],[f28976]) ).
fof(f29657,plain,
( spl698_340
| ~ spl698_196
| ~ spl698_287 ),
inference(avatar_split_clause,[],[f29639,f29408,f28996,f29654]) ).
fof(f29654,plain,
( spl698_340
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_340])]) ).
fof(f28996,plain,
( spl698_196
<=> class_HOL_Oequal(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_196])]) ).
fof(f29639,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_HOL_Obool)
| ~ spl698_196
| ~ spl698_287 ),
inference(resolution,[],[f29409,f28998]) ).
fof(f28998,plain,
( class_HOL_Oequal(tc_HOL_Obool)
| ~ spl698_196 ),
inference(avatar_component_clause,[],[f28996]) ).
fof(f29634,plain,
( spl698_339
| ~ spl698_218
| ~ spl698_236
| ~ spl698_273 ),
inference(avatar_split_clause,[],[f29626,f29352,f29182,f29097,f29631]) ).
fof(f29631,plain,
( spl698_339
<=> c_Int_OPls = c_Int_Opred(c_Int_Osucc(c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_339])]) ).
fof(f29097,plain,
( spl698_218
<=> c_Int_OPls = c_Int_OBit0(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_218])]) ).
fof(f29352,plain,
( spl698_273
<=> ! [X0] : c_Int_OBit0(X0) = c_Int_Opred(c_Int_OBit1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_273])]) ).
fof(f29626,plain,
( c_Int_OPls = c_Int_Opred(c_Int_Osucc(c_Int_OPls))
| ~ spl698_218
| ~ spl698_236
| ~ spl698_273 ),
inference(forward_demodulation,[],[f29624,f29099]) ).
fof(f29099,plain,
( c_Int_OPls = c_Int_OBit0(c_Int_OPls)
| ~ spl698_218 ),
inference(avatar_component_clause,[],[f29097]) ).
fof(f29624,plain,
( c_Int_OBit0(c_Int_OPls) = c_Int_Opred(c_Int_Osucc(c_Int_OPls))
| ~ spl698_236
| ~ spl698_273 ),
inference(superposition,[],[f29353,f29184]) ).
fof(f29353,plain,
( ! [X0] : c_Int_OBit0(X0) = c_Int_Opred(c_Int_OBit1(X0))
| ~ spl698_273 ),
inference(avatar_component_clause,[],[f29352]) ).
fof(f29622,plain,
spl698_338,
inference(avatar_split_clause,[],[f26456,f29620]) ).
fof(f26456,plain,
! [X0,X1] :
( c_Int_OPls != X1
| sP9(X0,X1) ),
inference(forward_demodulation,[],[f19571,f17436]) ).
fof(f19571,plain,
! [X0,X1] :
( sP9(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ),
inference(cnf_transformation,[],[f15235]) ).
fof(f15235,plain,
! [X0,X1] :
( ( sP9(X0,X1)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(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 ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
& hBOOL(hAPP(hAPP(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
| ~ sP9(X0,X1) ) ),
inference(rectify,[],[f15234]) ).
fof(f15234,plain,
! [X1,X0] :
( ( sP9(X1,X0)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(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 ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
& hBOOL(hAPP(hAPP(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
| ~ sP9(X1,X0) ) ),
inference(flattening,[],[f15233]) ).
fof(f15233,plain,
! [X1,X0] :
( ( sP9(X1,X0)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(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 ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
& hBOOL(hAPP(hAPP(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
| ~ sP9(X1,X0) ) ),
inference(nnf_transformation,[],[f14552]) ).
fof(f14552,plain,
! [X1,X0] :
( sP9(X1,X0)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
& hBOOL(hAPP(hAPP(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,[sP9])]) ).
fof(f29618,plain,
spl698_337,
inference(avatar_split_clause,[],[f25109,f29616]) ).
fof(f29616,plain,
( spl698_337
<=> ! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_337])]) ).
fof(f25109,plain,
! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(forward_demodulation,[],[f17815,f17436]) ).
fof(f17815,plain,
! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f5500]) ).
fof(f29614,plain,
spl698_336,
inference(avatar_split_clause,[],[f24994,f29612]) ).
fof(f29612,plain,
( spl698_336
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_336])]) ).
fof(f24994,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin),
inference(forward_demodulation,[],[f24993,f17436]) ).
fof(f24993,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin),
inference(forward_demodulation,[],[f17678,f17595]) ).
fof(f17678,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
inference(cnf_transformation,[],[f5364]) ).
fof(f5364,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
inference(rectify,[],[f2827]) ).
fof(f2827,axiom,
! [X32] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X32,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zmod__minus1__right) ).
fof(f29610,plain,
spl698_335,
inference(avatar_split_clause,[],[f24973,f29608]) ).
fof(f29608,plain,
( spl698_335
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OPls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_335])]) ).
fof(f24973,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OPls,X0),
inference(forward_demodulation,[],[f17625,f17436]) ).
fof(f17625,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),
inference(cnf_transformation,[],[f5311]) ).
fof(f5311,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),
inference(rectify,[],[f2106]) ).
fof(f2106,axiom,
! [X33] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zmod__zero) ).
fof(f29606,plain,
spl698_334,
inference(avatar_split_clause,[],[f24969,f29604]) ).
fof(f29604,plain,
( spl698_334
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_334])]) ).
fof(f24969,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(forward_demodulation,[],[f17602,f17436]) ).
fof(f17602,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f5288]) ).
fof(f5288,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(rectify,[],[f2103]) ).
fof(f2103,axiom,
! [X32] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X32,X32),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zmod__self) ).
fof(f29602,plain,
spl698_333,
inference(avatar_split_clause,[],[f24967,f29600]) ).
fof(f29600,plain,
( spl698_333
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_333])]) ).
fof(f24967,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X0)),
inference(forward_demodulation,[],[f17589,f17447]) ).
fof(f17589,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X0)),
inference(cnf_transformation,[],[f5275]) ).
fof(f5275,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X0)),
inference(rectify,[],[f1687]) ).
fof(f1687,axiom,
! [X191] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X191)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_vname_Osize_I2_J) ).
fof(f29598,plain,
spl698_332,
inference(avatar_split_clause,[],[f24966,f29596]) ).
fof(f29596,plain,
( spl698_332
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_332])]) ).
fof(f24966,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X0)),
inference(forward_demodulation,[],[f17588,f17447]) ).
fof(f17588,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X0)),
inference(cnf_transformation,[],[f5274]) ).
fof(f5274,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X0)),
inference(rectify,[],[f1684]) ).
fof(f1684,axiom,
! [X111] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X111)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_vname_Osize_I1_J) ).
fof(f29594,plain,
spl698_331,
inference(avatar_split_clause,[],[f24960,f29592]) ).
fof(f24960,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0),
inference(forward_demodulation,[],[f17582,f17447]) ).
fof(f17582,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X0),
inference(cnf_transformation,[],[f5268]) ).
fof(f5268,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X0),
inference(rectify,[],[f1483]) ).
fof(f1483,axiom,
! [X185] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X185),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat_Osimps_I2_J) ).
fof(f29589,plain,
~ spl698_330,
inference(avatar_split_clause,[],[f24910,f29586]) ).
fof(f29586,plain,
( spl698_330
<=> c_Int_OPls = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_330])]) ).
fof(f24910,plain,
c_Int_OPls != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
inference(forward_demodulation,[],[f17507,f24885]) ).
fof(f24885,plain,
c_Int_OPls = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(forward_demodulation,[],[f17473,f17436]) ).
fof(f17473,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(cnf_transformation,[],[f2578]) ).
fof(f2578,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zero__is__num__zero) ).
fof(f17507,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
inference(cnf_transformation,[],[f2800]) ).
fof(f2800,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_eq__number__of__Pls__Min) ).
fof(f29584,plain,
spl698_329,
inference(avatar_split_clause,[],[f24887,f29581]) ).
fof(f24887,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OPls),
inference(forward_demodulation,[],[f24886,f17447]) ).
fof(f24886,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(forward_demodulation,[],[f17474,f17436]) ).
fof(f17474,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f2443]) ).
fof(f2443,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_transfer__nat__int__numerals_I1_J) ).
fof(f29579,plain,
spl698_328,
inference(avatar_split_clause,[],[f24881,f29576]) ).
fof(f29576,plain,
( spl698_328
<=> c_HOL_Obool_Obool__size(c_fTrue) = c_Nat_Onat_Onat__size(c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_328])]) ).
fof(f24881,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Nat_Onat_Onat__size(c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17456,f17447]) ).
fof(f17456,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1836]) ).
fof(f1836,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat_Osize_I1_J) ).
fof(f29574,plain,
spl698_327,
inference(avatar_split_clause,[],[f24880,f29571]) ).
fof(f29571,plain,
( spl698_327
<=> c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_327])]) ).
fof(f24880,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17455,f17447]) ).
fof(f17455,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(cnf_transformation,[],[f2921]) ).
fof(f2921,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_code__numeral_Osize_I1_J) ).
fof(f29569,plain,
spl698_326,
inference(avatar_split_clause,[],[f20701,f29567]) ).
fof(f29567,plain,
( spl698_326
<=> ! [X2,X0,X1] :
( sP27(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_326])]) ).
fof(f20701,plain,
! [X2,X0,X1] :
( sP27(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f14581]) ).
fof(f14581,plain,
! [X0,X1,X2] :
( sP27(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(definition_folding,[],[f11756,f14580,f14579]) ).
fof(f14580,plain,
! [X1,X0,X2] :
( ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Oappend(X2),X1),X0))
<=> sP26(X2,X0,X1) )
| ~ sP27(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP27])]) ).
fof(f11756,plain,
! [X0,X1,X2] :
( ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Oappend(X2),X1),X0))
<=> ( ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
& c_List_Olinorder__class_Osorted(X2,X0)
& c_List_Olinorder__class_Osorted(X2,X1) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7620]) ).
fof(f7620,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Oappend(X2),X1),X0))
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1)))
=> ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4)) ) )
& c_List_Olinorder__class_Osorted(X2,X0)
& c_List_Olinorder__class_Osorted(X2,X1) ) ) ),
inference(rectify,[],[f4286]) ).
fof(f4286,axiom,
! [X259,X258,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Oappend(X4),X258),X259))
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X258)))
=> ! [X118] :
( hBOOL(hAPP(hAPP(c_member(X4),X118),hAPP(c_List_Oset(X4),X259)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X2),X118)) ) )
& c_List_Olinorder__class_Osorted(X4,X259)
& c_List_Olinorder__class_Osorted(X4,X258) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_sorted__append) ).
fof(f29565,plain,
spl698_325,
inference(avatar_split_clause,[],[f20255,f29563]) ).
fof(f29563,plain,
( spl698_325
<=> ! [X2,X0,X1] :
( sP25(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_325])]) ).
fof(f20255,plain,
! [X2,X0,X1] :
( sP25(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f14578]) ).
fof(f14578,plain,
! [X0,X1,X2] :
( sP25(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f11216,f14577,f14576]) ).
fof(f14576,plain,
! [X0,X2,X1] :
( sP24(X0,X2,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).
fof(f14577,plain,
! [X1,X2,X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> sP24(X0,X2,X1) )
| ~ sP25(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP25])]) ).
fof(f11216,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(ennf_transformation,[],[f7266]) ).
fof(f7266,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ) ),
inference(rectify,[],[f1537]) ).
fof(f1537,axiom,
! [X26,X6,X4] :
( class_Rings_Olinordered__ring__strict(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X26)),c_Groups_Ozero__class_Ozero(X4)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),c_Groups_Ozero__class_Ozero(X4)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X6)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_mult__le__0__iff) ).
fof(f29561,plain,
spl698_324,
inference(avatar_split_clause,[],[f20246,f29559]) ).
fof(f29559,plain,
( spl698_324
<=> ! [X2,X0,X1] :
( sP23(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_324])]) ).
fof(f20246,plain,
! [X2,X0,X1] :
( sP23(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f14575]) ).
fof(f14575,plain,
! [X0,X1,X2] :
( sP23(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f11215,f14574,f14573]) ).
fof(f14573,plain,
! [X2,X0,X1] :
( sP22(X2,X0,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
fof(f14574,plain,
! [X1,X0,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
<=> sP22(X2,X0,X1) )
| ~ sP23(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).
fof(f11215,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(ennf_transformation,[],[f7265]) ).
fof(f7265,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ) ),
inference(rectify,[],[f1538]) ).
fof(f1538,axiom,
! [X26,X6,X4] :
( class_Rings_Olinordered__ring__strict(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X26)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),c_Groups_Ozero__class_Ozero(X4)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X6)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zero__le__mult__iff) ).
fof(f29557,plain,
spl698_323,
inference(avatar_split_clause,[],[f20198,f29555]) ).
fof(f29555,plain,
( spl698_323
<=> ! [X2,X0,X1] :
( sP21(X1,X2,X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_323])]) ).
fof(f20198,plain,
! [X2,X0,X1] :
( sP21(X1,X2,X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(cnf_transformation,[],[f14572]) ).
fof(f14572,plain,
! [X0,X1,X2] :
( sP21(X1,X2,X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(definition_folding,[],[f11165,f14571,f14570]) ).
fof(f14570,plain,
! [X0,X2,X1] :
( sP20(X0,X2,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).
fof(f14571,plain,
! [X1,X2,X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> sP20(X0,X2,X1) )
| ~ sP21(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
fof(f11165,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(ennf_transformation,[],[f7234]) ).
fof(f7234,plain,
! [X0,X1,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ) ),
inference(rectify,[],[f2979]) ).
fof(f2979,axiom,
! [X26,X6,X4] :
( class_Fields_Olinordered__field__inverse__zero(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X6),X26)),c_Groups_Ozero__class_Ozero(X4)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),c_Groups_Ozero__class_Ozero(X4)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X6)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_divide__le__0__iff) ).
fof(f29553,plain,
spl698_322,
inference(avatar_split_clause,[],[f20189,f29551]) ).
fof(f29551,plain,
( spl698_322
<=> ! [X2,X0,X1] :
( sP19(X1,X2,X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_322])]) ).
fof(f20189,plain,
! [X2,X0,X1] :
( sP19(X1,X2,X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(cnf_transformation,[],[f14569]) ).
fof(f14569,plain,
! [X0,X1,X2] :
( sP19(X1,X2,X0)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(definition_folding,[],[f11164,f14568,f14567]) ).
fof(f14567,plain,
! [X0,X2,X1] :
( sP18(X0,X2,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f14568,plain,
! [X1,X2,X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> sP18(X0,X2,X1) )
| ~ sP19(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f11164,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(ennf_transformation,[],[f7233]) ).
fof(f7233,plain,
! [X0,X1,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ) ),
inference(rectify,[],[f2982]) ).
fof(f2982,axiom,
! [X26,X6,X4] :
( class_Fields_Olinordered__field__inverse__zero(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X6),X26)),c_Groups_Ozero__class_Ozero(X4)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),c_Groups_Ozero__class_Ozero(X4)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X6)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_divide__less__0__iff) ).
fof(f29549,plain,
spl698_321,
inference(avatar_split_clause,[],[f20180,f29547]) ).
fof(f29547,plain,
( spl698_321
<=> ! [X2,X0,X1] :
( sP17(X1,X0,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_321])]) ).
fof(f20180,plain,
! [X2,X0,X1] :
( sP17(X1,X0,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(cnf_transformation,[],[f14566]) ).
fof(f14566,plain,
! [X0,X1,X2] :
( sP17(X1,X0,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(definition_folding,[],[f11163,f14565,f14564]) ).
fof(f14564,plain,
! [X2,X0,X1] :
( sP16(X2,X0,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f14565,plain,
! [X1,X0,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X0)))
<=> sP16(X2,X0,X1) )
| ~ sP17(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f11163,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(ennf_transformation,[],[f7232]) ).
fof(f7232,plain,
! [X0,X1,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ) ),
inference(rectify,[],[f2980]) ).
fof(f2980,axiom,
! [X26,X6,X4] :
( class_Fields_Olinordered__field__inverse__zero(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X6),X26)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),c_Groups_Ozero__class_Ozero(X4)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X6)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zero__le__divide__iff) ).
fof(f29545,plain,
spl698_320,
inference(avatar_split_clause,[],[f20171,f29543]) ).
fof(f29543,plain,
( spl698_320
<=> ! [X2,X0,X1] :
( sP15(X1,X0,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_320])]) ).
fof(f20171,plain,
! [X2,X0,X1] :
( sP15(X1,X0,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(cnf_transformation,[],[f14563]) ).
fof(f14563,plain,
! [X0,X1,X2] :
( sP15(X1,X0,X2)
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(definition_folding,[],[f11162,f14562,f14561]) ).
fof(f14561,plain,
! [X2,X0,X1] :
( sP14(X2,X0,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f14562,plain,
! [X1,X0,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X0)))
<=> sP14(X2,X0,X1) )
| ~ sP15(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f11162,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(X2) ),
inference(ennf_transformation,[],[f7231]) ).
fof(f7231,plain,
! [X0,X1,X2] :
( class_Fields_Olinordered__field__inverse__zero(X2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X2),X1),X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ) ),
inference(rectify,[],[f2981]) ).
fof(f2981,axiom,
! [X26,X6,X4] :
( class_Fields_Olinordered__field__inverse__zero(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(X4),X6),X26)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),c_Groups_Ozero__class_Ozero(X4)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X6)) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_zero__less__divide__iff) ).
fof(f29541,plain,
spl698_319,
inference(avatar_split_clause,[],[f19822,f29539]) ).
fof(f29539,plain,
( spl698_319
<=> ! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X2,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_319])]) ).
fof(f19822,plain,
! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X2,X1,X0),
inference(cnf_transformation,[],[f6913]) ).
fof(f6913,plain,
! [X0,X1,X2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X2,X1,X0),
inference(rectify,[],[f168]) ).
fof(f168,axiom,
! [X55,X56,X51] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X51,X56,X55),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I14_J) ).
fof(f29537,plain,
spl698_318,
inference(avatar_split_clause,[],[f19820,f29535]) ).
fof(f29535,plain,
( spl698_318
<=> ! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X2,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_318])]) ).
fof(f19820,plain,
! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X2,X1,X0),
inference(cnf_transformation,[],[f6911]) ).
fof(f6911,plain,
! [X0,X1,X2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X2,X1,X0),
inference(rectify,[],[f108]) ).
fof(f108,axiom,
! [X10,X51,X69] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X69,X51,X10),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I10_J) ).
fof(f29533,plain,
spl698_317,
inference(avatar_split_clause,[],[f19410,f29531]) ).
fof(f29531,plain,
( spl698_317
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ sP4(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_317])]) ).
fof(f19410,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ sP4(X1,X0) ),
inference(cnf_transformation,[],[f15113]) ).
fof(f15113,plain,
! [X0,X1] :
( ( c_Wellfounded_Owf(X1,X0)
| ~ sP4(X1,X0) )
& ( sP4(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
inference(nnf_transformation,[],[f14543]) ).
fof(f14543,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> sP4(X1,X0) ),
inference(definition_folding,[],[f11101,f14542]) ).
fof(f14542,plain,
! [X1,X0] :
( sP4(X1,X0)
<=> ! [X2] :
( ? [X4] :
( ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X0)) )
& hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) )
| ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f11101,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> ! [X2] :
( ? [X4] :
( ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X0)) )
& hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) )
| ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ) ),
inference(ennf_transformation,[],[f6756]) ).
fof(f6756,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> ! [X2] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
=> ? [X4] :
( ! [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X0))
=> ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X2)) )
& hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ) ) ),
inference(rectify,[],[f4897]) ).
fof(f4897,axiom,
! [X60,X4] :
( c_Wellfounded_Owf(X4,X60)
<=> ! [X314] :
( ? [X2] : hBOOL(hAPP(hAPP(c_member(X4),X2),X314))
=> ? [X2] :
( ! [X115] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X115),X2)),X60))
=> ~ hBOOL(hAPP(hAPP(c_member(X4),X115),X314)) )
& hBOOL(hAPP(hAPP(c_member(X4),X2),X314)) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__eq__minimal) ).
fof(f29529,plain,
spl698_316,
inference(avatar_split_clause,[],[f19409,f29527]) ).
fof(f19409,plain,
! [X0,X1] :
( sP4(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f15113]) ).
fof(f29525,plain,
spl698_315,
inference(avatar_split_clause,[],[f19375,f29523]) ).
fof(f29523,plain,
( spl698_315
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Nitpick_Owf_H(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_315])]) ).
fof(f19375,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Nitpick_Owf_H(X1,X0) ),
inference(cnf_transformation,[],[f15071]) ).
fof(f29521,plain,
spl698_314,
inference(avatar_split_clause,[],[f19034,f29519]) ).
fof(f19034,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10728]) ).
fof(f10728,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6482]) ).
fof(f6482,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f3579]) ).
fof(f3579,axiom,
! [X60,X4] :
( c_Wellfounded_Owf(X4,X60)
=> c_Wellfounded_Oacyclic(X4,X60) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__acyclic) ).
fof(f29517,plain,
spl698_313,
inference(avatar_split_clause,[],[f18981,f29515]) ).
fof(f29515,plain,
( spl698_313
<=> ! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_313])]) ).
fof(f18981,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f10674]) ).
fof(f10674,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f6445]) ).
fof(f6445,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> class_Orderings_Oorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f5000]) ).
fof(f5000,axiom,
! [X323,X324] :
( class_Orderings_Oorder(X324)
=> class_Orderings_Oorder(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Orderings_Oorder) ).
fof(f29513,plain,
spl698_312,
inference(avatar_split_clause,[],[f18980,f29511]) ).
fof(f29511,plain,
( spl698_312
<=> ! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_312])]) ).
fof(f18980,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(cnf_transformation,[],[f10673]) ).
fof(f10673,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(ennf_transformation,[],[f6444]) ).
fof(f6444,plain,
! [X0,X1] :
( class_Orderings_Oord(X1)
=> class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(rectify,[],[f5002]) ).
fof(f5002,axiom,
! [X323,X324] :
( class_Orderings_Oord(X324)
=> class_Orderings_Oord(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Orderings_Oord) ).
fof(f29509,plain,
spl698_311,
inference(avatar_split_clause,[],[f18977,f29507]) ).
fof(f29507,plain,
( spl698_311
<=> ! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_311])]) ).
fof(f18977,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10670]) ).
fof(f10670,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6441]) ).
fof(f6441,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> class_Orderings_Opreorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f4997]) ).
fof(f4997,axiom,
! [X323,X324] :
( class_Orderings_Opreorder(X324)
=> class_Orderings_Opreorder(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Orderings_Opreorder) ).
fof(f29505,plain,
spl698_310,
inference(avatar_split_clause,[],[f18976,f29503]) ).
fof(f29503,plain,
( spl698_310
<=> ! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_310])]) ).
fof(f18976,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(cnf_transformation,[],[f10669]) ).
fof(f10669,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(ennf_transformation,[],[f6440]) ).
fof(f6440,plain,
! [X0,X1] :
( class_Groups_Ominus(X1)
=> class_Groups_Ominus(tc_fun(X0,X1)) ),
inference(rectify,[],[f5005]) ).
fof(f5005,axiom,
! [X323,X324] :
( class_Groups_Ominus(X324)
=> class_Groups_Ominus(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Groups_Ominus) ).
fof(f29501,plain,
spl698_309,
inference(avatar_split_clause,[],[f18966,f29499]) ).
fof(f29499,plain,
( spl698_309
<=> ! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_309])]) ).
fof(f18966,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10654]) ).
fof(f10654,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6430]) ).
fof(f6430,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Olattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4999]) ).
fof(f4999,axiom,
! [X323,X324] :
( class_Lattices_Olattice(X324)
=> class_Lattices_Olattice(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Lattices_Olattice) ).
fof(f29497,plain,
spl698_308,
inference(avatar_split_clause,[],[f18965,f29495]) ).
fof(f29495,plain,
( spl698_308
<=> ! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_308])]) ).
fof(f18965,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10653]) ).
fof(f10653,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6429]) ).
fof(f6429,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__inf(tc_fun(X0,X1)) ),
inference(rectify,[],[f4994]) ).
fof(f4994,axiom,
! [X323,X324] :
( class_Lattices_Olattice(X324)
=> class_Lattices_Osemilattice__inf(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Lattices_Osemilattice__inf) ).
fof(f29493,plain,
spl698_307,
inference(avatar_split_clause,[],[f18964,f29491]) ).
fof(f29491,plain,
( spl698_307
<=> ! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_307])]) ).
fof(f18964,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10652]) ).
fof(f10652,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6428]) ).
fof(f6428,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__sup(tc_fun(X0,X1)) ),
inference(rectify,[],[f4993]) ).
fof(f4993,axiom,
! [X323,X324] :
( class_Lattices_Olattice(X324)
=> class_Lattices_Osemilattice__sup(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Lattices_Osemilattice__sup) ).
fof(f29489,plain,
( ~ spl698_306
| ~ spl698_237
| ~ spl698_285 ),
inference(avatar_split_clause,[],[f29444,f29400,f29187,f29486]) ).
fof(f29486,plain,
( spl698_306
<=> c_Int_Osucc(c_Int_OPls) = c_Int_Opred(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_306])]) ).
fof(f29187,plain,
( spl698_237
<=> c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_237])]) ).
fof(f29400,plain,
( spl698_285
<=> ! [X1] : c_Int_Osucc(c_Int_OPls) != c_Int_OBit0(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_285])]) ).
fof(f29444,plain,
( c_Int_Osucc(c_Int_OPls) != c_Int_Opred(c_Int_OMin)
| ~ spl698_237
| ~ spl698_285 ),
inference(superposition,[],[f29401,f29189]) ).
fof(f29189,plain,
( c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin)
| ~ spl698_237 ),
inference(avatar_component_clause,[],[f29187]) ).
fof(f29401,plain,
( ! [X1] : c_Int_Osucc(c_Int_OPls) != c_Int_OBit0(X1)
| ~ spl698_285 ),
inference(avatar_component_clause,[],[f29400]) ).
fof(f29484,plain,
spl698_305,
inference(avatar_split_clause,[],[f18959,f29482]) ).
fof(f29482,plain,
( spl698_305
<=> ! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_305])]) ).
fof(f18959,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(cnf_transformation,[],[f10647]) ).
fof(f10647,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(ennf_transformation,[],[f6423]) ).
fof(f6423,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(X1)
=> class_Lattices_Odistrib__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4995]) ).
fof(f4995,axiom,
! [X323,X324] :
( class_Lattices_Odistrib__lattice(X324)
=> class_Lattices_Odistrib__lattice(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Lattices_Odistrib__lattice) ).
fof(f29480,plain,
spl698_304,
inference(avatar_split_clause,[],[f18853,f29478]) ).
fof(f29478,plain,
( spl698_304
<=> ! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_304])]) ).
fof(f18853,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(cnf_transformation,[],[f10540]) ).
fof(f10540,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(ennf_transformation,[],[f6337]) ).
fof(f6337,plain,
! [X0,X1] :
( class_Orderings_Obot(X1)
=> class_Orderings_Obot(tc_fun(X0,X1)) ),
inference(rectify,[],[f5003]) ).
fof(f5003,axiom,
! [X323,X324] :
( class_Orderings_Obot(X324)
=> class_Orderings_Obot(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Orderings_Obot) ).
fof(f29476,plain,
spl698_303,
inference(avatar_split_clause,[],[f18850,f29474]) ).
fof(f29474,plain,
( spl698_303
<=> ! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_303])]) ).
fof(f18850,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(cnf_transformation,[],[f10537]) ).
fof(f10537,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(ennf_transformation,[],[f6334]) ).
fof(f6334,plain,
! [X0,X1] :
( class_Groups_Ouminus(X1)
=> class_Groups_Ouminus(tc_fun(X0,X1)) ),
inference(rectify,[],[f5004]) ).
fof(f5004,axiom,
! [X323,X324] :
( class_Groups_Ouminus(X324)
=> class_Groups_Ouminus(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Groups_Ouminus) ).
fof(f29472,plain,
spl698_302,
inference(avatar_split_clause,[],[f18828,f29470]) ).
fof(f29470,plain,
( spl698_302
<=> ! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_302])]) ).
fof(f18828,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(cnf_transformation,[],[f10507]) ).
fof(f10507,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(ennf_transformation,[],[f6314]) ).
fof(f6314,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(X1)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4990]) ).
fof(f4990,axiom,
! [X323,X324] :
( class_Complete__Lattice_Ocomplete__lattice(X324)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f29468,plain,
spl698_301,
inference(avatar_split_clause,[],[f18822,f29466]) ).
fof(f29466,plain,
( spl698_301
<=> ! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_301])]) ).
fof(f18822,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f10501]) ).
fof(f10501,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f6308]) ).
fof(f6308,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
inference(rectify,[],[f4996]) ).
fof(f4996,axiom,
! [X323,X324] :
( class_Lattices_Oboolean__algebra(X324)
=> class_Lattices_Oboolean__algebra(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Lattices_Oboolean__algebra) ).
fof(f29464,plain,
spl698_300,
inference(avatar_split_clause,[],[f18812,f29462]) ).
fof(f29462,plain,
( spl698_300
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_300])]) ).
fof(f18812,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10491]) ).
fof(f10491,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6298]) ).
fof(f6298,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1)) ),
inference(rectify,[],[f4992]) ).
fof(f4992,axiom,
! [X323,X324] :
( class_Lattices_Obounded__lattice(X324)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Lattices_Obounded__lattice__bot) ).
fof(f29460,plain,
spl698_299,
inference(avatar_split_clause,[],[f18811,f29458]) ).
fof(f29458,plain,
( spl698_299
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_299])]) ).
fof(f18811,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10490]) ).
fof(f10490,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6297]) ).
fof(f6297,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice__top(tc_fun(X0,X1)) ),
inference(rectify,[],[f4991]) ).
fof(f4991,axiom,
! [X323,X324] :
( class_Lattices_Obounded__lattice(X324)
=> class_Lattices_Obounded__lattice__top(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Lattices_Obounded__lattice__top) ).
fof(f29456,plain,
spl698_298,
inference(avatar_split_clause,[],[f18810,f29454]) ).
fof(f29454,plain,
( spl698_298
<=> ! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_298])]) ).
fof(f18810,plain,
! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ),
inference(cnf_transformation,[],[f10489]) ).
fof(f10489,plain,
! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ),
inference(ennf_transformation,[],[f6296]) ).
fof(f6296,plain,
! [X0,X1] :
( class_Orderings_Otop(X1)
=> class_Orderings_Otop(tc_fun(X0,X1)) ),
inference(rectify,[],[f5001]) ).
fof(f5001,axiom,
! [X323,X324] :
( class_Orderings_Otop(X324)
=> class_Orderings_Otop(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Orderings_Otop) ).
fof(f29452,plain,
spl698_297,
inference(avatar_split_clause,[],[f18809,f29450]) ).
fof(f29450,plain,
( spl698_297
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_297])]) ).
fof(f18809,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10488]) ).
fof(f10488,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6295]) ).
fof(f6295,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4989]) ).
fof(f4989,axiom,
! [X323,X324] :
( class_Lattices_Obounded__lattice(X324)
=> class_Lattices_Obounded__lattice(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_fun__Lattices_Obounded__lattice) ).
fof(f29448,plain,
spl698_296,
inference(avatar_split_clause,[],[f18126,f29446]) ).
fof(f29446,plain,
( spl698_296
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_296])]) ).
fof(f18126,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0),
inference(cnf_transformation,[],[f5723]) ).
fof(f5723,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0),
inference(rectify,[],[f605]) ).
fof(f605,axiom,
! [X19,X4] : c_Fun_Oinj__on(X4,X4,c_COMBI(X4),X19),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_inj__on__id2) ).
fof(f29442,plain,
spl698_295,
inference(avatar_split_clause,[],[f18125,f29440]) ).
fof(f29440,plain,
( spl698_295
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_295])]) ).
fof(f18125,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0),
inference(cnf_transformation,[],[f5722]) ).
fof(f5722,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0),
inference(rectify,[],[f3485]) ).
fof(f3485,axiom,
! [X19,X4] : c_Fun_Oinj__on(X4,X4,c_Fun_Oid(X4),X19),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_inj__on__id) ).
fof(f29438,plain,
spl698_294,
inference(avatar_split_clause,[],[f18124,f29436]) ).
fof(f29436,plain,
( spl698_294
<=> ! [X0,X1] : c_Relation_Orefl__on(X1,X0,c_Relation_OId__on(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_294])]) ).
fof(f18124,plain,
! [X0,X1] : c_Relation_Orefl__on(X1,X0,c_Relation_OId__on(X1,X0)),
inference(cnf_transformation,[],[f5721]) ).
fof(f5721,plain,
! [X0,X1] : c_Relation_Orefl__on(X1,X0,c_Relation_OId__on(X1,X0)),
inference(rectify,[],[f3519]) ).
fof(f3519,axiom,
! [X19,X4] : c_Relation_Orefl__on(X4,X19,c_Relation_OId__on(X4,X19)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_refl__on__Id__on) ).
fof(f29434,plain,
spl698_293,
inference(avatar_split_clause,[],[f18123,f29432]) ).
fof(f29432,plain,
( spl698_293
<=> ! [X0,X1] : c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_293])]) ).
fof(f18123,plain,
! [X0,X1] : c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X0)),
inference(cnf_transformation,[],[f5720]) ).
fof(f5720,plain,
! [X0,X1] : c_Relation_Osingle__valued(X1,X1,c_Relation_OId__on(X1,X0)),
inference(rectify,[],[f4787]) ).
fof(f4787,axiom,
! [X19,X4] : c_Relation_Osingle__valued(X4,X4,c_Relation_OId__on(X4,X19)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_single__valued__Id__on) ).
fof(f29430,plain,
spl698_292,
inference(avatar_split_clause,[],[f18122,f29428]) ).
fof(f29428,plain,
( spl698_292
<=> ! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_292])]) ).
fof(f18122,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X0)),
inference(cnf_transformation,[],[f5719]) ).
fof(f5719,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X0)),
inference(rectify,[],[f3348]) ).
fof(f3348,axiom,
! [X1,X4] : c_Wellfounded_Owf(X4,hAPP(c_Wellfounded_Omeasure(X4),X1)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__measure) ).
fof(f29426,plain,
spl698_291,
inference(avatar_split_clause,[],[f18121,f29424]) ).
fof(f29424,plain,
( spl698_291
<=> ! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_291])]) ).
fof(f29422,plain,
spl698_290,
inference(avatar_split_clause,[],[f18120,f29420]) ).
fof(f29420,plain,
( spl698_290
<=> ! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_290])]) ).
fof(f18120,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f5717]) ).
fof(f5717,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(rectify,[],[f5221]) ).
fof(f5221,axiom,
! [X325,X23] : hAPP(c_COMBI(X23),X325) = X325,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__COMBI__1) ).
fof(f29418,plain,
spl698_289,
inference(avatar_split_clause,[],[f18118,f29416]) ).
fof(f29416,plain,
( spl698_289
<=> ! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_289])]) ).
fof(f18118,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0,
inference(cnf_transformation,[],[f5715]) ).
fof(f5715,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0,
inference(rectify,[],[f3483]) ).
fof(f3483,axiom,
! [X22,X23] : hAPP(c_Fun_Oid(X23),X22) = X22,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_id__apply) ).
fof(f29414,plain,
spl698_288,
inference(avatar_split_clause,[],[f18090,f29412]) ).
fof(f29412,plain,
( spl698_288
<=> ! [X0] : hAPP(c_Int_OAbs__Integ,sK165(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_288])]) ).
fof(f18090,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,sK165(X0)) = X0,
inference(cnf_transformation,[],[f14878]) ).
fof(f14878,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK165(X0)),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,sK165(X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK165])],[f10287,f14877]) ).
fof(f14877,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,X1) = X0 )
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK165(X0)),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,sK165(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f10287,plain,
! [X0] :
? [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,X1) = X0 ),
inference(ennf_transformation,[],[f5688]) ).
fof(f5688,plain,
! [X0] :
~ ! [X1] :
( hAPP(c_Int_OAbs__Integ,X1) = X0
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg)) ),
inference(rectify,[],[f3587]) ).
fof(f3587,axiom,
! [X20] :
~ ! [X115] :
( hAPP(c_Int_OAbs__Integ,X115) = X20
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X115),c_Int_OInteg)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Abs__Integ__cases) ).
fof(f29410,plain,
spl698_287,
inference(avatar_split_clause,[],[f17914,f29408]) ).
fof(f17914,plain,
! [X0] :
( c_fequal = c_HOL_Oequal__class_Oequal(X0)
| ~ class_HOL_Oequal(X0) ),
inference(cnf_transformation,[],[f10234]) ).
fof(f10234,plain,
! [X0] :
( c_fequal = c_HOL_Oequal__class_Oequal(X0)
| ~ class_HOL_Oequal(X0) ),
inference(ennf_transformation,[],[f5585]) ).
fof(f5585,plain,
! [X0] :
( class_HOL_Oequal(X0)
=> c_fequal = c_HOL_Oequal__class_Oequal(X0) ),
inference(rectify,[],[f4944]) ).
fof(f4944,axiom,
! [X4] :
( class_HOL_Oequal(X4)
=> c_fequal = c_HOL_Oequal__class_Oequal(X4) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_equal) ).
fof(f29406,plain,
spl698_286,
inference(avatar_split_clause,[],[f17890,f29404]) ).
fof(f29404,plain,
( spl698_286
<=> ! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_286])]) ).
fof(f17890,plain,
! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10211]) ).
fof(f10211,plain,
! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5562]) ).
fof(f5562,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0)) ),
inference(rectify,[],[f4268]) ).
fof(f4268,axiom,
! [X23] :
( class_Orderings_Olinorder(X23)
=> c_List_Olinorder__class_Osorted(X23,c_List_Olist_ONil(X23)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_sorted_Oequations_I1_J) ).
fof(f29402,plain,
( spl698_285
| ~ spl698_236
| ~ spl698_256 ),
inference(avatar_split_clause,[],[f29340,f29271,f29182,f29400]) ).
fof(f29271,plain,
( spl698_256
<=> ! [X0,X1] : c_Int_OBit0(X0) != c_Int_OBit1(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_256])]) ).
fof(f29340,plain,
( ! [X1] : c_Int_Osucc(c_Int_OPls) != c_Int_OBit0(X1)
| ~ spl698_236
| ~ spl698_256 ),
inference(superposition,[],[f29272,f29184]) ).
fof(f29272,plain,
( ! [X0,X1] : c_Int_OBit0(X0) != c_Int_OBit1(X1)
| ~ spl698_256 ),
inference(avatar_component_clause,[],[f29271]) ).
fof(f29398,plain,
spl698_284,
inference(avatar_split_clause,[],[f17878,f29396]) ).
fof(f17878,plain,
! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10199]) ).
fof(f10199,plain,
! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5550]) ).
fof(f5550,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f2666]) ).
fof(f2666,axiom,
! [X23] :
( class_Rings_Osemiring__1(X23)
=> c_Int_Oiszero(X23,c_Groups_Ozero__class_Ozero(X23)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_iszero__0) ).
fof(f29394,plain,
spl698_283,
inference(avatar_split_clause,[],[f17877,f29392]) ).
fof(f29392,plain,
( spl698_283
<=> ! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_283])]) ).
fof(f17877,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10198]) ).
fof(f10198,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5549]) ).
fof(f5549,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f2668]) ).
fof(f2668,axiom,
! [X23] :
( class_Rings_Osemiring__1(X23)
=> ~ c_Int_Oiszero(X23,c_Groups_Oone__class_Oone(X23)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_not__iszero__1) ).
fof(f29390,plain,
spl698_282,
inference(avatar_split_clause,[],[f17841,f29388]) ).
fof(f29388,plain,
( spl698_282
<=> ! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_282])]) ).
fof(f17841,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ),
inference(cnf_transformation,[],[f5513]) ).
fof(f5513,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ),
inference(rectify,[],[f5230]) ).
fof(f5230,axiom,
! [X5] :
( ~ hBOOL(X5)
| ~ hBOOL(hAPP(c_fNot,X5)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fNot__1) ).
fof(f29386,plain,
spl698_281,
inference(avatar_split_clause,[],[f17840,f29384]) ).
fof(f29384,plain,
( spl698_281
<=> ! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_281])]) ).
fof(f17840,plain,
! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f5512]) ).
fof(f5512,plain,
! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f5231]) ).
fof(f5231,axiom,
! [X5] :
( hBOOL(hAPP(c_fNot,X5))
| hBOOL(X5) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fNot__2) ).
fof(f29382,plain,
spl698_280,
inference(avatar_split_clause,[],[f17597,f29380]) ).
fof(f29380,plain,
( spl698_280
<=> ! [X0] : c_Wellfounded_Owf(tc_fun(X0,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_280])]) ).
fof(f17597,plain,
! [X0] : c_Wellfounded_Owf(tc_fun(X0,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X0)),
inference(cnf_transformation,[],[f5283]) ).
fof(f5283,plain,
! [X0] : c_Wellfounded_Owf(tc_fun(X0,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X0)),
inference(rectify,[],[f3351]) ).
fof(f3351,axiom,
! [X4] : c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__finite__psubset) ).
fof(f29378,plain,
spl698_279,
inference(avatar_split_clause,[],[f17596,f29376]) ).
fof(f29376,plain,
( spl698_279
<=> ! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_279])]) ).
fof(f17596,plain,
! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))),
inference(cnf_transformation,[],[f5282]) ).
fof(f5282,plain,
! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))),
inference(rectify,[],[f3972]) ).
fof(f3972,axiom,
! [X23] : hBOOL(hAPP(c_List_Odistinct(X23),c_List_Olist_ONil(X23))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_distinct_Osimps_I1_J) ).
fof(f29374,plain,
spl698_278,
inference(avatar_split_clause,[],[f17595,f29372]) ).
fof(f29370,plain,
spl698_277,
inference(avatar_split_clause,[],[f17594,f29368]) ).
fof(f29368,plain,
( spl698_277
<=> ! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_277])]) ).
fof(f17594,plain,
! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f5280]) ).
fof(f5280,plain,
! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0,
inference(rectify,[],[f1874]) ).
fof(f1874,axiom,
! [X88] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X88) = X88,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_nat__size) ).
fof(f29366,plain,
spl698_276,
inference(avatar_split_clause,[],[f17593,f29364]) ).
fof(f29364,plain,
( spl698_276
<=> ! [X0] : c_Nat_Ocompow(X0,X0) = c_Nat_Ofunpow(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_276])]) ).
fof(f29362,plain,
spl698_275,
inference(avatar_split_clause,[],[f17592,f29360]) ).
fof(f29360,plain,
( spl698_275
<=> ! [X0] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X0,tc_HOL_Obool) = c_Set_OBall(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_275])]) ).
fof(f17592,plain,
! [X0] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X0,tc_HOL_Obool) = c_Set_OBall(X0),
inference(cnf_transformation,[],[f5278]) ).
fof(f5278,plain,
! [X0] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X0,tc_HOL_Obool) = c_Set_OBall(X0),
inference(rectify,[],[f4416]) ).
fof(f4416,axiom,
! [X4] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(X4,tc_HOL_Obool) = c_Set_OBall(X4),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_INFI__bool__eq) ).
fof(f29358,plain,
spl698_274,
inference(avatar_split_clause,[],[f17591,f29356]) ).
fof(f29356,plain,
( spl698_274
<=> ! [X0] : c_Int_OBit1(X0) = c_Int_Osucc(c_Int_OBit0(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_274])]) ).
fof(f17591,plain,
! [X0] : c_Int_OBit1(X0) = c_Int_Osucc(c_Int_OBit0(X0)),
inference(cnf_transformation,[],[f5277]) ).
fof(f5277,plain,
! [X0] : c_Int_OBit1(X0) = c_Int_Osucc(c_Int_OBit0(X0)),
inference(rectify,[],[f2686]) ).
fof(f2686,axiom,
! [X112] : c_Int_OBit1(X112) = c_Int_Osucc(c_Int_OBit0(X112)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_succ__Bit0) ).
fof(f29354,plain,
spl698_273,
inference(avatar_split_clause,[],[f17590,f29352]) ).
fof(f17590,plain,
! [X0] : c_Int_OBit0(X0) = c_Int_Opred(c_Int_OBit1(X0)),
inference(cnf_transformation,[],[f5276]) ).
fof(f5276,plain,
! [X0] : c_Int_OBit0(X0) = c_Int_Opred(c_Int_OBit1(X0)),
inference(rectify,[],[f2867]) ).
fof(f2867,axiom,
! [X112] : c_Int_OBit0(X112) = c_Int_Opred(c_Int_OBit1(X112)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_pred__Bit1) ).
fof(f29350,plain,
spl698_272,
inference(avatar_split_clause,[],[f17454,f29347]) ).
fof(f29347,plain,
( spl698_272
<=> c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_272])]) ).
fof(f17454,plain,
c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
inference(cnf_transformation,[],[f4040]) ).
fof(f4040,axiom,
c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_transfer__nat__int__list__functions_I2_J) ).
fof(f29345,plain,
spl698_271,
inference(avatar_split_clause,[],[f17453,f29342]) ).
fof(f29342,plain,
( spl698_271
<=> c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_271])]) ).
fof(f17453,plain,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
inference(cnf_transformation,[],[f2562]) ).
fof(f2562,axiom,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_minus__Pls) ).
fof(f29338,plain,
( ~ spl698_270
| ~ spl698_223
| ~ spl698_237 ),
inference(avatar_split_clause,[],[f29322,f29187,f29121,f29335]) ).
fof(f29335,plain,
( spl698_270
<=> c_Int_OMin = c_Int_Opred(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_270])]) ).
fof(f29322,plain,
( c_Int_OMin != c_Int_Opred(c_Int_OMin)
| ~ spl698_223
| ~ spl698_237 ),
inference(superposition,[],[f29122,f29189]) ).
fof(f29332,plain,
( ~ spl698_269
| ~ spl698_222
| ~ spl698_236 ),
inference(avatar_split_clause,[],[f29321,f29182,f29117,f29329]) ).
fof(f29329,plain,
( spl698_269
<=> c_Int_OPls = c_Int_Osucc(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_269])]) ).
fof(f29321,plain,
( c_Int_OPls != c_Int_Osucc(c_Int_OPls)
| ~ spl698_222
| ~ spl698_236 ),
inference(superposition,[],[f29118,f29184]) ).
fof(f29327,plain,
( spl698_268
| ~ spl698_242 ),
inference(avatar_split_clause,[],[f29216,f29212,f29324]) ).
fof(f29324,plain,
( spl698_268
<=> c_Nat__Transfer_Onat__set(c_Option_Oset(tc_Int_Oint,c_Option_Ooption_ONone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_268])]) ).
fof(f29212,plain,
( spl698_242
<=> c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_242])]) ).
fof(f29216,plain,
( c_Nat__Transfer_Onat__set(c_Option_Oset(tc_Int_Oint,c_Option_Ooption_ONone(tc_Int_Oint)))
| ~ spl698_242 ),
inference(forward_demodulation,[],[f29214,f17660]) ).
fof(f29214,plain,
( c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))
| ~ spl698_242 ),
inference(avatar_component_clause,[],[f29212]) ).
fof(f29320,plain,
spl698_267,
inference(avatar_split_clause,[],[f24879,f29317]) ).
fof(f29317,plain,
( spl698_267
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_267])]) ).
fof(f24879,plain,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17450,f17447]) ).
fof(f17450,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f1419]) ).
fof(f1419,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_bot__nat__def) ).
fof(f29315,plain,
spl698_266,
inference(avatar_split_clause,[],[f24878,f29312]) ).
fof(f29312,plain,
( spl698_266
<=> c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_266])]) ).
fof(f24878,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17449,f17447]) ).
fof(f17449,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP),
inference(cnf_transformation,[],[f1773]) ).
fof(f1773,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osize_I1_J) ).
fof(f29310,plain,
spl698_265,
inference(avatar_split_clause,[],[f24877,f29307]) ).
fof(f29307,plain,
( spl698_265
<=> c_HOL_Obool_Obool__size(c_fTrue) = c_HOL_Obool_Obool__size(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_265])]) ).
fof(f24877,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_HOL_Obool_Obool__size(c_fFalse),
inference(forward_demodulation,[],[f17448,f17447]) ).
fof(f17448,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
inference(cnf_transformation,[],[f4935]) ).
fof(f4935,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_bool_Osize_I2_J) ).
fof(f29305,plain,
spl698_264,
inference(avatar_split_clause,[],[f18954,f29303]) ).
fof(f29303,plain,
( spl698_264
<=> ! [X0,X1] :
( sP1(X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_264])]) ).
fof(f18954,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f14537]) ).
fof(f14537,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(definition_folding,[],[f10645,f14536,f14535]) ).
fof(f10645,plain,
! [X0,X1] :
( ( c_List_Olinorder__class_Osorted(X1,X0)
<=> ( ? [X2,X3] :
( c_List_Olinorder__class_Osorted(X1,X2)
& ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2))) )
& hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) = X0 )
| c_List_Olist_ONil(X1) = X0 ) )
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6421]) ).
fof(f6421,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> ( c_List_Olinorder__class_Osorted(X1,X0)
<=> ( ? [X2,X3] :
( c_List_Olinorder__class_Osorted(X1,X2)
& ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) )
& hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) = X0 )
| c_List_Olist_ONil(X1) = X0 ) ) ),
inference(rectify,[],[f4507]) ).
fof(f4507,axiom,
! [X6,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_List_Olinorder__class_Osorted(X4,X6)
<=> ( ? [X268,X2] :
( c_List_Olinorder__class_Osorted(X4,X268)
& ! [X118] :
( hBOOL(hAPP(hAPP(c_member(X4),X118),hAPP(c_List_Oset(X4),X268)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X2),X118)) )
& hAPP(hAPP(c_List_Olist_OCons(X4),X2),X268) = X6 )
| c_List_Olist_ONil(X4) = X6 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_sorted_Osimps) ).
fof(f29301,plain,
spl698_263,
inference(avatar_split_clause,[],[f18116,f29299]) ).
fof(f29299,plain,
( spl698_263
<=> ! [X0,X1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_263])]) ).
fof(f18116,plain,
! [X0,X1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X0,X1),
inference(cnf_transformation,[],[f5713]) ).
fof(f5713,plain,
! [X0,X1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X0,X1),
inference(rectify,[],[f133]) ).
fof(f133,axiom,
! [X88,X92] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X92,X88,X92),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_evaln_OSkip) ).
fof(f29297,plain,
spl698_262,
inference(avatar_split_clause,[],[f18115,f29295]) ).
fof(f29295,plain,
( spl698_262
<=> ! [X0,X1] : c_List_Olist__all(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_262])]) ).
fof(f18115,plain,
! [X0,X1] : c_List_Olist__all(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5712]) ).
fof(f5712,plain,
! [X0,X1] : c_List_Olist__all(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4925]) ).
fof(f4925,axiom,
! [X5,X4] : c_List_Olist__all(X4,X5,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_list__all__simps_I2_J) ).
fof(f29293,plain,
spl698_261,
inference(avatar_split_clause,[],[f18114,f29291]) ).
fof(f18114,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,c_List_Omeasures(X1,X0)),
inference(cnf_transformation,[],[f5711]) ).
fof(f5711,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,c_List_Omeasures(X1,X0)),
inference(rectify,[],[f4553]) ).
fof(f4553,axiom,
! [X307,X4] : c_Wellfounded_Owf(X4,c_List_Omeasures(X4,X307)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__measures) ).
fof(f29289,plain,
spl698_260,
inference(avatar_split_clause,[],[f18113,f29287]) ).
fof(f18113,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X0)),
inference(cnf_transformation,[],[f5710]) ).
fof(f5710,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X0)),
inference(rectify,[],[f4270]) ).
fof(f4270,axiom,
! [X113,X114] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X114,X113)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_sorted__upt) ).
fof(f29285,plain,
spl698_259,
inference(avatar_split_clause,[],[f18112,f29283]) ).
fof(f29283,plain,
( spl698_259
<=> ! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_259])]) ).
fof(f18112,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)),
inference(cnf_transformation,[],[f5709]) ).
fof(f5709,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)),
inference(rectify,[],[f4271]) ).
fof(f4271,axiom,
! [X113,X114] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X114,X113)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_sorted__upto) ).
fof(f29281,plain,
spl698_258,
inference(avatar_split_clause,[],[f18111,f29279]) ).
fof(f29279,plain,
( spl698_258
<=> ! [X0,X1] : ~ c_List_Olist__ex(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_258])]) ).
fof(f18111,plain,
! [X0,X1] : ~ c_List_Olist__ex(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5708]) ).
fof(f5708,plain,
! [X0,X1] : ~ c_List_Olist__ex(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4605]) ).
fof(f4605,axiom,
! [X5,X4] : ~ c_List_Olist__ex(X4,X5,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_list__ex__simps_I2_J) ).
fof(f29277,plain,
spl698_257,
inference(avatar_split_clause,[],[f18110,f29275]) ).
fof(f29275,plain,
( spl698_257
<=> ! [X0,X1] : ~ c_List_Olist__ex1(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_257])]) ).
fof(f18110,plain,
! [X0,X1] : ~ c_List_Olist__ex1(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5707]) ).
fof(f5707,plain,
! [X0,X1] : ~ c_List_Olist__ex1(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4931]) ).
fof(f4931,axiom,
! [X5,X4] : ~ c_List_Olist__ex1(X4,X5,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_list__ex1__simps_I1_J) ).
fof(f29273,plain,
spl698_256,
inference(avatar_split_clause,[],[f18108,f29271]) ).
fof(f18108,plain,
! [X0,X1] : c_Int_OBit0(X0) != c_Int_OBit1(X1),
inference(cnf_transformation,[],[f5705]) ).
fof(f5705,plain,
! [X0,X1] : c_Int_OBit0(X0) != c_Int_OBit1(X1),
inference(rectify,[],[f2654]) ).
fof(f2654,axiom,
! [X124,X112] : c_Int_OBit1(X112) != c_Int_OBit0(X124),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rel__simps_I50_J) ).
fof(f29269,plain,
spl698_255,
inference(avatar_split_clause,[],[f18106,f29267]) ).
fof(f29267,plain,
( spl698_255
<=> ! [X0,X1] : c_Com_Ovname_OGlb(X0) != c_Com_Ovname_OLoc(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_255])]) ).
fof(f18106,plain,
! [X0,X1] : c_Com_Ovname_OGlb(X0) != c_Com_Ovname_OLoc(X1),
inference(cnf_transformation,[],[f5703]) ).
fof(f5703,plain,
! [X0,X1] : c_Com_Ovname_OGlb(X0) != c_Com_Ovname_OLoc(X1),
inference(rectify,[],[f190]) ).
fof(f190,axiom,
! [X111,X110] : c_Com_Ovname_OGlb(X111) != c_Com_Ovname_OLoc(X110),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_vname_Osimps_I4_J) ).
fof(f29265,plain,
spl698_254,
inference(avatar_split_clause,[],[f18104,f29263]) ).
fof(f29263,plain,
( spl698_254
<=> ! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_254])]) ).
fof(f18104,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X0),
inference(cnf_transformation,[],[f5701]) ).
fof(f5701,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X0),
inference(rectify,[],[f73]) ).
fof(f73,axiom,
! [X10,X51] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X51,X10),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I16_J) ).
fof(f29261,plain,
spl698_253,
inference(avatar_split_clause,[],[f18102,f29259]) ).
fof(f29259,plain,
( spl698_253
<=> ! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_253])]) ).
fof(f18102,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X0),
inference(cnf_transformation,[],[f5699]) ).
fof(f5699,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X0),
inference(rectify,[],[f69]) ).
fof(f69,axiom,
! [X51,X52] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X52,X51),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I8_J) ).
fof(f29257,plain,
spl698_252,
inference(avatar_split_clause,[],[f18100,f29255]) ).
fof(f29255,plain,
( spl698_252
<=> ! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_252])]) ).
fof(f18100,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X0),
inference(cnf_transformation,[],[f5697]) ).
fof(f5697,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X0),
inference(rectify,[],[f68]) ).
fof(f68,axiom,
! [X49,X50] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X50,X49),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_com_Osimps_I13_J) ).
fof(f29253,plain,
spl698_251,
inference(avatar_split_clause,[],[f17904,f29251]) ).
fof(f29251,plain,
( spl698_251
<=> ! [X0] :
( class_Enum_Oenum(tc_Option_Ooption(X0))
| ~ class_Enum_Oenum(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_251])]) ).
fof(f17904,plain,
! [X0] :
( class_Enum_Oenum(tc_Option_Ooption(X0))
| ~ class_Enum_Oenum(X0) ),
inference(cnf_transformation,[],[f10225]) ).
fof(f10225,plain,
! [X0] :
( class_Enum_Oenum(tc_Option_Ooption(X0))
| ~ class_Enum_Oenum(X0) ),
inference(ennf_transformation,[],[f5576]) ).
fof(f5576,plain,
! [X0] :
( class_Enum_Oenum(X0)
=> class_Enum_Oenum(tc_Option_Ooption(X0)) ),
inference(rectify,[],[f5161]) ).
fof(f5161,axiom,
! [X324] :
( class_Enum_Oenum(X324)
=> class_Enum_Oenum(tc_Option_Ooption(X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Option__Ooption__Enum_Oenum) ).
fof(f29249,plain,
spl698_250,
inference(avatar_split_clause,[],[f17902,f29247]) ).
fof(f29247,plain,
( spl698_250
<=> ! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_250])]) ).
fof(f17902,plain,
! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(cnf_transformation,[],[f10223]) ).
fof(f10223,plain,
! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(ennf_transformation,[],[f5574]) ).
fof(f5574,plain,
! [X0] :
( class_Finite__Set_Ofinite(X0)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X0)) ),
inference(rectify,[],[f5159]) ).
fof(f5159,axiom,
! [X324] :
( class_Finite__Set_Ofinite(X324)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X324)) ),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(f29245,plain,
spl698_249,
inference(avatar_split_clause,[],[f17581,f29243]) ).
fof(f29243,plain,
( spl698_249
<=> ! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_249])]) ).
fof(f17581,plain,
! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0),
inference(cnf_transformation,[],[f5267]) ).
fof(f5267,plain,
! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0),
inference(rectify,[],[f1236]) ).
fof(f1236,axiom,
! [X144] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X144),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_inj__Suc) ).
fof(f29241,plain,
spl698_248,
inference(avatar_split_clause,[],[f17580,f29239]) ).
fof(f29239,plain,
( spl698_248
<=> ! [X0] : c_Relation_Osingle__valued(X0,X0,c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_248])]) ).
fof(f17580,plain,
! [X0] : c_Relation_Osingle__valued(X0,X0,c_Relation_OId(X0)),
inference(cnf_transformation,[],[f5266]) ).
fof(f5266,plain,
! [X0] : c_Relation_Osingle__valued(X0,X0,c_Relation_OId(X0)),
inference(rectify,[],[f4784]) ).
fof(f4784,axiom,
! [X4] : c_Relation_Osingle__valued(X4,X4,c_Relation_OId(X4)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_single__valued__Id) ).
fof(f29237,plain,
spl698_247,
inference(avatar_split_clause,[],[f17579,f29235]) ).
fof(f29235,plain,
( spl698_247
<=> ! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_247])]) ).
fof(f17579,plain,
! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f5265]) ).
fof(f5265,plain,
! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(rectify,[],[f2908]) ).
fof(f2908,axiom,
! [X30] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).
fof(f29233,plain,
spl698_246,
inference(avatar_split_clause,[],[f17578,f29231]) ).
fof(f29231,plain,
( spl698_246
<=> ! [X0] : c_Int_Osucc(c_Int_Opred(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_246])]) ).
fof(f17578,plain,
! [X0] : c_Int_Osucc(c_Int_Opred(X0)) = X0,
inference(cnf_transformation,[],[f5264]) ).
fof(f5264,plain,
! [X0] : c_Int_Osucc(c_Int_Opred(X0)) = X0,
inference(rectify,[],[f2865]) ).
fof(f2865,axiom,
! [X22] : c_Int_Osucc(c_Int_Opred(X22)) = X22,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_succ__pred) ).
fof(f29229,plain,
spl698_245,
inference(avatar_split_clause,[],[f17576,f29227]) ).
fof(f29227,plain,
( spl698_245
<=> ! [X0] : hAPP(c_Nat_OSuc,X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl698_245])]) ).
fof(f17576,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(cnf_transformation,[],[f5262]) ).
fof(f5262,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(rectify,[],[f1262]) ).
fof(f1262,axiom,
! [X88] : hAPP(c_Nat_OSuc,X88) != X88,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_n__not__Suc__n) ).
fof(f29225,plain,
spl698_244,
inference(avatar_split_clause,[],[f17574,f29223]) ).
fof(f29223,plain,
( spl698_244
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_244])]) ).
fof(f17574,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X0),
inference(cnf_transformation,[],[f5260]) ).
fof(f5260,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X0),
inference(rectify,[],[f3032]) ).
fof(f3032,axiom,
! [X239] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X239),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_code__numeral_Osimps_I3_J) ).
fof(f29221,plain,
spl698_243,
inference(avatar_split_clause,[],[f17452,f29218]) ).
fof(f17452,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f3357]) ).
fof(f3357,axiom,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__pair__less) ).
fof(f29215,plain,
spl698_242,
inference(avatar_split_clause,[],[f17451,f29212]) ).
fof(f17451,plain,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
inference(cnf_transformation,[],[f2581]) ).
fof(f2581,axiom,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J) ).
fof(f29210,plain,
spl698_241,
inference(avatar_split_clause,[],[f17447,f29207]) ).
fof(f29207,plain,
( spl698_241
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_241])]) ).
fof(f29205,plain,
spl698_240,
inference(avatar_split_clause,[],[f17446,f29202]) ).
fof(f29202,plain,
( spl698_240
<=> c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_240])]) ).
fof(f17446,plain,
c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),
inference(cnf_transformation,[],[f1689]) ).
fof(f1689,axiom,
c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_inf__nat__def) ).
fof(f29200,plain,
spl698_239,
inference(avatar_split_clause,[],[f17445,f29197]) ).
fof(f29197,plain,
( spl698_239
<=> c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_239])]) ).
fof(f17445,plain,
c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),
inference(cnf_transformation,[],[f2256]) ).
fof(f2256,axiom,
c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_sup__nat__def) ).
fof(f29195,plain,
spl698_238,
inference(avatar_split_clause,[],[f17444,f29192]) ).
fof(f29192,plain,
( spl698_238
<=> c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_238])]) ).
fof(f17444,plain,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
inference(cnf_transformation,[],[f3477]) ).
fof(f3477,axiom,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_of__int__eq__id) ).
fof(f29190,plain,
spl698_237,
inference(avatar_split_clause,[],[f17443,f29187]) ).
fof(f17443,plain,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
inference(cnf_transformation,[],[f2874]) ).
fof(f2874,axiom,
c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_pred__Min) ).
fof(f29185,plain,
spl698_236,
inference(avatar_split_clause,[],[f17442,f29182]) ).
fof(f29180,plain,
spl698_235,
inference(avatar_split_clause,[],[f17441,f29177]) ).
fof(f29177,plain,
( spl698_235
<=> c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_235])]) ).
fof(f17441,plain,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f4661]) ).
fof(f4661,axiom,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_less__than__def) ).
fof(f29175,plain,
~ spl698_234,
inference(avatar_split_clause,[],[f17439,f29172]) ).
fof(f17439,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f2537]) ).
fof(f2537,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_not__neg__1) ).
fof(f29170,plain,
( ~ spl698_233
| spl698_232 ),
inference(avatar_split_clause,[],[f29165,f29161,f29167]) ).
fof(f29161,plain,
( spl698_232
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_232])]) ).
fof(f29165,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)))
| spl698_232 ),
inference(forward_demodulation,[],[f29163,f25465]) ).
fof(f29163,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
| spl698_232 ),
inference(avatar_component_clause,[],[f29161]) ).
fof(f29164,plain,
~ spl698_232,
inference(avatar_split_clause,[],[f17225,f29161]) ).
fof(f17225,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5244]) ).
fof(f5244,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(flattening,[],[f5243]) ).
fof(f5243,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(negated_conjecture,[],[f5242]) ).
fof(f5242,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',conj_1) ).
fof(f29157,plain,
~ spl698_231,
inference(avatar_split_clause,[],[f24876,f29154]) ).
fof(f29154,plain,
( spl698_231
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_231])]) ).
fof(f24876,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)),
inference(forward_demodulation,[],[f17440,f17436]) ).
fof(f17440,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(cnf_transformation,[],[f2535]) ).
fof(f2535,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_not__neg__0) ).
fof(f29152,plain,
~ spl698_230,
inference(avatar_split_clause,[],[f24875,f29149]) ).
fof(f29149,plain,
( spl698_230
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl698_230])]) ).
fof(f24875,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Int_OPls,
inference(forward_demodulation,[],[f17438,f17436]) ).
fof(f17438,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f1824]) ).
fof(f1824,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_int__0__neq__1) ).
fof(f29147,plain,
spl698_229,
inference(avatar_split_clause,[],[f18099,f29145]) ).
fof(f29145,plain,
( spl698_229
<=> ! [X0,X1] : class_HOL_Oequal(tc_prod(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_229])]) ).
fof(f18099,plain,
! [X0,X1] : class_HOL_Oequal(tc_prod(X1,X0)),
inference(cnf_transformation,[],[f5696]) ).
fof(f5696,plain,
! [X0,X1] : class_HOL_Oequal(tc_prod(X1,X0)),
inference(rectify,[],[f5165]) ).
fof(f5165,axiom,
! [X324,X323] : class_HOL_Oequal(tc_prod(X323,X324)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_prod__HOL_Oequal) ).
fof(f29143,plain,
spl698_228,
inference(avatar_split_clause,[],[f18098,f29141]) ).
fof(f29141,plain,
( spl698_228
<=> ! [X0,X1] : class_HOL_Oequal(tc_sum(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_228])]) ).
fof(f18098,plain,
! [X0,X1] : class_HOL_Oequal(tc_sum(X1,X0)),
inference(cnf_transformation,[],[f5695]) ).
fof(f5695,plain,
! [X0,X1] : class_HOL_Oequal(tc_sum(X1,X0)),
inference(rectify,[],[f5156]) ).
fof(f5156,axiom,
! [X324,X323] : class_HOL_Oequal(tc_sum(X323,X324)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_sum__HOL_Oequal) ).
fof(f29139,plain,
spl698_227,
inference(avatar_split_clause,[],[f18097,f29137]) ).
fof(f29137,plain,
( spl698_227
<=> ! [X0,X1] : class_Nat_Osize(tc_prod(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_227])]) ).
fof(f18097,plain,
! [X0,X1] : class_Nat_Osize(tc_prod(X1,X0)),
inference(cnf_transformation,[],[f5694]) ).
fof(f5694,plain,
! [X0,X1] : class_Nat_Osize(tc_prod(X1,X0)),
inference(rectify,[],[f5167]) ).
fof(f5167,axiom,
! [X324,X323] : class_Nat_Osize(tc_prod(X323,X324)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_prod__Nat_Osize) ).
fof(f29135,plain,
spl698_226,
inference(avatar_split_clause,[],[f18096,f29133]) ).
fof(f29133,plain,
( spl698_226
<=> ! [X0,X1] : class_Nat_Osize(tc_sum(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_226])]) ).
fof(f18096,plain,
! [X0,X1] : class_Nat_Osize(tc_sum(X1,X0)),
inference(cnf_transformation,[],[f5693]) ).
fof(f5693,plain,
! [X0,X1] : class_Nat_Osize(tc_sum(X1,X0)),
inference(rectify,[],[f5158]) ).
fof(f5158,axiom,
! [X324,X323] : class_Nat_Osize(tc_sum(X323,X324)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_sum__Nat_Osize) ).
fof(f29131,plain,
spl698_225,
inference(avatar_split_clause,[],[f17573,f29129]) ).
fof(f17573,plain,
! [X0] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X0)),
inference(cnf_transformation,[],[f5259]) ).
fof(f5259,plain,
! [X0] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X0)),
inference(rectify,[],[f3365]) ).
fof(f3365,axiom,
! [X35] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(X35)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__int__ge__less__than) ).
fof(f29127,plain,
spl698_224,
inference(avatar_split_clause,[],[f17572,f29125]) ).
fof(f17572,plain,
! [X0] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X0)),
inference(cnf_transformation,[],[f5258]) ).
fof(f5258,plain,
! [X0] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X0)),
inference(rectify,[],[f3364]) ).
fof(f3364,axiom,
! [X35] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(X35)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__int__ge__less__than2) ).
fof(f29123,plain,
spl698_223,
inference(avatar_split_clause,[],[f17569,f29121]) ).
fof(f17569,plain,
! [X0] : c_Int_OMin != c_Int_OBit0(X0),
inference(cnf_transformation,[],[f5255]) ).
fof(f5255,plain,
! [X0] : c_Int_OMin != c_Int_OBit0(X0),
inference(rectify,[],[f2787]) ).
fof(f2787,axiom,
! [X112] : c_Int_OBit0(X112) != c_Int_OMin,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rel__simps_I45_J) ).
fof(f29119,plain,
spl698_222,
inference(avatar_split_clause,[],[f17568,f29117]) ).
fof(f17568,plain,
! [X0] : c_Int_OPls != c_Int_OBit1(X0),
inference(cnf_transformation,[],[f5254]) ).
fof(f5254,plain,
! [X0] : c_Int_OPls != c_Int_OBit1(X0),
inference(rectify,[],[f2569]) ).
fof(f2569,axiom,
! [X124] : c_Int_OPls != c_Int_OBit1(X124),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rel__simps_I39_J) ).
fof(f29115,plain,
spl698_221,
inference(avatar_split_clause,[],[f17437,f29112]) ).
fof(f29112,plain,
( spl698_221
<=> c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_221])]) ).
fof(f17437,plain,
c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
inference(cnf_transformation,[],[f1268]) ).
fof(f1268,axiom,
c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_mono__Suc) ).
fof(f29110,plain,
spl698_220,
inference(avatar_split_clause,[],[f17436,f29107]) ).
fof(f29105,plain,
spl698_219,
inference(avatar_split_clause,[],[f17435,f29102]) ).
fof(f29102,plain,
( spl698_219
<=> c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral ),
introduced(avatar_definition,[new_symbols(naming,[spl698_219])]) ).
fof(f29100,plain,
spl698_218,
inference(avatar_split_clause,[],[f17434,f29097]) ).
fof(f17434,plain,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
inference(cnf_transformation,[],[f2652]) ).
fof(f2652,axiom,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Bit0__Pls) ).
fof(f29095,plain,
spl698_217,
inference(avatar_split_clause,[],[f17433,f29092]) ).
fof(f29092,plain,
( spl698_217
<=> c_Int_OPls = c_Int_Osucc(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_217])]) ).
fof(f17433,plain,
c_Int_OPls = c_Int_Osucc(c_Int_OMin),
inference(cnf_transformation,[],[f2813]) ).
fof(f2813,axiom,
c_Int_OPls = c_Int_Osucc(c_Int_OMin),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_succ__Min) ).
fof(f29090,plain,
spl698_216,
inference(avatar_split_clause,[],[f17432,f29087]) ).
fof(f17432,plain,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
inference(cnf_transformation,[],[f2782]) ).
fof(f2782,axiom,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Bit1__Min) ).
fof(f29085,plain,
spl698_215,
inference(avatar_split_clause,[],[f17431,f29082]) ).
fof(f29082,plain,
( spl698_215
<=> c_Int_OMin = c_Int_Opred(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_215])]) ).
fof(f17431,plain,
c_Int_OMin = c_Int_Opred(c_Int_OPls),
inference(cnf_transformation,[],[f2870]) ).
fof(f2870,axiom,
c_Int_OMin = c_Int_Opred(c_Int_OPls),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_pred__Pls) ).
fof(f29080,plain,
spl698_214,
inference(avatar_split_clause,[],[f17430,f29077]) ).
fof(f29077,plain,
( spl698_214
<=> c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_214])]) ).
fof(f17430,plain,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f4625]) ).
fof(f4625,axiom,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Code__Numeral_Oof__nat__code) ).
fof(f29075,plain,
spl698_213,
inference(avatar_split_clause,[],[f18093,f29073]) ).
fof(f29073,plain,
( spl698_213
<=> ! [X0,X1] : c_FunDef_Ois__measure(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_213])]) ).
fof(f18093,plain,
! [X0,X1] : c_FunDef_Ois__measure(X1,X0),
inference(cnf_transformation,[],[f5690]) ).
fof(f5690,plain,
! [X0,X1] : c_FunDef_Ois__measure(X1,X0),
inference(rectify,[],[f4941]) ).
fof(f4941,axiom,
! [X1,X4] : c_FunDef_Ois__measure(X4,X1),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_is__measure_Ointros) ).
fof(f29071,plain,
spl698_212,
inference(avatar_split_clause,[],[f17567,f29069]) ).
fof(f29069,plain,
( spl698_212
<=> ! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_212])]) ).
fof(f17567,plain,
! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal),
inference(cnf_transformation,[],[f5253]) ).
fof(f5253,plain,
! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal),
inference(rectify,[],[f1252]) ).
fof(f1252,axiom,
! [X4] : c_Equiv__Relations_Oequivp(X4,c_fequal),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_identity__equivp) ).
fof(f29067,plain,
spl698_211,
inference(avatar_split_clause,[],[f17566,f29065]) ).
fof(f17566,plain,
! [X0] : class_HOL_Oequal(tc_List_Olist(X0)),
inference(cnf_transformation,[],[f5252]) ).
fof(f5252,plain,
! [X0] : class_HOL_Oequal(tc_List_Olist(X0)),
inference(rectify,[],[f5153]) ).
fof(f5153,axiom,
! [X324] : class_HOL_Oequal(tc_List_Olist(X324)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_List__Olist__HOL_Oequal) ).
fof(f29063,plain,
spl698_210,
inference(avatar_split_clause,[],[f17565,f29061]) ).
fof(f17565,plain,
! [X0] : class_HOL_Oequal(tc_Option_Ooption(X0)),
inference(cnf_transformation,[],[f5251]) ).
fof(f5251,plain,
! [X0] : class_HOL_Oequal(tc_Option_Ooption(X0)),
inference(rectify,[],[f5160]) ).
fof(f5160,axiom,
! [X324] : class_HOL_Oequal(tc_Option_Ooption(X324)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Option__Ooption__HOL_Oequal) ).
fof(f29059,plain,
spl698_209,
inference(avatar_split_clause,[],[f17564,f29057]) ).
fof(f17564,plain,
! [X0] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X0)),
inference(cnf_transformation,[],[f5250]) ).
fof(f5250,plain,
! [X0] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X0)),
inference(rectify,[],[f5175]) ).
fof(f5175,axiom,
! [X324] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X324)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Hoare____Mirabelle__Otriple__HOL_Oequal) ).
fof(f29055,plain,
spl698_208,
inference(avatar_split_clause,[],[f17563,f29053]) ).
fof(f17563,plain,
! [X0] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X0)),
inference(cnf_transformation,[],[f5249]) ).
fof(f5249,plain,
! [X0] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X0)),
inference(rectify,[],[f5219]) ).
fof(f5219,axiom,
! [X324] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X324)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal) ).
fof(f29051,plain,
spl698_207,
inference(avatar_split_clause,[],[f17562,f29049]) ).
fof(f29049,plain,
( spl698_207
<=> ! [X0] : class_Nat_Osize(tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_207])]) ).
fof(f17562,plain,
! [X0] : class_Nat_Osize(tc_List_Olist(X0)),
inference(cnf_transformation,[],[f5248]) ).
fof(f5248,plain,
! [X0] : class_Nat_Osize(tc_List_Olist(X0)),
inference(rectify,[],[f5154]) ).
fof(f5154,axiom,
! [X324] : class_Nat_Osize(tc_List_Olist(X324)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_List__Olist__Nat_Osize) ).
fof(f29047,plain,
spl698_206,
inference(avatar_split_clause,[],[f17561,f29045]) ).
fof(f29045,plain,
( spl698_206
<=> ! [X0] : class_Nat_Osize(tc_Option_Ooption(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_206])]) ).
fof(f17561,plain,
! [X0] : class_Nat_Osize(tc_Option_Ooption(X0)),
inference(cnf_transformation,[],[f5247]) ).
fof(f5247,plain,
! [X0] : class_Nat_Osize(tc_Option_Ooption(X0)),
inference(rectify,[],[f5162]) ).
fof(f5162,axiom,
! [X324] : class_Nat_Osize(tc_Option_Ooption(X324)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Option__Ooption__Nat_Osize) ).
fof(f29043,plain,
spl698_205,
inference(avatar_split_clause,[],[f17560,f29041]) ).
fof(f29041,plain,
( spl698_205
<=> ! [X0] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_205])]) ).
fof(f17560,plain,
! [X0] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X0)),
inference(cnf_transformation,[],[f5246]) ).
fof(f5246,plain,
! [X0] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X0)),
inference(rectify,[],[f5176]) ).
fof(f5176,axiom,
! [X324] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X324)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).
fof(f29039,plain,
spl698_204,
inference(avatar_split_clause,[],[f17559,f29037]) ).
fof(f29037,plain,
( spl698_204
<=> ! [X0] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_204])]) ).
fof(f17559,plain,
! [X0] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)),
inference(cnf_transformation,[],[f5245]) ).
fof(f5245,plain,
! [X0] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)),
inference(rectify,[],[f5220]) ).
fof(f5220,axiom,
! [X324] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X324)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Lazy____Sequence__Olazy____sequence__Nat_Osize) ).
fof(f29035,plain,
spl698_203,
inference(avatar_split_clause,[],[f17429,f29032]) ).
fof(f17429,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f3343]) ).
fof(f3343,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__less__than) ).
fof(f29030,plain,
spl698_202,
inference(avatar_split_clause,[],[f17428,f29027]) ).
fof(f17428,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f3384]) ).
fof(f3384,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_wf__pred__nat) ).
fof(f29025,plain,
( spl698_201
| ~ spl698_200 ),
inference(avatar_split_clause,[],[f29020,f29016,f29022]) ).
fof(f29022,plain,
( spl698_201
<=> c_Nat__Transfer_Ois__nat(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_201])]) ).
fof(f29016,plain,
( spl698_200
<=> c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_200])]) ).
fof(f29020,plain,
( c_Nat__Transfer_Ois__nat(c_Int_OPls)
| ~ spl698_200 ),
inference(forward_demodulation,[],[f29018,f17436]) ).
fof(f29018,plain,
( c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl698_200 ),
inference(avatar_component_clause,[],[f29016]) ).
fof(f29019,plain,
spl698_200,
inference(avatar_split_clause,[],[f17427,f29016]) ).
fof(f17427,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f2911]) ).
fof(f2911,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).
fof(f29014,plain,
spl698_199,
inference(avatar_split_clause,[],[f17426,f29011]) ).
fof(f17426,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f2905]) ).
fof(f2905,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).
fof(f29009,plain,
~ spl698_198,
inference(avatar_split_clause,[],[f17424,f29006]) ).
fof(f29006,plain,
( spl698_198
<=> c_Int_OPls = c_Int_OMin ),
introduced(avatar_definition,[new_symbols(naming,[spl698_198])]) ).
fof(f17424,plain,
c_Int_OPls != c_Int_OMin,
inference(cnf_transformation,[],[f2775]) ).
fof(f2775,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',fact_rel__simps_I37_J) ).
fof(f29004,plain,
spl698_197,
inference(avatar_split_clause,[],[f17423,f29001]) ).
fof(f29001,plain,
( spl698_197
<=> hBOOL(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_197])]) ).
fof(f17423,plain,
hBOOL(c_fTrue),
inference(cnf_transformation,[],[f5229]) ).
fof(f5229,axiom,
hBOOL(c_fTrue),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fTrue__1) ).
fof(f28999,plain,
spl698_196,
inference(avatar_split_clause,[],[f17422,f28996]) ).
fof(f17422,plain,
class_HOL_Oequal(tc_HOL_Obool),
inference(cnf_transformation,[],[f5146]) ).
fof(f5146,axiom,
class_HOL_Oequal(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__HOL_Oequal) ).
fof(f28994,plain,
spl698_195,
inference(avatar_split_clause,[],[f17421,f28991]) ).
fof(f17421,plain,
class_HOL_Oequal(tc_Nat_Onat),
inference(cnf_transformation,[],[f5128]) ).
fof(f5128,axiom,
class_HOL_Oequal(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__HOL_Oequal) ).
fof(f28989,plain,
spl698_194,
inference(avatar_split_clause,[],[f17420,f28986]) ).
fof(f17420,plain,
class_HOL_Oequal(tc_Int_Oint),
inference(cnf_transformation,[],[f5080]) ).
fof(f5080,axiom,
class_HOL_Oequal(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__HOL_Oequal) ).
fof(f28984,plain,
spl698_193,
inference(avatar_split_clause,[],[f17419,f28981]) ).
fof(f17419,plain,
class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5217]) ).
fof(f5217,axiom,
class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__HOL_Oequal) ).
fof(f28979,plain,
spl698_192,
inference(avatar_split_clause,[],[f17418,f28976]) ).
fof(f17418,plain,
class_HOL_Oequal(tc_Com_Ostate),
inference(cnf_transformation,[],[f5149]) ).
fof(f5149,axiom,
class_HOL_Oequal(tc_Com_Ostate),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Com__Ostate__HOL_Oequal) ).
fof(f28974,plain,
spl698_191,
inference(avatar_split_clause,[],[f17417,f28971]) ).
fof(f17417,plain,
class_HOL_Oequal(tc_Code__Evaluation_Oterm),
inference(cnf_transformation,[],[f5173]) ).
fof(f5173,axiom,
class_HOL_Oequal(tc_Code__Evaluation_Oterm),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Evaluation__Oterm__HOL_Oequal) ).
fof(f28969,plain,
spl698_190,
inference(avatar_split_clause,[],[f17416,f28966]) ).
fof(f17416,plain,
class_HOL_Oequal(tc_Com_Ocom),
inference(cnf_transformation,[],[f5008]) ).
fof(f5008,axiom,
class_HOL_Oequal(tc_Com_Ocom),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Com__Ocom__HOL_Oequal) ).
fof(f28964,plain,
spl698_189,
inference(avatar_split_clause,[],[f17415,f28961]) ).
fof(f17415,plain,
class_HOL_Oequal(tc_Com_Ovname),
inference(cnf_transformation,[],[f5151]) ).
fof(f5151,axiom,
class_HOL_Oequal(tc_Com_Ovname),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Com__Ovname__HOL_Oequal) ).
fof(f28959,plain,
spl698_188,
inference(avatar_split_clause,[],[f17414,f28956]) ).
fof(f17414,plain,
class_HOL_Oequal(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5170]) ).
fof(f5170,axiom,
class_HOL_Oequal(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Product____Type__Ounit__HOL_Oequal) ).
fof(f28954,plain,
spl698_187,
inference(avatar_split_clause,[],[f17413,f28951]) ).
fof(f28951,plain,
( spl698_187
<=> class_Nat_Osize(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_187])]) ).
fof(f17413,plain,
class_Nat_Osize(tc_HOL_Obool),
inference(cnf_transformation,[],[f5148]) ).
fof(f5148,axiom,
class_Nat_Osize(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Nat_Osize) ).
fof(f28949,plain,
spl698_186,
inference(avatar_split_clause,[],[f17412,f28946]) ).
fof(f28946,plain,
( spl698_186
<=> class_Nat_Osize(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_186])]) ).
fof(f17412,plain,
class_Nat_Osize(tc_Nat_Onat),
inference(cnf_transformation,[],[f5129]) ).
fof(f5129,axiom,
class_Nat_Osize(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Nat_Osize) ).
fof(f28944,plain,
spl698_185,
inference(avatar_split_clause,[],[f17411,f28941]) ).
fof(f28941,plain,
( spl698_185
<=> class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_185])]) ).
fof(f17411,plain,
class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5218]) ).
fof(f5218,axiom,
class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Nat_Osize) ).
fof(f28939,plain,
spl698_184,
inference(avatar_split_clause,[],[f17410,f28936]) ).
fof(f28936,plain,
( spl698_184
<=> class_Nat_Osize(tc_Com_Ostate) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_184])]) ).
fof(f17410,plain,
class_Nat_Osize(tc_Com_Ostate),
inference(cnf_transformation,[],[f5150]) ).
fof(f5150,axiom,
class_Nat_Osize(tc_Com_Ostate),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Com__Ostate__Nat_Osize) ).
fof(f28934,plain,
spl698_183,
inference(avatar_split_clause,[],[f17409,f28931]) ).
fof(f28931,plain,
( spl698_183
<=> class_Nat_Osize(tc_Code__Evaluation_Oterm) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_183])]) ).
fof(f17409,plain,
class_Nat_Osize(tc_Code__Evaluation_Oterm),
inference(cnf_transformation,[],[f5174]) ).
fof(f5174,axiom,
class_Nat_Osize(tc_Code__Evaluation_Oterm),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Evaluation__Oterm__Nat_Osize) ).
fof(f28929,plain,
spl698_182,
inference(avatar_split_clause,[],[f17408,f28926]) ).
fof(f28926,plain,
( spl698_182
<=> class_Nat_Osize(tc_Com_Ocom) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_182])]) ).
fof(f17408,plain,
class_Nat_Osize(tc_Com_Ocom),
inference(cnf_transformation,[],[f5009]) ).
fof(f5009,axiom,
class_Nat_Osize(tc_Com_Ocom),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Com__Ocom__Nat_Osize) ).
fof(f28924,plain,
spl698_181,
inference(avatar_split_clause,[],[f17407,f28921]) ).
fof(f28921,plain,
( spl698_181
<=> class_Nat_Osize(tc_Com_Ovname) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_181])]) ).
fof(f17407,plain,
class_Nat_Osize(tc_Com_Ovname),
inference(cnf_transformation,[],[f5152]) ).
fof(f5152,axiom,
class_Nat_Osize(tc_Com_Ovname),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Com__Ovname__Nat_Osize) ).
fof(f28919,plain,
spl698_180,
inference(avatar_split_clause,[],[f17406,f28916]) ).
fof(f28916,plain,
( spl698_180
<=> class_Nat_Osize(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_180])]) ).
fof(f17406,plain,
class_Nat_Osize(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5172]) ).
fof(f5172,axiom,
class_Nat_Osize(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Product____Type__Ounit__Nat_Osize) ).
fof(f28914,plain,
spl698_179,
inference(avatar_split_clause,[],[f17405,f28911]) ).
fof(f28911,plain,
( spl698_179
<=> class_Enum_Oenum(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_179])]) ).
fof(f17405,plain,
class_Enum_Oenum(tc_HOL_Obool),
inference(cnf_transformation,[],[f5147]) ).
fof(f5147,axiom,
class_Enum_Oenum(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Enum_Oenum) ).
fof(f28909,plain,
spl698_178,
inference(avatar_split_clause,[],[f17404,f28906]) ).
fof(f28906,plain,
( spl698_178
<=> class_Enum_Oenum(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_178])]) ).
fof(f17404,plain,
class_Enum_Oenum(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5171]) ).
fof(f5171,axiom,
class_Enum_Oenum(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Product____Type__Ounit__Enum_Oenum) ).
fof(f28904,plain,
spl698_177,
inference(avatar_split_clause,[],[f17403,f28901]) ).
fof(f28901,plain,
( spl698_177
<=> class_Finite__Set_Ofinite(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_177])]) ).
fof(f17403,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(cnf_transformation,[],[f5138]) ).
fof(f5138,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(f28899,plain,
spl698_176,
inference(avatar_split_clause,[],[f17402,f28896]) ).
fof(f28896,plain,
( spl698_176
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_176])]) ).
fof(f17402,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5168]) ).
fof(f5168,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(f28894,plain,
spl698_175,
inference(avatar_split_clause,[],[f17401,f28891]) ).
fof(f28891,plain,
( spl698_175
<=> class_Orderings_Oorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_175])]) ).
fof(f17401,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f5140]) ).
fof(f5140,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Orderings_Oorder) ).
fof(f28889,plain,
spl698_174,
inference(avatar_split_clause,[],[f17400,f28886]) ).
fof(f28886,plain,
( spl698_174
<=> class_Orderings_Oorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_174])]) ).
fof(f17400,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5119]) ).
fof(f5119,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Orderings_Oorder) ).
fof(f28884,plain,
spl698_173,
inference(avatar_split_clause,[],[f17399,f28881]) ).
fof(f28881,plain,
( spl698_173
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_173])]) ).
fof(f17399,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5064]) ).
fof(f5064,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Orderings_Oorder) ).
fof(f28879,plain,
spl698_172,
inference(avatar_split_clause,[],[f17398,f28876]) ).
fof(f28876,plain,
( spl698_172
<=> class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_172])]) ).
fof(f17398,plain,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5209]) ).
fof(f5209,axiom,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Orderings_Oorder) ).
fof(f28874,plain,
spl698_171,
inference(avatar_split_clause,[],[f17397,f28871]) ).
fof(f28871,plain,
( spl698_171
<=> class_Orderings_Oord(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_171])]) ).
fof(f17397,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f5142]) ).
fof(f5142,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Orderings_Oord) ).
fof(f28869,plain,
spl698_170,
inference(avatar_split_clause,[],[f17396,f28866]) ).
fof(f28866,plain,
( spl698_170
<=> class_Orderings_Oord(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_170])]) ).
fof(f17396,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f5121]) ).
fof(f5121,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Orderings_Oord) ).
fof(f28864,plain,
spl698_169,
inference(avatar_split_clause,[],[f17395,f28861]) ).
fof(f28861,plain,
( spl698_169
<=> class_Orderings_Oord(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_169])]) ).
fof(f17395,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(cnf_transformation,[],[f5068]) ).
fof(f5068,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Orderings_Oord) ).
fof(f28859,plain,
spl698_168,
inference(avatar_split_clause,[],[f17394,f28856]) ).
fof(f28856,plain,
( spl698_168
<=> class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_168])]) ).
fof(f17394,plain,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5211]) ).
fof(f5211,axiom,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Orderings_Oord) ).
fof(f28854,plain,
spl698_167,
inference(avatar_split_clause,[],[f17393,f28851]) ).
fof(f28851,plain,
( spl698_167
<=> class_Orderings_Opreorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_167])]) ).
fof(f17393,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f5137]) ).
fof(f5137,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Orderings_Opreorder) ).
fof(f28849,plain,
spl698_166,
inference(avatar_split_clause,[],[f17392,f28846]) ).
fof(f28846,plain,
( spl698_166
<=> class_Orderings_Opreorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_166])]) ).
fof(f17392,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5111]) ).
fof(f5111,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Orderings_Opreorder) ).
fof(f28844,plain,
spl698_165,
inference(avatar_split_clause,[],[f17391,f28841]) ).
fof(f28841,plain,
( spl698_165
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_165])]) ).
fof(f17391,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5052]) ).
fof(f5052,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Orderings_Opreorder) ).
fof(f28839,plain,
spl698_164,
inference(avatar_split_clause,[],[f17390,f28836]) ).
fof(f28836,plain,
( spl698_164
<=> class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_164])]) ).
fof(f17390,plain,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5202]) ).
fof(f5202,axiom,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder) ).
fof(f28834,plain,
spl698_163,
inference(avatar_split_clause,[],[f17389,f28831]) ).
fof(f28831,plain,
( spl698_163
<=> class_Groups_Ominus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_163])]) ).
fof(f17389,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(cnf_transformation,[],[f5145]) ).
fof(f5145,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Groups_Ominus) ).
fof(f28829,plain,
spl698_162,
inference(avatar_split_clause,[],[f17388,f28826]) ).
fof(f28826,plain,
( spl698_162
<=> class_Groups_Ominus(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_162])]) ).
fof(f17388,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(cnf_transformation,[],[f5123]) ).
fof(f5123,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Ominus) ).
fof(f28824,plain,
spl698_161,
inference(avatar_split_clause,[],[f17387,f28821]) ).
fof(f28821,plain,
( spl698_161
<=> class_Groups_Ominus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_161])]) ).
fof(f17387,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(cnf_transformation,[],[f5073]) ).
fof(f5073,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Ominus) ).
fof(f28819,plain,
spl698_160,
inference(avatar_split_clause,[],[f17386,f28816]) ).
fof(f28816,plain,
( spl698_160
<=> class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_160])]) ).
fof(f17386,plain,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5212]) ).
fof(f5212,axiom,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Ominus) ).
fof(f28814,plain,
spl698_159,
inference(avatar_split_clause,[],[f17385,f28811]) ).
fof(f28811,plain,
( spl698_159
<=> class_Lattices_Olattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_159])]) ).
fof(f17385,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5139]) ).
fof(f5139,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Lattices_Olattice) ).
fof(f28809,plain,
spl698_158,
inference(avatar_split_clause,[],[f17384,f28806]) ).
fof(f28806,plain,
( spl698_158
<=> class_Lattices_Olattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_158])]) ).
fof(f17384,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f5117]) ).
fof(f5117,axiom,
class_Lattices_Olattice(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Lattices_Olattice) ).
fof(f28804,plain,
spl698_157,
inference(avatar_split_clause,[],[f17383,f28801]) ).
fof(f28801,plain,
( spl698_157
<=> class_Lattices_Olattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_157])]) ).
fof(f17383,plain,
class_Lattices_Olattice(tc_Int_Oint),
inference(cnf_transformation,[],[f5060]) ).
fof(f5060,axiom,
class_Lattices_Olattice(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Lattices_Olattice) ).
fof(f28799,plain,
spl698_156,
inference(avatar_split_clause,[],[f17382,f28796]) ).
fof(f28796,plain,
( spl698_156
<=> class_Lattices_Osemilattice__inf(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_156])]) ).
fof(f17382,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(cnf_transformation,[],[f5134]) ).
fof(f5134,axiom,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
fof(f28794,plain,
spl698_155,
inference(avatar_split_clause,[],[f17381,f28791]) ).
fof(f28791,plain,
( spl698_155
<=> class_Lattices_Osemilattice__inf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_155])]) ).
fof(f17381,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(cnf_transformation,[],[f5096]) ).
fof(f5096,axiom,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
fof(f28789,plain,
spl698_154,
inference(avatar_split_clause,[],[f17380,f28786]) ).
fof(f28786,plain,
( spl698_154
<=> class_Lattices_Osemilattice__inf(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_154])]) ).
fof(f17380,plain,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
inference(cnf_transformation,[],[f5033]) ).
fof(f5033,axiom,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Lattices_Osemilattice__inf) ).
fof(f28784,plain,
spl698_153,
inference(avatar_split_clause,[],[f17379,f28781]) ).
fof(f28781,plain,
( spl698_153
<=> class_Lattices_Osemilattice__sup(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_153])]) ).
fof(f17379,plain,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
inference(cnf_transformation,[],[f5133]) ).
fof(f5133,axiom,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
fof(f28779,plain,
spl698_152,
inference(avatar_split_clause,[],[f17378,f28776]) ).
fof(f28776,plain,
( spl698_152
<=> class_Lattices_Osemilattice__sup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_152])]) ).
fof(f17378,plain,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
inference(cnf_transformation,[],[f5095]) ).
fof(f5095,axiom,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
fof(f28774,plain,
spl698_151,
inference(avatar_split_clause,[],[f17377,f28771]) ).
fof(f28771,plain,
( spl698_151
<=> class_Lattices_Osemilattice__sup(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_151])]) ).
fof(f17377,plain,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
inference(cnf_transformation,[],[f5032]) ).
fof(f5032,axiom,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Lattices_Osemilattice__sup) ).
fof(f28769,plain,
spl698_150,
inference(avatar_split_clause,[],[f17376,f28766]) ).
fof(f28766,plain,
( spl698_150
<=> class_Lattices_Odistrib__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_150])]) ).
fof(f17376,plain,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5135]) ).
fof(f5135,axiom,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
fof(f28764,plain,
spl698_149,
inference(avatar_split_clause,[],[f17375,f28761]) ).
fof(f28761,plain,
( spl698_149
<=> class_Lattices_Odistrib__lattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_149])]) ).
fof(f17375,plain,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f5097]) ).
fof(f5097,axiom,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Lattices_Odistrib__lattice) ).
fof(f28759,plain,
spl698_148,
inference(avatar_split_clause,[],[f17374,f28756]) ).
fof(f28756,plain,
( spl698_148
<=> class_Lattices_Odistrib__lattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_148])]) ).
fof(f17374,plain,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
inference(cnf_transformation,[],[f5034]) ).
fof(f5034,axiom,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Lattices_Odistrib__lattice) ).
fof(f28754,plain,
spl698_147,
inference(avatar_split_clause,[],[f17373,f28751]) ).
fof(f28751,plain,
( spl698_147
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_147])]) ).
fof(f17373,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5112]) ).
fof(f5112,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Orderings_Olinorder) ).
fof(f28749,plain,
spl698_146,
inference(avatar_split_clause,[],[f17372,f28746]) ).
fof(f28746,plain,
( spl698_146
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_146])]) ).
fof(f17372,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5053]) ).
fof(f5053,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Orderings_Olinorder) ).
fof(f28744,plain,
spl698_145,
inference(avatar_split_clause,[],[f17371,f28741]) ).
fof(f28741,plain,
( spl698_145
<=> class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_145])]) ).
fof(f17371,plain,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5203]) ).
fof(f5203,axiom,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) ).
fof(f28739,plain,
spl698_144,
inference(avatar_split_clause,[],[f17370,f28736]) ).
fof(f28736,plain,
( spl698_144
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_144])]) ).
fof(f17370,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5103]) ).
fof(f5103,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(f28734,plain,
spl698_143,
inference(avatar_split_clause,[],[f17369,f28731]) ).
fof(f28731,plain,
( spl698_143
<=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_143])]) ).
fof(f17369,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5041]) ).
fof(f5041,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(f28729,plain,
spl698_142,
inference(avatar_split_clause,[],[f17368,f28726]) ).
fof(f28726,plain,
( spl698_142
<=> class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_142])]) ).
fof(f17368,plain,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5195]) ).
fof(f5195,axiom,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) ).
fof(f28724,plain,
spl698_141,
inference(avatar_split_clause,[],[f17367,f28721]) ).
fof(f28721,plain,
( spl698_141
<=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_141])]) ).
fof(f17367,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5099]) ).
fof(f5099,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(f28719,plain,
spl698_140,
inference(avatar_split_clause,[],[f17366,f28716]) ).
fof(f28716,plain,
( spl698_140
<=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_140])]) ).
fof(f17366,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5036]) ).
fof(f5036,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(f28714,plain,
spl698_139,
inference(avatar_split_clause,[],[f17365,f28711]) ).
fof(f28711,plain,
( spl698_139
<=> class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_139])]) ).
fof(f17365,plain,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5191]) ).
fof(f5191,axiom,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult) ).
fof(f28709,plain,
spl698_138,
inference(avatar_split_clause,[],[f17364,f28706]) ).
fof(f28706,plain,
( spl698_138
<=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_138])]) ).
fof(f17364,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f5094]) ).
fof(f5094,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(f28704,plain,
spl698_137,
inference(avatar_split_clause,[],[f17363,f28701]) ).
fof(f28701,plain,
( spl698_137
<=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_137])]) ).
fof(f17363,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(cnf_transformation,[],[f5031]) ).
fof(f5031,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(f28699,plain,
spl698_136,
inference(avatar_split_clause,[],[f17362,f28696]) ).
fof(f28696,plain,
( spl698_136
<=> class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_136])]) ).
fof(f17362,plain,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5189]) ).
fof(f5189,axiom,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) ).
fof(f28694,plain,
spl698_135,
inference(avatar_split_clause,[],[f17361,f28691]) ).
fof(f28691,plain,
( spl698_135
<=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_135])]) ).
fof(f17361,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(cnf_transformation,[],[f5106]) ).
fof(f5106,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(f28689,plain,
spl698_134,
inference(avatar_split_clause,[],[f17360,f28686]) ).
fof(f28686,plain,
( spl698_134
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_134])]) ).
fof(f17360,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f5046]) ).
fof(f5046,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Divides_Osemiring__div) ).
fof(f28684,plain,
spl698_133,
inference(avatar_split_clause,[],[f17359,f28681]) ).
fof(f28681,plain,
( spl698_133
<=> class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_133])]) ).
fof(f17359,plain,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5198]) ).
fof(f5198,axiom,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) ).
fof(f28679,plain,
spl698_132,
inference(avatar_split_clause,[],[f17358,f28676]) ).
fof(f28676,plain,
( spl698_132
<=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_132])]) ).
fof(f17358,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f5104]) ).
fof(f5104,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(f28674,plain,
spl698_131,
inference(avatar_split_clause,[],[f17357,f28671]) ).
fof(f28671,plain,
( spl698_131
<=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_131])]) ).
fof(f17357,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5044]) ).
fof(f5044,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(f28669,plain,
spl698_130,
inference(avatar_split_clause,[],[f17356,f28666]) ).
fof(f28666,plain,
( spl698_130
<=> class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_130])]) ).
fof(f17356,plain,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5196]) ).
fof(f5196,axiom,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).
fof(f28664,plain,
spl698_129,
inference(avatar_split_clause,[],[f17355,f28661]) ).
fof(f28661,plain,
( spl698_129
<=> class_Rings_Osemiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_129])]) ).
fof(f17355,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f5115]) ).
fof(f5115,axiom,
class_Rings_Osemiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Osemiring__1) ).
fof(f28659,plain,
spl698_128,
inference(avatar_split_clause,[],[f17354,f28656]) ).
fof(f17354,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5058]) ).
fof(f5058,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Osemiring__1) ).
fof(f28654,plain,
spl698_127,
inference(avatar_split_clause,[],[f17353,f28651]) ).
fof(f28651,plain,
( spl698_127
<=> class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_127])]) ).
fof(f17353,plain,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5206]) ).
fof(f5206,axiom,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).
fof(f28649,plain,
spl698_126,
inference(avatar_split_clause,[],[f17352,f28646]) ).
fof(f28646,plain,
( spl698_126
<=> class_Int_Onumber(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_126])]) ).
fof(f17352,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(cnf_transformation,[],[f5126]) ).
fof(f5126,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Int_Onumber) ).
fof(f28644,plain,
spl698_125,
inference(avatar_split_clause,[],[f17351,f28641]) ).
fof(f28641,plain,
( spl698_125
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_125])]) ).
fof(f17351,plain,
class_Int_Onumber(tc_Int_Oint),
inference(cnf_transformation,[],[f5078]) ).
fof(f5078,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Int_Onumber) ).
fof(f28639,plain,
spl698_124,
inference(avatar_split_clause,[],[f17350,f28636]) ).
fof(f28636,plain,
( spl698_124
<=> class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_124])]) ).
fof(f17350,plain,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5215]) ).
fof(f5215,axiom,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Int_Onumber) ).
fof(f28634,plain,
spl698_123,
inference(avatar_split_clause,[],[f17349,f28631]) ).
fof(f28631,plain,
( spl698_123
<=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_123])]) ).
fof(f17349,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f5086]) ).
fof(f5086,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(f28629,plain,
spl698_122,
inference(avatar_split_clause,[],[f17348,f28626]) ).
fof(f28626,plain,
( spl698_122
<=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_122])]) ).
fof(f17348,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5016]) ).
fof(f5016,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(f28624,plain,
spl698_121,
inference(avatar_split_clause,[],[f17347,f28621]) ).
fof(f28621,plain,
( spl698_121
<=> class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_121])]) ).
fof(f17347,plain,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5181]) ).
fof(f5181,axiom,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) ).
fof(f28619,plain,
spl698_120,
inference(avatar_split_clause,[],[f17346,f28616]) ).
fof(f28616,plain,
( spl698_120
<=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_120])]) ).
fof(f17346,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5088]) ).
fof(f5088,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(f28614,plain,
spl698_119,
inference(avatar_split_clause,[],[f17345,f28611]) ).
fof(f28611,plain,
( spl698_119
<=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_119])]) ).
fof(f17345,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5019]) ).
fof(f5019,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(f28609,plain,
spl698_118,
inference(avatar_split_clause,[],[f17344,f28606]) ).
fof(f28606,plain,
( spl698_118
<=> class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_118])]) ).
fof(f17344,plain,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5183]) ).
fof(f5183,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add) ).
fof(f28604,plain,
spl698_117,
inference(avatar_split_clause,[],[f17343,f28601]) ).
fof(f28601,plain,
( spl698_117
<=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_117])]) ).
fof(f17343,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5113]) ).
fof(f5113,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(f28599,plain,
spl698_116,
inference(avatar_split_clause,[],[f17342,f28596]) ).
fof(f28596,plain,
( spl698_116
<=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_116])]) ).
fof(f17342,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5054]) ).
fof(f5054,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(f28594,plain,
spl698_115,
inference(avatar_split_clause,[],[f17341,f28591]) ).
fof(f28591,plain,
( spl698_115
<=> class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_115])]) ).
fof(f17341,plain,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5204]) ).
fof(f5204,axiom,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) ).
fof(f28589,plain,
spl698_114,
inference(avatar_split_clause,[],[f17340,f28586]) ).
fof(f28586,plain,
( spl698_114
<=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_114])]) ).
fof(f17340,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5114]) ).
fof(f5114,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(f28584,plain,
spl698_113,
inference(avatar_split_clause,[],[f17339,f28581]) ).
fof(f28581,plain,
( spl698_113
<=> class_Groups_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_113])]) ).
fof(f17339,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5056]) ).
fof(f5056,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Omonoid__add) ).
fof(f28579,plain,
spl698_112,
inference(avatar_split_clause,[],[f17338,f28576]) ).
fof(f28576,plain,
( spl698_112
<=> class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_112])]) ).
fof(f17338,plain,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5205]) ).
fof(f5205,axiom,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) ).
fof(f28574,plain,
spl698_111,
inference(avatar_split_clause,[],[f17337,f28571]) ).
fof(f28571,plain,
( spl698_111
<=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_111])]) ).
fof(f17337,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5098]) ).
fof(f5098,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(f28569,plain,
spl698_110,
inference(avatar_split_clause,[],[f17336,f28566]) ).
fof(f28566,plain,
( spl698_110
<=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_110])]) ).
fof(f17336,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5035]) ).
fof(f5035,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(f28564,plain,
spl698_109,
inference(avatar_split_clause,[],[f17335,f28561]) ).
fof(f28561,plain,
( spl698_109
<=> class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_109])]) ).
fof(f17335,plain,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5190]) ).
fof(f5190,axiom,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) ).
fof(f28559,plain,
spl698_108,
inference(avatar_split_clause,[],[f17334,f28556]) ).
fof(f28556,plain,
( spl698_108
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_108])]) ).
fof(f17334,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[],[f5083]) ).
fof(f5083,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f28554,plain,
spl698_107,
inference(avatar_split_clause,[],[f17333,f28551]) ).
fof(f28551,plain,
( spl698_107
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_107])]) ).
fof(f17333,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[],[f5012]) ).
fof(f5012,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f28549,plain,
spl698_106,
inference(avatar_split_clause,[],[f17332,f28546]) ).
fof(f28546,plain,
( spl698_106
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_106])]) ).
fof(f17332,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5178]) ).
fof(f5178,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f28544,plain,
spl698_105,
inference(avatar_split_clause,[],[f17331,f28541]) ).
fof(f28541,plain,
( spl698_105
<=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_105])]) ).
fof(f17331,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f5116]) ).
fof(f5116,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(f28539,plain,
spl698_104,
inference(avatar_split_clause,[],[f17330,f28536]) ).
fof(f28536,plain,
( spl698_104
<=> class_Rings_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_104])]) ).
fof(f17330,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5059]) ).
fof(f5059,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Osemiring__0) ).
fof(f28534,plain,
spl698_103,
inference(avatar_split_clause,[],[f17329,f28531]) ).
fof(f28531,plain,
( spl698_103
<=> class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_103])]) ).
fof(f17329,plain,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5207]) ).
fof(f5207,axiom,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).
fof(f28529,plain,
spl698_102,
inference(avatar_split_clause,[],[f17328,f28526]) ).
fof(f28526,plain,
( spl698_102
<=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_102])]) ).
fof(f17328,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5087]) ).
fof(f5087,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(f28524,plain,
spl698_101,
inference(avatar_split_clause,[],[f17327,f28521]) ).
fof(f28521,plain,
( spl698_101
<=> class_Power_Opower(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_101])]) ).
fof(f17327,plain,
class_Power_Opower(tc_Nat_Onat),
inference(cnf_transformation,[],[f5124]) ).
fof(f5124,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Power_Opower) ).
fof(f28519,plain,
spl698_100,
inference(avatar_split_clause,[],[f17326,f28516]) ).
fof(f28516,plain,
( spl698_100
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_100])]) ).
fof(f17326,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5082]) ).
fof(f5082,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f28514,plain,
spl698_99,
inference(avatar_split_clause,[],[f17325,f28511]) ).
fof(f28511,plain,
( spl698_99
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_99])]) ).
fof(f17325,plain,
class_Power_Opower(tc_Int_Oint),
inference(cnf_transformation,[],[f5074]) ).
fof(f5074,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Power_Opower) ).
fof(f28509,plain,
spl698_98,
inference(avatar_split_clause,[],[f17324,f28506]) ).
fof(f28506,plain,
( spl698_98
<=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_98])]) ).
fof(f17324,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5017]) ).
fof(f5017,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(f28504,plain,
spl698_97,
inference(avatar_split_clause,[],[f17323,f28501]) ).
fof(f28501,plain,
( spl698_97
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_97])]) ).
fof(f17323,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5011]) ).
fof(f5011,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f28499,plain,
spl698_96,
inference(avatar_split_clause,[],[f17322,f28496]) ).
fof(f28496,plain,
( spl698_96
<=> class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_96])]) ).
fof(f17322,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5182]) ).
fof(f5182,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) ).
fof(f28494,plain,
spl698_95,
inference(avatar_split_clause,[],[f17321,f28491]) ).
fof(f28491,plain,
( spl698_95
<=> class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_95])]) ).
fof(f17321,plain,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5213]) ).
fof(f5213,axiom,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).
fof(f28489,plain,
spl698_94,
inference(avatar_split_clause,[],[f17320,f28486]) ).
fof(f28486,plain,
( spl698_94
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_94])]) ).
fof(f17320,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5177]) ).
fof(f5177,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f28484,plain,
spl698_93,
inference(avatar_split_clause,[],[f17319,f28481]) ).
fof(f28481,plain,
( spl698_93
<=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_93])]) ).
fof(f17319,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5090]) ).
fof(f5090,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(f28479,plain,
spl698_92,
inference(avatar_split_clause,[],[f17318,f28476]) ).
fof(f28476,plain,
( spl698_92
<=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_92])]) ).
fof(f17318,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5023]) ).
fof(f5023,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(f28474,plain,
spl698_91,
inference(avatar_split_clause,[],[f17317,f28471]) ).
fof(f28471,plain,
( spl698_91
<=> class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_91])]) ).
fof(f17317,plain,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5185]) ).
fof(f5185,axiom,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) ).
fof(f28469,plain,
spl698_90,
inference(avatar_split_clause,[],[f17316,f28466]) ).
fof(f28466,plain,
( spl698_90
<=> class_Orderings_Obot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_90])]) ).
fof(f17316,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(cnf_transformation,[],[f5143]) ).
fof(f5143,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Orderings_Obot) ).
fof(f28464,plain,
spl698_89,
inference(avatar_split_clause,[],[f17315,f28461]) ).
fof(f28461,plain,
( spl698_89
<=> class_Orderings_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_89])]) ).
fof(f17315,plain,
class_Orderings_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f5122]) ).
fof(f5122,axiom,
class_Orderings_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Orderings_Obot) ).
fof(f28459,plain,
spl698_88,
inference(avatar_split_clause,[],[f17314,f28456]) ).
fof(f28456,plain,
( spl698_88
<=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_88])]) ).
fof(f17314,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(cnf_transformation,[],[f5102]) ).
fof(f5102,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(f28454,plain,
spl698_87,
inference(avatar_split_clause,[],[f17313,f28451]) ).
fof(f28451,plain,
( spl698_87
<=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_87])]) ).
fof(f17313,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5101]) ).
fof(f5101,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(f28449,plain,
spl698_86,
inference(avatar_split_clause,[],[f17312,f28446]) ).
fof(f28446,plain,
( spl698_86
<=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_86])]) ).
fof(f17312,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5092]) ).
fof(f5092,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(f28444,plain,
spl698_85,
inference(avatar_split_clause,[],[f17311,f28441]) ).
fof(f28441,plain,
( spl698_85
<=> class_Smallcheck_Osmall(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_85])]) ).
fof(f17311,plain,
class_Smallcheck_Osmall(tc_Int_Oint),
inference(cnf_transformation,[],[f5057]) ).
fof(f5057,axiom,
class_Smallcheck_Osmall(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Smallcheck_Osmall) ).
fof(f28439,plain,
spl698_84,
inference(avatar_split_clause,[],[f17310,f28436]) ).
fof(f28436,plain,
( spl698_84
<=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_84])]) ).
fof(f17310,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5038]) ).
fof(f5038,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(f28434,plain,
spl698_83,
inference(avatar_split_clause,[],[f17309,f28431]) ).
fof(f28431,plain,
( spl698_83
<=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_83])]) ).
fof(f17309,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5040]) ).
fof(f5040,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(f28429,plain,
spl698_82,
inference(avatar_split_clause,[],[f17308,f28426]) ).
fof(f28426,plain,
( spl698_82
<=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_82])]) ).
fof(f17308,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5029]) ).
fof(f5029,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(f28424,plain,
spl698_81,
inference(avatar_split_clause,[],[f17307,f28421]) ).
fof(f28421,plain,
( spl698_81
<=> class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_81])]) ).
fof(f17307,plain,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5187]) ).
fof(f5187,axiom,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) ).
fof(f28419,plain,
spl698_80,
inference(avatar_split_clause,[],[f17306,f28416]) ).
fof(f28416,plain,
( spl698_80
<=> class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_80])]) ).
fof(f17306,plain,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5193]) ).
fof(f5193,axiom,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) ).
fof(f28414,plain,
spl698_79,
inference(avatar_split_clause,[],[f17305,f28411]) ).
fof(f28411,plain,
( spl698_79
<=> class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_79])]) ).
fof(f17305,plain,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5194]) ).
fof(f5194,axiom,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) ).
fof(f28409,plain,
spl698_78,
inference(avatar_split_clause,[],[f17304,f28406]) ).
fof(f28406,plain,
( spl698_78
<=> class_Smallcheck_Osmall(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_78])]) ).
fof(f17304,plain,
class_Smallcheck_Osmall(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5169]) ).
fof(f5169,axiom,
class_Smallcheck_Osmall(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Product____Type__Ounit__Smallcheck_Osmall) ).
fof(f28404,plain,
spl698_77,
inference(avatar_split_clause,[],[f17303,f28401]) ).
fof(f28401,plain,
( spl698_77
<=> class_Groups_Ouminus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_77])]) ).
fof(f17303,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(cnf_transformation,[],[f5144]) ).
fof(f5144,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Groups_Ouminus) ).
fof(f28399,plain,
spl698_76,
inference(avatar_split_clause,[],[f17302,f28396]) ).
fof(f28396,plain,
( spl698_76
<=> class_Rings_Osemiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_76])]) ).
fof(f17302,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5120]) ).
fof(f5120,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Osemiring) ).
fof(f28394,plain,
spl698_75,
inference(avatar_split_clause,[],[f17301,f28391]) ).
fof(f28391,plain,
( spl698_75
<=> class_Rings_Omult__zero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_75])]) ).
fof(f17301,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(cnf_transformation,[],[f5118]) ).
fof(f5118,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Omult__zero) ).
fof(f28389,plain,
spl698_74,
inference(avatar_split_clause,[],[f17300,f28386]) ).
fof(f28386,plain,
( spl698_74
<=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_74])]) ).
fof(f17300,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(cnf_transformation,[],[f5110]) ).
fof(f5110,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(f28384,plain,
spl698_73,
inference(avatar_split_clause,[],[f17299,f28381]) ).
fof(f28381,plain,
( spl698_73
<=> class_Groups_Ouminus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_73])]) ).
fof(f17299,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(cnf_transformation,[],[f5069]) ).
fof(f5069,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Ouminus) ).
fof(f28379,plain,
spl698_72,
inference(avatar_split_clause,[],[f17298,f28376]) ).
fof(f28376,plain,
( spl698_72
<=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_72])]) ).
fof(f17298,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(cnf_transformation,[],[f5050]) ).
fof(f5050,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(f28374,plain,
spl698_71,
inference(avatar_split_clause,[],[f17297,f28371]) ).
fof(f28371,plain,
( spl698_71
<=> class_Rings_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_71])]) ).
fof(f17297,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(cnf_transformation,[],[f5063]) ).
fof(f5063,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Omult__zero) ).
fof(f28369,plain,
spl698_70,
inference(avatar_split_clause,[],[f17296,f28366]) ).
fof(f28366,plain,
( spl698_70
<=> class_Rings_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_70])]) ).
fof(f17296,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5067]) ).
fof(f5067,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Osemiring) ).
fof(f28364,plain,
spl698_69,
inference(avatar_split_clause,[],[f17295,f28361]) ).
fof(f28361,plain,
( spl698_69
<=> class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_69])]) ).
fof(f17295,plain,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5210]) ).
fof(f5210,axiom,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring) ).
fof(f28359,plain,
spl698_68,
inference(avatar_split_clause,[],[f17294,f28356]) ).
fof(f28356,plain,
( spl698_68
<=> class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_68])]) ).
fof(f17294,plain,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5201]) ).
fof(f5201,axiom,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one) ).
fof(f28354,plain,
spl698_67,
inference(avatar_split_clause,[],[f17293,f28351]) ).
fof(f28351,plain,
( spl698_67
<=> class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_67])]) ).
fof(f17293,plain,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5208]) ).
fof(f5208,axiom,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero) ).
fof(f28349,plain,
spl698_66,
inference(avatar_split_clause,[],[f17292,f28346]) ).
fof(f28346,plain,
( spl698_66
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_66])]) ).
fof(f17292,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5085]) ).
fof(f5085,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add) ).
fof(f28344,plain,
spl698_65,
inference(avatar_split_clause,[],[f17291,f28341]) ).
fof(f28341,plain,
( spl698_65
<=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_65])]) ).
fof(f17291,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5093]) ).
fof(f5093,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(f28339,plain,
spl698_64,
inference(avatar_split_clause,[],[f17290,f28336]) ).
fof(f28336,plain,
( spl698_64
<=> class_Nat_Osemiring__char__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_64])]) ).
fof(f17290,plain,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f5109]) ).
fof(f5109,axiom,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Nat_Osemiring__char__0) ).
fof(f28334,plain,
spl698_63,
inference(avatar_split_clause,[],[f17289,f28331]) ).
fof(f28331,plain,
( spl698_63
<=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_63])]) ).
fof(f17289,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5100]) ).
fof(f5100,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(f28329,plain,
spl698_62,
inference(avatar_split_clause,[],[f17288,f28326]) ).
fof(f28326,plain,
( spl698_62
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_62])]) ).
fof(f17288,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5015]) ).
fof(f5015,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Olinordered__ab__semigroup__add) ).
fof(f28324,plain,
spl698_61,
inference(avatar_split_clause,[],[f17287,f28321]) ).
fof(f28321,plain,
( spl698_61
<=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_61])]) ).
fof(f17287,plain,
class_Nat_Osemiring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5048]) ).
fof(f5048,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Nat_Osemiring__char__0) ).
fof(f28319,plain,
spl698_60,
inference(avatar_split_clause,[],[f17286,f28316]) ).
fof(f28316,plain,
( spl698_60
<=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_60])]) ).
fof(f17286,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5037]) ).
fof(f5037,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(f28314,plain,
spl698_59,
inference(avatar_split_clause,[],[f17285,f28311]) ).
fof(f28311,plain,
( spl698_59
<=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_59])]) ).
fof(f17285,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5030]) ).
fof(f5030,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(f28309,plain,
spl698_58,
inference(avatar_split_clause,[],[f17284,f28306]) ).
fof(f28306,plain,
( spl698_58
<=> class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_58])]) ).
fof(f17284,plain,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5200]) ).
fof(f5200,axiom,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0) ).
fof(f28304,plain,
spl698_57,
inference(avatar_split_clause,[],[f17283,f28301]) ).
fof(f28301,plain,
( spl698_57
<=> class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_57])]) ).
fof(f17283,plain,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5192]) ).
fof(f5192,axiom,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) ).
fof(f28299,plain,
spl698_56,
inference(avatar_split_clause,[],[f17282,f28296]) ).
fof(f28296,plain,
( spl698_56
<=> class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_56])]) ).
fof(f17282,plain,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5188]) ).
fof(f5188,axiom,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) ).
fof(f28294,plain,
spl698_55,
inference(avatar_split_clause,[],[f17281,f28291]) ).
fof(f28291,plain,
( spl698_55
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_55])]) ).
fof(f17281,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5180]) ).
fof(f5180,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) ).
fof(f28289,plain,
spl698_54,
inference(avatar_split_clause,[],[f17280,f28286]) ).
fof(f28286,plain,
( spl698_54
<=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_54])]) ).
fof(f17280,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5091]) ).
fof(f5091,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(f28284,plain,
spl698_53,
inference(avatar_split_clause,[],[f17279,f28281]) ).
fof(f28281,plain,
( spl698_53
<=> class_Groups_Osemigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_53])]) ).
fof(f17279,plain,
class_Groups_Osemigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5105]) ).
fof(f5105,axiom,
class_Groups_Osemigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Osemigroup__add) ).
fof(f28279,plain,
spl698_52,
inference(avatar_split_clause,[],[f17278,f28276]) ).
fof(f28276,plain,
( spl698_52
<=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_52])]) ).
fof(f17278,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5107]) ).
fof(f5107,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(f28274,plain,
spl698_51,
inference(avatar_split_clause,[],[f17277,f28271]) ).
fof(f28271,plain,
( spl698_51
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_51])]) ).
fof(f17277,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5089]) ).
fof(f5089,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(f28269,plain,
spl698_50,
inference(avatar_split_clause,[],[f17276,f28266]) ).
fof(f28266,plain,
( spl698_50
<=> class_Groups_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_50])]) ).
fof(f17276,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f5125]) ).
fof(f5125,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Ozero) ).
fof(f28264,plain,
spl698_49,
inference(avatar_split_clause,[],[f17275,f28261]) ).
fof(f28261,plain,
( spl698_49
<=> class_Groups_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_49])]) ).
fof(f17275,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f5127]) ).
fof(f5127,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Groups_Oone) ).
fof(f28259,plain,
spl698_48,
inference(avatar_split_clause,[],[f17274,f28256]) ).
fof(f28256,plain,
( spl698_48
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_48])]) ).
fof(f17274,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f5084]) ).
fof(f5084,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(f28254,plain,
spl698_47,
inference(avatar_split_clause,[],[f17273,f28251]) ).
fof(f28251,plain,
( spl698_47
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_47])]) ).
fof(f17273,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5021]) ).
fof(f5021,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(f28249,plain,
spl698_46,
inference(avatar_split_clause,[],[f17272,f28246]) ).
fof(f28246,plain,
( spl698_46
<=> class_Groups_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_46])]) ).
fof(f17272,plain,
class_Groups_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f5079]) ).
fof(f5079,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Oone) ).
fof(f28244,plain,
spl698_45,
inference(avatar_split_clause,[],[f17271,f28241]) ).
fof(f28241,plain,
( spl698_45
<=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_45])]) ).
fof(f17271,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5026]) ).
fof(f5026,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(f28239,plain,
spl698_44,
inference(avatar_split_clause,[],[f17270,f28236]) ).
fof(f28236,plain,
( spl698_44
<=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_44])]) ).
fof(f17270,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5047]) ).
fof(f5047,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(f28234,plain,
spl698_43,
inference(avatar_split_clause,[],[f17269,f28231]) ).
fof(f28231,plain,
( spl698_43
<=> class_Groups_Osemigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_43])]) ).
fof(f17269,plain,
class_Groups_Osemigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5045]) ).
fof(f5045,axiom,
class_Groups_Osemigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Osemigroup__add) ).
fof(f28229,plain,
spl698_42,
inference(avatar_split_clause,[],[f17268,f28226]) ).
fof(f28226,plain,
( spl698_42
<=> class_Groups_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_42])]) ).
fof(f17268,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f5075]) ).
fof(f5075,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Ozero) ).
fof(f28224,plain,
spl698_41,
inference(avatar_split_clause,[],[f17267,f28221]) ).
fof(f28221,plain,
( spl698_41
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_41])]) ).
fof(f17267,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5013]) ).
fof(f5013,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(f28219,plain,
spl698_40,
inference(avatar_split_clause,[],[f17266,f28216]) ).
fof(f28216,plain,
( spl698_40
<=> class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_40])]) ).
fof(f17266,plain,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5199]) ).
fof(f5199,axiom,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring) ).
fof(f28214,plain,
spl698_39,
inference(avatar_split_clause,[],[f17265,f28211]) ).
fof(f28211,plain,
( spl698_39
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_39])]) ).
fof(f17265,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5184]) ).
fof(f5184,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) ).
fof(f28209,plain,
spl698_38,
inference(avatar_split_clause,[],[f17264,f28206]) ).
fof(f28206,plain,
( spl698_38
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_38])]) ).
fof(f17264,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5179]) ).
fof(f5179,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict) ).
fof(f28204,plain,
spl698_37,
inference(avatar_split_clause,[],[f17263,f28201]) ).
fof(f28201,plain,
( spl698_37
<=> class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_37])]) ).
fof(f17263,plain,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5197]) ).
fof(f5197,axiom,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add) ).
fof(f28199,plain,
spl698_36,
inference(avatar_split_clause,[],[f17262,f28196]) ).
fof(f28196,plain,
( spl698_36
<=> class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_36])]) ).
fof(f17262,plain,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5214]) ).
fof(f5214,axiom,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Ozero) ).
fof(f28194,plain,
spl698_35,
inference(avatar_split_clause,[],[f17261,f28191]) ).
fof(f28191,plain,
( spl698_35
<=> class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_35])]) ).
fof(f17261,plain,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5186]) ).
fof(f5186,axiom,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) ).
fof(f28189,plain,
spl698_34,
inference(avatar_split_clause,[],[f17260,f28186]) ).
fof(f28186,plain,
( spl698_34
<=> class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_34])]) ).
fof(f17260,plain,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5216]) ).
fof(f5216,axiom,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Code____Numeral__Ocode____numeral__Groups_Oone) ).
fof(f28184,plain,
spl698_33,
inference(avatar_split_clause,[],[f17259,f28181]) ).
fof(f28181,plain,
( spl698_33
<=> class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_33])]) ).
fof(f17259,plain,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5130]) ).
fof(f5130,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
fof(f28179,plain,
spl698_32,
inference(avatar_split_clause,[],[f17258,f28176]) ).
fof(f28176,plain,
( spl698_32
<=> class_Lattices_Oboolean__algebra(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_32])]) ).
fof(f17258,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(cnf_transformation,[],[f5136]) ).
fof(f5136,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(f28174,plain,
spl698_31,
inference(avatar_split_clause,[],[f17257,f28171]) ).
fof(f28171,plain,
( spl698_31
<=> class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_31])]) ).
fof(f17257,plain,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
inference(cnf_transformation,[],[f5131]) ).
fof(f5131,axiom,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
fof(f28169,plain,
spl698_30,
inference(avatar_split_clause,[],[f17256,f28166]) ).
fof(f28166,plain,
( spl698_30
<=> class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_30])]) ).
fof(f17256,plain,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
inference(cnf_transformation,[],[f5132]) ).
fof(f5132,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(f28164,plain,
spl698_29,
inference(avatar_split_clause,[],[f17255,f28161]) ).
fof(f28161,plain,
( spl698_29
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_29])]) ).
fof(f17255,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(cnf_transformation,[],[f5081]) ).
fof(f5081,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f28159,plain,
spl698_28,
inference(avatar_split_clause,[],[f17254,f28156]) ).
fof(f28156,plain,
( spl698_28
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_28])]) ).
fof(f17254,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(cnf_transformation,[],[f5010]) ).
fof(f5010,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f28154,plain,
spl698_27,
inference(avatar_split_clause,[],[f17253,f28151]) ).
fof(f28151,plain,
( spl698_27
<=> class_Lattices_Obounded__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_27])]) ).
fof(f17253,plain,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f4988]) ).
fof(f4988,axiom,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Lattices_Obounded__lattice) ).
fof(f28149,plain,
spl698_26,
inference(avatar_split_clause,[],[f17252,f28146]) ).
fof(f28146,plain,
( spl698_26
<=> class_Orderings_Otop(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_26])]) ).
fof(f17252,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(cnf_transformation,[],[f5141]) ).
fof(f5141,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_HOL__Obool__Orderings_Otop) ).
fof(f28144,plain,
spl698_25,
inference(avatar_split_clause,[],[f17251,f28141]) ).
fof(f17251,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5066]) ).
fof(f5066,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Int_Onumber__ring) ).
fof(f28139,plain,
spl698_24,
inference(avatar_split_clause,[],[f17250,f28136]) ).
fof(f28136,plain,
( spl698_24
<=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_24])]) ).
fof(f17250,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(cnf_transformation,[],[f5043]) ).
fof(f5043,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(f28134,plain,
spl698_23,
inference(avatar_split_clause,[],[f17249,f28131]) ).
fof(f28131,plain,
( spl698_23
<=> class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_23])]) ).
fof(f17249,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f5018]) ).
fof(f5018,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(f28129,plain,
spl698_22,
inference(avatar_split_clause,[],[f17248,f28126]) ).
fof(f28126,plain,
( spl698_22
<=> class_Rings_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_22])]) ).
fof(f17248,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5072]) ).
fof(f5072,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Oring__1) ).
fof(f28124,plain,
spl698_21,
inference(avatar_split_clause,[],[f17247,f28121]) ).
fof(f28121,plain,
( spl698_21
<=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_21])]) ).
fof(f17247,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5028]) ).
fof(f5028,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(f28119,plain,
spl698_20,
inference(avatar_split_clause,[],[f17246,f28116]) ).
fof(f28116,plain,
( spl698_20
<=> class_Groups_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_20])]) ).
fof(f17246,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5061]) ).
fof(f5061,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Ogroup__add) ).
fof(f28114,plain,
spl698_19,
inference(avatar_split_clause,[],[f17245,f28111]) ).
fof(f28111,plain,
( spl698_19
<=> class_Groups_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_19])]) ).
fof(f17245,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5049]) ).
fof(f5049,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Oab__group__add) ).
fof(f28109,plain,
spl698_18,
inference(avatar_split_clause,[],[f17244,f28106]) ).
fof(f28106,plain,
( spl698_18
<=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_18])]) ).
fof(f17244,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5020]) ).
fof(f5020,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(f28104,plain,
spl698_17,
inference(avatar_split_clause,[],[f17243,f28101]) ).
fof(f28101,plain,
( spl698_17
<=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_17])]) ).
fof(f17243,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5024]) ).
fof(f5024,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(f28099,plain,
spl698_16,
inference(avatar_split_clause,[],[f17242,f28096]) ).
fof(f28096,plain,
( spl698_16
<=> class_Rings_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_16])]) ).
fof(f17242,plain,
class_Rings_Oring(tc_Int_Oint),
inference(cnf_transformation,[],[f5076]) ).
fof(f5076,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Oring) ).
fof(f28094,plain,
spl698_15,
inference(avatar_split_clause,[],[f17241,f28091]) ).
fof(f28091,plain,
( spl698_15
<=> class_Rings_Oordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_15])]) ).
fof(f17241,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5051]) ).
fof(f5051,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Oordered__ring) ).
fof(f28089,plain,
spl698_14,
inference(avatar_split_clause,[],[f17240,f28086]) ).
fof(f28086,plain,
( spl698_14
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_14])]) ).
fof(f17240,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5065]) ).
fof(f5065,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Int_Oring__char__0) ).
fof(f28084,plain,
spl698_13,
inference(avatar_split_clause,[],[f17239,f28081]) ).
fof(f28081,plain,
( spl698_13
<=> class_Divides_Oring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_13])]) ).
fof(f17239,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f5062]) ).
fof(f5062,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Divides_Oring__div) ).
fof(f28079,plain,
spl698_12,
inference(avatar_split_clause,[],[f17238,f28076]) ).
fof(f28076,plain,
( spl698_12
<=> class_Orderings_Owellorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_12])]) ).
fof(f17238,plain,
class_Orderings_Owellorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5108]) ).
fof(f5108,axiom,
class_Orderings_Owellorder(tc_Nat_Onat),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Nat__Onat__Orderings_Owellorder) ).
fof(f28074,plain,
spl698_11,
inference(avatar_split_clause,[],[f17237,f28071]) ).
fof(f28071,plain,
( spl698_11
<=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_11])]) ).
fof(f17237,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5042]) ).
fof(f5042,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(f28069,plain,
spl698_10,
inference(avatar_split_clause,[],[f17236,f28066]) ).
fof(f28066,plain,
( spl698_10
<=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_10])]) ).
fof(f17236,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5022]) ).
fof(f5022,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(f28064,plain,
spl698_9,
inference(avatar_split_clause,[],[f17235,f28061]) ).
fof(f28061,plain,
( spl698_9
<=> class_Groups_Osgn__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_9])]) ).
fof(f17235,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(cnf_transformation,[],[f5070]) ).
fof(f5070,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Osgn__if) ).
fof(f28059,plain,
spl698_8,
inference(avatar_split_clause,[],[f17234,f28056]) ).
fof(f28056,plain,
( spl698_8
<=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_8])]) ).
fof(f17234,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5055]) ).
fof(f5055,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(f28054,plain,
spl698_7,
inference(avatar_split_clause,[],[f17233,f28051]) ).
fof(f28051,plain,
( spl698_7
<=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_7])]) ).
fof(f17233,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5025]) ).
fof(f5025,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(f28049,plain,
spl698_6,
inference(avatar_split_clause,[],[f17232,f28046]) ).
fof(f28046,plain,
( spl698_6
<=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_6])]) ).
fof(f17232,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5027]) ).
fof(f5027,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(f28044,plain,
spl698_5,
inference(avatar_split_clause,[],[f17231,f28041]) ).
fof(f28041,plain,
( spl698_5
<=> class_Groups_Oabs__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_5])]) ).
fof(f17231,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(cnf_transformation,[],[f5071]) ).
fof(f5071,axiom,
class_Groups_Oabs__if(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Groups_Oabs__if) ).
fof(f28039,plain,
spl698_4,
inference(avatar_split_clause,[],[f17230,f28036]) ).
fof(f28036,plain,
( spl698_4
<=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_4])]) ).
fof(f17230,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5014]) ).
fof(f5014,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(f28034,plain,
spl698_3,
inference(avatar_split_clause,[],[f17229,f28031]) ).
fof(f28031,plain,
( spl698_3
<=> class_Rings_Oordered__ring__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_3])]) ).
fof(f17229,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f5039]) ).
fof(f5039,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(f28029,plain,
spl698_2,
inference(avatar_split_clause,[],[f17228,f28026]) ).
fof(f28026,plain,
( spl698_2
<=> class_Rings_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_2])]) ).
fof(f17228,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(cnf_transformation,[],[f5077]) ).
fof(f5077,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',arity_Int__Oint__Rings_Oidom) ).
fof(f28024,plain,
~ spl698_1,
inference(avatar_split_clause,[],[f17227,f28021]) ).
fof(f28021,plain,
( spl698_1
<=> hBOOL(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl698_1])]) ).
fof(f17227,plain,
~ hBOOL(c_fFalse),
inference(cnf_transformation,[],[f5228]) ).
fof(f5228,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox/tmp/tmp.zg0HrBofC9/Vampire---4.8_22582',help_c__fFalse__1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.84/0.88 % Problem : SWW317+1 : TPTP v8.1.2. Released v5.2.0.
% 0.84/0.89 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.89/1.11 % Computer : n017.cluster.edu
% 0.89/1.11 % Model : x86_64 x86_64
% 0.89/1.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.89/1.11 % Memory : 8042.1875MB
% 0.89/1.11 % OS : Linux 3.10.0-693.el7.x86_64
% 0.89/1.11 % CPULimit : 300
% 0.89/1.11 % WCLimit : 300
% 0.89/1.11 % DateTime : Wed Aug 30 16:12:00 EDT 2023
% 0.89/1.11 % CPUTime :
% 0.96/1.17 % (22987)Running in auto input_syntax mode. Trying TPTP
% 1.33/1.55 % (22995)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 1.33/1.55 % (22993)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 1.33/1.55 % (22991)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 1.33/1.55 % (22994)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)
% 1.33/1.55 % (22997)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)
% 1.33/1.55 % (22999)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)
% 1.33/1.55 % (23001)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)
% 8.07/2.51 % (22997)First to succeed.
% 8.07/2.58 % (22997)Refutation found. Thanks to Tanya!
% 8.07/2.58 % SZS status Theorem for Vampire---4
% 8.07/2.58 % SZS output start Proof for Vampire---4
% See solution above
% 8.07/2.62 % (22997)------------------------------
% 8.07/2.62 % (22997)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 8.07/2.62 % (22997)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 8.07/2.62 % (22997)Termination reason: Refutation
% 8.07/2.62
% 8.07/2.62 % (22997)Memory used [KB]: 34285
% 8.07/2.62 % (22997)Time elapsed: 1.023 s
% 8.07/2.62 % (22997)------------------------------
% 8.07/2.62 % (22997)------------------------------
% 8.07/2.62 % (22987)Success in time 1.486 s
% 8.07/2.62 % Vampire---4.8 exiting
%------------------------------------------------------------------------------