TSTP Solution File: SWW394+1 by Vampire-SAT---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.9
% Problem : SWW394+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d SAT
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:51:36 EDT 2024
% Result : Theorem 9.36s 1.95s
% Output : Refutation 9.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2724
% Syntax : Number of formulae : 8050 (3124 unt; 0 def)
% Number of atoms : 18518 (4924 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 16020 (5552 ~;5306 |;2056 &)
% (1995 <=>;1111 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 1627 (1625 usr;1433 prp; 0-6 aty)
% Number of functors : 370 ( 370 usr; 33 con; 0-5 aty)
% Number of variables : 13316 (12726 !; 590 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f49588,plain,
$false,
inference(avatar_sat_refutation,[],[f29242,f29247,f29252,f29257,f29262,f29267,f29272,f29277,f29282,f29287,f29292,f29297,f29302,f29307,f29312,f29317,f29322,f29327,f29332,f29337,f29342,f29347,f29352,f29357,f29362,f29367,f29372,f29377,f29382,f29387,f29392,f29397,f29402,f29407,f29412,f29417,f29422,f29427,f29432,f29437,f29442,f29447,f29452,f29457,f29462,f29467,f29472,f29477,f29482,f29487,f29492,f29497,f29502,f29507,f29512,f29517,f29522,f29527,f29532,f29537,f29542,f29547,f29552,f29557,f29562,f29567,f29572,f29577,f29582,f29587,f29592,f29597,f29602,f29607,f29612,f29617,f29622,f29627,f29632,f29637,f29642,f29647,f29652,f29657,f29662,f29667,f29672,f29677,f29682,f29687,f29692,f29697,f29702,f29707,f29712,f29717,f29722,f29727,f29732,f29737,f29742,f29747,f29752,f29757,f29762,f29767,f29772,f29777,f29782,f29787,f29792,f29797,f29802,f29807,f29812,f29817,f29822,f29827,f29832,f29837,f29842,f29847,f29852,f29857,f29862,f29867,f29872,f29877,f29882,f29887,f29892,f29897,f29902,f29907,f29912,f29917,f29922,f29927,f29932,f29937,f29942,f29947,f29952,f29957,f29962,f29967,f29972,f29977,f29982,f29987,f29992,f29997,f30002,f30007,f30012,f30017,f30022,f30027,f30032,f30037,f30042,f30047,f30052,f30057,f30062,f30067,f30072,f30077,f30082,f30087,f30092,f30097,f30102,f30107,f30112,f30117,f30122,f30127,f30132,f30137,f30142,f30147,f30152,f30157,f30162,f30167,f30172,f30177,f30182,f30187,f30192,f30197,f30203,f30208,f30213,f30218,f30222,f30226,f30230,f30234,f30238,f30242,f30247,f30251,f30256,f30261,f30266,f30271,f30275,f30279,f30283,f30287,f30291,f30295,f30299,f30303,f30308,f30313,f30318,f30323,f30329,f30334,f30339,f30344,f30349,f30354,f30359,f30364,f30368,f30372,f30376,f30380,f30384,f30388,f30392,f30396,f30400,f30404,f30408,f30412,f30416,f30420,f30424,f30428,f30433,f30437,f30441,f30445,f30450,f30455,f30460,f30465,f30470,f30475,f30480,f30484,f30488,f30494,f30500,f30505,f30509,f30513,f30517,f30521,f30525,f30529,f30533,f30537,f30541,f30545,f30549,f30553,f30557,f30561,f30565,f30569,f30573,f30577,f30581,f30585,f30589,f30593,f30597,f30601,f30605,f30609,f30613,f30617,f30621,f30625,f30629,f30633,f30637,f30641,f30645,f30649,f30653,f30657,f30661,f30665,f30669,f30673,f30677,f30681,f30685,f30689,f30693,f30698,f30703,f30708,f30713,f30717,f30721,f30725,f30729,f30733,f30737,f30742,f30746,f30750,f30760,f30767,f30778,f30785,f30791,f30797,f30802,f30807,f30812,f30817,f30822,f30830,f30835,f30840,f30845,f30851,f30856,f30861,f30865,f30869,f30874,f30878,f30882,f30886,f30890,f30894,f30898,f30902,f30906,f30910,f30914,f30918,f30922,f30926,f30930,f30934,f30938,f30942,f30946,f30950,f30954,f30958,f30962,f30966,f30970,f30974,f30978,f30982,f30986,f30990,f30994,f30998,f31003,f31007,f31011,f31015,f31019,f31023,f31027,f31031,f31035,f31039,f31043,f31048,f31053,f31058,f31063,f31068,f31073,f31078,f31082,f31086,f31091,f31098,f31111,f31124,f31129,f31134,f31138,f31142,f31146,f31150,f31154,f31158,f31162,f31166,f31170,f31174,f31178,f31182,f31186,f31190,f31194,f31198,f31202,f31206,f31211,f31215,f31219,f31223,f31227,f31231,f31235,f31239,f31243,f31247,f31252,f31256,f31260,f31264,f31268,f31272,f31276,f31280,f31284,f31288,f31292,f31296,f31300,f31304,f31308,f31312,f31316,f31320,f31324,f31328,f31333,f31337,f31341,f31345,f31349,f31353,f31357,f31361,f31365,f31369,f31373,f31378,f31382,f31386,f31390,f31394,f31398,f31402,f31407,f31411,f31415,f31419,f31424,f31428,f31433,f31438,f31443,f31447,f31451,f31455,f31459,f31463,f31467,f31472,f31476,f31480,f31484,f31488,f31497,f31506,f31524,f31536,f31548,f31554,f31558,f31562,f31567,f31571,f31575,f31579,f31583,f31587,f31591,f31596,f31600,f31604,f31608,f31612,f31616,f31620,f31624,f31628,f31632,f31637,f31641,f31645,f31649,f31653,f31657,f31661,f31665,f31669,f31673,f31677,f31681,f31685,f31689,f31693,f31697,f31701,f31705,f31709,f31713,f31717,f31722,f31726,f31730,f31734,f31738,f31742,f31746,f31750,f31754,f31758,f31762,f31766,f31770,f31774,f31778,f31782,f31786,f31790,f31794,f31798,f31802,f31806,f31811,f31815,f31819,f31823,f31827,f31831,f31835,f31839,f31843,f31850,f31854,f31859,f31864,f31868,f31872,f31876,f31880,f31884,f31888,f31893,f31897,f31901,f31905,f31909,f31913,f31918,f31922,f31926,f31930,f31934,f31938,f31942,f31946,f31950,f31954,f31958,f31962,f31966,f31971,f31975,f31979,f31983,f31987,f31991,f31999,f32020,f32036,f32062,f32190,f32220,f32248,f32253,f32258,f32263,f32267,f32276,f32280,f32284,f32288,f32292,f32296,f32300,f32304,f32308,f32312,f32316,f32320,f32324,f32328,f32332,f32336,f32340,f32344,f32348,f32352,f32356,f32360,f32364,f32368,f32372,f32376,f32380,f32384,f32388,f32392,f32396,f32400,f32404,f32408,f32412,f32416,f32420,f32424,f32428,f32432,f32436,f32445,f32449,f32453,f32457,f32461,f32465,f32469,f32473,f32477,f32481,f32488,f32492,f32496,f32500,f32504,f32508,f32512,f32516,f32520,f32524,f32531,f32535,f32539,f32543,f32547,f32551,f32555,f32559,f32563,f32567,f32571,f32575,f32579,f32583,f32587,f32591,f32595,f32599,f32603,f32607,f32611,f32615,f32619,f32623,f32627,f32631,f32635,f32640,f32644,f32648,f32652,f32656,f32660,f32665,f32671,f32676,f32682,f32688,f32695,f32700,f32704,f32709,f32713,f32717,f32721,f32725,f32729,f32733,f32737,f32741,f32745,f32749,f32753,f32757,f32761,f32765,f32769,f32773,f32777,f32781,f32785,f32789,f32793,f32797,f32801,f32805,f32809,f32813,f32817,f32821,f32825,f32829,f32833,f32837,f32841,f32845,f32851,f32921,f33513,f33648,f33709,f33759,f33784,f33803,f33807,f33811,f33815,f33819,f33823,f33827,f33831,f33835,f33839,f33843,f33847,f33851,f33855,f33859,f33863,f33867,f33871,f33877,f33881,f33885,f33889,f33893,f33897,f33901,f33905,f33909,f33913,f33918,f33922,f33926,f33930,f33934,f33938,f33942,f33946,f33950,f33954,f33958,f33962,f33966,f33970,f33974,f33978,f33982,f33986,f33990,f33994,f33998,f34002,f34006,f34010,f34014,f34018,f34022,f34026,f34030,f34034,f34038,f34042,f34046,f34050,f34054,f34058,f34062,f34066,f34070,f34074,f34078,f34082,f34086,f34090,f34094,f34098,f34102,f34106,f34110,f34114,f34118,f34122,f34126,f34130,f34134,f34138,f34142,f34146,f34150,f34154,f34158,f34162,f34166,f34170,f34174,f34178,f34182,f34186,f34190,f34194,f34198,f34202,f34206,f34210,f34214,f34218,f34222,f34226,f34230,f34234,f34238,f34242,f34246,f34250,f34254,f34258,f34262,f34266,f34270,f34274,f34278,f34282,f34287,f34291,f34295,f34299,f34303,f34307,f34311,f34315,f34319,f34323,f34327,f34331,f34335,f34339,f34343,f34348,f34352,f34356,f34360,f34364,f34369,f34375,f34379,f34388,f34394,f34398,f34402,f34406,f34410,f34414,f34418,f34423,f34427,f34436,f34440,f34444,f34448,f34453,f34458,f34462,f34466,f34470,f34474,f34478,f34482,f34486,f34490,f34494,f34498,f34502,f34506,f34510,f34514,f34518,f34522,f34526,f34530,f34534,f34538,f34542,f34546,f34550,f34554,f34558,f34562,f34566,f34570,f34574,f34579,f34583,f34587,f34591,f34595,f34599,f34603,f34607,f34611,f34615,f34619,f34623,f34657,f34724,f35108,f35147,f35365,f35966,f36146,f36733,f37295,f37556,f37764,f37951,f37955,f37959,f37963,f37968,f37972,f37976,f37980,f37984,f37988,f37992,f37996,f38000,f38004,f38008,f38013,f38017,f38021,f38025,f38029,f38034,f38039,f38043,f38047,f38051,f38055,f38059,f38063,f38067,f38071,f38075,f38079,f38083,f38087,f38091,f38095,f38099,f38103,f38107,f38111,f38115,f38119,f38123,f38127,f38131,f38135,f38139,f38143,f38147,f38151,f38155,f38159,f38163,f38167,f38171,f38175,f38179,f38183,f38187,f38191,f38195,f38199,f38203,f38207,f38211,f38215,f38219,f38223,f38227,f38231,f38235,f38239,f38243,f38247,f38251,f38255,f38259,f38263,f38267,f38271,f38275,f38279,f38283,f38287,f38291,f38295,f38299,f38303,f38307,f38311,f38315,f38319,f38323,f38327,f38331,f38335,f38339,f38344,f38348,f38352,f38356,f38360,f38364,f38369,f38374,f38379,f38383,f38387,f38391,f38395,f38399,f38403,f38408,f38412,f38416,f38420,f38424,f38428,f38432,f38436,f38440,f38444,f38448,f38452,f38456,f38460,f38464,f38468,f38472,f38476,f38481,f39590,f39624,f40536,f40578,f40582,f40586,f40590,f40594,f40598,f40602,f40606,f40610,f40614,f40618,f40622,f40626,f40630,f40634,f40639,f40643,f40647,f40651,f40655,f40659,f40663,f40667,f40671,f40675,f40679,f40683,f40687,f40691,f40695,f40699,f40703,f40707,f40711,f40715,f40728,f40732,f40736,f40740,f40744,f40748,f40752,f40756,f40760,f40764,f40768,f40772,f40776,f40780,f40784,f40788,f40792,f40796,f40800,f40804,f40813,f40817,f40821,f40825,f40829,f40833,f40837,f40841,f40845,f40849,f40853,f40857,f40861,f40865,f40869,f40873,f40877,f40881,f40885,f40889,f40893,f40897,f40901,f40905,f40909,f40913,f40917,f40921,f40925,f40929,f40933,f40938,f40942,f40946,f40950,f40954,f40958,f40962,f40966,f40970,f40974,f40978,f40982,f40986,f40990,f40994,f40998,f41002,f41006,f41010,f41014,f41018,f41022,f41026,f41030,f41034,f41038,f41042,f41046,f41050,f41054,f41059,f41065,f41083,f41088,f41092,f41096,f41100,f41104,f41108,f41112,f41116,f41120,f41124,f41128,f41132,f41136,f41140,f41144,f41148,f41152,f41156,f41160,f41164,f41168,f41759,f41914,f43764,f44533,f44713,f44805,f44973,f45191,f45195,f45199,f45203,f45207,f45211,f45215,f45219,f45223,f45227,f45231,f45235,f45239,f45243,f45247,f45251,f45255,f45259,f45263,f45267,f45271,f45275,f45279,f45283,f45287,f45291,f45295,f45299,f45303,f45307,f45311,f45315,f45319,f45323,f45327,f45331,f45335,f45339,f45343,f45347,f45351,f45355,f45359,f45363,f45367,f45372,f45376,f45380,f45384,f45388,f45392,f45396,f45400,f45404,f45408,f45412,f45417,f45421,f45425,f45429,f45433,f45437,f45441,f45445,f45449,f45453,f45457,f45487,f45491,f45495,f45499,f45503,f45507,f45511,f45515,f45519,f45523,f45528,f45532,f45536,f45540,f45544,f45548,f45552,f45556,f45560,f45564,f45568,f45572,f45576,f45580,f45584,f45588,f45592,f45596,f45600,f45604,f45608,f45612,f45616,f45620,f45624,f45628,f45632,f45636,f45640,f45644,f45648,f45652,f45656,f45660,f45664,f45668,f45672,f45676,f45680,f45684,f45688,f45692,f45696,f45700,f45704,f45708,f45712,f45716,f45720,f45724,f45728,f45732,f45737,f45743,f45750,f45754,f45758,f45762,f45766,f45770,f45774,f45778,f45783,f45788,f45794,f45799,f45804,f45823,f45827,f45831,f45835,f45839,f45843,f45847,f45851,f45855,f45859,f45863,f45867,f45871,f45875,f45879,f45883,f45887,f45891,f45895,f45899,f45903,f45907,f45911,f45915,f45919,f45923,f45930,f45934,f45939,f45944,f45948,f45952,f45956,f45960,f45964,f46013,f46266,f47686,f48177,f48478,f49320,f49587]) ).
fof(f49587,plain,
( spl647_259
| ~ spl647_1432 ),
inference(avatar_contradiction_clause,[],[f49584]) ).
fof(f49584,plain,
( $false
| spl647_259
| ~ spl647_1432 ),
inference(resolution,[],[f49319,f30499]) ).
fof(f30499,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(c_fequal,v_t),hAPP(c_fequal,v_t))
| spl647_259 ),
inference(avatar_component_clause,[],[f30497]) ).
fof(f30497,plain,
( spl647_259
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(c_fequal,v_t),hAPP(c_fequal,v_t)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_259])]) ).
fof(f49319,plain,
( ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X1)
| ~ spl647_1432 ),
inference(avatar_component_clause,[],[f49318]) ).
fof(f49318,plain,
( spl647_1432
<=> ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1432])]) ).
fof(f49320,plain,
( spl647_1432
| ~ spl647_522
| ~ spl647_1350 ),
inference(avatar_split_clause,[],[f49223,f45626,f31683,f49318]) ).
fof(f31683,plain,
( spl647_522
<=> ! [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,[spl647_522])]) ).
fof(f45626,plain,
( spl647_1350
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X2,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1350])]) ).
fof(f49223,plain,
( ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X0,X1,X1)
| ~ spl647_522
| ~ spl647_1350 ),
inference(resolution,[],[f45627,f31684]) ).
fof(f31684,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X0))
| ~ spl647_522 ),
inference(avatar_component_clause,[],[f31683]) ).
fof(f45627,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)),X1),X0))
| c_Hoare__Mirabelle_Ohoare__derivs(X2,X0,X1) )
| ~ spl647_1350 ),
inference(avatar_component_clause,[],[f45626]) ).
fof(f48478,plain,
( spl647_1431
| ~ spl647_540
| ~ spl647_1250 ),
inference(avatar_split_clause,[],[f48326,f45197,f31756,f48476]) ).
fof(f48476,plain,
( spl647_1431
<=> ! [X0,X1] : sP8(c_Quotient_ORespects(X0,c_fequal),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1431])]) ).
fof(f31756,plain,
( spl647_540
<=> ! [X0,X1] :
( sP8(X1,X0)
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_540])]) ).
fof(f45197,plain,
( spl647_1250
<=> ! [X0,X1] : hBOOL(hAPP(c_Quotient_ORespects(X0,c_fequal),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1250])]) ).
fof(f48326,plain,
( ! [X0,X1] : sP8(c_Quotient_ORespects(X0,c_fequal),X1)
| ~ spl647_540
| ~ spl647_1250 ),
inference(resolution,[],[f45198,f31757]) ).
fof(f31757,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| sP8(X1,X0) )
| ~ spl647_540 ),
inference(avatar_component_clause,[],[f31756]) ).
fof(f45198,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Quotient_ORespects(X0,c_fequal),X1))
| ~ spl647_1250 ),
inference(avatar_component_clause,[],[f45197]) ).
fof(f48177,plain,
( spl647_1430
| ~ spl647_348
| ~ spl647_1232 ),
inference(avatar_split_clause,[],[f44976,f41138,f30900,f48175]) ).
fof(f48175,plain,
( spl647_1430
<=> ! [X0] :
( sP12(c_Int_OPls,X0)
| ~ sP11(X0,c_Int_OPls) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1430])]) ).
fof(f30900,plain,
( spl647_348
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_348])]) ).
fof(f41138,plain,
( spl647_1232
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Int_OPls))
| sP12(X0,X1)
| ~ sP11(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1232])]) ).
fof(f44976,plain,
( ! [X0] :
( sP12(c_Int_OPls,X0)
| ~ sP11(X0,c_Int_OPls) )
| ~ spl647_348
| ~ spl647_1232 ),
inference(resolution,[],[f41139,f30901]) ).
fof(f30901,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0))
| ~ spl647_348 ),
inference(avatar_component_clause,[],[f30900]) ).
fof(f41139,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Int_OPls))
| sP12(X0,X1)
| ~ sP11(X1,X0) )
| ~ spl647_1232 ),
inference(avatar_component_clause,[],[f41138]) ).
fof(f47686,plain,
( spl647_1429
| ~ spl647_338
| ~ spl647_1232 ),
inference(avatar_split_clause,[],[f44974,f41138,f30858,f47684]) ).
fof(f47684,plain,
( spl647_1429
<=> ! [X0] :
( sP12(c_Int_OMin,X0)
| ~ sP11(X0,c_Int_OMin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1429])]) ).
fof(f30858,plain,
( spl647_338
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_338])]) ).
fof(f44974,plain,
( ! [X0] :
( sP12(c_Int_OMin,X0)
| ~ sP11(X0,c_Int_OMin) )
| ~ spl647_338
| ~ spl647_1232 ),
inference(resolution,[],[f41139,f30860]) ).
fof(f30860,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls))
| ~ spl647_338 ),
inference(avatar_component_clause,[],[f30858]) ).
fof(f46266,plain,
( spl647_1428
| ~ spl647_309
| ~ spl647_385
| ~ spl647_573
| ~ spl647_1221 ),
inference(avatar_split_clause,[],[f44800,f41094,f31895,f31050,f30700,f46263]) ).
fof(f46263,plain,
( spl647_1428
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1428])]) ).
fof(f30700,plain,
( spl647_309
<=> 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,[spl647_309])]) ).
fof(f31050,plain,
( spl647_385
<=> 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,[spl647_385])]) ).
fof(f31895,plain,
( spl647_573
<=> ! [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,[spl647_573])]) ).
fof(f41094,plain,
( spl647_1221
<=> ! [X0] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X0)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1221])]) ).
fof(f44800,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl647_309
| ~ spl647_385
| ~ spl647_573
| ~ spl647_1221 ),
inference(forward_demodulation,[],[f44799,f31896]) ).
fof(f31896,plain,
( ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0
| ~ spl647_573 ),
inference(avatar_component_clause,[],[f31895]) ).
fof(f44799,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Nat_Onat_Onat__size(c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl647_309
| ~ spl647_385
| ~ spl647_1221 ),
inference(forward_demodulation,[],[f44766,f31052]) ).
fof(f31052,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))
| ~ spl647_385 ),
inference(avatar_component_clause,[],[f31050]) ).
fof(f44766,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)))
| ~ spl647_309
| ~ spl647_1221 ),
inference(superposition,[],[f41095,f30702]) ).
fof(f30702,plain,
( c_HOL_Obool_Obool__size(c_fTrue) = c_Nat_Onat_Onat__size(c_HOL_Obool_Obool__size(c_fTrue))
| ~ spl647_309 ),
inference(avatar_component_clause,[],[f30700]) ).
fof(f41095,plain,
( ! [X0] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X0)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl647_1221 ),
inference(avatar_component_clause,[],[f41094]) ).
fof(f46013,plain,
spl647_1427,
inference(avatar_split_clause,[],[f28526,f46011]) ).
fof(f46011,plain,
( spl647_1427
<=> ! [X2,X0] : c_List_Oinsert(X2,X0,c_List_Olist_ONil(X2)) = hAPP(c_List_Orev(X2),c_List_Oinsert(X2,X0,c_List_Olist_ONil(X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1427])]) ).
fof(f28526,plain,
! [X2,X0] : c_List_Oinsert(X2,X0,c_List_Olist_ONil(X2)) = hAPP(c_List_Orev(X2),c_List_Oinsert(X2,X0,c_List_Olist_ONil(X2))),
inference(forward_demodulation,[],[f25607,f17921]) ).
fof(f17921,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,[],[f5813]) ).
fof(f5813,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,[],[f4521]) ).
fof(f4521,axiom,
! [X19,X20] : hAPP(hAPP(c_List_Olist_OCons(X20),X19),c_List_Olist_ONil(X20)) = c_List_Oinsert(X20,X19,c_List_Olist_ONil(X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f25607,plain,
! [X2,X0] : hAPP(hAPP(c_List_Olist_OCons(X2),X0),c_List_Olist_ONil(X2)) = hAPP(c_List_Orev(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X0),c_List_Olist_ONil(X2))),
inference(equality_resolution,[],[f21415]) ).
fof(f21415,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_List_Olist_OCons(X2),X0),c_List_Olist_ONil(X2)) = hAPP(c_List_Orev(X2),X1)
| hAPP(hAPP(c_List_Olist_OCons(X2),X0),c_List_Olist_ONil(X2)) != X1 ),
inference(cnf_transformation,[],[f15954]) ).
fof(f15954,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_List_Olist_OCons(X2),X0),c_List_Olist_ONil(X2)) = hAPP(c_List_Orev(X2),X1)
| hAPP(hAPP(c_List_Olist_OCons(X2),X0),c_List_Olist_ONil(X2)) != X1 )
& ( hAPP(hAPP(c_List_Olist_OCons(X2),X0),c_List_Olist_ONil(X2)) = X1
| hAPP(hAPP(c_List_Olist_OCons(X2),X0),c_List_Olist_ONil(X2)) != hAPP(c_List_Orev(X2),X1) ) ),
inference(nnf_transformation,[],[f8211]) ).
fof(f8211,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_List_Olist_OCons(X2),X0),c_List_Olist_ONil(X2)) = hAPP(c_List_Orev(X2),X1)
<=> hAPP(hAPP(c_List_Olist_OCons(X2),X0),c_List_Olist_ONil(X2)) = X1 ),
inference(rectify,[],[f4439]) ).
fof(f4439,axiom,
! [X13,X203,X4] :
( hAPP(hAPP(c_List_Olist_OCons(X4),X13),c_List_Olist_ONil(X4)) = hAPP(c_List_Orev(X4),X203)
<=> hAPP(hAPP(c_List_Olist_OCons(X4),X13),c_List_Olist_ONil(X4)) = X203 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45964,plain,
spl647_1426,
inference(avatar_split_clause,[],[f28494,f45962]) ).
fof(f45962,plain,
( spl647_1426
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK383(X0,X1,X2)))
| sP41(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1426])]) ).
fof(f28494,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK383(X0,X1,X2)))
| sP41(X0,X1,X2) ),
inference(forward_demodulation,[],[f21313,f17135]) ).
fof(f17135,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
inference(cnf_transformation,[],[f1272]) ).
fof(f1272,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f21313,plain,
! [X2,X0,X1] :
( sP41(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK383(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15870]) ).
fof(f15870,plain,
! [X0,X1,X2] :
( ( sP41(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK382(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK382(X0,X1,X2))),sK383(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK383(X0,X1,X2)),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK383(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) )
& ( ! [X5] :
( hBOOL(hAPP(X0,X5))
| ! [X6] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ sP41(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK382,sK383])],[f15867,f15869,f15868]) ).
fof(f15868,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& ? [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) )
=> ( ~ hBOOL(hAPP(X0,sK382(X0,X1,X2)))
& ? [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK382(X0,X1,X2))),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f15869,plain,
! [X0,X1,X2] :
( ? [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK382(X0,X1,X2))),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) )
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK382(X0,X1,X2))),sK383(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK383(X0,X1,X2)),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK383(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15867,plain,
! [X0,X1,X2] :
( ( sP41(X0,X1,X2)
| ( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& ? [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) )
& ( ! [X5] :
( hBOOL(hAPP(X0,X5))
| ! [X6] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ sP41(X0,X1,X2) ) ),
inference(rectify,[],[f15866]) ).
fof(f15866,plain,
! [X2,X1,X0] :
( ( sP41(X2,X1,X0)
| ( ? [X5] :
( ~ hBOOL(hAPP(X2,X5))
& ? [X6] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
& ( ! [X5] :
( hBOOL(hAPP(X2,X5))
| ! [X6] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ sP41(X2,X1,X0) ) ),
inference(flattening,[],[f15865]) ).
fof(f15865,plain,
! [X2,X1,X0] :
( ( sP41(X2,X1,X0)
| ( ? [X5] :
( ~ hBOOL(hAPP(X2,X5))
& ? [X6] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
& ( ! [X5] :
( hBOOL(hAPP(X2,X5))
| ! [X6] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ sP41(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14545]) ).
fof(f14545,plain,
! [X2,X1,X0] :
( sP41(X2,X1,X0)
<=> ( ! [X5] :
( hBOOL(hAPP(X2,X5))
| ! [X6] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP41])]) ).
fof(f45960,plain,
spl647_1425,
inference(avatar_split_clause,[],[f28489,f45958]) ).
fof(f45958,plain,
( spl647_1425
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK381(X0,X1,X2)),c_Int_OPls))
| sP42(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1425])]) ).
fof(f28489,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK381(X0,X1,X2)),c_Int_OPls))
| sP42(X0,X1,X2) ),
inference(forward_demodulation,[],[f21308,f17135]) ).
fof(f21308,plain,
! [X2,X0,X1] :
( sP42(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK381(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f15864]) ).
fof(f15864,plain,
! [X0,X1,X2] :
( ( sP42(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK380(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK380(X0,X1,X2))),sK381(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK381(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK381(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
& ( ! [X5] :
( hBOOL(hAPP(X0,X5))
| ! [X6] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X6)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP42(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK380,sK381])],[f15861,f15863,f15862]) ).
fof(f15862,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& ? [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) ) )
=> ( ~ hBOOL(hAPP(X0,sK380(X0,X1,X2)))
& ? [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK380(X0,X1,X2))),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f15863,plain,
! [X0,X1,X2] :
( ? [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK380(X0,X1,X2))),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) )
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK380(X0,X1,X2))),sK381(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK381(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK381(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15861,plain,
! [X0,X1,X2] :
( ( sP42(X0,X1,X2)
| ( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& ? [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
& ( ! [X5] :
( hBOOL(hAPP(X0,X5))
| ! [X6] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X6)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP42(X0,X1,X2) ) ),
inference(rectify,[],[f15860]) ).
fof(f15860,plain,
! [X2,X1,X0] :
( ( sP42(X2,X1,X0)
| ( ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& ? [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
& ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| ! [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP42(X2,X1,X0) ) ),
inference(flattening,[],[f15859]) ).
fof(f15859,plain,
! [X2,X1,X0] :
( ( sP42(X2,X1,X0)
| ( ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& ? [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) ) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
& ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| ! [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP42(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14546]) ).
fof(f14546,plain,
! [X2,X1,X0] :
( sP42(X2,X1,X0)
<=> ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| ! [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP42])]) ).
fof(f45956,plain,
spl647_1424,
inference(avatar_split_clause,[],[f28468,f45954]) ).
fof(f45954,plain,
( spl647_1424
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK374(X0,X1,X2)))
| sP36(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1424])]) ).
fof(f28468,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK374(X0,X1,X2)))
| sP36(X0,X1,X2) ),
inference(forward_demodulation,[],[f21235,f17135]) ).
fof(f21235,plain,
! [X2,X0,X1] :
( sP36(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK374(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15818]) ).
fof(f15818,plain,
! [X0,X1,X2] :
( ( sP36(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK374(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK373(X0,X1,X2))),sK374(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK374(X0,X1,X2)),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK374(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ sP36(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK373,sK374])],[f15816,f15817]) ).
fof(f15817,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) )
=> ( ~ hBOOL(hAPP(X0,sK374(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK373(X0,X1,X2))),sK374(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK374(X0,X1,X2)),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK374(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15816,plain,
! [X0,X1,X2] :
( ( sP36(X0,X1,X2)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ sP36(X0,X1,X2) ) ),
inference(rectify,[],[f15815]) ).
fof(f15815,plain,
! [X2,X1,X0] :
( ( sP36(X2,X1,X0)
| ( ? [X5,X6] :
( ~ hBOOL(hAPP(X2,X6))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X2,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ sP36(X2,X1,X0) ) ),
inference(flattening,[],[f15814]) ).
fof(f15814,plain,
! [X2,X1,X0] :
( ( sP36(X2,X1,X0)
| ( ? [X5,X6] :
( ~ hBOOL(hAPP(X2,X6))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X2,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ sP36(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14537]) ).
fof(f14537,plain,
! [X2,X1,X0] :
( sP36(X2,X1,X0)
<=> ( ! [X5,X6] :
( hBOOL(hAPP(X2,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP36])]) ).
fof(f45952,plain,
spl647_1423,
inference(avatar_split_clause,[],[f28463,f45950]) ).
fof(f45950,plain,
( spl647_1423
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK372(X0,X1,X2)),c_Int_OPls))
| sP37(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1423])]) ).
fof(f28463,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK372(X0,X1,X2)),c_Int_OPls))
| sP37(X0,X1,X2) ),
inference(forward_demodulation,[],[f21230,f17135]) ).
fof(f21230,plain,
! [X2,X0,X1] :
( sP37(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK372(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f15813]) ).
fof(f15813,plain,
! [X0,X1,X2] :
( ( sP37(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK372(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK371(X0,X1,X2))),sK372(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK372(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK372(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X6)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP37(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK371,sK372])],[f15811,f15812]) ).
fof(f15812,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) )
=> ( ~ hBOOL(hAPP(X0,sK372(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK371(X0,X1,X2))),sK372(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK372(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK372(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15811,plain,
! [X0,X1,X2] :
( ( sP37(X0,X1,X2)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X6)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP37(X0,X1,X2) ) ),
inference(rectify,[],[f15810]) ).
fof(f15810,plain,
! [X2,X1,X0] :
( ( sP37(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP37(X2,X1,X0) ) ),
inference(flattening,[],[f15809]) ).
fof(f15809,plain,
! [X2,X1,X0] :
( ( sP37(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP37(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14538]) ).
fof(f14538,plain,
! [X2,X1,X0] :
( sP37(X2,X1,X0)
<=> ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP37])]) ).
fof(f45948,plain,
spl647_1422,
inference(avatar_split_clause,[],[f28298,f45946]) ).
fof(f45946,plain,
( spl647_1422
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK289(X0,X1,X2)))
| sP28(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1422])]) ).
fof(f28298,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK289(X0,X1,X2)))
| sP28(X0,X1,X2) ),
inference(forward_demodulation,[],[f20826,f17135]) ).
fof(f20826,plain,
! [X2,X0,X1] :
( sP28(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK289(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15575]) ).
fof(f15575,plain,
! [X0,X1,X2] :
( ( sP28(X0,X1,X2)
| ( ~ hBOOL(hAPP(hAPP(X0,sK288(X0,X1,X2)),sK289(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK288(X0,X1,X2))),sK289(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK289(X0,X1,X2)),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK289(X0,X1,X2))) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(hAPP(X0,X5),X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) )
| ~ sP28(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK288,sK289])],[f15573,f15574]) ).
fof(f15574,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(hAPP(X0,X3),X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) )
=> ( ~ hBOOL(hAPP(hAPP(X0,sK288(X0,X1,X2)),sK289(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK288(X0,X1,X2))),sK289(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK289(X0,X1,X2)),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK289(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15573,plain,
! [X0,X1,X2] :
( ( sP28(X0,X1,X2)
| ? [X3,X4] :
( ~ hBOOL(hAPP(hAPP(X0,X3),X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(hAPP(X0,X5),X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) )
| ~ sP28(X0,X1,X2) ) ),
inference(rectify,[],[f15572]) ).
fof(f15572,plain,
! [X1,X0,X2] :
( ( sP28(X1,X0,X2)
| ? [X3,X4] :
( ~ hBOOL(hAPP(hAPP(X1,X3),X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X0
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) )
| ~ sP28(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f14523]) ).
fof(f14523,plain,
! [X1,X0,X2] :
( sP28(X1,X0,X2)
<=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP28])]) ).
fof(f45944,plain,
spl647_1421,
inference(avatar_split_clause,[],[f28235,f45942]) ).
fof(f45942,plain,
( spl647_1421
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK269(X0,X1,X2)),c_Int_OPls))
| sP26(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1421])]) ).
fof(f28235,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK269(X0,X1,X2)),c_Int_OPls))
| sP26(X0,X1,X2) ),
inference(forward_demodulation,[],[f20785,f17135]) ).
fof(f20785,plain,
! [X2,X0,X1] :
( sP26(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK269(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f15539]) ).
fof(f15539,plain,
! [X0,X1,X2] :
( ( sP26(X0,X1,X2)
| ( ~ hBOOL(hAPP(hAPP(X0,sK268(X0,X1,X2)),sK269(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK268(X0,X1,X2))),sK269(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK269(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK269(X0,X1,X2))) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(hAPP(X0,X5),X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X6)) )
| ~ sP26(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK268,sK269])],[f15537,f15538]) ).
fof(f15538,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(hAPP(X0,X3),X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) )
=> ( ~ hBOOL(hAPP(hAPP(X0,sK268(X0,X1,X2)),sK269(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK268(X0,X1,X2))),sK269(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK269(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK269(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15537,plain,
! [X0,X1,X2] :
( ( sP26(X0,X1,X2)
| ? [X3,X4] :
( ~ hBOOL(hAPP(hAPP(X0,X3),X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(hAPP(X0,X5),X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X6),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X6)) )
| ~ sP26(X0,X1,X2) ) ),
inference(rectify,[],[f15536]) ).
fof(f15536,plain,
! [X1,X0,X2] :
( ( sP26(X1,X0,X2)
| ? [X3,X4] :
( ~ hBOOL(hAPP(hAPP(X1,X3),X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X0
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) )
| ~ sP26(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f14520]) ).
fof(f14520,plain,
! [X1,X0,X2] :
( sP26(X1,X0,X2)
<=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP26])]) ).
fof(f45939,plain,
( spl647_1420
| ~ spl647_1419 ),
inference(avatar_split_clause,[],[f45935,f45932,f45937]) ).
fof(f45937,plain,
( spl647_1420
<=> ! [X2,X0,X1] : c_List_Olast(X2,hAPP(c_List_Orotate1(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X0),X1))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1420])]) ).
fof(f45932,plain,
( spl647_1419
<=> ! [X2,X0,X1] : c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X1),c_List_Oinsert(X2,X0,c_List_Olist_ONil(X2)))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1419])]) ).
fof(f45935,plain,
( ! [X2,X0,X1] : c_List_Olast(X2,hAPP(c_List_Orotate1(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X0),X1))) = X0
| ~ spl647_1419 ),
inference(forward_demodulation,[],[f45933,f28660]) ).
fof(f28660,plain,
! [X2,X0,X1] : hAPP(c_List_Orotate1(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = hAPP(hAPP(c_List_Oappend(X2),X0),c_List_Oinsert(X2,X1,c_List_Olist_ONil(X2))),
inference(forward_demodulation,[],[f21730,f17921]) ).
fof(f21730,plain,
! [X2,X0,X1] : 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))),
inference(cnf_transformation,[],[f8446]) ).
fof(f8446,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,[],[f4018]) ).
fof(f4018,axiom,
! [X201,X19,X4,X20] :
( hAPP(c_List_Orotate1(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X19),X201)) = hAPP(hAPP(c_List_Oappend(X4),X201),hAPP(hAPP(c_List_Olist_OCons(X4),X19),c_List_Olist_ONil(X4)))
& c_List_Olist_ONil(X20) = hAPP(c_List_Orotate1(X20),c_List_Olist_ONil(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45933,plain,
( ! [X2,X0,X1] : c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X1),c_List_Oinsert(X2,X0,c_List_Olist_ONil(X2)))) = X0
| ~ spl647_1419 ),
inference(avatar_component_clause,[],[f45932]) ).
fof(f45934,plain,
spl647_1419,
inference(avatar_split_clause,[],[f27812,f45932]) ).
fof(f27812,plain,
! [X2,X0,X1] : c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X1),c_List_Oinsert(X2,X0,c_List_Olist_ONil(X2)))) = X0,
inference(forward_demodulation,[],[f19637,f17921]) ).
fof(f19637,plain,
! [X2,X0,X1] : c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X0),c_List_Olist_ONil(X2)))) = X0,
inference(cnf_transformation,[],[f6991]) ).
fof(f6991,plain,
! [X0,X1,X2] : c_List_Olast(X2,hAPP(hAPP(c_List_Oappend(X2),X1),hAPP(hAPP(c_List_Olist_OCons(X2),X0),c_List_Olist_ONil(X2)))) = X0,
inference(rectify,[],[f4109]) ).
fof(f4109,axiom,
! [X19,X201,X20] : c_List_Olast(X20,hAPP(hAPP(c_List_Oappend(X20),X201),hAPP(hAPP(c_List_Olist_OCons(X20),X19),c_List_Olist_ONil(X20)))) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45930,plain,
spl647_1418,
inference(avatar_split_clause,[],[f27806,f45928]) ).
fof(f45928,plain,
( spl647_1418
<=> ! [X2,X0,X1] : hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)),c_HOL_Obool_Obool__size(c_fTrue)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1418])]) ).
fof(f27806,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)),c_HOL_Obool_Obool__size(c_fTrue)) = X1,
inference(forward_demodulation,[],[f19621,f17145]) ).
fof(f17145,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
inference(cnf_transformation,[],[f3713]) ).
fof(f3713,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f19621,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(cnf_transformation,[],[f6975]) ).
fof(f6975,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Onth(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rectify,[],[f3777]) ).
fof(f3777,axiom,
! [X201,X19,X20] : hAPP(hAPP(c_List_Onth(X20),hAPP(hAPP(c_List_Olist_OCons(X20),X19),X201)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45923,plain,
spl647_1417,
inference(avatar_split_clause,[],[f27562,f45921]) ).
fof(f45921,plain,
( spl647_1417
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Int_OPls))
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1417])]) ).
fof(f27562,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Int_OPls))
| ~ sP12(X0,X1) ),
inference(forward_demodulation,[],[f27561,f17285]) ).
fof(f17285,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(cnf_transformation,[],[f5263]) ).
fof(f5263,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(rectify,[],[f1207]) ).
fof(f1207,axiom,
! [X53] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X53) = X53,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f27561,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Int_OPls))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP12(X0,X1) ),
inference(forward_demodulation,[],[f27560,f17285]) ).
fof(f27560,plain,
! [X0,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_Int_OPls))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP12(X0,X1) ),
inference(forward_demodulation,[],[f19317,f17135]) ).
fof(f19317,plain,
! [X0,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)))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f15141]) ).
fof(f15141,plain,
! [X0,X1] :
( ( sP12(X0,X1)
| ( ~ sP11(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(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))) ) )
| ~ sP12(X0,X1) ) ),
inference(flattening,[],[f15140]) ).
fof(f15140,plain,
! [X0,X1] :
( ( sP12(X0,X1)
| ( ~ sP11(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(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))) ) )
| ~ sP12(X0,X1) ) ),
inference(nnf_transformation,[],[f14497]) ).
fof(f14497,plain,
! [X0,X1] :
( sP12(X0,X1)
<=> ( ( sP11(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,[sP12])]) ).
fof(f45919,plain,
spl647_1416,
inference(avatar_split_clause,[],[f27558,f45917]) ).
fof(f45917,plain,
( spl647_1416
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Int_OPls))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1416])]) ).
fof(f27558,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Int_OPls))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP12(X0,X1) ),
inference(forward_demodulation,[],[f27557,f17285]) ).
fof(f27557,plain,
! [X0,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_Int_OPls))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP12(X0,X1) ),
inference(forward_demodulation,[],[f27556,f17135]) ).
fof(f27556,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP12(X0,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(forward_demodulation,[],[f19320,f17285]) ).
fof(f19320,plain,
! [X0,X1] :
( sP12(X0,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(cnf_transformation,[],[f15141]) ).
fof(f45915,plain,
spl647_1415,
inference(avatar_split_clause,[],[f27552,f45913]) ).
fof(f45913,plain,
( spl647_1415
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1415])]) ).
fof(f27552,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
inference(forward_demodulation,[],[f19314,f17285]) ).
fof(f19314,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)) = X1
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f15139]) ).
fof(f15139,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(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)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
& hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)) = X1 )
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ) ),
inference(flattening,[],[f15138]) ).
fof(f15138,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(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)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
& hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)) = X1 )
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ) ),
inference(nnf_transformation,[],[f6829]) ).
fof(f6829,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
& hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)) = X1 ) ),
inference(rectify,[],[f1833]) ).
fof(f1833,axiom,
! [X73,X47] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X47) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X73)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X73)))
& hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X73)) = X47 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45911,plain,
spl647_1414,
inference(avatar_split_clause,[],[f27498,f45909]) ).
fof(f45909,plain,
( spl647_1414
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1414])]) ).
fof(f27498,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f19191,f17397]) ).
fof(f17397,plain,
! [X0] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),
inference(cnf_transformation,[],[f5375]) ).
fof(f5375,plain,
! [X0] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),
inference(rectify,[],[f2206]) ).
fof(f2206,axiom,
! [X46] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X46)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f19191,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f15048]) ).
fof(f15048,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X1)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ) ),
inference(nnf_transformation,[],[f6779]) ).
fof(f6779,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X1)) ),
inference(rectify,[],[f524]) ).
fof(f524,axiom,
! [X46,X47] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X47),X46))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X46)),X47)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45907,plain,
spl647_1413,
inference(avatar_split_clause,[],[f27497,f45905]) ).
fof(f45905,plain,
( spl647_1413
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1413])]) ).
fof(f27497,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ),
inference(forward_demodulation,[],[f19192,f17397]) ).
fof(f19192,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X1)) ),
inference(cnf_transformation,[],[f15048]) ).
fof(f45903,plain,
spl647_1412,
inference(avatar_split_clause,[],[f27491,f45901]) ).
fof(f45901,plain,
( spl647_1412
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(X0,c_HOL_Obool_Obool__size(c_fTrue)))
| sP8(X0,X1)
| ~ hBOOL(hAPP(X0,sK195(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1412])]) ).
fof(f27491,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(X0,c_HOL_Obool_Obool__size(c_fTrue)))
| sP8(X0,X1)
| ~ hBOOL(hAPP(X0,sK195(X0,X1))) ),
inference(forward_demodulation,[],[f19184,f17145]) ).
fof(f19184,plain,
! [X0,X1] :
( sP8(X0,X1)
| ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(X0,sK195(X0,X1))) ),
inference(cnf_transformation,[],[f15041]) ).
fof(f15041,plain,
! [X0,X1] :
( ( sP8(X0,X1)
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(X0,sK195(X0,X1)))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK195(X0,X1)) = X1 ) )
& ( ( ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [X3] :
( hBOOL(hAPP(X0,X3))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3) != X1 ) )
| ~ sP8(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK195])],[f15039,f15040]) ).
fof(f15040,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP(X0,X2))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X1 )
=> ( ~ hBOOL(hAPP(X0,sK195(X0,X1)))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK195(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f15039,plain,
! [X0,X1] :
( ( sP8(X0,X1)
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ? [X2] :
( ~ hBOOL(hAPP(X0,X2))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X1 ) )
& ( ( ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [X3] :
( hBOOL(hAPP(X0,X3))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3) != X1 ) )
| ~ sP8(X0,X1) ) ),
inference(rectify,[],[f15038]) ).
fof(f15038,plain,
! [X1,X0] :
( ( sP8(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 ) )
& ( ( ( 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 ) )
| ~ sP8(X1,X0) ) ),
inference(flattening,[],[f15037]) ).
fof(f15037,plain,
! [X1,X0] :
( ( sP8(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 ) )
& ( ( ( 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 ) )
| ~ sP8(X1,X0) ) ),
inference(nnf_transformation,[],[f14490]) ).
fof(f14490,plain,
! [X1,X0] :
( sP8(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,[sP8])]) ).
fof(f45899,plain,
spl647_1411,
inference(avatar_split_clause,[],[f27483,f45897]) ).
fof(f45897,plain,
( spl647_1411
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| c_HOL_Obool_Obool__size(c_fTrue) = X0
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1411])]) ).
fof(f27483,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| c_HOL_Obool_Obool__size(c_fTrue) = X0
| ~ sP7(X0,X1) ),
inference(forward_demodulation,[],[f27482,f17135]) ).
fof(f27482,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ sP7(X0,X1) ),
inference(forward_demodulation,[],[f19144,f17145]) ).
fof(f19144,plain,
! [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))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f15007]) ).
fof(f15007,plain,
! [X0,X1] :
( ( sP7(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)) ) )
& ( ( ( 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)) ) )
| ~ sP7(X0,X1) ) ),
inference(flattening,[],[f15006]) ).
fof(f15006,plain,
! [X0,X1] :
( ( sP7(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)) ) )
& ( ( ( 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)) ) )
| ~ sP7(X0,X1) ) ),
inference(nnf_transformation,[],[f14488]) ).
fof(f14488,plain,
! [X0,X1] :
( sP7(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,[sP7])]) ).
fof(f45895,plain,
spl647_1410,
inference(avatar_split_clause,[],[f27475,f45893]) ).
fof(f45893,plain,
( spl647_1410
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| c_HOL_Obool_Obool__size(c_fTrue) = X0
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1410])]) ).
fof(f27475,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| c_HOL_Obool_Obool__size(c_fTrue) = X0
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f27474,f17135]) ).
fof(f27474,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ sP6(X0,X1) ),
inference(forward_demodulation,[],[f19136,f17145]) ).
fof(f19136,plain,
! [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))
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f15004]) ).
fof(f15004,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)) ) )
& ( ( ( 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)) ) )
| ~ sP6(X0,X1) ) ),
inference(rectify,[],[f15003]) ).
fof(f15003,plain,
! [X1,X0] :
( ( sP6(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)) ) )
& ( ( ( 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)) ) )
| ~ sP6(X1,X0) ) ),
inference(flattening,[],[f15002]) ).
fof(f15002,plain,
! [X1,X0] :
( ( sP6(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)) ) )
& ( ( ( 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)) ) )
| ~ sP6(X1,X0) ) ),
inference(nnf_transformation,[],[f14486]) ).
fof(f14486,plain,
! [X1,X0] :
( sP6(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,[sP6])]) ).
fof(f45891,plain,
spl647_1409,
inference(avatar_split_clause,[],[f26600,f45889]) ).
fof(f45889,plain,
( spl647_1409
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| c_Nitpick_Onat__gcd(X0,X1) = c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1409])]) ).
fof(f26600,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| c_Nitpick_Onat__gcd(X0,X1) = c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1)) ),
inference(forward_demodulation,[],[f18186,f17145]) ).
fof(f18186,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 ),
inference(cnf_transformation,[],[f10449]) ).
fof(f10449,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,[],[f6070]) ).
fof(f6070,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,[],[f2068]) ).
fof(f2068,axiom,
! [X19,X21] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X21
=> c_Nitpick_Onat__gcd(X19,X21) = c_Nitpick_Onat__gcd(X21,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X19,X21)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X21
=> c_Nitpick_Onat__gcd(X19,X21) = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45887,plain,
spl647_1408,
inference(avatar_split_clause,[],[f26463,f45885]) ).
fof(f45885,plain,
( spl647_1408
<=> ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1408])]) ).
fof(f26463,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0))),
inference(forward_demodulation,[],[f26462,f17876]) ).
fof(f17876,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X0),
inference(cnf_transformation,[],[f5768]) ).
fof(f5768,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X0),
inference(rectify,[],[f2659]) ).
fof(f2659,axiom,
! [X68,X97] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X97,X68) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X97),X68),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f26462,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X0))),
inference(forward_demodulation,[],[f24348,f17893]) ).
fof(f17893,plain,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X0)),
inference(cnf_transformation,[],[f5785]) ).
fof(f5785,plain,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X0)),
inference(rectify,[],[f2755]) ).
fof(f2755,axiom,
! [X68,X97] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X97,X68) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X97),hAPP(c_Nat_OSuc,X68)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f24348,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),hAPP(c_Nat_OSuc,X0)))),
inference(definition_unfolding,[],[f17956,f17267,f17880]) ).
fof(f17880,plain,
! [X0,X1] : c_List_Oupt(X1,X0) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0)),
inference(cnf_transformation,[],[f5772]) ).
fof(f5772,plain,
! [X0,X1] : c_List_Oupt(X1,X0) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0)),
inference(rectify,[],[f4378]) ).
fof(f4378,axiom,
! [X46,X47] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X47),X46)) = c_List_Oupt(X47,X46),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17267,plain,
! [X0] : c_List_Oset(X0) = c_List_Omember(X0),
inference(cnf_transformation,[],[f5245]) ).
fof(f5245,plain,
! [X0] : c_List_Oset(X0) = c_List_Omember(X0),
inference(rectify,[],[f4668]) ).
fof(f4668,axiom,
! [X4] : c_List_Oset(X4) = c_List_Omember(X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17956,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X0))),
inference(cnf_transformation,[],[f5848]) ).
fof(f5848,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X1),hAPP(c_Nat_OSuc,X0))),
inference(rectify,[],[f4390]) ).
fof(f4390,axiom,
! [X47,X46] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X46,X47) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X46),hAPP(c_Nat_OSuc,X47))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45883,plain,
( spl647_1407
| ~ spl647_392
| ~ spl647_1243 ),
inference(avatar_split_clause,[],[f45459,f43762,f31084,f45881]) ).
fof(f45881,plain,
( spl647_1407
<=> ! [X0] :
( ~ c_Nat__Transfer_Ois__nat(X0)
| sP11(X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1407])]) ).
fof(f31084,plain,
( spl647_392
<=> ! [X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_392])]) ).
fof(f43762,plain,
( spl647_1243
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| ~ c_Nat__Transfer_Ois__nat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1243])]) ).
fof(f45459,plain,
( ! [X0] :
( ~ c_Nat__Transfer_Ois__nat(X0)
| sP11(X0,X0) )
| ~ spl647_392
| ~ spl647_1243 ),
inference(resolution,[],[f43763,f31085]) ).
fof(f31085,plain,
( ! [X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X1,X1) )
| ~ spl647_392 ),
inference(avatar_component_clause,[],[f31084]) ).
fof(f43763,plain,
( ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| ~ c_Nat__Transfer_Ois__nat(X0) )
| ~ spl647_1243 ),
inference(avatar_component_clause,[],[f43762]) ).
fof(f45879,plain,
spl647_1406,
inference(avatar_split_clause,[],[f26461,f45877]) ).
fof(f45877,plain,
( spl647_1406
<=> ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1406])]) ).
fof(f26461,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_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin),X0),
inference(forward_demodulation,[],[f17955,f24214]) ).
fof(f24214,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definition_unfolding,[],[f17372,f17339]) ).
fof(f17339,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(cnf_transformation,[],[f5317]) ).
fof(f5317,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(rectify,[],[f1986]) ).
fof(f1986,axiom,
! [X53] : c_Int_Osucc(X53) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X53),c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17372,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,[],[f5350]) ).
fof(f5350,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,[],[f1320]) ).
fof(f1320,axiom,
! [X53] : c_Int_Osucc(X53) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17955,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,[],[f5847]) ).
fof(f5847,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,[],[f2663]) ).
fof(f2663,axiom,
! [X68,X97] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X97,X68) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X97),c_Groups_Oone__class_Oone(tc_Int_Oint)),X68),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45875,plain,
spl647_1405,
inference(avatar_split_clause,[],[f26460,f45873]) ).
fof(f45873,plain,
( spl647_1405
<=> ! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1405])]) ).
fof(f26460,plain,
! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),
inference(forward_demodulation,[],[f17934,f17145]) ).
fof(f17934,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),
inference(cnf_transformation,[],[f5826]) ).
fof(f5826,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),
inference(rectify,[],[f884]) ).
fof(f884,axiom,
! [X45,X44] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X44),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X45)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45871,plain,
spl647_1404,
inference(avatar_split_clause,[],[f26459,f45869]) ).
fof(f45869,plain,
( spl647_1404
<=> ! [X0,X1] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1404])]) ).
fof(f26459,plain,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0))),
inference(forward_demodulation,[],[f24339,f17893]) ).
fof(f24339,plain,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X0)))),
inference(definition_unfolding,[],[f17914,f17267,f17880]) ).
fof(f17914,plain,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X1,hAPP(c_Nat_OSuc,X0))),
inference(cnf_transformation,[],[f5806]) ).
fof(f5806,plain,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X1,hAPP(c_Nat_OSuc,X0))),
inference(rectify,[],[f4387]) ).
fof(f4387,axiom,
! [X47,X46] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X46,X47) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(X46,hAPP(c_Nat_OSuc,X47))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45867,plain,
spl647_1403,
inference(avatar_split_clause,[],[f26458,f45865]) ).
fof(f45865,plain,
( spl647_1403
<=> ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1403])]) ).
fof(f26458,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0))),
inference(forward_demodulation,[],[f24338,f17892]) ).
fof(f17892,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X0),
inference(cnf_transformation,[],[f5784]) ).
fof(f5784,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X0),
inference(rectify,[],[f2770]) ).
fof(f2770,axiom,
! [X68,X97] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X97,X68) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X97)),X68),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f24338,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X0))),
inference(definition_unfolding,[],[f17913,f17267,f17880]) ).
fof(f17913,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X1),X0)),
inference(cnf_transformation,[],[f5805]) ).
fof(f5805,plain,
! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X1),X0)),
inference(rectify,[],[f4391]) ).
fof(f4391,axiom,
! [X47,X46] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X46,X47) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,X46),X47)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45863,plain,
spl647_1402,
inference(avatar_split_clause,[],[f26405,f45861]) ).
fof(f45861,plain,
( spl647_1402
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Int_OPls))
| c_HOL_Obool_Obool__size(c_fTrue) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1402])]) ).
fof(f26405,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Int_OPls))
| c_HOL_Obool_Obool__size(c_fTrue) = X0 ),
inference(forward_demodulation,[],[f26404,f17135]) ).
fof(f26404,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(forward_demodulation,[],[f17746,f17145]) ).
fof(f17746,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f14708]) ).
fof(f14708,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(nnf_transformation,[],[f5652]) ).
fof(f5652,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f1251]) ).
fof(f1251,axiom,
! [X46] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X46)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X46 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45859,plain,
spl647_1401,
inference(avatar_split_clause,[],[f26400,f45857]) ).
fof(f45857,plain,
( spl647_1401
<=> ! [X0] :
( c_Int_OPls = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1401])]) ).
fof(f26400,plain,
! [X0] :
( c_Int_OPls = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(forward_demodulation,[],[f17744,f17135]) ).
fof(f17744,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f14707]) ).
fof(f14707,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(nnf_transformation,[],[f5651]) ).
fof(f5651,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ),
inference(rectify,[],[f1380]) ).
fof(f1380,axiom,
! [X17] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X17)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45855,plain,
spl647_1400,
inference(avatar_split_clause,[],[f26369,f45853]) ).
fof(f45853,plain,
( spl647_1400
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0))
| hAPP(c_Nat_OSuc,sK99(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1400])]) ).
fof(f26369,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0))
| hAPP(c_Nat_OSuc,sK99(X0)) = X0 ),
inference(forward_demodulation,[],[f17708,f17145]) ).
fof(f17708,plain,
! [X0] :
( hAPP(c_Nat_OSuc,sK99(X0)) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ),
inference(cnf_transformation,[],[f14689]) ).
fof(f14689,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ! [X1] : hAPP(c_Nat_OSuc,X1) != X0 )
& ( hAPP(c_Nat_OSuc,sK99(X0)) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK99])],[f14687,f14688]) ).
fof(f14688,plain,
! [X0] :
( ? [X2] : hAPP(c_Nat_OSuc,X2) = X0
=> hAPP(c_Nat_OSuc,sK99(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f14687,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ! [X1] : hAPP(c_Nat_OSuc,X1) != X0 )
& ( ? [X2] : hAPP(c_Nat_OSuc,X2) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
inference(rectify,[],[f14686]) ).
fof(f14686,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| ! [X1] : hAPP(c_Nat_OSuc,X1) != X0 )
& ( ? [X1] : hAPP(c_Nat_OSuc,X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
inference(nnf_transformation,[],[f5633]) ).
fof(f5633,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
<=> ? [X1] : hAPP(c_Nat_OSuc,X1) = X0 ),
inference(rectify,[],[f866]) ).
fof(f866,axiom,
! [X46] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X46))
<=> ? [X82] : hAPP(c_Nat_OSuc,X82) = X46 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45851,plain,
spl647_1399,
inference(avatar_split_clause,[],[f26365,f45849]) ).
fof(f45849,plain,
( spl647_1399
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1399])]) ).
fof(f26365,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f26364,f17285]) ).
fof(f26364,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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin)))) ),
inference(forward_demodulation,[],[f24274,f17285]) ).
fof(f24274,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),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin)))) ),
inference(definition_unfolding,[],[f17686,f24151]) ).
fof(f24151,plain,
! [X0] : c_Int_OBit1(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin),
inference(definition_unfolding,[],[f17280,f17339]) ).
fof(f17280,plain,
! [X0] : c_Int_OBit1(X0) = c_Int_Osucc(c_Int_OBit0(X0)),
inference(cnf_transformation,[],[f5258]) ).
fof(f5258,plain,
! [X0] : c_Int_OBit1(X0) = c_Int_Osucc(c_Int_OBit0(X0)),
inference(rectify,[],[f1528]) ).
fof(f1528,axiom,
! [X53] : c_Int_OBit1(X53) = c_Int_Osucc(c_Int_OBit0(X53)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17686,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,[],[f14675]) ).
fof(f14675,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,[],[f5622]) ).
fof(f5622,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,[],[f1372]) ).
fof(f1372,axiom,
! [X59] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X59))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X59))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45847,plain,
spl647_1398,
inference(avatar_split_clause,[],[f26363,f45845]) ).
fof(f45845,plain,
( spl647_1398
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1398])]) ).
fof(f26363,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin))) ),
inference(forward_demodulation,[],[f26362,f17285]) ).
fof(f26362,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f24273,f17285]) ).
fof(f24273,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(definition_unfolding,[],[f17687,f24151]) ).
fof(f17687,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,[],[f14675]) ).
fof(f45843,plain,
spl647_1397,
inference(avatar_split_clause,[],[f26233,f45841]) ).
fof(f45841,plain,
( spl647_1397
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X0))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK90(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1397])]) ).
fof(f26233,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X0))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK90(X0)) = X0 ),
inference(forward_demodulation,[],[f17611,f17135]) ).
fof(f17611,plain,
! [X0] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK90(X0)) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ),
inference(cnf_transformation,[],[f14636]) ).
fof(f14636,plain,
! [X0] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK90(X0)) = X0
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK90(X0))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK90])],[f10403,f14635]) ).
fof(f14635,plain,
! [X0] :
( ? [X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) )
=> ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK90(X0)) = X0
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK90(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f10403,plain,
! [X0] :
( ? [X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = 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_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ),
inference(ennf_transformation,[],[f5574]) ).
fof(f5574,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> ? [X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ) ),
inference(rectify,[],[f1330]) ).
fof(f1330,axiom,
! [X53] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X53))
=> ? [X109] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X109) = X53
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X109)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45839,plain,
spl647_1396,
inference(avatar_split_clause,[],[f26175,f45837]) ).
fof(f45837,plain,
( spl647_1396
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Int_Onat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1396])]) ).
fof(f26175,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Int_Onat,X0)) ),
inference(forward_demodulation,[],[f26174,f17285]) ).
fof(f26174,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Int_Onat,X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f26173,f25910]) ).
fof(f25910,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17166,f17145]) ).
fof(f17166,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f888]) ).
fof(f888,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f26173,plain,
! [X0] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),hAPP(c_Int_Onat,X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f26172,f17145]) ).
fof(f26172,plain,
! [X0] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f17514,f26052]) ).
fof(f26052,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X0),
inference(forward_demodulation,[],[f17395,f17285]) ).
fof(f17395,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,[],[f5373]) ).
fof(f5373,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,[],[f1786]) ).
fof(f1786,axiom,
! [X74] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X74) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X74)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17514,plain,
! [X0] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f10315]) ).
fof(f10315,plain,
! [X0] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(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),X0))) )
& ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ),
inference(ennf_transformation,[],[f5484]) ).
fof(f5484,plain,
! [X0] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(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),X0)))
=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ) ),
inference(rectify,[],[f1817]) ).
fof(f1817,axiom,
! [X111] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X111)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X111)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X111))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X111)))
=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X111)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45835,plain,
spl647_1395,
inference(avatar_split_clause,[],[f26082,f45833]) ).
fof(f45833,plain,
( spl647_1395
<=> ! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X0),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1395])]) ).
fof(f26082,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X0),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)),
inference(forward_demodulation,[],[f17457,f17400]) ).
fof(f17400,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),
inference(cnf_transformation,[],[f5378]) ).
fof(f5378,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),
inference(rectify,[],[f2772]) ).
fof(f2772,axiom,
! [X48] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X48)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X48),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17457,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X0),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)),
inference(cnf_transformation,[],[f5435]) ).
fof(f5435,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X0),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)),
inference(rectify,[],[f2407]) ).
fof(f2407,axiom,
! [X48] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X48)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X48),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X48)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45831,plain,
spl647_1394,
inference(avatar_split_clause,[],[f26076,f45829]) ).
fof(f45829,plain,
( spl647_1394
<=> ! [X0] : c_Int_OPls != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1394])]) ).
fof(f26076,plain,
! [X0] : c_Int_OPls != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0),
inference(forward_demodulation,[],[f17438,f17135]) ).
fof(f17438,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0),
inference(cnf_transformation,[],[f5416]) ).
fof(f5416,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0),
inference(rectify,[],[f1147]) ).
fof(f1147,axiom,
! [X27] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X27)),X27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45827,plain,
spl647_1393,
inference(avatar_split_clause,[],[f26073,f45825]) ).
fof(f45825,plain,
( spl647_1393
<=> ! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1393])]) ).
fof(f26073,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0))),
inference(forward_demodulation,[],[f26072,f17400]) ).
fof(f26072,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)))),
inference(forward_demodulation,[],[f26071,f26051]) ).
fof(f26051,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue)),X0),
inference(forward_demodulation,[],[f17393,f17145]) ).
fof(f17393,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f5371]) ).
fof(f5371,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(rectify,[],[f2757]) ).
fof(f2757,axiom,
! [X46] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X46) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X46),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f26071,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue)),hAPP(c_Nat_OSuc,X0)))),
inference(forward_demodulation,[],[f24224,f17145]) ).
fof(f24224,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X0)))),
inference(definition_unfolding,[],[f17433,f17267,f17880]) ).
fof(f17433,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0))),
inference(cnf_transformation,[],[f5411]) ).
fof(f5411,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0))),
inference(rectify,[],[f4392]) ).
fof(f4392,axiom,
! [X46] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X46) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,X46))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45823,plain,
spl647_1392,
inference(avatar_split_clause,[],[f26062,f45821]) ).
fof(f45821,plain,
( spl647_1392
<=> ! [X0] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1392])]) ).
fof(f26062,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0))),
inference(forward_demodulation,[],[f26061,f26051]) ).
fof(f26061,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue)),X0))),
inference(forward_demodulation,[],[f24218,f17145]) ).
fof(f24218,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0) = hAPP(c_List_Omember(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))),
inference(definition_unfolding,[],[f17408,f17267,f17880]) ).
fof(f17408,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)),
inference(cnf_transformation,[],[f5386]) ).
fof(f5386,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0)),
inference(rectify,[],[f4388]) ).
fof(f4388,axiom,
! [X46] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X46) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X46)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45804,plain,
( spl647_1391
| ~ spl647_597
| ~ spl647_1390 ),
inference(avatar_split_clause,[],[f45800,f45797,f31997,f45802]) ).
fof(f45802,plain,
( spl647_1391
<=> ! [X0] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,sK109(X0)))),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1391])]) ).
fof(f31997,plain,
( spl647_597
<=> ! [X0] : hAPP(c_Code__Numeral_Onat__of,X0) = sK109(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_597])]) ).
fof(f45797,plain,
( spl647_1390
<=> ! [X0] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0)))),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1390])]) ).
fof(f45800,plain,
( ! [X0] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,sK109(X0)))),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X0
| ~ spl647_597
| ~ spl647_1390 ),
inference(forward_demodulation,[],[f45798,f31998]) ).
fof(f31998,plain,
( ! [X0] : hAPP(c_Code__Numeral_Onat__of,X0) = sK109(X0)
| ~ spl647_597 ),
inference(avatar_component_clause,[],[f31997]) ).
fof(f45798,plain,
( ! [X0] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0)))),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X0
| ~ spl647_1390 ),
inference(avatar_component_clause,[],[f45797]) ).
fof(f45799,plain,
spl647_1390,
inference(avatar_split_clause,[],[f26044,f45797]) ).
fof(f26044,plain,
! [X0] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0)))),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X0,
inference(forward_demodulation,[],[f24217,f17134]) ).
fof(f17134,plain,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
inference(cnf_transformation,[],[f2158]) ).
fof(f2158,axiom,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f24217,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0)))),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X0,
inference(definition_unfolding,[],[f17379,f17371]) ).
fof(f17371,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,[],[f5349]) ).
fof(f5349,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,[],[f4208]) ).
fof(f4208,axiom,
! [X53] : c_Code__Numeral_OSuc__code__numeral(X53) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X53))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17379,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,[],[f5357]) ).
fof(f5357,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,[],[f2065]) ).
fof(f2065,axiom,
! [X44] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(X44)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45794,plain,
spl647_1389,
inference(avatar_split_clause,[],[f25970,f45791]) ).
fof(f45791,plain,
( spl647_1389
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1389])]) ).
fof(f25970,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))))),
inference(forward_demodulation,[],[f25969,f17135]) ).
fof(f25969,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))))),
inference(forward_demodulation,[],[f25968,f25909]) ).
fof(f25909,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin),
inference(forward_demodulation,[],[f24173,f17133]) ).
fof(f17133,plain,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
inference(cnf_transformation,[],[f1454]) ).
fof(f1454,axiom,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f24173,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin),
inference(definition_unfolding,[],[f17163,f24151]) ).
fof(f17163,plain,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin),
inference(cnf_transformation,[],[f2003]) ).
fof(f2003,axiom,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f25968,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))),
inference(forward_demodulation,[],[f24184,f17133]) ).
fof(f24184,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin))))),
inference(definition_unfolding,[],[f17220,f24151]) ).
fof(f17220,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(cnf_transformation,[],[f1560]) ).
fof(f1560,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45788,plain,
spl647_1388,
inference(avatar_split_clause,[],[f25924,f45785]) ).
fof(f45785,plain,
( spl647_1388
<=> c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1388])]) ).
fof(f25924,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))),c_Int_OMin))),
inference(forward_demodulation,[],[f25923,f25909]) ).
fof(f25923,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))),c_Int_OMin))),
inference(forward_demodulation,[],[f24175,f17133]) ).
fof(f24175,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin))),c_Int_OMin))),
inference(definition_unfolding,[],[f17177,f24151,f24151]) ).
fof(f17177,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,[],[f2148]) ).
fof(f2148,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45783,plain,
( spl647_1387
| ~ spl647_923
| ~ spl647_1378 ),
inference(avatar_split_clause,[],[f45744,f45740,f34500,f45780]) ).
fof(f45780,plain,
( spl647_1387
<=> c_Wellfounded_OwfP(tc_Nat_Onat,c_Orderings_Oord__class_Oless(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1387])]) ).
fof(f34500,plain,
( spl647_923
<=> ! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| c_Wellfounded_OwfP(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_923])]) ).
fof(f45740,plain,
( spl647_1378
<=> c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1378])]) ).
fof(f45744,plain,
( c_Wellfounded_OwfP(tc_Nat_Onat,c_Orderings_Oord__class_Oless(tc_Nat_Onat))
| ~ spl647_923
| ~ spl647_1378 ),
inference(resolution,[],[f45742,f34501]) ).
fof(f34501,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| c_Wellfounded_OwfP(X1,X0) )
| ~ spl647_923 ),
inference(avatar_component_clause,[],[f34500]) ).
fof(f45742,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))
| ~ spl647_1378 ),
inference(avatar_component_clause,[],[f45740]) ).
fof(f45778,plain,
spl647_1386,
inference(avatar_split_clause,[],[f25746,f45776]) ).
fof(f45776,plain,
( spl647_1386
<=> ! [X0,X3,X2,X1] : hAPP(c_Product__Type_OPair(X3,X2),X0) = hAPP(c_Random_Oiterate(X3,X2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1386])]) ).
fof(f25746,plain,
! [X2,X3,X0,X1] : hAPP(c_Product__Type_OPair(X3,X2),X0) = hAPP(c_Random_Oiterate(X3,X2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),X1),X0),
inference(equality_resolution,[],[f23006]) ).
fof(f23006,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(c_Product__Type_OPair(X3,X2),X0) = hAPP(c_Random_Oiterate(X3,X2,X4,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X4 ),
inference(cnf_transformation,[],[f13573]) ).
fof(f13573,plain,
! [X0,X1,X2,X3,X4] :
( ( hAPP(c_Random_Oiterate(X3,X2,X4,X1),X0) = hAPP(hAPP(c_Product__Type_Oscomp(X2,X3,X2,tc_prod(X3,X2)),hAPP(X1,X0)),c_Random_Oiterate(X3,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X4),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1))
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X4 )
& ( hAPP(c_Product__Type_OPair(X3,X2),X0) = hAPP(c_Random_Oiterate(X3,X2,X4,X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X4 ) ),
inference(ennf_transformation,[],[f9338]) ).
fof(f9338,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X4
=> hAPP(c_Random_Oiterate(X3,X2,X4,X1),X0) = hAPP(hAPP(c_Product__Type_Oscomp(X2,X3,X2,tc_prod(X3,X2)),hAPP(X1,X0)),c_Random_Oiterate(X3,X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X4),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X4
=> hAPP(c_Product__Type_OPair(X3,X2),X0) = hAPP(c_Random_Oiterate(X3,X2,X4,X1),X0) ) ),
inference(rectify,[],[f3531]) ).
fof(f3531,axiom,
! [X13,X1,X4,X14,X48] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X48
=> hAPP(c_Random_Oiterate(X14,X4,X48,X1),X13) = hAPP(hAPP(c_Product__Type_Oscomp(X4,X14,X4,tc_prod(X14,X4)),hAPP(X1,X13)),c_Random_Oiterate(X14,X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X48),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X1)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X48
=> hAPP(c_Product__Type_OPair(X14,X4),X13) = hAPP(c_Random_Oiterate(X14,X4,X48,X1),X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45774,plain,
spl647_1385,
inference(avatar_split_clause,[],[f25647,f45772]) ).
fof(f45772,plain,
( spl647_1385
<=> ! [X0,X1,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)))
| ~ class_Rings_Odvd(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1385])]) ).
fof(f25647,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0)))
| ~ class_Rings_Odvd(X3) ),
inference(equality_resolution,[],[f21871]) ).
fof(f21871,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X2))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
| ~ class_Rings_Odvd(X3) ),
inference(cnf_transformation,[],[f12740]) ).
fof(f12740,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X2))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
| ~ class_Rings_Odvd(X3) ),
inference(flattening,[],[f12739]) ).
fof(f12739,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X2))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) != X2
| ~ class_Rings_Odvd(X3) ),
inference(ennf_transformation,[],[f8576]) ).
fof(f8576,plain,
! [X0,X1,X2,X3] :
( class_Rings_Odvd(X3)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X1),X0) = X2
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X3),X1),X2)) ) ),
inference(rectify,[],[f4973]) ).
fof(f4973,axiom,
! [X53,X25,X26,X20] :
( class_Rings_Odvd(X20)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),X25),X53) = X26
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X20),X25),X26)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45770,plain,
spl647_1384,
inference(avatar_split_clause,[],[f25305,f45768]) ).
fof(f45768,plain,
( spl647_1384
<=> ! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1))),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1384])]) ).
fof(f25305,plain,
! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1))),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(equality_resolution,[],[f18394]) ).
fof(f18394,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)),c_Groups_Ozero__class_Ozero(X1)))
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f14765]) ).
fof(f14765,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)),c_Groups_Ozero__class_Ozero(X1)))
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)),c_Groups_Ozero__class_Ozero(X1))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(nnf_transformation,[],[f10573]) ).
fof(f10573,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)),c_Groups_Ozero__class_Ozero(X1)))
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f6201]) ).
fof(f6201,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)),c_Groups_Ozero__class_Ozero(X1)))
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f1356]) ).
fof(f1356,axiom,
! [X5,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(c_Groups_Oabs__class_Oabs(X4),X5)),c_Groups_Ozero__class_Ozero(X4)))
<=> c_Groups_Ozero__class_Ozero(X4) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45766,plain,
spl647_1383,
inference(avatar_split_clause,[],[f25304,f45764]) ).
fof(f45764,plain,
( spl647_1383
<=> ! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1383])]) ).
fof(f25304,plain,
! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),c_Groups_Ozero__class_Ozero(X1))))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(equality_resolution,[],[f18391]) ).
fof(f18391,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f14764]) ).
fof(f14764,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)))
| c_Groups_Ozero__class_Ozero(X1) = X0 )
& ( c_Groups_Ozero__class_Ozero(X1) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X0))) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(nnf_transformation,[],[f10572]) ).
fof(f10572,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)))
<=> c_Groups_Ozero__class_Ozero(X1) != X0 )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f6200]) ).
fof(f6200,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)))
<=> c_Groups_Ozero__class_Ozero(X1) != X0 ) ),
inference(rectify,[],[f1359]) ).
fof(f1359,axiom,
! [X5,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(c_Groups_Oabs__class_Oabs(X4),X5)))
<=> c_Groups_Ozero__class_Ozero(X4) != X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45762,plain,
spl647_1382,
inference(avatar_split_clause,[],[f24850,f45760]) ).
fof(f45760,plain,
( spl647_1382
<=> ! [X2,X0,X1] :
( c_List_Oall__interval__nat(X2,X1,X0)
| ~ c_List_Olist__all(tc_Nat_Onat,X2,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1382])]) ).
fof(f24850,plain,
! [X2,X0,X1] :
( c_List_Oall__interval__nat(X2,X1,X0)
| ~ c_List_Olist__all(tc_Nat_Onat,X2,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) ),
inference(definition_unfolding,[],[f21210,f17880]) ).
fof(f21210,plain,
! [X2,X0,X1] :
( c_List_Oall__interval__nat(X2,X1,X0)
| ~ c_List_Olist__all(tc_Nat_Onat,X2,c_List_Oupt(X1,X0)) ),
inference(cnf_transformation,[],[f15796]) ).
fof(f15796,plain,
! [X0,X1,X2] :
( ( c_List_Olist__all(tc_Nat_Onat,X2,c_List_Oupt(X1,X0))
| ~ c_List_Oall__interval__nat(X2,X1,X0) )
& ( c_List_Oall__interval__nat(X2,X1,X0)
| ~ c_List_Olist__all(tc_Nat_Onat,X2,c_List_Oupt(X1,X0)) ) ),
inference(nnf_transformation,[],[f8156]) ).
fof(f8156,plain,
! [X0,X1,X2] :
( c_List_Olist__all(tc_Nat_Onat,X2,c_List_Oupt(X1,X0))
<=> c_List_Oall__interval__nat(X2,X1,X0) ),
inference(rectify,[],[f4866]) ).
fof(f4866,axiom,
! [X62,X63,X23] :
( c_List_Olist__all(tc_Nat_Onat,X23,c_List_Oupt(X63,X62))
<=> c_List_Oall__interval__nat(X23,X63,X62) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45758,plain,
spl647_1381,
inference(avatar_split_clause,[],[f24849,f45756]) ).
fof(f45756,plain,
( spl647_1381
<=> ! [X2,X0,X1] :
( c_List_Olist__all(tc_Nat_Onat,X2,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0)))
| ~ c_List_Oall__interval__nat(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1381])]) ).
fof(f24849,plain,
! [X2,X0,X1] :
( c_List_Olist__all(tc_Nat_Onat,X2,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0)))
| ~ c_List_Oall__interval__nat(X2,X1,X0) ),
inference(definition_unfolding,[],[f21211,f17880]) ).
fof(f21211,plain,
! [X2,X0,X1] :
( c_List_Olist__all(tc_Nat_Onat,X2,c_List_Oupt(X1,X0))
| ~ c_List_Oall__interval__nat(X2,X1,X0) ),
inference(cnf_transformation,[],[f15796]) ).
fof(f45754,plain,
spl647_1380,
inference(avatar_split_clause,[],[f24215,f45752]) ).
fof(f45752,plain,
( spl647_1380
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),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,[spl647_1380])]) ).
fof(f24215,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definition_unfolding,[],[f17373,f17340]) ).
fof(f17340,plain,
! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X0),
inference(cnf_transformation,[],[f5318]) ).
fof(f5318,plain,
! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X0),
inference(rectify,[],[f1982]) ).
fof(f1982,axiom,
! [X53] : c_Int_Opred(X53) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X53),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17373,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,[],[f5351]) ).
fof(f5351,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,[],[f1319]) ).
fof(f1319,axiom,
! [X53] : c_Int_Opred(X53) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X53),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45750,plain,
spl647_1379,
inference(avatar_split_clause,[],[f24214,f45748]) ).
fof(f45748,plain,
( spl647_1379
<=> ! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin) = 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,[spl647_1379])]) ).
fof(f45743,plain,
( spl647_1378
| ~ spl647_274
| ~ spl647_1377 ),
inference(avatar_split_clause,[],[f45738,f45734,f30559,f45740]) ).
fof(f30559,plain,
( spl647_274
<=> ! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_274])]) ).
fof(f45734,plain,
( spl647_1377
<=> c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1377])]) ).
fof(f45738,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))
| ~ spl647_274
| ~ spl647_1377 ),
inference(forward_demodulation,[],[f45736,f30560]) ).
fof(f30560,plain,
( ! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0
| ~ spl647_274 ),
inference(avatar_component_clause,[],[f30559]) ).
fof(f45736,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat))))
| ~ spl647_1377 ),
inference(avatar_component_clause,[],[f45734]) ).
fof(f45737,plain,
spl647_1377,
inference(avatar_split_clause,[],[f24187,f45734]) ).
fof(f24187,plain,
c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
inference(definition_unfolding,[],[f17224,f19585]) ).
fof(f19585,plain,
! [X2,X0,X1] : c_Product__Type_Oprod_Oprod__case(X2,X1,X0) = c_Product__Type_Ointernal__split(X2,X1,X0),
inference(cnf_transformation,[],[f6939]) ).
fof(f6939,plain,
! [X0,X1,X2] : c_Product__Type_Oprod_Oprod__case(X2,X1,X0) = c_Product__Type_Ointernal__split(X2,X1,X0),
inference(rectify,[],[f3712]) ).
fof(f3712,axiom,
! [X96,X14,X4] : c_Product__Type_Oprod_Oprod__case(X4,X14,X96) = c_Product__Type_Ointernal__split(X4,X14,X96),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17224,plain,
c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
inference(cnf_transformation,[],[f3373]) ).
fof(f3373,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45732,plain,
spl647_1376,
inference(avatar_split_clause,[],[f23913,f45730]) ).
fof(f45730,plain,
( spl647_1376
<=> ! [X5,X4,X0,X3,X2,X1] :
( X0 = X2
| c_Nitpick_Opair__box_OPairBox(X5,X4,X1,X0) != c_Nitpick_Opair__box_OPairBox(X5,X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1376])]) ).
fof(f23913,plain,
! [X2,X3,X0,X1,X4,X5] :
( X0 = X2
| c_Nitpick_Opair__box_OPairBox(X5,X4,X1,X0) != c_Nitpick_Opair__box_OPairBox(X5,X4,X3,X2) ),
inference(cnf_transformation,[],[f16831]) ).
fof(f16831,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Nitpick_Opair__box_OPairBox(X5,X4,X1,X0) = c_Nitpick_Opair__box_OPairBox(X5,X4,X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Nitpick_Opair__box_OPairBox(X5,X4,X1,X0) != c_Nitpick_Opair__box_OPairBox(X5,X4,X3,X2) ) ),
inference(flattening,[],[f16830]) ).
fof(f16830,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Nitpick_Opair__box_OPairBox(X5,X4,X1,X0) = c_Nitpick_Opair__box_OPairBox(X5,X4,X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Nitpick_Opair__box_OPairBox(X5,X4,X1,X0) != c_Nitpick_Opair__box_OPairBox(X5,X4,X3,X2) ) ),
inference(nnf_transformation,[],[f9976]) ).
fof(f9976,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Nitpick_Opair__box_OPairBox(X5,X4,X1,X0) = c_Nitpick_Opair__box_OPairBox(X5,X4,X3,X2)
<=> ( X0 = X2
& X1 = X3 ) ),
inference(rectify,[],[f1053]) ).
fof(f1053,axiom,
! [X93,X94,X12,X5,X14,X4] :
( c_Nitpick_Opair__box_OPairBox(X4,X14,X5,X12) = c_Nitpick_Opair__box_OPairBox(X4,X14,X94,X93)
<=> ( X12 = X93
& X5 = X94 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45728,plain,
spl647_1375,
inference(avatar_split_clause,[],[f23912,f45726]) ).
fof(f45726,plain,
( spl647_1375
<=> ! [X5,X4,X0,X3,X2,X1] :
( X1 = X3
| c_Nitpick_Opair__box_OPairBox(X5,X4,X1,X0) != c_Nitpick_Opair__box_OPairBox(X5,X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1375])]) ).
fof(f23912,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X3
| c_Nitpick_Opair__box_OPairBox(X5,X4,X1,X0) != c_Nitpick_Opair__box_OPairBox(X5,X4,X3,X2) ),
inference(cnf_transformation,[],[f16831]) ).
fof(f45724,plain,
spl647_1374,
inference(avatar_split_clause,[],[f23859,f45722]) ).
fof(f45722,plain,
( spl647_1374
<=> ! [X3,X4,X0,X5,X2,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X4,X3,X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1374])]) ).
fof(f23859,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X4,X3,X2,X1),X0)) ),
inference(cnf_transformation,[],[f14291]) ).
fof(f14291,plain,
! [X0,X1,X2,X3,X4,X5] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X4,X3,X2,X1),X0)) ),
inference(ennf_transformation,[],[f9935]) ).
fof(f9935,plain,
! [X0,X1,X2,X3,X4,X5] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X5,X4,X3,X2,X1),X0))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X1)) ),
inference(rectify,[],[f215]) ).
fof(f215,axiom,
! [X13,X9,X17,X1,X14,X4] :
( hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X14,X1,X17,X9),X13))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45720,plain,
spl647_1373,
inference(avatar_split_clause,[],[f23496,f45718]) ).
fof(f45718,plain,
( spl647_1373
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(c_Set_Oimage(X4,X3,X2),X1) = X0
| ~ c_Fun_Obij__betw(X4,X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1373])]) ).
fof(f23496,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(c_Set_Oimage(X4,X3,X2),X1) = X0
| ~ c_Fun_Obij__betw(X4,X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16655]) ).
fof(f16655,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Fun_Obij__betw(X4,X3,X2,X1,X0)
| hAPP(c_Set_Oimage(X4,X3,X2),X1) != X0
| ~ c_Fun_Oinj__on(X4,X3,X2,X1) )
& ( ( hAPP(c_Set_Oimage(X4,X3,X2),X1) = X0
& c_Fun_Oinj__on(X4,X3,X2,X1) )
| ~ c_Fun_Obij__betw(X4,X3,X2,X1,X0) ) ),
inference(flattening,[],[f16654]) ).
fof(f16654,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Fun_Obij__betw(X4,X3,X2,X1,X0)
| hAPP(c_Set_Oimage(X4,X3,X2),X1) != X0
| ~ c_Fun_Oinj__on(X4,X3,X2,X1) )
& ( ( hAPP(c_Set_Oimage(X4,X3,X2),X1) = X0
& c_Fun_Oinj__on(X4,X3,X2,X1) )
| ~ c_Fun_Obij__betw(X4,X3,X2,X1,X0) ) ),
inference(nnf_transformation,[],[f9711]) ).
fof(f9711,plain,
! [X0,X1,X2,X3,X4] :
( c_Fun_Obij__betw(X4,X3,X2,X1,X0)
<=> ( hAPP(c_Set_Oimage(X4,X3,X2),X1) = X0
& c_Fun_Oinj__on(X4,X3,X2,X1) ) ),
inference(rectify,[],[f4829]) ).
fof(f4829,axiom,
! [X18,X9,X1,X14,X4] :
( c_Fun_Obij__betw(X4,X14,X1,X9,X18)
<=> ( hAPP(c_Set_Oimage(X4,X14,X1),X9) = X18
& c_Fun_Oinj__on(X4,X14,X1,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45716,plain,
spl647_1372,
inference(avatar_split_clause,[],[f22899,f45714]) ).
fof(f45714,plain,
( spl647_1372
<=> ! [X2,X4,X0,X3,X1] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X4),X3),X2),X1),X0) = c_New__DSequence_Oneg__single(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1372])]) ).
fof(f22899,plain,
! [X2,X3,X0,X1,X4] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X4),X3),X2),X1),X0) = c_New__DSequence_Oneg__single(X4,X3),
inference(cnf_transformation,[],[f9233]) ).
fof(f9233,plain,
! [X0,X1,X2,X3,X4] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X4),X3),X2),X1),X0) = c_New__DSequence_Oneg__single(X4,X3),
inference(rectify,[],[f4593]) ).
fof(f4593,axiom,
! [X243,X244,X245,X13,X4] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(X4),X13),X245),X244),X243) = c_New__DSequence_Oneg__single(X4,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45712,plain,
spl647_1371,
inference(avatar_split_clause,[],[f22898,f45710]) ).
fof(f45710,plain,
( spl647_1371
<=> ! [X2,X4,X0,X3,X1] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X4),X3),X2),X1),X0) = c_New__DSequence_Opos__single(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1371])]) ).
fof(f22898,plain,
! [X2,X3,X0,X1,X4] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X4),X3),X2),X1),X0) = c_New__DSequence_Opos__single(X4,X3),
inference(cnf_transformation,[],[f9232]) ).
fof(f9232,plain,
! [X0,X1,X2,X3,X4] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X4),X3),X2),X1),X0) = c_New__DSequence_Opos__single(X4,X3),
inference(rectify,[],[f4597]) ).
fof(f4597,axiom,
! [X243,X244,X245,X13,X4] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(X4),X13),X245),X244),X243) = c_New__DSequence_Opos__single(X4,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45708,plain,
spl647_1370,
inference(avatar_split_clause,[],[f22639,f45706]) ).
fof(f45706,plain,
( spl647_1370
<=> ! [X0,X3,X2,X1] :
( c_List_Olist_ONil(X3) = X0
| c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Omap(X3,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1370])]) ).
fof(f22639,plain,
! [X2,X3,X0,X1] :
( c_List_Olist_ONil(X3) = X0
| c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Omap(X3,X2),X1),X0) ),
inference(cnf_transformation,[],[f16314]) ).
fof(f16314,plain,
! [X0,X1,X2,X3] :
( ( c_List_Olist_ONil(X2) = hAPP(hAPP(c_List_Omap(X3,X2),X1),X0)
| c_List_Olist_ONil(X3) != X0 )
& ( c_List_Olist_ONil(X3) = X0
| c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Omap(X3,X2),X1),X0) ) ),
inference(nnf_transformation,[],[f9153]) ).
fof(f9153,plain,
! [X0,X1,X2,X3] :
( c_List_Olist_ONil(X2) = hAPP(hAPP(c_List_Omap(X3,X2),X1),X0)
<=> c_List_Olist_ONil(X3) = X0 ),
inference(rectify,[],[f4129]) ).
fof(f4129,axiom,
! [X203,X1,X4,X14] :
( c_List_Olist_ONil(X4) = hAPP(hAPP(c_List_Omap(X14,X4),X1),X203)
<=> c_List_Olist_ONil(X14) = X203 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45704,plain,
spl647_1369,
inference(avatar_split_clause,[],[f22637,f45702]) ).
fof(f45702,plain,
( spl647_1369
<=> ! [X0,X3,X2,X1] :
( c_List_Olist_ONil(X3) = X2
| c_List_Olist_ONil(X3) != hAPP(hAPP(c_List_Olist__update(X3,X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1369])]) ).
fof(f22637,plain,
! [X2,X3,X0,X1] :
( c_List_Olist_ONil(X3) = X2
| c_List_Olist_ONil(X3) != hAPP(hAPP(c_List_Olist__update(X3,X2),X1),X0) ),
inference(cnf_transformation,[],[f16313]) ).
fof(f16313,plain,
! [X0,X1,X2,X3] :
( ( c_List_Olist_ONil(X3) = hAPP(hAPP(c_List_Olist__update(X3,X2),X1),X0)
| c_List_Olist_ONil(X3) != X2 )
& ( c_List_Olist_ONil(X3) = X2
| c_List_Olist_ONil(X3) != hAPP(hAPP(c_List_Olist__update(X3,X2),X1),X0) ) ),
inference(nnf_transformation,[],[f9152]) ).
fof(f9152,plain,
! [X0,X1,X2,X3] :
( c_List_Olist_ONil(X3) = hAPP(hAPP(c_List_Olist__update(X3,X2),X1),X0)
<=> c_List_Olist_ONil(X3) = X2 ),
inference(rectify,[],[f3902]) ).
fof(f3902,axiom,
! [X13,X48,X203,X4] :
( c_List_Olist_ONil(X4) = hAPP(hAPP(c_List_Olist__update(X4,X203),X48),X13)
<=> c_List_Olist_ONil(X4) = X203 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45700,plain,
spl647_1368,
inference(avatar_split_clause,[],[f22624,f45698]) ).
fof(f45698,plain,
( spl647_1368
<=> ! [X0,X3,X2,X1] :
( c_List_Olist__ex1(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
| ~ sP61(X0,X2,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1368])]) ).
fof(f22624,plain,
! [X2,X3,X0,X1] :
( c_List_Olist__ex1(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
| ~ sP61(X0,X2,X3,X1) ),
inference(cnf_transformation,[],[f16304]) ).
fof(f16304,plain,
! [X0,X1,X2,X3] :
( ( c_List_Olist__ex1(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
| ~ sP61(X0,X2,X3,X1) )
& ( sP61(X0,X2,X3,X1)
| ~ c_List_Olist__ex1(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0)) ) ),
inference(nnf_transformation,[],[f14581]) ).
fof(f14581,plain,
! [X0,X1,X2,X3] :
( c_List_Olist__ex1(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
<=> sP61(X0,X2,X3,X1) ),
inference(definition_folding,[],[f13559,f14580]) ).
fof(f14580,plain,
! [X0,X2,X3,X1] :
( sP61(X0,X2,X3,X1)
<=> ( ( c_List_Olist__ex1(X3,X2,X0)
| hBOOL(hAPP(X2,X1)) )
& ( c_List_Olist__all(X3,hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),X2))),hAPP(c_fequal,X1)),X0)
| ~ hBOOL(hAPP(X2,X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP61])]) ).
fof(f13559,plain,
! [X0,X1,X2,X3] :
( c_List_Olist__ex1(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
<=> ( ( c_List_Olist__ex1(X3,X2,X0)
| hBOOL(hAPP(X2,X1)) )
& ( c_List_Olist__all(X3,hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),X2))),hAPP(c_fequal,X1)),X0)
| ~ hBOOL(hAPP(X2,X1)) ) ) ),
inference(ennf_transformation,[],[f9147]) ).
fof(f9147,plain,
! [X0,X1,X2,X3] :
( c_List_Olist__ex1(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
<=> ( ( ~ hBOOL(hAPP(X2,X1))
=> c_List_Olist__ex1(X3,X2,X0) )
& ( hBOOL(hAPP(X2,X1))
=> c_List_Olist__all(X3,hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),X2))),hAPP(c_fequal,X1)),X0) ) ) ),
inference(rectify,[],[f4577]) ).
fof(f4577,axiom,
! [X203,X13,X23,X4] :
( c_List_Olist__ex1(X4,X23,hAPP(hAPP(c_List_Olist_OCons(X4),X13),X203))
<=> ( ( ~ hBOOL(hAPP(X23,X13))
=> c_List_Olist__ex1(X4,X23,X203) )
& ( hBOOL(hAPP(X23,X13))
=> c_List_Olist__all(X4,hAPP(hAPP(c_COMBS(X4,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4),c_fNot),X23))),hAPP(c_fequal,X13)),X203) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45696,plain,
spl647_1367,
inference(avatar_split_clause,[],[f22623,f45694]) ).
fof(f45694,plain,
( spl647_1367
<=> ! [X0,X3,X2,X1] :
( sP61(X0,X2,X3,X1)
| ~ c_List_Olist__ex1(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1367])]) ).
fof(f22623,plain,
! [X2,X3,X0,X1] :
( sP61(X0,X2,X3,X1)
| ~ c_List_Olist__ex1(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0)) ),
inference(cnf_transformation,[],[f16304]) ).
fof(f45692,plain,
spl647_1366,
inference(avatar_split_clause,[],[f22602,f45690]) ).
fof(f45690,plain,
( spl647_1366
<=> ! [X0,X3,X2,X1] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
| sK483(X0,X1,X3) != sK484(X0,X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1366])]) ).
fof(f22602,plain,
! [X2,X3,X0,X1] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
| sK483(X0,X1,X3) != sK484(X0,X1,X3) ),
inference(cnf_transformation,[],[f16286]) ).
fof(f16286,plain,
! [X0,X1,X2,X3] :
( ( c_Fun_Oinj__on(X3,X2,X1,X0)
| ( sK483(X0,X1,X3) != sK484(X0,X1,X3)
& hAPP(X1,sK483(X0,X1,X3)) = hAPP(X1,sK484(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),sK484(X0,X1,X3)),X0))
& hBOOL(hAPP(hAPP(c_member(X3),sK483(X0,X1,X3)),X0)) ) )
& ( ! [X6] :
( ! [X7] :
( X6 = X7
| hAPP(X1,X6) != hAPP(X1,X7)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X7),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X0)) )
| ~ c_Fun_Oinj__on(X3,X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK483,sK484])],[f16283,f16285,f16284]) ).
fof(f16284,plain,
! [X0,X1,X3] :
( ? [X4] :
( ? [X5] :
( X4 != X5
& hAPP(X1,X5) = hAPP(X1,X4)
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) )
=> ( ? [X5] :
( sK483(X0,X1,X3) != X5
& hAPP(X1,X5) = hAPP(X1,sK483(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),sK483(X0,X1,X3)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16285,plain,
! [X0,X1,X3] :
( ? [X5] :
( sK483(X0,X1,X3) != X5
& hAPP(X1,X5) = hAPP(X1,sK483(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
=> ( sK483(X0,X1,X3) != sK484(X0,X1,X3)
& hAPP(X1,sK483(X0,X1,X3)) = hAPP(X1,sK484(X0,X1,X3))
& hBOOL(hAPP(hAPP(c_member(X3),sK484(X0,X1,X3)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f16283,plain,
! [X0,X1,X2,X3] :
( ( c_Fun_Oinj__on(X3,X2,X1,X0)
| ? [X4] :
( ? [X5] :
( X4 != X5
& hAPP(X1,X5) = hAPP(X1,X4)
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) )
& ( ! [X6] :
( ! [X7] :
( X6 = X7
| hAPP(X1,X6) != hAPP(X1,X7)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X7),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X0)) )
| ~ c_Fun_Oinj__on(X3,X2,X1,X0) ) ),
inference(rectify,[],[f16282]) ).
fof(f16282,plain,
! [X0,X1,X2,X3] :
( ( c_Fun_Oinj__on(X3,X2,X1,X0)
| ? [X4] :
( ? [X5] :
( X4 != X5
& hAPP(X1,X5) = hAPP(X1,X4)
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) )
& ( ! [X4] :
( ! [X5] :
( X4 = X5
| hAPP(X1,X5) != hAPP(X1,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) )
| ~ c_Fun_Oinj__on(X3,X2,X1,X0) ) ),
inference(nnf_transformation,[],[f13558]) ).
fof(f13558,plain,
! [X0,X1,X2,X3] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
<=> ! [X4] :
( ! [X5] :
( X4 = X5
| hAPP(X1,X5) != hAPP(X1,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) ),
inference(flattening,[],[f13557]) ).
fof(f13557,plain,
! [X0,X1,X2,X3] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
<=> ! [X4] :
( ! [X5] :
( X4 = X5
| hAPP(X1,X5) != hAPP(X1,X4)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X0)) ) ),
inference(ennf_transformation,[],[f9140]) ).
fof(f9140,plain,
! [X0,X1,X2,X3] :
( c_Fun_Oinj__on(X3,X2,X1,X0)
<=> ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X3),X4),X0))
=> ! [X5] :
( hBOOL(hAPP(hAPP(c_member(X3),X5),X0))
=> ( hAPP(X1,X5) = hAPP(X1,X4)
=> X4 = X5 ) ) ) ),
inference(rectify,[],[f3043]) ).
fof(f3043,axiom,
! [X9,X1,X14,X4] :
( c_Fun_Oinj__on(X4,X14,X1,X9)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),X9))
=> ! [X43] :
( hBOOL(hAPP(hAPP(c_member(X4),X43),X9))
=> ( hAPP(X1,X2) = hAPP(X1,X43)
=> X2 = X43 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45688,plain,
spl647_1365,
inference(avatar_split_clause,[],[f22562,f45686]) ).
fof(f45686,plain,
( spl647_1365
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK472(X0,X1,X2)),X1))
| ~ sP58(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1365])]) ).
fof(f22562,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK472(X0,X1,X2)),X1))
| ~ sP58(X0,X1,X2) ),
inference(cnf_transformation,[],[f16254]) ).
fof(f16254,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK472(X0,X1,X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X0,sK472(X0,X1,X2))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK472(X0,X1,X2)),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),sK472(X0,X1,X2))) )
| ~ sP58(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK472])],[f16252,f16253]) ).
fof(f16253,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X0,X3)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)) )
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK472(X0,X1,X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X0,sK472(X0,X1,X2))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK472(X0,X1,X2)),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),sK472(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f16252,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X3),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X0,X3)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X3)) )
| ~ sP58(X0,X1,X2) ),
inference(rectify,[],[f16251]) ).
fof(f16251,plain,
! [X1,X2,X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,X4)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)) )
| ~ sP58(X1,X2,X3) ),
inference(nnf_transformation,[],[f14574]) ).
fof(f14574,plain,
! [X1,X2,X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(X1,X4)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X3),X4)) )
| ~ sP58(X1,X2,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP58])]) ).
fof(f45684,plain,
spl647_1364,
inference(avatar_split_clause,[],[f22561,f45682]) ).
fof(f45682,plain,
( spl647_1364
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),sK472(X0,X1,X2)))
| ~ sP58(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1364])]) ).
fof(f22561,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),sK472(X0,X1,X2)))
| ~ sP58(X0,X1,X2) ),
inference(cnf_transformation,[],[f16254]) ).
fof(f45680,plain,
spl647_1363,
inference(avatar_split_clause,[],[f22391,f45678]) ).
fof(f45678,plain,
( spl647_1363
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1363])]) ).
fof(f22391,plain,
! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X0)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),X0)) ),
inference(cnf_transformation,[],[f13386]) ).
fof(f13386,plain,
! [X0,X1,X2,X3] :
( ( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X0)
& c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_HOL_Obool)))) )
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),X0)) ),
inference(ennf_transformation,[],[f8998]) ).
fof(f8998,plain,
! [X0,X1,X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),X0))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X0)
& c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X3)),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X3),tc_HOL_Obool)))) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X6,X8,X3,X4] :
( c_Hoare__Mirabelle_Ohoare__derivs(X4,X3,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),X8),X6))
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X4,X3,X6)
& c_Hoare__Mirabelle_Ohoare__derivs(X4,X3,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),X8),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45676,plain,
spl647_1362,
inference(avatar_split_clause,[],[f22275,f45674]) ).
fof(f45674,plain,
( spl647_1362
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),sK434(X0,X1,X2)),X2))
| ~ sP56(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1362])]) ).
fof(f22275,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),sK434(X0,X1,X2)),X2))
| ~ sP56(X0,X1,X2) ),
inference(cnf_transformation,[],[f16162]) ).
fof(f16162,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X0),sK434(X0,X1,X2)),sK435(X0,X1,X2))))
& hBOOL(hAPP(X1,sK435(X0,X1,X2)))
& ~ hBOOL(hAPP(hAPP(c_member(X0),sK434(X0,X1,X2)),sK435(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK434(X0,X1,X2)),X2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X0),sK435(X0,X1,X2))) )
| ~ sP56(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK434,sK435])],[f16160,f16161]) ).
fof(f16161,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X0),X3),X4)))
& hBOOL(hAPP(X1,X4))
& ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X3),X2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X4)) )
=> ( ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X0),sK434(X0,X1,X2)),sK435(X0,X1,X2))))
& hBOOL(hAPP(X1,sK435(X0,X1,X2)))
& ~ hBOOL(hAPP(hAPP(c_member(X0),sK434(X0,X1,X2)),sK435(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK434(X0,X1,X2)),X2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X0),sK435(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f16160,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X0),X3),X4)))
& hBOOL(hAPP(X1,X4))
& ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X3),X2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X4)) )
| ~ sP56(X0,X1,X2) ),
inference(rectify,[],[f16159]) ).
fof(f16159,plain,
! [X3,X0,X1] :
( ? [X4,X5] :
( ~ hBOOL(hAPP(X0,hAPP(hAPP(c_Set_Oinsert(X3),X4),X5)))
& hBOOL(hAPP(X0,X5))
& ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X5))
& hBOOL(hAPP(hAPP(c_member(X3),X4),X1))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5)) )
| ~ sP56(X3,X0,X1) ),
inference(nnf_transformation,[],[f14570]) ).
fof(f14570,plain,
! [X3,X0,X1] :
( ? [X4,X5] :
( ~ hBOOL(hAPP(X0,hAPP(hAPP(c_Set_Oinsert(X3),X4),X5)))
& hBOOL(hAPP(X0,X5))
& ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X5))
& hBOOL(hAPP(hAPP(c_member(X3),X4),X1))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X5)) )
| ~ sP56(X3,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP56])]) ).
fof(f45672,plain,
spl647_1361,
inference(avatar_split_clause,[],[f21321,f45670]) ).
fof(f45670,plain,
( spl647_1361
<=> ! [X2,X0,X1] :
( sP44(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK385(X0,X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1361])]) ).
fof(f21321,plain,
! [X2,X0,X1] :
( sP44(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK385(X0,X1,X2)),X2)) ),
inference(cnf_transformation,[],[f15876]) ).
fof(f15876,plain,
! [X0,X1,X2] :
( ( sP44(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK384(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK384(X0,X1,X2))),sK385(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK385(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
| ~ sP44(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK384,sK385])],[f15874,f15875]) ).
fof(f15875,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,sK384(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK384(X0,X1,X2))),sK385(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK385(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15874,plain,
! [X0,X1,X2] :
( ( sP44(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
| ~ sP44(X0,X1,X2) ) ),
inference(rectify,[],[f15873]) ).
fof(f15873,plain,
! [X2,X1,X0] :
( ( sP44(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
| ~ sP44(X2,X1,X0) ) ),
inference(flattening,[],[f15872]) ).
fof(f15872,plain,
! [X2,X1,X0] :
( ( sP44(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
| ~ sP44(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14549]) ).
fof(f14549,plain,
! [X2,X1,X0] :
( sP44(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,[sP44])]) ).
fof(f45668,plain,
spl647_1360,
inference(avatar_split_clause,[],[f21314,f45666]) ).
fof(f45666,plain,
( spl647_1360
<=> ! [X2,X0,X1] :
( sP41(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK383(X0,X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1360])]) ).
fof(f21314,plain,
! [X2,X0,X1] :
( sP41(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK383(X0,X1,X2)),X2)) ),
inference(cnf_transformation,[],[f15870]) ).
fof(f45664,plain,
spl647_1359,
inference(avatar_split_clause,[],[f21307,f45662]) ).
fof(f45662,plain,
( spl647_1359
<=> ! [X2,X0,X1] :
( sP42(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK381(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1359])]) ).
fof(f21307,plain,
! [X2,X0,X1] :
( sP42(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK381(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15864]) ).
fof(f45660,plain,
spl647_1358,
inference(avatar_split_clause,[],[f21243,f45658]) ).
fof(f45658,plain,
( spl647_1358
<=> ! [X2,X0,X1] :
( sP39(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK376(X0,X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1358])]) ).
fof(f21243,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK376(X0,X1,X2)),X2)) ),
inference(cnf_transformation,[],[f15824]) ).
fof(f15824,plain,
! [X0,X1,X2] :
( ( sP39(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK376(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK375(X0,X1,X2))),sK376(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK376(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
| ~ sP39(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK375,sK376])],[f15822,f15823]) ).
fof(f15823,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,sK376(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK375(X0,X1,X2))),sK376(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK376(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15822,plain,
! [X0,X1,X2] :
( ( sP39(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
| ~ sP39(X0,X1,X2) ) ),
inference(rectify,[],[f15821]) ).
fof(f15821,plain,
! [X2,X1,X0] :
( ( sP39(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
| ~ sP39(X2,X1,X0) ) ),
inference(flattening,[],[f15820]) ).
fof(f15820,plain,
! [X2,X1,X0] :
( ( sP39(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
| ~ sP39(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14541]) ).
fof(f14541,plain,
! [X2,X1,X0] :
( sP39(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,[sP39])]) ).
fof(f45656,plain,
( spl647_1357
| ~ spl647_896
| ~ spl647_1243 ),
inference(avatar_split_clause,[],[f45465,f43762,f34377,f45654]) ).
fof(f45654,plain,
( spl647_1357
<=> ! [X0] : ~ c_Nat__Transfer_Ois__nat(sK218(c_Nat__Numeral_Oneg,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1357])]) ).
fof(f34377,plain,
( spl647_896
<=> ! [X0] : hBOOL(hAPP(c_Nat__Numeral_Oneg,sK218(c_Nat__Numeral_Oneg,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_896])]) ).
fof(f45465,plain,
( ! [X0] : ~ c_Nat__Transfer_Ois__nat(sK218(c_Nat__Numeral_Oneg,X0))
| ~ spl647_896
| ~ spl647_1243 ),
inference(resolution,[],[f43763,f34378]) ).
fof(f34378,plain,
( ! [X0] : hBOOL(hAPP(c_Nat__Numeral_Oneg,sK218(c_Nat__Numeral_Oneg,X0)))
| ~ spl647_896 ),
inference(avatar_component_clause,[],[f34377]) ).
fof(f45652,plain,
spl647_1356,
inference(avatar_split_clause,[],[f21236,f45650]) ).
fof(f45650,plain,
( spl647_1356
<=> ! [X2,X0,X1] :
( sP36(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK374(X0,X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1356])]) ).
fof(f21236,plain,
! [X2,X0,X1] :
( sP36(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK374(X0,X1,X2)),X2)) ),
inference(cnf_transformation,[],[f15818]) ).
fof(f45648,plain,
spl647_1355,
inference(avatar_split_clause,[],[f21229,f45646]) ).
fof(f45646,plain,
( spl647_1355
<=> ! [X2,X0,X1] :
( sP37(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK372(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1355])]) ).
fof(f21229,plain,
! [X2,X0,X1] :
( sP37(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK372(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15813]) ).
fof(f45644,plain,
spl647_1354,
inference(avatar_split_clause,[],[f21221,f45642]) ).
fof(f45642,plain,
( spl647_1354
<=> ! [X2,X0,X1] :
( hAPP(c_List_Ofilter(X2,X1),X0) = X0
| ~ hBOOL(hAPP(X1,sK370(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1354])]) ).
fof(f21221,plain,
! [X2,X0,X1] :
( hAPP(c_List_Ofilter(X2,X1),X0) = X0
| ~ hBOOL(hAPP(X1,sK370(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15806]) ).
fof(f15806,plain,
! [X0,X1,X2] :
( ( hAPP(c_List_Ofilter(X2,X1),X0) = X0
| ( ~ hBOOL(hAPP(X1,sK370(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK370(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| hAPP(c_List_Ofilter(X2,X1),X0) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK370])],[f15804,f15805]) ).
fof(f15805,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
=> ( ~ hBOOL(hAPP(X1,sK370(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK370(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15804,plain,
! [X0,X1,X2] :
( ( hAPP(c_List_Ofilter(X2,X1),X0) = X0
| ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| hAPP(c_List_Ofilter(X2,X1),X0) != X0 ) ),
inference(rectify,[],[f15803]) ).
fof(f15803,plain,
! [X0,X1,X2] :
( ( hAPP(c_List_Ofilter(X2,X1),X0) = X0
| ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X3] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
| hAPP(c_List_Ofilter(X2,X1),X0) != X0 ) ),
inference(nnf_transformation,[],[f12610]) ).
fof(f12610,plain,
! [X0,X1,X2] :
( hAPP(c_List_Ofilter(X2,X1),X0) = X0
<=> ! [X3] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
inference(ennf_transformation,[],[f8160]) ).
fof(f8160,plain,
! [X0,X1,X2] :
( hAPP(c_List_Ofilter(X2,X1),X0) = X0
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0)))
=> hBOOL(hAPP(X1,X3)) ) ),
inference(rectify,[],[f4320]) ).
fof(f4320,axiom,
! [X203,X23,X4] :
( hAPP(c_List_Ofilter(X4,X23),X203) = X203
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X203)))
=> hBOOL(hAPP(X23,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45640,plain,
spl647_1353,
inference(avatar_split_clause,[],[f21135,f45638]) ).
fof(f45638,plain,
( spl647_1353
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| hBOOL(hAPP(hAPP(c_member(X2),sK354(X0,X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1353])]) ).
fof(f21135,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| hBOOL(hAPP(hAPP(c_member(X2),sK354(X0,X1,X2)),X1)) ),
inference(cnf_transformation,[],[f15733]) ).
fof(f15733,plain,
! [X0,X1,X2] :
( ( c_Relation_Ototal__on(X2,X1,X0)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK354(X0,X1,X2)),sK353(X0,X1,X2))),X0))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK353(X0,X1,X2)),sK354(X0,X1,X2))),X0))
& sK353(X0,X1,X2) != sK354(X0,X1,X2)
& hBOOL(hAPP(hAPP(c_member(X2),sK354(X0,X1,X2)),X1))
& hBOOL(hAPP(hAPP(c_member(X2),sK353(X0,X1,X2)),X1)) ) )
& ( ! [X5] :
( ! [X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X6),X5)),X0))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X5),X6)),X0))
| X5 = X6
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X1)) )
| ~ c_Relation_Ototal__on(X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK353,sK354])],[f15730,f15732,f15731]) ).
fof(f15731,plain,
! [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X3)),X0))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X4)),X0))
& X3 != X4
& hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) )
=> ( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),sK353(X0,X1,X2))),X0))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK353(X0,X1,X2)),X4)),X0))
& sK353(X0,X1,X2) != X4
& hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& hBOOL(hAPP(hAPP(c_member(X2),sK353(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15732,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),sK353(X0,X1,X2))),X0))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK353(X0,X1,X2)),X4)),X0))
& sK353(X0,X1,X2) != X4
& hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK354(X0,X1,X2)),sK353(X0,X1,X2))),X0))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK353(X0,X1,X2)),sK354(X0,X1,X2))),X0))
& sK353(X0,X1,X2) != sK354(X0,X1,X2)
& hBOOL(hAPP(hAPP(c_member(X2),sK354(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15730,plain,
! [X0,X1,X2] :
( ( c_Relation_Ototal__on(X2,X1,X0)
| ? [X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X3)),X0))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X4)),X0))
& X3 != X4
& hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) )
& ( ! [X5] :
( ! [X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X6),X5)),X0))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X5),X6)),X0))
| X5 = X6
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X1)) )
| ~ c_Relation_Ototal__on(X2,X1,X0) ) ),
inference(rectify,[],[f15729]) ).
fof(f15729,plain,
! [X0,X1,X2] :
( ( c_Relation_Ototal__on(X2,X1,X0)
| ? [X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X3)),X0))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X4)),X0))
& X3 != X4
& hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) )
& ( ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X3)),X0))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X4)),X0))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) )
| ~ c_Relation_Ototal__on(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f12596]) ).
fof(f12596,plain,
! [X0,X1,X2] :
( c_Relation_Ototal__on(X2,X1,X0)
<=> ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X3)),X0))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X4)),X0))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) ),
inference(flattening,[],[f12595]) ).
fof(f12595,plain,
! [X0,X1,X2] :
( c_Relation_Ototal__on(X2,X1,X0)
<=> ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X3)),X0))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X4)),X0))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) ),
inference(ennf_transformation,[],[f8137]) ).
fof(f8137,plain,
! [X0,X1,X2] :
( c_Relation_Ototal__on(X2,X1,X0)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
=> ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
=> ( X3 != X4
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),X3)),X0))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X4)),X0)) ) ) ) ) ),
inference(rectify,[],[f3655]) ).
fof(f3655,axiom,
! [X116,X9,X4] :
( c_Relation_Ototal__on(X4,X9,X116)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),X9))
=> ! [X43] :
( hBOOL(hAPP(hAPP(c_member(X4),X43),X9))
=> ( X2 != X43
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X43),X2)),X116))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X43)),X116)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45636,plain,
spl647_1352,
inference(avatar_split_clause,[],[f21134,f45634]) ).
fof(f45634,plain,
( spl647_1352
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| hBOOL(hAPP(hAPP(c_member(X2),sK353(X0,X1,X2)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1352])]) ).
fof(f21134,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| hBOOL(hAPP(hAPP(c_member(X2),sK353(X0,X1,X2)),X1)) ),
inference(cnf_transformation,[],[f15733]) ).
fof(f45632,plain,
spl647_1351,
inference(avatar_split_clause,[],[f20928,f45630]) ).
fof(f45630,plain,
( spl647_1351
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(X2,X0)
| ~ c_Wellfounded_Owf(X2,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1351])]) ).
fof(f20928,plain,
! [X2,X0,X1] :
( c_Wellfounded_Owf(X2,X0)
| ~ c_Wellfounded_Owf(X2,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X0)) ),
inference(cnf_transformation,[],[f12437]) ).
fof(f12437,plain,
! [X0,X1,X2] :
( c_Wellfounded_Owf(X2,X0)
| ~ c_Wellfounded_Owf(X2,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X0)) ),
inference(ennf_transformation,[],[f8024]) ).
fof(f8024,plain,
! [X0,X1,X2] :
( c_Wellfounded_Owf(X2,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X2,X2),tc_HOL_Obool),X1),X0))
=> c_Wellfounded_Owf(X2,X0) ),
inference(rectify,[],[f3665]) ).
fof(f3665,axiom,
! [X138,X46,X4] :
( c_Wellfounded_Owf(X4,hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),X46),X138))
=> c_Wellfounded_Owf(X4,X138) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45628,plain,
spl647_1350,
inference(avatar_split_clause,[],[f20891,f45626]) ).
fof(f20891,plain,
! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X2,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)),X1),X0)) ),
inference(cnf_transformation,[],[f12398]) ).
fof(f12398,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Ohoare__derivs(X2,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)),X1),X0)) ),
inference(ennf_transformation,[],[f7989]) ).
fof(f7989,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)),X1),X0))
=> c_Hoare__Mirabelle_Ohoare__derivs(X2,X0,X1) ),
inference(rectify,[],[f135]) ).
fof(f135,axiom,
! [X3,X6,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)),X6),X3))
=> c_Hoare__Mirabelle_Ohoare__derivs(X4,X3,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45624,plain,
spl647_1349,
inference(avatar_split_clause,[],[f20827,f45622]) ).
fof(f45622,plain,
( spl647_1349
<=> ! [X2,X0,X1] :
( sP28(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK289(X0,X1,X2)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1349])]) ).
fof(f20827,plain,
! [X2,X0,X1] :
( sP28(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK289(X0,X1,X2)),X2)) ),
inference(cnf_transformation,[],[f15575]) ).
fof(f45620,plain,
spl647_1348,
inference(avatar_split_clause,[],[f20784,f45618]) ).
fof(f45618,plain,
( spl647_1348
<=> ! [X2,X0,X1] :
( sP26(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK269(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1348])]) ).
fof(f20784,plain,
! [X2,X0,X1] :
( sP26(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK269(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15539]) ).
fof(f45616,plain,
spl647_1347,
inference(avatar_split_clause,[],[f20714,f45614]) ).
fof(f45614,plain,
( spl647_1347
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK266(X0,X1)),X1))
| ~ sP25(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1347])]) ).
fof(f20714,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK266(X0,X1)),X1))
| ~ sP25(X0,X1) ),
inference(cnf_transformation,[],[f15526]) ).
fof(f15526,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)),sK265(X0,X1)),sK266(X0,X1))
& sK265(X0,X1) != sK266(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK266(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK265(X0,X1)),X1)) )
| ~ sP25(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK265,sK266])],[f15523,f15525,f15524]) ).
fof(f15524,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)),sK265(X0,X1)),X3)
& sK265(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)),sK265(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15525,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)),sK265(X0,X1)),X3)
& sK265(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)),sK265(X0,X1)),sK266(X0,X1))
& sK265(X0,X1) != sK266(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK266(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15523,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)) )
| ~ sP25(X0,X1) ),
inference(rectify,[],[f15522]) ).
fof(f15522,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)) )
| ~ sP25(X2,X1) ),
inference(nnf_transformation,[],[f14518]) ).
fof(f14518,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)) )
| ~ sP25(X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP25])]) ).
fof(f45612,plain,
( spl647_1346
| ~ spl647_885
| ~ spl647_1243 ),
inference(avatar_split_clause,[],[f45463,f43762,f34329,f45610]) ).
fof(f45610,plain,
( spl647_1346
<=> ! [X0] : ~ c_Nat__Transfer_Ois__nat(c_Hilbert__Choice_OEps(X0,c_Nat__Numeral_Oneg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1346])]) ).
fof(f34329,plain,
( spl647_885
<=> ! [X0] : hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Hilbert__Choice_OEps(X0,c_Nat__Numeral_Oneg))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_885])]) ).
fof(f45463,plain,
( ! [X0] : ~ c_Nat__Transfer_Ois__nat(c_Hilbert__Choice_OEps(X0,c_Nat__Numeral_Oneg))
| ~ spl647_885
| ~ spl647_1243 ),
inference(resolution,[],[f43763,f34330]) ).
fof(f34330,plain,
( ! [X0] : hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Hilbert__Choice_OEps(X0,c_Nat__Numeral_Oneg)))
| ~ spl647_885 ),
inference(avatar_component_clause,[],[f34329]) ).
fof(f45608,plain,
spl647_1345,
inference(avatar_split_clause,[],[f20713,f45606]) ).
fof(f45606,plain,
( spl647_1345
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK265(X0,X1)),X1))
| ~ sP25(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1345])]) ).
fof(f20713,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK265(X0,X1)),X1))
| ~ sP25(X0,X1) ),
inference(cnf_transformation,[],[f15526]) ).
fof(f45604,plain,
spl647_1344,
inference(avatar_split_clause,[],[f20694,f45602]) ).
fof(f45602,plain,
( spl647_1344
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),sK262(X0,X1,X2)),X1))
| ~ sP23(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1344])]) ).
fof(f20694,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),sK262(X0,X1,X2)),X1))
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f15514]) ).
fof(f15514,plain,
! [X0,X1,X2] :
( ( sP23(X0,X1,X2)
| ! [X3] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(X0,sK261(X0,X1,X2,X3))
& sK261(X0,X1,X2,X3) != X3
& hBOOL(hAPP(hAPP(c_member(X2),sK261(X0,X1,X2,X3)),X1)) )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(X0,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) )
& ( ( ! [X6] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X6)
| sK262(X0,X1,X2) = X6
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1)) )
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(X0,sK262(X0,X1,X2))
& hBOOL(hAPP(hAPP(c_member(X2),sK262(X0,X1,X2)),X1)) )
| ~ sP23(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK261,sK262])],[f15511,f15513,f15512]) ).
fof(f15512,plain,
! [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_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(X0,sK261(X0,X1,X2,X3))
& sK261(X0,X1,X2,X3) != X3
& hBOOL(hAPP(hAPP(c_member(X2),sK261(X0,X1,X2,X3)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15513,plain,
! [X0,X1,X2] :
( ? [X5] :
( ! [X6] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X6)
| X5 = X6
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1)) )
& hAPP(X0,X5) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(X2),X5),X1)) )
=> ( ! [X6] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X6)
| sK262(X0,X1,X2) = X6
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1)) )
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(X0,sK262(X0,X1,X2))
& hBOOL(hAPP(hAPP(c_member(X2),sK262(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15511,plain,
! [X0,X1,X2] :
( ( sP23(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)) ) )
& ( ? [X5] :
( ! [X6] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X6)
| X5 = X6
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1)) )
& hAPP(X0,X5) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(X2),X5),X1)) )
| ~ sP23(X0,X1,X2) ) ),
inference(rectify,[],[f15510]) ).
fof(f15510,plain,
! [X0,X1,X2] :
( ( sP23(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)) ) )
& ( ? [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)) )
| ~ sP23(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14515]) ).
fof(f14515,plain,
! [X0,X1,X2] :
( sP23(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,[sP23])]) ).
fof(f45600,plain,
spl647_1343,
inference(avatar_split_clause,[],[f20682,f45598]) ).
fof(f45598,plain,
( spl647_1343
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),sK259(X0,X1,X2)),X1))
| ~ sP21(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1343])]) ).
fof(f20682,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),sK259(X0,X1,X2)),X1))
| ~ sP21(X0,X1,X2) ),
inference(cnf_transformation,[],[f15503]) ).
fof(f15503,plain,
! [X0,X1,X2] :
( ( sP21(X0,X1,X2)
| ! [X3] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(X0,sK258(X0,X1,X2,X3))
& sK258(X0,X1,X2,X3) != X3
& hBOOL(hAPP(hAPP(c_member(X2),sK258(X0,X1,X2,X3)),X1)) )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(X0,X3)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) )
& ( ( ! [X6] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X6)
| sK259(X0,X1,X2) = X6
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1)) )
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,sK259(X0,X1,X2))
& hBOOL(hAPP(hAPP(c_member(X2),sK259(X0,X1,X2)),X1)) )
| ~ sP21(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK258,sK259])],[f15500,f15502,f15501]) ).
fof(f15501,plain,
! [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_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(X0,sK258(X0,X1,X2,X3))
& sK258(X0,X1,X2,X3) != X3
& hBOOL(hAPP(hAPP(c_member(X2),sK258(X0,X1,X2,X3)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15502,plain,
! [X0,X1,X2] :
( ? [X5] :
( ! [X6] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X6)
| X5 = X6
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1)) )
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,X5)
& hBOOL(hAPP(hAPP(c_member(X2),X5),X1)) )
=> ( ! [X6] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X6)
| sK259(X0,X1,X2) = X6
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1)) )
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,sK259(X0,X1,X2))
& hBOOL(hAPP(hAPP(c_member(X2),sK259(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15500,plain,
! [X0,X1,X2] :
( ( sP21(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)) ) )
& ( ? [X5] :
( ! [X6] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X6)
| X5 = X6
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1)) )
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,X5)
& hBOOL(hAPP(hAPP(c_member(X2),X5),X1)) )
| ~ sP21(X0,X1,X2) ) ),
inference(rectify,[],[f15499]) ).
fof(f15499,plain,
! [X0,X1,X2] :
( ( sP21(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)) ) )
& ( ? [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)) )
| ~ sP21(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14512]) ).
fof(f14512,plain,
! [X0,X1,X2] :
( sP21(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,[sP21])]) ).
fof(f45596,plain,
spl647_1342,
inference(avatar_split_clause,[],[f20621,f45594]) ).
fof(f45594,plain,
( spl647_1342
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),c_Enum_On__lists(X2,X0,X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1342])]) ).
fof(f20621,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),c_Enum_On__lists(X2,X0,X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
inference(cnf_transformation,[],[f12147]) ).
fof(f12147,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),c_Enum_On__lists(X2,X0,X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
inference(ennf_transformation,[],[f7814]) ).
fof(f7814,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_List_Odistinct(X2),X1))
=> hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X2)),c_Enum_On__lists(X2,X0,X1))) ),
inference(rectify,[],[f4260]) ).
fof(f4260,axiom,
! [X44,X201,X20] :
( hBOOL(hAPP(c_List_Odistinct(X20),X201))
=> hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(X20)),c_Enum_On__lists(X20,X44,X201))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45592,plain,
spl647_1341,
inference(avatar_split_clause,[],[f20620,f45590]) ).
fof(f45590,plain,
( spl647_1341
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X2),hAPP(c_List_Ofilter(X2,X0),X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1341])]) ).
fof(f20620,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X2),hAPP(c_List_Ofilter(X2,X0),X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
inference(cnf_transformation,[],[f12146]) ).
fof(f12146,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_List_Odistinct(X2),hAPP(c_List_Ofilter(X2,X0),X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
inference(ennf_transformation,[],[f7813]) ).
fof(f7813,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_List_Odistinct(X2),X1))
=> hBOOL(hAPP(c_List_Odistinct(X2),hAPP(c_List_Ofilter(X2,X0),X1))) ),
inference(rectify,[],[f4317]) ).
fof(f4317,axiom,
! [X23,X203,X4] :
( hBOOL(hAPP(c_List_Odistinct(X4),X203))
=> hBOOL(hAPP(c_List_Odistinct(X4),hAPP(c_List_Ofilter(X4,X23),X203))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45588,plain,
spl647_1340,
inference(avatar_split_clause,[],[f20613,f45586]) ).
fof(f45586,plain,
( spl647_1340
<=> ! [X2,X0,X1] :
( c_Equiv__Relations_Oequiv(X2,X1,X0)
| ~ c_Relation_Otrans(X2,X0)
| ~ c_Relation_Osym(X2,X0)
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1340])]) ).
fof(f20613,plain,
! [X2,X0,X1] :
( c_Equiv__Relations_Oequiv(X2,X1,X0)
| ~ c_Relation_Otrans(X2,X0)
| ~ c_Relation_Osym(X2,X0)
| ~ c_Relation_Orefl__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f12139]) ).
fof(f12139,plain,
! [X0,X1,X2] :
( c_Equiv__Relations_Oequiv(X2,X1,X0)
| ~ c_Relation_Otrans(X2,X0)
| ~ c_Relation_Osym(X2,X0)
| ~ c_Relation_Orefl__on(X2,X1,X0) ),
inference(flattening,[],[f12138]) ).
fof(f12138,plain,
! [X0,X1,X2] :
( c_Equiv__Relations_Oequiv(X2,X1,X0)
| ~ c_Relation_Otrans(X2,X0)
| ~ c_Relation_Osym(X2,X0)
| ~ c_Relation_Orefl__on(X2,X1,X0) ),
inference(ennf_transformation,[],[f7806]) ).
fof(f7806,plain,
! [X0,X1,X2] :
( c_Relation_Orefl__on(X2,X1,X0)
=> ( c_Relation_Osym(X2,X0)
=> ( c_Relation_Otrans(X2,X0)
=> c_Equiv__Relations_Oequiv(X2,X1,X0) ) ) ),
inference(rectify,[],[f4763]) ).
fof(f4763,axiom,
! [X116,X9,X4] :
( c_Relation_Orefl__on(X4,X9,X116)
=> ( c_Relation_Osym(X4,X116)
=> ( c_Relation_Otrans(X4,X116)
=> c_Equiv__Relations_Oequiv(X4,X9,X116) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45584,plain,
spl647_1339,
inference(avatar_split_clause,[],[f20565,f45582]) ).
fof(f45582,plain,
( spl647_1339
<=> ! [X4,X0,X2,X1] :
( hBOOL(hAPP(X0,sK248(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,X4))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1339])]) ).
fof(f20565,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(X0,sK248(X0,X1,X2)))
| ~ hBOOL(hAPP(X0,X4))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(cnf_transformation,[],[f15482]) ).
fof(f15482,plain,
! [X0,X1,X2] :
( ( ( ( hBOOL(hAPP(X0,sK248(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK248(X0,X1,X2)),c_Quotient_ORespects(X2,X1))) )
| ! [X4] : ~ hBOOL(hAPP(X0,X4)) )
& ( hBOOL(hAPP(X0,sK249(X0)))
| ! [X6] :
( ~ hBOOL(hAPP(X0,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),c_Quotient_ORespects(X2,X1))) ) ) )
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK248,sK249])],[f15479,f15481,f15480]) ).
fof(f15480,plain,
! [X0,X1,X2] :
( ? [X3] :
( hBOOL(hAPP(X0,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),c_Quotient_ORespects(X2,X1))) )
=> ( hBOOL(hAPP(X0,sK248(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK248(X0,X1,X2)),c_Quotient_ORespects(X2,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15481,plain,
! [X0] :
( ? [X5] : hBOOL(hAPP(X0,X5))
=> hBOOL(hAPP(X0,sK249(X0))) ),
introduced(choice_axiom,[]) ).
fof(f15479,plain,
! [X0,X1,X2] :
( ( ( ? [X3] :
( hBOOL(hAPP(X0,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),c_Quotient_ORespects(X2,X1))) )
| ! [X4] : ~ hBOOL(hAPP(X0,X4)) )
& ( ? [X5] : hBOOL(hAPP(X0,X5))
| ! [X6] :
( ~ hBOOL(hAPP(X0,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),c_Quotient_ORespects(X2,X1))) ) ) )
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(rectify,[],[f15478]) ).
fof(f15478,plain,
! [X0,X1,X2] :
( ( ( ? [X3] :
( hBOOL(hAPP(X0,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),c_Quotient_ORespects(X2,X1))) )
| ! [X4] : ~ hBOOL(hAPP(X0,X4)) )
& ( ? [X4] : hBOOL(hAPP(X0,X4))
| ! [X3] :
( ~ hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),c_Quotient_ORespects(X2,X1))) ) ) )
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(nnf_transformation,[],[f12080]) ).
fof(f12080,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( hBOOL(hAPP(X0,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),c_Quotient_ORespects(X2,X1))) )
<=> ? [X4] : hBOOL(hAPP(X0,X4)) )
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(ennf_transformation,[],[f7759]) ).
fof(f7759,plain,
! [X0,X1,X2] :
( c_Equiv__Relations_Oequivp(X2,X1)
=> ( ? [X3] :
( hBOOL(hAPP(X0,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),c_Quotient_ORespects(X2,X1))) )
<=> ? [X4] : hBOOL(hAPP(X0,X4)) ) ),
inference(rectify,[],[f4851]) ).
fof(f4851,axiom,
! [X23,X138,X4] :
( c_Equiv__Relations_Oequivp(X4,X138)
=> ( ? [X2] :
( hBOOL(hAPP(X23,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),c_Quotient_ORespects(X4,X138))) )
<=> ? [X124] : hBOOL(hAPP(X23,X124)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45580,plain,
spl647_1338,
inference(avatar_split_clause,[],[f20446,f45578]) ).
fof(f45578,plain,
( spl647_1338
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X1))
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1338])]) ).
fof(f20446,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X1))
| ~ class_Lattices_Olattice(X2) ),
inference(cnf_transformation,[],[f11939]) ).
fof(f11939,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X1))
| ~ class_Lattices_Olattice(X2) ),
inference(ennf_transformation,[],[f7669]) ).
fof(f7669,plain,
! [X0,X1,X2] :
( class_Lattices_Olattice(X2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X1)) ),
inference(rectify,[],[f344]) ).
fof(f344,axiom,
! [X21,X19,X20] :
( class_Lattices_Olattice(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20),X19),X21)),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45576,plain,
spl647_1337,
inference(avatar_split_clause,[],[f20445,f45574]) ).
fof(f45574,plain,
( spl647_1337
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X0))
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1337])]) ).
fof(f20445,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X0))
| ~ class_Lattices_Olattice(X2) ),
inference(cnf_transformation,[],[f11938]) ).
fof(f11938,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X0))
| ~ class_Lattices_Olattice(X2) ),
inference(ennf_transformation,[],[f7668]) ).
fof(f7668,plain,
! [X0,X1,X2] :
( class_Lattices_Olattice(X2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X0)) ),
inference(rectify,[],[f342]) ).
fof(f342,axiom,
! [X21,X19,X20] :
( class_Lattices_Olattice(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20),X19),X21)),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45572,plain,
spl647_1336,
inference(avatar_split_clause,[],[f20444,f45570]) ).
fof(f45570,plain,
( spl647_1336
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X0),X1)))
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1336])]) ).
fof(f20444,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X0),X1)))
| ~ class_Lattices_Olattice(X2) ),
inference(cnf_transformation,[],[f11937]) ).
fof(f11937,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X0),X1)))
| ~ class_Lattices_Olattice(X2) ),
inference(ennf_transformation,[],[f7667]) ).
fof(f7667,plain,
! [X0,X1,X2] :
( class_Lattices_Olattice(X2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X0),X1))) ),
inference(rectify,[],[f171]) ).
fof(f171,axiom,
! [X19,X21,X20] :
( class_Lattices_Olattice(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20),X19),X21))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45568,plain,
spl647_1335,
inference(avatar_split_clause,[],[f20443,f45566]) ).
fof(f45566,plain,
( spl647_1335
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X0)))
| ~ class_Lattices_Olattice(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1335])]) ).
fof(f20443,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X0)))
| ~ class_Lattices_Olattice(X2) ),
inference(cnf_transformation,[],[f11936]) ).
fof(f11936,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X0)))
| ~ class_Lattices_Olattice(X2) ),
inference(ennf_transformation,[],[f7666]) ).
fof(f7666,plain,
! [X0,X1,X2] :
( class_Lattices_Olattice(X2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X0))) ),
inference(rectify,[],[f169]) ).
fof(f169,axiom,
! [X21,X19,X20] :
( class_Lattices_Olattice(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),X19),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20),X19),X21))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45564,plain,
spl647_1334,
inference(avatar_split_clause,[],[f20430,f45562]) ).
fof(f45562,plain,
( spl647_1334
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X1))
| ~ class_Lattices_Osemilattice__inf(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1334])]) ).
fof(f20430,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X1))
| ~ class_Lattices_Osemilattice__inf(X2) ),
inference(cnf_transformation,[],[f11922]) ).
fof(f11922,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X1))
| ~ class_Lattices_Osemilattice__inf(X2) ),
inference(ennf_transformation,[],[f7656]) ).
fof(f7656,plain,
! [X0,X1,X2] :
( class_Lattices_Osemilattice__inf(X2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X1)) ),
inference(rectify,[],[f343]) ).
fof(f343,axiom,
! [X21,X19,X20] :
( class_Lattices_Osemilattice__inf(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20),X19),X21)),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45560,plain,
spl647_1333,
inference(avatar_split_clause,[],[f20429,f45558]) ).
fof(f45558,plain,
( spl647_1333
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X0))
| ~ class_Lattices_Osemilattice__inf(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1333])]) ).
fof(f20429,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X0))
| ~ class_Lattices_Osemilattice__inf(X2) ),
inference(cnf_transformation,[],[f11921]) ).
fof(f11921,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X0))
| ~ class_Lattices_Osemilattice__inf(X2) ),
inference(ennf_transformation,[],[f7655]) ).
fof(f7655,plain,
! [X0,X1,X2] :
( class_Lattices_Osemilattice__inf(X2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X2),X1),X0)),X0)) ),
inference(rectify,[],[f341]) ).
fof(f341,axiom,
! [X21,X19,X20] :
( class_Lattices_Osemilattice__inf(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20),X19),X21)),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45556,plain,
spl647_1332,
inference(avatar_split_clause,[],[f20420,f45554]) ).
fof(f45554,plain,
( spl647_1332
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X0)))
| ~ class_Lattices_Osemilattice__sup(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1332])]) ).
fof(f20420,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X0)))
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(cnf_transformation,[],[f11911]) ).
fof(f11911,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X0)))
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(ennf_transformation,[],[f7647]) ).
fof(f7647,plain,
! [X0,X1,X2] :
( class_Lattices_Osemilattice__sup(X2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X0))) ),
inference(rectify,[],[f170]) ).
fof(f170,axiom,
! [X21,X19,X20] :
( class_Lattices_Osemilattice__sup(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),X19),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20),X19),X21))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45552,plain,
spl647_1331,
inference(avatar_split_clause,[],[f20419,f45550]) ).
fof(f45550,plain,
( spl647_1331
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X0),X1)))
| ~ class_Lattices_Osemilattice__sup(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1331])]) ).
fof(f20419,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X0),X1)))
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(cnf_transformation,[],[f11910]) ).
fof(f11910,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X0),X1)))
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(ennf_transformation,[],[f7646]) ).
fof(f7646,plain,
! [X0,X1,X2] :
( class_Lattices_Osemilattice__sup(X2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X0),X1))) ),
inference(rectify,[],[f172]) ).
fof(f172,axiom,
! [X19,X21,X20] :
( class_Lattices_Osemilattice__sup(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),X21),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20),X19),X21))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45548,plain,
spl647_1330,
inference(avatar_split_clause,[],[f20405,f45546]) ).
fof(f45546,plain,
( spl647_1330
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP(c_SetInterval_Oord__class_OlessThan(X2),X0) != hAPP(c_SetInterval_Oord__class_OlessThan(X2),X1)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1330])]) ).
fof(f20405,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(c_SetInterval_Oord__class_OlessThan(X2),X0) != hAPP(c_SetInterval_Oord__class_OlessThan(X2),X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f15442]) ).
fof(f15442,plain,
! [X0,X1,X2] :
( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(X2),X0) = hAPP(c_SetInterval_Oord__class_OlessThan(X2),X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_SetInterval_Oord__class_OlessThan(X2),X0) != hAPP(c_SetInterval_Oord__class_OlessThan(X2),X1) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(nnf_transformation,[],[f11897]) ).
fof(f11897,plain,
! [X0,X1,X2] :
( ( hAPP(c_SetInterval_Oord__class_OlessThan(X2),X0) = hAPP(c_SetInterval_Oord__class_OlessThan(X2),X1)
<=> X0 = X1 )
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7637]) ).
fof(f7637,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( hAPP(c_SetInterval_Oord__class_OlessThan(X2),X0) = hAPP(c_SetInterval_Oord__class_OlessThan(X2),X1)
<=> X0 = X1 ) ),
inference(rectify,[],[f2406]) ).
fof(f2406,axiom,
! [X15,X13,X4] :
( class_Orderings_Olinorder(X4)
=> ( hAPP(c_SetInterval_Oord__class_OlessThan(X4),X13) = hAPP(c_SetInterval_Oord__class_OlessThan(X4),X15)
<=> X13 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45544,plain,
spl647_1329,
inference(avatar_split_clause,[],[f20403,f45542]) ).
fof(f45542,plain,
( spl647_1329
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP(c_SetInterval_Oord__class_OatMost(X2),X1) != hAPP(c_SetInterval_Oord__class_OatMost(X2),X0)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1329])]) ).
fof(f20403,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(c_SetInterval_Oord__class_OatMost(X2),X1) != hAPP(c_SetInterval_Oord__class_OatMost(X2),X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f15441]) ).
fof(f15441,plain,
! [X0,X1,X2] :
( ( ( hAPP(c_SetInterval_Oord__class_OatMost(X2),X1) = hAPP(c_SetInterval_Oord__class_OatMost(X2),X0)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_SetInterval_Oord__class_OatMost(X2),X1) != hAPP(c_SetInterval_Oord__class_OatMost(X2),X0) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(nnf_transformation,[],[f11896]) ).
fof(f11896,plain,
! [X0,X1,X2] :
( ( hAPP(c_SetInterval_Oord__class_OatMost(X2),X1) = hAPP(c_SetInterval_Oord__class_OatMost(X2),X0)
<=> X0 = X1 )
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7636]) ).
fof(f7636,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( hAPP(c_SetInterval_Oord__class_OatMost(X2),X1) = hAPP(c_SetInterval_Oord__class_OatMost(X2),X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f2750]) ).
fof(f2750,axiom,
! [X15,X13,X4] :
( class_Orderings_Olinorder(X4)
=> ( hAPP(c_SetInterval_Oord__class_OatMost(X4),X13) = hAPP(c_SetInterval_Oord__class_OatMost(X4),X15)
<=> X13 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45540,plain,
spl647_1328,
inference(avatar_split_clause,[],[f20401,f45538]) ).
fof(f45538,plain,
( spl647_1328
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP(c_SetInterval_Oord__class_OatLeast(X2),X0) != hAPP(c_SetInterval_Oord__class_OatLeast(X2),X1)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1328])]) ).
fof(f20401,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(c_SetInterval_Oord__class_OatLeast(X2),X0) != hAPP(c_SetInterval_Oord__class_OatLeast(X2),X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f15440]) ).
fof(f15440,plain,
! [X0,X1,X2] :
( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(X2),X0) = hAPP(c_SetInterval_Oord__class_OatLeast(X2),X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_SetInterval_Oord__class_OatLeast(X2),X0) != hAPP(c_SetInterval_Oord__class_OatLeast(X2),X1) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(nnf_transformation,[],[f11895]) ).
fof(f11895,plain,
! [X0,X1,X2] :
( ( hAPP(c_SetInterval_Oord__class_OatLeast(X2),X0) = hAPP(c_SetInterval_Oord__class_OatLeast(X2),X1)
<=> X0 = X1 )
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7635]) ).
fof(f7635,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( hAPP(c_SetInterval_Oord__class_OatLeast(X2),X0) = hAPP(c_SetInterval_Oord__class_OatLeast(X2),X1)
<=> X0 = X1 ) ),
inference(rectify,[],[f2951]) ).
fof(f2951,axiom,
! [X15,X13,X4] :
( class_Orderings_Olinorder(X4)
=> ( hAPP(c_SetInterval_Oord__class_OatLeast(X4),X13) = hAPP(c_SetInterval_Oord__class_OatLeast(X4),X15)
<=> X13 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45536,plain,
spl647_1327,
inference(avatar_split_clause,[],[f20399,f45534]) ).
fof(f45534,plain,
( spl647_1327
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP(c_SetInterval_Oord__class_OgreaterThan(X2),X1) != hAPP(c_SetInterval_Oord__class_OgreaterThan(X2),X0)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1327])]) ).
fof(f20399,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(c_SetInterval_Oord__class_OgreaterThan(X2),X1) != hAPP(c_SetInterval_Oord__class_OgreaterThan(X2),X0)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f15439]) ).
fof(f15439,plain,
! [X0,X1,X2] :
( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X2),X1) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X2),X0)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_SetInterval_Oord__class_OgreaterThan(X2),X1) != hAPP(c_SetInterval_Oord__class_OgreaterThan(X2),X0) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(nnf_transformation,[],[f11894]) ).
fof(f11894,plain,
! [X0,X1,X2] :
( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X2),X1) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X2),X0)
<=> X0 = X1 )
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7634]) ).
fof(f7634,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X2),X1) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X2),X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f2881]) ).
fof(f2881,axiom,
! [X15,X13,X4] :
( class_Orderings_Olinorder(X4)
=> ( hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X13) = hAPP(c_SetInterval_Oord__class_OgreaterThan(X4),X15)
<=> X13 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45532,plain,
spl647_1326,
inference(avatar_split_clause,[],[f20246,f45530]) ).
fof(f45530,plain,
( spl647_1326
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,c_List_Olinorder__class_Oinsort__insert__key(X2,X2,c_COMBI(X2),X0,X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1326])]) ).
fof(f20246,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,c_List_Olinorder__class_Oinsort__insert__key(X2,X2,c_COMBI(X2),X0,X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f11688]) ).
fof(f11688,plain,
! [X0,X1,X2] :
( c_List_Olinorder__class_Osorted(X2,c_List_Olinorder__class_Oinsort__insert__key(X2,X2,c_COMBI(X2),X0,X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f11687]) ).
fof(f11687,plain,
! [X0,X1,X2] :
( c_List_Olinorder__class_Osorted(X2,c_List_Olinorder__class_Oinsort__insert__key(X2,X2,c_COMBI(X2),X0,X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7526]) ).
fof(f7526,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_List_Olinorder__class_Osorted(X2,X1)
=> c_List_Olinorder__class_Osorted(X2,c_List_Olinorder__class_Oinsort__insert__key(X2,X2,c_COMBI(X2),X0,X1)) ) ),
inference(rectify,[],[f4403]) ).
fof(f4403,axiom,
! [X13,X203,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_List_Olinorder__class_Osorted(X4,X203)
=> c_List_Olinorder__class_Osorted(X4,c_List_Olinorder__class_Oinsort__insert__key(X4,X4,c_COMBI(X4),X13,X203)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45528,plain,
( ~ spl647_1325
| ~ spl647_963
| ~ spl647_1243 ),
inference(avatar_split_clause,[],[f45464,f43762,f37553,f45525]) ).
fof(f45525,plain,
( spl647_1325
<=> c_Nat__Transfer_Ois__nat(sK196(c_Nat__Numeral_Oneg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1325])]) ).
fof(f37553,plain,
( spl647_963
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,sK196(c_Nat__Numeral_Oneg))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_963])]) ).
fof(f45464,plain,
( ~ c_Nat__Transfer_Ois__nat(sK196(c_Nat__Numeral_Oneg))
| ~ spl647_963
| ~ spl647_1243 ),
inference(resolution,[],[f43763,f37555]) ).
fof(f37555,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,sK196(c_Nat__Numeral_Oneg)))
| ~ spl647_963 ),
inference(avatar_component_clause,[],[f37553]) ).
fof(f45523,plain,
spl647_1324,
inference(avatar_split_clause,[],[f20219,f45521]) ).
fof(f45521,plain,
( spl647_1324
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X1),X0)),X1))
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1324])]) ).
fof(f20219,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X1),X0)),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f11651]) ).
fof(f11651,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X1),X0)),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7499]) ).
fof(f7499,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X1),X0)),X1)) ),
inference(rectify,[],[f1067]) ).
fof(f1067,axiom,
! [X21,X19,X20] :
( class_Orderings_Olinorder(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(hAPP(c_Orderings_Oord__class_Omin(X20),X19),X21)),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45519,plain,
spl647_1323,
inference(avatar_split_clause,[],[f20218,f45517]) ).
fof(f45517,plain,
( spl647_1323
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X1),X0)),X0))
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1323])]) ).
fof(f20218,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X1),X0)),X0))
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f11650]) ).
fof(f11650,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X1),X0)),X0))
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7498]) ).
fof(f7498,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Orderings_Oord__class_Omin(X2),X1),X0)),X0)) ),
inference(rectify,[],[f1068]) ).
fof(f1068,axiom,
! [X21,X19,X20] :
( class_Orderings_Olinorder(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),hAPP(hAPP(c_Orderings_Oord__class_Omin(X20),X19),X21)),X21)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45515,plain,
spl647_1322,
inference(avatar_split_clause,[],[f20217,f45513]) ).
fof(f45513,plain,
( spl647_1322
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X0),X1)))
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1322])]) ).
fof(f20217,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X0),X1)))
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f11649]) ).
fof(f11649,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X0),X1)))
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7497]) ).
fof(f7497,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X0),X1))) ),
inference(rectify,[],[f2448]) ).
fof(f2448,axiom,
! [X19,X21,X20] :
( class_Orderings_Olinorder(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),X21),hAPP(hAPP(c_Orderings_Oord__class_Omax(X20),X19),X21))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45511,plain,
spl647_1321,
inference(avatar_split_clause,[],[f20216,f45509]) ).
fof(f45509,plain,
( spl647_1321
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X1),X0)))
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1321])]) ).
fof(f20216,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X1),X0)))
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f11648]) ).
fof(f11648,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X1),X0)))
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7496]) ).
fof(f7496,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),hAPP(hAPP(c_Orderings_Oord__class_Omax(X2),X1),X0))) ),
inference(rectify,[],[f2449]) ).
fof(f2449,axiom,
! [X21,X19,X20] :
( class_Orderings_Olinorder(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),X19),hAPP(hAPP(c_Orderings_Oord__class_Omax(X20),X19),X21))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45507,plain,
spl647_1320,
inference(avatar_split_clause,[],[f20193,f45505]) ).
fof(f45505,plain,
( spl647_1320
<=> ! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0)
| ~ class_Divides_Osemiring__div(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1320])]) ).
fof(f20193,plain,
! [X2,X0,X1] :
( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(cnf_transformation,[],[f11618]) ).
fof(f11618,plain,
! [X0,X1,X2] :
( c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f7474]) ).
fof(f7474,plain,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Divides_Odiv__class_Omod(X2,X1,X0) = c_Divides_Odiv__class_Omod(X2,c_Divides_Odiv__class_Omod(X2,X1,X0),X0) ),
inference(rectify,[],[f1577]) ).
fof(f1577,axiom,
! [X25,X26,X20] :
( class_Divides_Osemiring__div(X20)
=> c_Divides_Odiv__class_Omod(X20,X26,X25) = c_Divides_Odiv__class_Omod(X20,c_Divides_Odiv__class_Omod(X20,X26,X25),X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45503,plain,
spl647_1319,
inference(avatar_split_clause,[],[f20192,f45501]) ).
fof(f45501,plain,
( spl647_1319
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
| ~ class_Divides_Osemiring__div(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1319])]) ).
fof(f20192,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
| ~ class_Divides_Osemiring__div(X2) ),
inference(cnf_transformation,[],[f11617]) ).
fof(f11617,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1)
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f7473]) ).
fof(f7473,plain,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X1) ),
inference(rectify,[],[f1635]) ).
fof(f1635,axiom,
! [X26,X25,X20] :
( class_Divides_Osemiring__div(X20)
=> c_Groups_Ozero__class_Ozero(X20) = c_Divides_Odiv__class_Omod(X20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),X25),X26),X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45499,plain,
spl647_1318,
inference(avatar_split_clause,[],[f20191,f45497]) ).
fof(f45497,plain,
( spl647_1318
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0)
| ~ class_Divides_Osemiring__div(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1318])]) ).
fof(f20191,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(cnf_transformation,[],[f11616]) ).
fof(f11616,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f7472]) ).
fof(f7472,plain,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Groups_Ozero__class_Ozero(X2) = c_Divides_Odiv__class_Omod(X2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0),X0) ),
inference(rectify,[],[f1634]) ).
fof(f1634,axiom,
! [X25,X26,X20] :
( class_Divides_Osemiring__div(X20)
=> c_Groups_Ozero__class_Ozero(X20) = c_Divides_Odiv__class_Omod(X20,hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),X26),X25),X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45495,plain,
spl647_1317,
inference(avatar_split_clause,[],[f20190,f45493]) ).
fof(f45493,plain,
( spl647_1317
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),c_Divides_Odiv__class_Omod(X2,X1,X0)),X0)
| ~ class_Divides_Osemiring__div(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1317])]) ).
fof(f20190,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),c_Divides_Odiv__class_Omod(X2,X1,X0)),X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(cnf_transformation,[],[f11615]) ).
fof(f11615,plain,
! [X0,X1,X2] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),c_Divides_Odiv__class_Omod(X2,X1,X0)),X0)
| ~ class_Divides_Osemiring__div(X2) ),
inference(ennf_transformation,[],[f7471]) ).
fof(f7471,plain,
! [X0,X1,X2] :
( class_Divides_Osemiring__div(X2)
=> c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X2),c_Divides_Odiv__class_Omod(X2,X1,X0)),X0) ),
inference(rectify,[],[f1575]) ).
fof(f1575,axiom,
! [X25,X26,X20] :
( class_Divides_Osemiring__div(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20),c_Divides_Odiv__class_Omod(X20,X26,X25)),X25) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45491,plain,
spl647_1316,
inference(avatar_split_clause,[],[f20180,f45489]) ).
fof(f45489,plain,
( spl647_1316
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
| ~ class_Rings_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1316])]) ).
fof(f20180,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f11605]) ).
fof(f11605,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f7461]) ).
fof(f7461,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0))) ),
inference(rectify,[],[f4978]) ).
fof(f4978,axiom,
! [X25,X26,X20] :
( class_Rings_Ocomm__semiring__1(X20)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X20),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),X26),X25))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45487,plain,
spl647_1315,
inference(avatar_split_clause,[],[f20179,f45485]) ).
fof(f45485,plain,
( spl647_1315
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)))
| ~ class_Rings_Ocomm__semiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1315])]) ).
fof(f20179,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(cnf_transformation,[],[f11604]) ).
fof(f11604,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1)))
| ~ class_Rings_Ocomm__semiring__1(X2) ),
inference(ennf_transformation,[],[f7460]) ).
fof(f7460,plain,
! [X0,X1,X2] :
( class_Rings_Ocomm__semiring__1(X2)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X2),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X0),X1))) ),
inference(rectify,[],[f4977]) ).
fof(f4977,axiom,
! [X25,X26,X20] :
( class_Rings_Ocomm__semiring__1(X20)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X20),X26),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),X25),X26))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45457,plain,
spl647_1314,
inference(avatar_split_clause,[],[f20107,f45455]) ).
fof(f45455,plain,
( spl647_1314
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X0)
| ~ class_Nat_Osemiring__char__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1314])]) ).
fof(f20107,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X0)
| ~ class_Nat_Osemiring__char__0(X2) ),
inference(cnf_transformation,[],[f15373]) ).
fof(f15373,plain,
! [X0,X1,X2] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X0)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X0) ) )
| ~ class_Nat_Osemiring__char__0(X2) ),
inference(nnf_transformation,[],[f11497]) ).
fof(f11497,plain,
! [X0,X1,X2] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X0)
<=> X0 = X1 )
| ~ class_Nat_Osemiring__char__0(X2) ),
inference(ennf_transformation,[],[f7395]) ).
fof(f7395,plain,
! [X0,X1,X2] :
( class_Nat_Osemiring__char__0(X2)
=> ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X2),X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f1217]) ).
fof(f1217,axiom,
! [X46,X47,X4] :
( class_Nat_Osemiring__char__0(X4)
=> ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X47) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X46)
<=> X46 = X47 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45453,plain,
spl647_1313,
inference(avatar_split_clause,[],[f20086,f45451]) ).
fof(f45451,plain,
( spl647_1313
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X0)
| ~ class_Lattices_Oboolean__algebra(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1313])]) ).
fof(f20086,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X0)
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(cnf_transformation,[],[f15363]) ).
fof(f15363,plain,
! [X0,X1,X2] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X0)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X0) ) )
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(nnf_transformation,[],[f11476]) ).
fof(f11476,plain,
! [X0,X1,X2] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X0)
<=> X0 = X1 )
| ~ class_Lattices_Oboolean__algebra(X2) ),
inference(ennf_transformation,[],[f7380]) ).
fof(f7380,plain,
! [X0,X1,X2] :
( class_Lattices_Oboolean__algebra(X2)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f1419]) ).
fof(f1419,axiom,
! [X15,X13,X4] :
( class_Lattices_Oboolean__algebra(X4)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X4),X13) = hAPP(c_Groups_Ouminus__class_Ouminus(X4),X15)
<=> X13 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45449,plain,
spl647_1312,
inference(avatar_split_clause,[],[f20073,f45447]) ).
fof(f45447,plain,
( spl647_1312
<=> ! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X0
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X0) != X1
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1312])]) ).
fof(f20073,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = X0
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X0) != X1
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(cnf_transformation,[],[f15358]) ).
fof(f15358,plain,
! [X0,X1,X2] :
( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X0) = X1
| c_Groups_Ozero__class_Ozero(X2) != X0 )
& ( c_Groups_Ozero__class_Ozero(X2) = X0
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X0) != X1 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(nnf_transformation,[],[f11466]) ).
fof(f11466,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X0) = X1
<=> c_Groups_Ozero__class_Ozero(X2) = X0 )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(ennf_transformation,[],[f7372]) ).
fof(f7372,plain,
! [X0,X1,X2] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X0) = X1
<=> c_Groups_Ozero__class_Ozero(X2) = X0 ) ),
inference(rectify,[],[f748]) ).
fof(f748,axiom,
! [X5,X12,X4] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X4)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X12),X5) = X12
<=> c_Groups_Ozero__class_Ozero(X4) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45445,plain,
spl647_1311,
inference(avatar_split_clause,[],[f19972,f45443]) ).
fof(f45443,plain,
( spl647_1311
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0)
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1311])]) ).
fof(f19972,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0)
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f15334]) ).
fof(f15334,plain,
! [X0,X1,X2] :
( ( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0)
| X0 != X1 )
& ( X0 = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0) ) )
| ~ class_Groups_Ogroup__add(X2) ),
inference(nnf_transformation,[],[f11375]) ).
fof(f11375,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0)
<=> X0 = X1 )
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f7297]) ).
fof(f7297,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f763]) ).
fof(f763,axiom,
! [X12,X5,X4] :
( class_Groups_Ogroup__add(X4)
=> ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X5),X12) = c_Groups_Ozero__class_Ozero(X4)
<=> X5 = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45441,plain,
spl647_1310,
inference(avatar_split_clause,[],[f19970,f45439]) ).
fof(f45439,plain,
( spl647_1310
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X0)
| ~ class_Groups_Ogroup__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1310])]) ).
fof(f19970,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X0)
| ~ class_Groups_Ogroup__add(X2) ),
inference(cnf_transformation,[],[f15333]) ).
fof(f15333,plain,
! [X0,X1,X2] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X0)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) != hAPP(c_Groups_Ouminus__class_Ouminus(X2),X0) ) )
| ~ class_Groups_Ogroup__add(X2) ),
inference(nnf_transformation,[],[f11374]) ).
fof(f11374,plain,
! [X0,X1,X2] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X0)
<=> X0 = X1 )
| ~ class_Groups_Ogroup__add(X2) ),
inference(ennf_transformation,[],[f7296]) ).
fof(f7296,plain,
! [X0,X1,X2] :
( class_Groups_Ogroup__add(X2)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X2),X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X2),X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f1423]) ).
fof(f1423,axiom,
! [X12,X5,X4] :
( class_Groups_Ogroup__add(X4)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X4),X12) = hAPP(c_Groups_Ouminus__class_Ouminus(X4),X5)
<=> X5 = X12 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45437,plain,
spl647_1309,
inference(avatar_split_clause,[],[f19955,f45435]) ).
fof(f45435,plain,
( spl647_1309
<=> ! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0)
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1309])]) ).
fof(f19955,plain,
! [X2,X0,X1] :
( X0 = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0)
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f15329]) ).
fof(f15329,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| c_Groups_Ozero__class_Ozero(X2) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0) )
& ( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0)
| X0 != X1 ) )
| ~ class_Groups_Oab__group__add(X2) ),
inference(nnf_transformation,[],[f11361]) ).
fof(f11361,plain,
! [X0,X1,X2] :
( ( X0 = X1
<=> c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0) )
| ~ class_Groups_Oab__group__add(X2) ),
inference(ennf_transformation,[],[f7284]) ).
fof(f7284,plain,
! [X0,X1,X2] :
( class_Groups_Oab__group__add(X2)
=> ( X0 = X1
<=> c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0) ) ),
inference(rectify,[],[f764]) ).
fof(f764,axiom,
! [X12,X5,X4] :
( class_Groups_Oab__group__add(X4)
=> ( X5 = X12
<=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X4),X5),X12) = c_Groups_Ozero__class_Ozero(X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45433,plain,
spl647_1308,
inference(avatar_split_clause,[],[f19915,f45431]) ).
fof(f45431,plain,
( spl647_1308
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) != hAPP(c_Int_Oring__1__class_Oof__int(X2),X0)
| ~ class_Int_Oring__char__0(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1308])]) ).
fof(f19915,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) != hAPP(c_Int_Oring__1__class_Oof__int(X2),X0)
| ~ class_Int_Oring__char__0(X2) ),
inference(cnf_transformation,[],[f15312]) ).
fof(f15312,plain,
! [X0,X1,X2] :
( ( ( hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = hAPP(c_Int_Oring__1__class_Oof__int(X2),X0)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) != hAPP(c_Int_Oring__1__class_Oof__int(X2),X0) ) )
| ~ class_Int_Oring__char__0(X2) ),
inference(nnf_transformation,[],[f11344]) ).
fof(f11344,plain,
! [X0,X1,X2] :
( ( hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = hAPP(c_Int_Oring__1__class_Oof__int(X2),X0)
<=> X0 = X1 )
| ~ class_Int_Oring__char__0(X2) ),
inference(ennf_transformation,[],[f7268]) ).
fof(f7268,plain,
! [X0,X1,X2] :
( class_Int_Oring__char__0(X2)
=> ( hAPP(c_Int_Oring__1__class_Oof__int(X2),X1) = hAPP(c_Int_Oring__1__class_Oof__int(X2),X0)
<=> X0 = X1 ) ),
inference(rectify,[],[f2025]) ).
fof(f2025,axiom,
! [X17,X59,X4] :
( class_Int_Oring__char__0(X4)
=> ( hAPP(c_Int_Oring__1__class_Oof__int(X4),X59) = hAPP(c_Int_Oring__1__class_Oof__int(X4),X17)
<=> X17 = X59 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45429,plain,
spl647_1307,
inference(avatar_split_clause,[],[f19890,f45427]) ).
fof(f45427,plain,
( spl647_1307
<=> ! [X4,X0,X2,X1] :
( c_FunDef_OTHE__default(X1,X0,X2) = X0
| sK220(X2) = X4
| ~ hBOOL(hAPP(X2,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1307])]) ).
fof(f19890,plain,
! [X2,X0,X1,X4] :
( c_FunDef_OTHE__default(X1,X0,X2) = X0
| sK220(X2) = X4
| ~ hBOOL(hAPP(X2,X4)) ),
inference(cnf_transformation,[],[f15305]) ).
fof(f15305,plain,
! [X0,X1,X2] :
( ( c_FunDef_OTHE__default(X1,X0,X2) = X0
| ( ! [X4] :
( sK220(X2) = X4
| ~ hBOOL(hAPP(X2,X4)) )
& hBOOL(hAPP(X2,sK220(X2))) ) )
& ( c_FunDef_OTHE__default(X1,X0,X2) = c_HOL_OThe(X1,X2)
| ! [X5] :
( ( sK221(X2,X5) != X5
& hBOOL(hAPP(X2,sK221(X2,X5))) )
| ~ hBOOL(hAPP(X2,X5)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK220,sK221])],[f11323,f15304,f15303]) ).
fof(f15303,plain,
! [X2] :
( ? [X3] :
( ! [X4] :
( X3 = X4
| ~ hBOOL(hAPP(X2,X4)) )
& hBOOL(hAPP(X2,X3)) )
=> ( ! [X4] :
( sK220(X2) = X4
| ~ hBOOL(hAPP(X2,X4)) )
& hBOOL(hAPP(X2,sK220(X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15304,plain,
! [X2,X5] :
( ? [X6] :
( X5 != X6
& hBOOL(hAPP(X2,X6)) )
=> ( sK221(X2,X5) != X5
& hBOOL(hAPP(X2,sK221(X2,X5))) ) ),
introduced(choice_axiom,[]) ).
fof(f11323,plain,
! [X0,X1,X2] :
( ( c_FunDef_OTHE__default(X1,X0,X2) = X0
| ? [X3] :
( ! [X4] :
( X3 = X4
| ~ hBOOL(hAPP(X2,X4)) )
& hBOOL(hAPP(X2,X3)) ) )
& ( c_FunDef_OTHE__default(X1,X0,X2) = c_HOL_OThe(X1,X2)
| ! [X5] :
( ? [X6] :
( X5 != X6
& hBOOL(hAPP(X2,X6)) )
| ~ hBOOL(hAPP(X2,X5)) ) ) ),
inference(ennf_transformation,[],[f7221]) ).
fof(f7221,plain,
! [X0,X1,X2] :
( ( ~ ? [X3] :
( ! [X4] :
( hBOOL(hAPP(X2,X4))
=> X3 = X4 )
& hBOOL(hAPP(X2,X3)) )
=> c_FunDef_OTHE__default(X1,X0,X2) = X0 )
& ( ? [X5] :
( ! [X6] :
( hBOOL(hAPP(X2,X6))
=> X5 = X6 )
& hBOOL(hAPP(X2,X5)) )
=> c_FunDef_OTHE__default(X1,X0,X2) = c_HOL_OThe(X1,X2) ) ),
inference(rectify,[],[f4673]) ).
fof(f4673,axiom,
! [X10,X4,X23] :
( ( ~ ? [X2] :
( ! [X38] :
( hBOOL(hAPP(X23,X38))
=> X2 = X38 )
& hBOOL(hAPP(X23,X2)) )
=> c_FunDef_OTHE__default(X4,X10,X23) = X10 )
& ( ? [X2] :
( ! [X38] :
( hBOOL(hAPP(X23,X38))
=> X2 = X38 )
& hBOOL(hAPP(X23,X2)) )
=> c_HOL_OThe(X4,X23) = c_FunDef_OTHE__default(X4,X10,X23) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45425,plain,
spl647_1306,
inference(avatar_split_clause,[],[f19624,f45423]) ).
fof(f45423,plain,
( spl647_1306
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1306])]) ).
fof(f19624,plain,
! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),X1))),
inference(cnf_transformation,[],[f6978]) ).
fof(f6978,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),X1))),
inference(rectify,[],[f132]) ).
fof(f132,axiom,
! [X5,X18,X4] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X18),hAPP(hAPP(c_Set_Oinsert(X4),X5),X18))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45421,plain,
spl647_1305,
inference(avatar_split_clause,[],[f19622,f45419]) ).
fof(f45419,plain,
( spl647_1305
<=> ! [X2,X0,X1] : hAPP(hAPP(c_List_Olist__update(X2,X1),X0),hAPP(hAPP(c_List_Onth(X2),X1),X0)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1305])]) ).
fof(f19622,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Olist__update(X2,X1),X0),hAPP(hAPP(c_List_Onth(X2),X1),X0)) = X1,
inference(cnf_transformation,[],[f6976]) ).
fof(f6976,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Olist__update(X2,X1),X0),hAPP(hAPP(c_List_Onth(X2),X1),X0)) = X1,
inference(rectify,[],[f3836]) ).
fof(f3836,axiom,
! [X55,X201,X20] : hAPP(hAPP(c_List_Olist__update(X20,X201),X55),hAPP(hAPP(c_List_Onth(X20),X201),X55)) = X201,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45417,plain,
( spl647_1304
| spl647_327
| ~ spl647_1127 ),
inference(avatar_split_clause,[],[f41809,f40689,f30799,f45414]) ).
fof(f45414,plain,
( spl647_1304
<=> c_List_Olist_ONil(tc_Int_Oint) = c_List_Oupto(c_Int_OPls,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1304])]) ).
fof(f30799,plain,
( spl647_327
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_327])]) ).
fof(f40689,plain,
( spl647_1127
<=> ! [X0,X1] :
( c_List_Olist_ONil(tc_Int_Oint) = c_List_Oupto(X1,X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1127])]) ).
fof(f41809,plain,
( c_List_Olist_ONil(tc_Int_Oint) = c_List_Oupto(c_Int_OPls,c_Int_OMin)
| spl647_327
| ~ spl647_1127 ),
inference(resolution,[],[f40690,f30801]) ).
fof(f30801,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| spl647_327 ),
inference(avatar_component_clause,[],[f30799]) ).
fof(f40690,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0))
| c_List_Olist_ONil(tc_Int_Oint) = c_List_Oupto(X1,X0) )
| ~ spl647_1127 ),
inference(avatar_component_clause,[],[f40689]) ).
fof(f45412,plain,
spl647_1303,
inference(avatar_split_clause,[],[f19620,f45410]) ).
fof(f45410,plain,
( spl647_1303
<=> ! [X2,X0,X1] : hAPP(hAPP(c_List_Odrop(X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1303])]) ).
fof(f19620,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Odrop(X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X0,
inference(cnf_transformation,[],[f6974]) ).
fof(f6974,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Odrop(X2),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X0,
inference(rectify,[],[f3990]) ).
fof(f3990,axiom,
! [X201,X19,X20] : hAPP(hAPP(c_List_Odrop(X20),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(X20),X19),X201)) = X201,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45408,plain,
spl647_1302,
inference(avatar_split_clause,[],[f19619,f45406]) ).
fof(f45406,plain,
( spl647_1302
<=> ! [X2,X0,X1] : c_Lazy__Sequence_Oflat(X2,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(X2),X1,X0)) = c_Lazy__Sequence_Oappend(X2,X1,c_Lazy__Sequence_Oflat(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1302])]) ).
fof(f19619,plain,
! [X2,X0,X1] : c_Lazy__Sequence_Oflat(X2,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(X2),X1,X0)) = c_Lazy__Sequence_Oappend(X2,X1,c_Lazy__Sequence_Oflat(X2,X0)),
inference(cnf_transformation,[],[f6973]) ).
fof(f6973,plain,
! [X0,X1,X2] : c_Lazy__Sequence_Oflat(X2,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(X2),X1,X0)) = c_Lazy__Sequence_Oappend(X2,X1,c_Lazy__Sequence_Oflat(X2,X0)),
inference(rectify,[],[f4865]) ).
fof(f4865,axiom,
! [X276,X254,X20] : c_Lazy__Sequence_Oflat(X20,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(X20),X254,X276)) = c_Lazy__Sequence_Oappend(X20,X254,c_Lazy__Sequence_Oflat(X20,X276)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45404,plain,
spl647_1301,
inference(avatar_split_clause,[],[f19617,f45402]) ).
fof(f45402,plain,
( spl647_1301
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X2,X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1301])]) ).
fof(f19617,plain,
! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X2,X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(cnf_transformation,[],[f6971]) ).
fof(f6971,plain,
! [X0,X1,X2] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X2,X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(rectify,[],[f2842]) ).
fof(f2842,axiom,
! [X1,X4,X14] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X14,X4,X1),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45400,plain,
spl647_1300,
inference(avatar_split_clause,[],[f19616,f45398]) ).
fof(f45398,plain,
( spl647_1300
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Relation_OImage(X2,X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1300])]) ).
fof(f19616,plain,
! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Relation_OImage(X2,X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(cnf_transformation,[],[f6970]) ).
fof(f6970,plain,
! [X0,X1,X2] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Relation_OImage(X2,X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(rectify,[],[f2977]) ).
fof(f2977,axiom,
! [X138,X4,X14] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Relation_OImage(X14,X4,X138),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45396,plain,
spl647_1299,
inference(avatar_split_clause,[],[f19615,f45394]) ).
fof(f45394,plain,
( spl647_1299
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = hAPP(c_Set_Ovimage(X2,X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1299])]) ).
fof(f19615,plain,
! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = hAPP(c_Set_Ovimage(X2,X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(cnf_transformation,[],[f6969]) ).
fof(f6969,plain,
! [X0,X1,X2] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = hAPP(c_Set_Ovimage(X2,X1,X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(rectify,[],[f3135]) ).
fof(f3135,axiom,
! [X1,X14,X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Set_Ovimage(X4,X14,X1),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45392,plain,
spl647_1298,
inference(avatar_split_clause,[],[f19614,f45390]) ).
fof(f45390,plain,
( spl647_1298
<=> ! [X2,X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) = hAPP(c_Set_Ovimage(X2,X1,X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1298])]) ).
fof(f19614,plain,
! [X2,X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) = hAPP(c_Set_Ovimage(X2,X1,X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(cnf_transformation,[],[f6968]) ).
fof(f6968,plain,
! [X0,X1,X2] : c_Orderings_Otop__class_Otop(tc_fun(X2,tc_HOL_Obool)) = hAPP(c_Set_Ovimage(X2,X1,X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),
inference(rectify,[],[f3141]) ).
fof(f3141,axiom,
! [X1,X14,X4] : c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Set_Ovimage(X4,X14,X1),c_Orderings_Otop__class_Otop(tc_fun(X14,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45388,plain,
spl647_1297,
inference(avatar_split_clause,[],[f19229,f45386]) ).
fof(f45386,plain,
( spl647_1297
<=> ! [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)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1297])]) ).
fof(f19229,plain,
! [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(cnf_transformation,[],[f15077]) ).
fof(f15077,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,[],[f15076]) ).
fof(f15076,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,[],[f6796]) ).
fof(f6796,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,[],[f1163]) ).
fof(f1163,axiom,
! [X59,X17] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X17),X59))
<=> ( X17 != X59
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X17),X59)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45384,plain,
spl647_1296,
inference(avatar_split_clause,[],[f19124,f45382]) ).
fof(f45382,plain,
( spl647_1296
<=> ! [X0,X1] :
( sP5(X0,X1)
| hBOOL(hAPP(hAPP(c_member(X0),sK185(X0,X1)),sK183(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1296])]) ).
fof(f19124,plain,
! [X0,X1] :
( sP5(X0,X1)
| hBOOL(hAPP(hAPP(c_member(X0),sK185(X0,X1)),sK183(X0,X1))) ),
inference(cnf_transformation,[],[f14997]) ).
fof(f14997,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ( ! [X3] :
( ( hBOOL(hAPP(hAPP(c_member(X0),sK184(X0,X1,X3)),sK183(X0,X1)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK184(X0,X1,X3)),X3)),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(X0),X3),sK183(X0,X1))) )
& hBOOL(hAPP(hAPP(c_member(X0),sK185(X0,X1)),sK183(X0,X1))) ) )
& ( ! [X6] :
( ( ! [X8] :
( ~ hBOOL(hAPP(hAPP(c_member(X0),X8),X6))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X8),sK186(X0,X1,X6))),X1)) )
& hBOOL(hAPP(hAPP(c_member(X0),sK186(X0,X1,X6)),X6)) )
| ! [X9] : ~ hBOOL(hAPP(hAPP(c_member(X0),X9),X6)) )
| ~ sP5(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK183,sK184,sK185,sK186])],[f14992,f14996,f14995,f14994,f14993]) ).
fof(f14993,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_member(X0),X4),X2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X4),X3)),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X2)) )
& ? [X5] : hBOOL(hAPP(hAPP(c_member(X0),X5),X2)) )
=> ( ! [X3] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_member(X0),X4),sK183(X0,X1)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X4),X3)),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(X0),X3),sK183(X0,X1))) )
& ? [X5] : hBOOL(hAPP(hAPP(c_member(X0),X5),sK183(X0,X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f14994,plain,
! [X0,X1,X3] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_member(X0),X4),sK183(X0,X1)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X4),X3)),X1)) )
=> ( hBOOL(hAPP(hAPP(c_member(X0),sK184(X0,X1,X3)),sK183(X0,X1)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK184(X0,X1,X3)),X3)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f14995,plain,
! [X0,X1] :
( ? [X5] : hBOOL(hAPP(hAPP(c_member(X0),X5),sK183(X0,X1)))
=> hBOOL(hAPP(hAPP(c_member(X0),sK185(X0,X1)),sK183(X0,X1))) ),
introduced(choice_axiom,[]) ).
fof(f14996,plain,
! [X0,X1,X6] :
( ? [X7] :
( ! [X8] :
( ~ hBOOL(hAPP(hAPP(c_member(X0),X8),X6))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X8),X7)),X1)) )
& hBOOL(hAPP(hAPP(c_member(X0),X7),X6)) )
=> ( ! [X8] :
( ~ hBOOL(hAPP(hAPP(c_member(X0),X8),X6))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X8),sK186(X0,X1,X6))),X1)) )
& hBOOL(hAPP(hAPP(c_member(X0),sK186(X0,X1,X6)),X6)) ) ),
introduced(choice_axiom,[]) ).
fof(f14992,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ? [X2] :
( ! [X3] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_member(X0),X4),X2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X4),X3)),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X2)) )
& ? [X5] : hBOOL(hAPP(hAPP(c_member(X0),X5),X2)) ) )
& ( ! [X6] :
( ? [X7] :
( ! [X8] :
( ~ hBOOL(hAPP(hAPP(c_member(X0),X8),X6))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X8),X7)),X1)) )
& hBOOL(hAPP(hAPP(c_member(X0),X7),X6)) )
| ! [X9] : ~ hBOOL(hAPP(hAPP(c_member(X0),X9),X6)) )
| ~ sP5(X0,X1) ) ),
inference(rectify,[],[f14991]) ).
fof(f14991,plain,
! [X1,X0] :
( ( sP5(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)) ) )
& ( ! [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)) )
| ~ sP5(X1,X0) ) ),
inference(nnf_transformation,[],[f14484]) ).
fof(f14484,plain,
! [X1,X0] :
( sP5(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,[sP5])]) ).
fof(f45380,plain,
spl647_1295,
inference(avatar_split_clause,[],[f19121,f45378]) ).
fof(f45378,plain,
( spl647_1295
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_member(X1),sK182(X0,X1)),c_Wellfounded_Oacc(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1295])]) ).
fof(f19121,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_member(X1),sK182(X0,X1)),c_Wellfounded_Oacc(X1,X0))) ),
inference(cnf_transformation,[],[f14990]) ).
fof(f14990,plain,
! [X0,X1] :
( ( c_Wellfounded_Owf(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_member(X1),sK182(X0,X1)),c_Wellfounded_Oacc(X1,X0))) )
& ( ! [X3] : hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X0)))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK182])],[f14988,f14989]) ).
fof(f14989,plain,
! [X0,X1] :
( ? [X2] : ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X0)))
=> ~ hBOOL(hAPP(hAPP(c_member(X1),sK182(X0,X1)),c_Wellfounded_Oacc(X1,X0))) ),
introduced(choice_axiom,[]) ).
fof(f14988,plain,
! [X0,X1] :
( ( c_Wellfounded_Owf(X1,X0)
| ? [X2] : ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X0))) )
& ( ! [X3] : hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X0)))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
inference(rectify,[],[f14987]) ).
fof(f14987,plain,
! [X0,X1] :
( ( c_Wellfounded_Owf(X1,X0)
| ? [X2] : ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X0))) )
& ( ! [X2] : hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X0)))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
inference(nnf_transformation,[],[f6759]) ).
fof(f6759,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> ! [X2] : hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X0))) ),
inference(rectify,[],[f3381]) ).
fof(f3381,axiom,
! [X116,X4] :
( c_Wellfounded_Owf(X4,X116)
<=> ! [X2] : hBOOL(hAPP(hAPP(c_member(X4),X2),c_Wellfounded_Oacc(X4,X116))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45376,plain,
spl647_1294,
inference(avatar_split_clause,[],[f19076,f45374]) ).
fof(f45374,plain,
( spl647_1294
<=> ! [X4,X0,X3] :
( hBOOL(hAPP(hAPP(X0,X4),X4))
| ~ hBOOL(hAPP(hAPP(X0,X3),X4))
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1294])]) ).
fof(f19076,plain,
! [X3,X0,X4] :
( hBOOL(hAPP(hAPP(X0,X4),X4))
| ~ hBOOL(hAPP(hAPP(X0,X3),X4))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f14944]) ).
fof(f14944,plain,
! [X0] :
( ( sP4(X0)
| ( ( hAPP(X0,sK167(X0)) != hAPP(X0,sK166(X0))
| ~ hBOOL(hAPP(hAPP(X0,sK167(X0)),sK167(X0)))
| ~ hBOOL(hAPP(hAPP(X0,sK166(X0)),sK166(X0)))
| ~ hBOOL(hAPP(hAPP(X0,sK166(X0)),sK167(X0))) )
& ( ( hAPP(X0,sK167(X0)) = hAPP(X0,sK166(X0))
& hBOOL(hAPP(hAPP(X0,sK167(X0)),sK167(X0)))
& hBOOL(hAPP(hAPP(X0,sK166(X0)),sK166(X0))) )
| hBOOL(hAPP(hAPP(X0,sK166(X0)),sK167(X0))) ) ) )
& ( ! [X3,X4] :
( ( hBOOL(hAPP(hAPP(X0,X3),X4))
| hAPP(X0,X4) != hAPP(X0,X3)
| ~ hBOOL(hAPP(hAPP(X0,X4),X4))
| ~ hBOOL(hAPP(hAPP(X0,X3),X3)) )
& ( ( hAPP(X0,X4) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(X0,X4),X4))
& hBOOL(hAPP(hAPP(X0,X3),X3)) )
| ~ hBOOL(hAPP(hAPP(X0,X3),X4)) ) )
| ~ sP4(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK166,sK167])],[f14942,f14943]) ).
fof(f14943,plain,
! [X0] :
( ? [X1,X2] :
( ( hAPP(X0,X2) != hAPP(X0,X1)
| ~ hBOOL(hAPP(hAPP(X0,X2),X2))
| ~ hBOOL(hAPP(hAPP(X0,X1),X1))
| ~ hBOOL(hAPP(hAPP(X0,X1),X2)) )
& ( ( hAPP(X0,X2) = hAPP(X0,X1)
& hBOOL(hAPP(hAPP(X0,X2),X2))
& hBOOL(hAPP(hAPP(X0,X1),X1)) )
| hBOOL(hAPP(hAPP(X0,X1),X2)) ) )
=> ( ( hAPP(X0,sK167(X0)) != hAPP(X0,sK166(X0))
| ~ hBOOL(hAPP(hAPP(X0,sK167(X0)),sK167(X0)))
| ~ hBOOL(hAPP(hAPP(X0,sK166(X0)),sK166(X0)))
| ~ hBOOL(hAPP(hAPP(X0,sK166(X0)),sK167(X0))) )
& ( ( hAPP(X0,sK167(X0)) = hAPP(X0,sK166(X0))
& hBOOL(hAPP(hAPP(X0,sK167(X0)),sK167(X0)))
& hBOOL(hAPP(hAPP(X0,sK166(X0)),sK166(X0))) )
| hBOOL(hAPP(hAPP(X0,sK166(X0)),sK167(X0))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f14942,plain,
! [X0] :
( ( sP4(X0)
| ? [X1,X2] :
( ( hAPP(X0,X2) != hAPP(X0,X1)
| ~ hBOOL(hAPP(hAPP(X0,X2),X2))
| ~ hBOOL(hAPP(hAPP(X0,X1),X1))
| ~ hBOOL(hAPP(hAPP(X0,X1),X2)) )
& ( ( hAPP(X0,X2) = hAPP(X0,X1)
& hBOOL(hAPP(hAPP(X0,X2),X2))
& hBOOL(hAPP(hAPP(X0,X1),X1)) )
| hBOOL(hAPP(hAPP(X0,X1),X2)) ) ) )
& ( ! [X3,X4] :
( ( hBOOL(hAPP(hAPP(X0,X3),X4))
| hAPP(X0,X4) != hAPP(X0,X3)
| ~ hBOOL(hAPP(hAPP(X0,X4),X4))
| ~ hBOOL(hAPP(hAPP(X0,X3),X3)) )
& ( ( hAPP(X0,X4) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(X0,X4),X4))
& hBOOL(hAPP(hAPP(X0,X3),X3)) )
| ~ hBOOL(hAPP(hAPP(X0,X3),X4)) ) )
| ~ sP4(X0) ) ),
inference(rectify,[],[f14941]) ).
fof(f14941,plain,
! [X0] :
( ( sP4(X0)
| ? [X2,X3] :
( ( hAPP(X0,X2) != hAPP(X0,X3)
| ~ hBOOL(hAPP(hAPP(X0,X3),X3))
| ~ hBOOL(hAPP(hAPP(X0,X2),X2))
| ~ hBOOL(hAPP(hAPP(X0,X2),X3)) )
& ( ( hAPP(X0,X2) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(X0,X3),X3))
& hBOOL(hAPP(hAPP(X0,X2),X2)) )
| hBOOL(hAPP(hAPP(X0,X2),X3)) ) ) )
& ( ! [X2,X3] :
( ( hBOOL(hAPP(hAPP(X0,X2),X3))
| hAPP(X0,X2) != hAPP(X0,X3)
| ~ hBOOL(hAPP(hAPP(X0,X3),X3))
| ~ hBOOL(hAPP(hAPP(X0,X2),X2)) )
& ( ( hAPP(X0,X2) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(X0,X3),X3))
& hBOOL(hAPP(hAPP(X0,X2),X2)) )
| ~ hBOOL(hAPP(hAPP(X0,X2),X3)) ) )
| ~ sP4(X0) ) ),
inference(flattening,[],[f14940]) ).
fof(f14940,plain,
! [X0] :
( ( sP4(X0)
| ? [X2,X3] :
( ( hAPP(X0,X2) != hAPP(X0,X3)
| ~ hBOOL(hAPP(hAPP(X0,X3),X3))
| ~ hBOOL(hAPP(hAPP(X0,X2),X2))
| ~ hBOOL(hAPP(hAPP(X0,X2),X3)) )
& ( ( hAPP(X0,X2) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(X0,X3),X3))
& hBOOL(hAPP(hAPP(X0,X2),X2)) )
| hBOOL(hAPP(hAPP(X0,X2),X3)) ) ) )
& ( ! [X2,X3] :
( ( hBOOL(hAPP(hAPP(X0,X2),X3))
| hAPP(X0,X2) != hAPP(X0,X3)
| ~ hBOOL(hAPP(hAPP(X0,X3),X3))
| ~ hBOOL(hAPP(hAPP(X0,X2),X2)) )
& ( ( hAPP(X0,X2) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(X0,X3),X3))
& hBOOL(hAPP(hAPP(X0,X2),X2)) )
| ~ hBOOL(hAPP(hAPP(X0,X2),X3)) ) )
| ~ sP4(X0) ) ),
inference(nnf_transformation,[],[f14482]) ).
fof(f14482,plain,
! [X0] :
( sP4(X0)
<=> ! [X2,X3] :
( hBOOL(hAPP(hAPP(X0,X2),X3))
<=> ( hAPP(X0,X2) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(X0,X3),X3))
& hBOOL(hAPP(hAPP(X0,X2),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f45372,plain,
( spl647_1293
| ~ spl647_337
| ~ spl647_1125 ),
inference(avatar_split_clause,[],[f41765,f40681,f30853,f45369]) ).
fof(f45369,plain,
( spl647_1293
<=> c_Lazy__Sequence_Oempty(tc_Int_Oint) = c_Lazy__Sequence_Osmall__lazy_H(c_Int_OMin,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1293])]) ).
fof(f30853,plain,
( spl647_337
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_337])]) ).
fof(f40681,plain,
( spl647_1125
<=> ! [X0,X1] :
( c_Lazy__Sequence_Oempty(tc_Int_Oint) = c_Lazy__Sequence_Osmall__lazy_H(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1125])]) ).
fof(f41765,plain,
( c_Lazy__Sequence_Oempty(tc_Int_Oint) = c_Lazy__Sequence_Osmall__lazy_H(c_Int_OMin,c_Int_OPls)
| ~ spl647_337
| ~ spl647_1125 ),
inference(resolution,[],[f40682,f30855]) ).
fof(f30855,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls))
| ~ spl647_337 ),
inference(avatar_component_clause,[],[f30853]) ).
fof(f40682,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| c_Lazy__Sequence_Oempty(tc_Int_Oint) = c_Lazy__Sequence_Osmall__lazy_H(X1,X0) )
| ~ spl647_1125 ),
inference(avatar_component_clause,[],[f40681]) ).
fof(f45367,plain,
spl647_1292,
inference(avatar_split_clause,[],[f19075,f45365]) ).
fof(f45365,plain,
( spl647_1292
<=> ! [X4,X0,X3] :
( hBOOL(hAPP(hAPP(X0,X3),X3))
| ~ hBOOL(hAPP(hAPP(X0,X3),X4))
| ~ sP4(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1292])]) ).
fof(f19075,plain,
! [X3,X0,X4] :
( hBOOL(hAPP(hAPP(X0,X3),X3))
| ~ hBOOL(hAPP(hAPP(X0,X3),X4))
| ~ sP4(X0) ),
inference(cnf_transformation,[],[f14944]) ).
fof(f45363,plain,
spl647_1291,
inference(avatar_split_clause,[],[f19038,f45361]) ).
fof(f45361,plain,
( spl647_1291
<=> ! [X0,X1] :
( X0 = X1
| hAPP(X1,sK157(X0,X1)) != hAPP(X0,sK157(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1291])]) ).
fof(f19038,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X1,sK157(X0,X1)) != hAPP(X0,sK157(X0,X1)) ),
inference(cnf_transformation,[],[f14910]) ).
fof(f14910,plain,
! [X0,X1] :
( X0 = X1
| hAPP(X1,sK157(X0,X1)) != hAPP(X0,sK157(X0,X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK157])],[f11263,f14909]) ).
fof(f14909,plain,
! [X0,X1] :
( ? [X2] : hAPP(X1,X2) != hAPP(X0,X2)
=> hAPP(X1,sK157(X0,X1)) != hAPP(X0,sK157(X0,X1)) ),
introduced(choice_axiom,[]) ).
fof(f11263,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] : hAPP(X1,X2) != hAPP(X0,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ! [X2] : hAPP(X1,X2) = hAPP(X0,X2)
=> X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45359,plain,
spl647_1290,
inference(avatar_split_clause,[],[f18779,f45357]) ).
fof(f45357,plain,
( spl647_1290
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1290])]) ).
fof(f18779,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f10958]) ).
fof(f10958,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ),
inference(ennf_transformation,[],[f6516]) ).
fof(f6516,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ),
inference(rectify,[],[f528]) ).
fof(f528,axiom,
! [X44,X45] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X44))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45355,plain,
spl647_1289,
inference(avatar_split_clause,[],[f18598,f45353]) ).
fof(f45353,plain,
( spl647_1289
<=> ! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),sK122(X0,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1289])]) ).
fof(f18598,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),sK122(X0,X1)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f14798]) ).
fof(f14798,plain,
! [X0,X1] :
( ( ! [X3] :
( sK122(X0,X1) = X3
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X3))
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| hAPP(c_List_Oset(X1),X3) != X0 )
& hBOOL(hAPP(c_List_Odistinct(X1),sK122(X0,X1)))
& c_List_Olinorder__class_Osorted(X1,sK122(X0,X1))
& hAPP(c_List_Oset(X1),sK122(X0,X1)) = X0 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Orderings_Olinorder(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK122])],[f10779,f14797]) ).
fof(f14797,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( X2 = X3
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X3))
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| hAPP(c_List_Oset(X1),X3) != X0 )
& hBOOL(hAPP(c_List_Odistinct(X1),X2))
& c_List_Olinorder__class_Osorted(X1,X2)
& hAPP(c_List_Oset(X1),X2) = X0 )
=> ( ! [X3] :
( sK122(X0,X1) = X3
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X3))
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| hAPP(c_List_Oset(X1),X3) != X0 )
& hBOOL(hAPP(c_List_Odistinct(X1),sK122(X0,X1)))
& c_List_Olinorder__class_Osorted(X1,sK122(X0,X1))
& hAPP(c_List_Oset(X1),sK122(X0,X1)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f10779,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( X2 = X3
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X3))
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| hAPP(c_List_Oset(X1),X3) != X0 )
& hBOOL(hAPP(c_List_Odistinct(X1),X2))
& c_List_Olinorder__class_Osorted(X1,X2)
& hAPP(c_List_Oset(X1),X2) = X0 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Orderings_Olinorder(X1) ),
inference(flattening,[],[f10778]) ).
fof(f10778,plain,
! [X0,X1] :
( ? [X2] :
( ! [X3] :
( X2 = X3
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X3))
| ~ c_List_Olinorder__class_Osorted(X1,X3)
| hAPP(c_List_Oset(X1),X3) != X0 )
& hBOOL(hAPP(c_List_Odistinct(X1),X2))
& c_List_Olinorder__class_Osorted(X1,X2)
& hAPP(c_List_Oset(X1),X2) = X0 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6378]) ).
fof(f6378,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
=> ? [X2] :
( ! [X3] :
( ( hBOOL(hAPP(c_List_Odistinct(X1),X3))
& c_List_Olinorder__class_Osorted(X1,X3)
& hAPP(c_List_Oset(X1),X3) = X0 )
=> X2 = X3 )
& hBOOL(hAPP(c_List_Odistinct(X1),X2))
& c_List_Olinorder__class_Osorted(X1,X2)
& hAPP(c_List_Oset(X1),X2) = X0 ) ) ),
inference(rectify,[],[f4542]) ).
fof(f4542,axiom,
! [X9,X4] :
( class_Orderings_Olinorder(X4)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X9))
=> ? [X2] :
( ! [X38] :
( ( hBOOL(hAPP(c_List_Odistinct(X4),X38))
& c_List_Olinorder__class_Osorted(X4,X38)
& hAPP(c_List_Oset(X4),X38) = X9 )
=> X2 = X38 )
& hBOOL(hAPP(c_List_Odistinct(X4),X2))
& c_List_Olinorder__class_Osorted(X4,X2)
& hAPP(c_List_Oset(X4),X2) = X9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45351,plain,
spl647_1288,
inference(avatar_split_clause,[],[f18588,f45349]) ).
fof(f45349,plain,
( spl647_1288
<=> ! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X0)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1288])]) ).
fof(f18588,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X0)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10763]) ).
fof(f10763,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X0)))
& c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osorted__list__of__set(X1,X0))
& hAPP(c_List_Oset(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X0)) = X0 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Orderings_Olinorder(X1) ),
inference(flattening,[],[f10762]) ).
fof(f10762,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X0)))
& c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osorted__list__of__set(X1,X0))
& hAPP(c_List_Oset(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X0)) = X0 )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6370]) ).
fof(f6370,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
=> ( hBOOL(hAPP(c_List_Odistinct(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X0)))
& c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osorted__list__of__set(X1,X0))
& hAPP(c_List_Oset(X1),c_List_Olinorder__class_Osorted__list__of__set(X1,X0)) = X0 ) ) ),
inference(rectify,[],[f4427]) ).
fof(f4427,axiom,
! [X9,X4] :
( class_Orderings_Olinorder(X4)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X9))
=> ( hBOOL(hAPP(c_List_Odistinct(X4),c_List_Olinorder__class_Osorted__list__of__set(X4,X9)))
& c_List_Olinorder__class_Osorted(X4,c_List_Olinorder__class_Osorted__list__of__set(X4,X9))
& hAPP(c_List_Oset(X4),c_List_Olinorder__class_Osorted__list__of__set(X4,X9)) = X9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45347,plain,
spl647_1287,
inference(avatar_split_clause,[],[f18558,f45345]) ).
fof(f45345,plain,
( spl647_1287
<=> ! [X0,X1] :
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),X0) = hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(c_List_Orev(X1),X0))
| ~ class_Groups_Ocomm__monoid__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1287])]) ).
fof(f18558,plain,
! [X0,X1] :
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),X0) = hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(c_List_Orev(X1),X0))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(cnf_transformation,[],[f10726]) ).
fof(f10726,plain,
! [X0,X1] :
( hAPP(c_List_Omonoid__add__class_Olistsum(X1),X0) = hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(c_List_Orev(X1),X0))
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(ennf_transformation,[],[f6342]) ).
fof(f6342,plain,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X1),X0) = hAPP(c_List_Omonoid__add__class_Olistsum(X1),hAPP(c_List_Orev(X1),X0)) ),
inference(rectify,[],[f4452]) ).
fof(f4452,axiom,
! [X201,X20] :
( class_Groups_Ocomm__monoid__add(X20)
=> hAPP(c_List_Omonoid__add__class_Olistsum(X20),X201) = hAPP(c_List_Omonoid__add__class_Olistsum(X20),hAPP(c_List_Orev(X20),X201)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45343,plain,
spl647_1286,
inference(avatar_split_clause,[],[f18547,f45341]) ).
fof(f45341,plain,
( spl647_1286
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1286])]) ).
fof(f18547,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f10714]) ).
fof(f10714,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(flattening,[],[f10713]) ).
fof(f10713,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f6331]) ).
fof(f6331,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Ozero__class_Ozero(X1)),X0))
=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f4898]) ).
fof(f4898,axiom,
! [X26,X20] :
( class_Rings_Ocomm__semiring__1(X20)
=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X20),c_Groups_Ozero__class_Ozero(X20)),X26))
=> c_Groups_Ozero__class_Ozero(X20) = X26 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45339,plain,
spl647_1285,
inference(avatar_split_clause,[],[f18487,f45337]) ).
fof(f45337,plain,
( spl647_1285
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0)
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1285])]) ).
fof(f18487,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f10651]) ).
fof(f10651,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f6275]) ).
fof(f6275,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0) ),
inference(rectify,[],[f1491]) ).
fof(f1491,axiom,
! [X19,X20] :
( class_Lattices_Oboolean__algebra(X20)
=> c_Orderings_Obot__class_Obot(X20) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20),hAPP(c_Groups_Ouminus__class_Ouminus(X20),X19)),X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45335,plain,
spl647_1284,
inference(avatar_split_clause,[],[f18486,f45333]) ).
fof(f45333,plain,
( spl647_1284
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0))
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1284])]) ).
fof(f18486,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f10650]) ).
fof(f10650,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f6274]) ).
fof(f6274,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)) ),
inference(rectify,[],[f1492]) ).
fof(f1492,axiom,
! [X19,X20] :
( class_Lattices_Oboolean__algebra(X20)
=> c_Orderings_Obot__class_Obot(X20) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20),X19),hAPP(c_Groups_Ouminus__class_Ouminus(X20),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45331,plain,
spl647_1283,
inference(avatar_split_clause,[],[f18485,f45329]) ).
fof(f45329,plain,
( spl647_1283
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0)
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1283])]) ).
fof(f18485,plain,
! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f10649]) ).
fof(f10649,plain,
! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0)
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f6273]) ).
fof(f6273,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0) ),
inference(rectify,[],[f2110]) ).
fof(f2110,axiom,
! [X19,X20] :
( class_Lattices_Oboolean__algebra(X20)
=> c_Orderings_Otop__class_Otop(X20) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20),hAPP(c_Groups_Ouminus__class_Ouminus(X20),X19)),X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45327,plain,
spl647_1282,
inference(avatar_split_clause,[],[f18484,f45325]) ).
fof(f45325,plain,
( spl647_1282
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0))
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1282])]) ).
fof(f18484,plain,
! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f10648]) ).
fof(f10648,plain,
! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f6272]) ).
fof(f6272,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)) ),
inference(rectify,[],[f2111]) ).
fof(f2111,axiom,
! [X19,X20] :
( class_Lattices_Oboolean__algebra(X20)
=> c_Orderings_Otop__class_Otop(X20) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20),X19),hAPP(c_Groups_Ouminus__class_Ouminus(X20),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45323,plain,
spl647_1281,
inference(avatar_split_clause,[],[f18396,f45321]) ).
fof(f45321,plain,
( spl647_1281
<=> ! [X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0))
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1281])]) ).
fof(f18396,plain,
! [X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f10575]) ).
fof(f10575,plain,
! [X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(ennf_transformation,[],[f6203]) ).
fof(f6203,plain,
! [X0,X1] :
( class_Rings_Olinordered__idom(X1)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)) ),
inference(rectify,[],[f1346]) ).
fof(f1346,axiom,
! [X44,X20] :
( class_Rings_Olinordered__idom(X20)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20),X44) = hAPP(c_Groups_Oabs__class_Oabs(X20),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45319,plain,
spl647_1280,
inference(avatar_split_clause,[],[f18381,f45317]) ).
fof(f45317,plain,
( spl647_1280
<=> ! [X0,X1] :
( hAPP(c_Groups_Oabs__class_Oabs(X1),X0) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1280])]) ).
fof(f18381,plain,
! [X0,X1] :
( hAPP(c_Groups_Oabs__class_Oabs(X1),X0) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f10559]) ).
fof(f10559,plain,
! [X0,X1] :
( hAPP(c_Groups_Oabs__class_Oabs(X1),X0) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f6191]) ).
fof(f6191,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> hAPP(c_Groups_Oabs__class_Oabs(X1),X0) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)) ),
inference(rectify,[],[f1465]) ).
fof(f1465,axiom,
! [X26,X20] :
( class_Groups_Oordered__ab__group__add__abs(X20)
=> hAPP(c_Groups_Oabs__class_Oabs(X20),X26) = hAPP(c_Groups_Oabs__class_Oabs(X20),hAPP(c_Groups_Ouminus__class_Ouminus(X20),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45315,plain,
spl647_1279,
inference(avatar_split_clause,[],[f18380,f45313]) ).
fof(f45313,plain,
( spl647_1279
<=> ! [X0,X1] :
( hAPP(c_Groups_Oabs__class_Oabs(X1),X0) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1279])]) ).
fof(f18380,plain,
! [X0,X1] :
( hAPP(c_Groups_Oabs__class_Oabs(X1),X0) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f10558]) ).
fof(f10558,plain,
! [X0,X1] :
( hAPP(c_Groups_Oabs__class_Oabs(X1),X0) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f6190]) ).
fof(f6190,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> hAPP(c_Groups_Oabs__class_Oabs(X1),X0) = hAPP(c_Groups_Oabs__class_Oabs(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)) ),
inference(rectify,[],[f1335]) ).
fof(f1335,axiom,
! [X26,X20] :
( class_Groups_Oordered__ab__group__add__abs(X20)
=> hAPP(c_Groups_Oabs__class_Oabs(X20),X26) = hAPP(c_Groups_Oabs__class_Oabs(X20),hAPP(c_Groups_Oabs__class_Oabs(X20),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45311,plain,
spl647_1278,
inference(avatar_split_clause,[],[f18365,f45309]) ).
fof(f45309,plain,
( spl647_1278
<=> ! [X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0) = hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ class_Rings_Oring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1278])]) ).
fof(f18365,plain,
! [X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0) = hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ class_Rings_Oring__1(X1) ),
inference(cnf_transformation,[],[f10544]) ).
fof(f10544,plain,
! [X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0) = hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ class_Rings_Oring__1(X1) ),
inference(ennf_transformation,[],[f6178]) ).
fof(f6178,plain,
! [X0,X1] :
( class_Rings_Oring__1(X1)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0) = hAPP(c_Int_Oring__1__class_Oof__int(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
inference(rectify,[],[f2039]) ).
fof(f2039,axiom,
! [X44,X20] :
( class_Rings_Oring__1(X20)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20),X44) = hAPP(c_Int_Oring__1__class_Oof__int(X20),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45307,plain,
spl647_1277,
inference(avatar_split_clause,[],[f18345,f45305]) ).
fof(f45305,plain,
( spl647_1277
<=> ! [X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1277])]) ).
fof(f18345,plain,
! [X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f10530]) ).
fof(f10530,plain,
! [X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f6164]) ).
fof(f6164,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ),
inference(rectify,[],[f1484]) ).
fof(f1484,axiom,
! [X26,X20] :
( class_Groups_Ogroup__add(X20)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X20),X26) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20),c_Groups_Ozero__class_Ozero(X20)),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45303,plain,
spl647_1276,
inference(avatar_split_clause,[],[f18344,f45301]) ).
fof(f45301,plain,
( spl647_1276
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0)
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1276])]) ).
fof(f18344,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f10529]) ).
fof(f10529,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f6163]) ).
fof(f6163,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0) ),
inference(rectify,[],[f1481]) ).
fof(f1481,axiom,
! [X26,X20] :
( class_Groups_Ogroup__add(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(c_Groups_Ouminus__class_Ouminus(X20),X26)),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45299,plain,
spl647_1275,
inference(avatar_split_clause,[],[f18343,f45297]) ).
fof(f45297,plain,
( spl647_1275
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0))
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1275])]) ).
fof(f18343,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0))
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f10528]) ).
fof(f10528,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0))
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f6162]) ).
fof(f6162,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)) ),
inference(rectify,[],[f1479]) ).
fof(f1479,axiom,
! [X26,X20] :
( class_Groups_Ogroup__add(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),X26),hAPP(c_Groups_Ouminus__class_Ouminus(X20),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45295,plain,
spl647_1274,
inference(avatar_split_clause,[],[f18315,f45293]) ).
fof(f45293,plain,
( spl647_1274
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0)
| ~ class_Groups_Oab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1274])]) ).
fof(f18315,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0)
| ~ class_Groups_Oab__group__add(X1) ),
inference(cnf_transformation,[],[f10509]) ).
fof(f10509,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0)
| ~ class_Groups_Oab__group__add(X1) ),
inference(ennf_transformation,[],[f6145]) ).
fof(f6145,plain,
! [X0,X1] :
( class_Groups_Oab__group__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)),X0) ),
inference(rectify,[],[f1482]) ).
fof(f1482,axiom,
! [X26,X20] :
( class_Groups_Oab__group__add(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(c_Groups_Ouminus__class_Ouminus(X20),X26)),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45291,plain,
spl647_1273,
inference(avatar_split_clause,[],[f18291,f45289]) ).
fof(f45289,plain,
( spl647_1273
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1273])]) ).
fof(f18291,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f6124]) ).
fof(f6124,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ),
inference(rectify,[],[f497]) ).
fof(f497,axiom,
! [X44,X45] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X45))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45287,plain,
( spl647_1272
| ~ spl647_946
| ~ spl647_1101 ),
inference(avatar_split_clause,[],[f41206,f40584,f34593,f45285]) ).
fof(f45285,plain,
( spl647_1272
<=> ! [X0] : hBOOL(hAPP(c_Int_OInteg,hAPP(c_Int_ORep__Integ,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1272])]) ).
fof(f34593,plain,
( spl647_946
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| hBOOL(hAPP(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_946])]) ).
fof(f40584,plain,
( spl647_1101
<=> ! [X0] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X0)),c_Int_OInteg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1101])]) ).
fof(f41206,plain,
( ! [X0] : hBOOL(hAPP(c_Int_OInteg,hAPP(c_Int_ORep__Integ,X0)))
| ~ spl647_946
| ~ spl647_1101 ),
inference(resolution,[],[f40585,f34594]) ).
fof(f34594,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| hBOOL(hAPP(X0,X1)) )
| ~ spl647_946 ),
inference(avatar_component_clause,[],[f34593]) ).
fof(f40585,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X0)),c_Int_OInteg))
| ~ spl647_1101 ),
inference(avatar_component_clause,[],[f40584]) ).
fof(f45283,plain,
spl647_1271,
inference(avatar_split_clause,[],[f18290,f45281]) ).
fof(f45281,plain,
( spl647_1271
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1271])]) ).
fof(f18290,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f6123]) ).
fof(f6123,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) ),
inference(rectify,[],[f1165]) ).
fof(f1165,axiom,
! [X87,X27] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),X27))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X27),X87)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45279,plain,
spl647_1270,
inference(avatar_split_clause,[],[f18272,f45277]) ).
fof(f45277,plain,
( spl647_1270
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Olog(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1270])]) ).
fof(f18272,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Olog(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ),
inference(cnf_transformation,[],[f10492]) ).
fof(f10492,plain,
! [X0,X1] :
( ( c_Random_Olog(X1,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
& ( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Olog(X1,X0)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X0),X1))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
inference(flattening,[],[f10491]) ).
fof(f10491,plain,
! [X0,X1] :
( ( c_Random_Olog(X1,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),X1)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
& ( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Olog(X1,X0)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X0),X1))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
inference(ennf_transformation,[],[f6109]) ).
fof(f6109,plain,
! [X0,X1] :
( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
=> c_Random_Olog(X1,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),X1))) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X1),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Olog(X1,X0) ) ),
inference(rectify,[],[f2155]) ).
fof(f2155,axiom,
! [X55,X25] :
( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X55),X25))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X25),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
=> c_Random_Olog(X25,X55) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Random_Olog(X25,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X55),X25))) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X55),X25))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X25),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Olog(X25,X55) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45275,plain,
spl647_1269,
inference(avatar_split_clause,[],[f18174,f45273]) ).
fof(f45273,plain,
( spl647_1269
<=> ! [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 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1269])]) ).
fof(f18174,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 ),
inference(cnf_transformation,[],[f10444]) ).
fof(f10444,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,[],[f6065]) ).
fof(f6065,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,[],[f2160]) ).
fof(f2160,axiom,
! [X53,X74] :
( ( X53 != X74
=> c_Random_Oinc__shift(X74,X53) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X53),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) )
& ( X53 = X74
=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X74,X53) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45271,plain,
spl647_1268,
inference(avatar_split_clause,[],[f17950,f45269]) ).
fof(f45269,plain,
( spl647_1268
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)),hAPP(c_Nat_OSuc,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1268])]) ).
fof(f17950,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)),hAPP(c_Nat_OSuc,X1))),
inference(cnf_transformation,[],[f5842]) ).
fof(f5842,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)),hAPP(c_Nat_OSuc,X1))),
inference(rectify,[],[f474]) ).
fof(f474,axiom,
! [X44,X45] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),X44)),hAPP(c_Nat_OSuc,X45))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45267,plain,
spl647_1267,
inference(avatar_split_clause,[],[f17949,f45265]) ).
fof(f45265,plain,
( spl647_1267
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1267])]) ).
fof(f17949,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)))),
inference(cnf_transformation,[],[f5841]) ).
fof(f5841,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)))),
inference(rectify,[],[f651]) ).
fof(f651,axiom,
! [X45,X55] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X55),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),X45)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45263,plain,
spl647_1266,
inference(avatar_split_clause,[],[f17948,f45261]) ).
fof(f45261,plain,
( spl647_1266
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1266])]) ).
fof(f17948,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)))),
inference(cnf_transformation,[],[f5840]) ).
fof(f5840,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)))),
inference(rectify,[],[f650]) ).
fof(f650,axiom,
! [X45,X55] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X55),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X55)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45259,plain,
spl647_1265,
inference(avatar_split_clause,[],[f17947,f45257]) ).
fof(f45257,plain,
( spl647_1265
<=> ! [X0,X1] : c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X0)) = c_List_Otranspose(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1265])]) ).
fof(f17947,plain,
! [X0,X1] : c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X0)) = c_List_Otranspose(X1,X0),
inference(cnf_transformation,[],[f5839]) ).
fof(f5839,plain,
! [X0,X1] : c_List_Otranspose(X1,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),X0)) = c_List_Otranspose(X1,X0),
inference(rectify,[],[f4339]) ).
fof(f4339,axiom,
! [X239,X20] : c_List_Otranspose(X20,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X20)),c_List_Olist_ONil(X20)),X239)) = c_List_Otranspose(X20,X239),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45255,plain,
spl647_1264,
inference(avatar_split_clause,[],[f17945,f45253]) ).
fof(f45253,plain,
( spl647_1264
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X1) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1264])]) ).
fof(f17945,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X1) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0)),
inference(cnf_transformation,[],[f5837]) ).
fof(f5837,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X1) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0)),
inference(rectify,[],[f2661]) ).
fof(f2661,axiom,
! [X68,X97] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X97,X68)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X68),X97),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45251,plain,
spl647_1263,
inference(avatar_split_clause,[],[f17941,f45249]) ).
fof(f45249,plain,
( spl647_1263
<=> ! [X0,X1] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orev(X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1263])]) ).
fof(f17941,plain,
! [X0,X1] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orev(X1),X0)),
inference(cnf_transformation,[],[f5833]) ).
fof(f5833,plain,
! [X0,X1] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orev(X1),X0)),
inference(rectify,[],[f4453]) ).
fof(f4453,axiom,
! [X201,X20] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X201) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),hAPP(c_List_Orev(X20),X201)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45247,plain,
spl647_1262,
inference(avatar_split_clause,[],[f17940,f45245]) ).
fof(f45245,plain,
( spl647_1262
<=> ! [X0,X1] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orotate1(X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1262])]) ).
fof(f17940,plain,
! [X0,X1] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orotate1(X1),X0)),
inference(cnf_transformation,[],[f5832]) ).
fof(f5832,plain,
! [X0,X1] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),hAPP(c_List_Orotate1(X1),X0)),
inference(rectify,[],[f4001]) ).
fof(f4001,axiom,
! [X201,X20] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),X201) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),hAPP(c_List_Orotate1(X20),X201)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45243,plain,
( spl647_1261
| ~ spl647_473
| ~ spl647_1085 ),
inference(avatar_split_clause,[],[f40507,f38438,f31440,f45241]) ).
fof(f45241,plain,
( spl647_1261
<=> ! [X0] : c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1261])]) ).
fof(f31440,plain,
( spl647_473
<=> 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,[spl647_473])]) ).
fof(f38438,plain,
( spl647_1085
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1085])]) ).
fof(f40507,plain,
( ! [X0] : c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X0))
| ~ spl647_473
| ~ spl647_1085 ),
inference(resolution,[],[f38439,f31442]) ).
fof(f31442,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl647_473 ),
inference(avatar_component_clause,[],[f31440]) ).
fof(f38439,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0)) )
| ~ spl647_1085 ),
inference(avatar_component_clause,[],[f38438]) ).
fof(f45239,plain,
spl647_1260,
inference(avatar_split_clause,[],[f17668,f45237]) ).
fof(f45237,plain,
( spl647_1260
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK96(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1260])]) ).
fof(f17668,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK96(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f14663]) ).
fof(f14663,plain,
! [X0] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| ! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK96(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK96(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),sK97(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK96,sK97])],[f14660,f14662,f14661]) ).
fof(f14661,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) )
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK96(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK96(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14662,plain,
! [X0] :
( ? [X3] :
! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
=> ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),sK97(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14660,plain,
! [X0] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) )
& ( ? [X3] :
! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0)) ) ),
inference(rectify,[],[f14659]) ).
fof(f14659,plain,
! [X0] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) )
& ( ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0)) ) ),
inference(nnf_transformation,[],[f10437]) ).
fof(f10437,plain,
! [X0] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) ),
inference(ennf_transformation,[],[f5613]) ).
fof(f5613,plain,
! [X0] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X1)) ) ),
inference(rectify,[],[f2414]) ).
fof(f2414,axiom,
! [X103] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X103))
<=> ? [X82] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X103))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X82)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45235,plain,
spl647_1259,
inference(avatar_split_clause,[],[f17667,f45233]) ).
fof(f45233,plain,
( spl647_1259
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK96(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1259])]) ).
fof(f17667,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK96(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f14663]) ).
fof(f45231,plain,
spl647_1258,
inference(avatar_split_clause,[],[f17665,f45229]) ).
fof(f45229,plain,
( spl647_1258
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK94(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1258])]) ).
fof(f17665,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK94(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f14658]) ).
fof(f14658,plain,
! [X0] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| ! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK94(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK94(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK95(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK94,sK95])],[f14655,f14657,f14656]) ).
fof(f14656,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) )
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK94(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK94(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14657,plain,
! [X0] :
( ? [X3] :
! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
=> ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK95(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14655,plain,
! [X0] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) )
& ( ? [X3] :
! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0)) ) ),
inference(rectify,[],[f14654]) ).
fof(f14654,plain,
! [X0] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| ! [X1] :
? [X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) )
& ( ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0)) ) ),
inference(nnf_transformation,[],[f10436]) ).
fof(f10436,plain,
! [X0] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0)) ) ),
inference(ennf_transformation,[],[f5612]) ).
fof(f5612,plain,
! [X0] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
<=> ? [X1] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) ) ),
inference(rectify,[],[f2413]) ).
fof(f2413,axiom,
! [X103] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X103))
<=> ? [X82] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X103))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X82)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45227,plain,
spl647_1257,
inference(avatar_split_clause,[],[f17664,f45225]) ).
fof(f45225,plain,
( spl647_1257
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK94(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1257])]) ).
fof(f17664,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK94(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f14658]) ).
fof(f45223,plain,
spl647_1256,
inference(avatar_split_clause,[],[f17638,f45221]) ).
fof(f45221,plain,
( spl647_1256
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Rings_Olinordered__idom(X0)
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1256])]) ).
fof(f17638,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Rings_Olinordered__idom(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f10429]) ).
fof(f10429,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Rings_Olinordered__idom(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(flattening,[],[f10428]) ).
fof(f10428,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Rings_Olinordered__idom(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f5598]) ).
fof(f5598,plain,
! [X0] :
( ( class_Rings_Olinordered__idom(X0)
& class_Int_Onumber__ring(X0) )
=> c_Groups_Oone__class_Oone(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin)) ),
inference(rectify,[],[f1997]) ).
fof(f1997,axiom,
! [X20] :
( ( class_Rings_Olinordered__idom(X20)
& class_Int_Onumber__ring(X20) )
=> c_Groups_Oone__class_Oone(X20) = hAPP(c_Groups_Oabs__class_Oabs(X20),hAPP(c_Int_Onumber__class_Onumber__of(X20),c_Int_OMin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45219,plain,
spl647_1255,
inference(avatar_split_clause,[],[f17582,f45217]) ).
fof(f45217,plain,
( spl647_1255
<=> ! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Orderings_Oord_Omax(X0,hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X0)))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1255])]) ).
fof(f17582,plain,
! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Orderings_Oord_Omax(X0,hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X0)))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10375]) ).
fof(f10375,plain,
! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Orderings_Oord_Omax(X0,hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X0)))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5547]) ).
fof(f5547,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_Orderings_Oord__class_Omin(X0) = c_Orderings_Oord_Omax(X0,hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X0))) ),
inference(rectify,[],[f2316]) ).
fof(f2316,axiom,
! [X4] :
( class_Orderings_Olinorder(X4)
=> c_Orderings_Oord__class_Omin(X4) = c_Orderings_Oord_Omax(X4,hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45215,plain,
spl647_1254,
inference(avatar_split_clause,[],[f17581,f45213]) ).
fof(f45213,plain,
( spl647_1254
<=> ! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Orderings_Oord_Omin(X0,hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X0)))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1254])]) ).
fof(f17581,plain,
! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Orderings_Oord_Omin(X0,hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X0)))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10374]) ).
fof(f10374,plain,
! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Orderings_Oord_Omin(X0,hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X0)))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5546]) ).
fof(f5546,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_Orderings_Oord__class_Omax(X0) = c_Orderings_Oord_Omin(X0,hAPP(c_COMBC(X0,X0,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X0))) ),
inference(rectify,[],[f2487]) ).
fof(f2487,axiom,
! [X4] :
( class_Orderings_Olinorder(X4)
=> c_Orderings_Oord__class_Omax(X4) = c_Orderings_Oord_Omin(X4,hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45211,plain,
spl647_1253,
inference(avatar_split_clause,[],[f17436,f45209]) ).
fof(f45209,plain,
( spl647_1253
<=> ! [X0] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1253])]) ).
fof(f17436,plain,
! [X0] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X0)) = X0,
inference(cnf_transformation,[],[f5414]) ).
fof(f5414,plain,
! [X0] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X0)) = X0,
inference(rectify,[],[f2878]) ).
fof(f2878,axiom,
! [X9] : hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X9)) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45207,plain,
spl647_1252,
inference(avatar_split_clause,[],[f17435,f45205]) ).
fof(f45205,plain,
( spl647_1252
<=> ! [X0] : hAPP(c_Set_OPow(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1252])]) ).
fof(f17435,plain,
! [X0] : hAPP(c_Set_OPow(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool)),
inference(cnf_transformation,[],[f5413]) ).
fof(f5413,plain,
! [X0] : hAPP(c_Set_OPow(X0),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool)),
inference(rectify,[],[f2077]) ).
fof(f2077,axiom,
! [X4] : hAPP(c_Set_OPow(X4),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45203,plain,
spl647_1251,
inference(avatar_split_clause,[],[f17431,f45201]) ).
fof(f45201,plain,
( spl647_1251
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Relation_OField(X0),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1251])]) ).
fof(f17431,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Relation_OField(X0),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f5409]) ).
fof(f5409,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Relation_OField(X0),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f2812]) ).
fof(f2812,axiom,
! [X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Relation_OField(X4),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45199,plain,
( spl647_1250
| ~ spl647_306
| ~ spl647_1029 ),
inference(avatar_split_clause,[],[f39347,f38209,f30687,f45197]) ).
fof(f30687,plain,
( spl647_306
<=> ! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_306])]) ).
fof(f38209,plain,
( spl647_1029
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Quotient_ORespects(X2,X1),X0))
| ~ hBOOL(hAPP(hAPP(X1,X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1029])]) ).
fof(f39347,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Quotient_ORespects(X0,c_fequal),X1))
| ~ spl647_306
| ~ spl647_1029 ),
inference(resolution,[],[f38210,f30688]) ).
fof(f30688,plain,
( ! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1))
| ~ spl647_306 ),
inference(avatar_component_clause,[],[f30687]) ).
fof(f38210,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X1,X0),X0))
| hBOOL(hAPP(c_Quotient_ORespects(X2,X1),X0)) )
| ~ spl647_1029 ),
inference(avatar_component_clause,[],[f38209]) ).
fof(f45195,plain,
spl647_1249,
inference(avatar_split_clause,[],[f17430,f45193]) ).
fof(f45193,plain,
( spl647_1249
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1249])]) ).
fof(f17430,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(cnf_transformation,[],[f5408]) ).
fof(f5408,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))),
inference(rectify,[],[f2102]) ).
fof(f2102,axiom,
! [X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f45191,plain,
spl647_1248,
inference(avatar_split_clause,[],[f17429,f45189]) ).
fof(f45189,plain,
( spl647_1248
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1248])]) ).
fof(f17429,plain,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(cnf_transformation,[],[f5407]) ).
fof(f5407,plain,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(rectify,[],[f2103]) ).
fof(f2103,axiom,
! [X4] : c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f44973,plain,
( spl647_1247
| ~ spl647_913
| ~ spl647_930 ),
inference(avatar_split_clause,[],[f37629,f34528,f34460,f44971]) ).
fof(f44971,plain,
( spl647_1247
<=> ! [X0,X1] : sP10(c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1247])]) ).
fof(f34460,plain,
( spl647_913
<=> ! [X0,X1] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_913])]) ).
fof(f34528,plain,
( spl647_930
<=> ! [X0,X1] :
( c_Int_OPls != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| sP10(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_930])]) ).
fof(f37629,plain,
( ! [X0,X1] : sP10(c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),X1)
| ~ spl647_913
| ~ spl647_930 ),
inference(trivial_inequality_removal,[],[f37625]) ).
fof(f37625,plain,
( ! [X0,X1] :
( c_Int_OPls != c_Int_OPls
| sP10(c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1),X1) )
| ~ spl647_913
| ~ spl647_930 ),
inference(superposition,[],[f34529,f34461]) ).
fof(f34461,plain,
( ! [X0,X1] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)),X0)
| ~ spl647_913 ),
inference(avatar_component_clause,[],[f34460]) ).
fof(f34529,plain,
( ! [X0,X1] :
( c_Int_OPls != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| sP10(X1,X0) )
| ~ spl647_930 ),
inference(avatar_component_clause,[],[f34528]) ).
fof(f44805,plain,
( spl647_1246
| ~ spl647_576
| ~ spl647_927 ),
inference(avatar_split_clause,[],[f37586,f34516,f31907,f44803]) ).
fof(f44803,plain,
( spl647_1246
<=> ! [X0] :
( sP7(c_HOL_Obool_Obool__size(c_fTrue),X0)
| c_Nat__Transfer_Ois__nat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1246])]) ).
fof(f31907,plain,
( spl647_576
<=> ! [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,[spl647_576])]) ).
fof(f34516,plain,
( spl647_927
<=> ! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| sP7(c_HOL_Obool_Obool__size(c_fTrue),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_927])]) ).
fof(f37586,plain,
( ! [X0] :
( sP7(c_HOL_Obool_Obool__size(c_fTrue),X0)
| c_Nat__Transfer_Ois__nat(X0) )
| ~ spl647_576
| ~ spl647_927 ),
inference(resolution,[],[f34517,f31908]) ).
fof(f31908,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| c_Nat__Transfer_Ois__nat(X0) )
| ~ spl647_576 ),
inference(avatar_component_clause,[],[f31907]) ).
fof(f34517,plain,
( ! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| sP7(c_HOL_Obool_Obool__size(c_fTrue),X1) )
| ~ spl647_927 ),
inference(avatar_component_clause,[],[f34516]) ).
fof(f44713,plain,
( spl647_1245
| ~ spl647_576
| ~ spl647_925 ),
inference(avatar_split_clause,[],[f37558,f34508,f31907,f44711]) ).
fof(f44711,plain,
( spl647_1245
<=> ! [X0] :
( sP6(c_HOL_Obool_Obool__size(c_fTrue),X0)
| c_Nat__Transfer_Ois__nat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1245])]) ).
fof(f34508,plain,
( spl647_925
<=> ! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| sP6(c_HOL_Obool_Obool__size(c_fTrue),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_925])]) ).
fof(f37558,plain,
( ! [X0] :
( sP6(c_HOL_Obool_Obool__size(c_fTrue),X0)
| c_Nat__Transfer_Ois__nat(X0) )
| ~ spl647_576
| ~ spl647_925 ),
inference(resolution,[],[f34509,f31908]) ).
fof(f34509,plain,
( ! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| sP6(c_HOL_Obool_Obool__size(c_fTrue),X1) )
| ~ spl647_925 ),
inference(avatar_component_clause,[],[f34508]) ).
fof(f44533,plain,
( spl647_1244
| ~ spl647_576
| ~ spl647_908 ),
inference(avatar_split_clause,[],[f37404,f34438,f31907,f44531]) ).
fof(f44531,plain,
( spl647_1244
<=> ! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Nat__Transfer_Ois__nat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1244])]) ).
fof(f34438,plain,
( spl647_908
<=> ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_908])]) ).
fof(f37404,plain,
( ! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Nat__Transfer_Ois__nat(X0) )
| ~ spl647_576
| ~ spl647_908 ),
inference(resolution,[],[f34439,f31908]) ).
fof(f34439,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) )
| ~ spl647_908 ),
inference(avatar_component_clause,[],[f34438]) ).
fof(f43764,plain,
( spl647_1243
| ~ spl647_577
| ~ spl647_907 ),
inference(avatar_split_clause,[],[f37386,f34434,f31911,f43762]) ).
fof(f31911,plain,
( spl647_577
<=> ! [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,[spl647_577])]) ).
fof(f34434,plain,
( spl647_907
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_907])]) ).
fof(f37386,plain,
( ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| ~ c_Nat__Transfer_Ois__nat(X0) )
| ~ spl647_577
| ~ spl647_907 ),
inference(resolution,[],[f34435,f31912]) ).
fof(f31912,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| ~ c_Nat__Transfer_Ois__nat(X0) )
| ~ spl647_577 ),
inference(avatar_component_clause,[],[f31911]) ).
fof(f34435,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) )
| ~ spl647_907 ),
inference(avatar_component_clause,[],[f34434]) ).
fof(f41914,plain,
( ~ spl647_1241
| spl647_1242
| ~ spl647_345
| ~ spl647_597
| ~ spl647_822 ),
inference(avatar_split_clause,[],[f35447,f34076,f31997,f30888,f41912,f41908]) ).
fof(f41908,plain,
( spl647_1241
<=> hBOOL(sK162(c_Code__Numeral_Onat__of)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1241])]) ).
fof(f41912,plain,
( spl647_1242
<=> ! [X0] : hBOOL(sK109(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1242])]) ).
fof(f30888,plain,
( spl647_345
<=> ! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_345])]) ).
fof(f34076,plain,
( spl647_822
<=> ! [X0,X1] :
( hBOOL(hAPP(X1,X0))
| ~ hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Oof__nat,sK162(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_822])]) ).
fof(f35447,plain,
( ! [X0] :
( hBOOL(sK109(X0))
| ~ hBOOL(sK162(c_Code__Numeral_Onat__of)) )
| ~ spl647_345
| ~ spl647_597
| ~ spl647_822 ),
inference(forward_demodulation,[],[f35412,f31998]) ).
fof(f35412,plain,
( ! [X0] :
( ~ hBOOL(sK162(c_Code__Numeral_Onat__of))
| hBOOL(hAPP(c_Code__Numeral_Onat__of,X0)) )
| ~ spl647_345
| ~ spl647_822 ),
inference(superposition,[],[f34077,f30889]) ).
fof(f30889,plain,
( ! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0
| ~ spl647_345 ),
inference(avatar_component_clause,[],[f30888]) ).
fof(f34077,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Oof__nat,sK162(X1))))
| hBOOL(hAPP(X1,X0)) )
| ~ spl647_822 ),
inference(avatar_component_clause,[],[f34076]) ).
fof(f41759,plain,
( spl647_1240
| ~ spl647_561
| ~ spl647_817 ),
inference(avatar_split_clause,[],[f35342,f34056,f31841,f41757]) ).
fof(f41757,plain,
( spl647_1240
<=> ! [X0] :
( c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_fequal,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1240])]) ).
fof(f31841,plain,
( spl647_561
<=> ! [X2,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_561])]) ).
fof(f34056,plain,
( spl647_817
<=> ! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X0),X1))
| ~ c_Nat__Transfer_Onat__set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_817])]) ).
fof(f35342,plain,
( ! [X0] :
( c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_fequal,X0)) )
| ~ spl647_561
| ~ spl647_817 ),
inference(resolution,[],[f34057,f31842]) ).
fof(f31842,plain,
( ! [X2,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X1)))
| ~ spl647_561 ),
inference(avatar_component_clause,[],[f31841]) ).
fof(f34057,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X0),X1))
| c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Onat__set(X1) )
| ~ spl647_817 ),
inference(avatar_component_clause,[],[f34056]) ).
fof(f41168,plain,
spl647_1239,
inference(avatar_split_clause,[],[f28904,f41166]) ).
fof(f41166,plain,
( spl647_1239
<=> ! [X2,X1,X3] : c_List_Olist_ONil(X3) != hAPP(hAPP(c_List_Oappend(X3),X2),c_List_Oinsert(X3,X1,c_List_Olist_ONil(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1239])]) ).
fof(f28904,plain,
! [X2,X3,X1] : c_List_Olist_ONil(X3) != hAPP(hAPP(c_List_Oappend(X3),X2),c_List_Oinsert(X3,X1,c_List_Olist_ONil(X3))),
inference(forward_demodulation,[],[f25731,f17921]) ).
fof(f25731,plain,
! [X2,X3,X1] : c_List_Olist_ONil(X3) != hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3))),
inference(equality_resolution,[],[f22707]) ).
fof(f22707,plain,
! [X2,X3,X0,X1] :
( c_List_Olist_ONil(X3) != X0
| hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3))) != X0 ),
inference(cnf_transformation,[],[f16369]) ).
fof(f16369,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3))) = X0
| c_List_Olast(X3,X0) != X1
| c_List_Obutlast(X3,X0) != X2
| c_List_Olist_ONil(X3) = X0 )
& ( ( c_List_Olast(X3,X0) = X1
& c_List_Obutlast(X3,X0) = X2
& c_List_Olist_ONil(X3) != X0 )
| hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3))) != X0 ) ),
inference(flattening,[],[f16368]) ).
fof(f16368,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3))) = X0
| c_List_Olast(X3,X0) != X1
| c_List_Obutlast(X3,X0) != X2
| c_List_Olist_ONil(X3) = X0 )
& ( ( c_List_Olast(X3,X0) = X1
& c_List_Obutlast(X3,X0) = X2
& c_List_Olist_ONil(X3) != X0 )
| hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3))) != X0 ) ),
inference(nnf_transformation,[],[f9180]) ).
fof(f9180,plain,
! [X0,X1,X2,X3] :
( hAPP(hAPP(c_List_Oappend(X3),X2),hAPP(hAPP(c_List_Olist_OCons(X3),X1),c_List_Olist_ONil(X3))) = X0
<=> ( c_List_Olast(X3,X0) = X1
& c_List_Obutlast(X3,X0) = X2
& c_List_Olist_ONil(X3) != X0 ) ),
inference(rectify,[],[f4111]) ).
fof(f4111,axiom,
! [X202,X13,X203,X4] :
( hAPP(hAPP(c_List_Oappend(X4),X203),hAPP(hAPP(c_List_Olist_OCons(X4),X13),c_List_Olist_ONil(X4))) = X202
<=> ( c_List_Olast(X4,X202) = X13
& c_List_Obutlast(X4,X202) = X203
& c_List_Olist_ONil(X4) != X202 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41164,plain,
spl647_1238,
inference(avatar_split_clause,[],[f28729,f41162]) ).
fof(f41162,plain,
( spl647_1238
<=> ! [X0,X3,X2,X1] :
( hAPP(c_fequal,X0) != c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1238])]) ).
fof(f28729,plain,
! [X2,X3,X0,X1] :
( hAPP(c_fequal,X0) != c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1)
| X1 = X2
| ~ class_Orderings_Oorder(X3) ),
inference(forward_demodulation,[],[f22194,f26468]) ).
fof(f26468,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,[],[f17991,f17793]) ).
fof(f17793,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(cnf_transformation,[],[f5685]) ).
fof(f5685,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(rectify,[],[f3234]) ).
fof(f3234,axiom,
! [X23,X4] : hAPP(c_Set_OCollect(X4),X23) = X23,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17991,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,[],[f5883]) ).
fof(f5883,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,[],[f3249]) ).
fof(f3249,axiom,
! [X5,X4] : hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X4),hAPP(c_fequal,X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f22194,plain,
! [X2,X3,X0,X1] :
( X1 = X2
| hAPP(hAPP(c_Set_Oinsert(X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f16136]) ).
fof(f16136,plain,
! [X0,X1,X2,X3] :
( ( ( hAPP(hAPP(c_Set_Oinsert(X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1)
| X0 != X1
| X1 != X2 )
& ( ( X0 = X1
& X1 = X2 )
| hAPP(hAPP(c_Set_Oinsert(X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1) ) )
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f16135]) ).
fof(f16135,plain,
! [X0,X1,X2,X3] :
( ( ( hAPP(hAPP(c_Set_Oinsert(X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1)
| X0 != X1
| X1 != X2 )
& ( ( X0 = X1
& X1 = X2 )
| hAPP(hAPP(c_Set_Oinsert(X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1) ) )
| ~ class_Orderings_Oorder(X3) ),
inference(nnf_transformation,[],[f13144]) ).
fof(f13144,plain,
! [X0,X1,X2,X3] :
( ( hAPP(hAPP(c_Set_Oinsert(X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1)
<=> ( X0 = X1
& X1 = X2 ) )
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f8838]) ).
fof(f8838,plain,
! [X0,X1,X2,X3] :
( class_Orderings_Oorder(X3)
=> ( hAPP(hAPP(c_Set_Oinsert(X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1)
<=> ( X0 = X1
& X1 = X2 ) ) ),
inference(rectify,[],[f2583]) ).
fof(f2583,axiom,
! [X11,X12,X5,X4] :
( class_Orderings_Oorder(X4)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X12) = hAPP(hAPP(c_Set_Oinsert(X4),X11),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))
<=> ( X11 = X12
& X5 = X12 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41160,plain,
spl647_1237,
inference(avatar_split_clause,[],[f28728,f41158]) ).
fof(f41158,plain,
( spl647_1237
<=> ! [X0,X3,X2,X1] :
( hAPP(c_fequal,X0) != c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1)
| X0 = X1
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1237])]) ).
fof(f28728,plain,
! [X2,X3,X0,X1] :
( hAPP(c_fequal,X0) != c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1)
| X0 = X1
| ~ class_Orderings_Oorder(X3) ),
inference(forward_demodulation,[],[f22195,f26468]) ).
fof(f22195,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| hAPP(hAPP(c_Set_Oinsert(X3),X0),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) != c_SetInterval_Oord__class_OatLeastAtMost(X3,X2,X1)
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f16136]) ).
fof(f41156,plain,
spl647_1236,
inference(avatar_split_clause,[],[f28571,f41154]) ).
fof(f41154,plain,
( spl647_1236
<=> ! [X0,X3,X2,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X3,X2)),c_Nitpick_Opair__box_OPairBox(X3,X2,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1236])]) ).
fof(f28571,plain,
! [X2,X3,X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X3,X2)),c_Nitpick_Opair__box_OPairBox(X3,X2,X1,X0)),
inference(forward_demodulation,[],[f21565,f17145]) ).
fof(f21565,plain,
! [X2,X3,X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X3,X2)),c_Nitpick_Opair__box_OPairBox(X3,X2,X1,X0)),
inference(cnf_transformation,[],[f8282]) ).
fof(f8282,plain,
! [X0,X1,X2,X3] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X3,X2)),c_Nitpick_Opair__box_OPairBox(X3,X2,X1,X0)),
inference(rectify,[],[f1127]) ).
fof(f1127,axiom,
! [X25,X26,X4,X20] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X20,X4)),c_Nitpick_Opair__box_OPairBox(X20,X4,X26,X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41152,plain,
spl647_1235,
inference(avatar_split_clause,[],[f28437,f41150]) ).
fof(f41150,plain,
( spl647_1235
<=> ! [X2,X1] :
( ~ sP35(c_HOL_Obool_Obool__size(c_fTrue),X1,X2)
| c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1235])]) ).
fof(f28437,plain,
! [X2,X1] :
( ~ sP35(c_HOL_Obool_Obool__size(c_fTrue),X1,X2)
| c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1) ),
inference(forward_demodulation,[],[f28436,f17145]) ).
fof(f28436,plain,
! [X2,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| ~ sP35(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2) ),
inference(forward_demodulation,[],[f25559,f17145]) ).
fof(f25559,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| ~ sP35(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2) ),
inference(equality_resolution,[],[f21179]) ).
fof(f21179,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| ~ sP35(X0,X1,X2) ),
inference(cnf_transformation,[],[f15777]) ).
fof(f15777,plain,
! [X0,X1,X2] :
( ( sP35(X0,X1,X2)
| ( ~ sP34(X1,X0)
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
& c_Groups_Ozero__class_Ozero(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),X1)),X0)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)) != X2 )
& ( ( ( sP34(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| c_Groups_Ozero__class_Ozero(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),X1)),X0)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X1)) = X2 )
| ~ sP35(X0,X1,X2) ) ),
inference(rectify,[],[f15776]) ).
fof(f15776,plain,
! [X1,X0,X2] :
( ( sP35(X1,X0,X2)
| ( ~ sP34(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 )
& ( ( ( sP34(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 )
| ~ sP35(X1,X0,X2) ) ),
inference(flattening,[],[f15775]) ).
fof(f15775,plain,
! [X1,X0,X2] :
( ( sP35(X1,X0,X2)
| ( ~ sP34(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 )
& ( ( ( sP34(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 )
| ~ sP35(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f14535]) ).
fof(f14535,plain,
! [X1,X0,X2] :
( sP35(X1,X0,X2)
<=> ( ( sP34(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,[sP35])]) ).
fof(f41148,plain,
spl647_1234,
inference(avatar_split_clause,[],[f28211,f41146]) ).
fof(f41146,plain,
( spl647_1234
<=> ! [X2,X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,sK262(X0,X1,X2))
| ~ sP23(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1234])]) ).
fof(f28211,plain,
! [X2,X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,sK262(X0,X1,X2))
| ~ sP23(X0,X1,X2) ),
inference(forward_demodulation,[],[f28210,f25910]) ).
fof(f28210,plain,
! [X2,X0,X1] :
( hAPP(X0,sK262(X0,X1,X2)) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))
| ~ sP23(X0,X1,X2) ),
inference(forward_demodulation,[],[f20695,f17145]) ).
fof(f20695,plain,
! [X2,X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(X0,sK262(X0,X1,X2))
| ~ sP23(X0,X1,X2) ),
inference(cnf_transformation,[],[f15514]) ).
fof(f41144,plain,
spl647_1233,
inference(avatar_split_clause,[],[f28074,f41142]) ).
fof(f41142,plain,
( spl647_1233
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Ofilter(X2,hAPP(c_fequal,hAPP(X1,X0))),X0))
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1233])]) ).
fof(f28074,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Ofilter(X2,hAPP(c_fequal,hAPP(X1,X0))),X0))
| ~ class_Orderings_Olinorder(X2) ),
inference(forward_demodulation,[],[f20227,f26495]) ).
fof(f26495,plain,
! [X0,X1] : hAPP(c_fequal,X0) = hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0),
inference(forward_demodulation,[],[f26494,f26468]) ).
fof(f26494,plain,
! [X0,X1] : hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0) = hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(forward_demodulation,[],[f18078,f17793]) ).
fof(f18078,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(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0)),
inference(cnf_transformation,[],[f5970]) ).
fof(f5970,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(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0)),
inference(rectify,[],[f3248]) ).
fof(f3248,axiom,
! [X5,X4] : hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X4),hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f20227,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBC(X2,X2,tc_HOL_Obool),c_fequal),hAPP(X1,X0))),X0))
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f11659]) ).
fof(f11659,plain,
! [X0,X1,X2] :
( c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBC(X2,X2,tc_HOL_Obool),c_fequal),hAPP(X1,X0))),X0))
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7507]) ).
fof(f7507,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> c_List_Olinorder__class_Osorted(X2,hAPP(c_List_Ofilter(X2,hAPP(hAPP(c_COMBC(X2,X2,tc_HOL_Obool),c_fequal),hAPP(X1,X0))),X0)) ),
inference(rectify,[],[f4422]) ).
fof(f4422,axiom,
! [X203,X0,X4] :
( class_Orderings_Olinorder(X4)
=> c_List_Olinorder__class_Osorted(X4,hAPP(c_List_Ofilter(X4,hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),hAPP(X0,X203))),X203)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41140,plain,
spl647_1232,
inference(avatar_split_clause,[],[f27554,f41138]) ).
fof(f27554,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Int_OPls))
| sP12(X0,X1)
| ~ sP11(X1,X0) ),
inference(forward_demodulation,[],[f27553,f17285]) ).
fof(f27553,plain,
! [X0,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_Int_OPls))
| sP12(X0,X1)
| ~ sP11(X1,X0) ),
inference(forward_demodulation,[],[f19322,f17135]) ).
fof(f19322,plain,
! [X0,X1] :
( sP12(X0,X1)
| ~ sP11(X1,X0)
| ~ 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(cnf_transformation,[],[f15141]) ).
fof(f41136,plain,
spl647_1231,
inference(avatar_split_clause,[],[f27551,f41134]) ).
fof(f41134,plain,
( spl647_1231
<=> ! [X0,X1] :
( 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_Int_OPls),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1231])]) ).
fof(f27551,plain,
! [X0,X1] :
( 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_Int_OPls),X0)) ),
inference(forward_demodulation,[],[f27550,f17285]) ).
fof(f27550,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
inference(forward_demodulation,[],[f27549,f17135]) ).
fof(f27549,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
inference(forward_demodulation,[],[f19315,f17285]) ).
fof(f19315,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f15139]) ).
fof(f41132,plain,
spl647_1230,
inference(avatar_split_clause,[],[f27541,f41130]) ).
fof(f41130,plain,
( spl647_1230
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| c_HOL_Obool_Obool__size(c_fTrue) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1230])]) ).
fof(f27541,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| c_HOL_Obool_Obool__size(c_fTrue) = X1 ),
inference(forward_demodulation,[],[f27540,f17145]) ).
fof(f27540,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ),
inference(forward_demodulation,[],[f19299,f17145]) ).
fof(f19299,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ),
inference(cnf_transformation,[],[f15125]) ).
fof(f15125,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ) ),
inference(flattening,[],[f15124]) ).
fof(f15124,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ) ),
inference(nnf_transformation,[],[f6822]) ).
fof(f6822,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
inference(rectify,[],[f783]) ).
fof(f783,axiom,
! [X46,X47] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X46)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X46
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X47 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41128,plain,
spl647_1229,
inference(avatar_split_clause,[],[f27539,f41126]) ).
fof(f41126,plain,
( spl647_1229
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| c_HOL_Obool_Obool__size(c_fTrue) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1229])]) ).
fof(f27539,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| c_HOL_Obool_Obool__size(c_fTrue) = X0 ),
inference(forward_demodulation,[],[f27538,f17145]) ).
fof(f27538,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ),
inference(forward_demodulation,[],[f19300,f17145]) ).
fof(f19300,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ),
inference(cnf_transformation,[],[f15125]) ).
fof(f41124,plain,
spl647_1228,
inference(avatar_split_clause,[],[f26927,f41122]) ).
fof(f41122,plain,
( spl647_1228
<=> ! [X0,X1] :
( c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)
| ~ class_Int_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1228])]) ).
fof(f26927,plain,
! [X0,X1] :
( c_Int_Oiszero(X1,c_Groups_Ozero__class_Ozero(X1))
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(inner_rewriting,[],[f26926]) ).
fof(f26926,plain,
! [X0,X1] :
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),X0))
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f26925,f17321]) ).
fof(f17321,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(cnf_transformation,[],[f5299]) ).
fof(f5299,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(rectify,[],[f1278]) ).
fof(f1278,axiom,
! [X53] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X53),c_Int_OPls) = X53,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f26925,plain,
! [X0,X1] :
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls)))
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f18467,f17989]) ).
fof(f17989,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f5881]) ).
fof(f5881,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)),
inference(rectify,[],[f1521]) ).
fof(f1521,axiom,
! [X87,X27] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X27),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X87)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X27),X87),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f18467,plain,
! [X0,X1] :
( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f14782]) ).
fof(f14782,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)
| ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
& ( c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Onumber__class_Onumber__of(X1),X0) ) )
| ~ class_Int_Onumber__ring(X1) ),
inference(nnf_transformation,[],[f10632]) ).
fof(f10632,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)
<=> c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f6256]) ).
fof(f6256,plain,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)
<=> c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ),
inference(rectify,[],[f1718]) ).
fof(f1718,axiom,
! [X13,X4] :
( class_Int_Onumber__ring(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Int_Onumber__class_Onumber__of(X4),X13)
<=> c_Int_Oiszero(X4,hAPP(c_Int_Onumber__class_Onumber__of(X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41120,plain,
spl647_1227,
inference(avatar_split_clause,[],[f26608,f41118]) ).
fof(f41118,plain,
( spl647_1227
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| c_List_Olist_ONil(tc_List_Olist(X0)) = c_Enum_On__lists(X0,X1,c_List_Olist_ONil(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1227])]) ).
fof(f26608,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| c_List_Olist_ONil(tc_List_Olist(X0)) = c_Enum_On__lists(X0,X1,c_List_Olist_ONil(X0)) ),
inference(forward_demodulation,[],[f18194,f17145]) ).
fof(f18194,plain,
! [X0,X1] :
( c_List_Olist_ONil(tc_List_Olist(X0)) = c_Enum_On__lists(X0,X1,c_List_Olist_ONil(X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(cnf_transformation,[],[f10453]) ).
fof(f10453,plain,
! [X0,X1] :
( ( c_List_Olist_ONil(tc_List_Olist(X0)) = c_Enum_On__lists(X0,X1,c_List_Olist_ONil(X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X0)),c_List_Olist_ONil(X0)),c_List_Olist_ONil(tc_List_Olist(X0))) = c_Enum_On__lists(X0,X1,c_List_Olist_ONil(X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(ennf_transformation,[],[f6074]) ).
fof(f6074,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> c_List_Olist_ONil(tc_List_Olist(X0)) = c_Enum_On__lists(X0,X1,c_List_Olist_ONil(X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X0)),c_List_Olist_ONil(X0)),c_List_Olist_ONil(tc_List_Olist(X0))) = c_Enum_On__lists(X0,X1,c_List_Olist_ONil(X0)) ) ),
inference(rectify,[],[f4262]) ).
fof(f4262,axiom,
! [X20,X44] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X44
=> c_List_Olist_ONil(tc_List_Olist(X20)) = c_Enum_On__lists(X20,X44,c_List_Olist_ONil(X20)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X44
=> hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X20)),c_List_Olist_ONil(X20)),c_List_Olist_ONil(tc_List_Olist(X20))) = c_Enum_On__lists(X20,X44,c_List_Olist_ONil(X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41116,plain,
spl647_1226,
inference(avatar_split_clause,[],[f26468,f41114]) ).
fof(f41114,plain,
( spl647_1226
<=> ! [X0,X1] : hAPP(c_fequal,X0) = hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1226])]) ).
fof(f41112,plain,
spl647_1225,
inference(avatar_split_clause,[],[f26457,f41110]) ).
fof(f41110,plain,
( spl647_1225
<=> ! [X0,X1] : c_Relation_OId(X1) = hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_HOL_Obool_Obool__size(c_fTrue)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1225])]) ).
fof(f26457,plain,
! [X0,X1] : c_Relation_OId(X1) = hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_HOL_Obool_Obool__size(c_fTrue)),X0),
inference(forward_demodulation,[],[f17910,f17145]) ).
fof(f17910,plain,
! [X0,X1] : c_Relation_OId(X1) = hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f5802]) ).
fof(f5802,plain,
! [X0,X1] : c_Relation_OId(X1) = hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(rectify,[],[f3674]) ).
fof(f3674,axiom,
! [X138,X4] : c_Relation_OId(X4) = hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X138),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41108,plain,
spl647_1224,
inference(avatar_split_clause,[],[f26334,f41106]) ).
fof(f41106,plain,
( spl647_1224
<=> ! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Int_Onat,X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Int_OPls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1224])]) ).
fof(f26334,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Int_Onat,X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Int_OPls)) ),
inference(forward_demodulation,[],[f26333,f17145]) ).
fof(f26333,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Int_OPls))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onat,X0) ),
inference(forward_demodulation,[],[f17671,f17135]) ).
fof(f17671,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onat,X0) ),
inference(cnf_transformation,[],[f14665]) ).
fof(f14665,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,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__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onat,X0) ) ),
inference(nnf_transformation,[],[f5615]) ).
fof(f5615,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(rectify,[],[f1802]) ).
fof(f1802,axiom,
! [X63] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X63)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X63),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41104,plain,
spl647_1223,
inference(avatar_split_clause,[],[f26227,f41102]) ).
fof(f41102,plain,
( spl647_1223
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Int_OPls))
| c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1223])]) ).
fof(f26227,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Int_OPls))
| c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,X0) ),
inference(forward_demodulation,[],[f26226,f17135]) ).
fof(f26226,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(forward_demodulation,[],[f17607,f17145]) ).
fof(f17607,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f10400]) ).
fof(f10400,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(ennf_transformation,[],[f5571]) ).
fof(f5571,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0) ),
inference(rectify,[],[f1803]) ).
fof(f1803,axiom,
! [X27] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X27),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41100,plain,
spl647_1222,
inference(avatar_split_clause,[],[f26190,f41098]) ).
fof(f41098,plain,
( spl647_1222
<=> ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Int_OPls))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1222])]) ).
fof(f26190,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Int_OPls))
| hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0) = X0 ),
inference(forward_demodulation,[],[f17523,f17135]) ).
fof(f17523,plain,
! [X0] :
( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f10319]) ).
fof(f10319,plain,
! [X0] :
( ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(ennf_transformation,[],[f5488]) ).
fof(f5488,plain,
! [X0] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0) = X0 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0) ) ),
inference(rectify,[],[f1543]) ).
fof(f1543,axiom,
! [X55] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X55),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X55) = X55 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X55),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X55) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X55) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41096,plain,
spl647_1221,
inference(avatar_split_clause,[],[f26078,f41094]) ).
fof(f26078,plain,
! [X0] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X0)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f26077,f25910]) ).
fof(f26077,plain,
! [X0] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X0)),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f17442,f17145]) ).
fof(f17442,plain,
! [X0] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X0)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f5420]) ).
fof(f5420,plain,
! [X0] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X0)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rectify,[],[f2164]) ).
fof(f2164,axiom,
! [X137] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X137)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X137)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41092,plain,
spl647_1220,
inference(avatar_split_clause,[],[f26075,f41090]) ).
fof(f41090,plain,
( spl647_1220
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1220])]) ).
fof(f26075,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),c_Int_OPls)),
inference(forward_demodulation,[],[f17437,f17135]) ).
fof(f17437,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(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,[],[f5415]) ).
fof(f5415,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(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,[],[f1541]) ).
fof(f1541,axiom,
! [X44] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41088,plain,
( spl647_1219
| ~ spl647_597
| ~ spl647_1218 ),
inference(avatar_split_clause,[],[f41084,f41081,f31997,f41086]) ).
fof(f41086,plain,
( spl647_1219
<=> ! [X0] : hAPP(c_Nat_OSuc,c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X0)) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,sK109(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1219])]) ).
fof(f41081,plain,
( spl647_1218
<=> ! [X0] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0)))) = hAPP(c_Nat_OSuc,c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1218])]) ).
fof(f41084,plain,
( ! [X0] : hAPP(c_Nat_OSuc,c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X0)) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,sK109(X0))))
| ~ spl647_597
| ~ spl647_1218 ),
inference(forward_demodulation,[],[f41082,f31998]) ).
fof(f41082,plain,
( ! [X0] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0)))) = hAPP(c_Nat_OSuc,c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X0))
| ~ spl647_1218 ),
inference(avatar_component_clause,[],[f41081]) ).
fof(f41083,plain,
spl647_1218,
inference(avatar_split_clause,[],[f26067,f41081]) ).
fof(f26067,plain,
! [X0] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0)))) = hAPP(c_Nat_OSuc,c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X0)),
inference(forward_demodulation,[],[f26066,f17387]) ).
fof(f17387,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,[],[f5365]) ).
fof(f5365,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,[],[f666]) ).
fof(f666,axiom,
! [X44] : hAPP(c_Nat_OSuc,X44) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f26066,plain,
! [X0] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X0)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f26065,f25910]) ).
fof(f26065,plain,
! [X0] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X0)),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f24223,f17145]) ).
fof(f24223,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X0)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0)))),
inference(definition_unfolding,[],[f17427,f17371]) ).
fof(f17427,plain,
! [X0] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X0)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f5405]) ).
fof(f5405,plain,
! [X0] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X0)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rectify,[],[f2051]) ).
fof(f2051,axiom,
! [X130] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X130)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41065,plain,
( spl647_1217
| ~ spl647_331
| ~ spl647_497
| ~ spl647_1216 ),
inference(avatar_split_clause,[],[f41060,f41056,f31581,f30819,f41062]) ).
fof(f41062,plain,
( spl647_1217
<=> hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1217])]) ).
fof(f30819,plain,
( spl647_331
<=> c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_331])]) ).
fof(f31581,plain,
( spl647_497
<=> ! [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,[spl647_497])]) ).
fof(f41056,plain,
( spl647_1216
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1216])]) ).
fof(f41060,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl647_331
| ~ spl647_497
| ~ spl647_1216 ),
inference(forward_demodulation,[],[f41058,f32001]) ).
fof(f32001,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)
| ~ spl647_331
| ~ spl647_497 ),
inference(superposition,[],[f31582,f30821]) ).
fof(f30821,plain,
( c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl647_331 ),
inference(avatar_component_clause,[],[f30819]) ).
fof(f31582,plain,
( ! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = X0
| ~ spl647_497 ),
inference(avatar_component_clause,[],[f31581]) ).
fof(f41058,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl647_1216 ),
inference(avatar_component_clause,[],[f41056]) ).
fof(f41059,plain,
spl647_1216,
inference(avatar_split_clause,[],[f25963,f41056]) ).
fof(f25963,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f25962,f25910]) ).
fof(f25962,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f25961,f17145]) ).
fof(f25961,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))),
inference(forward_demodulation,[],[f25960,f25909]) ).
fof(f25960,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))),
inference(forward_demodulation,[],[f24182,f17133]) ).
fof(f24182,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin))),
inference(definition_unfolding,[],[f17218,f24151]) ).
fof(f17218,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(cnf_transformation,[],[f1559]) ).
fof(f1559,axiom,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41054,plain,
spl647_1215,
inference(avatar_split_clause,[],[f25595,f41052]) ).
fof(f41052,plain,
( spl647_1215
<=> ! [X4,X0,X2] :
( hBOOL(hAPP(X0,X4))
| ~ sP47(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1215])]) ).
fof(f25595,plain,
! [X2,X0,X4] :
( hBOOL(hAPP(X0,X4))
| ~ sP47(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4),X2) ),
inference(equality_resolution,[],[f21345]) ).
fof(f21345,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(X0,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4) != X1
| ~ sP47(X0,X1,X2) ),
inference(cnf_transformation,[],[f15895]) ).
fof(f15895,plain,
! [X0,X1,X2] :
( ( sP47(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK388(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),sK388(X0,X1,X2)) = X1 )
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ) )
& ( ( ! [X4] :
( hBOOL(hAPP(X0,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4) != X1 )
& ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ) )
| ~ sP47(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK388])],[f15893,f15894]) ).
fof(f15894,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3) = X1 )
=> ( ~ hBOOL(hAPP(X0,sK388(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),sK388(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f15893,plain,
! [X0,X1,X2] :
( ( sP47(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3) = X1 )
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ) )
& ( ( ! [X4] :
( hBOOL(hAPP(X0,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4) != X1 )
& ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ) )
| ~ sP47(X0,X1,X2) ) ),
inference(rectify,[],[f15892]) ).
fof(f15892,plain,
! [X2,X1,X0] :
( ( sP47(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) )
& ( ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) )
| ~ sP47(X2,X1,X0) ) ),
inference(flattening,[],[f15891]) ).
fof(f15891,plain,
! [X2,X1,X0] :
( ( sP47(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) )
& ( ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) )
| ~ sP47(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14555]) ).
fof(f14555,plain,
! [X2,X1,X0] :
( sP47(X2,X1,X0)
<=> ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP47])]) ).
fof(f41050,plain,
spl647_1214,
inference(avatar_split_clause,[],[f25594,f41048]) ).
fof(f41048,plain,
( spl647_1214
<=> ! [X4,X0,X2] :
( hBOOL(hAPP(X0,X4))
| ~ sP46(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1214])]) ).
fof(f25594,plain,
! [X2,X0,X4] :
( hBOOL(hAPP(X0,X4))
| ~ sP46(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4),X2) ),
inference(equality_resolution,[],[f21337]) ).
fof(f21337,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(X0,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4) != X1
| ~ sP46(X0,X1,X2) ),
inference(cnf_transformation,[],[f15889]) ).
fof(f15889,plain,
! [X0,X1,X2] :
( ( sP46(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK387(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),sK387(X0,X1,X2)) = X1 )
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ) )
& ( ( ! [X4] :
( hBOOL(hAPP(X0,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4) != X1 )
& ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ) )
| ~ sP46(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK387])],[f15887,f15888]) ).
fof(f15888,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3) = X1 )
=> ( ~ hBOOL(hAPP(X0,sK387(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),sK387(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f15887,plain,
! [X0,X1,X2] :
( ( sP46(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X3) = X1 )
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ) )
& ( ( ! [X4] :
( hBOOL(hAPP(X0,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4) != X1 )
& ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X2)) ) )
| ~ sP46(X0,X1,X2) ) ),
inference(rectify,[],[f15886]) ).
fof(f15886,plain,
! [X2,X1,X0] :
( ( sP46(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) )
& ( ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) )
| ~ sP46(X2,X1,X0) ) ),
inference(flattening,[],[f15885]) ).
fof(f15885,plain,
! [X2,X1,X0] :
( ( sP46(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) )
& ( ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) )
| ~ sP46(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14553]) ).
fof(f14553,plain,
! [X2,X1,X0] :
( sP46(X2,X1,X0)
<=> ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP46])]) ).
fof(f41046,plain,
spl647_1213,
inference(avatar_split_clause,[],[f25298,f41044]) ).
fof(f41044,plain,
( spl647_1213
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1213])]) ).
fof(f25298,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(equality_resolution,[],[f18323]) ).
fof(f18323,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),X0)
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f14748]) ).
fof(f14748,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),X0) ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f10516]) ).
fof(f10516,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f6150]) ).
fof(f6150,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f954]) ).
fof(f954,axiom,
! [X5,X4] :
( class_Groups_Olinordered__ab__group__add(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X4),X5),X5)
<=> c_Groups_Ozero__class_Ozero(X4) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41042,plain,
spl647_1212,
inference(avatar_split_clause,[],[f25289,f41040]) ).
fof(f41040,plain,
( spl647_1212
<=> ! [X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1212])]) ).
fof(f25289,plain,
! [X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),c_Groups_Oone__class_Oone(X1))
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(equality_resolution,[],[f18300]) ).
fof(f18300,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0)
| c_Groups_Oone__class_Oone(X1) != X0
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(cnf_transformation,[],[f14739]) ).
fof(f14739,plain,
! [X0,X1] :
( ( ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0)
| ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1)) != X0
& c_Groups_Oone__class_Oone(X1) != X0 ) )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0
| c_Groups_Oone__class_Oone(X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(flattening,[],[f14738]) ).
fof(f14738,plain,
! [X0,X1] :
( ( ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0)
| ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1)) != X0
& c_Groups_Oone__class_Oone(X1) != X0 ) )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0
| c_Groups_Oone__class_Oone(X1) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(nnf_transformation,[],[f10499]) ).
fof(f10499,plain,
! [X0,X1] :
( ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0)
<=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0 ) )
| ~ class_Rings_Oring__1__no__zero__divisors(X1) ),
inference(ennf_transformation,[],[f6137]) ).
fof(f6137,plain,
! [X0,X1] :
( class_Rings_Oring__1__no__zero__divisors(X1)
=> ( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),X0)
<=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Oone__class_Oone(X1)) = X0
| c_Groups_Oone__class_Oone(X1) = X0 ) ) ),
inference(rectify,[],[f1490]) ).
fof(f1490,axiom,
! [X13,X4] :
( class_Rings_Oring__1__no__zero__divisors(X4)
=> ( c_Groups_Oone__class_Oone(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X13),X13)
<=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X4),c_Groups_Oone__class_Oone(X4)) = X13
| c_Groups_Oone__class_Oone(X4) = X13 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41038,plain,
spl647_1211,
inference(avatar_split_clause,[],[f24573,f41036]) ).
fof(f41036,plain,
( spl647_1211
<=> ! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(c_List_Omember(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1211])]) ).
fof(f24573,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(c_List_Omember(X1),X0) ),
inference(definition_unfolding,[],[f19306,f17267]) ).
fof(f19306,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(c_List_Oset(X1),X0) ),
inference(cnf_transformation,[],[f15134]) ).
fof(f15134,plain,
! [X0,X1] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_List_Oset(X1),X0)
| c_List_Olist_ONil(X1) != X0 )
& ( c_List_Olist_ONil(X1) = X0
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(c_List_Oset(X1),X0) ) ),
inference(nnf_transformation,[],[f6825]) ).
fof(f6825,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_List_Oset(X1),X0)
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f3900]) ).
fof(f3900,axiom,
! [X203,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_List_Oset(X4),X203)
<=> c_List_Olist_ONil(X4) = X203 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41034,plain,
spl647_1210,
inference(avatar_split_clause,[],[f24203,f41032]) ).
fof(f41032,plain,
( spl647_1210
<=> ! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X0)),c_Int_OMin) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1210])]) ).
fof(f24203,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X0)),c_Int_OMin) = X0,
inference(definition_unfolding,[],[f17268,f17339,f17340]) ).
fof(f17268,plain,
! [X0] : c_Int_Osucc(c_Int_Opred(X0)) = X0,
inference(cnf_transformation,[],[f5246]) ).
fof(f5246,plain,
! [X0] : c_Int_Osucc(c_Int_Opred(X0)) = X0,
inference(rectify,[],[f1317]) ).
fof(f1317,axiom,
! [X19] : c_Int_Osucc(c_Int_Opred(X19)) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41030,plain,
spl647_1209,
inference(avatar_split_clause,[],[f23957,f41028]) ).
fof(f41028,plain,
( spl647_1209
<=> ! [X3,X4,X0,X5,X2,X1] :
( X4 = X5
| X1 = X2
| ~ sP87(X0,X1,X2,X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1209])]) ).
fof(f23957,plain,
! [X2,X3,X0,X1,X4,X5] :
( X4 = X5
| X1 = X2
| ~ sP87(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f16857]) ).
fof(f16857,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( sP87(X0,X1,X2,X3,X4,X5)
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),X0))
| X4 != X5 )
& ( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olistrel1(X3,X0))) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X2),X1)),X0))
& X4 = X5 )
| ( X1 = X2
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X3),tc_List_Olist(X3))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X3),tc_List_Olist(X3)),X4),X5)),c_List_Olistrel1(X3,X0))) )
| ~ sP87(X0,X1,X2,X3,X4,X5) ) ),
inference(rectify,[],[f16856]) ).
fof(f16856,plain,
! [X0,X1,X3,X5,X4,X2] :
( ( sP87(X0,X1,X3,X5,X4,X2)
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X1)),X0))
| X2 != X4 )
& ( X1 != X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X4),X2)),c_List_Olistrel1(X5,X0))) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X1)),X0))
& X2 = X4 )
| ( X1 = X3
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X4),X2)),c_List_Olistrel1(X5,X0))) )
| ~ sP87(X0,X1,X3,X5,X4,X2) ) ),
inference(flattening,[],[f16855]) ).
fof(f16855,plain,
! [X0,X1,X3,X5,X4,X2] :
( ( sP87(X0,X1,X3,X5,X4,X2)
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X1)),X0))
| X2 != X4 )
& ( X1 != X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X4),X2)),c_List_Olistrel1(X5,X0))) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X1)),X0))
& X2 = X4 )
| ( X1 = X3
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X4),X2)),c_List_Olistrel1(X5,X0))) )
| ~ sP87(X0,X1,X3,X5,X4,X2) ) ),
inference(nnf_transformation,[],[f14628]) ).
fof(f14628,plain,
! [X0,X1,X3,X5,X4,X2] :
( sP87(X0,X1,X3,X5,X4,X2)
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X3),X1)),X0))
& X2 = X4 )
| ( X1 = X3
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X4),X2)),c_List_Olistrel1(X5,X0))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP87])]) ).
fof(f41026,plain,
spl647_1208,
inference(avatar_split_clause,[],[f23949,f41024]) ).
fof(f41024,plain,
( spl647_1208
<=> ! [X3,X4,X0,X5,X2,X1] :
( X4 = X5
| X2 = X3
| ~ sP86(X0,X1,X2,X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1208])]) ).
fof(f23949,plain,
! [X2,X3,X0,X1,X4,X5] :
( X4 = X5
| X2 = X3
| ~ sP86(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f16853]) ).
fof(f16853,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( sP86(X0,X1,X2,X3,X4,X5)
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olistrel1(X1,X0)))
| X4 != X5 )
& ( X2 != X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X0)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X1),tc_List_Olist(X1)),X3),X2)),c_List_Olistrel1(X1,X0)))
& X4 = X5 )
| ( X2 = X3
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X0)) )
| ~ sP86(X0,X1,X2,X3,X4,X5) ) ),
inference(rectify,[],[f16852]) ).
fof(f16852,plain,
! [X0,X5,X1,X3,X4,X2] :
( ( sP86(X0,X5,X1,X3,X4,X2)
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X3),X1)),c_List_Olistrel1(X5,X0)))
| X2 != X4 )
& ( X1 != X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X2)),X0)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X3),X1)),c_List_Olistrel1(X5,X0)))
& X2 = X4 )
| ( X1 = X3
& hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X2)),X0)) )
| ~ sP86(X0,X5,X1,X3,X4,X2) ) ),
inference(flattening,[],[f16851]) ).
fof(f16851,plain,
! [X0,X5,X1,X3,X4,X2] :
( ( sP86(X0,X5,X1,X3,X4,X2)
| ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X3),X1)),c_List_Olistrel1(X5,X0)))
| X2 != X4 )
& ( X1 != X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X2)),X0)) ) ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X3),X1)),c_List_Olistrel1(X5,X0)))
& X2 = X4 )
| ( X1 = X3
& hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X2)),X0)) )
| ~ sP86(X0,X5,X1,X3,X4,X2) ) ),
inference(nnf_transformation,[],[f14626]) ).
fof(f14626,plain,
! [X0,X5,X1,X3,X4,X2] :
( sP86(X0,X5,X1,X3,X4,X2)
<=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(X5),tc_List_Olist(X5)),X3),X1)),c_List_Olistrel1(X5,X0)))
& X2 = X4 )
| ( X1 = X3
& hBOOL(hAPP(hAPP(c_member(tc_prod(X5,X5)),hAPP(hAPP(c_Product__Type_OPair(X5,X5),X4),X2)),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP86])]) ).
fof(f41022,plain,
spl647_1207,
inference(avatar_split_clause,[],[f23832,f41020]) ).
fof(f41020,plain,
( spl647_1207
<=> ! [X5,X4,X0,X3,X2,X1] :
( hAPP(X2,hAPP(X3,X0)) = X0
| ~ c_Typedef_Otype__definition(X5,X4,X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1207])]) ).
fof(f23832,plain,
! [X2,X3,X0,X1,X4,X5] :
( hAPP(X2,hAPP(X3,X0)) = X0
| ~ c_Typedef_Otype__definition(X5,X4,X3,X2,X1) ),
inference(cnf_transformation,[],[f14253]) ).
fof(f14253,plain,
! [X0,X1,X2,X3,X4,X5] :
( hAPP(X2,hAPP(X3,X0)) = X0
| ~ c_Typedef_Otype__definition(X5,X4,X3,X2,X1) ),
inference(ennf_transformation,[],[f9911]) ).
fof(f9911,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Typedef_Otype__definition(X5,X4,X3,X2,X1)
=> hAPP(X2,hAPP(X3,X0)) = X0 ),
inference(rectify,[],[f3104]) ).
fof(f3104,axiom,
! [X13,X9,X179,X180,X14,X4] :
( c_Typedef_Otype__definition(X4,X14,X180,X179,X9)
=> hAPP(X179,hAPP(X180,X13)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41018,plain,
spl647_1206,
inference(avatar_split_clause,[],[f23498,f41016]) ).
fof(f41016,plain,
( spl647_1206
<=> ! [X4,X0,X3,X2,X1] :
( hAPP(X2,X1) = X0
| c_Fun_Ofun__upd(X4,X3,X2,X1,X0) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1206])]) ).
fof(f23498,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X2,X1) = X0
| c_Fun_Ofun__upd(X4,X3,X2,X1,X0) != X2 ),
inference(cnf_transformation,[],[f16656]) ).
fof(f16656,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Fun_Ofun__upd(X4,X3,X2,X1,X0) = X2
| hAPP(X2,X1) != X0 )
& ( hAPP(X2,X1) = X0
| c_Fun_Ofun__upd(X4,X3,X2,X1,X0) != X2 ) ),
inference(nnf_transformation,[],[f9712]) ).
fof(f9712,plain,
! [X0,X1,X2,X3,X4] :
( c_Fun_Ofun__upd(X4,X3,X2,X1,X0) = X2
<=> hAPP(X2,X1) = X0 ),
inference(rectify,[],[f2926]) ).
fof(f2926,axiom,
! [X15,X13,X1,X14,X4] :
( c_Fun_Ofun__upd(X4,X14,X1,X13,X15) = X1
<=> hAPP(X1,X13) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41014,plain,
spl647_1205,
inference(avatar_split_clause,[],[f23217,f41012]) ).
fof(f41012,plain,
( spl647_1205
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0))
| ~ sP72(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1205])]) ).
fof(f23217,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0))
| ~ sP72(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16551]) ).
fof(f16551,plain,
! [X0,X1,X2,X3,X4] :
( ( sP72(X0,X1,X2,X3,X4)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0))
| ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X3),X0))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X4)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X4)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X4),X3)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X3),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X4)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X4)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X4),X3)) ) )
| ~ sP72(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16550]) ).
fof(f16550,plain,
! [X0,X1,X4,X2,X3] :
( ( sP72(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)) ) )
& ( ( 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)) ) )
| ~ sP72(X0,X1,X4,X2,X3) ) ),
inference(flattening,[],[f16549]) ).
fof(f16549,plain,
! [X0,X1,X4,X2,X3] :
( ( sP72(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)) ) )
& ( ( 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)) ) )
| ~ sP72(X0,X1,X4,X2,X3) ) ),
inference(nnf_transformation,[],[f14599]) ).
fof(f14599,plain,
! [X0,X1,X4,X2,X3] :
( sP72(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,[sP72])]) ).
fof(f41010,plain,
spl647_1204,
inference(avatar_split_clause,[],[f23167,f41008]) ).
fof(f41008,plain,
( spl647_1204
<=> ! [X4,X0,X3,X2,X1] :
( c_List_Olist_ONil(X3) != hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X2),X1),X0)
| ~ class_Orderings_Olinorder(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1204])]) ).
fof(f23167,plain,
! [X2,X3,X0,X1,X4] :
( c_List_Olist_ONil(X3) != hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X2),X1),X0)
| ~ class_Orderings_Olinorder(X4) ),
inference(cnf_transformation,[],[f13763]) ).
fof(f13763,plain,
! [X0,X1,X2,X3,X4] :
( c_List_Olist_ONil(X3) != hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X2),X1),X0)
| ~ class_Orderings_Olinorder(X4) ),
inference(ennf_transformation,[],[f9463]) ).
fof(f9463,plain,
! [X0,X1,X2,X3,X4] :
( class_Orderings_Olinorder(X4)
=> c_List_Olist_ONil(X3) != hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X3,X4,X2),X1),X0) ),
inference(rectify,[],[f4092]) ).
fof(f4092,axiom,
! [X203,X5,X1,X4,X14] :
( class_Orderings_Olinorder(X14)
=> c_List_Olist_ONil(X4) != hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X4,X14,X1),X5),X203) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f41006,plain,
spl647_1203,
inference(avatar_split_clause,[],[f22890,f41004]) ).
fof(f41004,plain,
( spl647_1203
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,sK507(X0,X1,X2,X3)))
| ~ sP70(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1203])]) ).
fof(f22890,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,sK507(X0,X1,X2,X3)))
| ~ sP70(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16496]) ).
fof(f16496,plain,
! [X0,X1,X2,X3] :
( ( sP70(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))) ) )
& ( ( hBOOL(hAPP(X0,sK507(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X3),sK507(X0,X1,X2,X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) )
| ~ sP70(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK507])],[f16494,f16495]) ).
fof(f16495,plain,
! [X0,X1,X2,X3] :
( ? [X5] :
( hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) )
=> ( hBOOL(hAPP(X0,sK507(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X3),sK507(X0,X1,X2,X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f16494,plain,
! [X0,X1,X2,X3] :
( ( sP70(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),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) )
| ~ sP70(X0,X1,X2,X3) ) ),
inference(rectify,[],[f16493]) ).
fof(f16493,plain,
! [X0,X1,X2,X3] :
( ( sP70(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))) ) )
& ( ? [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))) )
| ~ sP70(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f14596]) ).
fof(f14596,plain,
! [X0,X1,X2,X3] :
( sP70(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,[sP70])]) ).
fof(f41002,plain,
spl647_1202,
inference(avatar_split_clause,[],[f22877,f41000]) ).
fof(f41000,plain,
( spl647_1202
<=> ! [X0,X3,X2,X1] :
( sP69(X0,X1,X3,X2)
| ~ hBOOL(hAPP(X0,sK503(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1202])]) ).
fof(f22877,plain,
! [X2,X3,X0,X1] :
( sP69(X0,X1,X3,X2)
| ~ hBOOL(hAPP(X0,sK503(X0,X1,X2,X3))) ),
inference(cnf_transformation,[],[f16481]) ).
fof(f16481,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))) )
| ~ sP69(X0,X1,X3,X2) )
& ( sP69(X0,X1,X3,X2)
| ( ~ hBOOL(hAPP(X0,sK503(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X3),sK503(X0,X1,X2,X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK503])],[f16479,f16480]) ).
fof(f16480,plain,
! [X0,X1,X2,X3] :
( ? [X5] :
( ~ hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) )
=> ( ~ hBOOL(hAPP(X0,sK503(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X3),sK503(X0,X1,X2,X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f16479,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))) )
| ~ sP69(X0,X1,X3,X2) )
& ( sP69(X0,X1,X3,X2)
| ? [X5] :
( ~ hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) ) ) ),
inference(rectify,[],[f16478]) ).
fof(f16478,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))) )
| ~ sP69(X0,X1,X3,X2) )
& ( sP69(X0,X1,X3,X2)
| ? [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))) ) ) ),
inference(nnf_transformation,[],[f14595]) ).
fof(f14595,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))) )
<=> sP69(X0,X1,X3,X2) ),
inference(definition_folding,[],[f13570,f14594]) ).
fof(f14594,plain,
! [X0,X1,X3,X2] :
( sP69(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,[sP69])]) ).
fof(f13570,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(ennf_transformation,[],[f9226]) ).
fof(f9226,plain,
! [X0,X1,X2,X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1)))
=> hBOOL(hAPP(X0,X4)) )
<=> ( ! [X5] :
( hBOOL(hAPP(hAPP(c_member(X3),X5),X1))
=> hBOOL(hAPP(X0,X5)) )
& ! [X6] :
( hBOOL(hAPP(hAPP(c_member(X3),X6),X2))
=> hBOOL(hAPP(X0,X6)) ) ) ),
inference(rectify,[],[f69]) ).
fof(f69,axiom,
! [X23,X18,X9,X4] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X9),X18)))
=> hBOOL(hAPP(X23,X2)) )
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),X18))
=> hBOOL(hAPP(X23,X2)) )
& ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),X9))
=> hBOOL(hAPP(X23,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40998,plain,
spl647_1201,
inference(avatar_split_clause,[],[f22635,f40996]) ).
fof(f40996,plain,
( spl647_1201
<=> ! [X0,X3,X2,X1] :
( c_List_Olist__all(X3,X2,X0)
| ~ c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1201])]) ).
fof(f22635,plain,
! [X2,X3,X0,X1] :
( c_List_Olist__all(X3,X2,X0)
| ~ c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0)) ),
inference(cnf_transformation,[],[f16312]) ).
fof(f16312,plain,
! [X0,X1,X2,X3] :
( ( c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
| ~ c_List_Olist__all(X3,X2,X0)
| ~ hBOOL(hAPP(X2,X1)) )
& ( ( c_List_Olist__all(X3,X2,X0)
& hBOOL(hAPP(X2,X1)) )
| ~ c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0)) ) ),
inference(flattening,[],[f16311]) ).
fof(f16311,plain,
! [X0,X1,X2,X3] :
( ( c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
| ~ c_List_Olist__all(X3,X2,X0)
| ~ hBOOL(hAPP(X2,X1)) )
& ( ( c_List_Olist__all(X3,X2,X0)
& hBOOL(hAPP(X2,X1)) )
| ~ c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0)) ) ),
inference(nnf_transformation,[],[f9151]) ).
fof(f9151,plain,
! [X0,X1,X2,X3] :
( c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
<=> ( c_List_Olist__all(X3,X2,X0)
& hBOOL(hAPP(X2,X1)) ) ),
inference(rectify,[],[f4574]) ).
fof(f4574,axiom,
! [X203,X13,X23,X4] :
( c_List_Olist__all(X4,X23,hAPP(hAPP(c_List_Olist_OCons(X4),X13),X203))
<=> ( c_List_Olist__all(X4,X23,X203)
& hBOOL(hAPP(X23,X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40994,plain,
spl647_1200,
inference(avatar_split_clause,[],[f22634,f40992]) ).
fof(f40992,plain,
( spl647_1200
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X2,X1))
| ~ c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1200])]) ).
fof(f22634,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X2,X1))
| ~ c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0)) ),
inference(cnf_transformation,[],[f16312]) ).
fof(f40990,plain,
spl647_1199,
inference(avatar_split_clause,[],[f22632,f40988]) ).
fof(f40988,plain,
( spl647_1199
<=> ! [X0,X3,X2,X1] :
( c_List_Olist__all(X3,X2,X0)
| ~ c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1199])]) ).
fof(f22632,plain,
! [X2,X3,X0,X1] :
( c_List_Olist__all(X3,X2,X0)
| ~ c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0)) ),
inference(cnf_transformation,[],[f16310]) ).
fof(f16310,plain,
! [X0,X1,X2,X3] :
( ( c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0))
| ~ c_List_Olist__all(X3,X2,X0)
| ~ c_List_Olist__all(X3,X2,X1) )
& ( ( c_List_Olist__all(X3,X2,X0)
& c_List_Olist__all(X3,X2,X1) )
| ~ c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0)) ) ),
inference(flattening,[],[f16309]) ).
fof(f16309,plain,
! [X0,X1,X2,X3] :
( ( c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0))
| ~ c_List_Olist__all(X3,X2,X0)
| ~ c_List_Olist__all(X3,X2,X1) )
& ( ( c_List_Olist__all(X3,X2,X0)
& c_List_Olist__all(X3,X2,X1) )
| ~ c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0)) ) ),
inference(nnf_transformation,[],[f9150]) ).
fof(f9150,plain,
! [X0,X1,X2,X3] :
( c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0))
<=> ( c_List_Olist__all(X3,X2,X0)
& c_List_Olist__all(X3,X2,X1) ) ),
inference(rectify,[],[f4565]) ).
fof(f4565,axiom,
! [X202,X203,X23,X4] :
( c_List_Olist__all(X4,X23,hAPP(hAPP(c_List_Oappend(X4),X203),X202))
<=> ( c_List_Olist__all(X4,X23,X202)
& c_List_Olist__all(X4,X23,X203) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40986,plain,
spl647_1198,
inference(avatar_split_clause,[],[f22631,f40984]) ).
fof(f40984,plain,
( spl647_1198
<=> ! [X0,X3,X2,X1] :
( c_List_Olist__all(X3,X2,X1)
| ~ c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1198])]) ).
fof(f22631,plain,
! [X2,X3,X0,X1] :
( c_List_Olist__all(X3,X2,X1)
| ~ c_List_Olist__all(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0)) ),
inference(cnf_transformation,[],[f16310]) ).
fof(f40982,plain,
spl647_1197,
inference(avatar_split_clause,[],[f22630,f40980]) ).
fof(f40980,plain,
( spl647_1197
<=> ! [X0,X3,X2,X1] :
( c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
| ~ c_List_Olist__ex(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1197])]) ).
fof(f22630,plain,
! [X2,X3,X0,X1] :
( c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
| ~ c_List_Olist__ex(X3,X2,X0) ),
inference(cnf_transformation,[],[f16308]) ).
fof(f16308,plain,
! [X0,X1,X2,X3] :
( ( c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
| ( ~ c_List_Olist__ex(X3,X2,X0)
& ~ hBOOL(hAPP(X2,X1)) ) )
& ( c_List_Olist__ex(X3,X2,X0)
| hBOOL(hAPP(X2,X1))
| ~ c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0)) ) ),
inference(flattening,[],[f16307]) ).
fof(f16307,plain,
! [X0,X1,X2,X3] :
( ( c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
| ( ~ c_List_Olist__ex(X3,X2,X0)
& ~ hBOOL(hAPP(X2,X1)) ) )
& ( c_List_Olist__ex(X3,X2,X0)
| hBOOL(hAPP(X2,X1))
| ~ c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0)) ) ),
inference(nnf_transformation,[],[f9149]) ).
fof(f9149,plain,
! [X0,X1,X2,X3] :
( c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
<=> ( c_List_Olist__ex(X3,X2,X0)
| hBOOL(hAPP(X2,X1)) ) ),
inference(rectify,[],[f4559]) ).
fof(f4559,axiom,
! [X203,X13,X23,X4] :
( c_List_Olist__ex(X4,X23,hAPP(hAPP(c_List_Olist_OCons(X4),X13),X203))
<=> ( c_List_Olist__ex(X4,X23,X203)
| hBOOL(hAPP(X23,X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40978,plain,
spl647_1196,
inference(avatar_split_clause,[],[f22629,f40976]) ).
fof(f40976,plain,
( spl647_1196
<=> ! [X0,X3,X2,X1] :
( c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1196])]) ).
fof(f22629,plain,
! [X2,X3,X0,X1] :
( c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Olist_OCons(X3),X1),X0))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(cnf_transformation,[],[f16308]) ).
fof(f40974,plain,
spl647_1195,
inference(avatar_split_clause,[],[f22627,f40972]) ).
fof(f40972,plain,
( spl647_1195
<=> ! [X0,X3,X2,X1] :
( c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0))
| ~ c_List_Olist__ex(X3,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1195])]) ).
fof(f22627,plain,
! [X2,X3,X0,X1] :
( c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0))
| ~ c_List_Olist__ex(X3,X2,X0) ),
inference(cnf_transformation,[],[f16306]) ).
fof(f16306,plain,
! [X0,X1,X2,X3] :
( ( c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0))
| ( ~ c_List_Olist__ex(X3,X2,X0)
& ~ c_List_Olist__ex(X3,X2,X1) ) )
& ( c_List_Olist__ex(X3,X2,X0)
| c_List_Olist__ex(X3,X2,X1)
| ~ c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0)) ) ),
inference(flattening,[],[f16305]) ).
fof(f16305,plain,
! [X0,X1,X2,X3] :
( ( c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0))
| ( ~ c_List_Olist__ex(X3,X2,X0)
& ~ c_List_Olist__ex(X3,X2,X1) ) )
& ( c_List_Olist__ex(X3,X2,X0)
| c_List_Olist__ex(X3,X2,X1)
| ~ c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0)) ) ),
inference(nnf_transformation,[],[f9148]) ).
fof(f9148,plain,
! [X0,X1,X2,X3] :
( c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0))
<=> ( c_List_Olist__ex(X3,X2,X0)
| c_List_Olist__ex(X3,X2,X1) ) ),
inference(rectify,[],[f4556]) ).
fof(f4556,axiom,
! [X202,X203,X23,X4] :
( c_List_Olist__ex(X4,X23,hAPP(hAPP(c_List_Oappend(X4),X203),X202))
<=> ( c_List_Olist__ex(X4,X23,X202)
| c_List_Olist__ex(X4,X23,X203) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40970,plain,
spl647_1194,
inference(avatar_split_clause,[],[f22626,f40968]) ).
fof(f40968,plain,
( spl647_1194
<=> ! [X0,X3,X2,X1] :
( c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0))
| ~ c_List_Olist__ex(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1194])]) ).
fof(f22626,plain,
! [X2,X3,X0,X1] :
( c_List_Olist__ex(X3,X2,hAPP(hAPP(c_List_Oappend(X3),X1),X0))
| ~ c_List_Olist__ex(X3,X2,X1) ),
inference(cnf_transformation,[],[f16306]) ).
fof(f40966,plain,
spl647_1193,
inference(avatar_split_clause,[],[f22621,f40964]) ).
fof(f40964,plain,
( spl647_1193
<=> ! [X0,X3,X2,X1] :
( sP61(X0,X1,X2,X3)
| ~ c_List_Olist__ex1(X2,X1,X0)
| hBOOL(hAPP(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1193])]) ).
fof(f22621,plain,
! [X2,X3,X0,X1] :
( sP61(X0,X1,X2,X3)
| ~ c_List_Olist__ex1(X2,X1,X0)
| hBOOL(hAPP(X1,X3)) ),
inference(cnf_transformation,[],[f16303]) ).
fof(f16303,plain,
! [X0,X1,X2,X3] :
( ( sP61(X0,X1,X2,X3)
| ( ~ c_List_Olist__ex1(X2,X1,X0)
& ~ hBOOL(hAPP(X1,X3)) )
| ( ~ c_List_Olist__all(X2,hAPP(hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2),c_fNot),X1))),hAPP(c_fequal,X3)),X0)
& hBOOL(hAPP(X1,X3)) ) )
& ( ( ( c_List_Olist__ex1(X2,X1,X0)
| hBOOL(hAPP(X1,X3)) )
& ( c_List_Olist__all(X2,hAPP(hAPP(c_COMBS(X2,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2),c_fNot),X1))),hAPP(c_fequal,X3)),X0)
| ~ hBOOL(hAPP(X1,X3)) ) )
| ~ sP61(X0,X1,X2,X3) ) ),
inference(rectify,[],[f16302]) ).
fof(f16302,plain,
! [X0,X2,X3,X1] :
( ( sP61(X0,X2,X3,X1)
| ( ~ c_List_Olist__ex1(X3,X2,X0)
& ~ hBOOL(hAPP(X2,X1)) )
| ( ~ c_List_Olist__all(X3,hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),X2))),hAPP(c_fequal,X1)),X0)
& hBOOL(hAPP(X2,X1)) ) )
& ( ( ( c_List_Olist__ex1(X3,X2,X0)
| hBOOL(hAPP(X2,X1)) )
& ( c_List_Olist__all(X3,hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),X2))),hAPP(c_fequal,X1)),X0)
| ~ hBOOL(hAPP(X2,X1)) ) )
| ~ sP61(X0,X2,X3,X1) ) ),
inference(flattening,[],[f16301]) ).
fof(f16301,plain,
! [X0,X2,X3,X1] :
( ( sP61(X0,X2,X3,X1)
| ( ~ c_List_Olist__ex1(X3,X2,X0)
& ~ hBOOL(hAPP(X2,X1)) )
| ( ~ c_List_Olist__all(X3,hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),X2))),hAPP(c_fequal,X1)),X0)
& hBOOL(hAPP(X2,X1)) ) )
& ( ( ( c_List_Olist__ex1(X3,X2,X0)
| hBOOL(hAPP(X2,X1)) )
& ( c_List_Olist__all(X3,hAPP(hAPP(c_COMBS(X3,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X3),c_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X3),c_fNot),X2))),hAPP(c_fequal,X1)),X0)
| ~ hBOOL(hAPP(X2,X1)) ) )
| ~ sP61(X0,X2,X3,X1) ) ),
inference(nnf_transformation,[],[f14580]) ).
fof(f40962,plain,
spl647_1192,
inference(avatar_split_clause,[],[f22618,f40960]) ).
fof(f40960,plain,
( spl647_1192
<=> ! [X0,X3,X2,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| hBOOL(hAPP(X1,X3))
| ~ sP61(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1192])]) ).
fof(f22618,plain,
! [X2,X3,X0,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| hBOOL(hAPP(X1,X3))
| ~ sP61(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16303]) ).
fof(f40958,plain,
spl647_1191,
inference(avatar_split_clause,[],[f22616,f40956]) ).
fof(f40956,plain,
( spl647_1191
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
| ~ hBOOL(hAPP(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1191])]) ).
fof(f22616,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
| ~ hBOOL(hAPP(X1,X0)) ),
inference(cnf_transformation,[],[f16300]) ).
fof(f16300,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
| ( ~ hBOOL(hAPP(X1,X0))
& X0 != X2 ) )
& ( hBOOL(hAPP(X1,X0))
| X0 = X2
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0)) ) ),
inference(flattening,[],[f16299]) ).
fof(f16299,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
| ( ~ hBOOL(hAPP(X1,X0))
& X0 != X2 ) )
& ( hBOOL(hAPP(X1,X0))
| X0 = X2
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0)) ) ),
inference(nnf_transformation,[],[f9146]) ).
fof(f9146,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
<=> ( hBOOL(hAPP(X1,X0))
| X0 = X2 ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X13,X9,X15,X4] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X4),X15),X9),X13))
<=> ( hBOOL(hAPP(X9,X13))
| X13 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40954,plain,
spl647_1190,
inference(avatar_split_clause,[],[f22606,f40952]) ).
fof(f40952,plain,
( spl647_1190
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(c_Predicate_ODomainP(X3,X2,X1),X0))
| ~ hBOOL(hAPP(hAPP(X1,X0),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1190])]) ).
fof(f22606,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(c_Predicate_ODomainP(X3,X2,X1),X0))
| ~ hBOOL(hAPP(hAPP(X1,X0),X4)) ),
inference(cnf_transformation,[],[f16294]) ).
fof(f16294,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(c_Predicate_ODomainP(X3,X2,X1),X0))
| ! [X4] : ~ hBOOL(hAPP(hAPP(X1,X0),X4)) )
& ( hBOOL(hAPP(hAPP(X1,X0),sK486(X0,X1)))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(X3,X2,X1),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK486])],[f16292,f16293]) ).
fof(f16293,plain,
! [X0,X1] :
( ? [X5] : hBOOL(hAPP(hAPP(X1,X0),X5))
=> hBOOL(hAPP(hAPP(X1,X0),sK486(X0,X1))) ),
introduced(choice_axiom,[]) ).
fof(f16292,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(c_Predicate_ODomainP(X3,X2,X1),X0))
| ! [X4] : ~ hBOOL(hAPP(hAPP(X1,X0),X4)) )
& ( ? [X5] : hBOOL(hAPP(hAPP(X1,X0),X5))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(X3,X2,X1),X0)) ) ),
inference(rectify,[],[f16291]) ).
fof(f16291,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(c_Predicate_ODomainP(X3,X2,X1),X0))
| ! [X4] : ~ hBOOL(hAPP(hAPP(X1,X0),X4)) )
& ( ? [X4] : hBOOL(hAPP(hAPP(X1,X0),X4))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(X3,X2,X1),X0)) ) ),
inference(nnf_transformation,[],[f9142]) ).
fof(f9142,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Predicate_ODomainP(X3,X2,X1),X0))
<=> ? [X4] : hBOOL(hAPP(hAPP(X1,X0),X4)) ),
inference(rectify,[],[f3409]) ).
fof(f3409,axiom,
! [X34,X116,X14,X4] :
( hBOOL(hAPP(c_Predicate_ODomainP(X4,X14,X116),X34))
<=> ? [X124] : hBOOL(hAPP(hAPP(X116,X34),X124)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40950,plain,
spl647_1189,
inference(avatar_split_clause,[],[f22604,f40948]) ).
fof(f40948,plain,
( spl647_1189
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(c_Predicate_ORangeP(X3,X2,X1),X0))
| ~ hBOOL(hAPP(hAPP(X1,X4),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1189])]) ).
fof(f22604,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(c_Predicate_ORangeP(X3,X2,X1),X0))
| ~ hBOOL(hAPP(hAPP(X1,X4),X0)) ),
inference(cnf_transformation,[],[f16290]) ).
fof(f16290,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(c_Predicate_ORangeP(X3,X2,X1),X0))
| ! [X4] : ~ hBOOL(hAPP(hAPP(X1,X4),X0)) )
& ( hBOOL(hAPP(hAPP(X1,sK485(X0,X1)),X0))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(X3,X2,X1),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK485])],[f16288,f16289]) ).
fof(f16289,plain,
! [X0,X1] :
( ? [X5] : hBOOL(hAPP(hAPP(X1,X5),X0))
=> hBOOL(hAPP(hAPP(X1,sK485(X0,X1)),X0)) ),
introduced(choice_axiom,[]) ).
fof(f16288,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(c_Predicate_ORangeP(X3,X2,X1),X0))
| ! [X4] : ~ hBOOL(hAPP(hAPP(X1,X4),X0)) )
& ( ? [X5] : hBOOL(hAPP(hAPP(X1,X5),X0))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(X3,X2,X1),X0)) ) ),
inference(rectify,[],[f16287]) ).
fof(f16287,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(c_Predicate_ORangeP(X3,X2,X1),X0))
| ! [X4] : ~ hBOOL(hAPP(hAPP(X1,X4),X0)) )
& ( ? [X4] : hBOOL(hAPP(hAPP(X1,X4),X0))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(X3,X2,X1),X0)) ) ),
inference(nnf_transformation,[],[f9141]) ).
fof(f9141,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Predicate_ORangeP(X3,X2,X1),X0))
<=> ? [X4] : hBOOL(hAPP(hAPP(X1,X4),X0)) ),
inference(rectify,[],[f3352]) ).
fof(f3352,axiom,
! [X33,X116,X14,X4] :
( hBOOL(hAPP(c_Predicate_ORangeP(X4,X14,X116),X33))
<=> ? [X39] : hBOOL(hAPP(hAPP(X116,X39),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40946,plain,
spl647_1188,
inference(avatar_split_clause,[],[f21568,f40944]) ).
fof(f40944,plain,
( spl647_1188
<=> ! [X0,X3,X2,X1] : hAPP(c_Product__Type_Ofst(X3,X2),hAPP(hAPP(c_Product__Type_OPair(X3,X2),X1),X0)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1188])]) ).
fof(f21568,plain,
! [X2,X3,X0,X1] : hAPP(c_Product__Type_Ofst(X3,X2),hAPP(hAPP(c_Product__Type_OPair(X3,X2),X1),X0)) = X1,
inference(cnf_transformation,[],[f8285]) ).
fof(f8285,plain,
! [X0,X1,X2,X3] : hAPP(c_Product__Type_Ofst(X3,X2),hAPP(hAPP(c_Product__Type_OPair(X3,X2),X1),X0)) = X1,
inference(rectify,[],[f2377]) ).
fof(f2377,axiom,
! [X25,X26,X4,X20] : hAPP(c_Product__Type_Ofst(X20,X4),hAPP(hAPP(c_Product__Type_OPair(X20,X4),X26),X25)) = X26,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40942,plain,
spl647_1187,
inference(avatar_split_clause,[],[f21567,f40940]) ).
fof(f40940,plain,
( spl647_1187
<=> ! [X0,X3,X2,X1] : hAPP(c_Product__Type_Osnd(X3,X2),hAPP(hAPP(c_Product__Type_OPair(X3,X2),X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1187])]) ).
fof(f21567,plain,
! [X2,X3,X0,X1] : hAPP(c_Product__Type_Osnd(X3,X2),hAPP(hAPP(c_Product__Type_OPair(X3,X2),X1),X0)) = X0,
inference(cnf_transformation,[],[f8284]) ).
fof(f8284,plain,
! [X0,X1,X2,X3] : hAPP(c_Product__Type_Osnd(X3,X2),hAPP(hAPP(c_Product__Type_OPair(X3,X2),X1),X0)) = X0,
inference(rectify,[],[f2359]) ).
fof(f2359,axiom,
! [X25,X26,X20,X4] : hAPP(c_Product__Type_Osnd(X4,X20),hAPP(hAPP(c_Product__Type_OPair(X4,X20),X26),X25)) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40938,plain,
( ~ spl647_26
| ~ spl647_1186
| ~ spl647_263
| ~ spl647_906 ),
inference(avatar_split_clause,[],[f34430,f34425,f30515,f40935,f29364]) ).
fof(f29364,plain,
( spl647_26
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_26])]) ).
fof(f40935,plain,
( spl647_1186
<=> c_Int_Oiszero(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1186])]) ).
fof(f30515,plain,
( spl647_263
<=> ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_263])]) ).
fof(f34425,plain,
( spl647_906
<=> ! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_906])]) ).
fof(f34430,plain,
( ~ c_Int_Oiszero(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Int_Onumber__ring(tc_Int_Oint)
| ~ spl647_263
| ~ spl647_906 ),
inference(superposition,[],[f34426,f30516]) ).
fof(f30516,plain,
( ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0
| ~ spl647_263 ),
inference(avatar_component_clause,[],[f30515]) ).
fof(f34426,plain,
( ! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Int_Onumber__ring(X0) )
| ~ spl647_906 ),
inference(avatar_component_clause,[],[f34425]) ).
fof(f40933,plain,
spl647_1185,
inference(avatar_split_clause,[],[f21566,f40931]) ).
fof(f40931,plain,
( spl647_1185
<=> ! [X0,X3,X2,X1] : hAPP(hAPP(c_Finite__Set_Ofold(X3,X2,X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1185])]) ).
fof(f21566,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_Finite__Set_Ofold(X3,X2,X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) = X0,
inference(cnf_transformation,[],[f8283]) ).
fof(f8283,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_Finite__Set_Ofold(X3,X2,X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) = X0,
inference(rectify,[],[f358]) ).
fof(f358,axiom,
! [X17,X1,X4,X14] : hAPP(hAPP(c_Finite__Set_Ofold(X14,X4,X1),X17),c_Orderings_Obot__class_Obot(tc_fun(X14,tc_HOL_Obool))) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40929,plain,
spl647_1184,
inference(avatar_split_clause,[],[f21351,f40927]) ).
fof(f40927,plain,
( spl647_1184
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
| ~ sP47(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1184])]) ).
fof(f21351,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
| ~ sP47(X2,X1,X0) ),
inference(cnf_transformation,[],[f15896]) ).
fof(f15896,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
| ~ sP47(X2,X1,X0) )
& ( sP47(X2,X1,X0)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0))) ) ),
inference(nnf_transformation,[],[f14556]) ).
fof(f14556,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
<=> sP47(X2,X1,X0) ),
inference(definition_folding,[],[f12621,f14555]) ).
fof(f12621,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
<=> ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) ) ),
inference(ennf_transformation,[],[f8187]) ).
fof(f8187,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
<=> ~ ( ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X3) = X1 )
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) ) ),
inference(rectify,[],[f922]) ).
fof(f922,axiom,
! [X12,X5,X23] :
( hBOOL(hAPP(X23,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),X12)))
<=> ~ ( ? [X84] :
( ~ hBOOL(hAPP(X23,X84))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X84) = X5 )
| ( ~ hBOOL(hAPP(X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),X12)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40925,plain,
spl647_1183,
inference(avatar_split_clause,[],[f21350,f40923]) ).
fof(f40923,plain,
( spl647_1183
<=> ! [X2,X0,X1] :
( sP47(X2,X1,X0)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1183])]) ).
fof(f21350,plain,
! [X2,X0,X1] :
( sP47(X2,X1,X0)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0))) ),
inference(cnf_transformation,[],[f15896]) ).
fof(f40921,plain,
spl647_1182,
inference(avatar_split_clause,[],[f21343,f40919]) ).
fof(f40919,plain,
( spl647_1182
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
| ~ sP46(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1182])]) ).
fof(f21343,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
| ~ sP46(X2,X1,X0) ),
inference(cnf_transformation,[],[f15890]) ).
fof(f15890,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
| ~ sP46(X2,X1,X0) )
& ( sP46(X2,X1,X0)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0))) ) ),
inference(nnf_transformation,[],[f14554]) ).
fof(f14554,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
<=> sP46(X2,X1,X0) ),
inference(definition_folding,[],[f12620,f14553]) ).
fof(f12620,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
<=> ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X3) != X1 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) ) ),
inference(ennf_transformation,[],[f8186]) ).
fof(f8186,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
<=> ( ! [X3] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X3) = X1
=> hBOOL(hAPP(X2,X3)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
=> hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
inference(rectify,[],[f923]) ).
fof(f923,axiom,
! [X12,X5,X23] :
( hBOOL(hAPP(X23,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X5),X12)))
<=> ( ! [X84] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),X84) = X5
=> hBOOL(hAPP(X23,X84)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),X12))
=> hBOOL(hAPP(X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40917,plain,
spl647_1181,
inference(avatar_split_clause,[],[f21342,f40915]) ).
fof(f40915,plain,
( spl647_1181
<=> ! [X2,X0,X1] :
( sP46(X2,X1,X0)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1181])]) ).
fof(f21342,plain,
! [X2,X0,X1] :
( sP46(X2,X1,X0)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0))) ),
inference(cnf_transformation,[],[f15890]) ).
fof(f40913,plain,
spl647_1180,
inference(avatar_split_clause,[],[f21335,f40911]) ).
fof(f40911,plain,
( spl647_1180
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
| ~ sP45(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1180])]) ).
fof(f21335,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
| ~ sP45(X2,X0,X1) ),
inference(cnf_transformation,[],[f15884]) ).
fof(f15884,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
| ( ~ sP45(X2,X0,X1)
& ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) )
& ( sP45(X2,X0,X1)
| ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0))) ) ),
inference(flattening,[],[f15883]) ).
fof(f15883,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
| ( ~ sP45(X2,X0,X1)
& ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) )
& ( sP45(X2,X0,X1)
| ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0))) ) ),
inference(nnf_transformation,[],[f14552]) ).
fof(f14552,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
<=> ( sP45(X2,X0,X1)
| ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ) ),
inference(definition_folding,[],[f8185,f14551]) ).
fof(f14551,plain,
! [X2,X0,X1] :
( sP45(X2,X0,X1)
<=> ? [X3] :
( hBOOL(hAPP(X2,X3))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X3))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP45])]) ).
fof(f8185,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
<=> ( ? [X3] :
( hBOOL(hAPP(X2,X3))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X3))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X1)) )
| ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ) ),
inference(rectify,[],[f1843]) ).
fof(f1843,axiom,
! [X46,X47,X23] :
( hBOOL(hAPP(X23,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X47),X46)))
<=> ( ? [X118] :
( hBOOL(hAPP(X23,X118))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X47),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X46),hAPP(c_Nat_OSuc,X118))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X46),X118)),X47)) )
| ( hBOOL(hAPP(X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X46 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40909,plain,
spl647_1179,
inference(avatar_split_clause,[],[f21325,f40907]) ).
fof(f40907,plain,
( spl647_1179
<=> ! [X2,X0,X1] :
( sP44(X2,X1,X0)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1179])]) ).
fof(f21325,plain,
! [X2,X0,X1] :
( sP44(X2,X1,X0)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0))) ),
inference(cnf_transformation,[],[f15878]) ).
fof(f15878,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
| ~ sP44(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP44(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0))) ) ),
inference(flattening,[],[f15877]) ).
fof(f15877,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
| ~ sP44(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP44(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0))) ) ),
inference(nnf_transformation,[],[f14550]) ).
fof(f14550,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
<=> ( sP44(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(definition_folding,[],[f12619,f14549]) ).
fof(f12619,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),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 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(flattening,[],[f12618]) ).
fof(f12618,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),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 )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(ennf_transformation,[],[f8184]) ).
fof(f8184,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0))
=> ( 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(X2,X3)) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
=> hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
inference(rectify,[],[f1820]) ).
fof(f1820,axiom,
! [X48,X46,X23] :
( hBOOL(hAPP(X23,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X46),X48)))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X48
=> ! [X86,X83] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X83),X48))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X86)),X83) = X46
=> hBOOL(hAPP(X23,X86)) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X48
=> hBOOL(hAPP(X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40905,plain,
spl647_1178,
inference(avatar_split_clause,[],[f21318,f40903]) ).
fof(f40903,plain,
( spl647_1178
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)))
| ~ sP43(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1178])]) ).
fof(f21318,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)))
| ~ sP43(X0,X1,X2) ),
inference(cnf_transformation,[],[f15871]) ).
fof(f15871,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)))
| ~ sP43(X0,X1,X2) )
& ( sP43(X0,X1,X2)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0))) ) ),
inference(nnf_transformation,[],[f14548]) ).
fof(f14548,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)))
<=> sP43(X0,X1,X2) ),
inference(definition_folding,[],[f12617,f14547,f14546,f14545]) ).
fof(f14547,plain,
! [X0,X1,X2] :
( sP43(X0,X1,X2)
<=> ( sP42(X2,X1,X0)
& sP41(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,[sP43])]) ).
fof(f12617,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)))
<=> ( ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| ! [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [X5] :
( hBOOL(hAPP(X2,X5))
| ! [X6] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
inference(ennf_transformation,[],[f8183]) ).
fof(f8183,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X3] :
( ? [X4] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) )
=> hBOOL(hAPP(X2,X3)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> ! [X5] :
( ? [X6] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) )
=> hBOOL(hAPP(X2,X5)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
=> hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
inference(rectify,[],[f1707]) ).
fof(f1707,axiom,
! [X48,X46,X23] :
( hBOOL(hAPP(X23,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X46),X48)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X86] :
( ? [X83] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X86)),X83) = X46
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X83),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),X83)) )
=> hBOOL(hAPP(X23,X86)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))
=> ! [X86] :
( ? [X83] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X86)),X83) = X46
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X83),X48))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X83)) )
=> hBOOL(hAPP(X23,X86)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X48
=> hBOOL(hAPP(X23,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40901,plain,
spl647_1177,
inference(avatar_split_clause,[],[f21317,f40899]) ).
fof(f40899,plain,
( spl647_1177
<=> ! [X2,X0,X1] :
( sP43(X0,X1,X2)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1177])]) ).
fof(f21317,plain,
! [X2,X0,X1] :
( sP43(X0,X1,X2)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0))) ),
inference(cnf_transformation,[],[f15871]) ).
fof(f40897,plain,
spl647_1176,
inference(avatar_split_clause,[],[f21290,f40895]) ).
fof(f40895,plain,
( spl647_1176
<=> ! [X2,X0,X1] :
( c_List_Olist_ONil(X2) = X0
| c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Oappend(X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1176])]) ).
fof(f21290,plain,
! [X2,X0,X1] :
( c_List_Olist_ONil(X2) = X0
| c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Oappend(X2),X1),X0) ),
inference(cnf_transformation,[],[f15851]) ).
fof(f15851,plain,
! [X0,X1,X2] :
( ( c_List_Olist_ONil(X2) = hAPP(hAPP(c_List_Oappend(X2),X1),X0)
| c_List_Olist_ONil(X2) != X0
| c_List_Olist_ONil(X2) != X1 )
& ( ( c_List_Olist_ONil(X2) = X0
& c_List_Olist_ONil(X2) = X1 )
| c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Oappend(X2),X1),X0) ) ),
inference(flattening,[],[f15850]) ).
fof(f15850,plain,
! [X0,X1,X2] :
( ( c_List_Olist_ONil(X2) = hAPP(hAPP(c_List_Oappend(X2),X1),X0)
| c_List_Olist_ONil(X2) != X0
| c_List_Olist_ONil(X2) != X1 )
& ( ( c_List_Olist_ONil(X2) = X0
& c_List_Olist_ONil(X2) = X1 )
| c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Oappend(X2),X1),X0) ) ),
inference(nnf_transformation,[],[f8179]) ).
fof(f8179,plain,
! [X0,X1,X2] :
( c_List_Olist_ONil(X2) = hAPP(hAPP(c_List_Oappend(X2),X1),X0)
<=> ( c_List_Olist_ONil(X2) = X0
& c_List_Olist_ONil(X2) = X1 ) ),
inference(rectify,[],[f3959]) ).
fof(f3959,axiom,
! [X202,X203,X4] :
( c_List_Olist_ONil(X4) = hAPP(hAPP(c_List_Oappend(X4),X203),X202)
<=> ( c_List_Olist_ONil(X4) = X202
& c_List_Olist_ONil(X4) = X203 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40893,plain,
spl647_1175,
inference(avatar_split_clause,[],[f21289,f40891]) ).
fof(f40891,plain,
( spl647_1175
<=> ! [X2,X0,X1] :
( c_List_Olist_ONil(X2) = X1
| c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Oappend(X2),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1175])]) ).
fof(f21289,plain,
! [X2,X0,X1] :
( c_List_Olist_ONil(X2) = X1
| c_List_Olist_ONil(X2) != hAPP(hAPP(c_List_Oappend(X2),X1),X0) ),
inference(cnf_transformation,[],[f15851]) ).
fof(f40889,plain,
spl647_1174,
inference(avatar_split_clause,[],[f21267,f40887]) ).
fof(f40887,plain,
( spl647_1174
<=> ! [X2,X0,X1] :
( hAPP(c_Finite__Set_Ocard(X0),sK379(X0,X1,X2)) = X1
| ~ sP40(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1174])]) ).
fof(f21267,plain,
! [X2,X0,X1] :
( hAPP(c_Finite__Set_Ocard(X0),sK379(X0,X1,X2)) = X1
| ~ sP40(X0,X1,X2) ),
inference(cnf_transformation,[],[f15840]) ).
fof(f15840,plain,
! [X0,X1,X2] :
( ( sP40(X0,X1,X2)
| ! [X3,X4] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != X4
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| hAPP(c_Finite__Set_Ocard(X0),X4) != X1
| hBOOL(hAPP(hAPP(c_member(X0),X3),X4))
| hAPP(hAPP(c_Set_Oinsert(X0),X3),X4) != X2 ) )
& ( ( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = sK379(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& hAPP(c_Finite__Set_Ocard(X0),sK379(X0,X1,X2)) = X1
& ~ hBOOL(hAPP(hAPP(c_member(X0),sK378(X0,X1,X2)),sK379(X0,X1,X2)))
& hAPP(hAPP(c_Set_Oinsert(X0),sK378(X0,X1,X2)),sK379(X0,X1,X2)) = X2 )
| ~ sP40(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK378,sK379])],[f15838,f15839]) ).
fof(f15839,plain,
! [X0,X1,X2] :
( ? [X5,X6] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X6
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& hAPP(c_Finite__Set_Ocard(X0),X6) = X1
& ~ hBOOL(hAPP(hAPP(c_member(X0),X5),X6))
& hAPP(hAPP(c_Set_Oinsert(X0),X5),X6) = X2 )
=> ( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = sK379(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& hAPP(c_Finite__Set_Ocard(X0),sK379(X0,X1,X2)) = X1
& ~ hBOOL(hAPP(hAPP(c_member(X0),sK378(X0,X1,X2)),sK379(X0,X1,X2)))
& hAPP(hAPP(c_Set_Oinsert(X0),sK378(X0,X1,X2)),sK379(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f15838,plain,
! [X0,X1,X2] :
( ( sP40(X0,X1,X2)
| ! [X3,X4] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != X4
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| hAPP(c_Finite__Set_Ocard(X0),X4) != X1
| hBOOL(hAPP(hAPP(c_member(X0),X3),X4))
| hAPP(hAPP(c_Set_Oinsert(X0),X3),X4) != X2 ) )
& ( ? [X5,X6] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X6
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& hAPP(c_Finite__Set_Ocard(X0),X6) = X1
& ~ hBOOL(hAPP(hAPP(c_member(X0),X5),X6))
& hAPP(hAPP(c_Set_Oinsert(X0),X5),X6) = X2 )
| ~ sP40(X0,X1,X2) ) ),
inference(rectify,[],[f15837]) ).
fof(f15837,plain,
! [X2,X0,X1] :
( ( sP40(X2,X0,X1)
| ! [X3,X4] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != X4
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| hAPP(c_Finite__Set_Ocard(X2),X4) != X0
| hBOOL(hAPP(hAPP(c_member(X2),X3),X4))
| hAPP(hAPP(c_Set_Oinsert(X2),X3),X4) != X1 ) )
& ( ? [X3,X4] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X4
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& hAPP(c_Finite__Set_Ocard(X2),X4) = X0
& ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4))
& hAPP(hAPP(c_Set_Oinsert(X2),X3),X4) = X1 )
| ~ sP40(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f14543]) ).
fof(f14543,plain,
! [X2,X0,X1] :
( sP40(X2,X0,X1)
<=> ? [X3,X4] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X4
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& hAPP(c_Finite__Set_Ocard(X2),X4) = X0
& ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4))
& hAPP(hAPP(c_Set_Oinsert(X2),X3),X4) = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP40])]) ).
fof(f40885,plain,
spl647_1173,
inference(avatar_split_clause,[],[f21197,f40883]) ).
fof(f40883,plain,
( spl647_1173
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_List_Olistsp(X2,X1),X0))
| ~ hBOOL(hAPP(X1,sK366(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1173])]) ).
fof(f21197,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_List_Olistsp(X2,X1),X0))
| ~ hBOOL(hAPP(X1,sK366(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15784]) ).
fof(f15784,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_List_Olistsp(X2,X1),X0))
| ( ~ hBOOL(hAPP(X1,sK366(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK366(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ hBOOL(hAPP(c_List_Olistsp(X2,X1),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK366])],[f15782,f15783]) ).
fof(f15783,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
=> ( ~ hBOOL(hAPP(X1,sK366(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK366(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15782,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_List_Olistsp(X2,X1),X0))
| ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ hBOOL(hAPP(c_List_Olistsp(X2,X1),X0)) ) ),
inference(rectify,[],[f15781]) ).
fof(f15781,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_List_Olistsp(X2,X1),X0))
| ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X3] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
| ~ hBOOL(hAPP(c_List_Olistsp(X2,X1),X0)) ) ),
inference(nnf_transformation,[],[f12606]) ).
fof(f12606,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_List_Olistsp(X2,X1),X0))
<=> ! [X3] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
inference(ennf_transformation,[],[f8150]) ).
fof(f8150,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_List_Olistsp(X2,X1),X0))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0)))
=> hBOOL(hAPP(X1,X3)) ) ),
inference(rectify,[],[f4224]) ).
fof(f4224,axiom,
! [X203,X9,X4] :
( hBOOL(hAPP(c_List_Olistsp(X4,X9),X203))
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X203)))
=> hBOOL(hAPP(X9,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40881,plain,
spl647_1172,
inference(avatar_split_clause,[],[f21175,f40879]) ).
fof(f40879,plain,
( spl647_1172
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Predicate_OPowp(X2,X1),X0))
| ~ hBOOL(hAPP(X1,sK365(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1172])]) ).
fof(f21175,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Predicate_OPowp(X2,X1),X0))
| ~ hBOOL(hAPP(X1,sK365(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15773]) ).
fof(f15773,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Predicate_OPowp(X2,X1),X0))
| ( ~ hBOOL(hAPP(X1,sK365(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK365(X0,X1,X2)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X0)) )
| ~ hBOOL(hAPP(c_Predicate_OPowp(X2,X1),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK365])],[f15771,f15772]) ).
fof(f15772,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0)) )
=> ( ~ hBOOL(hAPP(X1,sK365(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK365(X0,X1,X2)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f15771,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Predicate_OPowp(X2,X1),X0))
| ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X0)) )
| ~ hBOOL(hAPP(c_Predicate_OPowp(X2,X1),X0)) ) ),
inference(rectify,[],[f15770]) ).
fof(f15770,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Predicate_OPowp(X2,X1),X0))
| ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0)) ) )
& ( ! [X3] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X0)) )
| ~ hBOOL(hAPP(c_Predicate_OPowp(X2,X1),X0)) ) ),
inference(nnf_transformation,[],[f12604]) ).
fof(f12604,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Predicate_OPowp(X2,X1),X0))
<=> ! [X3] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X0)) ) ),
inference(ennf_transformation,[],[f8147]) ).
fof(f8147,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Predicate_OPowp(X2,X1),X0))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
=> hBOOL(hAPP(X1,X3)) ) ),
inference(rectify,[],[f3430]) ).
fof(f3430,axiom,
! [X18,X9,X4] :
( hBOOL(hAPP(c_Predicate_OPowp(X4,X9),X18))
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),X18))
=> hBOOL(hAPP(X9,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40877,plain,
spl647_1171,
inference(avatar_split_clause,[],[f21172,f40875]) ).
fof(f40875,plain,
( spl647_1171
<=> ! [X2,X0,X1] :
( c_List_OtakeWhile(X2,X1,X0) = X0
| ~ hBOOL(hAPP(X1,sK364(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1171])]) ).
fof(f21172,plain,
! [X2,X0,X1] :
( c_List_OtakeWhile(X2,X1,X0) = X0
| ~ hBOOL(hAPP(X1,sK364(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15769]) ).
fof(f15769,plain,
! [X0,X1,X2] :
( ( c_List_OtakeWhile(X2,X1,X0) = X0
| ( ~ hBOOL(hAPP(X1,sK364(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK364(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| c_List_OtakeWhile(X2,X1,X0) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK364])],[f15767,f15768]) ).
fof(f15768,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
=> ( ~ hBOOL(hAPP(X1,sK364(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK364(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15767,plain,
! [X0,X1,X2] :
( ( c_List_OtakeWhile(X2,X1,X0) = X0
| ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| c_List_OtakeWhile(X2,X1,X0) != X0 ) ),
inference(rectify,[],[f15766]) ).
fof(f15766,plain,
! [X0,X1,X2] :
( ( c_List_OtakeWhile(X2,X1,X0) = X0
| ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X3] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
| c_List_OtakeWhile(X2,X1,X0) != X0 ) ),
inference(nnf_transformation,[],[f12603]) ).
fof(f12603,plain,
! [X0,X1,X2] :
( c_List_OtakeWhile(X2,X1,X0) = X0
<=> ! [X3] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
inference(ennf_transformation,[],[f8146]) ).
fof(f8146,plain,
! [X0,X1,X2] :
( c_List_OtakeWhile(X2,X1,X0) = X0
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0)))
=> hBOOL(hAPP(X1,X3)) ) ),
inference(rectify,[],[f4476]) ).
fof(f4476,axiom,
! [X203,X23,X4] :
( c_List_OtakeWhile(X4,X23,X203) = X203
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X203)))
=> hBOOL(hAPP(X23,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40873,plain,
spl647_1170,
inference(avatar_split_clause,[],[f21155,f40871]) ).
fof(f40871,plain,
( spl647_1170
<=> ! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| sK359(X0,X1,X2) != sK360(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1170])]) ).
fof(f21155,plain,
! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| sK359(X0,X1,X2) != sK360(X0,X1,X2) ),
inference(cnf_transformation,[],[f15752]) ).
fof(f15752,plain,
! [X0,X1,X2] :
( ( c_Relation_Osingle__valued(X2,X1,X0)
| ( sK359(X0,X1,X2) != sK360(X0,X1,X2)
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),sK358(X0,X1,X2)),sK360(X0,X1,X2))),X0))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),sK358(X0,X1,X2)),sK359(X0,X1,X2))),X0)) ) )
& ( ! [X6,X7] :
( ! [X8] :
( X7 = X8
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X6),X8)),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X6),X7)),X0)) )
| ~ c_Relation_Osingle__valued(X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK358,sK359,sK360])],[f15749,f15751,f15750]) ).
fof(f15750,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ? [X5] :
( X4 != X5
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X5)),X0)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X4)),X0)) )
=> ( ? [X5] :
( sK359(X0,X1,X2) != X5
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),sK358(X0,X1,X2)),X5)),X0)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),sK358(X0,X1,X2)),sK359(X0,X1,X2))),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f15751,plain,
! [X0,X1,X2] :
( ? [X5] :
( sK359(X0,X1,X2) != X5
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),sK358(X0,X1,X2)),X5)),X0)) )
=> ( sK359(X0,X1,X2) != sK360(X0,X1,X2)
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),sK358(X0,X1,X2)),sK360(X0,X1,X2))),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f15749,plain,
! [X0,X1,X2] :
( ( c_Relation_Osingle__valued(X2,X1,X0)
| ? [X3,X4] :
( ? [X5] :
( X4 != X5
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X5)),X0)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X4)),X0)) ) )
& ( ! [X6,X7] :
( ! [X8] :
( X7 = X8
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X6),X8)),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X6),X7)),X0)) )
| ~ c_Relation_Osingle__valued(X2,X1,X0) ) ),
inference(rectify,[],[f15748]) ).
fof(f15748,plain,
! [X0,X1,X2] :
( ( c_Relation_Osingle__valued(X2,X1,X0)
| ? [X3,X4] :
( ? [X5] :
( X4 != X5
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X5)),X0)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X4)),X0)) ) )
& ( ! [X3,X4] :
( ! [X5] :
( X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X5)),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X4)),X0)) )
| ~ c_Relation_Osingle__valued(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f12600]) ).
fof(f12600,plain,
! [X0,X1,X2] :
( c_Relation_Osingle__valued(X2,X1,X0)
<=> ! [X3,X4] :
( ! [X5] :
( X4 = X5
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X5)),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X4)),X0)) ) ),
inference(ennf_transformation,[],[f8142]) ).
fof(f8142,plain,
! [X0,X1,X2] :
( c_Relation_Osingle__valued(X2,X1,X0)
<=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X4)),X0))
=> ! [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X5)),X0))
=> X4 = X5 ) ) ),
inference(rectify,[],[f3681]) ).
fof(f3681,axiom,
! [X116,X14,X4] :
( c_Relation_Osingle__valued(X4,X14,X116)
<=> ! [X2,X38] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X14)),hAPP(hAPP(c_Product__Type_OPair(X4,X14),X2),X38)),X116))
=> ! [X88] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X14)),hAPP(hAPP(c_Product__Type_OPair(X4,X14),X2),X88)),X116))
=> X38 = X88 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40869,plain,
spl647_1169,
inference(avatar_split_clause,[],[f21136,f40867]) ).
fof(f40867,plain,
( spl647_1169
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| sK353(X0,X1,X2) != sK354(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1169])]) ).
fof(f21136,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| sK353(X0,X1,X2) != sK354(X0,X1,X2) ),
inference(cnf_transformation,[],[f15733]) ).
fof(f40865,plain,
spl647_1168,
inference(avatar_split_clause,[],[f20683,f40863]) ).
fof(f40863,plain,
( spl647_1168
<=> ! [X2,X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,sK259(X0,X1,X2))
| ~ sP21(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1168])]) ).
fof(f20683,plain,
! [X2,X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,sK259(X0,X1,X2))
| ~ sP21(X0,X1,X2) ),
inference(cnf_transformation,[],[f15503]) ).
fof(f40861,plain,
spl647_1167,
inference(avatar_split_clause,[],[f20618,f40859]) ).
fof(f40859,plain,
( spl647_1167
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X2),c_List_OtakeWhile(X2,X0,X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1167])]) ).
fof(f20618,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X2),c_List_OtakeWhile(X2,X0,X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
inference(cnf_transformation,[],[f12144]) ).
fof(f12144,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_List_Odistinct(X2),c_List_OtakeWhile(X2,X0,X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
inference(ennf_transformation,[],[f7811]) ).
fof(f7811,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_List_Odistinct(X2),X1))
=> hBOOL(hAPP(c_List_Odistinct(X2),c_List_OtakeWhile(X2,X0,X1))) ),
inference(rectify,[],[f4484]) ).
fof(f4484,axiom,
! [X23,X203,X4] :
( hBOOL(hAPP(c_List_Odistinct(X4),X203))
=> hBOOL(hAPP(c_List_Odistinct(X4),c_List_OtakeWhile(X4,X23,X203))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40857,plain,
spl647_1166,
inference(avatar_split_clause,[],[f20617,f40855]) ).
fof(f40855,plain,
( spl647_1166
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oremove1(X2,X0,X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1166])]) ).
fof(f20617,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oremove1(X2,X0,X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
inference(cnf_transformation,[],[f12143]) ).
fof(f12143,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oremove1(X2,X0,X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
inference(ennf_transformation,[],[f7810]) ).
fof(f7810,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_List_Odistinct(X2),X1))
=> hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oremove1(X2,X0,X1))) ),
inference(rectify,[],[f3879]) ).
fof(f3879,axiom,
! [X19,X201,X20] :
( hBOOL(hAPP(c_List_Odistinct(X20),X201))
=> hBOOL(hAPP(c_List_Odistinct(X20),c_List_Oremove1(X20,X19,X201))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40853,plain,
spl647_1165,
inference(avatar_split_clause,[],[f20614,f40851]) ).
fof(f40851,plain,
( spl647_1165
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oinsert(X2,X0,X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1165])]) ).
fof(f20614,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oinsert(X2,X0,X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
inference(cnf_transformation,[],[f12140]) ).
fof(f12140,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oinsert(X2,X0,X1)))
| ~ hBOOL(hAPP(c_List_Odistinct(X2),X1)) ),
inference(ennf_transformation,[],[f7807]) ).
fof(f7807,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_List_Odistinct(X2),X1))
=> hBOOL(hAPP(c_List_Odistinct(X2),c_List_Oinsert(X2,X0,X1))) ),
inference(rectify,[],[f4518]) ).
fof(f4518,axiom,
! [X19,X201,X20] :
( hBOOL(hAPP(c_List_Odistinct(X20),X201))
=> hBOOL(hAPP(c_List_Odistinct(X20),c_List_Oinsert(X20,X19,X201))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40849,plain,
spl647_1164,
inference(avatar_split_clause,[],[f20391,f40847]) ).
fof(f40847,plain,
( spl647_1164
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,X0)
| ~ c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0))
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1164])]) ).
fof(f20391,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,X0)
| ~ c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0))
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f15433]) ).
fof(f15433,plain,
! [X0,X1,X2] :
( ( ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),sK241(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK241(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olinorder__class_Osorted(X2,X0) )
& ( ( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
& c_List_Olinorder__class_Osorted(X2,X0) )
| ~ c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK241])],[f15431,f15432]) ).
fof(f15432,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),sK241(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK241(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15431,plain,
! [X0,X1,X2] :
( ( ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0))
| ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olinorder__class_Osorted(X2,X0) )
& ( ( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
& c_List_Olinorder__class_Osorted(X2,X0) )
| ~ c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(rectify,[],[f15430]) ).
fof(f15430,plain,
! [X0,X1,X2] :
( ( ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0))
| ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olinorder__class_Osorted(X2,X0) )
& ( ( ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
& c_List_Olinorder__class_Osorted(X2,X0) )
| ~ c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f15429]) ).
fof(f15429,plain,
! [X0,X1,X2] :
( ( ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0))
| ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olinorder__class_Osorted(X2,X0) )
& ( ( ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
& c_List_Olinorder__class_Osorted(X2,X0) )
| ~ c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(nnf_transformation,[],[f11892]) ).
fof(f11892,plain,
! [X0,X1,X2] :
( ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0))
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
& c_List_Olinorder__class_Osorted(X2,X0) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7632]) ).
fof(f7632,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0))
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X3)) )
& c_List_Olinorder__class_Osorted(X2,X0) ) ) ),
inference(rectify,[],[f4423]) ).
fof(f4423,axiom,
! [X203,X13,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Olist_OCons(X4),X13),X203))
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X203)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X2)) )
& c_List_Olinorder__class_Osorted(X4,X203) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40845,plain,
spl647_1163,
inference(avatar_split_clause,[],[f20245,f40843]) ).
fof(f40843,plain,
( spl647_1163
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Otake(X2),X0),X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1163])]) ).
fof(f20245,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Otake(X2),X0),X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f11686]) ).
fof(f11686,plain,
! [X0,X1,X2] :
( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Otake(X2),X0),X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f11685]) ).
fof(f11685,plain,
! [X0,X1,X2] :
( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Otake(X2),X0),X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7525]) ).
fof(f7525,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_List_Olinorder__class_Osorted(X2,X1)
=> c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Otake(X2),X0),X1)) ) ),
inference(rectify,[],[f4406]) ).
fof(f4406,axiom,
! [X44,X201,X20] :
( class_Orderings_Olinorder(X20)
=> ( c_List_Olinorder__class_Osorted(X20,X201)
=> c_List_Olinorder__class_Osorted(X20,hAPP(hAPP(c_List_Otake(X20),X44),X201)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40841,plain,
spl647_1162,
inference(avatar_split_clause,[],[f20244,f40839]) ).
fof(f40839,plain,
( spl647_1162
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Odrop(X2),X0),X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1162])]) ).
fof(f20244,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Odrop(X2),X0),X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f11684]) ).
fof(f11684,plain,
! [X0,X1,X2] :
( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Odrop(X2),X0),X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f11683]) ).
fof(f11683,plain,
! [X0,X1,X2] :
( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Odrop(X2),X0),X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7524]) ).
fof(f7524,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_List_Olinorder__class_Osorted(X2,X1)
=> c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Odrop(X2),X0),X1)) ) ),
inference(rectify,[],[f4404]) ).
fof(f4404,axiom,
! [X44,X201,X20] :
( class_Orderings_Olinorder(X20)
=> ( c_List_Olinorder__class_Osorted(X20,X201)
=> c_List_Olinorder__class_Osorted(X20,hAPP(hAPP(c_List_Odrop(X20),X44),X201)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40837,plain,
spl647_1161,
inference(avatar_split_clause,[],[f19612,f40835]) ).
fof(f40835,plain,
( spl647_1161
<=> ! [X2,X0,X1] : c_List_Olist_ONil(tc_prod(X2,X1)) = hAPP(hAPP(c_List_Ozip(X2,X1),X0),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1161])]) ).
fof(f19612,plain,
! [X2,X0,X1] : c_List_Olist_ONil(tc_prod(X2,X1)) = hAPP(hAPP(c_List_Ozip(X2,X1),X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f6966]) ).
fof(f6966,plain,
! [X0,X1,X2] : c_List_Olist_ONil(tc_prod(X2,X1)) = hAPP(hAPP(c_List_Ozip(X2,X1),X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f3894]) ).
fof(f3894,axiom,
! [X201,X4,X20] : hAPP(hAPP(c_List_Ozip(X20,X4),X201),c_List_Olist_ONil(X4)) = c_List_Olist_ONil(tc_prod(X20,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40833,plain,
spl647_1160,
inference(avatar_split_clause,[],[f19611,f40831]) ).
fof(f40831,plain,
( spl647_1160
<=> ! [X2,X0,X1] : c_List_Oinsert(X2,X1,c_List_Oremdups(X2,X0)) = c_List_Oremdups(X2,c_List_Oinsert(X2,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1160])]) ).
fof(f19611,plain,
! [X2,X0,X1] : c_List_Oinsert(X2,X1,c_List_Oremdups(X2,X0)) = c_List_Oremdups(X2,c_List_Oinsert(X2,X1,X0)),
inference(cnf_transformation,[],[f6965]) ).
fof(f6965,plain,
! [X0,X1,X2] : c_List_Oinsert(X2,X1,c_List_Oremdups(X2,X0)) = c_List_Oremdups(X2,c_List_Oinsert(X2,X1,X0)),
inference(rectify,[],[f4517]) ).
fof(f4517,axiom,
! [X201,X19,X20] : c_List_Oinsert(X20,X19,c_List_Oremdups(X20,X201)) = c_List_Oremdups(X20,c_List_Oinsert(X20,X19,X201)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40829,plain,
spl647_1159,
inference(avatar_split_clause,[],[f19609,f40827]) ).
fof(f40827,plain,
( spl647_1159
<=> ! [X2,X0,X1] : c_List_Olist_ONil(tc_prod(X2,X1)) = hAPP(hAPP(c_List_Ozip(X2,X1),c_List_Olist_ONil(X2)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1159])]) ).
fof(f19609,plain,
! [X2,X0,X1] : c_List_Olist_ONil(tc_prod(X2,X1)) = hAPP(hAPP(c_List_Ozip(X2,X1),c_List_Olist_ONil(X2)),X0),
inference(cnf_transformation,[],[f6963]) ).
fof(f6963,plain,
! [X0,X1,X2] : c_List_Olist_ONil(tc_prod(X2,X1)) = hAPP(hAPP(c_List_Ozip(X2,X1),c_List_Olist_ONil(X2)),X0),
inference(rectify,[],[f3895]) ).
fof(f3895,axiom,
! [X200,X4,X20] : c_List_Olist_ONil(tc_prod(X20,X4)) = hAPP(hAPP(c_List_Ozip(X20,X4),c_List_Olist_ONil(X20)),X200),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40825,plain,
spl647_1158,
inference(avatar_split_clause,[],[f19571,f40823]) ).
fof(f40823,plain,
( spl647_1158
<=> ! [X2,X0,X1] : hAPP(c_Set_OPow(X1),X0) != hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1158])]) ).
fof(f19571,plain,
! [X2,X0,X1] : hAPP(c_Set_OPow(X1),X0) != hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X2),X0),
inference(cnf_transformation,[],[f11302]) ).
fof(f11302,plain,
! [X0,X1,X2] : hAPP(c_Set_OPow(X1),X0) != hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X2),X0),
inference(flattening,[],[f11301]) ).
fof(f11301,plain,
! [X0,X1,X2] : hAPP(c_Set_OPow(X1),X0) != hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X2),X0),
inference(ennf_transformation,[],[f6925]) ).
fof(f6925,plain,
! [X0,X1] :
~ ? [X2] : hAPP(c_Set_OPow(X1),X0) = hAPP(c_Set_Oimage(X1,tc_fun(X1,tc_HOL_Obool),X2),X0),
inference(rectify,[],[f2877]) ).
fof(f2877,axiom,
! [X9,X4] :
~ ? [X164] : hAPP(c_Set_OPow(X4),X9) = hAPP(c_Set_Oimage(X4,tc_fun(X4,tc_HOL_Obool),X164),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40821,plain,
spl647_1157,
inference(avatar_split_clause,[],[f19283,f40819]) ).
fof(f40819,plain,
( spl647_1157
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1157])]) ).
fof(f19283,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
inference(cnf_transformation,[],[f15116]) ).
fof(f15116,plain,
! [X0,X1] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1 )
& ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
inference(flattening,[],[f15115]) ).
fof(f15115,plain,
! [X0,X1] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1 )
& ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
inference(nnf_transformation,[],[f6818]) ).
fof(f6818,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
<=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 ) ),
inference(rectify,[],[f503]) ).
fof(f503,axiom,
! [X46,X47] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X47),X46)
<=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X46
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X47 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40817,plain,
spl647_1156,
inference(avatar_split_clause,[],[f19282,f40815]) ).
fof(f40815,plain,
( spl647_1156
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1156])]) ).
fof(f19282,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
inference(cnf_transformation,[],[f15116]) ).
fof(f40813,plain,
( ~ spl647_1154
| ~ spl647_1155
| ~ spl647_707
| ~ spl647_906 ),
inference(avatar_split_clause,[],[f34429,f34425,f32685,f40810,f40806]) ).
fof(f40806,plain,
( spl647_1154
<=> class_Int_Onumber__ring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1154])]) ).
fof(f40810,plain,
( spl647_1155
<=> c_Int_Oiszero(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1155])]) ).
fof(f32685,plain,
( spl647_707
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_707])]) ).
fof(f34429,plain,
( ~ c_Int_Oiszero(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Int_Onumber__ring(tc_Nat_Onat)
| ~ spl647_707
| ~ spl647_906 ),
inference(superposition,[],[f34426,f32687]) ).
fof(f32687,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl647_707 ),
inference(avatar_component_clause,[],[f32685]) ).
fof(f40804,plain,
spl647_1153,
inference(avatar_split_clause,[],[f19273,f40802]) ).
fof(f40802,plain,
( spl647_1153
<=> ! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X0)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1153])]) ).
fof(f19273,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X0)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(cnf_transformation,[],[f15111]) ).
fof(f15111,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X0)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) )
& ( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X0))) ) ),
inference(nnf_transformation,[],[f6816]) ).
fof(f6816,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X0)))
<=> hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(rectify,[],[f4435]) ).
fof(f4435,axiom,
! [X203,X4] :
( hBOOL(hAPP(c_List_Odistinct(X4),hAPP(c_List_Orev(X4),X203)))
<=> hBOOL(hAPP(c_List_Odistinct(X4),X203)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40800,plain,
spl647_1152,
inference(avatar_split_clause,[],[f19272,f40798]) ).
fof(f40798,plain,
( spl647_1152
<=> ! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1152])]) ).
fof(f19272,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X0))) ),
inference(cnf_transformation,[],[f15111]) ).
fof(f40796,plain,
spl647_1151,
inference(avatar_split_clause,[],[f19271,f40794]) ).
fof(f40794,plain,
( spl647_1151
<=> ! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X0)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1151])]) ).
fof(f19271,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X0)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(cnf_transformation,[],[f15110]) ).
fof(f15110,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X0)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) )
& ( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X0))) ) ),
inference(nnf_transformation,[],[f6815]) ).
fof(f6815,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X0)))
<=> hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(rectify,[],[f3992]) ).
fof(f3992,axiom,
! [X203,X4] :
( hBOOL(hAPP(c_List_Odistinct(X4),hAPP(c_List_Orotate1(X4),X203)))
<=> hBOOL(hAPP(c_List_Odistinct(X4),X203)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40792,plain,
spl647_1150,
inference(avatar_split_clause,[],[f19270,f40790]) ).
fof(f40790,plain,
( spl647_1150
<=> ! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1150])]) ).
fof(f19270,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X0))) ),
inference(cnf_transformation,[],[f15110]) ).
fof(f40788,plain,
spl647_1149,
inference(avatar_split_clause,[],[f19205,f40786]) ).
fof(f40786,plain,
( spl647_1149
<=> ! [X0,X1] :
( c_List_Otranspose(X1,X0) = c_List_Olist_ONil(tc_List_Olist(X1))
| c_List_Olist_ONil(X1) != sK199(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1149])]) ).
fof(f19205,plain,
! [X0,X1] :
( c_List_Otranspose(X1,X0) = c_List_Olist_ONil(tc_List_Olist(X1))
| c_List_Olist_ONil(X1) != sK199(X0,X1) ),
inference(cnf_transformation,[],[f15063]) ).
fof(f15063,plain,
! [X0,X1] :
( ( c_List_Otranspose(X1,X0) = c_List_Olist_ONil(tc_List_Olist(X1))
| ( c_List_Olist_ONil(X1) != sK199(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),sK199(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) ) )
& ( ! [X3] :
( c_List_Olist_ONil(X1) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) )
| c_List_Otranspose(X1,X0) != c_List_Olist_ONil(tc_List_Olist(X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK199])],[f15061,f15062]) ).
fof(f15062,plain,
! [X0,X1] :
( ? [X2] :
( c_List_Olist_ONil(X1) != X2
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) )
=> ( c_List_Olist_ONil(X1) != sK199(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),sK199(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15061,plain,
! [X0,X1] :
( ( c_List_Otranspose(X1,X0) = c_List_Olist_ONil(tc_List_Olist(X1))
| ? [X2] :
( c_List_Olist_ONil(X1) != X2
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) ) )
& ( ! [X3] :
( c_List_Olist_ONil(X1) = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) )
| c_List_Otranspose(X1,X0) != c_List_Olist_ONil(tc_List_Olist(X1)) ) ),
inference(rectify,[],[f15060]) ).
fof(f15060,plain,
! [X0,X1] :
( ( c_List_Otranspose(X1,X0) = c_List_Olist_ONil(tc_List_Olist(X1))
| ? [X2] :
( c_List_Olist_ONil(X1) != X2
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) ) )
& ( ! [X2] :
( c_List_Olist_ONil(X1) = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) )
| c_List_Otranspose(X1,X0) != c_List_Olist_ONil(tc_List_Olist(X1)) ) ),
inference(nnf_transformation,[],[f11290]) ).
fof(f11290,plain,
! [X0,X1] :
( c_List_Otranspose(X1,X0) = c_List_Olist_ONil(tc_List_Olist(X1))
<=> ! [X2] :
( c_List_Olist_ONil(X1) = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) ) ),
inference(ennf_transformation,[],[f6785]) ).
fof(f6785,plain,
! [X0,X1] :
( c_List_Otranspose(X1,X0) = c_List_Olist_ONil(tc_List_Olist(X1))
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X2),hAPP(c_List_Oset(tc_List_Olist(X1)),X0)))
=> c_List_Olist_ONil(X1) = X2 ) ),
inference(rectify,[],[f4346]) ).
fof(f4346,axiom,
! [X203,X4] :
( c_List_Olist_ONil(tc_List_Olist(X4)) = c_List_Otranspose(X4,X203)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X4)),X2),hAPP(c_List_Oset(tc_List_Olist(X4)),X203)))
=> c_List_Olist_ONil(X4) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40784,plain,
spl647_1148,
inference(avatar_split_clause,[],[f19117,f40782]) ).
fof(f40782,plain,
( spl647_1148
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X0),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1148])]) ).
fof(f19117,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X0),X0)) ),
inference(cnf_transformation,[],[f14981]) ).
fof(f14981,plain,
! [X0,X1] :
( ( c_Wellfounded_Owf(X1,X0)
| ~ c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X0),X0)) )
& ( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X0),X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
inference(nnf_transformation,[],[f6757]) ).
fof(f6757,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X0),X0)) ),
inference(rectify,[],[f3363]) ).
fof(f3363,axiom,
! [X138,X4] :
( c_Wellfounded_Owf(X4,X138)
<=> c_Wellfounded_Owf(X4,hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X4),X138),X138)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40780,plain,
spl647_1147,
inference(avatar_split_clause,[],[f19116,f40778]) ).
fof(f40778,plain,
( spl647_1147
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X0),X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1147])]) ).
fof(f19116,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X0),X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f14981]) ).
fof(f40776,plain,
spl647_1146,
inference(avatar_split_clause,[],[f18854,f40774]) ).
fof(f40774,plain,
( spl647_1146
<=> ! [X5,X0,X1] :
( hBOOL(hAPP(X0,sK151(X0,X1)))
| ~ hBOOL(hAPP(X0,X5))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1146])]) ).
fof(f18854,plain,
! [X0,X1,X5] :
( hBOOL(hAPP(X0,sK151(X0,X1)))
| ~ hBOOL(hAPP(X0,X5))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f14873]) ).
fof(f14873,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(X0,sK150(X0)))
| ! [X3] :
( ~ hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))) ) )
& ( ( hBOOL(hAPP(X0,sK151(X0,X1)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK151(X0,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))) )
| ! [X5] : ~ hBOOL(hAPP(X0,X5)) ) )
| ~ sP3(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK150,sK151])],[f14870,f14872,f14871]) ).
fof(f14871,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X0,sK150(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14872,plain,
! [X0,X1] :
( ? [X4] :
( hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))) )
=> ( hBOOL(hAPP(X0,sK151(X0,X1)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK151(X0,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f14870,plain,
! [X0,X1] :
( ( ( ? [X2] : hBOOL(hAPP(X0,X2))
| ! [X3] :
( ~ hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))) ) )
& ( ? [X4] :
( hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))) )
| ! [X5] : ~ hBOOL(hAPP(X0,X5)) ) )
| ~ sP3(X0,X1) ),
inference(rectify,[],[f14869]) ).
fof(f14869,plain,
! [X0,X1] :
( ( ( ? [X4] : hBOOL(hAPP(X0,X4))
| ! [X5] :
( ~ hBOOL(hAPP(X0,X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X5),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))) ) )
& ( ? [X5] :
( hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X5),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))) )
| ! [X4] : ~ hBOOL(hAPP(X0,X4)) ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f14480]) ).
fof(f14480,plain,
! [X0,X1] :
( ( ? [X4] : hBOOL(hAPP(X0,X4))
<=> ? [X5] :
( hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X5),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))) ) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f40772,plain,
spl647_1145,
inference(avatar_split_clause,[],[f18808,f40770]) ).
fof(f40770,plain,
( spl647_1145
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1145])]) ).
fof(f18808,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X0)) ),
inference(cnf_transformation,[],[f10991]) ).
fof(f10991,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X0)) ),
inference(flattening,[],[f10990]) ).
fof(f10990,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X0)) ),
inference(ennf_transformation,[],[f6544]) ).
fof(f6544,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X1,X1)),X0))
=> ( c_Wellfounded_Oacyclic(X1,X0)
=> c_Wellfounded_Owf(X1,X0) ) ),
inference(rectify,[],[f3436]) ).
fof(f3436,axiom,
! [X116,X4] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X4,X4)),X116))
=> ( c_Wellfounded_Oacyclic(X4,X116)
=> c_Wellfounded_Owf(X4,X116) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40768,plain,
spl647_1144,
inference(avatar_split_clause,[],[f18773,f40766]) ).
fof(f40766,plain,
( spl647_1144
<=> ! [X0,X1] :
( c_List_Olist_ONil(tc_Int_Oint) = c_List_Oupto(X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1144])]) ).
fof(f18773,plain,
! [X0,X1] :
( c_List_Olist_ONil(tc_Int_Oint) = c_List_Oupto(X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f10952]) ).
fof(f10952,plain,
! [X0,X1] :
( c_List_Olist_ONil(tc_Int_Oint) = c_List_Oupto(X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ),
inference(ennf_transformation,[],[f6510]) ).
fof(f6510,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
=> c_List_Olist_ONil(tc_Int_Oint) = c_List_Oupto(X0,X1) ),
inference(rectify,[],[f3885]) ).
fof(f3885,axiom,
! [X55,X54] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X54),X55))
=> c_List_Oupto(X55,X54) = c_List_Olist_ONil(tc_Int_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40764,plain,
spl647_1143,
inference(avatar_split_clause,[],[f18731,f40762]) ).
fof(f40762,plain,
( spl647_1143
<=> ! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Otl(X1),X0)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1143])]) ).
fof(f18731,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Otl(X1),X0)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(cnf_transformation,[],[f10913]) ).
fof(f10913,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Otl(X1),X0)))
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(ennf_transformation,[],[f6480]) ).
fof(f6480,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
=> hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Otl(X1),X0))) ),
inference(rectify,[],[f4038]) ).
fof(f4038,axiom,
! [X201,X20] :
( hBOOL(hAPP(c_List_Odistinct(X20),X201))
=> hBOOL(hAPP(c_List_Odistinct(X20),hAPP(c_List_Otl(X20),X201))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40760,plain,
spl647_1142,
inference(avatar_split_clause,[],[f18654,f40758]) ).
fof(f40758,plain,
( spl647_1142
<=> ! [X0,X1] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X0))
| ~ c_Nat__Transfer_Onat__set(X0)
| ~ c_Nat__Transfer_Onat__set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1142])]) ).
fof(f18654,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X0))
| ~ c_Nat__Transfer_Onat__set(X0)
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(cnf_transformation,[],[f10825]) ).
fof(f10825,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X0))
| ~ c_Nat__Transfer_Onat__set(X0)
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(flattening,[],[f10824]) ).
fof(f10824,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X0))
| ~ c_Nat__Transfer_Onat__set(X0)
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(ennf_transformation,[],[f6416]) ).
fof(f6416,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(X1)
=> ( c_Nat__Transfer_Onat__set(X0)
=> c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X0)) ) ),
inference(rectify,[],[f2932]) ).
fof(f2932,axiom,
! [X18,X9] :
( c_Nat__Transfer_Onat__set(X9)
=> ( c_Nat__Transfer_Onat__set(X18)
=> c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X9),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40756,plain,
spl647_1141,
inference(avatar_split_clause,[],[f18653,f40754]) ).
fof(f40754,plain,
( spl647_1141
<=> ! [X0,X1] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X0))
| ~ c_Nat__Transfer_Onat__set(X0)
| ~ c_Nat__Transfer_Onat__set(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1141])]) ).
fof(f18653,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X0))
| ~ c_Nat__Transfer_Onat__set(X0)
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(cnf_transformation,[],[f10823]) ).
fof(f10823,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X0))
| ~ c_Nat__Transfer_Onat__set(X0)
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(flattening,[],[f10822]) ).
fof(f10822,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X0))
| ~ c_Nat__Transfer_Onat__set(X0)
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(ennf_transformation,[],[f6415]) ).
fof(f6415,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(X1)
=> ( c_Nat__Transfer_Onat__set(X0)
=> c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X1),X0)) ) ),
inference(rectify,[],[f2933]) ).
fof(f2933,axiom,
! [X18,X9] :
( c_Nat__Transfer_Onat__set(X9)
=> ( c_Nat__Transfer_Onat__set(X18)
=> c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X9),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40752,plain,
spl647_1140,
inference(avatar_split_clause,[],[f18526,f40750]) ).
fof(f40750,plain,
( spl647_1140
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)))
| ~ class_Rings_Olinordered__semidom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1140])]) ).
fof(f18526,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(cnf_transformation,[],[f10693]) ).
fof(f10693,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(ennf_transformation,[],[f6311]) ).
fof(f6311,plain,
! [X0,X1] :
( class_Rings_Olinordered__semidom(X1)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0))) ),
inference(rectify,[],[f1237]) ).
fof(f1237,axiom,
! [X44,X20] :
( class_Rings_Olinordered__semidom(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),c_Groups_Ozero__class_Ozero(X20)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20),X44))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40748,plain,
spl647_1139,
inference(avatar_split_clause,[],[f18525,f40746]) ).
fof(f40746,plain,
( spl647_1139
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1139])]) ).
fof(f18525,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(cnf_transformation,[],[f10692]) ).
fof(f10692,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Olinordered__semidom(X1) ),
inference(ennf_transformation,[],[f6310]) ).
fof(f6310,plain,
! [X0,X1] :
( class_Rings_Olinordered__semidom(X1)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(rectify,[],[f1238]) ).
fof(f1238,axiom,
! [X45,X20] :
( class_Rings_Olinordered__semidom(X20)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20),X45)),c_Groups_Ozero__class_Ozero(X20))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40744,plain,
spl647_1138,
inference(avatar_split_clause,[],[f18519,f40742]) ).
fof(f40742,plain,
( spl647_1138
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)),c_Nat_Osemiring__1__class_ONats(X1)))
| ~ class_Rings_Osemiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1138])]) ).
fof(f18519,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)),c_Nat_Osemiring__1__class_ONats(X1)))
| ~ class_Rings_Osemiring__1(X1) ),
inference(cnf_transformation,[],[f10686]) ).
fof(f10686,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)),c_Nat_Osemiring__1__class_ONats(X1)))
| ~ class_Rings_Osemiring__1(X1) ),
inference(ennf_transformation,[],[f6305]) ).
fof(f6305,plain,
! [X0,X1] :
( class_Rings_Osemiring__1(X1)
=> hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)),c_Nat_Osemiring__1__class_ONats(X1))) ),
inference(rectify,[],[f1325]) ).
fof(f1325,axiom,
! [X46,X4] :
( class_Rings_Osemiring__1(X4)
=> hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X46)),c_Nat_Osemiring__1__class_ONats(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40740,plain,
spl647_1137,
inference(avatar_split_clause,[],[f18435,f40738]) ).
fof(f40738,plain,
( spl647_1137
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Int_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1137])]) ).
fof(f18435,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f10604]) ).
fof(f10604,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f6229]) ).
fof(f6229,plain,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)),c_Int_Oring__1__class_OInts(X1))) ),
inference(rectify,[],[f1107]) ).
fof(f1107,axiom,
! [X59,X4] :
( class_Int_Onumber__ring(X4)
=> hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Int_Onumber__class_Onumber__of(X4),X59)),c_Int_Oring__1__class_OInts(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40736,plain,
spl647_1136,
inference(avatar_split_clause,[],[f18434,f40734]) ).
fof(f40734,plain,
( spl647_1136
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)),X0) = X0
| ~ class_Int_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1136])]) ).
fof(f18434,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)),X0) = X0
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f10603]) ).
fof(f10603,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)),X0) = X0
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f6228]) ).
fof(f6228,plain,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)),X0) = X0 ),
inference(rectify,[],[f1283]) ).
fof(f1283,axiom,
! [X26,X20] :
( class_Int_Onumber__ring(X20)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),hAPP(c_Int_Onumber__class_Onumber__of(X20),c_Int_OPls)),X26) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40732,plain,
spl647_1135,
inference(avatar_split_clause,[],[f18433,f40730]) ).
fof(f40730,plain,
( spl647_1135
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)) = X0
| ~ class_Int_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1135])]) ).
fof(f18433,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)) = X0
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f10602]) ).
fof(f10602,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)) = X0
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f6227]) ).
fof(f6227,plain,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OPls)) = X0 ),
inference(rectify,[],[f1284]) ).
fof(f1284,axiom,
! [X26,X20] :
( class_Int_Onumber__ring(X20)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),X26),hAPP(c_Int_Onumber__class_Onumber__of(X20),c_Int_OPls)) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40728,plain,
spl647_1134,
inference(avatar_split_clause,[],[f18389,f40726]) ).
fof(f40726,plain,
( spl647_1134
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Groups_Oabs__class_Oabs(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1134])]) ).
fof(f18389,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Groups_Oabs__class_Oabs(X1),X0)
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f14763]) ).
fof(f14763,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Oabs__class_Oabs(X1),X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Groups_Oabs__class_Oabs(X1),X0) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(nnf_transformation,[],[f10571]) ).
fof(f10571,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Oabs__class_Oabs(X1),X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f6199]) ).
fof(f6199,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Oabs__class_Oabs(X1),X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f1339]) ).
fof(f1339,axiom,
! [X5,X4] :
( class_Groups_Oordered__ab__group__add__abs(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Groups_Oabs__class_Oabs(X4),X5)
<=> c_Groups_Ozero__class_Ozero(X4) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40715,plain,
spl647_1133,
inference(avatar_split_clause,[],[f18379,f40713]) ).
fof(f40713,plain,
( spl647_1133
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1133])]) ).
fof(f18379,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f10557]) ).
fof(f10557,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f6189]) ).
fof(f6189,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Groups_Ozero__class_Ozero(X1)),hAPP(c_Groups_Oabs__class_Oabs(X1),X0))) ),
inference(rectify,[],[f1357]) ).
fof(f1357,axiom,
! [X26,X20] :
( class_Groups_Oordered__ab__group__add__abs(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),c_Groups_Ozero__class_Ozero(X20)),hAPP(c_Groups_Oabs__class_Oabs(X20),X26))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40711,plain,
spl647_1132,
inference(avatar_split_clause,[],[f18378,f40709]) ).
fof(f40709,plain,
( spl647_1132
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1132])]) ).
fof(f18378,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f10556]) ).
fof(f10556,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f6188]) ).
fof(f6188,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)),c_Groups_Ozero__class_Ozero(X1))) ),
inference(rectify,[],[f1358]) ).
fof(f1358,axiom,
! [X26,X20] :
( class_Groups_Oordered__ab__group__add__abs(X20)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20),hAPP(c_Groups_Oabs__class_Oabs(X20),X26)),c_Groups_Ozero__class_Ozero(X20))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40707,plain,
spl647_1131,
inference(avatar_split_clause,[],[f18364,f40705]) ).
fof(f40705,plain,
( spl647_1131
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1131])]) ).
fof(f18364,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(cnf_transformation,[],[f10543]) ).
fof(f10543,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(ennf_transformation,[],[f6177]) ).
fof(f6177,plain,
! [X0,X1] :
( class_Rings_Oring__1(X1)
=> hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),X0)),c_Int_Oring__1__class_OInts(X1))) ),
inference(rectify,[],[f1250]) ).
fof(f1250,axiom,
! [X46,X4] :
( class_Rings_Oring__1(X4)
=> hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X4),X46)),c_Int_Oring__1__class_OInts(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40703,plain,
spl647_1130,
inference(avatar_split_clause,[],[f18363,f40701]) ).
fof(f40701,plain,
( spl647_1130
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1130])]) ).
fof(f18363,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(cnf_transformation,[],[f10542]) ).
fof(f10542,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)),c_Int_Oring__1__class_OInts(X1)))
| ~ class_Rings_Oring__1(X1) ),
inference(ennf_transformation,[],[f6176]) ).
fof(f6176,plain,
! [X0,X1] :
( class_Rings_Oring__1(X1)
=> hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)),c_Int_Oring__1__class_OInts(X1))) ),
inference(rectify,[],[f2041]) ).
fof(f2041,axiom,
! [X17,X4] :
( class_Rings_Oring__1(X4)
=> hBOOL(hAPP(hAPP(c_member(X4),hAPP(c_Int_Oring__1__class_Oof__int(X4),X17)),c_Int_Oring__1__class_OInts(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40699,plain,
spl647_1129,
inference(avatar_split_clause,[],[f18346,f40697]) ).
fof(f40697,plain,
( spl647_1129
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1129])]) ).
fof(f18346,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f14757]) ).
fof(f14757,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) ) )
| ~ class_Groups_Ogroup__add(X1) ),
inference(nnf_transformation,[],[f10531]) ).
fof(f10531,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f6165]) ).
fof(f6165,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f1434]) ).
fof(f1434,axiom,
! [X5,X4] :
( class_Groups_Ogroup__add(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Groups_Ouminus__class_Ouminus(X4),X5)
<=> c_Groups_Ozero__class_Ozero(X4) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40695,plain,
spl647_1128,
inference(avatar_split_clause,[],[f18273,f40693]) ).
fof(f40693,plain,
( spl647_1128
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Olog(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1128])]) ).
fof(f18273,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Olog(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X0),X1)) ),
inference(cnf_transformation,[],[f10492]) ).
fof(f40691,plain,
spl647_1127,
inference(avatar_split_clause,[],[f18236,f40689]) ).
fof(f18236,plain,
! [X0,X1] :
( c_List_Olist_ONil(tc_Int_Oint) = c_List_Oupto(X1,X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f10473]) ).
fof(f10473,plain,
! [X0,X1] :
( ( c_List_Olist_ONil(tc_Int_Oint) = c_List_Oupto(X1,X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) )
& ( c_List_Oupto(X1,X0) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X1),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) ) ),
inference(ennf_transformation,[],[f6094]) ).
fof(f6094,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0))
=> c_List_Olist_ONil(tc_Int_Oint) = c_List_Oupto(X1,X0) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0))
=> c_List_Oupto(X1,X0) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X1),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)) ) ),
inference(rectify,[],[f3920]) ).
fof(f3920,axiom,
! [X54,X55] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X55),X54))
=> c_List_Oupto(X55,X54) = c_List_Olist_ONil(tc_Int_Oint) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X55),X54))
=> c_List_Oupto(X55,X54) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X55),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X55),c_Groups_Oone__class_Oone(tc_Int_Oint)),X54)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40687,plain,
spl647_1126,
inference(avatar_split_clause,[],[f18229,f40685]) ).
fof(f40685,plain,
( spl647_1126
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1126])]) ).
fof(f18229,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ),
inference(cnf_transformation,[],[f10470]) ).
fof(f10470,plain,
! [X0,X1] :
( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0),X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) ),
inference(ennf_transformation,[],[f6091]) ).
fof(f6091,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0),X0) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) = X1 ) ),
inference(rectify,[],[f1780]) ).
fof(f1780,axiom,
! [X44,X45] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X44))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X45,X44) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),X44),X44) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X45),X44))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X45,X44) = X45 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40683,plain,
spl647_1125,
inference(avatar_split_clause,[],[f18225,f40681]) ).
fof(f18225,plain,
! [X0,X1] :
( c_Lazy__Sequence_Oempty(tc_Int_Oint) = c_Lazy__Sequence_Osmall__lazy_H(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f10468]) ).
fof(f10468,plain,
! [X0,X1] :
( ( c_Lazy__Sequence_Osmall__lazy_H(X1,X0) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X0),c_Lazy__Sequence_Osmall__lazy_H(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) )
& ( c_Lazy__Sequence_Oempty(tc_Int_Oint) = c_Lazy__Sequence_Osmall__lazy_H(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ) ),
inference(ennf_transformation,[],[f6089]) ).
fof(f6089,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
=> c_Lazy__Sequence_Osmall__lazy_H(X1,X0) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X0),c_Lazy__Sequence_Osmall__lazy_H(X1,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
=> c_Lazy__Sequence_Oempty(tc_Int_Oint) = c_Lazy__Sequence_Osmall__lazy_H(X1,X0) ) ),
inference(rectify,[],[f4656]) ).
fof(f4656,axiom,
! [X55,X30] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X55))
=> c_Lazy__Sequence_Osmall__lazy_H(X30,X55) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X55),c_Lazy__Sequence_Osmall__lazy_H(X30,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X55),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X30),X55))
=> c_Lazy__Sequence_Osmall__lazy_H(X30,X55) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40679,plain,
spl647_1124,
inference(avatar_split_clause,[],[f18224,f40677]) ).
fof(f40677,plain,
( spl647_1124
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Quickcheck_Obeyond(X1,X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1124])]) ).
fof(f18224,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Quickcheck_Obeyond(X1,X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X0)) ),
inference(cnf_transformation,[],[f10467]) ).
fof(f10467,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Quickcheck_Obeyond(X1,X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X0)) )
& ( c_Quickcheck_Obeyond(X1,X0) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X0)) ) ),
inference(ennf_transformation,[],[f6088]) ).
fof(f6088,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X0))
=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Quickcheck_Obeyond(X1,X0) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X0))
=> c_Quickcheck_Obeyond(X1,X0) = X0 ) ),
inference(rectify,[],[f4801]) ).
fof(f4801,axiom,
! [X56,X53] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X53),X56))
=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Quickcheck_Obeyond(X53,X56) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X53),X56))
=> c_Quickcheck_Obeyond(X53,X56) = X56 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40675,plain,
spl647_1123,
inference(avatar_split_clause,[],[f17933,f40673]) ).
fof(f40673,plain,
( spl647_1123
<=> ! [X0,X1] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1123])]) ).
fof(f17933,plain,
! [X0,X1] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),X0),
inference(cnf_transformation,[],[f5825]) ).
fof(f5825,plain,
! [X0,X1] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X1),X0),
inference(rectify,[],[f3090]) ).
fof(f3090,axiom,
! [X103,X48] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),X48),X103),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40671,plain,
spl647_1122,
inference(avatar_split_clause,[],[f17932,f40669]) ).
fof(f40669,plain,
( spl647_1122
<=> ! [X0,X1] : c_Relation_Oirrefl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X0),c_Relation_OId(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1122])]) ).
fof(f17932,plain,
! [X0,X1] : c_Relation_Oirrefl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X0),c_Relation_OId(X1))),
inference(cnf_transformation,[],[f5824]) ).
fof(f5824,plain,
! [X0,X1] : c_Relation_Oirrefl(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X1,X1),tc_HOL_Obool)),X0),c_Relation_OId(X1))),
inference(rectify,[],[f3616]) ).
fof(f3616,axiom,
! [X116,X4] : c_Relation_Oirrefl(X4,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(X4,X4),tc_HOL_Obool)),X116),c_Relation_OId(X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40667,plain,
spl647_1121,
inference(avatar_split_clause,[],[f17931,f40665]) ).
fof(f40665,plain,
( spl647_1121
<=> ! [X0,X1] : c_Predicate_Opred__comp(X1,X1,X1,c_fequal,c_Predicate_Opred__comp(X1,X1,X1,X0,c_fequal)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1121])]) ).
fof(f17931,plain,
! [X0,X1] : c_Predicate_Opred__comp(X1,X1,X1,c_fequal,c_Predicate_Opred__comp(X1,X1,X1,X0,c_fequal)) = X0,
inference(cnf_transformation,[],[f5823]) ).
fof(f5823,plain,
! [X0,X1] : c_Predicate_Opred__comp(X1,X1,X1,c_fequal,c_Predicate_Opred__comp(X1,X1,X1,X0,c_fequal)) = X0,
inference(rectify,[],[f4648]) ).
fof(f4648,axiom,
! [X138,X4] : c_Predicate_Opred__comp(X4,X4,X4,c_fequal,c_Predicate_Opred__comp(X4,X4,X4,X138,c_fequal)) = X138,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40663,plain,
spl647_1120,
inference(avatar_split_clause,[],[f17929,f40661]) ).
fof(f40661,plain,
( spl647_1120
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1120])]) ).
fof(f17929,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X0) = X0,
inference(cnf_transformation,[],[f5821]) ).
fof(f5821,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))),X0) = X0,
inference(rectify,[],[f2087]) ).
fof(f2087,axiom,
! [X18,X4] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))),X18) = X18,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40659,plain,
spl647_1119,
inference(avatar_split_clause,[],[f17928,f40657]) ).
fof(f40657,plain,
( spl647_1119
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1119])]) ).
fof(f17928,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X0) = X0,
inference(cnf_transformation,[],[f5820]) ).
fof(f5820,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X0) = X0,
inference(rectify,[],[f116]) ).
fof(f116,axiom,
! [X18,X4] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X18) = X18,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40655,plain,
spl647_1118,
inference(avatar_split_clause,[],[f17927,f40653]) ).
fof(f40653,plain,
( spl647_1118
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1118])]) ).
fof(f17927,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X0) = X1,
inference(cnf_transformation,[],[f5819]) ).
fof(f5819,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X0) = X1,
inference(rectify,[],[f631]) ).
fof(f631,axiom,
! [X44,X45] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X44)),X44) = X45,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40651,plain,
spl647_1117,
inference(avatar_split_clause,[],[f17926,f40649]) ).
fof(f40649,plain,
( spl647_1117
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1117])]) ).
fof(f17926,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X1) = X0,
inference(cnf_transformation,[],[f5818]) ).
fof(f5818,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X1) = X0,
inference(rectify,[],[f632]) ).
fof(f632,axiom,
! [X45,X44] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X45)),X44) = X45,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40647,plain,
spl647_1116,
inference(avatar_split_clause,[],[f17925,f40645]) ).
fof(f40645,plain,
( spl647_1116
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1116])]) ).
fof(f17925,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X0,
inference(cnf_transformation,[],[f5817]) ).
fof(f5817,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X0,
inference(rectify,[],[f114]) ).
fof(f114,axiom,
! [X9,X4] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40643,plain,
spl647_1115,
inference(avatar_split_clause,[],[f17924,f40641]) ).
fof(f40641,plain,
( spl647_1115
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1115])]) ).
fof(f17924,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = X0,
inference(cnf_transformation,[],[f5816]) ).
fof(f5816,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool))) = X0,
inference(rectify,[],[f2088]) ).
fof(f2088,axiom,
! [X9,X4] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X9),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40639,plain,
spl647_1114,
inference(avatar_split_clause,[],[f17923,f40637]) ).
fof(f40637,plain,
( spl647_1114
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1114])]) ).
fof(f17923,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X0,
inference(cnf_transformation,[],[f5815]) ).
fof(f5815,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X0,
inference(rectify,[],[f117]) ).
fof(f117,axiom,
! [X9,X4] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40634,plain,
spl647_1113,
inference(avatar_split_clause,[],[f17922,f40632]) ).
fof(f40632,plain,
( spl647_1113
<=> ! [X0,X1] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1113])]) ).
fof(f17922,plain,
! [X0,X1] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X0)) = X0,
inference(cnf_transformation,[],[f5814]) ).
fof(f5814,plain,
! [X0,X1] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X1,tc_HOL_Obool)),X0)) = X0,
inference(rectify,[],[f1727]) ).
fof(f1727,axiom,
! [X9,X4] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X4,tc_HOL_Obool)),X9)) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40630,plain,
spl647_1112,
inference(avatar_split_clause,[],[f17921,f40628]) ).
fof(f40628,plain,
( spl647_1112
<=> ! [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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1112])]) ).
fof(f40626,plain,
spl647_1111,
inference(avatar_split_clause,[],[f17920,f40624]) ).
fof(f40624,plain,
( spl647_1111
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1111])]) ).
fof(f17920,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),
inference(cnf_transformation,[],[f5812]) ).
fof(f5812,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1),
inference(rectify,[],[f557]) ).
fof(f557,axiom,
! [X44,X45] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X44) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X45),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40622,plain,
spl647_1110,
inference(avatar_split_clause,[],[f17919,f40620]) ).
fof(f40620,plain,
( spl647_1110
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1110])]) ).
fof(f17919,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),
inference(cnf_transformation,[],[f5811]) ).
fof(f5811,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1),
inference(rectify,[],[f1159]) ).
fof(f1159,axiom,
! [X87,X27] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X27),X87) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X87),X27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40618,plain,
spl647_1109,
inference(avatar_split_clause,[],[f17918,f40616]) ).
fof(f40616,plain,
( spl647_1109
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1109])]) ).
fof(f17918,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1),
inference(cnf_transformation,[],[f5810]) ).
fof(f5810,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1),
inference(rectify,[],[f565]) ).
fof(f565,axiom,
! [X44,X45] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X44) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X45),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40614,plain,
spl647_1108,
inference(avatar_split_clause,[],[f17917,f40612]) ).
fof(f40612,plain,
( spl647_1108
<=> ! [X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1108])]) ).
fof(f17917,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1),
inference(cnf_transformation,[],[f5809]) ).
fof(f5809,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1),
inference(rectify,[],[f1151]) ).
fof(f1151,axiom,
! [X87,X27] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X27),X87) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X87),X27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40610,plain,
spl647_1107,
inference(avatar_split_clause,[],[f17916,f40608]) ).
fof(f40608,plain,
( spl647_1107
<=> ! [X0,X1] : hAPP(c_Relation_ODomain(X1,X1),X0) = hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Otrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1107])]) ).
fof(f17916,plain,
! [X0,X1] : hAPP(c_Relation_ODomain(X1,X1),X0) = hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Otrancl(X1,X0)),
inference(cnf_transformation,[],[f5808]) ).
fof(f5808,plain,
! [X0,X1] : hAPP(c_Relation_ODomain(X1,X1),X0) = hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Otrancl(X1,X0)),
inference(rectify,[],[f3550]) ).
fof(f3550,axiom,
! [X116,X4] : hAPP(c_Relation_ODomain(X4,X4),X116) = hAPP(c_Relation_ODomain(X4,X4),c_Transitive__Closure_Otrancl(X4,X116)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40606,plain,
spl647_1106,
inference(avatar_split_clause,[],[f17915,f40604]) ).
fof(f40604,plain,
( spl647_1106
<=> ! [X0,X1] : hAPP(c_Relation_ORange(X1,X1),X0) = hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Otrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1106])]) ).
fof(f17915,plain,
! [X0,X1] : hAPP(c_Relation_ORange(X1,X1),X0) = hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Otrancl(X1,X0)),
inference(cnf_transformation,[],[f5807]) ).
fof(f5807,plain,
! [X0,X1] : hAPP(c_Relation_ORange(X1,X1),X0) = hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Otrancl(X1,X0)),
inference(rectify,[],[f3551]) ).
fof(f3551,axiom,
! [X116,X4] : hAPP(c_Relation_ORange(X4,X4),X116) = hAPP(c_Relation_ORange(X4,X4),c_Transitive__Closure_Otrancl(X4,X116)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40602,plain,
spl647_1105,
inference(avatar_split_clause,[],[f17912,f40600]) ).
fof(f40600,plain,
( spl647_1105
<=> ! [X0,X1] : hAPP(c_Relation_OField(X1),X0) = hAPP(c_Relation_OField(X1),hAPP(c_Relation_Oconverse(X1,X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1105])]) ).
fof(f17912,plain,
! [X0,X1] : hAPP(c_Relation_OField(X1),X0) = hAPP(c_Relation_OField(X1),hAPP(c_Relation_Oconverse(X1,X1),X0)),
inference(cnf_transformation,[],[f5804]) ).
fof(f5804,plain,
! [X0,X1] : hAPP(c_Relation_OField(X1),X0) = hAPP(c_Relation_OField(X1),hAPP(c_Relation_Oconverse(X1,X1),X0)),
inference(rectify,[],[f3627]) ).
fof(f3627,axiom,
! [X116,X4] : hAPP(c_Relation_OField(X4),X116) = hAPP(c_Relation_OField(X4),hAPP(c_Relation_Oconverse(X4,X4),X116)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40598,plain,
spl647_1104,
inference(avatar_split_clause,[],[f17911,f40596]) ).
fof(f40596,plain,
( spl647_1104
<=> ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1104])]) ).
fof(f17911,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X0),X0),
inference(cnf_transformation,[],[f5803]) ).
fof(f5803,plain,
! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X0),X0),
inference(rectify,[],[f115]) ).
fof(f115,axiom,
! [X9,X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X4,tc_HOL_Obool)),X9),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40594,plain,
( spl647_1103
| ~ spl647_348
| ~ spl647_1085 ),
inference(avatar_split_clause,[],[f40501,f38438,f30900,f40592]) ).
fof(f40592,plain,
( spl647_1103
<=> ! [X0] : c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OPls,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1103])]) ).
fof(f40501,plain,
( ! [X0] : c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Int_OPls,X0))
| ~ spl647_348
| ~ spl647_1085 ),
inference(resolution,[],[f38439,f30901]) ).
fof(f40590,plain,
spl647_1102,
inference(avatar_split_clause,[],[f17423,f40588]) ).
fof(f40588,plain,
( spl647_1102
<=> ! [X0] : c_Wellfounded_OwfP(X0,hAPP(c_COMBK(tc_fun(X0,tc_HOL_Obool),X0),hAPP(c_COMBK(tc_HOL_Obool,X0),c_fFalse))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1102])]) ).
fof(f17423,plain,
! [X0] : c_Wellfounded_OwfP(X0,hAPP(c_COMBK(tc_fun(X0,tc_HOL_Obool),X0),hAPP(c_COMBK(tc_HOL_Obool,X0),c_fFalse))),
inference(cnf_transformation,[],[f5401]) ).
fof(f5401,plain,
! [X0] : c_Wellfounded_OwfP(X0,hAPP(c_COMBK(tc_fun(X0,tc_HOL_Obool),X0),hAPP(c_COMBK(tc_HOL_Obool,X0),c_fFalse))),
inference(rectify,[],[f3419]) ).
fof(f3419,axiom,
! [X4] : c_Wellfounded_OwfP(X4,hAPP(c_COMBK(tc_fun(X4,tc_HOL_Obool),X4),hAPP(c_COMBK(tc_HOL_Obool,X4),c_fFalse))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40586,plain,
spl647_1101,
inference(avatar_split_clause,[],[f17422,f40584]) ).
fof(f17422,plain,
! [X0] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X0)),c_Int_OInteg)),
inference(cnf_transformation,[],[f5400]) ).
fof(f5400,plain,
! [X0] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X0)),c_Int_OInteg)),
inference(rectify,[],[f3077]) ).
fof(f3077,axiom,
! [X13] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X13)),c_Int_OInteg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40582,plain,
spl647_1100,
inference(avatar_split_clause,[],[f17418,f40580]) ).
fof(f40580,plain,
( spl647_1100
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X0),hAPP(c_COMBK(tc_HOL_Obool,X0),c_fFalse)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1100])]) ).
fof(f17418,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X0),hAPP(c_COMBK(tc_HOL_Obool,X0),c_fFalse)),
inference(cnf_transformation,[],[f5396]) ).
fof(f5396,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X0),hAPP(c_COMBK(tc_HOL_Obool,X0),c_fFalse)),
inference(rectify,[],[f3230]) ).
fof(f3230,axiom,
! [X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X4),hAPP(c_COMBK(tc_HOL_Obool,X4),c_fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40578,plain,
spl647_1099,
inference(avatar_split_clause,[],[f17417,f40576]) ).
fof(f40576,plain,
( spl647_1099
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X0),hAPP(c_COMBK(tc_HOL_Obool,X0),c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1099])]) ).
fof(f17417,plain,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X0),hAPP(c_COMBK(tc_HOL_Obool,X0),c_fTrue)),
inference(cnf_transformation,[],[f5395]) ).
fof(f5395,plain,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X0),hAPP(c_COMBK(tc_HOL_Obool,X0),c_fTrue)),
inference(rectify,[],[f3227]) ).
fof(f3227,axiom,
! [X4] : c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X4),hAPP(c_COMBK(tc_HOL_Obool,X4),c_fTrue)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f40536,plain,
( spl647_1098
| spl647_327
| ~ spl647_1080 ),
inference(avatar_split_clause,[],[f40456,f38418,f30799,f40533]) ).
fof(f40533,plain,
( spl647_1098
<=> c_Int_OPls = c_Nat__Transfer_Otsub(c_Int_OMin,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1098])]) ).
fof(f38418,plain,
( spl647_1080
<=> ! [X0,X1] :
( c_Int_OPls = c_Nat__Transfer_Otsub(X0,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1080])]) ).
fof(f40456,plain,
( c_Int_OPls = c_Nat__Transfer_Otsub(c_Int_OMin,c_Int_OPls)
| spl647_327
| ~ spl647_1080 ),
inference(resolution,[],[f38419,f30801]) ).
fof(f38419,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0))
| c_Int_OPls = c_Nat__Transfer_Otsub(X0,X1) )
| ~ spl647_1080 ),
inference(avatar_component_clause,[],[f38418]) ).
fof(f39624,plain,
( spl647_1097
| ~ spl647_946
| ~ spl647_976 ),
inference(avatar_split_clause,[],[f38748,f37994,f34593,f39622]) ).
fof(f39622,plain,
( spl647_1097
<=> ! [X0] : hBOOL(hAPP(c_Int_OInteg,sK108(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1097])]) ).
fof(f37994,plain,
( spl647_976
<=> ! [X0] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK108(X0)),c_Int_OInteg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_976])]) ).
fof(f38748,plain,
( ! [X0] : hBOOL(hAPP(c_Int_OInteg,sK108(X0)))
| ~ spl647_946
| ~ spl647_976 ),
inference(resolution,[],[f37995,f34594]) ).
fof(f37995,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK108(X0)),c_Int_OInteg))
| ~ spl647_976 ),
inference(avatar_component_clause,[],[f37994]) ).
fof(f39590,plain,
( spl647_1096
| ~ spl647_472
| ~ spl647_945 ),
inference(avatar_split_clause,[],[f37812,f34589,f31435,f39588]) ).
fof(f39588,plain,
( spl647_1096
<=> ! [X0,X1] : sP29(c_Groups_Oone__class_Oone(tc_Int_Oint),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1096])]) ).
fof(f31435,plain,
( spl647_472
<=> 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,[spl647_472])]) ).
fof(f34589,plain,
( spl647_945
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP29(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_945])]) ).
fof(f37812,plain,
( ! [X0,X1] : sP29(c_Groups_Oone__class_Oone(tc_Int_Oint),X0,X1)
| ~ spl647_472
| ~ spl647_945 ),
inference(resolution,[],[f34590,f31437]) ).
fof(f31437,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl647_472 ),
inference(avatar_component_clause,[],[f31435]) ).
fof(f34590,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP29(X2,X0,X1) )
| ~ spl647_945 ),
inference(avatar_component_clause,[],[f34589]) ).
fof(f38481,plain,
spl647_1095,
inference(avatar_split_clause,[],[f28924,f38479]) ).
fof(f38479,plain,
( spl647_1095
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(c_fequal,X1)),X0))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1095])]) ).
fof(f28924,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(c_fequal,X1)),X0))
| X0 = X1 ),
inference(forward_demodulation,[],[f22751,f26468]) ).
fof(f22751,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)) ),
inference(cnf_transformation,[],[f16393]) ).
fof(f16393,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0))
| X0 != X1 )
& ( X0 = X1
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)) ) ),
inference(nnf_transformation,[],[f9189]) ).
fof(f9189,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0))
<=> X0 = X1 ),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X12,X5,X1,X4] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X1,hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X12))
<=> X5 = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38476,plain,
spl647_1094,
inference(avatar_split_clause,[],[f28476,f38474]) ).
fof(f38474,plain,
( spl647_1094
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_HOL_Obool_Obool__size(c_fTrue))))
| hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1094])]) ).
fof(f28476,plain,
! [X2,X1] :
( ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_HOL_Obool_Obool__size(c_fTrue))))
| hBOOL(hAPP(X2,X1)) ),
inference(forward_demodulation,[],[f25567,f17145]) ).
fof(f25567,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(equality_resolution,[],[f21246]) ).
fof(f21246,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f15826]) ).
fof(f15826,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
| ~ sP39(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP39(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0))) ) ),
inference(flattening,[],[f15825]) ).
fof(f15825,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
| ~ sP39(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP39(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0))) ) ),
inference(nnf_transformation,[],[f14542]) ).
fof(f14542,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
<=> ( sP39(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(definition_folding,[],[f12614,f14541]) ).
fof(f12614,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,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 )
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(flattening,[],[f12613]) ).
fof(f12613,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,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 )
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(ennf_transformation,[],[f8162]) ).
fof(f8162,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0))
=> ( 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(X2,X4)) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
=> hBOOL(hAPP(X2,X1)) ) ) ),
inference(rectify,[],[f1828]) ).
fof(f1828,axiom,
! [X48,X46,X23] :
( hBOOL(hAPP(X23,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X46,X48)))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X48
=> ! [X86,X83] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X83),X48))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X86)),X83) = X46
=> hBOOL(hAPP(X23,X83)) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X48
=> hBOOL(hAPP(X23,X46)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38472,plain,
spl647_1093,
inference(avatar_split_clause,[],[f28370,f38470]) ).
fof(f38470,plain,
( spl647_1093
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1093])]) ).
fof(f28370,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
| X0 = X1 ),
inference(forward_demodulation,[],[f20978,f26468]) ).
fof(f20978,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))) ),
inference(cnf_transformation,[],[f12486]) ).
fof(f12486,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))) ),
inference(ennf_transformation,[],[f8061]) ).
fof(f8061,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))
=> X0 = X1 ),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X5,X12,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),X12),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))))
=> X5 = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38468,plain,
spl647_1092,
inference(avatar_split_clause,[],[f27688,f38466]) ).
fof(f38466,plain,
( spl647_1092
<=> ! [X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1092])]) ).
fof(f27688,plain,
! [X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),c_Int_OMin))),
inference(forward_demodulation,[],[f25431,f24214]) ).
fof(f25431,plain,
! [X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(equality_resolution,[],[f19466]) ).
fof(f19466,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| X0 != X1 ),
inference(cnf_transformation,[],[f15222]) ).
fof(f15222,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ( 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(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(flattening,[],[f15221]) ).
fof(f15221,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ( 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(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
inference(nnf_transformation,[],[f6885]) ).
fof(f6885,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> ( X0 = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ) ),
inference(rectify,[],[f1149]) ).
fof(f1149,axiom,
! [X17,X59] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X59),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X17),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> ( X17 = X59
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X59),X17)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38464,plain,
spl647_1091,
inference(avatar_split_clause,[],[f27644,f38462]) ).
fof(f38462,plain,
( spl647_1091
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| sP14(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1091])]) ).
fof(f27644,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| sP14(X0,X1) ),
inference(forward_demodulation,[],[f27643,f25910]) ).
fof(f27643,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) != hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))
| sP14(X0,X1) ),
inference(forward_demodulation,[],[f19417,f17145]) ).
fof(f19417,plain,
! [X0,X1] :
( sP14(X0,X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ),
inference(cnf_transformation,[],[f15195]) ).
fof(f15195,plain,
! [X0,X1] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ~ sP14(X0,X1) )
& ( sP14(X0,X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ) ),
inference(nnf_transformation,[],[f14502]) ).
fof(f14502,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
<=> sP14(X0,X1) ),
inference(definition_folding,[],[f6864,f14501]) ).
fof(f14501,plain,
! [X0,X1] :
( sP14(X0,X1)
<=> ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f6864,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
<=> ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
inference(rectify,[],[f869]) ).
fof(f869,axiom,
! [X46,X47] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X46) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X46
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X47 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X46
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X47 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38460,plain,
spl647_1090,
inference(avatar_split_clause,[],[f27642,f38458]) ).
fof(f38458,plain,
( spl647_1090
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ~ sP14(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1090])]) ).
fof(f27642,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ~ sP14(X0,X1) ),
inference(forward_demodulation,[],[f27641,f25910]) ).
fof(f27641,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))
| ~ sP14(X0,X1) ),
inference(forward_demodulation,[],[f19418,f17145]) ).
fof(f19418,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ~ sP14(X0,X1) ),
inference(cnf_transformation,[],[f15195]) ).
fof(f38456,plain,
spl647_1089,
inference(avatar_split_clause,[],[f27624,f38454]) ).
fof(f38454,plain,
( spl647_1089
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1089])]) ).
fof(f27624,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| sP13(X0,X1) ),
inference(forward_demodulation,[],[f27623,f25910]) ).
fof(f27623,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) != hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))
| sP13(X0,X1) ),
inference(forward_demodulation,[],[f19409,f17145]) ).
fof(f19409,plain,
! [X0,X1] :
( sP13(X0,X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ),
inference(cnf_transformation,[],[f15192]) ).
fof(f15192,plain,
! [X0,X1] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ~ sP13(X0,X1) )
& ( sP13(X0,X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ) ),
inference(nnf_transformation,[],[f14500]) ).
fof(f14500,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
<=> sP13(X0,X1) ),
inference(definition_folding,[],[f6863,f14499]) ).
fof(f14499,plain,
! [X0,X1] :
( sP13(X0,X1)
<=> ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f6863,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
<=> ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
inference(rectify,[],[f870]) ).
fof(f870,axiom,
! [X46,X47] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X46) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X46
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X47 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X46
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X47 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38452,plain,
spl647_1088,
inference(avatar_split_clause,[],[f27622,f38450]) ).
fof(f38450,plain,
( spl647_1088
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ~ sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1088])]) ).
fof(f27622,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ~ sP13(X0,X1) ),
inference(forward_demodulation,[],[f27621,f25910]) ).
fof(f27621,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))
| ~ sP13(X0,X1) ),
inference(forward_demodulation,[],[f19410,f17145]) ).
fof(f19410,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f15192]) ).
fof(f38448,plain,
spl647_1087,
inference(avatar_split_clause,[],[f27511,f38446]) ).
fof(f38446,plain,
( spl647_1087
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0)
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1087])]) ).
fof(f27511,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0)
| c_List_Olist_ONil(X1) = X0 ),
inference(forward_demodulation,[],[f19264,f17145]) ).
fof(f19264,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0) ),
inference(cnf_transformation,[],[f15107]) ).
fof(f15107,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0)
| c_List_Olist_ONil(X1) != X0 )
& ( c_List_Olist_ONil(X1) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0) ) ),
inference(nnf_transformation,[],[f6812]) ).
fof(f6812,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0)
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f3898]) ).
fof(f3898,axiom,
! [X203,X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X203)
<=> c_List_Olist_ONil(X4) = X203 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38444,plain,
spl647_1086,
inference(avatar_split_clause,[],[f27501,f38442]) ).
fof(f38442,plain,
( spl647_1086
<=> ! [X2,X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1086])]) ).
fof(f27501,plain,
! [X2,X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),X0),
inference(forward_demodulation,[],[f25369,f17145]) ).
fof(f25369,plain,
! [X2,X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2),X0),
inference(equality_resolution,[],[f19196]) ).
fof(f19196,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) != X1 ),
inference(cnf_transformation,[],[f15056]) ).
fof(f15056,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
| ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) != X1 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),sK198(X0,X1)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK198])],[f15054,f15055]) ).
fof(f15055,plain,
! [X0,X1] :
( ? [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3) = X1
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),sK198(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f15054,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
| ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) != X1 )
& ( ? [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) ) ),
inference(rectify,[],[f15053]) ).
fof(f15053,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
| ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) != X1 )
& ( ? [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0) ) ),
inference(nnf_transformation,[],[f6781]) ).
fof(f6781,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)
<=> ? [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X2) = X1 ),
inference(rectify,[],[f1777]) ).
fof(f1777,axiom,
! [X10,X47] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X47,X10)
<=> ? [X118] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X10),X118) = X47 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38440,plain,
spl647_1085,
inference(avatar_split_clause,[],[f27200,f38438]) ).
fof(f27200,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0)) ),
inference(forward_demodulation,[],[f18886,f17135]) ).
fof(f18886,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(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(cnf_transformation,[],[f11078]) ).
fof(f11078,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(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(ennf_transformation,[],[f6604]) ).
fof(f6604,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0)) ),
inference(rectify,[],[f2939]) ).
fof(f2939,axiom,
! [X15,X13] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13))
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X13,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38436,plain,
spl647_1084,
inference(avatar_split_clause,[],[f27035,f38434]) ).
fof(f38434,plain,
( spl647_1084
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1084])]) ).
fof(f27035,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) != X1 ),
inference(forward_demodulation,[],[f18814,f17145]) ).
fof(f18814,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) != X1 ),
inference(cnf_transformation,[],[f10997]) ).
fof(f10997,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) != X1 ),
inference(ennf_transformation,[],[f6549]) ).
fof(f6549,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) = X1
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f784]) ).
fof(f784,axiom,
! [X44,X45] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X44) = X45
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X44 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38432,plain,
spl647_1083,
inference(avatar_split_clause,[],[f26951,f38430]) ).
fof(f38430,plain,
( spl647_1083
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_HOL_Obool_Obool__size(c_fTrue))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1083])]) ).
fof(f26951,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_HOL_Obool_Obool__size(c_fTrue))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(forward_demodulation,[],[f18541,f17145]) ).
fof(f18541,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f10707]) ).
fof(f10707,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f6325]) ).
fof(f6325,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(rectify,[],[f1771]) ).
fof(f1771,axiom,
! [X19,X20] :
( class_Rings_Ocomm__semiring__1(X20)
=> c_Groups_Oone__class_Oone(X20) = hAPP(hAPP(c_Power_Opower__class_Opower(X20),X19),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38428,plain,
spl647_1082,
inference(avatar_split_clause,[],[f26932,f38426]) ).
fof(f38426,plain,
( spl647_1082
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_HOL_Obool_Obool__size(c_fTrue))
| ~ class_Power_Opower(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1082])]) ).
fof(f26932,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_HOL_Obool_Obool__size(c_fTrue))
| ~ class_Power_Opower(X1) ),
inference(forward_demodulation,[],[f18508,f17145]) ).
fof(f18508,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Power_Opower(X1) ),
inference(cnf_transformation,[],[f10674]) ).
fof(f10674,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Power_Opower(X1) ),
inference(ennf_transformation,[],[f6294]) ).
fof(f6294,plain,
! [X0,X1] :
( class_Power_Opower(X1)
=> c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(rectify,[],[f1923]) ).
fof(f1923,axiom,
! [X26,X20] :
( class_Power_Opower(X20)
=> c_Groups_Oone__class_Oone(X20) = hAPP(hAPP(c_Power_Opower__class_Opower(X20),X26),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38424,plain,
spl647_1081,
inference(avatar_split_clause,[],[f26822,f38422]) ).
fof(f38422,plain,
( spl647_1081
<=> ! [X0,X1] :
( c_Int_OPls = X0
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)
| ~ class_Int_Oring__char__0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1081])]) ).
fof(f26822,plain,
! [X0,X1] :
( c_Int_OPls = X0
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)
| ~ class_Int_Oring__char__0(X1) ),
inference(forward_demodulation,[],[f18311,f17135]) ).
fof(f18311,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)
| ~ class_Int_Oring__char__0(X1) ),
inference(cnf_transformation,[],[f14744]) ).
fof(f14744,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Oring__1__class_Oof__int(X1),X0) ) )
| ~ class_Int_Oring__char__0(X1) ),
inference(nnf_transformation,[],[f10507]) ).
fof(f10507,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
| ~ class_Int_Oring__char__0(X1) ),
inference(ennf_transformation,[],[f6143]) ).
fof(f6143,plain,
! [X0,X1] :
( class_Int_Oring__char__0(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
inference(rectify,[],[f2029]) ).
fof(f2029,axiom,
! [X17,X4] :
( class_Int_Oring__char__0(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Int_Oring__1__class_Oof__int(X4),X17)
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38420,plain,
spl647_1080,
inference(avatar_split_clause,[],[f26688,f38418]) ).
fof(f26688,plain,
! [X0,X1] :
( c_Int_OPls = c_Nat__Transfer_Otsub(X0,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) ),
inference(forward_demodulation,[],[f18234,f17135]) ).
fof(f18234,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f10472]) ).
fof(f10472,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) )
& ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),X1) = c_Nat__Transfer_Otsub(X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) ) ),
inference(ennf_transformation,[],[f6093]) ).
fof(f6093,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X0,X1) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),X1) = c_Nat__Transfer_Otsub(X0,X1) ) ),
inference(rectify,[],[f1263]) ).
fof(f1263,axiom,
! [X19,X21] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21),X19))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X19,X21) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X21),X19))
=> c_Nat__Transfer_Otsub(X19,X21) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X19),X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38416,plain,
spl647_1079,
inference(avatar_split_clause,[],[f26611,f38414]) ).
fof(f38414,plain,
( spl647_1079
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Finite__Set_Ocard(X1),X0)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1079])]) ).
fof(f26611,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Finite__Set_Ocard(X1),X0)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(forward_demodulation,[],[f18198,f17145]) ).
fof(f18198,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(cnf_transformation,[],[f10455]) ).
fof(f10455,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) )
& ( hAPP(c_Finite__Set_Ocard(X1),X0) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ) ),
inference(ennf_transformation,[],[f6076]) ).
fof(f6076,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
=> hAPP(c_Finite__Set_Ocard(X1),X0) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X1,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) ) ),
inference(rectify,[],[f2228]) ).
fof(f2228,axiom,
! [X9,X4] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X9))
=> hAPP(c_Finite__Set_Ocard(X4),X9) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X9))
=> hAPP(c_Finite__Set_Ocard(X4),X9) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X4,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X4),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38412,plain,
spl647_1078,
inference(avatar_split_clause,[],[f26495,f38410]) ).
fof(f38410,plain,
( spl647_1078
<=> ! [X0,X1] : hAPP(c_fequal,X0) = hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1078])]) ).
fof(f38408,plain,
spl647_1077,
inference(avatar_split_clause,[],[f26436,f38406]) ).
fof(f38406,plain,
( spl647_1077
<=> ! [X4,X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK105(X0)))
| ~ hBOOL(hAPP(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1077])]) ).
fof(f26436,plain,
! [X0,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK105(X0)))
| ~ hBOOL(hAPP(X0,X4)) ),
inference(forward_demodulation,[],[f17760,f17135]) ).
fof(f17760,plain,
! [X0,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK105(X0)))
| ~ hBOOL(hAPP(X0,X4)) ),
inference(cnf_transformation,[],[f14726]) ).
fof(f14726,plain,
! [X0] :
( ( hBOOL(hAPP(X0,sK104(X0)))
| ! [X2] :
( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) )
& ( ( hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK105(X0))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK105(X0))) )
| ! [X4] : ~ hBOOL(hAPP(X0,X4)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK104,sK105])],[f14723,f14725,f14724]) ).
fof(f14724,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP(X0,X1))
=> hBOOL(hAPP(X0,sK104(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14725,plain,
! [X0] :
( ? [X3] :
( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X3)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) )
=> ( hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK105(X0))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK105(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f14723,plain,
! [X0] :
( ( ? [X1] : hBOOL(hAPP(X0,X1))
| ! [X2] :
( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) )
& ( ? [X3] :
( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X3)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) )
| ! [X4] : ~ hBOOL(hAPP(X0,X4)) ) ),
inference(rectify,[],[f14722]) ).
fof(f14722,plain,
! [X0] :
( ( ? [X1] : hBOOL(hAPP(X0,X1))
| ! [X2] :
( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) )
& ( ? [X2] :
( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) )
| ! [X1] : ~ hBOOL(hAPP(X0,X1)) ) ),
inference(nnf_transformation,[],[f5658]) ).
fof(f5658,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP(X0,X1))
<=> ? [X2] :
( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) ),
inference(rectify,[],[f1773]) ).
fof(f1773,axiom,
! [X23] :
( ? [X124] : hBOOL(hAPP(X23,X124))
<=> ? [X2] :
( hBOOL(hAPP(X23,hAPP(c_Int_Onat,X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38403,plain,
spl647_1076,
inference(avatar_split_clause,[],[f26431,f38401]) ).
fof(f38401,plain,
( spl647_1076
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK100(X0)))
| hBOOL(hAPP(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1076])]) ).
fof(f26431,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK100(X0)))
| hBOOL(hAPP(X0,X1)) ),
inference(forward_demodulation,[],[f17755,f17135]) ).
fof(f17755,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK100(X0))) ),
inference(cnf_transformation,[],[f14716]) ).
fof(f14716,plain,
! [X0] :
( ( ! [X1] : hBOOL(hAPP(X0,X1))
| ( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK100(X0))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK100(X0))) ) )
& ( ! [X3] :
( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) )
| ~ hBOOL(hAPP(X0,sK101(X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK100,sK101])],[f14713,f14715,f14714]) ).
fof(f14714,plain,
! [X0] :
( ? [X2] :
( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) )
=> ( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK100(X0))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK100(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f14715,plain,
! [X0] :
( ? [X4] : ~ hBOOL(hAPP(X0,X4))
=> ~ hBOOL(hAPP(X0,sK101(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14713,plain,
! [X0] :
( ( ! [X1] : hBOOL(hAPP(X0,X1))
| ? [X2] :
( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) )
& ( ! [X3] :
( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X3)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X3)) )
| ? [X4] : ~ hBOOL(hAPP(X0,X4)) ) ),
inference(rectify,[],[f14712]) ).
fof(f14712,plain,
! [X0] :
( ( ! [X1] : hBOOL(hAPP(X0,X1))
| ? [X2] :
( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) )
& ( ! [X2] :
( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) )
| ? [X1] : ~ hBOOL(hAPP(X0,X1)) ) ),
inference(nnf_transformation,[],[f10439]) ).
fof(f10439,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(X0,X1))
<=> ! [X2] :
( hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) ),
inference(ennf_transformation,[],[f5656]) ).
fof(f5656,plain,
! [X0] :
( ! [X1] : hBOOL(hAPP(X0,X1))
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
=> hBOOL(hAPP(X0,hAPP(c_Int_Onat,X2))) ) ),
inference(rectify,[],[f1774]) ).
fof(f1774,axiom,
! [X23] :
( ! [X124] : hBOOL(hAPP(X23,X124))
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
=> hBOOL(hAPP(X23,hAPP(c_Int_Onat,X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38399,plain,
spl647_1075,
inference(avatar_split_clause,[],[f26386,f38397]) ).
fof(f38397,plain,
( spl647_1075
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_HOL_Obool_Obool__size(c_fTrue) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1075])]) ).
fof(f26386,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_HOL_Obool_Obool__size(c_fTrue) = X0 ),
inference(forward_demodulation,[],[f26385,f25910]) ).
fof(f26385,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))))
| c_HOL_Obool_Obool__size(c_fTrue) = X0 ),
inference(forward_demodulation,[],[f26384,f17145]) ).
fof(f26384,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(forward_demodulation,[],[f17734,f17145]) ).
fof(f17734,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(cnf_transformation,[],[f14702]) ).
fof(f14702,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
inference(nnf_transformation,[],[f5646]) ).
fof(f5646,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f867]) ).
fof(f867,axiom,
! [X46] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X46 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38395,plain,
spl647_1074,
inference(avatar_split_clause,[],[f26367,f38393]) ).
fof(f38393,plain,
( spl647_1074
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)))
| c_HOL_Obool_Obool__size(c_fTrue) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1074])]) ).
fof(f26367,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)))
| c_HOL_Obool_Obool__size(c_fTrue) = X0 ),
inference(forward_demodulation,[],[f26366,f17145]) ).
fof(f26366,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(forward_demodulation,[],[f17706,f17145]) ).
fof(f17706,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f14685]) ).
fof(f14685,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(nnf_transformation,[],[f5632]) ).
fof(f5632,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f785]) ).
fof(f785,axiom,
! [X46] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X46),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X46 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38391,plain,
spl647_1073,
inference(avatar_split_clause,[],[f26340,f38389]) ).
fof(f38389,plain,
( spl647_1073
<=> ! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) != sK98(X0)
| c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1073])]) ).
fof(f26340,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) != sK98(X0)
| c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X0) ),
inference(forward_demodulation,[],[f26339,f17145]) ).
fof(f26339,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != sK98(X0) ),
inference(forward_demodulation,[],[f17677,f17145]) ).
fof(f17677,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != sK98(X0) ),
inference(cnf_transformation,[],[f14670]) ).
fof(f14670,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != sK98(X0)
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK98(X0)),hAPP(c_List_Oset(tc_Nat_Onat),X0))) ) )
& ( ! [X2] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),hAPP(c_List_Oset(tc_Nat_Onat),X0))) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK98])],[f14668,f14669]) ).
fof(f14669,plain,
! [X0] :
( ? [X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X0))) )
=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != sK98(X0)
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK98(X0)),hAPP(c_List_Oset(tc_Nat_Onat),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f14668,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X0)
| ? [X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X0))) ) )
& ( ! [X2] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),hAPP(c_List_Oset(tc_Nat_Onat),X0))) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X0) ) ),
inference(rectify,[],[f14667]) ).
fof(f14667,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X0)
| ? [X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X0))) ) )
& ( ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X0))) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X0) ) ),
inference(nnf_transformation,[],[f10438]) ).
fof(f10438,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X0)
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X0))) ) ),
inference(ennf_transformation,[],[f5617]) ).
fof(f5617,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X0)
<=> ! [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),hAPP(c_List_Oset(tc_Nat_Onat),X0)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
inference(rectify,[],[f3826]) ).
fof(f3826,axiom,
! [X210] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X210)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),hAPP(c_List_Oset(tc_Nat_Onat),X210)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38387,plain,
spl647_1072,
inference(avatar_split_clause,[],[f26330,f38385]) ).
fof(f38385,plain,
( spl647_1072
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1072])]) ).
fof(f26330,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0)) ),
inference(forward_demodulation,[],[f26329,f25911]) ).
fof(f25911,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,[],[f17167,f17145]) ).
fof(f17167,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,[],[f4170]) ).
fof(f4170,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f26329,plain,
! [X0] :
( hAPP(c_Code__Numeral_Oof__nat,c_HOL_Obool_Obool__size(c_fTrue)) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0)) ),
inference(forward_demodulation,[],[f17669,f17145]) ).
fof(f17669,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0))
| hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ),
inference(cnf_transformation,[],[f14664]) ).
fof(f14664,plain,
! [X0] :
( ( hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0))
| hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ) ),
inference(nnf_transformation,[],[f5614]) ).
fof(f5614,plain,
! [X0] :
( hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0)) ),
inference(rectify,[],[f4187]) ).
fof(f4187,axiom,
! [X63] :
( hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X63
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X63)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38383,plain,
spl647_1071,
inference(avatar_split_clause,[],[f26216,f38381]) ).
fof(f38381,plain,
( spl647_1071
<=> ! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1071])]) ).
fof(f26216,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0)) ),
inference(forward_demodulation,[],[f26215,f17145]) ).
fof(f26215,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(forward_demodulation,[],[f17598,f17145]) ).
fof(f17598,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f10390]) ).
fof(f10390,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(ennf_transformation,[],[f5562]) ).
fof(f5562,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ),
inference(rectify,[],[f776]) ).
fof(f776,axiom,
! [X44] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X44
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38379,plain,
spl647_1070,
inference(avatar_split_clause,[],[f26212,f38377]) ).
fof(f38377,plain,
( spl647_1070
<=> ! [X0] :
( c_Int_OPls = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1070])]) ).
fof(f26212,plain,
! [X0] :
( c_Int_OPls = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X0) ),
inference(forward_demodulation,[],[f17596,f17135]) ).
fof(f17596,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ),
inference(cnf_transformation,[],[f10388]) ).
fof(f10388,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ),
inference(ennf_transformation,[],[f5560]) ).
fof(f5560,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X0) ),
inference(rectify,[],[f1649]) ).
fof(f1649,axiom,
! [X26] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X26
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38374,plain,
( spl647_1069
| ~ spl647_331
| ~ spl647_497
| ~ spl647_1068 ),
inference(avatar_split_clause,[],[f38370,f38367,f31581,f30819,f38372]) ).
fof(f38372,plain,
( spl647_1069
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1069])]) ).
fof(f38367,plain,
( spl647_1068
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1068])]) ).
fof(f38370,plain,
( ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Int_Onumber__ring(X0) )
| ~ spl647_331
| ~ spl647_497
| ~ spl647_1068 ),
inference(forward_demodulation,[],[f38368,f32001]) ).
fof(f38368,plain,
( ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) )
| ~ spl647_1068 ),
inference(avatar_component_clause,[],[f38367]) ).
fof(f38369,plain,
spl647_1068,
inference(avatar_split_clause,[],[f26199,f38367]) ).
fof(f26199,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f26198,f25909]) ).
fof(f26198,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f24252,f17133]) ).
fof(f24252,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) ),
inference(definition_unfolding,[],[f17543,f24151]) ).
fof(f17543,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,[],[f10336]) ).
fof(f10336,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,[],[f5508]) ).
fof(f5508,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,[],[f1383]) ).
fof(f1383,axiom,
! [X20] :
( class_Int_Onumber__ring(X20)
=> c_Groups_Oone__class_Oone(X20) = hAPP(c_Int_Onumber__class_Onumber__of(X20),c_Int_OBit1(c_Int_OPls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38364,plain,
spl647_1067,
inference(avatar_split_clause,[],[f26166,f38362]) ).
fof(f38362,plain,
( spl647_1067
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1067])]) ).
fof(f26166,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X0)) ),
inference(forward_demodulation,[],[f26165,f17285]) ).
fof(f26165,plain,
! [X0] :
( c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f26164,f17135]) ).
fof(f26164,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f17512,f26052]) ).
fof(f17512,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f10314]) ).
fof(f10314,plain,
! [X0] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| 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_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ),
inference(ennf_transformation,[],[f5483]) ).
fof(f5483,plain,
! [X0] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( 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_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ) ),
inference(rectify,[],[f1299]) ).
fof(f1299,axiom,
! [X74] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X74)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X74) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X74)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X74)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X74)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38360,plain,
spl647_1066,
inference(avatar_split_clause,[],[f26163,f38358]) ).
fof(f38358,plain,
( spl647_1066
<=> ! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1066])]) ).
fof(f26163,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X0)) = X0 ),
inference(forward_demodulation,[],[f26162,f17285]) ).
fof(f26162,plain,
! [X0] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X0)) = X0
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f26161,f17285]) ).
fof(f26161,plain,
! [X0] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f17513,f26052]) ).
fof(f17513,plain,
! [X0] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f10314]) ).
fof(f38356,plain,
spl647_1065,
inference(avatar_split_clause,[],[f26160,f38354]) ).
fof(f38354,plain,
( spl647_1065
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1065])]) ).
fof(f26160,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X0)) ),
inference(forward_demodulation,[],[f26159,f17285]) ).
fof(f26159,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f17510,f26052]) ).
fof(f17510,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f10313]) ).
fof(f10313,plain,
! [X0] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X0)) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ),
inference(ennf_transformation,[],[f5482]) ).
fof(f5482,plain,
! [X0] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X0)) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ) ),
inference(rectify,[],[f1311]) ).
fof(f1311,axiom,
! [X74] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X74)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X74)) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X74)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X74)))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X74)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38352,plain,
spl647_1064,
inference(avatar_split_clause,[],[f26064,f38350]) ).
fof(f38350,plain,
( spl647_1064
<=> ! [X0] : hAPP(c_Int_Onat,X0) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Int_OPls),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1064])]) ).
fof(f26064,plain,
! [X0] : hAPP(c_Int_Onat,X0) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Int_OPls),X0)),
inference(forward_demodulation,[],[f17421,f17135]) ).
fof(f17421,plain,
! [X0] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) = hAPP(c_Int_Onat,X0),
inference(cnf_transformation,[],[f5399]) ).
fof(f5399,plain,
! [X0] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) = hAPP(c_Int_Onat,X0),
inference(rectify,[],[f2817]) ).
fof(f2817,axiom,
! [X68] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X68)) = hAPP(c_Int_Onat,X68),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38348,plain,
spl647_1063,
inference(avatar_split_clause,[],[f26060,f38346]) ).
fof(f38346,plain,
( spl647_1063
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1063])]) ).
fof(f26060,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(forward_demodulation,[],[f17406,f17145]) ).
fof(f17406,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(cnf_transformation,[],[f5384]) ).
fof(f5384,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(rectify,[],[f1814]) ).
fof(f1814,axiom,
! [X44] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38344,plain,
spl647_1062,
inference(avatar_split_clause,[],[f25976,f38341]) ).
fof(f38341,plain,
( spl647_1062
<=> hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1062])]) ).
fof(f25976,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f25975,f25963]) ).
fof(f25975,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))),
inference(forward_demodulation,[],[f25974,f25909]) ).
fof(f25974,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))),
inference(forward_demodulation,[],[f24186,f17133]) ).
fof(f24186,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin))),
inference(definition_unfolding,[],[f17223,f24151]) ).
fof(f17223,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))),
inference(cnf_transformation,[],[f2113]) ).
fof(f2113,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38339,plain,
spl647_1061,
inference(avatar_split_clause,[],[f25823,f38337]) ).
fof(f38337,plain,
( spl647_1061
<=> ! [X4,X0,X2] : sP81(X0,hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0),X2,c_List_Olist_ONil(X2),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1061])]) ).
fof(f25823,plain,
! [X2,X0,X4] : sP81(X0,hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0),X2,c_List_Olist_ONil(X2),X4),
inference(equality_resolution,[],[f25822]) ).
fof(f25822,plain,
! [X2,X3,X0,X4] :
( sP81(X0,hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0),X2,X3,X4)
| c_List_Olist_ONil(X2) != X3 ),
inference(equality_resolution,[],[f23599]) ).
fof(f23599,plain,
! [X2,X3,X0,X1,X4] :
( sP81(X0,X1,X2,X3,X4)
| hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0) != X1
| c_List_Olist_ONil(X2) != X3 ),
inference(cnf_transformation,[],[f16729]) ).
fof(f16729,plain,
! [X0,X1,X2,X3,X4] :
( ( sP81(X0,X1,X2,X3,X4)
| ( ! [X5] :
( hAPP(hAPP(c_List_Oappend(X2),X5),X1) != X0
| hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5) != X3 )
& ( hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0) != X1
| c_List_Olist_ONil(X2) != X3 ) ) )
& ( ( hAPP(hAPP(c_List_Oappend(X2),sK577(X0,X1,X2,X3,X4)),X1) = X0
& hAPP(hAPP(c_List_Olist_OCons(X2),X4),sK577(X0,X1,X2,X3,X4)) = X3 )
| ( hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0) = X1
& c_List_Olist_ONil(X2) = X3 )
| ~ sP81(X0,X1,X2,X3,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK577])],[f16727,f16728]) ).
fof(f16728,plain,
! [X0,X1,X2,X3,X4] :
( ? [X6] :
( hAPP(hAPP(c_List_Oappend(X2),X6),X1) = X0
& hAPP(hAPP(c_List_Olist_OCons(X2),X4),X6) = X3 )
=> ( hAPP(hAPP(c_List_Oappend(X2),sK577(X0,X1,X2,X3,X4)),X1) = X0
& hAPP(hAPP(c_List_Olist_OCons(X2),X4),sK577(X0,X1,X2,X3,X4)) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f16727,plain,
! [X0,X1,X2,X3,X4] :
( ( sP81(X0,X1,X2,X3,X4)
| ( ! [X5] :
( hAPP(hAPP(c_List_Oappend(X2),X5),X1) != X0
| hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5) != X3 )
& ( hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0) != X1
| c_List_Olist_ONil(X2) != X3 ) ) )
& ( ? [X6] :
( hAPP(hAPP(c_List_Oappend(X2),X6),X1) = X0
& hAPP(hAPP(c_List_Olist_OCons(X2),X4),X6) = X3 )
| ( hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0) = X1
& c_List_Olist_ONil(X2) = X3 )
| ~ sP81(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16726]) ).
fof(f16726,plain,
! [X2,X0,X4,X1,X3] :
( ( sP81(X2,X0,X4,X1,X3)
| ( ! [X5] :
( hAPP(hAPP(c_List_Oappend(X4),X5),X0) != X2
| hAPP(hAPP(c_List_Olist_OCons(X4),X3),X5) != X1 )
& ( hAPP(hAPP(c_List_Olist_OCons(X4),X3),X2) != X0
| c_List_Olist_ONil(X4) != X1 ) ) )
& ( ? [X5] :
( hAPP(hAPP(c_List_Oappend(X4),X5),X0) = X2
& hAPP(hAPP(c_List_Olist_OCons(X4),X3),X5) = X1 )
| ( hAPP(hAPP(c_List_Olist_OCons(X4),X3),X2) = X0
& c_List_Olist_ONil(X4) = X1 )
| ~ sP81(X2,X0,X4,X1,X3) ) ),
inference(flattening,[],[f16725]) ).
fof(f16725,plain,
! [X2,X0,X4,X1,X3] :
( ( sP81(X2,X0,X4,X1,X3)
| ( ! [X5] :
( hAPP(hAPP(c_List_Oappend(X4),X5),X0) != X2
| hAPP(hAPP(c_List_Olist_OCons(X4),X3),X5) != X1 )
& ( hAPP(hAPP(c_List_Olist_OCons(X4),X3),X2) != X0
| c_List_Olist_ONil(X4) != X1 ) ) )
& ( ? [X5] :
( hAPP(hAPP(c_List_Oappend(X4),X5),X0) = X2
& hAPP(hAPP(c_List_Olist_OCons(X4),X3),X5) = X1 )
| ( hAPP(hAPP(c_List_Olist_OCons(X4),X3),X2) = X0
& c_List_Olist_ONil(X4) = X1 )
| ~ sP81(X2,X0,X4,X1,X3) ) ),
inference(nnf_transformation,[],[f14616]) ).
fof(f14616,plain,
! [X2,X0,X4,X1,X3] :
( sP81(X2,X0,X4,X1,X3)
<=> ( ? [X5] :
( hAPP(hAPP(c_List_Oappend(X4),X5),X0) = X2
& hAPP(hAPP(c_List_Olist_OCons(X4),X3),X5) = X1 )
| ( hAPP(hAPP(c_List_Olist_OCons(X4),X3),X2) = X0
& c_List_Olist_ONil(X4) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP81])]) ).
fof(f38335,plain,
spl647_1060,
inference(avatar_split_clause,[],[f25819,f38333]) ).
fof(f38333,plain,
( spl647_1060
<=> ! [X4,X0,X2] : sP80(X0,hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0),X2,c_List_Olist_ONil(X2),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1060])]) ).
fof(f25819,plain,
! [X2,X0,X4] : sP80(X0,hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0),X2,c_List_Olist_ONil(X2),X4),
inference(equality_resolution,[],[f25818]) ).
fof(f25818,plain,
! [X2,X3,X0,X4] :
( sP80(X0,hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0),X2,X3,X4)
| c_List_Olist_ONil(X2) != X3 ),
inference(equality_resolution,[],[f23591]) ).
fof(f23591,plain,
! [X2,X3,X0,X1,X4] :
( sP80(X0,X1,X2,X3,X4)
| hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0) != X1
| c_List_Olist_ONil(X2) != X3 ),
inference(cnf_transformation,[],[f16723]) ).
fof(f16723,plain,
! [X0,X1,X2,X3,X4] :
( ( sP80(X0,X1,X2,X3,X4)
| ( ! [X5] :
( hAPP(hAPP(c_List_Oappend(X2),X5),X1) != X0
| hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5) != X3 )
& ( hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0) != X1
| c_List_Olist_ONil(X2) != X3 ) ) )
& ( ( hAPP(hAPP(c_List_Oappend(X2),sK576(X0,X1,X2,X3,X4)),X1) = X0
& hAPP(hAPP(c_List_Olist_OCons(X2),X4),sK576(X0,X1,X2,X3,X4)) = X3 )
| ( hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0) = X1
& c_List_Olist_ONil(X2) = X3 )
| ~ sP80(X0,X1,X2,X3,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK576])],[f16721,f16722]) ).
fof(f16722,plain,
! [X0,X1,X2,X3,X4] :
( ? [X6] :
( hAPP(hAPP(c_List_Oappend(X2),X6),X1) = X0
& hAPP(hAPP(c_List_Olist_OCons(X2),X4),X6) = X3 )
=> ( hAPP(hAPP(c_List_Oappend(X2),sK576(X0,X1,X2,X3,X4)),X1) = X0
& hAPP(hAPP(c_List_Olist_OCons(X2),X4),sK576(X0,X1,X2,X3,X4)) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f16721,plain,
! [X0,X1,X2,X3,X4] :
( ( sP80(X0,X1,X2,X3,X4)
| ( ! [X5] :
( hAPP(hAPP(c_List_Oappend(X2),X5),X1) != X0
| hAPP(hAPP(c_List_Olist_OCons(X2),X4),X5) != X3 )
& ( hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0) != X1
| c_List_Olist_ONil(X2) != X3 ) ) )
& ( ? [X6] :
( hAPP(hAPP(c_List_Oappend(X2),X6),X1) = X0
& hAPP(hAPP(c_List_Olist_OCons(X2),X4),X6) = X3 )
| ( hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0) = X1
& c_List_Olist_ONil(X2) = X3 )
| ~ sP80(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16720]) ).
fof(f16720,plain,
! [X0,X2,X4,X3,X1] :
( ( sP80(X0,X2,X4,X3,X1)
| ( ! [X5] :
( hAPP(hAPP(c_List_Oappend(X4),X5),X2) != X0
| hAPP(hAPP(c_List_Olist_OCons(X4),X1),X5) != X3 )
& ( hAPP(hAPP(c_List_Olist_OCons(X4),X1),X0) != X2
| c_List_Olist_ONil(X4) != X3 ) ) )
& ( ? [X5] :
( hAPP(hAPP(c_List_Oappend(X4),X5),X2) = X0
& hAPP(hAPP(c_List_Olist_OCons(X4),X1),X5) = X3 )
| ( hAPP(hAPP(c_List_Olist_OCons(X4),X1),X0) = X2
& c_List_Olist_ONil(X4) = X3 )
| ~ sP80(X0,X2,X4,X3,X1) ) ),
inference(flattening,[],[f16719]) ).
fof(f16719,plain,
! [X0,X2,X4,X3,X1] :
( ( sP80(X0,X2,X4,X3,X1)
| ( ! [X5] :
( hAPP(hAPP(c_List_Oappend(X4),X5),X2) != X0
| hAPP(hAPP(c_List_Olist_OCons(X4),X1),X5) != X3 )
& ( hAPP(hAPP(c_List_Olist_OCons(X4),X1),X0) != X2
| c_List_Olist_ONil(X4) != X3 ) ) )
& ( ? [X5] :
( hAPP(hAPP(c_List_Oappend(X4),X5),X2) = X0
& hAPP(hAPP(c_List_Olist_OCons(X4),X1),X5) = X3 )
| ( hAPP(hAPP(c_List_Olist_OCons(X4),X1),X0) = X2
& c_List_Olist_ONil(X4) = X3 )
| ~ sP80(X0,X2,X4,X3,X1) ) ),
inference(nnf_transformation,[],[f14614]) ).
fof(f14614,plain,
! [X0,X2,X4,X3,X1] :
( sP80(X0,X2,X4,X3,X1)
<=> ( ? [X5] :
( hAPP(hAPP(c_List_Oappend(X4),X5),X2) = X0
& hAPP(hAPP(c_List_Olist_OCons(X4),X1),X5) = X3 )
| ( hAPP(hAPP(c_List_Olist_OCons(X4),X1),X0) = X2
& c_List_Olist_ONil(X4) = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP80])]) ).
fof(f38331,plain,
spl647_1059,
inference(avatar_split_clause,[],[f25449,f38329]) ).
fof(f38329,plain,
( spl647_1059
<=> ! [X2,X0] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),X0)
| ~ class_Rings_Oring__no__zero__divisors(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1059])]) ).
fof(f25449,plain,
! [X2,X0] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),c_Groups_Ozero__class_Ozero(X2)),X0)
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(equality_resolution,[],[f19896]) ).
fof(f19896,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) != X1
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(cnf_transformation,[],[f15307]) ).
fof(f15307,plain,
! [X0,X1,X2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
| ( c_Groups_Ozero__class_Ozero(X2) != X0
& c_Groups_Ozero__class_Ozero(X2) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2) ) )
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(flattening,[],[f15306]) ).
fof(f15306,plain,
! [X0,X1,X2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
| ( c_Groups_Ozero__class_Ozero(X2) != X0
& c_Groups_Ozero__class_Ozero(X2) != X1 ) )
& ( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) != c_Groups_Ozero__class_Ozero(X2) ) )
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(nnf_transformation,[],[f11326]) ).
fof(f11326,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1 ) )
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(ennf_transformation,[],[f7255]) ).
fof(f7255,plain,
! [X0,X1,X2] :
( class_Rings_Oring__no__zero__divisors(X2)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
<=> ( c_Groups_Ozero__class_Ozero(X2) = X0
| c_Groups_Ozero__class_Ozero(X2) = X1 ) ) ),
inference(rectify,[],[f758]) ).
fof(f758,axiom,
! [X12,X5,X4] :
( class_Rings_Oring__no__zero__divisors(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X5),X12)
<=> ( c_Groups_Ozero__class_Ozero(X4) = X12
| c_Groups_Ozero__class_Ozero(X4) = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38327,plain,
spl647_1058,
inference(avatar_split_clause,[],[f25448,f38325]) ).
fof(f38325,plain,
( spl647_1058
<=> ! [X2,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Oring__no__zero__divisors(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1058])]) ).
fof(f25448,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),c_Groups_Ozero__class_Ozero(X2))
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(equality_resolution,[],[f19897]) ).
fof(f19897,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0) = c_Groups_Ozero__class_Ozero(X2)
| c_Groups_Ozero__class_Ozero(X2) != X0
| ~ class_Rings_Oring__no__zero__divisors(X2) ),
inference(cnf_transformation,[],[f15307]) ).
fof(f38323,plain,
( spl647_1057
| spl647_326
| ~ spl647_952 ),
inference(avatar_split_clause,[],[f37916,f34617,f30794,f38321]) ).
fof(f38321,plain,
( spl647_1057
<=> ! [X0,X1] : sP41(X0,X1,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1057])]) ).
fof(f30794,plain,
( spl647_326
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_326])]) ).
fof(f34617,plain,
( spl647_952
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP41(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_952])]) ).
fof(f37916,plain,
( ! [X0,X1] : sP41(X0,X1,c_Int_OMin)
| spl647_326
| ~ spl647_952 ),
inference(resolution,[],[f34618,f30796]) ).
fof(f30796,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| spl647_326 ),
inference(avatar_component_clause,[],[f30794]) ).
fof(f34618,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP41(X0,X1,X2) )
| ~ spl647_952 ),
inference(avatar_component_clause,[],[f34617]) ).
fof(f38319,plain,
spl647_1056,
inference(avatar_split_clause,[],[f24910,f38317]) ).
fof(f38317,plain,
( spl647_1056
<=> ! [X0,X3,X2,X1] : c_Product__Type_Ocurry(X3,X2,X1,hAPP(c_Product__Type_Ointernal__split(X3,X2,X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1056])]) ).
fof(f24910,plain,
! [X2,X3,X0,X1] : c_Product__Type_Ocurry(X3,X2,X1,hAPP(c_Product__Type_Ointernal__split(X3,X2,X1),X0)) = X0,
inference(definition_unfolding,[],[f21562,f19585]) ).
fof(f21562,plain,
! [X2,X3,X0,X1] : c_Product__Type_Ocurry(X3,X2,X1,hAPP(c_Product__Type_Oprod_Oprod__case(X3,X2,X1),X0)) = X0,
inference(cnf_transformation,[],[f8279]) ).
fof(f8279,plain,
! [X0,X1,X2,X3] : c_Product__Type_Ocurry(X3,X2,X1,hAPP(c_Product__Type_Oprod_Oprod__case(X3,X2,X1),X0)) = X0,
inference(rectify,[],[f4814]) ).
fof(f4814,axiom,
! [X1,X96,X14,X4] : c_Product__Type_Ocurry(X4,X14,X96,hAPP(c_Product__Type_Oprod_Oprod__case(X4,X14,X96),X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38315,plain,
spl647_1055,
inference(avatar_split_clause,[],[f24909,f38313]) ).
fof(f38313,plain,
( spl647_1055
<=> ! [X0,X3,X2,X1] : hAPP(c_Product__Type_Ointernal__split(X3,X2,X1),c_Product__Type_Ocurry(X3,X2,X1,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1055])]) ).
fof(f24909,plain,
! [X2,X3,X0,X1] : hAPP(c_Product__Type_Ointernal__split(X3,X2,X1),c_Product__Type_Ocurry(X3,X2,X1,X0)) = X0,
inference(definition_unfolding,[],[f21561,f19585]) ).
fof(f21561,plain,
! [X2,X3,X0,X1] : hAPP(c_Product__Type_Oprod_Oprod__case(X3,X2,X1),c_Product__Type_Ocurry(X3,X2,X1,X0)) = X0,
inference(cnf_transformation,[],[f8278]) ).
fof(f8278,plain,
! [X0,X1,X2,X3] : hAPP(c_Product__Type_Oprod_Oprod__case(X3,X2,X1),c_Product__Type_Ocurry(X3,X2,X1,X0)) = X0,
inference(rectify,[],[f4815]) ).
fof(f4815,axiom,
! [X1,X96,X14,X4] : hAPP(c_Product__Type_Oprod_Oprod__case(X4,X14,X96),c_Product__Type_Ocurry(X4,X14,X96,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38311,plain,
spl647_1054,
inference(avatar_split_clause,[],[f24332,f38309]) ).
fof(f38309,plain,
( spl647_1054
<=> ! [X0,X1] : hAPP(c_List_Omember(X1),X0) = hAPP(c_List_Omember(X1),hAPP(c_List_Orev(X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1054])]) ).
fof(f24332,plain,
! [X0,X1] : hAPP(c_List_Omember(X1),X0) = hAPP(c_List_Omember(X1),hAPP(c_List_Orev(X1),X0)),
inference(definition_unfolding,[],[f17891,f17267,f17267]) ).
fof(f17891,plain,
! [X0,X1] : hAPP(c_List_Oset(X1),X0) = hAPP(c_List_Oset(X1),hAPP(c_List_Orev(X1),X0)),
inference(cnf_transformation,[],[f5783]) ).
fof(f5783,plain,
! [X0,X1] : hAPP(c_List_Oset(X1),X0) = hAPP(c_List_Oset(X1),hAPP(c_List_Orev(X1),X0)),
inference(rectify,[],[f4446]) ).
fof(f4446,axiom,
! [X203,X4] : hAPP(c_List_Oset(X4),X203) = hAPP(c_List_Oset(X4),hAPP(c_List_Orev(X4),X203)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38307,plain,
spl647_1053,
inference(avatar_split_clause,[],[f24331,f38305]) ).
fof(f38305,plain,
( spl647_1053
<=> ! [X0,X1] : hAPP(c_List_Omember(X1),X0) = hAPP(c_List_Omember(X1),hAPP(c_List_Orotate1(X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1053])]) ).
fof(f24331,plain,
! [X0,X1] : hAPP(c_List_Omember(X1),X0) = hAPP(c_List_Omember(X1),hAPP(c_List_Orotate1(X1),X0)),
inference(definition_unfolding,[],[f17890,f17267,f17267]) ).
fof(f17890,plain,
! [X0,X1] : hAPP(c_List_Oset(X1),X0) = hAPP(c_List_Oset(X1),hAPP(c_List_Orotate1(X1),X0)),
inference(cnf_transformation,[],[f5782]) ).
fof(f5782,plain,
! [X0,X1] : hAPP(c_List_Oset(X1),X0) = hAPP(c_List_Oset(X1),hAPP(c_List_Orotate1(X1),X0)),
inference(rectify,[],[f4003]) ).
fof(f4003,axiom,
! [X203,X4] : hAPP(c_List_Oset(X4),X203) = hAPP(c_List_Oset(X4),hAPP(c_List_Orotate1(X4),X203)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38303,plain,
spl647_1052,
inference(avatar_split_clause,[],[f24312,f38301]) ).
fof(f38301,plain,
( spl647_1052
<=> ! [X0,X1] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1052])]) ).
fof(f24312,plain,
! [X0,X1] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X0)))),
inference(definition_unfolding,[],[f17830,f17872]) ).
fof(f17872,plain,
! [X0,X1] : c_Divides_Odivmod__nat(X1,X0) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X0)),
inference(cnf_transformation,[],[f5764]) ).
fof(f5764,plain,
! [X0,X1] : c_Divides_Odivmod__nat(X1,X0) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X1,X0)),
inference(rectify,[],[f3121]) ).
fof(f3121,axiom,
! [X46,X47] : c_Divides_Odivmod__nat(X47,X46) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X47,X46)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17830,plain,
! [X0,X1] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),c_Divides_Odivmod__nat(X1,X0))),
inference(cnf_transformation,[],[f5722]) ).
fof(f5722,plain,
! [X0,X1] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),c_Divides_Odivmod__nat(X1,X0))),
inference(rectify,[],[f2303]) ).
fof(f2303,axiom,
! [X44,X45] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X45,X44),c_Divides_Odivmod__nat(X45,X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38299,plain,
spl647_1051,
inference(avatar_split_clause,[],[f24266,f38297]) ).
fof(f38297,plain,
( spl647_1051
<=> ! [X0] :
( c_Int_OMin = X0
| c_Int_OMin != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1051])]) ).
fof(f24266,plain,
! [X0] :
( c_Int_OMin = X0
| c_Int_OMin != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin) ),
inference(definition_unfolding,[],[f17655,f24151]) ).
fof(f17655,plain,
! [X0] :
( c_Int_OMin = X0
| c_Int_OMin != c_Int_OBit1(X0) ),
inference(cnf_transformation,[],[f14650]) ).
fof(f14650,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,[],[f5608]) ).
fof(f5608,plain,
! [X0] :
( c_Int_OMin = c_Int_OBit1(X0)
<=> c_Int_OMin = X0 ),
inference(rectify,[],[f1958]) ).
fof(f1958,axiom,
! [X97] :
( c_Int_OBit1(X97) = c_Int_OMin
<=> c_Int_OMin = X97 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38295,plain,
spl647_1050,
inference(avatar_split_clause,[],[f23501,f38293]) ).
fof(f38293,plain,
( spl647_1050
<=> ! [X4,X0,X3,X2,X1] :
( X0 = X2
| c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) != c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1050])]) ).
fof(f23501,plain,
! [X2,X3,X0,X1,X4] :
( X0 = X2
| c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) != c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) ),
inference(cnf_transformation,[],[f16658]) ).
fof(f16658,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) = c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) != c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) ) ),
inference(flattening,[],[f16657]) ).
fof(f16657,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) = c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) != c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) ) ),
inference(nnf_transformation,[],[f9713]) ).
fof(f9713,plain,
! [X0,X1,X2,X3,X4] :
( c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) = c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2)
<=> ( X0 = X2
& X1 = X3 ) ),
inference(rectify,[],[f4653]) ).
fof(f4653,axiom,
! [X255,X94,X256,X5,X4] :
( c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X5,X256) = c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X94,X255)
<=> ( X255 = X256
& X5 = X94 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38291,plain,
spl647_1049,
inference(avatar_split_clause,[],[f23500,f38289]) ).
fof(f38289,plain,
( spl647_1049
<=> ! [X4,X0,X3,X2,X1] :
( X1 = X3
| c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) != c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1049])]) ).
fof(f23500,plain,
! [X2,X3,X0,X1,X4] :
( X1 = X3
| c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) != c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) ),
inference(cnf_transformation,[],[f16658]) ).
fof(f38287,plain,
spl647_1048,
inference(avatar_split_clause,[],[f22778,f38285]) ).
fof(f38285,plain,
( spl647_1048
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ sP66(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1048])]) ).
fof(f22778,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ sP66(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16409]) ).
fof(f16409,plain,
! [X0,X1,X2,X3] :
( ( sP66(X0,X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ( ( ~ sP65(X3,X0,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
& ( ( sP65(X3,X0,X1,X2)
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X0))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X2)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X3)) ) )
| ~ sP66(X0,X1,X2,X3) ) ),
inference(rectify,[],[f16408]) ).
fof(f16408,plain,
! [X0,X1,X3,X2] :
( ( sP66(X0,X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ( ( ~ sP65(X2,X0,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
& ( ( sP65(X2,X0,X1,X3)
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2)) ) )
| ~ sP66(X0,X1,X3,X2) ) ),
inference(flattening,[],[f16407]) ).
fof(f16407,plain,
! [X0,X1,X3,X2] :
( ( sP66(X0,X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ( ( ~ sP65(X2,X0,X1,X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) )
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2)) ) )
& ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
& ( ( sP65(X2,X0,X1,X3)
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2)) ) )
| ~ sP66(X0,X1,X3,X2) ) ),
inference(nnf_transformation,[],[f14588]) ).
fof(f14588,plain,
! [X0,X1,X3,X2] :
( sP66(X0,X1,X3,X2)
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
& ( ( sP65(X2,X0,X1,X3)
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X2),X0))
& hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X3)) )
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X3),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP66])]) ).
fof(f38283,plain,
spl647_1047,
inference(avatar_split_clause,[],[f22274,f38281]) ).
fof(f38281,plain,
( spl647_1047
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X0),sK435(X0,X1,X2)))
| ~ sP56(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1047])]) ).
fof(f22274,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X0),sK435(X0,X1,X2)))
| ~ sP56(X0,X1,X2) ),
inference(cnf_transformation,[],[f16162]) ).
fof(f38279,plain,
( spl647_1046
| ~ spl647_383
| ~ spl647_952 ),
inference(avatar_split_clause,[],[f37908,f34617,f31041,f38277]) ).
fof(f38277,plain,
( spl647_1046
<=> ! [X0,X1] : sP41(X0,X1,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1046])]) ).
fof(f31041,plain,
( spl647_383
<=> ! [X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_383])]) ).
fof(f37908,plain,
( ! [X0,X1] : sP41(X0,X1,c_Int_OPls)
| ~ spl647_383
| ~ spl647_952 ),
inference(resolution,[],[f34618,f31042]) ).
fof(f31042,plain,
( ! [X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1))
| ~ spl647_383 ),
inference(avatar_component_clause,[],[f31041]) ).
fof(f38275,plain,
spl647_1045,
inference(avatar_split_clause,[],[f22241,f38273]) ).
fof(f38273,plain,
( spl647_1045
<=> ! [X0,X3,X2,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1045])]) ).
fof(f22241,plain,
! [X2,X3,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X1) ),
inference(cnf_transformation,[],[f13198]) ).
fof(f13198,plain,
! [X0,X1,X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X1) ),
inference(flattening,[],[f13197]) ).
fof(f13197,plain,
! [X0,X1,X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X1)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X2)
| ~ c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X1) ),
inference(ennf_transformation,[],[f8878]) ).
fof(f8878,plain,
! [X0,X1,X2,X3] :
( c_Hoare__Mirabelle_Ohoare__derivs(X3,X2,X1)
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X2)
=> c_Hoare__Mirabelle_Ohoare__derivs(X3,X0,X1) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X3,X6,X7,X4] :
( c_Hoare__Mirabelle_Ohoare__derivs(X4,X7,X6)
=> ( c_Hoare__Mirabelle_Ohoare__derivs(X4,X3,X7)
=> c_Hoare__Mirabelle_Ohoare__derivs(X4,X3,X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38271,plain,
spl647_1044,
inference(avatar_split_clause,[],[f22224,f38269]) ).
fof(f38269,plain,
( spl647_1044
<=> ! [X0,X3,X2,X1] :
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(X3,X1),X2),X0))
| ~ c_Wellfounded_Owf(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1044])]) ).
fof(f22224,plain,
! [X2,X3,X0,X1] :
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(X3,X1),X2),X0))
| ~ c_Wellfounded_Owf(X3,X2) ),
inference(cnf_transformation,[],[f13174]) ).
fof(f13174,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(X3,X1),X2),X0))
| ~ c_Wellfounded_Owf(X3,X2) ),
inference(ennf_transformation,[],[f8857]) ).
fof(f8857,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Owf(X3,X2)
=> c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(X3,X1),X2),X0)) ),
inference(rectify,[],[f3359]) ).
fof(f3359,axiom,
! [X1,X14,X116,X4] :
( c_Wellfounded_Owf(X4,X116)
=> c_Wellfounded_Owf(X14,hAPP(hAPP(c_Relation_Oinv__image(X4,X14),X116),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38267,plain,
spl647_1043,
inference(avatar_split_clause,[],[f22222,f38265]) ).
fof(f38265,plain,
( spl647_1043
<=> ! [X0,X3,X2,X1] :
( c_Relation_Otrans(X1,hAPP(hAPP(c_Relation_Oinv__image(X3,X1),X2),X0))
| ~ c_Relation_Otrans(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1043])]) ).
fof(f22222,plain,
! [X2,X3,X0,X1] :
( c_Relation_Otrans(X1,hAPP(hAPP(c_Relation_Oinv__image(X3,X1),X2),X0))
| ~ c_Relation_Otrans(X3,X2) ),
inference(cnf_transformation,[],[f13171]) ).
fof(f13171,plain,
! [X0,X1,X2,X3] :
( c_Relation_Otrans(X1,hAPP(hAPP(c_Relation_Oinv__image(X3,X1),X2),X0))
| ~ c_Relation_Otrans(X3,X2) ),
inference(ennf_transformation,[],[f8855]) ).
fof(f8855,plain,
! [X0,X1,X2,X3] :
( c_Relation_Otrans(X3,X2)
=> c_Relation_Otrans(X1,hAPP(hAPP(c_Relation_Oinv__image(X3,X1),X2),X0)) ),
inference(rectify,[],[f4712]) ).
fof(f4712,axiom,
! [X1,X14,X116,X4] :
( c_Relation_Otrans(X4,X116)
=> c_Relation_Otrans(X14,hAPP(hAPP(c_Relation_Oinv__image(X4,X14),X116),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38263,plain,
spl647_1042,
inference(avatar_split_clause,[],[f22220,f38261]) ).
fof(f38261,plain,
( spl647_1042
<=> ! [X0,X3,X2,X1] :
( c_Relation_Osym(X1,hAPP(hAPP(c_Relation_Oinv__image(X3,X1),X2),X0))
| ~ c_Relation_Osym(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1042])]) ).
fof(f22220,plain,
! [X2,X3,X0,X1] :
( c_Relation_Osym(X1,hAPP(hAPP(c_Relation_Oinv__image(X3,X1),X2),X0))
| ~ c_Relation_Osym(X3,X2) ),
inference(cnf_transformation,[],[f13168]) ).
fof(f13168,plain,
! [X0,X1,X2,X3] :
( c_Relation_Osym(X1,hAPP(hAPP(c_Relation_Oinv__image(X3,X1),X2),X0))
| ~ c_Relation_Osym(X3,X2) ),
inference(ennf_transformation,[],[f8853]) ).
fof(f8853,plain,
! [X0,X1,X2,X3] :
( c_Relation_Osym(X3,X2)
=> c_Relation_Osym(X1,hAPP(hAPP(c_Relation_Oinv__image(X3,X1),X2),X0)) ),
inference(rectify,[],[f4760]) ).
fof(f4760,axiom,
! [X1,X14,X116,X4] :
( c_Relation_Osym(X4,X116)
=> c_Relation_Osym(X14,hAPP(hAPP(c_Relation_Oinv__image(X4,X14),X116),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38259,plain,
spl647_1041,
inference(avatar_split_clause,[],[f22211,f38257]) ).
fof(f38257,plain,
( spl647_1041
<=> ! [X0,X3,X2,X1] :
( c_Quotient_OBabs(X3,X1,c_Quotient_ORespects(X3,X2),X0) = X0
| ~ c_Equiv__Relations_Oequivp(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1041])]) ).
fof(f22211,plain,
! [X2,X3,X0,X1] :
( c_Quotient_OBabs(X3,X1,c_Quotient_ORespects(X3,X2),X0) = X0
| ~ c_Equiv__Relations_Oequivp(X3,X2) ),
inference(cnf_transformation,[],[f13158]) ).
fof(f13158,plain,
! [X0,X1,X2,X3] :
( c_Quotient_OBabs(X3,X1,c_Quotient_ORespects(X3,X2),X0) = X0
| ~ c_Equiv__Relations_Oequivp(X3,X2) ),
inference(ennf_transformation,[],[f8847]) ).
fof(f8847,plain,
! [X0,X1,X2,X3] :
( c_Equiv__Relations_Oequivp(X3,X2)
=> c_Quotient_OBabs(X3,X1,c_Quotient_ORespects(X3,X2),X0) = X0 ),
inference(rectify,[],[f4855]) ).
fof(f4855,axiom,
! [X23,X14,X138,X4] :
( c_Equiv__Relations_Oequivp(X4,X138)
=> c_Quotient_OBabs(X4,X14,c_Quotient_ORespects(X4,X138),X23) = X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38255,plain,
spl647_1040,
inference(avatar_split_clause,[],[f21563,f38253]) ).
fof(f38253,plain,
( spl647_1040
<=> ! [X0,X3,X2,X1] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1040])]) ).
fof(f21563,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X0)),
inference(cnf_transformation,[],[f8280]) ).
fof(f8280,plain,
! [X0,X1,X2,X3] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),X0)),
inference(rectify,[],[f258]) ).
fof(f258,axiom,
! [X17,X1,X14,X4] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X4,X14,X1,X17,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38251,plain,
spl647_1039,
inference(avatar_split_clause,[],[f21295,f38249]) ).
fof(f38249,plain,
( spl647_1039
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP(c_List_Orev(X2),X0) != hAPP(c_List_Orev(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1039])]) ).
fof(f21295,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(c_List_Orev(X2),X0) != hAPP(c_List_Orev(X2),X1) ),
inference(cnf_transformation,[],[f15854]) ).
fof(f15854,plain,
! [X0,X1,X2] :
( ( hAPP(c_List_Orev(X2),X0) = hAPP(c_List_Orev(X2),X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_List_Orev(X2),X0) != hAPP(c_List_Orev(X2),X1) ) ),
inference(nnf_transformation,[],[f8181]) ).
fof(f8181,plain,
! [X0,X1,X2] :
( hAPP(c_List_Orev(X2),X0) = hAPP(c_List_Orev(X2),X1)
<=> X0 = X1 ),
inference(rectify,[],[f4449]) ).
fof(f4449,axiom,
! [X202,X203,X4] :
( hAPP(c_List_Orev(X4),X203) = hAPP(c_List_Orev(X4),X202)
<=> X202 = X203 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38247,plain,
spl647_1038,
inference(avatar_split_clause,[],[f21284,f38245]) ).
fof(f38245,plain,
( spl647_1038
<=> ! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,hAPP(c_Relation_Oconverse(X2,X2),X0))
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1038])]) ).
fof(f21284,plain,
! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,hAPP(c_Relation_Oconverse(X2,X2),X0))
| ~ c_Relation_Orefl__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f15847]) ).
fof(f15847,plain,
! [X0,X1,X2] :
( ( c_Relation_Orefl__on(X2,X1,hAPP(c_Relation_Oconverse(X2,X2),X0))
| ~ c_Relation_Orefl__on(X2,X1,X0) )
& ( c_Relation_Orefl__on(X2,X1,X0)
| ~ c_Relation_Orefl__on(X2,X1,hAPP(c_Relation_Oconverse(X2,X2),X0)) ) ),
inference(nnf_transformation,[],[f8176]) ).
fof(f8176,plain,
! [X0,X1,X2] :
( c_Relation_Orefl__on(X2,X1,hAPP(c_Relation_Oconverse(X2,X2),X0))
<=> c_Relation_Orefl__on(X2,X1,X0) ),
inference(rectify,[],[f3625]) ).
fof(f3625,axiom,
! [X116,X9,X4] :
( c_Relation_Orefl__on(X4,X9,hAPP(c_Relation_Oconverse(X4,X4),X116))
<=> c_Relation_Orefl__on(X4,X9,X116) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38243,plain,
spl647_1037,
inference(avatar_split_clause,[],[f21283,f38241]) ).
fof(f38241,plain,
( spl647_1037
<=> ! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ c_Relation_Orefl__on(X2,X1,hAPP(c_Relation_Oconverse(X2,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1037])]) ).
fof(f21283,plain,
! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ c_Relation_Orefl__on(X2,X1,hAPP(c_Relation_Oconverse(X2,X2),X0)) ),
inference(cnf_transformation,[],[f15847]) ).
fof(f38239,plain,
spl647_1036,
inference(avatar_split_clause,[],[f21282,f38237]) ).
fof(f38237,plain,
( spl647_1036
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,hAPP(c_Relation_Oconverse(X2,X2),X0))
| ~ c_Relation_Ototal__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1036])]) ).
fof(f21282,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,hAPP(c_Relation_Oconverse(X2,X2),X0))
| ~ c_Relation_Ototal__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f15846]) ).
fof(f15846,plain,
! [X0,X1,X2] :
( ( c_Relation_Ototal__on(X2,X1,hAPP(c_Relation_Oconverse(X2,X2),X0))
| ~ c_Relation_Ototal__on(X2,X1,X0) )
& ( c_Relation_Ototal__on(X2,X1,X0)
| ~ c_Relation_Ototal__on(X2,X1,hAPP(c_Relation_Oconverse(X2,X2),X0)) ) ),
inference(nnf_transformation,[],[f8175]) ).
fof(f8175,plain,
! [X0,X1,X2] :
( c_Relation_Ototal__on(X2,X1,hAPP(c_Relation_Oconverse(X2,X2),X0))
<=> c_Relation_Ototal__on(X2,X1,X0) ),
inference(rectify,[],[f3629]) ).
fof(f3629,axiom,
! [X116,X9,X4] :
( c_Relation_Ototal__on(X4,X9,hAPP(c_Relation_Oconverse(X4,X4),X116))
<=> c_Relation_Ototal__on(X4,X9,X116) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38235,plain,
( spl647_1035
| ~ spl647_383
| ~ spl647_951 ),
inference(avatar_split_clause,[],[f37896,f34613,f31041,f38233]) ).
fof(f38233,plain,
( spl647_1035
<=> ! [X0,X1] : sP42(X0,X1,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1035])]) ).
fof(f34613,plain,
( spl647_951
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP42(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_951])]) ).
fof(f37896,plain,
( ! [X0,X1] : sP42(X0,X1,c_Int_OPls)
| ~ spl647_383
| ~ spl647_951 ),
inference(resolution,[],[f34614,f31042]) ).
fof(f34614,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP42(X0,X1,X2) )
| ~ spl647_951 ),
inference(avatar_component_clause,[],[f34613]) ).
fof(f38231,plain,
spl647_1034,
inference(avatar_split_clause,[],[f21281,f38229]) ).
fof(f38229,plain,
( spl647_1034
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| ~ c_Relation_Ototal__on(X2,X1,hAPP(c_Relation_Oconverse(X2,X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1034])]) ).
fof(f21281,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| ~ c_Relation_Ototal__on(X2,X1,hAPP(c_Relation_Oconverse(X2,X2),X0)) ),
inference(cnf_transformation,[],[f15846]) ).
fof(f38227,plain,
spl647_1033,
inference(avatar_split_clause,[],[f21275,f38225]) ).
fof(f38225,plain,
( spl647_1033
<=> ! [X2,X0,X1] :
( c_List_Olist_ONil(X1) = X0
| hAPP(hAPP(c_List_Oappend(X1),X2),X0) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1033])]) ).
fof(f21275,plain,
! [X2,X0,X1] :
( c_List_Olist_ONil(X1) = X0
| hAPP(hAPP(c_List_Oappend(X1),X2),X0) != X2 ),
inference(cnf_transformation,[],[f15843]) ).
fof(f15843,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_List_Oappend(X1),X2),X0) = X2
| c_List_Olist_ONil(X1) != X0 )
& ( c_List_Olist_ONil(X1) = X0
| hAPP(hAPP(c_List_Oappend(X1),X2),X0) != X2 ) ),
inference(nnf_transformation,[],[f8172]) ).
fof(f8172,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_List_Oappend(X1),X2),X0) = X2
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f3961]) ).
fof(f3961,axiom,
! [X202,X4,X203] :
( hAPP(hAPP(c_List_Oappend(X4),X203),X202) = X203
<=> c_List_Olist_ONil(X4) = X202 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38223,plain,
spl647_1032,
inference(avatar_split_clause,[],[f21273,f38221]) ).
fof(f38221,plain,
( spl647_1032
<=> ! [X2,X0,X1] :
( c_List_Olist_ONil(X1) = X0
| hAPP(hAPP(c_List_Oappend(X1),X0),X2) != X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1032])]) ).
fof(f21273,plain,
! [X2,X0,X1] :
( c_List_Olist_ONil(X1) = X0
| hAPP(hAPP(c_List_Oappend(X1),X0),X2) != X2 ),
inference(cnf_transformation,[],[f15842]) ).
fof(f15842,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_List_Oappend(X1),X0),X2) = X2
| c_List_Olist_ONil(X1) != X0 )
& ( c_List_Olist_ONil(X1) = X0
| hAPP(hAPP(c_List_Oappend(X1),X0),X2) != X2 ) ),
inference(nnf_transformation,[],[f8171]) ).
fof(f8171,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_List_Oappend(X1),X0),X2) = X2
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f3960]) ).
fof(f3960,axiom,
! [X203,X4,X202] :
( hAPP(hAPP(c_List_Oappend(X4),X203),X202) = X202
<=> c_List_Olist_ONil(X4) = X203 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38219,plain,
spl647_1031,
inference(avatar_split_clause,[],[f21272,f38217]) ).
fof(f38217,plain,
( spl647_1031
<=> ! [X2,X0,X1] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Finite__Set_Ocard(X2),X1)
| ~ sP40(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1031])]) ).
fof(f21272,plain,
! [X2,X0,X1] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Finite__Set_Ocard(X2),X1)
| ~ sP40(X2,X0,X1) ),
inference(cnf_transformation,[],[f15841]) ).
fof(f15841,plain,
! [X0,X1,X2] :
( ( hAPP(c_Nat_OSuc,X0) = hAPP(c_Finite__Set_Ocard(X2),X1)
| ~ sP40(X2,X0,X1) )
& ( sP40(X2,X0,X1)
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Finite__Set_Ocard(X2),X1) ) ),
inference(nnf_transformation,[],[f14544]) ).
fof(f14544,plain,
! [X0,X1,X2] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Finite__Set_Ocard(X2),X1)
<=> sP40(X2,X0,X1) ),
inference(definition_folding,[],[f12616,f14543]) ).
fof(f12616,plain,
! [X0,X1,X2] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Finite__Set_Ocard(X2),X1)
<=> ? [X3,X4] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X4
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& hAPP(c_Finite__Set_Ocard(X2),X4) = X0
& ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4))
& hAPP(hAPP(c_Set_Oinsert(X2),X3),X4) = X1 ) ),
inference(ennf_transformation,[],[f8170]) ).
fof(f8170,plain,
! [X0,X1,X2] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Finite__Set_Ocard(X2),X1)
<=> ? [X3,X4] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
=> c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = X4 )
& hAPP(c_Finite__Set_Ocard(X2),X4) = X0
& ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X4))
& hAPP(hAPP(c_Set_Oinsert(X2),X3),X4) = X1 ) ),
inference(rectify,[],[f955]) ).
fof(f955,axiom,
! [X48,X9,X4] :
( hAPP(c_Finite__Set_Ocard(X4),X9) = hAPP(c_Nat_OSuc,X48)
<=> ? [X85,X32] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X48
=> c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = X32 )
& hAPP(c_Finite__Set_Ocard(X4),X32) = X48
& ~ hBOOL(hAPP(hAPP(c_member(X4),X85),X32))
& hAPP(hAPP(c_Set_Oinsert(X4),X85),X32) = X9 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38215,plain,
spl647_1030,
inference(avatar_split_clause,[],[f21271,f38213]) ).
fof(f38213,plain,
( spl647_1030
<=> ! [X2,X0,X1] :
( sP40(X2,X0,X1)
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Finite__Set_Ocard(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1030])]) ).
fof(f21271,plain,
! [X2,X0,X1] :
( sP40(X2,X0,X1)
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Finite__Set_Ocard(X2),X1) ),
inference(cnf_transformation,[],[f15841]) ).
fof(f38211,plain,
spl647_1029,
inference(avatar_split_clause,[],[f21177,f38209]) ).
fof(f21177,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Quotient_ORespects(X2,X1),X0))
| ~ hBOOL(hAPP(hAPP(X1,X0),X0)) ),
inference(cnf_transformation,[],[f15774]) ).
fof(f15774,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Quotient_ORespects(X2,X1),X0))
| ~ hBOOL(hAPP(hAPP(X1,X0),X0)) )
& ( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ hBOOL(hAPP(c_Quotient_ORespects(X2,X1),X0)) ) ),
inference(nnf_transformation,[],[f8148]) ).
fof(f8148,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Quotient_ORespects(X2,X1),X0))
<=> hBOOL(hAPP(hAPP(X1,X0),X0)) ),
inference(rectify,[],[f4852]) ).
fof(f4852,axiom,
! [X13,X138,X4] :
( hBOOL(hAPP(c_Quotient_ORespects(X4,X138),X13))
<=> hBOOL(hAPP(hAPP(X138,X13),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38207,plain,
spl647_1028,
inference(avatar_split_clause,[],[f21176,f38205]) ).
fof(f38205,plain,
( spl647_1028
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ hBOOL(hAPP(c_Quotient_ORespects(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1028])]) ).
fof(f21176,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ hBOOL(hAPP(c_Quotient_ORespects(X2,X1),X0)) ),
inference(cnf_transformation,[],[f15774]) ).
fof(f38203,plain,
spl647_1027,
inference(avatar_split_clause,[],[f19608,f38201]) ).
fof(f38201,plain,
( spl647_1027
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1027])]) ).
fof(f19608,plain,
! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X1),X0))),
inference(cnf_transformation,[],[f6962]) ).
fof(f6962,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X1),X0))),
inference(rectify,[],[f127]) ).
fof(f127,axiom,
! [X18,X5,X4] : hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(hAPP(c_Set_Oinsert(X4),X5),X18))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38199,plain,
spl647_1026,
inference(avatar_split_clause,[],[f19607,f38197]) ).
fof(f38197,plain,
( spl647_1026
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Nitpick_Ofrac(X2),X1),X0) = c_Nitpick_OAbs__Frac(X2,c_Nitpick_Onorm__frac(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1026])]) ).
fof(f19607,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Nitpick_Ofrac(X2),X1),X0) = c_Nitpick_OAbs__Frac(X2,c_Nitpick_Onorm__frac(X1,X0)),
inference(cnf_transformation,[],[f6961]) ).
fof(f6961,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Nitpick_Ofrac(X2),X1),X0) = c_Nitpick_OAbs__Frac(X2,c_Nitpick_Onorm__frac(X1,X0)),
inference(rectify,[],[f3113]) ).
fof(f3113,axiom,
! [X25,X26,X20] : hAPP(hAPP(c_Nitpick_Ofrac(X20),X26),X25) = c_Nitpick_OAbs__Frac(X20,c_Nitpick_Onorm__frac(X26,X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38195,plain,
spl647_1025,
inference(avatar_split_clause,[],[f19606,f38193]) ).
fof(f38193,plain,
( spl647_1025
<=> ! [X2,X0,X1] : hAPP(c_Finite__Set_Ofold1(X2,X1),X0) = c_HOL_OThe(X2,c_Finite__Set_Ofold1Set(X2,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1025])]) ).
fof(f19606,plain,
! [X2,X0,X1] : hAPP(c_Finite__Set_Ofold1(X2,X1),X0) = c_HOL_OThe(X2,c_Finite__Set_Ofold1Set(X2,X1,X0)),
inference(cnf_transformation,[],[f6960]) ).
fof(f6960,plain,
! [X0,X1,X2] : hAPP(c_Finite__Set_Ofold1(X2,X1),X0) = c_HOL_OThe(X2,c_Finite__Set_Ofold1Set(X2,X1,X0)),
inference(rectify,[],[f3122]) ).
fof(f3122,axiom,
! [X9,X1,X4] : hAPP(c_Finite__Set_Ofold1(X4,X1),X9) = c_HOL_OThe(X4,c_Finite__Set_Ofold1Set(X4,X1,X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38191,plain,
( spl647_1024
| spl647_326
| ~ spl647_950 ),
inference(avatar_split_clause,[],[f37870,f34609,f30794,f38189]) ).
fof(f38189,plain,
( spl647_1024
<=> ! [X0,X1] : sP36(X0,X1,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1024])]) ).
fof(f34609,plain,
( spl647_950
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP36(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_950])]) ).
fof(f37870,plain,
( ! [X0,X1] : sP36(X0,X1,c_Int_OMin)
| spl647_326
| ~ spl647_950 ),
inference(resolution,[],[f34610,f30796]) ).
fof(f34610,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP36(X0,X1,X2) )
| ~ spl647_950 ),
inference(avatar_component_clause,[],[f34609]) ).
fof(f38187,plain,
spl647_1023,
inference(avatar_split_clause,[],[f19310,f38185]) ).
fof(f38185,plain,
( spl647_1023
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1023])]) ).
fof(f19310,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
inference(cnf_transformation,[],[f15136]) ).
fof(f15136,plain,
! [X0,X1] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ) ),
inference(nnf_transformation,[],[f6827]) ).
fof(f6827,plain,
! [X0,X1] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
<=> X0 = X1 ),
inference(rectify,[],[f1269]) ).
fof(f1269,axiom,
! [X15,X13] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X13) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15)
<=> X13 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38183,plain,
spl647_1022,
inference(avatar_split_clause,[],[f19281,f38181]) ).
fof(f38181,plain,
( spl647_1022
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| ~ sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1022])]) ).
fof(f19281,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f15114]) ).
fof(f15114,plain,
! [X0,X1] :
( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| ~ sP9(X0,X1) )
& ( sP9(X0,X1)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) ) ),
inference(nnf_transformation,[],[f14493]) ).
fof(f14493,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
<=> sP9(X0,X1) ),
inference(definition_folding,[],[f6817,f14492]) ).
fof(f14492,plain,
! [X0,X1] :
( sP9(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,[sP9])]) ).
fof(f6817,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
<=> ( ( 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 ) ) ),
inference(rectify,[],[f2005]) ).
fof(f2005,axiom,
! [X46,X47] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X47),X46)
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X46
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X47 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X46
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X47 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38179,plain,
spl647_1021,
inference(avatar_split_clause,[],[f19280,f38177]) ).
fof(f38177,plain,
( spl647_1021
<=> ! [X0,X1] :
( sP9(X0,X1)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1021])]) ).
fof(f19280,plain,
! [X0,X1] :
( sP9(X0,X1)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) ),
inference(cnf_transformation,[],[f15114]) ).
fof(f38175,plain,
spl647_1020,
inference(avatar_split_clause,[],[f19156,f38173]) ).
fof(f38173,plain,
( spl647_1020
<=> ! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| sK187(X0,X1) != sK188(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1020])]) ).
fof(f19156,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| sK187(X0,X1) != sK188(X0,X1) ),
inference(cnf_transformation,[],[f15014]) ).
fof(f15014,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| ( hAPP(hAPP(c_List_Onth(X1),X0),sK187(X0,X1)) = hAPP(hAPP(c_List_Onth(X1),X0),sK188(X0,X1))
& sK187(X0,X1) != sK188(X0,X1)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK188(X0,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK187(X0,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) ) )
& ( ! [X4] :
( ! [X5] :
( hAPP(hAPP(c_List_Onth(X1),X0),X4) != hAPP(hAPP(c_List_Onth(X1),X0),X5)
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) )
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK187,sK188])],[f15011,f15013,f15012]) ).
fof(f15012,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( hAPP(hAPP(c_List_Onth(X1),X0),X2) = hAPP(hAPP(c_List_Onth(X1),X0),X3)
& X2 != X3
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) )
=> ( ? [X3] :
( hAPP(hAPP(c_List_Onth(X1),X0),X3) = hAPP(hAPP(c_List_Onth(X1),X0),sK187(X0,X1))
& sK187(X0,X1) != X3
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK187(X0,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15013,plain,
! [X0,X1] :
( ? [X3] :
( hAPP(hAPP(c_List_Onth(X1),X0),X3) = hAPP(hAPP(c_List_Onth(X1),X0),sK187(X0,X1))
& sK187(X0,X1) != X3
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) )
=> ( hAPP(hAPP(c_List_Onth(X1),X0),sK187(X0,X1)) = hAPP(hAPP(c_List_Onth(X1),X0),sK188(X0,X1))
& sK187(X0,X1) != sK188(X0,X1)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK188(X0,X1)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15011,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| ? [X2] :
( ? [X3] :
( hAPP(hAPP(c_List_Onth(X1),X0),X2) = hAPP(hAPP(c_List_Onth(X1),X0),X3)
& X2 != X3
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) ) )
& ( ! [X4] :
( ! [X5] :
( hAPP(hAPP(c_List_Onth(X1),X0),X4) != hAPP(hAPP(c_List_Onth(X1),X0),X5)
| X4 = X5
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X5),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) )
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ) ),
inference(rectify,[],[f15010]) ).
fof(f15010,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| ? [X2] :
( ? [X3] :
( hAPP(hAPP(c_List_Onth(X1),X0),X2) = hAPP(hAPP(c_List_Onth(X1),X0),X3)
& X2 != X3
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) ) )
& ( ! [X2] :
( ! [X3] :
( hAPP(hAPP(c_List_Onth(X1),X0),X2) != hAPP(hAPP(c_List_Onth(X1),X0),X3)
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) )
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ) ),
inference(nnf_transformation,[],[f11286]) ).
fof(f11286,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
<=> ! [X2] :
( ! [X3] :
( hAPP(hAPP(c_List_Onth(X1),X0),X2) != hAPP(hAPP(c_List_Onth(X1),X0),X3)
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) ) ),
inference(flattening,[],[f11285]) ).
fof(f11285,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
<=> ! [X2] :
( ! [X3] :
( hAPP(hAPP(c_List_Onth(X1),X0),X2) != hAPP(hAPP(c_List_Onth(X1),X0),X3)
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0))) ) ),
inference(ennf_transformation,[],[f6767]) ).
fof(f6767,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0)))
=> ! [X3] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X3),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0)))
=> ( X2 != X3
=> hAPP(hAPP(c_List_Onth(X1),X0),X2) != hAPP(hAPP(c_List_Onth(X1),X0),X3) ) ) ) ),
inference(rectify,[],[f3868]) ).
fof(f3868,axiom,
! [X203,X4] :
( hBOOL(hAPP(c_List_Odistinct(X4),X203))
<=> ! [X86] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X86),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X203)))
=> ! [X83] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X83),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),X203)))
=> ( X83 != X86
=> hAPP(hAPP(c_List_Onth(X4),X203),X86) != hAPP(hAPP(c_List_Onth(X4),X203),X83) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38171,plain,
spl647_1019,
inference(avatar_split_clause,[],[f19120,f38169]) ).
fof(f38169,plain,
( spl647_1019
<=> ! [X0,X1,X3] :
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X0)))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1019])]) ).
fof(f19120,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X0)))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f14990]) ).
fof(f38167,plain,
spl647_1018,
inference(avatar_split_clause,[],[f18681,f38165]) ).
fof(f38165,plain,
( spl647_1018
<=> ! [X0,X1] :
( c_Equiv__Relations_Oequivp(X1,X0)
| ~ c_Predicate_Otransp(X1,X0)
| ~ c_Predicate_Osymp(X1,X0)
| ~ c_Predicate_Oreflp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1018])]) ).
fof(f18681,plain,
! [X0,X1] :
( c_Equiv__Relations_Oequivp(X1,X0)
| ~ c_Predicate_Otransp(X1,X0)
| ~ c_Predicate_Osymp(X1,X0)
| ~ c_Predicate_Oreflp(X1,X0) ),
inference(cnf_transformation,[],[f10864]) ).
fof(f10864,plain,
! [X0,X1] :
( c_Equiv__Relations_Oequivp(X1,X0)
| ~ c_Predicate_Otransp(X1,X0)
| ~ c_Predicate_Osymp(X1,X0)
| ~ c_Predicate_Oreflp(X1,X0) ),
inference(flattening,[],[f10863]) ).
fof(f10863,plain,
! [X0,X1] :
( c_Equiv__Relations_Oequivp(X1,X0)
| ~ c_Predicate_Otransp(X1,X0)
| ~ c_Predicate_Osymp(X1,X0)
| ~ c_Predicate_Oreflp(X1,X0) ),
inference(ennf_transformation,[],[f6438]) ).
fof(f6438,plain,
! [X0,X1] :
( c_Predicate_Oreflp(X1,X0)
=> ( c_Predicate_Osymp(X1,X0)
=> ( c_Predicate_Otransp(X1,X0)
=> c_Equiv__Relations_Oequivp(X1,X0) ) ) ),
inference(rectify,[],[f4739]) ).
fof(f4739,axiom,
! [X138,X4] :
( c_Predicate_Oreflp(X4,X138)
=> ( c_Predicate_Osymp(X4,X138)
=> ( c_Predicate_Otransp(X4,X138)
=> c_Equiv__Relations_Oequivp(X4,X138) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38163,plain,
spl647_1017,
inference(avatar_split_clause,[],[f18652,f38161]) ).
fof(f38161,plain,
( spl647_1017
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,sK137(X0)))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1017])]) ).
fof(f18652,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,sK137(X0)))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f14832]) ).
fof(f14832,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(X0,sK137(X0)))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0)) )
& ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ! [X3] : ~ hBOOL(hAPP(X0,X3)) ) )
| ~ class_Enum_Oenum(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK137])],[f14830,f14831]) ).
fof(f14831,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X0,sK137(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14830,plain,
! [X0,X1] :
( ( ( ? [X2] : hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0)) )
& ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ! [X3] : ~ hBOOL(hAPP(X0,X3)) ) )
| ~ class_Enum_Oenum(X1) ),
inference(rectify,[],[f14829]) ).
fof(f14829,plain,
! [X0,X1] :
( ( ( ? [X2] : hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0)) )
& ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ! [X2] : ~ hBOOL(hAPP(X0,X2)) ) )
| ~ class_Enum_Oenum(X1) ),
inference(nnf_transformation,[],[f10821]) ).
fof(f10821,plain,
! [X0,X1] :
( ( ? [X2] : hBOOL(hAPP(X0,X2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0)) )
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6414]) ).
fof(f6414,plain,
! [X0,X1] :
( class_Enum_Oenum(X1)
=> ( ? [X2] : hBOOL(hAPP(X0,X2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0)) ) ),
inference(rectify,[],[f4536]) ).
fof(f4536,axiom,
! [X23,X4] :
( class_Enum_Oenum(X4)
=> ( ? [X124] : hBOOL(hAPP(X23,X124))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X4),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38159,plain,
spl647_1016,
inference(avatar_split_clause,[],[f18649,f38157]) ).
fof(f38157,plain,
( spl647_1016
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ~ hBOOL(hAPP(X0,sK136(X0)))
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1016])]) ).
fof(f18649,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ~ hBOOL(hAPP(X0,sK136(X0)))
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f14828]) ).
fof(f14828,plain,
! [X0,X1] :
( ( ( ! [X2] : hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0)) )
& ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ~ hBOOL(hAPP(X0,sK136(X0))) ) )
| ~ class_Enum_Oenum(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK136])],[f14826,f14827]) ).
fof(f14827,plain,
! [X0] :
( ? [X3] : ~ hBOOL(hAPP(X0,X3))
=> ~ hBOOL(hAPP(X0,sK136(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14826,plain,
! [X0,X1] :
( ( ( ! [X2] : hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0)) )
& ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ? [X3] : ~ hBOOL(hAPP(X0,X3)) ) )
| ~ class_Enum_Oenum(X1) ),
inference(rectify,[],[f14825]) ).
fof(f14825,plain,
! [X0,X1] :
( ( ( ! [X2] : hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0)) )
& ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ? [X2] : ~ hBOOL(hAPP(X0,X2)) ) )
| ~ class_Enum_Oenum(X1) ),
inference(nnf_transformation,[],[f10820]) ).
fof(f10820,plain,
! [X0,X1] :
( ( ! [X2] : hBOOL(hAPP(X0,X2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0)) )
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6413]) ).
fof(f6413,plain,
! [X0,X1] :
( class_Enum_Oenum(X1)
=> ( ! [X2] : hBOOL(hAPP(X0,X2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0)) ) ),
inference(rectify,[],[f4549]) ).
fof(f4549,axiom,
! [X23,X4] :
( class_Enum_Oenum(X4)
=> ( ! [X124] : hBOOL(hAPP(X23,X124))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X4),X23)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38155,plain,
spl647_1015,
inference(avatar_split_clause,[],[f18647,f38153]) ).
fof(f38153,plain,
( spl647_1015
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,sK135(X0)))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1015])]) ).
fof(f18647,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,sK135(X0)))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f14824]) ).
fof(f14824,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ! [X2] : ~ hBOOL(hAPP(X0,X2)) )
& ( hBOOL(hAPP(X0,sK135(X0)))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0)) ) )
| ~ class_Enum_Oenum(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK135])],[f14822,f14823]) ).
fof(f14823,plain,
! [X0] :
( ? [X3] : hBOOL(hAPP(X0,X3))
=> hBOOL(hAPP(X0,sK135(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14822,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ! [X2] : ~ hBOOL(hAPP(X0,X2)) )
& ( ? [X3] : hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0)) ) )
| ~ class_Enum_Oenum(X1) ),
inference(rectify,[],[f14821]) ).
fof(f14821,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ! [X2] : ~ hBOOL(hAPP(X0,X2)) )
& ( ? [X2] : hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0)) ) )
| ~ class_Enum_Oenum(X1) ),
inference(nnf_transformation,[],[f10819]) ).
fof(f10819,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
<=> ? [X2] : hBOOL(hAPP(X0,X2)) )
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6412]) ).
fof(f6412,plain,
! [X0,X1] :
( class_Enum_Oenum(X1)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
<=> ? [X2] : hBOOL(hAPP(X0,X2)) ) ),
inference(rectify,[],[f4537]) ).
fof(f4537,axiom,
! [X23,X4] :
( class_Enum_Oenum(X4)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X4),X23))
<=> ? [X124] : hBOOL(hAPP(X23,X124)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38151,plain,
spl647_1014,
inference(avatar_split_clause,[],[f18646,f38149]) ).
fof(f38149,plain,
( spl647_1014
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ~ hBOOL(hAPP(X0,sK134(X0)))
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1014])]) ).
fof(f18646,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ~ hBOOL(hAPP(X0,sK134(X0)))
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f14820]) ).
fof(f14820,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ~ hBOOL(hAPP(X0,sK134(X0))) )
& ( ! [X3] : hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0)) ) )
| ~ class_Enum_Oenum(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK134])],[f14818,f14819]) ).
fof(f14819,plain,
! [X0] :
( ? [X2] : ~ hBOOL(hAPP(X0,X2))
=> ~ hBOOL(hAPP(X0,sK134(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14818,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ? [X2] : ~ hBOOL(hAPP(X0,X2)) )
& ( ! [X3] : hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0)) ) )
| ~ class_Enum_Oenum(X1) ),
inference(rectify,[],[f14817]) ).
fof(f14817,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ? [X2] : ~ hBOOL(hAPP(X0,X2)) )
& ( ! [X2] : hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0)) ) )
| ~ class_Enum_Oenum(X1) ),
inference(nnf_transformation,[],[f10818]) ).
fof(f10818,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
<=> ! [X2] : hBOOL(hAPP(X0,X2)) )
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6411]) ).
fof(f6411,plain,
! [X0,X1] :
( class_Enum_Oenum(X1)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
<=> ! [X2] : hBOOL(hAPP(X0,X2)) ) ),
inference(rectify,[],[f4548]) ).
fof(f4548,axiom,
! [X23,X4] :
( class_Enum_Oenum(X4)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X4),X23))
<=> ! [X124] : hBOOL(hAPP(X23,X124)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38147,plain,
( spl647_1013
| ~ spl647_383
| ~ spl647_950 ),
inference(avatar_split_clause,[],[f37862,f34609,f31041,f38145]) ).
fof(f38145,plain,
( spl647_1013
<=> ! [X0,X1] : sP36(X0,X1,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1013])]) ).
fof(f37862,plain,
( ! [X0,X1] : sP36(X0,X1,c_Int_OPls)
| ~ spl647_383
| ~ spl647_950 ),
inference(resolution,[],[f34610,f31042]) ).
fof(f38143,plain,
spl647_1012,
inference(avatar_split_clause,[],[f18607,f38141]) ).
fof(f38141,plain,
( spl647_1012
<=> ! [X0,X1] :
( c_List_Olinorder__class_Osorted(X0,sK126(X0,X1))
| c_List_Olist_ONil(X0) = X1
| ~ sP0(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1012])]) ).
fof(f18607,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X0,sK126(X0,X1))
| c_List_Olist_ONil(X0) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f14807]) ).
fof(f14807,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),sK125(X0,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X0),sK125(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,sK126(X0,X1))
& ! [X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK127(X0,X1)),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X7),hAPP(c_List_Oset(X0),sK126(X0,X1)))) )
& hAPP(hAPP(c_List_Olist_OCons(X0),sK127(X0,X1)),sK126(X0,X1)) = X1 )
| c_List_Olist_ONil(X0) = X1
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK125,sK126,sK127])],[f14804,f14806,f14805]) ).
fof(f14805,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),sK125(X0,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X0),sK125(X0,X2,X3)),hAPP(c_List_Oset(X0),X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f14806,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,sK126(X0,X1))
& ! [X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK127(X0,X1)),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X7),hAPP(c_List_Oset(X0),sK126(X0,X1)))) )
& hAPP(hAPP(c_List_Olist_OCons(X0),sK127(X0,X1)),sK126(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f14804,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,[],[f14803]) ).
fof(f14803,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,[],[f14802]) ).
fof(f14802,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,[],[f14475]) ).
fof(f14475,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(f38139,plain,
spl647_1011,
inference(avatar_split_clause,[],[f18597,f38137]) ).
fof(f38137,plain,
( spl647_1011
<=> ! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,sK122(X0,X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1011])]) ).
fof(f18597,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,sK122(X0,X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f14798]) ).
fof(f38135,plain,
spl647_1010,
inference(avatar_split_clause,[],[f18587,f38133]) ).
fof(f38133,plain,
( spl647_1010
<=> ! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osorted__list__of__set(X1,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1010])]) ).
fof(f18587,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osorted__list__of__set(X1,X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10763]) ).
fof(f38131,plain,
spl647_1009,
inference(avatar_split_clause,[],[f18554,f38129]) ).
fof(f38129,plain,
( spl647_1009
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1009])]) ).
fof(f18554,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f10721]) ).
fof(f10721,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f6338]) ).
fof(f6338,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ),
inference(rectify,[],[f1631]) ).
fof(f1631,axiom,
! [X26,X20] :
( class_Divides_Osemiring__div(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20),c_Groups_Ozero__class_Ozero(X20)),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38127,plain,
spl647_1008,
inference(avatar_split_clause,[],[f18553,f38125]) ).
fof(f38125,plain,
( spl647_1008
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1008])]) ).
fof(f18553,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f10720]) ).
fof(f10720,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f6337]) ).
fof(f6337,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(rectify,[],[f1632]) ).
fof(f1632,axiom,
! [X26,X20] :
( class_Divides_Osemiring__div(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20),X26),c_Groups_Ozero__class_Ozero(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38123,plain,
spl647_1007,
inference(avatar_split_clause,[],[f18543,f38121]) ).
fof(f38121,plain,
( spl647_1007
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1007])]) ).
fof(f18543,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f10709]) ).
fof(f10709,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f6327]) ).
fof(f6327,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ),
inference(rectify,[],[f761]) ).
fof(f761,axiom,
! [X26,X20] :
( class_Rings_Ocomm__semiring__1(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),c_Groups_Ozero__class_Ozero(X20)),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38119,plain,
spl647_1006,
inference(avatar_split_clause,[],[f18542,f38117]) ).
fof(f38117,plain,
( spl647_1006
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1006])]) ).
fof(f18542,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f10708]) ).
fof(f10708,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f6326]) ).
fof(f6326,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(rectify,[],[f759]) ).
fof(f759,axiom,
! [X26,X20] :
( class_Rings_Ocomm__semiring__1(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),X26),c_Groups_Ozero__class_Ozero(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38115,plain,
spl647_1005,
inference(avatar_split_clause,[],[f18516,f38113]) ).
fof(f38113,plain,
( spl647_1005
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0)
| ~ class_Groups_Omonoid__mult(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1005])]) ).
fof(f18516,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(cnf_transformation,[],[f10683]) ).
fof(f10683,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0)
| ~ class_Groups_Omonoid__mult(X1) ),
inference(ennf_transformation,[],[f6302]) ).
fof(f6302,plain,
! [X0,X1] :
( class_Groups_Omonoid__mult(X1)
=> c_Groups_Oone__class_Oone(X1) = hAPP(hAPP(c_Power_Opower__class_Opower(X1),c_Groups_Oone__class_Oone(X1)),X0) ),
inference(rectify,[],[f1907]) ).
fof(f1907,axiom,
! [X44,X20] :
( class_Groups_Omonoid__mult(X20)
=> c_Groups_Oone__class_Oone(X20) = hAPP(hAPP(c_Power_Opower__class_Opower(X20),c_Groups_Oone__class_Oone(X20)),X44) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38111,plain,
spl647_1004,
inference(avatar_split_clause,[],[f18505,f38109]) ).
fof(f38109,plain,
( spl647_1004
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Rings_Omult__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1004])]) ).
fof(f18505,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Rings_Omult__zero(X1) ),
inference(cnf_transformation,[],[f10671]) ).
fof(f10671,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0)
| ~ class_Rings_Omult__zero(X1) ),
inference(ennf_transformation,[],[f6291]) ).
fof(f6291,plain,
! [X0,X1] :
( class_Rings_Omult__zero(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Ozero__class_Ozero(X1)),X0) ),
inference(rectify,[],[f762]) ).
fof(f762,axiom,
! [X26,X20] :
( class_Rings_Omult__zero(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),c_Groups_Ozero__class_Ozero(X20)),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38107,plain,
spl647_1003,
inference(avatar_split_clause,[],[f18504,f38105]) ).
fof(f38105,plain,
( spl647_1003
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Omult__zero(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1003])]) ).
fof(f18504,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Omult__zero(X1) ),
inference(cnf_transformation,[],[f10670]) ).
fof(f10670,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Omult__zero(X1) ),
inference(ennf_transformation,[],[f6290]) ).
fof(f6290,plain,
! [X0,X1] :
( class_Rings_Omult__zero(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Ozero__class_Ozero(X1)) ),
inference(rectify,[],[f760]) ).
fof(f760,axiom,
! [X26,X20] :
( class_Rings_Omult__zero(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),X26),c_Groups_Ozero__class_Ozero(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38103,plain,
( spl647_1002
| ~ spl647_383
| ~ spl647_949 ),
inference(avatar_split_clause,[],[f37850,f34605,f31041,f38101]) ).
fof(f38101,plain,
( spl647_1002
<=> ! [X0,X1] : sP37(X0,X1,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1002])]) ).
fof(f34605,plain,
( spl647_949
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP37(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_949])]) ).
fof(f37850,plain,
( ! [X0,X1] : sP37(X0,X1,c_Int_OPls)
| ~ spl647_383
| ~ spl647_949 ),
inference(resolution,[],[f34606,f31042]) ).
fof(f34606,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP37(X0,X1,X2) )
| ~ spl647_949 ),
inference(avatar_component_clause,[],[f34605]) ).
fof(f38099,plain,
spl647_1001,
inference(avatar_split_clause,[],[f18481,f38097]) ).
fof(f38097,plain,
( spl647_1001
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X0)
| ~ class_Lattices_Obounded__lattice__bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1001])]) ).
fof(f18481,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X0)
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(cnf_transformation,[],[f10645]) ).
fof(f10645,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X0)
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(ennf_transformation,[],[f6269]) ).
fof(f6269,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(X1)
=> c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Obot__class_Obot(X1)),X0) ),
inference(rectify,[],[f347]) ).
fof(f347,axiom,
! [X19,X20] :
( class_Lattices_Obounded__lattice__bot(X20)
=> c_Orderings_Obot__class_Obot(X20) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20),c_Orderings_Obot__class_Obot(X20)),X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38095,plain,
spl647_1000,
inference(avatar_split_clause,[],[f18480,f38093]) ).
fof(f38093,plain,
( spl647_1000
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),c_Orderings_Obot__class_Obot(X1))
| ~ class_Lattices_Obounded__lattice__bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1000])]) ).
fof(f18480,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),c_Orderings_Obot__class_Obot(X1))
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(cnf_transformation,[],[f10644]) ).
fof(f10644,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),c_Orderings_Obot__class_Obot(X1))
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(ennf_transformation,[],[f6268]) ).
fof(f6268,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(X1)
=> c_Orderings_Obot__class_Obot(X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),c_Orderings_Obot__class_Obot(X1)) ),
inference(rectify,[],[f348]) ).
fof(f348,axiom,
! [X19,X20] :
( class_Lattices_Obounded__lattice__bot(X20)
=> c_Orderings_Obot__class_Obot(X20) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20),X19),c_Orderings_Obot__class_Obot(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38091,plain,
spl647_999,
inference(avatar_split_clause,[],[f18479,f38089]) ).
fof(f38089,plain,
( spl647_999
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X0)
| ~ class_Lattices_Obounded__lattice__top(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_999])]) ).
fof(f18479,plain,
! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X0)
| ~ class_Lattices_Obounded__lattice__top(X1) ),
inference(cnf_transformation,[],[f10643]) ).
fof(f10643,plain,
! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X0)
| ~ class_Lattices_Obounded__lattice__top(X1) ),
inference(ennf_transformation,[],[f6267]) ).
fof(f6267,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(X1)
=> c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Otop__class_Otop(X1)),X0) ),
inference(rectify,[],[f2095]) ).
fof(f2095,axiom,
! [X19,X20] :
( class_Lattices_Obounded__lattice__top(X20)
=> c_Orderings_Otop__class_Otop(X20) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20),c_Orderings_Otop__class_Otop(X20)),X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38087,plain,
spl647_998,
inference(avatar_split_clause,[],[f18478,f38085]) ).
fof(f38085,plain,
( spl647_998
<=> ! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),c_Orderings_Otop__class_Otop(X1))
| ~ class_Lattices_Obounded__lattice__top(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_998])]) ).
fof(f18478,plain,
! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),c_Orderings_Otop__class_Otop(X1))
| ~ class_Lattices_Obounded__lattice__top(X1) ),
inference(cnf_transformation,[],[f10642]) ).
fof(f10642,plain,
! [X0,X1] :
( c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),c_Orderings_Otop__class_Otop(X1))
| ~ class_Lattices_Obounded__lattice__top(X1) ),
inference(ennf_transformation,[],[f6266]) ).
fof(f6266,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(X1)
=> c_Orderings_Otop__class_Otop(X1) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),c_Orderings_Otop__class_Otop(X1)) ),
inference(rectify,[],[f2096]) ).
fof(f2096,axiom,
! [X19,X20] :
( class_Lattices_Obounded__lattice__top(X20)
=> c_Orderings_Otop__class_Otop(X20) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20),X19),c_Orderings_Otop__class_Otop(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38083,plain,
spl647_997,
inference(avatar_split_clause,[],[f18410,f38081]) ).
fof(f38081,plain,
( spl647_997
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Osgn__class_Osgn(X1,X0)
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_997])]) ).
fof(f18410,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Osgn__class_Osgn(X1,X0)
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f14768]) ).
fof(f14768,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Osgn__class_Osgn(X1,X0) ) )
| ~ class_Rings_Olinordered__idom(X1) ),
inference(nnf_transformation,[],[f10590]) ).
fof(f10590,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Rings_Olinordered__idom(X1) ),
inference(ennf_transformation,[],[f6215]) ).
fof(f6215,plain,
! [X0,X1] :
( class_Rings_Olinordered__idom(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f2056]) ).
fof(f2056,axiom,
! [X5,X4] :
( class_Rings_Olinordered__idom(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) = c_Groups_Osgn__class_Osgn(X4,X5)
<=> c_Groups_Ozero__class_Ozero(X4) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38079,plain,
spl647_996,
inference(avatar_split_clause,[],[f18377,f38077]) ).
fof(f38077,plain,
( spl647_996
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_996])]) ).
fof(f18377,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(cnf_transformation,[],[f10555]) ).
fof(f10555,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),hAPP(c_Groups_Oabs__class_Oabs(X1),X0)))
| ~ class_Groups_Oordered__ab__group__add__abs(X1) ),
inference(ennf_transformation,[],[f6187]) ).
fof(f6187,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add__abs(X1)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),hAPP(c_Groups_Oabs__class_Oabs(X1),X0))) ),
inference(rectify,[],[f1337]) ).
fof(f1337,axiom,
! [X26,X20] :
( class_Groups_Oordered__ab__group__add__abs(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),X26),hAPP(c_Groups_Oabs__class_Oabs(X20),X26))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38075,plain,
spl647_995,
inference(avatar_split_clause,[],[f18318,f38073]) ).
fof(f38073,plain,
( spl647_995
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) != X0
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_995])]) ).
fof(f18318,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) != X0
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f14746]) ).
fof(f14746,plain,
! [X0,X1] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) = X0
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) != X0 ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f10514]) ).
fof(f10514,plain,
! [X0,X1] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) = X0
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f6148]) ).
fof(f6148,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) = X0
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f1433]) ).
fof(f1433,axiom,
! [X5,X4] :
( class_Groups_Olinordered__ab__group__add(X4)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X4),X5) = X5
<=> c_Groups_Ozero__class_Ozero(X4) = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38071,plain,
spl647_994,
inference(avatar_split_clause,[],[f18223,f38069]) ).
fof(f38069,plain,
( spl647_994
<=> ! [X0,X1] :
( c_Quickcheck_Obeyond(X1,X0) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_994])]) ).
fof(f18223,plain,
! [X0,X1] :
( c_Quickcheck_Obeyond(X1,X0) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X1),X0)) ),
inference(cnf_transformation,[],[f10467]) ).
fof(f38067,plain,
spl647_993,
inference(avatar_split_clause,[],[f17909,f38065]) ).
fof(f38065,plain,
( spl647_993
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X0),hAPP(c_Set_OPow(X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_993])]) ).
fof(f17909,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X0),hAPP(c_Set_OPow(X1),X0))),
inference(cnf_transformation,[],[f5801]) ).
fof(f5801,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X0),hAPP(c_Set_OPow(X1),X0))),
inference(rectify,[],[f1962]) ).
fof(f1962,axiom,
! [X9,X4] : hBOOL(hAPP(hAPP(c_member(tc_fun(X4,tc_HOL_Obool)),X9),hAPP(c_Set_OPow(X4),X9))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38063,plain,
spl647_992,
inference(avatar_split_clause,[],[f17908,f38061]) ).
fof(f38061,plain,
( spl647_992
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_992])]) ).
fof(f17908,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X0)),
inference(cnf_transformation,[],[f5800]) ).
fof(f5800,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),X0)),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X9,X4] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38059,plain,
( spl647_991
| ~ spl647_337
| ~ spl647_944 ),
inference(avatar_split_clause,[],[f37810,f34585,f30853,f38057]) ).
fof(f38057,plain,
( spl647_991
<=> ! [X0,X1] : sP27(c_Int_OMin,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_991])]) ).
fof(f34585,plain,
( spl647_944
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP27(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_944])]) ).
fof(f37810,plain,
( ! [X0,X1] : sP27(c_Int_OMin,X0,X1)
| ~ spl647_337
| ~ spl647_944 ),
inference(resolution,[],[f34586,f30855]) ).
fof(f34586,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP27(X2,X0,X1) )
| ~ spl647_944 ),
inference(avatar_component_clause,[],[f34585]) ).
fof(f38055,plain,
spl647_990,
inference(avatar_split_clause,[],[f17907,f38053]) ).
fof(f38053,plain,
( spl647_990
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_990])]) ).
fof(f17907,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)),X1)),
inference(cnf_transformation,[],[f5799]) ).
fof(f5799,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)),X1)),
inference(rectify,[],[f541]) ).
fof(f541,axiom,
! [X44,X45] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),X44)),X45)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38051,plain,
spl647_989,
inference(avatar_split_clause,[],[f17906,f38049]) ).
fof(f38049,plain,
( spl647_989
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_989])]) ).
fof(f17906,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)),X1)),
inference(cnf_transformation,[],[f5798]) ).
fof(f5798,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)),X1)),
inference(rectify,[],[f1741]) ).
fof(f1741,axiom,
! [X44,X45] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X45),X44)),X45)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38047,plain,
spl647_988,
inference(avatar_split_clause,[],[f17905,f38045]) ).
fof(f38045,plain,
( spl647_988
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_988])]) ).
fof(f17905,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5797]) ).
fof(f5797,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f2091]) ).
fof(f2091,axiom,
! [X9,X4] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X9),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38043,plain,
spl647_987,
inference(avatar_split_clause,[],[f17904,f38041]) ).
fof(f38041,plain,
( spl647_987
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_987])]) ).
fof(f17904,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0))),
inference(cnf_transformation,[],[f5796]) ).
fof(f5796,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0))),
inference(rectify,[],[f621]) ).
fof(f621,axiom,
! [X45,X44] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X44),X45))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38039,plain,
spl647_986,
inference(avatar_split_clause,[],[f17903,f38037]) ).
fof(f38037,plain,
( spl647_986
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_986])]) ).
fof(f17903,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1))),
inference(cnf_transformation,[],[f5795]) ).
fof(f5795,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1))),
inference(rectify,[],[f620]) ).
fof(f620,axiom,
! [X45,X44] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38034,plain,
spl647_985,
inference(avatar_split_clause,[],[f17902,f38032]) ).
fof(f38032,plain,
( spl647_985
<=> ! [X0,X1] : c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_985])]) ).
fof(f17902,plain,
! [X0,X1] : c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0)) = X0,
inference(cnf_transformation,[],[f5794]) ).
fof(f5794,plain,
! [X0,X1] : c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0)) = X0,
inference(rectify,[],[f3404]) ).
fof(f3404,axiom,
! [X5,X4] : c_HOL_OThe(X4,hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X5)) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38029,plain,
spl647_984,
inference(avatar_split_clause,[],[f17901,f38027]) ).
fof(f38027,plain,
( spl647_984
<=> ! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_984])]) ).
fof(f17901,plain,
! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0)) = X0,
inference(cnf_transformation,[],[f5793]) ).
fof(f5793,plain,
! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0)) = X0,
inference(rectify,[],[f3518]) ).
fof(f3518,axiom,
! [X13,X4] : c_Hilbert__Choice_OEps(X4,hAPP(hAPP(c_COMBC(X4,X4,tc_HOL_Obool),c_fequal),X13)) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38025,plain,
spl647_983,
inference(avatar_split_clause,[],[f17900,f38023]) ).
fof(f38023,plain,
( spl647_983
<=> ! [X0,X1] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_983])]) ).
fof(f17900,plain,
! [X0,X1] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f5792]) ).
fof(f5792,plain,
! [X0,X1] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X1,X1),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f3660]) ).
fof(f3660,axiom,
! [X138,X4] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X4,X4),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X138) = X138,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38021,plain,
spl647_982,
inference(avatar_split_clause,[],[f17893,f38019]) ).
fof(f38019,plain,
( spl647_982
<=> ! [X0,X1] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),hAPP(c_Nat_OSuc,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_982])]) ).
fof(f38017,plain,
spl647_981,
inference(avatar_split_clause,[],[f17892,f38015]) ).
fof(f38015,plain,
( spl647_981
<=> ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_981])]) ).
fof(f38013,plain,
( spl647_980
| spl647_327
| ~ spl647_927 ),
inference(avatar_split_clause,[],[f37589,f34516,f30799,f38010]) ).
fof(f38010,plain,
( spl647_980
<=> sP7(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_980])]) ).
fof(f37589,plain,
( sP7(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OMin)
| spl647_327
| ~ spl647_927 ),
inference(resolution,[],[f34517,f30801]) ).
fof(f38008,plain,
spl647_979,
inference(avatar_split_clause,[],[f17884,f38006]) ).
fof(f38006,plain,
( spl647_979
<=> ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_979])]) ).
fof(f17884,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X0)),
inference(cnf_transformation,[],[f5776]) ).
fof(f5776,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X0)),
inference(rectify,[],[f612]) ).
fof(f612,axiom,
! [X55,X54] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X54),X55)),X55)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38004,plain,
spl647_978,
inference(avatar_split_clause,[],[f17883,f38002]) ).
fof(f38002,plain,
( spl647_978
<=> ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_978])]) ).
fof(f17883,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X1)),
inference(cnf_transformation,[],[f5775]) ).
fof(f5775,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)),X1)),
inference(rectify,[],[f611]) ).
fof(f611,axiom,
! [X54,X55] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X55),X54)),X55)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f38000,plain,
spl647_977,
inference(avatar_split_clause,[],[f17882,f37998]) ).
fof(f37998,plain,
( spl647_977
<=> ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_977])]) ).
fof(f17882,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5774]) ).
fof(f5774,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f243]) ).
fof(f243,axiom,
! [X9,X4] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X9),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f37996,plain,
spl647_976,
inference(avatar_split_clause,[],[f17767,f37994]) ).
fof(f17767,plain,
! [X0] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK108(X0)),c_Int_OInteg)),
inference(cnf_transformation,[],[f14733]) ).
fof(f14733,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK108(X0)),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,sK108(X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK108])],[f10441,f14732]) ).
fof(f14732,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)),sK108(X0)),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,sK108(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f10441,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,[],[f5660]) ).
fof(f5660,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,[],[f3442]) ).
fof(f3442,axiom,
! [X13] :
~ ! [X38] :
( hAPP(c_Int_OAbs__Integ,X38) = X13
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X38),c_Int_OInteg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f37992,plain,
spl647_975,
inference(avatar_split_clause,[],[f17765,f37990]) ).
fof(f37990,plain,
( spl647_975
<=> ! [X2,X0] :
( hBOOL(hAPP(X0,sK106(X0)))
| ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_975])]) ).
fof(f17765,plain,
! [X2,X0] :
( hBOOL(hAPP(X0,sK106(X0)))
| ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(cnf_transformation,[],[f14731]) ).
fof(f14731,plain,
! [X0] :
( ( ( hBOOL(hAPP(X0,sK106(X0)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK106(X0))) )
| ! [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
& ( hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK107(X0))))
| ! [X4] :
( ~ hBOOL(hAPP(X0,X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK106,sK107])],[f14728,f14730,f14729]) ).
fof(f14729,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP(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(X0,sK106(X0)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK106(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f14730,plain,
! [X0] :
( ? [X3] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
=> hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK107(X0)))) ),
introduced(choice_axiom,[]) ).
fof(f14728,plain,
! [X0] :
( ( ? [X1] :
( hBOOL(hAPP(X0,X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| ! [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
& ( ? [X3] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
| ! [X4] :
( ~ hBOOL(hAPP(X0,X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) ) ),
inference(rectify,[],[f14727]) ).
fof(f14727,plain,
! [X0] :
( ( ? [X1] :
( hBOOL(hAPP(X0,X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| ! [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
& ( ? [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ! [X1] :
( ~ hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ) ),
inference(nnf_transformation,[],[f5659]) ).
fof(f5659,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP(X0,X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
<=> ? [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(rectify,[],[f1220]) ).
fof(f1220,axiom,
! [X23] :
( ? [X2] :
( hBOOL(hAPP(X23,X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) )
<=> ? [X2] : hBOOL(hAPP(X23,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f37988,plain,
spl647_974,
inference(avatar_split_clause,[],[f17758,f37986]) ).
fof(f37986,plain,
( spl647_974
<=> ! [X0,X3] :
( hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
| ~ hBOOL(hAPP(X0,sK103(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_974])]) ).
fof(f17758,plain,
! [X3,X0] :
( hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
| ~ hBOOL(hAPP(X0,sK103(X0))) ),
inference(cnf_transformation,[],[f14721]) ).
fof(f14721,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP(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(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK102(X0)))) )
& ( ! [X3] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
| ( ~ hBOOL(hAPP(X0,sK103(X0)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK103(X0))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK102,sK103])],[f14718,f14720,f14719]) ).
fof(f14719,plain,
! [X0] :
( ? [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
=> ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK102(X0)))) ),
introduced(choice_axiom,[]) ).
fof(f14720,plain,
! [X0] :
( ? [X4] :
( ~ hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) )
=> ( ~ hBOOL(hAPP(X0,sK103(X0)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK103(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f14718,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| ? [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
& ( ! [X3] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
| ? [X4] :
( ~ hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) ) ),
inference(rectify,[],[f14717]) ).
fof(f14717,plain,
! [X0] :
( ( ! [X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| ? [X2] : ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) )
& ( ! [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2)))
| ? [X1] :
( ~ hBOOL(hAPP(X0,X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ) ),
inference(nnf_transformation,[],[f10440]) ).
fof(f10440,plain,
! [X0] :
( ! [X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
<=> ! [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(ennf_transformation,[],[f5657]) ).
fof(f5657,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(X0,X1)) )
<=> ! [X2] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(rectify,[],[f1221]) ).
fof(f1221,axiom,
! [X23] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
=> hBOOL(hAPP(X23,X2)) )
<=> ! [X2] : hBOOL(hAPP(X23,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f37984,plain,
spl647_973,
inference(avatar_split_clause,[],[f17704,f37982]) ).
fof(f37982,plain,
( spl647_973
<=> ! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_973])]) ).
fof(f17704,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(cnf_transformation,[],[f14684]) ).
fof(f14684,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(nnf_transformation,[],[f5631]) ).
fof(f5631,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f4937]) ).
fof(f4937,axiom,
! [X47] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X47),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X47 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f37980,plain,
spl647_972,
inference(avatar_split_clause,[],[f17561,f37978]) ).
fof(f37978,plain,
( spl647_972
<=> ! [X0] :
( c_List_Omonoid__add__class_Olistsum(X0) = c_List_Ofoldl(X0,X0,c_Groups_Oplus__class_Oplus(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Omonoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_972])]) ).
fof(f17561,plain,
! [X0] :
( c_List_Omonoid__add__class_Olistsum(X0) = c_List_Ofoldl(X0,X0,c_Groups_Oplus__class_Oplus(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Omonoid__add(X0) ),
inference(cnf_transformation,[],[f10354]) ).
fof(f10354,plain,
! [X0] :
( c_List_Omonoid__add__class_Olistsum(X0) = c_List_Ofoldl(X0,X0,c_Groups_Oplus__class_Oplus(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Omonoid__add(X0) ),
inference(ennf_transformation,[],[f5526]) ).
fof(f5526,plain,
! [X0] :
( class_Groups_Omonoid__add(X0)
=> c_List_Omonoid__add__class_Olistsum(X0) = c_List_Ofoldl(X0,X0,c_Groups_Oplus__class_Oplus(X0),c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f4068]) ).
fof(f4068,axiom,
! [X4] :
( class_Groups_Omonoid__add(X4)
=> c_List_Omonoid__add__class_Olistsum(X4) = c_List_Ofoldl(X4,X4,c_Groups_Oplus__class_Oplus(X4),c_Groups_Ozero__class_Ozero(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f37976,plain,
spl647_971,
inference(avatar_split_clause,[],[f17545,f37974]) ).
fof(f37974,plain,
( spl647_971
<=> ! [X0] :
( hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_971])]) ).
fof(f17545,plain,
! [X0] :
( hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f10338]) ).
fof(f10338,plain,
! [X0] :
( hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f5510]) ).
fof(f5510,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f1996]) ).
fof(f1996,axiom,
! [X20] :
( class_Int_Onumber__ring(X20)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X20),c_Groups_Oone__class_Oone(X20)) = hAPP(c_Int_Onumber__class_Onumber__of(X20),c_Int_OMin) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f37972,plain,
spl647_970,
inference(avatar_split_clause,[],[f17416,f37970]) ).
fof(f37970,plain,
( spl647_970
<=> ! [X0] : c_Relation_Orefl__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_970])]) ).
fof(f17416,plain,
! [X0] : c_Relation_Orefl__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f5394]) ).
fof(f5394,plain,
! [X0] : c_Relation_Orefl__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f3257]) ).
fof(f3257,axiom,
! [X4] : c_Relation_Orefl__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f37968,plain,
( spl647_969
| spl647_327
| ~ spl647_925 ),
inference(avatar_split_clause,[],[f37561,f34508,f30799,f37965]) ).
fof(f37965,plain,
( spl647_969
<=> sP6(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_969])]) ).
fof(f37561,plain,
( sP6(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OMin)
| spl647_327
| ~ spl647_925 ),
inference(resolution,[],[f34509,f30801]) ).
fof(f37963,plain,
spl647_968,
inference(avatar_split_clause,[],[f17415,f37961]) ).
fof(f37961,plain,
( spl647_968
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_968])]) ).
fof(f17415,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))),
inference(cnf_transformation,[],[f5393]) ).
fof(f5393,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X0))),
inference(rectify,[],[f489]) ).
fof(f489,axiom,
! [X45] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X45),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),X45))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f37959,plain,
spl647_967,
inference(avatar_split_clause,[],[f17413,f37957]) ).
fof(f37957,plain,
( spl647_967
<=> ! [X0] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X0))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_967])]) ).
fof(f17413,plain,
! [X0] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X0))))),
inference(cnf_transformation,[],[f5391]) ).
fof(f5391,plain,
! [X0] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X0))))),
inference(rectify,[],[f1544]) ).
fof(f1544,axiom,
! [X44] : hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,X44))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f37955,plain,
spl647_966,
inference(avatar_split_clause,[],[f17410,f37953]) ).
fof(f37953,plain,
( spl647_966
<=> ! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_966])]) ).
fof(f17410,plain,
! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f5388]) ).
fof(f5388,plain,
! [X0] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(rectify,[],[f1348]) ).
fof(f1348,axiom,
! [X45] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X45)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f37951,plain,
spl647_965,
inference(avatar_split_clause,[],[f17407,f37949]) ).
fof(f37949,plain,
( spl647_965
<=> ! [X0] : c_Fun_Oid(X0) = c_Hilbert__Choice_Oinv__into(X0,X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),c_Fun_Oid(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_965])]) ).
fof(f17407,plain,
! [X0] : c_Fun_Oid(X0) = c_Hilbert__Choice_Oinv__into(X0,X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),c_Fun_Oid(X0)),
inference(cnf_transformation,[],[f5385]) ).
fof(f5385,plain,
! [X0] : c_Fun_Oid(X0) = c_Hilbert__Choice_Oinv__into(X0,X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),c_Fun_Oid(X0)),
inference(rectify,[],[f4789]) ).
fof(f4789,axiom,
! [X4] : c_Fun_Oid(X4) = c_Hilbert__Choice_Oinv__into(X4,X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),c_Fun_Oid(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f37764,plain,
( spl647_964
| ~ spl647_476
| ~ spl647_930 ),
inference(avatar_split_clause,[],[f37630,f34528,f31453,f37762]) ).
fof(f37762,plain,
( spl647_964
<=> ! [X0] : sP10(c_Int_OPls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_964])]) ).
fof(f31453,plain,
( spl647_476
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OPls),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_476])]) ).
fof(f37630,plain,
( ! [X0] : sP10(c_Int_OPls,X0)
| ~ spl647_476
| ~ spl647_930 ),
inference(trivial_inequality_removal,[],[f37624]) ).
fof(f37624,plain,
( ! [X0] :
( c_Int_OPls != c_Int_OPls
| sP10(c_Int_OPls,X0) )
| ~ spl647_476
| ~ spl647_930 ),
inference(superposition,[],[f34529,f31454]) ).
fof(f31454,plain,
( ! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OPls),X0)
| ~ spl647_476 ),
inference(avatar_component_clause,[],[f31453]) ).
fof(f37556,plain,
( spl647_963
| ~ spl647_829
| ~ spl647_885 ),
inference(avatar_split_clause,[],[f37228,f34329,f34104,f37553]) ).
fof(f34104,plain,
( spl647_829
<=> ! [X0,X1] :
( hBOOL(hAPP(X1,sK196(X1)))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_829])]) ).
fof(f37228,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,sK196(c_Nat__Numeral_Oneg)))
| ~ spl647_829
| ~ spl647_885 ),
inference(resolution,[],[f34330,f34105]) ).
fof(f34105,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| hBOOL(hAPP(X1,sK196(X1))) )
| ~ spl647_829 ),
inference(avatar_component_clause,[],[f34104]) ).
fof(f37295,plain,
( spl647_962
| ~ spl647_555
| ~ spl647_898
| ~ spl647_899 ),
inference(avatar_split_clause,[],[f37290,f34396,f34391,f31817,f37292]) ).
fof(f37292,plain,
( spl647_962
<=> c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olist_ONil(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_962])]) ).
fof(f31817,plain,
( spl647_555
<=> ! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_555])]) ).
fof(f34391,plain,
( spl647_898
<=> c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_898])]) ).
fof(f34396,plain,
( spl647_899
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_899])]) ).
fof(f37290,plain,
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olist_ONil(tc_Nat_Onat))
| ~ spl647_555
| ~ spl647_898
| ~ spl647_899 ),
inference(forward_demodulation,[],[f37280,f34393]) ).
fof(f34393,plain,
( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ spl647_898 ),
inference(avatar_component_clause,[],[f34391]) ).
fof(f37280,plain,
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| ~ spl647_555
| ~ spl647_899 ),
inference(superposition,[],[f31818,f34397]) ).
fof(f34397,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_HOL_Obool_Obool__size(c_fTrue))
| ~ spl647_899 ),
inference(avatar_component_clause,[],[f34396]) ).
fof(f31818,plain,
( ! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0)))
| ~ spl647_555 ),
inference(avatar_component_clause,[],[f31817]) ).
fof(f36733,plain,
( spl647_961
| ~ spl647_336
| ~ spl647_741 ),
inference(avatar_split_clause,[],[f33776,f32827,f30848,f36731]) ).
fof(f36731,plain,
( spl647_961
<=> ! [X0] :
( c_Int_OPls = X0
| ~ sP11(X0,c_Int_OMin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_961])]) ).
fof(f30848,plain,
( spl647_336
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_336])]) ).
fof(f32827,plain,
( spl647_741
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Int_OPls = X0
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_741])]) ).
fof(f33776,plain,
( ! [X0] :
( c_Int_OPls = X0
| ~ sP11(X0,c_Int_OMin) )
| ~ spl647_336
| ~ spl647_741 ),
inference(resolution,[],[f32828,f30850]) ).
fof(f30850,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))
| ~ spl647_336 ),
inference(avatar_component_clause,[],[f30848]) ).
fof(f32828,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Int_OPls = X0
| ~ sP11(X0,X1) )
| ~ spl647_741 ),
inference(avatar_component_clause,[],[f32827]) ).
fof(f36146,plain,
( spl647_960
| ~ spl647_336
| ~ spl647_726 ),
inference(avatar_split_clause,[],[f33731,f32767,f30848,f36143]) ).
fof(f36143,plain,
( spl647_960
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_960])]) ).
fof(f32767,plain,
( spl647_726
<=> ! [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,[spl647_726])]) ).
fof(f33731,plain,
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OMin)
| ~ spl647_336
| ~ spl647_726 ),
inference(resolution,[],[f32768,f30850]) ).
fof(f32768,plain,
( ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,X0) )
| ~ spl647_726 ),
inference(avatar_component_clause,[],[f32767]) ).
fof(f35966,plain,
( ~ spl647_959
| ~ spl647_473
| ~ spl647_675 ),
inference(avatar_split_clause,[],[f33376,f32549,f31440,f35963]) ).
fof(f35963,plain,
( spl647_959
<=> sP30(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_959])]) ).
fof(f32549,plain,
( spl647_675
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP30(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_675])]) ).
fof(f33376,plain,
( ~ sP30(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint))
| ~ spl647_473
| ~ spl647_675 ),
inference(resolution,[],[f32550,f31442]) ).
fof(f32550,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP30(X0,X1,X2) )
| ~ spl647_675 ),
inference(avatar_component_clause,[],[f32549]) ).
fof(f35365,plain,
( spl647_958
| ~ spl647_494
| ~ spl647_819 ),
inference(avatar_split_clause,[],[f35356,f34064,f31569,f35363]) ).
fof(f35363,plain,
( spl647_958
<=> ! [X0] :
( c_Nat__Transfer_Ois__nat(c_Int_OBit0(X0))
| ~ c_Nat__Transfer_Ois__nat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_958])]) ).
fof(f31569,plain,
( spl647_494
<=> ! [X0] : c_Int_OBit0(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_494])]) ).
fof(f34064,plain,
( spl647_819
<=> ! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_819])]) ).
fof(f35356,plain,
( ! [X0] :
( c_Nat__Transfer_Ois__nat(c_Int_OBit0(X0))
| ~ c_Nat__Transfer_Ois__nat(X0) )
| ~ spl647_494
| ~ spl647_819 ),
inference(duplicate_literal_removal,[],[f35353]) ).
fof(f35353,plain,
( ! [X0] :
( c_Nat__Transfer_Ois__nat(c_Int_OBit0(X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X0) )
| ~ spl647_494
| ~ spl647_819 ),
inference(superposition,[],[f34065,f31570]) ).
fof(f31570,plain,
( ! [X0] : c_Int_OBit0(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0)
| ~ spl647_494 ),
inference(avatar_component_clause,[],[f31569]) ).
fof(f34065,plain,
( ! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) )
| ~ spl647_819 ),
inference(avatar_component_clause,[],[f34064]) ).
fof(f35147,plain,
( ~ spl647_957
| ~ spl647_472
| ~ spl647_675 ),
inference(avatar_split_clause,[],[f33375,f32549,f31435,f35144]) ).
fof(f35144,plain,
( spl647_957
<=> sP30(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls,c_Orderings_Oord__class_Oless(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_957])]) ).
fof(f33375,plain,
( ~ sP30(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls,c_Orderings_Oord__class_Oless(tc_Int_Oint))
| ~ spl647_472
| ~ spl647_675 ),
inference(resolution,[],[f32550,f31437]) ).
fof(f35108,plain,
( spl647_956
| ~ spl647_428
| ~ spl647_675 ),
inference(avatar_split_clause,[],[f33364,f32549,f31254,f35106]) ).
fof(f35106,plain,
( spl647_956
<=> ! [X0,X1] :
( ~ sP30(X0,X1,c_fimplies)
| ~ hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_956])]) ).
fof(f31254,plain,
( spl647_428
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_428])]) ).
fof(f33364,plain,
( ! [X0,X1] :
( ~ sP30(X0,X1,c_fimplies)
| ~ hBOOL(X0) )
| ~ spl647_428
| ~ spl647_675 ),
inference(resolution,[],[f32550,f31255]) ).
fof(f31255,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) )
| ~ spl647_428 ),
inference(avatar_component_clause,[],[f31254]) ).
fof(f34724,plain,
( spl647_955
| ~ spl647_378
| ~ spl647_754 ),
inference(avatar_split_clause,[],[f34626,f33800,f31021,f34721]) ).
fof(f34721,plain,
( spl647_955
<=> c_Relation_Osym(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_955])]) ).
fof(f31021,plain,
( spl647_378
<=> ! [X2,X0,X1] :
( c_Relation_Osym(X2,X0)
| ~ c_Equiv__Relations_Oequiv(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_378])]) ).
fof(f33800,plain,
( spl647_754
<=> c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_754])]) ).
fof(f34626,plain,
( c_Relation_Osym(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel)
| ~ spl647_378
| ~ spl647_754 ),
inference(resolution,[],[f33802,f31022]) ).
fof(f31022,plain,
( ! [X2,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X2,X1,X0)
| c_Relation_Osym(X2,X0) )
| ~ spl647_378 ),
inference(avatar_component_clause,[],[f31021]) ).
fof(f33802,plain,
( c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel)
| ~ spl647_754 ),
inference(avatar_component_clause,[],[f33800]) ).
fof(f34657,plain,
( spl647_954
| ~ spl647_379
| ~ spl647_754 ),
inference(avatar_split_clause,[],[f34625,f33800,f31025,f34654]) ).
fof(f34654,plain,
( spl647_954
<=> c_Relation_Otrans(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_954])]) ).
fof(f31025,plain,
( spl647_379
<=> ! [X2,X0,X1] :
( c_Relation_Otrans(X2,X0)
| ~ c_Equiv__Relations_Oequiv(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_379])]) ).
fof(f34625,plain,
( c_Relation_Otrans(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel)
| ~ spl647_379
| ~ spl647_754 ),
inference(resolution,[],[f33802,f31026]) ).
fof(f31026,plain,
( ! [X2,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X2,X1,X0)
| c_Relation_Otrans(X2,X0) )
| ~ spl647_379 ),
inference(avatar_component_clause,[],[f31025]) ).
fof(f34623,plain,
spl647_953,
inference(avatar_split_clause,[],[f28570,f34621]) ).
fof(f34621,plain,
( spl647_953
<=> ! [X2,X0,X1,X3] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_953])]) ).
fof(f28570,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X2,
inference(forward_demodulation,[],[f21560,f17145]) ).
fof(f21560,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(cnf_transformation,[],[f8277]) ).
fof(f8277,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_Power_Opower_Opower(X3,X2,X1),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X2,
inference(rectify,[],[f2008]) ).
fof(f2008,axiom,
! [X5,X128,X129,X4] : hAPP(hAPP(c_Power_Opower_Opower(X4,X129,X128),X5),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X129,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34619,plain,
spl647_952,
inference(avatar_split_clause,[],[f28495,f34617]) ).
fof(f28495,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP41(X0,X1,X2) ),
inference(forward_demodulation,[],[f21312,f17135]) ).
fof(f21312,plain,
! [X2,X0,X1] :
( sP41(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(cnf_transformation,[],[f15870]) ).
fof(f34615,plain,
spl647_951,
inference(avatar_split_clause,[],[f28490,f34613]) ).
fof(f28490,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP42(X0,X1,X2) ),
inference(forward_demodulation,[],[f21306,f17135]) ).
fof(f21306,plain,
! [X2,X0,X1] :
( sP42(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f15864]) ).
fof(f34611,plain,
spl647_950,
inference(avatar_split_clause,[],[f28469,f34609]) ).
fof(f28469,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP36(X0,X1,X2) ),
inference(forward_demodulation,[],[f21234,f17135]) ).
fof(f21234,plain,
! [X2,X0,X1] :
( sP36(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(cnf_transformation,[],[f15818]) ).
fof(f34607,plain,
spl647_949,
inference(avatar_split_clause,[],[f28464,f34605]) ).
fof(f28464,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP37(X0,X1,X2) ),
inference(forward_demodulation,[],[f21228,f17135]) ).
fof(f21228,plain,
! [X2,X0,X1] :
( sP37(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f15813]) ).
fof(f34603,plain,
( spl647_948
| ~ spl647_429
| ~ spl647_675 ),
inference(avatar_split_clause,[],[f33363,f32549,f31258,f34601]) ).
fof(f34601,plain,
( spl647_948
<=> ! [X0,X1] :
( ~ sP30(X0,X1,c_fimplies)
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_948])]) ).
fof(f31258,plain,
( spl647_429
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_429])]) ).
fof(f33363,plain,
( ! [X0,X1] :
( ~ sP30(X0,X1,c_fimplies)
| hBOOL(X1) )
| ~ spl647_429
| ~ spl647_675 ),
inference(resolution,[],[f32550,f31259]) ).
fof(f31259,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) )
| ~ spl647_429 ),
inference(avatar_component_clause,[],[f31258]) ).
fof(f34599,plain,
spl647_947,
inference(avatar_split_clause,[],[f28435,f34597]) ).
fof(f34597,plain,
( spl647_947
<=> ! [X2,X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| sP34(X1,X0)
| ~ sP35(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_947])]) ).
fof(f28435,plain,
! [X2,X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| sP34(X1,X0)
| ~ sP35(X0,X1,X2) ),
inference(forward_demodulation,[],[f21180,f17145]) ).
fof(f21180,plain,
! [X2,X0,X1] :
( sP34(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP35(X0,X1,X2) ),
inference(cnf_transformation,[],[f15777]) ).
fof(f34595,plain,
spl647_946,
inference(avatar_split_clause,[],[f28332,f34593]) ).
fof(f28332,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| hBOOL(hAPP(X0,X1)) ),
inference(forward_demodulation,[],[f20892,f17793]) ).
fof(f20892,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_Set_OCollect(X2),X0))) ),
inference(cnf_transformation,[],[f12399]) ).
fof(f12399,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_Set_OCollect(X2),X0))) ),
inference(ennf_transformation,[],[f7990]) ).
fof(f7990,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_Set_OCollect(X2),X0)))
=> hBOOL(hAPP(X0,X1)) ),
inference(rectify,[],[f3239]) ).
fof(f3239,axiom,
! [X23,X5,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(c_Set_OCollect(X4),X23)))
=> hBOOL(hAPP(X23,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34591,plain,
spl647_945,
inference(avatar_split_clause,[],[f28300,f34589]) ).
fof(f28300,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP29(X2,X0,X1) ),
inference(forward_demodulation,[],[f20830,f17135]) ).
fof(f20830,plain,
! [X2,X0,X1] :
( sP29(X2,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(cnf_transformation,[],[f14525]) ).
fof(f14525,plain,
! [X0,X1,X2] :
( sP29(X2,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(definition_folding,[],[f12343,f14524,f14523]) ).
fof(f14524,plain,
! [X2,X0,X1] :
( ( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> sP28(X1,X0,X2) )
| ~ sP29(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP29])]) ).
fof(f12343,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(flattening,[],[f12342]) ).
fof(f12342,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ),
inference(ennf_transformation,[],[f7946]) ).
fof(f7946,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
=> ( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> ! [X3,X4] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X0
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X4),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X4)) )
=> hBOOL(hAPP(hAPP(X1,X3),X4)) ) ) ),
inference(rectify,[],[f1673]) ).
fof(f1673,axiom,
! [X46,X23,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))
=> ( hBOOL(hAPP(hAPP(X23,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X46),X48)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X46,X48)))
<=> ! [X86,X83] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X86)),X83) = X46
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X83),X48))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X83)) )
=> hBOOL(hAPP(hAPP(X23,X86),X83)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34587,plain,
spl647_944,
inference(avatar_split_clause,[],[f28237,f34585]) ).
fof(f28237,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP27(X2,X0,X1) ),
inference(forward_demodulation,[],[f20788,f17135]) ).
fof(f20788,plain,
! [X2,X0,X1] :
( sP27(X2,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f14522]) ).
fof(f14522,plain,
! [X0,X1,X2] :
( sP27(X2,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(definition_folding,[],[f12313,f14521,f14520]) ).
fof(f14521,plain,
! [X2,X0,X1] :
( ( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> sP26(X1,X0,X2) )
| ~ sP27(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP27])]) ).
fof(f12313,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(flattening,[],[f12312]) ).
fof(f12312,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> ! [X3,X4] :
( hBOOL(hAPP(hAPP(X1,X3),X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) ) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(ennf_transformation,[],[f7929]) ).
fof(f7929,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(X1,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X2)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X2)))
<=> ! [X3,X4] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),X3)),X4) = X0
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),X4)) )
=> hBOOL(hAPP(hAPP(X1,X3),X4)) ) ) ),
inference(rectify,[],[f1672]) ).
fof(f1672,axiom,
! [X46,X23,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(X23,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X46),X48)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X46,X48)))
<=> ! [X86,X83] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X86)),X83) = X46
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X83),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),X83)) )
=> hBOOL(hAPP(hAPP(X23,X86),X83)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34583,plain,
spl647_943,
inference(avatar_split_clause,[],[f28159,f34581]) ).
fof(f34581,plain,
( spl647_943
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_943])]) ).
fof(f28159,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(forward_demodulation,[],[f20602,f17793]) ).
fof(f20602,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(c_Set_OCollect(X0),X2)))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(cnf_transformation,[],[f12128]) ).
fof(f12128,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(c_Set_OCollect(X0),X2)))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(ennf_transformation,[],[f7796]) ).
fof(f7796,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,X1))
=> hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(c_Set_OCollect(X0),X2))) ),
inference(rectify,[],[f3219]) ).
fof(f3219,axiom,
! [X4,X5,X23] :
( hBOOL(hAPP(X23,X5))
=> hBOOL(hAPP(hAPP(c_member(X4),X5),hAPP(c_Set_OCollect(X4),X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34579,plain,
spl647_942,
inference(avatar_split_clause,[],[f27912,f34576]) ).
fof(f34576,plain,
( spl647_942
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_942])]) ).
fof(f27912,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f27911,f26039]) ).
fof(f26039,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,[],[f17367,f17145]) ).
fof(f17367,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,[],[f5345]) ).
fof(f5345,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,[],[f796]) ).
fof(f796,axiom,
! [X44] : 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)),X44),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f27911,plain,
! [X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X1)),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f27910,f26039]) ).
fof(f27910,plain,
! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0)),
inference(forward_demodulation,[],[f25442,f17145]) ).
fof(f25442,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),
inference(equality_resolution,[],[f19851]) ).
fof(f19851,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f11306]) ).
fof(f11306,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) ),
inference(ennf_transformation,[],[f7204]) ).
fof(f7204,plain,
! [X0,X1,X2] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)) ) ),
inference(rectify,[],[f1762]) ).
fof(f1762,axiom,
! [X44,X45,X53] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X53
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X45),X44) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X45)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X44)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X53
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X45)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X44)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34574,plain,
spl647_941,
inference(avatar_split_clause,[],[f27640,f34572]) ).
fof(f34572,plain,
( spl647_941
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP14(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_941])]) ).
fof(f27640,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP14(X0,X1) ),
inference(forward_demodulation,[],[f27639,f25910]) ).
fof(f27639,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP14(X0,X1) ),
inference(forward_demodulation,[],[f27638,f17145]) ).
fof(f27638,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP14(X0,X1) ),
inference(forward_demodulation,[],[f19411,f17145]) ).
fof(f19411,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP14(X0,X1) ),
inference(cnf_transformation,[],[f15194]) ).
fof(f15194,plain,
! [X0,X1] :
( ( sP14(X0,X1)
| ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP14(X0,X1) ) ),
inference(flattening,[],[f15193]) ).
fof(f15193,plain,
! [X0,X1] :
( ( sP14(X0,X1)
| ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP14(X0,X1) ) ),
inference(nnf_transformation,[],[f14501]) ).
fof(f34570,plain,
spl647_940,
inference(avatar_split_clause,[],[f27637,f34568]) ).
fof(f34568,plain,
( spl647_940
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP14(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_940])]) ).
fof(f27637,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP14(X0,X1) ),
inference(forward_demodulation,[],[f27636,f17145]) ).
fof(f27636,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP14(X0,X1) ),
inference(forward_demodulation,[],[f19412,f17145]) ).
fof(f19412,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP14(X0,X1) ),
inference(cnf_transformation,[],[f15194]) ).
fof(f34566,plain,
spl647_939,
inference(avatar_split_clause,[],[f27635,f34564]) ).
fof(f34564,plain,
( spl647_939
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP14(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_939])]) ).
fof(f27635,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP14(X0,X1) ),
inference(forward_demodulation,[],[f27634,f25910]) ).
fof(f27634,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP14(X0,X1) ),
inference(forward_demodulation,[],[f27633,f17145]) ).
fof(f27633,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP14(X0,X1) ),
inference(forward_demodulation,[],[f27632,f25910]) ).
fof(f27632,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP14(X0,X1) ),
inference(forward_demodulation,[],[f19413,f17145]) ).
fof(f19413,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP14(X0,X1) ),
inference(cnf_transformation,[],[f15194]) ).
fof(f34562,plain,
spl647_938,
inference(avatar_split_clause,[],[f27631,f34560]) ).
fof(f34560,plain,
( spl647_938
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP14(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_938])]) ).
fof(f27631,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP14(X0,X1) ),
inference(forward_demodulation,[],[f27630,f17145]) ).
fof(f27630,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP14(X0,X1) ),
inference(forward_demodulation,[],[f27629,f25910]) ).
fof(f27629,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP14(X0,X1) ),
inference(forward_demodulation,[],[f19414,f17145]) ).
fof(f19414,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP14(X0,X1) ),
inference(cnf_transformation,[],[f15194]) ).
fof(f34558,plain,
( spl647_937
| ~ spl647_426
| ~ spl647_675 ),
inference(avatar_split_clause,[],[f33362,f32549,f31245,f34556]) ).
fof(f34556,plain,
( spl647_937
<=> ! [X0,X1] :
( ~ sP30(X0,X1,c_fdisj)
| ~ hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_937])]) ).
fof(f31245,plain,
( spl647_426
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_426])]) ).
fof(f33362,plain,
( ! [X0,X1] :
( ~ sP30(X0,X1,c_fdisj)
| ~ hBOOL(X0) )
| ~ spl647_426
| ~ spl647_675 ),
inference(resolution,[],[f32550,f31246]) ).
fof(f31246,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) )
| ~ spl647_426 ),
inference(avatar_component_clause,[],[f31245]) ).
fof(f34554,plain,
spl647_936,
inference(avatar_split_clause,[],[f27620,f34552]) ).
fof(f34552,plain,
( spl647_936
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_936])]) ).
fof(f27620,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP13(X0,X1) ),
inference(forward_demodulation,[],[f27619,f25910]) ).
fof(f27619,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP13(X0,X1) ),
inference(forward_demodulation,[],[f27618,f17145]) ).
fof(f27618,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP13(X0,X1) ),
inference(forward_demodulation,[],[f19403,f17145]) ).
fof(f19403,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f15191]) ).
fof(f15191,plain,
! [X0,X1] :
( ( sP13(X0,X1)
| ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP13(X0,X1) ) ),
inference(flattening,[],[f15190]) ).
fof(f15190,plain,
! [X0,X1] :
( ( sP13(X0,X1)
| ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP13(X0,X1) ) ),
inference(nnf_transformation,[],[f14499]) ).
fof(f34550,plain,
spl647_935,
inference(avatar_split_clause,[],[f27617,f34548]) ).
fof(f34548,plain,
( spl647_935
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_935])]) ).
fof(f27617,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP13(X0,X1) ),
inference(forward_demodulation,[],[f27616,f17145]) ).
fof(f27616,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP13(X0,X1) ),
inference(forward_demodulation,[],[f19404,f17145]) ).
fof(f19404,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f15191]) ).
fof(f34546,plain,
spl647_934,
inference(avatar_split_clause,[],[f27615,f34544]) ).
fof(f34544,plain,
( spl647_934
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_934])]) ).
fof(f27615,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP13(X0,X1) ),
inference(forward_demodulation,[],[f27614,f25910]) ).
fof(f27614,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP13(X0,X1) ),
inference(forward_demodulation,[],[f27613,f17145]) ).
fof(f27613,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP13(X0,X1) ),
inference(forward_demodulation,[],[f27612,f25910]) ).
fof(f27612,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP13(X0,X1) ),
inference(forward_demodulation,[],[f19405,f17145]) ).
fof(f19405,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f15191]) ).
fof(f34542,plain,
spl647_933,
inference(avatar_split_clause,[],[f27611,f34540]) ).
fof(f34540,plain,
( spl647_933
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_933])]) ).
fof(f27611,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP13(X0,X1) ),
inference(forward_demodulation,[],[f27610,f17145]) ).
fof(f27610,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP13(X0,X1) ),
inference(forward_demodulation,[],[f27609,f25910]) ).
fof(f27609,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP13(X0,X1) ),
inference(forward_demodulation,[],[f19406,f17145]) ).
fof(f19406,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f15191]) ).
fof(f34538,plain,
spl647_932,
inference(avatar_split_clause,[],[f27544,f34536]) ).
fof(f34536,plain,
( spl647_932
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| hBOOL(hAPP(X0,sK205(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_932])]) ).
fof(f27544,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| hBOOL(hAPP(X0,sK205(X0))) ),
inference(forward_demodulation,[],[f19305,f17793]) ).
fof(f19305,plain,
! [X0,X1] :
( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK205(X0))) ),
inference(cnf_transformation,[],[f15133]) ).
fof(f15133,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK205(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,[sK205])],[f15131,f15132]) ).
fof(f15132,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X0,sK205(X0))) ),
introduced(choice_axiom,[]) ).
fof(f15131,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,[],[f15130]) ).
fof(f15130,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,[],[f6824]) ).
fof(f6824,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,[],[f3233]) ).
fof(f3233,axiom,
! [X23,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X4),X23)
<=> ! [X2] : ~ hBOOL(hAPP(X23,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34534,plain,
spl647_931,
inference(avatar_split_clause,[],[f27542,f34532]) ).
fof(f34532,plain,
( spl647_931
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| hBOOL(hAPP(X0,sK204(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_931])]) ).
fof(f27542,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| hBOOL(hAPP(X0,sK204(X0))) ),
inference(forward_demodulation,[],[f19303,f17793]) ).
fof(f19303,plain,
! [X0,X1] :
( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK204(X0))) ),
inference(cnf_transformation,[],[f15129]) ).
fof(f15129,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK204(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,[sK204])],[f15127,f15128]) ).
fof(f15128,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X0,sK204(X0))) ),
introduced(choice_axiom,[]) ).
fof(f15127,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,[],[f15126]) ).
fof(f15126,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,[],[f6823]) ).
fof(f6823,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,[],[f3232]) ).
fof(f3232,axiom,
! [X23,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X4),X23)
<=> ! [X2] : ~ hBOOL(hAPP(X23,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34530,plain,
spl647_930,
inference(avatar_split_clause,[],[f27534,f34528]) ).
fof(f27534,plain,
! [X0,X1] :
( c_Int_OPls != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| sP10(X1,X0) ),
inference(forward_demodulation,[],[f19295,f17135]) ).
fof(f19295,plain,
! [X0,X1] :
( sP10(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0) ),
inference(cnf_transformation,[],[f15122]) ).
fof(f15122,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| ~ sP10(X1,X0) )
& ( sP10(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0) ) ),
inference(nnf_transformation,[],[f14495]) ).
fof(f14495,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
<=> sP10(X1,X0) ),
inference(definition_folding,[],[f6820,f14494]) ).
fof(f14494,plain,
! [X1,X0] :
( sP10(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,[sP10])]) ).
fof(f6820,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),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 ) ),
inference(rectify,[],[f1686]) ).
fof(f1686,axiom,
! [X48,X63] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X63),X48)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),X63))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X63),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X63),X48))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X63)) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X48 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34526,plain,
spl647_929,
inference(avatar_split_clause,[],[f27533,f34524]) ).
fof(f34524,plain,
( spl647_929
<=> ! [X0,X1] :
( c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| ~ sP10(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_929])]) ).
fof(f27533,plain,
! [X0,X1] :
( c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| ~ sP10(X1,X0) ),
inference(forward_demodulation,[],[f19296,f17135]) ).
fof(f19296,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| ~ sP10(X1,X0) ),
inference(cnf_transformation,[],[f15122]) ).
fof(f34522,plain,
spl647_928,
inference(avatar_split_clause,[],[f27499,f34520]) ).
fof(f34520,plain,
( spl647_928
<=> ! [X2,X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_928])]) ).
fof(f27499,plain,
! [X2,X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),X0),
inference(forward_demodulation,[],[f25368,f17135]) ).
fof(f25368,plain,
! [X2,X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2),X0),
inference(equality_resolution,[],[f19194]) ).
fof(f19194,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) != X1 ),
inference(cnf_transformation,[],[f15052]) ).
fof(f15052,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
| ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) != X1 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),sK197(X0,X1)) = X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK197])],[f15050,f15051]) ).
fof(f15051,plain,
! [X0,X1] :
( ? [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3) = X1
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),sK197(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f15050,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
| ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) != X1 )
& ( ? [X3] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3) = X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) ) ),
inference(rectify,[],[f15049]) ).
fof(f15049,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
| ! [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) != X1 )
& ( ? [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) = X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0) ) ),
inference(nnf_transformation,[],[f6780]) ).
fof(f6780,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)
<=> ? [X2] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X2) = X1 ),
inference(rectify,[],[f1658]) ).
fof(f1658,axiom,
! [X10,X47] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X47,X10)
<=> ? [X118] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X10),X118) = X47 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34518,plain,
spl647_927,
inference(avatar_split_clause,[],[f27480,f34516]) ).
fof(f27480,plain,
! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| sP7(c_HOL_Obool_Obool__size(c_fTrue),X1) ),
inference(forward_demodulation,[],[f27479,f17135]) ).
fof(f27479,plain,
! [X1] :
( sP7(c_HOL_Obool_Obool__size(c_fTrue),X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(forward_demodulation,[],[f25356,f17145]) ).
fof(f25356,plain,
! [X1] :
( sP7(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)),X1)) ),
inference(equality_resolution,[],[f19147]) ).
fof(f19147,plain,
! [X0,X1] :
( sP7(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)) ),
inference(cnf_transformation,[],[f15007]) ).
fof(f34514,plain,
( spl647_926
| ~ spl647_427
| ~ spl647_675 ),
inference(avatar_split_clause,[],[f33361,f32549,f31250,f34512]) ).
fof(f34512,plain,
( spl647_926
<=> ! [X0,X1] :
( ~ sP30(X0,X1,c_fdisj)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_926])]) ).
fof(f31250,plain,
( spl647_427
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_427])]) ).
fof(f33361,plain,
( ! [X0,X1] :
( ~ sP30(X0,X1,c_fdisj)
| ~ hBOOL(X1) )
| ~ spl647_427
| ~ spl647_675 ),
inference(resolution,[],[f32550,f31251]) ).
fof(f31251,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) )
| ~ spl647_427 ),
inference(avatar_component_clause,[],[f31250]) ).
fof(f34510,plain,
spl647_925,
inference(avatar_split_clause,[],[f27472,f34508]) ).
fof(f27472,plain,
! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| sP6(c_HOL_Obool_Obool__size(c_fTrue),X1) ),
inference(forward_demodulation,[],[f27471,f17135]) ).
fof(f27471,plain,
! [X1] :
( sP6(c_HOL_Obool_Obool__size(c_fTrue),X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(forward_demodulation,[],[f25351,f17145]) ).
fof(f25351,plain,
! [X1] :
( sP6(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)),X1)) ),
inference(equality_resolution,[],[f19139]) ).
fof(f19139,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)) ),
inference(cnf_transformation,[],[f15004]) ).
fof(f34506,plain,
spl647_924,
inference(avatar_split_clause,[],[f27468,f34504]) ).
fof(f34504,plain,
( spl647_924
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_924])]) ).
fof(f27468,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| ~ c_Wellfounded_OwfP(X1,X0) ),
inference(forward_demodulation,[],[f24550,f17793]) ).
fof(f24550,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0)))
| ~ c_Wellfounded_OwfP(X1,X0) ),
inference(definition_unfolding,[],[f19097,f19585]) ).
fof(f19097,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0)))
| ~ c_Wellfounded_OwfP(X1,X0) ),
inference(cnf_transformation,[],[f14958]) ).
fof(f14958,plain,
! [X0,X1] :
( ( c_Wellfounded_OwfP(X1,X0)
| ~ c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0))) )
& ( c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0)))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
inference(nnf_transformation,[],[f6750]) ).
fof(f6750,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
<=> c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0))) ),
inference(rectify,[],[f3418]) ).
fof(f3418,axiom,
! [X116,X4] :
( c_Wellfounded_OwfP(X4,X116)
<=> c_Wellfounded_Owf(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),X116))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34502,plain,
spl647_923,
inference(avatar_split_clause,[],[f27467,f34500]) ).
fof(f27467,plain,
! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| c_Wellfounded_OwfP(X1,X0) ),
inference(forward_demodulation,[],[f24549,f17793]) ).
fof(f24549,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
| ~ c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))) ),
inference(definition_unfolding,[],[f19098,f19585]) ).
fof(f19098,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
| ~ c_Wellfounded_Owf(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0))) ),
inference(cnf_transformation,[],[f14958]) ).
fof(f34498,plain,
spl647_922,
inference(avatar_split_clause,[],[f27464,f34496]) ).
fof(f34496,plain,
( spl647_922
<=> ! [X0,X1] :
( c_Relation_Otrans(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| ~ c_Predicate_Otransp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_922])]) ).
fof(f27464,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| ~ c_Predicate_Otransp(X1,X0) ),
inference(forward_demodulation,[],[f24548,f17793]) ).
fof(f24548,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0)))
| ~ c_Predicate_Otransp(X1,X0) ),
inference(definition_unfolding,[],[f19069,f19585]) ).
fof(f19069,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0)))
| ~ c_Predicate_Otransp(X1,X0) ),
inference(cnf_transformation,[],[f14934]) ).
fof(f14934,plain,
! [X0,X1] :
( ( c_Predicate_Otransp(X1,X0)
| ~ c_Relation_Otrans(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0))) )
& ( c_Relation_Otrans(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0)))
| ~ c_Predicate_Otransp(X1,X0) ) ),
inference(nnf_transformation,[],[f6744]) ).
fof(f6744,plain,
! [X0,X1] :
( c_Predicate_Otransp(X1,X0)
<=> c_Relation_Otrans(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0))) ),
inference(rectify,[],[f4726]) ).
fof(f4726,axiom,
! [X116,X4] :
( c_Predicate_Otransp(X4,X116)
<=> c_Relation_Otrans(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),X116))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34494,plain,
spl647_921,
inference(avatar_split_clause,[],[f27463,f34492]) ).
fof(f34492,plain,
( spl647_921
<=> ! [X0,X1] :
( ~ c_Relation_Otrans(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| c_Predicate_Otransp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_921])]) ).
fof(f27463,plain,
! [X0,X1] :
( ~ c_Relation_Otrans(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| c_Predicate_Otransp(X1,X0) ),
inference(forward_demodulation,[],[f24547,f17793]) ).
fof(f24547,plain,
! [X0,X1] :
( c_Predicate_Otransp(X1,X0)
| ~ c_Relation_Otrans(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))) ),
inference(definition_unfolding,[],[f19070,f19585]) ).
fof(f19070,plain,
! [X0,X1] :
( c_Predicate_Otransp(X1,X0)
| ~ c_Relation_Otrans(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0))) ),
inference(cnf_transformation,[],[f14934]) ).
fof(f34490,plain,
spl647_920,
inference(avatar_split_clause,[],[f27462,f34488]) ).
fof(f34488,plain,
( spl647_920
<=> ! [X0,X1] :
( c_Relation_Osym(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| ~ c_Predicate_Osymp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_920])]) ).
fof(f27462,plain,
! [X0,X1] :
( c_Relation_Osym(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| ~ c_Predicate_Osymp(X1,X0) ),
inference(forward_demodulation,[],[f24546,f17793]) ).
fof(f24546,plain,
! [X0,X1] :
( c_Relation_Osym(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0)))
| ~ c_Predicate_Osymp(X1,X0) ),
inference(definition_unfolding,[],[f19067,f19585]) ).
fof(f19067,plain,
! [X0,X1] :
( c_Relation_Osym(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0)))
| ~ c_Predicate_Osymp(X1,X0) ),
inference(cnf_transformation,[],[f14933]) ).
fof(f14933,plain,
! [X0,X1] :
( ( c_Predicate_Osymp(X1,X0)
| ~ c_Relation_Osym(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0))) )
& ( c_Relation_Osym(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0)))
| ~ c_Predicate_Osymp(X1,X0) ) ),
inference(nnf_transformation,[],[f6743]) ).
fof(f6743,plain,
! [X0,X1] :
( c_Predicate_Osymp(X1,X0)
<=> c_Relation_Osym(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0))) ),
inference(rectify,[],[f4765]) ).
fof(f4765,axiom,
! [X116,X4] :
( c_Predicate_Osymp(X4,X116)
<=> c_Relation_Osym(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),X116))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34486,plain,
spl647_919,
inference(avatar_split_clause,[],[f27461,f34484]) ).
fof(f34484,plain,
( spl647_919
<=> ! [X0,X1] :
( ~ c_Relation_Osym(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| c_Predicate_Osymp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_919])]) ).
fof(f27461,plain,
! [X0,X1] :
( ~ c_Relation_Osym(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| c_Predicate_Osymp(X1,X0) ),
inference(forward_demodulation,[],[f24545,f17793]) ).
fof(f24545,plain,
! [X0,X1] :
( c_Predicate_Osymp(X1,X0)
| ~ c_Relation_Osym(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))) ),
inference(definition_unfolding,[],[f19068,f19585]) ).
fof(f19068,plain,
! [X0,X1] :
( c_Predicate_Osymp(X1,X0)
| ~ c_Relation_Osym(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0))) ),
inference(cnf_transformation,[],[f14933]) ).
fof(f34482,plain,
spl647_918,
inference(avatar_split_clause,[],[f26976,f34480]) ).
fof(f34480,plain,
( spl647_918
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_918])]) ).
fof(f26976,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0))
| ~ c_Wellfounded_OwfP(X1,X0) ),
inference(forward_demodulation,[],[f24490,f17793]) ).
fof(f24490,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Ointernal__split(X1,X1,tc_HOL_Obool),X0)))
| ~ c_Wellfounded_OwfP(X1,X0) ),
inference(definition_unfolding,[],[f18690,f19585]) ).
fof(f18690,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0)))
| ~ c_Wellfounded_OwfP(X1,X0) ),
inference(cnf_transformation,[],[f10871]) ).
fof(f10871,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0)))
| ~ c_Wellfounded_OwfP(X1,X0) ),
inference(ennf_transformation,[],[f6443]) ).
fof(f6443,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
=> c_Wellfounded_Oacyclic(X1,hAPP(c_Set_OCollect(tc_prod(X1,X1)),hAPP(c_Product__Type_Oprod_Oprod__case(X1,X1,tc_HOL_Obool),X0))) ),
inference(rectify,[],[f3425]) ).
fof(f3425,axiom,
! [X116,X4] :
( c_Wellfounded_OwfP(X4,X116)
=> c_Wellfounded_Oacyclic(X4,hAPP(c_Set_OCollect(tc_prod(X4,X4)),hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),X116))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34478,plain,
spl647_917,
inference(avatar_split_clause,[],[f26961,f34476]) ).
fof(f34476,plain,
( spl647_917
<=> ! [X0,X1] :
( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_917])]) ).
fof(f26961,plain,
! [X0,X1] :
( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(forward_demodulation,[],[f18575,f26468]) ).
fof(f18575,plain,
! [X0,X1] :
( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__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,[],[f10744]) ).
fof(f10744,plain,
! [X0,X1] :
( c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__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,[],[f6359]) ).
fof(f6359,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> c_Big__Operators_Olattice_OInf__fin(X1,c_Orderings_Oord__class_Omin(X1),hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f1176]) ).
fof(f1176,axiom,
! [X13,X4] :
( class_Orderings_Olinorder(X4)
=> c_Big__Operators_Olattice_OInf__fin(X4,c_Orderings_Oord__class_Omin(X4),hAPP(hAPP(c_Set_Oinsert(X4),X13),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34474,plain,
spl647_916,
inference(avatar_split_clause,[],[f26960,f34472]) ).
fof(f34472,plain,
( spl647_916
<=> ! [X0,X1] :
( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_916])]) ).
fof(f26960,plain,
! [X0,X1] :
( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(forward_demodulation,[],[f18574,f26468]) ).
fof(f18574,plain,
! [X0,X1] :
( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__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,[],[f10743]) ).
fof(f10743,plain,
! [X0,X1] :
( c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__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,[],[f6358]) ).
fof(f6358,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> c_Big__Operators_Olattice_OSup__fin(X1,c_Orderings_Oord__class_Omax(X1),hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f2498]) ).
fof(f2498,axiom,
! [X13,X4] :
( class_Orderings_Olinorder(X4)
=> c_Big__Operators_Olattice_OSup__fin(X4,c_Orderings_Oord__class_Omax(X4),hAPP(hAPP(c_Set_Oinsert(X4),X13),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34470,plain,
( spl647_915
| ~ spl647_475
| ~ spl647_675 ),
inference(avatar_split_clause,[],[f33359,f32549,f31449,f34468]) ).
fof(f34468,plain,
( spl647_915
<=> ! [X0] : ~ sP30(X0,c_HOL_Obool_Obool__size(c_fTrue),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_915])]) ).
fof(f31449,plain,
( spl647_475
<=> ! [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,[spl647_475])]) ).
fof(f33359,plain,
( ! [X0] : ~ sP30(X0,c_HOL_Obool_Obool__size(c_fTrue),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat))
| ~ spl647_475
| ~ spl647_675 ),
inference(resolution,[],[f32550,f31450]) ).
fof(f31450,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0))
| ~ spl647_475 ),
inference(avatar_component_clause,[],[f31449]) ).
fof(f34466,plain,
spl647_914,
inference(avatar_split_clause,[],[f26613,f34464]) ).
fof(f34464,plain,
( spl647_914
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = c_Nitpick_Ocard_H(X1,X0)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_914])]) ).
fof(f26613,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = c_Nitpick_Ocard_H(X1,X0)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(forward_demodulation,[],[f18200,f17145]) ).
fof(f18200,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nitpick_Ocard_H(X1,X0)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(cnf_transformation,[],[f10456]) ).
fof(f10456,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nitpick_Ocard_H(X1,X0)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) )
& ( c_Nitpick_Ocard_H(X1,X0) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Hilbert__Choice_OEps(tc_List_Olist(X1),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_List_Oset(X1))),X0))),c_List_Odistinct(X1))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ) ),
inference(ennf_transformation,[],[f6077]) ).
fof(f6077,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nitpick_Ocard_H(X1,X0) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
=> c_Nitpick_Ocard_H(X1,X0) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_Hilbert__Choice_OEps(tc_List_Olist(X1),hAPP(hAPP(c_COMBS(tc_List_Olist(X1),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X1)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X1),tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X1)),c_fequal),c_List_Oset(X1))),X0))),c_List_Odistinct(X1)))) ) ),
inference(rectify,[],[f3870]) ).
fof(f3870,axiom,
! [X9,X4] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X9))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nitpick_Ocard_H(X4,X9) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X9))
=> c_Nitpick_Ocard_H(X4,X9) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X4)),c_Hilbert__Choice_OEps(tc_List_Olist(X4),hAPP(hAPP(c_COMBS(tc_List_Olist(X4),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X4)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X4),tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X4,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X4)),c_fequal),c_List_Oset(X4))),X9))),c_List_Odistinct(X4)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34462,plain,
spl647_913,
inference(avatar_split_clause,[],[f26456,f34460]) ).
fof(f26456,plain,
! [X0,X1] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)),X0),
inference(forward_demodulation,[],[f17885,f17135]) ).
fof(f17885,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)),X0),
inference(cnf_transformation,[],[f5777]) ).
fof(f5777,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)),X0),
inference(rectify,[],[f1574]) ).
fof(f1574,axiom,
! [X25,X26] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,X26,X25)),X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34458,plain,
spl647_912,
inference(avatar_split_clause,[],[f26452,f34456]) ).
fof(f34456,plain,
( spl647_912
<=> ! [X0,X1] : c_Fun_Oid(X1) = hAPP(hAPP(c_Nat_Ocompow(X1,X1),c_HOL_Obool_Obool__size(c_fTrue)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_912])]) ).
fof(f26452,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,[],[f17870,f17145]) ).
fof(f17870,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,[],[f5762]) ).
fof(f5762,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,[],[f3683]) ).
fof(f3683,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34453,plain,
spl647_911,
inference(avatar_split_clause,[],[f26399,f34450]) ).
fof(f34450,plain,
( spl647_911
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Int_OPls)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_911])]) ).
fof(f26399,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Int_OPls)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f25268,f17135]) ).
fof(f25268,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(equality_resolution,[],[f17745]) ).
fof(f17745,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ),
inference(cnf_transformation,[],[f14707]) ).
fof(f34448,plain,
spl647_910,
inference(avatar_split_clause,[],[f26326,f34446]) ).
fof(f34446,plain,
( spl647_910
<=> ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Int_OPls))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_910])]) ).
fof(f26326,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Int_OPls))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f17659,f17135]) ).
fof(f17659,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(cnf_transformation,[],[f14652]) ).
fof(f14652,plain,
! [X0] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
inference(nnf_transformation,[],[f5610]) ).
fof(f5610,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(rectify,[],[f1291]) ).
fof(f1291,axiom,
! [X112] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X112))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X112),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34444,plain,
spl647_909,
inference(avatar_split_clause,[],[f26325,f34442]) ).
fof(f34442,plain,
( spl647_909
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Int_OPls))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_909])]) ).
fof(f26325,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Int_OPls))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f17660,f17135]) ).
fof(f17660,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f14652]) ).
fof(f34440,plain,
spl647_908,
inference(avatar_split_clause,[],[f26324,f34438]) ).
fof(f26324,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f17649,f17135]) ).
fof(f17649,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(cnf_transformation,[],[f14647]) ).
fof(f14647,plain,
! [X0] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,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))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
inference(nnf_transformation,[],[f5605]) ).
fof(f5605,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ),
inference(rectify,[],[f1290]) ).
fof(f1290,axiom,
! [X13] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X13))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34436,plain,
spl647_907,
inference(avatar_split_clause,[],[f26323,f34434]) ).
fof(f26323,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f17650,f17135]) ).
fof(f17650,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,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,[],[f14647]) ).
fof(f34427,plain,
( spl647_906
| ~ spl647_331
| ~ spl647_497
| ~ spl647_904 ),
inference(avatar_split_clause,[],[f34419,f34416,f31581,f30819,f34425]) ).
fof(f34416,plain,
( spl647_904
<=> ! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)))
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_904])]) ).
fof(f34419,plain,
( ! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Int_Onumber__ring(X0) )
| ~ spl647_331
| ~ spl647_497
| ~ spl647_904 ),
inference(forward_demodulation,[],[f34417,f32001]) ).
fof(f34417,plain,
( ! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)))
| ~ class_Int_Onumber__ring(X0) )
| ~ spl647_904 ),
inference(avatar_component_clause,[],[f34416]) ).
fof(f34423,plain,
( spl647_905
| ~ spl647_478
| ~ spl647_675 ),
inference(avatar_split_clause,[],[f33356,f32549,f31461,f34421]) ).
fof(f34421,plain,
( spl647_905
<=> ! [X0] : ~ sP30(X0,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_905])]) ).
fof(f31461,plain,
( spl647_478
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_478])]) ).
fof(f33356,plain,
( ! [X0] : ~ sP30(X0,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Rings_Odvd__class_Odvd(tc_Nat_Onat))
| ~ spl647_478
| ~ spl647_675 ),
inference(resolution,[],[f32550,f31462]) ).
fof(f31462,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0))
| ~ spl647_478 ),
inference(avatar_component_clause,[],[f31461]) ).
fof(f34418,plain,
spl647_904,
inference(avatar_split_clause,[],[f26197,f34416]) ).
fof(f26197,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f26196,f25909]) ).
fof(f26196,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f24251,f17133]) ).
fof(f24251,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin)))
| ~ class_Int_Onumber__ring(X0) ),
inference(definition_unfolding,[],[f17540,f24151]) ).
fof(f17540,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,[],[f10333]) ).
fof(f10333,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,[],[f5505]) ).
fof(f5505,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,[],[f1715]) ).
fof(f1715,axiom,
! [X20] :
( class_Int_Onumber__ring(X20)
=> ~ c_Int_Oiszero(X20,hAPP(c_Int_Onumber__class_Onumber__of(X20),c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34414,plain,
spl647_903,
inference(avatar_split_clause,[],[f26074,f34412]) ).
fof(f34412,plain,
( spl647_903
<=> ! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_903])]) ).
fof(f26074,plain,
! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Int_OMin),
inference(forward_demodulation,[],[f17434,f17285]) ).
fof(f17434,plain,
! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
inference(cnf_transformation,[],[f5412]) ).
fof(f5412,plain,
! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
inference(rectify,[],[f2010]) ).
fof(f2010,axiom,
! [X26] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X26) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34410,plain,
spl647_902,
inference(avatar_split_clause,[],[f26070,f34408]) ).
fof(f34408,plain,
( spl647_902
<=> ! [X0] : hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Int_OPls),c_Int_OPls) = c_Divides_OposDivAlg(c_Int_OPls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_902])]) ).
fof(f26070,plain,
! [X0] : hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Int_OPls),c_Int_OPls) = c_Divides_OposDivAlg(c_Int_OPls,X0),
inference(forward_demodulation,[],[f17432,f17135]) ).
fof(f17432,plain,
! [X0] : hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),
inference(cnf_transformation,[],[f5410]) ).
fof(f5410,plain,
! [X0] : hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),
inference(rectify,[],[f2270]) ).
fof(f2270,axiom,
! [X25] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34406,plain,
spl647_901,
inference(avatar_split_clause,[],[f26059,f34404]) ).
fof(f34404,plain,
( spl647_901
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_901])]) ).
fof(f26059,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)),X0),
inference(forward_demodulation,[],[f17405,f17135]) ).
fof(f17405,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)),X0),
inference(cnf_transformation,[],[f5383]) ).
fof(f5383,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)),X0),
inference(rectify,[],[f1514]) ).
fof(f1514,axiom,
! [X27] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X27)),X27),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34402,plain,
spl647_900,
inference(avatar_split_clause,[],[f26051,f34400]) ).
fof(f34400,plain,
( spl647_900
<=> ! [X0] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_900])]) ).
fof(f34398,plain,
spl647_899,
inference(avatar_split_clause,[],[f26050,f34396]) ).
fof(f26050,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17389,f17145]) ).
fof(f17389,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f5367]) ).
fof(f5367,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f2756]) ).
fof(f2756,axiom,
! [X47] : c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X47),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34394,plain,
( spl647_898
| ~ spl647_897 ),
inference(avatar_split_clause,[],[f34389,f34386,f34391]) ).
fof(f34386,plain,
( spl647_897
<=> ! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_HOL_Obool_Obool__size(c_fTrue))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_897])]) ).
fof(f34389,plain,
( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ spl647_897 ),
inference(forward_demodulation,[],[f34387,f26050]) ).
fof(f34387,plain,
( ! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_HOL_Obool_Obool__size(c_fTrue)))
| ~ spl647_897 ),
inference(avatar_component_clause,[],[f34386]) ).
fof(f34388,plain,
spl647_897,
inference(avatar_split_clause,[],[f26011,f34386]) ).
fof(f26011,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f24206,f17145]) ).
fof(f24206,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(definition_unfolding,[],[f17292,f17880]) ).
fof(f17292,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f5270]) ).
fof(f5270,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f4376]) ).
fof(f4376,axiom,
! [X55] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X55,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34379,plain,
( spl647_896
| ~ spl647_336
| ~ spl647_669 ),
inference(avatar_split_clause,[],[f33213,f32522,f30848,f34377]) ).
fof(f32522,plain,
( spl647_669
<=> ! [X0,X1,X3] :
( hBOOL(hAPP(X0,sK218(X0,X1)))
| ~ hBOOL(hAPP(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_669])]) ).
fof(f33213,plain,
( ! [X0] : hBOOL(hAPP(c_Nat__Numeral_Oneg,sK218(c_Nat__Numeral_Oneg,X0)))
| ~ spl647_336
| ~ spl647_669 ),
inference(resolution,[],[f32523,f30850]) ).
fof(f32523,plain,
( ! [X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X3))
| hBOOL(hAPP(X0,sK218(X0,X1))) )
| ~ spl647_669 ),
inference(avatar_component_clause,[],[f32522]) ).
fof(f34375,plain,
( spl647_895
| ~ spl647_331
| ~ spl647_497
| ~ spl647_894 ),
inference(avatar_split_clause,[],[f34370,f34366,f31581,f30819,f34372]) ).
fof(f34372,plain,
( spl647_895
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_895])]) ).
fof(f34366,plain,
( spl647_894
<=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_894])]) ).
fof(f34370,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)
| ~ spl647_331
| ~ spl647_497
| ~ spl647_894 ),
inference(forward_demodulation,[],[f34368,f32001]) ).
fof(f34368,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)
| ~ spl647_894 ),
inference(avatar_component_clause,[],[f34366]) ).
fof(f34369,plain,
spl647_894,
inference(avatar_split_clause,[],[f25909,f34366]) ).
fof(f34364,plain,
spl647_893,
inference(avatar_split_clause,[],[f25745,f34362]) ).
fof(f34362,plain,
( spl647_893
<=> ! [X0,X3,X2,X1] : c_Lazy__Sequence_Oempty(X2) = hAPP(c_New__DSequence_Opos__decr__bind(X3,X2,X1,X0),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_893])]) ).
fof(f25745,plain,
! [X2,X3,X0,X1] : c_Lazy__Sequence_Oempty(X2) = hAPP(c_New__DSequence_Opos__decr__bind(X3,X2,X1,X0),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(equality_resolution,[],[f23004]) ).
fof(f23004,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(c_New__DSequence_Opos__decr__bind(X3,X2,X1,X0),X4) = c_Lazy__Sequence_Oempty(X2)
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X4 ),
inference(cnf_transformation,[],[f13572]) ).
fof(f13572,plain,
! [X0,X1,X2,X3,X4] :
( ( hAPP(c_New__DSequence_Opos__decr__bind(X3,X2,X1,X0),X4) = hAPP(c_Lazy__Sequence_Obind(X3,X2,hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X4),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)),X0),X4))
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X4 )
& ( hAPP(c_New__DSequence_Opos__decr__bind(X3,X2,X1,X0),X4) = c_Lazy__Sequence_Oempty(X2)
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X4 ) ),
inference(ennf_transformation,[],[f9337]) ).
fof(f9337,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X4
=> hAPP(c_New__DSequence_Opos__decr__bind(X3,X2,X1,X0),X4) = hAPP(c_Lazy__Sequence_Obind(X3,X2,hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X4),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X2)),X0),X4)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X4
=> hAPP(c_New__DSequence_Opos__decr__bind(X3,X2,X1,X0),X4) = c_Lazy__Sequence_Oempty(X2) ) ),
inference(rectify,[],[f4584]) ).
fof(f4584,axiom,
! [X1,X13,X4,X14,X63] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X63
=> hAPP(c_New__DSequence_Opos__decr__bind(X14,X4,X13,X1),X63) = hAPP(c_Lazy__Sequence_Obind(X14,X4,hAPP(X13,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X63),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X14,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X4)),X1),X63)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X63
=> hAPP(c_New__DSequence_Opos__decr__bind(X14,X4,X13,X1),X63) = c_Lazy__Sequence_Oempty(X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34360,plain,
spl647_892,
inference(avatar_split_clause,[],[f25744,f34358]) ).
fof(f34358,plain,
( spl647_892
<=> ! [X0,X3,X2,X1] : c_Lazy__Sequence_Ohit__bound(X2) = hAPP(c_New__DSequence_Oneg__decr__bind(X3,X2,X1,X0),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_892])]) ).
fof(f25744,plain,
! [X2,X3,X0,X1] : c_Lazy__Sequence_Ohit__bound(X2) = hAPP(c_New__DSequence_Oneg__decr__bind(X3,X2,X1,X0),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(equality_resolution,[],[f23002]) ).
fof(f23002,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(c_New__DSequence_Oneg__decr__bind(X3,X2,X1,X0),X4) = c_Lazy__Sequence_Ohit__bound(X2)
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X4 ),
inference(cnf_transformation,[],[f13571]) ).
fof(f13571,plain,
! [X0,X1,X2,X3,X4] :
( ( hAPP(c_New__DSequence_Oneg__decr__bind(X3,X2,X1,X0),X4) = c_Lazy__Sequence_Ohb__bind(X3,X2,hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X4),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))),X0),X4))
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X4 )
& ( hAPP(c_New__DSequence_Oneg__decr__bind(X3,X2,X1,X0),X4) = c_Lazy__Sequence_Ohit__bound(X2)
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X4 ) ),
inference(ennf_transformation,[],[f9336]) ).
fof(f9336,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X4
=> hAPP(c_New__DSequence_Oneg__decr__bind(X3,X2,X1,X0),X4) = c_Lazy__Sequence_Ohb__bind(X3,X2,hAPP(X1,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X4),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X3,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X2))),X0),X4)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X4
=> hAPP(c_New__DSequence_Oneg__decr__bind(X3,X2,X1,X0),X4) = c_Lazy__Sequence_Ohit__bound(X2) ) ),
inference(rectify,[],[f4583]) ).
fof(f4583,axiom,
! [X1,X13,X4,X14,X63] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X63
=> hAPP(c_New__DSequence_Oneg__decr__bind(X14,X4,X13,X1),X63) = c_Lazy__Sequence_Ohb__bind(X14,X4,hAPP(X13,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X63),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X14,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X4))),X1),X63)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X63
=> hAPP(c_New__DSequence_Oneg__decr__bind(X14,X4,X13,X1),X63) = c_Lazy__Sequence_Ohit__bound(X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34356,plain,
spl647_891,
inference(avatar_split_clause,[],[f25632,f34354]) ).
fof(f34354,plain,
( spl647_891
<=> ! [X0,X1,X3] : c_List_Oremove1(X1,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_891])]) ).
fof(f25632,plain,
! [X3,X0,X1] : c_List_Oremove1(X1,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X0)) = X0,
inference(equality_resolution,[],[f21731]) ).
fof(f21731,plain,
! [X2,X3,X0,X1] :
( c_List_Oremove1(X1,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X0)) = X0
| X2 != X3 ),
inference(cnf_transformation,[],[f12631]) ).
fof(f12631,plain,
! [X0,X1,X2,X3] :
( ( c_List_Oremove1(X1,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X0)) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Oremove1(X1,X3,X0))
| X2 = X3 )
& ( c_List_Oremove1(X1,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X0)) = X0
| X2 != X3 ) ),
inference(ennf_transformation,[],[f8447]) ).
fof(f8447,plain,
! [X0,X1,X2,X3] :
( ( X2 != X3
=> c_List_Oremove1(X1,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X0)) = hAPP(hAPP(c_List_Olist_OCons(X1),X2),c_List_Oremove1(X1,X3,X0)) )
& ( X2 = X3
=> c_List_Oremove1(X1,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X2),X0)) = X0 ) ),
inference(rectify,[],[f3882]) ).
fof(f3882,axiom,
! [X201,X20,X21,X19] :
( ( X19 != X21
=> c_List_Oremove1(X20,X19,hAPP(hAPP(c_List_Olist_OCons(X20),X21),X201)) = hAPP(hAPP(c_List_Olist_OCons(X20),X21),c_List_Oremove1(X20,X19,X201)) )
& ( X19 = X21
=> c_List_Oremove1(X20,X19,hAPP(hAPP(c_List_Olist_OCons(X20),X21),X201)) = X201 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34352,plain,
spl647_890,
inference(avatar_split_clause,[],[f25473,f34350]) ).
fof(f34350,plain,
( spl647_890
<=> ! [X2,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),c_Groups_Ozero__class_Ozero(X2)) = X1
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_890])]) ).
fof(f25473,plain,
! [X2,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),c_Groups_Ozero__class_Ozero(X2)) = X1
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(equality_resolution,[],[f20074]) ).
fof(f20074,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X2),X1),X0) = X1
| c_Groups_Ozero__class_Ozero(X2) != X0
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X2) ),
inference(cnf_transformation,[],[f15358]) ).
fof(f34348,plain,
spl647_889,
inference(avatar_split_clause,[],[f25459,f34346]) ).
fof(f34346,plain,
( spl647_889
<=> ! [X2,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X1)
| ~ class_Groups_Oab__group__add(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_889])]) ).
fof(f25459,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X1)
| ~ class_Groups_Oab__group__add(X2) ),
inference(equality_resolution,[],[f19954]) ).
fof(f19954,plain,
! [X2,X0,X1] :
( c_Groups_Ozero__class_Ozero(X2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X2),X1),X0)
| X0 != X1
| ~ class_Groups_Oab__group__add(X2) ),
inference(cnf_transformation,[],[f15329]) ).
fof(f34343,plain,
spl647_888,
inference(avatar_split_clause,[],[f25271,f34341]) ).
fof(f34341,plain,
( spl647_888
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_888])]) ).
fof(f25271,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),X0) = X0,
inference(equality_resolution,[],[f24409]) ).
fof(f24409,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X0) = X0
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X1 ),
inference(definition_unfolding,[],[f18175,f17887]) ).
fof(f17887,plain,
! [X0,X1] : c_Code__Numeral_Onat__of__aux(X1,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X0),
inference(cnf_transformation,[],[f5779]) ).
fof(f5779,plain,
! [X0,X1] : c_Code__Numeral_Onat__of__aux(X1,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X1)),X0),
inference(rectify,[],[f4207]) ).
fof(f4207,axiom,
! [X44,X55] : c_Code__Numeral_Onat__of__aux(X55,X44) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X55)),X44),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f18175,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,[],[f10445]) ).
fof(f10445,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,[],[f6066]) ).
fof(f6066,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,[],[f1721]) ).
fof(f1721,axiom,
! [X44,X55] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X55
=> c_Code__Numeral_Onat__of__aux(X55,X44) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X55),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X44)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X55
=> c_Code__Numeral_Onat__of__aux(X55,X44) = X44 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34339,plain,
spl647_887,
inference(avatar_split_clause,[],[f24325,f34337]) ).
fof(f34337,plain,
( spl647_887
<=> ! [X0,X1] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0) = hAPP(c_List_Omember(tc_Int_Oint),c_List_Oupto(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_887])]) ).
fof(f24325,plain,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0) = hAPP(c_List_Omember(tc_Int_Oint),c_List_Oupto(X1,X0)),
inference(definition_unfolding,[],[f17877,f17267]) ).
fof(f17877,plain,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,X0)),
inference(cnf_transformation,[],[f5769]) ).
fof(f5769,plain,
! [X0,X1] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,X0)),
inference(rectify,[],[f3824]) ).
fof(f3824,axiom,
! [X62,X63] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X63,X62) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X63,X62)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34335,plain,
spl647_886,
inference(avatar_split_clause,[],[f24324,f34333]) ).
fof(f34333,plain,
( spl647_886
<=> ! [X0,X1] : hAPP(c_List_Omember(X1),X0) = hAPP(c_List_Omember(X1),c_List_Oremdups(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_886])]) ).
fof(f24324,plain,
! [X0,X1] : hAPP(c_List_Omember(X1),X0) = hAPP(c_List_Omember(X1),c_List_Oremdups(X1,X0)),
inference(definition_unfolding,[],[f17875,f17267,f17267]) ).
fof(f17875,plain,
! [X0,X1] : hAPP(c_List_Oset(X1),X0) = hAPP(c_List_Oset(X1),c_List_Oremdups(X1,X0)),
inference(cnf_transformation,[],[f5767]) ).
fof(f5767,plain,
! [X0,X1] : hAPP(c_List_Oset(X1),X0) = hAPP(c_List_Oset(X1),c_List_Oremdups(X1,X0)),
inference(rectify,[],[f4274]) ).
fof(f4274,axiom,
! [X203,X4] : hAPP(c_List_Oset(X4),X203) = hAPP(c_List_Oset(X4),c_List_Oremdups(X4,X203)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34331,plain,
( spl647_885
| ~ spl647_336
| ~ spl647_652 ),
inference(avatar_split_clause,[],[f33003,f32451,f30848,f34329]) ).
fof(f32451,plain,
( spl647_652
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ~ hBOOL(hAPP(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_652])]) ).
fof(f33003,plain,
( ! [X0] : hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Hilbert__Choice_OEps(X0,c_Nat__Numeral_Oneg)))
| ~ spl647_336
| ~ spl647_652 ),
inference(resolution,[],[f32452,f30850]) ).
fof(f32452,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) )
| ~ spl647_652 ),
inference(avatar_component_clause,[],[f32451]) ).
fof(f34327,plain,
spl647_884,
inference(avatar_split_clause,[],[f24306,f34325]) ).
fof(f34325,plain,
( spl647_884
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_884])]) ).
fof(f24306,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0)))),
inference(definition_unfolding,[],[f17807,f17880]) ).
fof(f17807,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X0))),
inference(cnf_transformation,[],[f5699]) ).
fof(f5699,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X0))),
inference(rectify,[],[f4381]) ).
fof(f4381,axiom,
! [X54,X55] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X55,X54))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34323,plain,
spl647_883,
inference(avatar_split_clause,[],[f23642,f34321]) ).
fof(f34321,plain,
( spl647_883
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| X0 = X3
| ~ sP82(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_883])]) ).
fof(f23642,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X0 = X3
| ~ sP82(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16767]) ).
fof(f16767,plain,
! [X0,X1,X2,X3] :
( ( sP82(X0,X1,X2,X3)
| ( ( X0 != X1
| X2 != X3 )
& ( X0 != X3
| X1 != X2 ) ) )
& ( ( X0 = X1
& X2 = X3 )
| ( X0 = X3
& X1 = X2 )
| ~ sP82(X0,X1,X2,X3) ) ),
inference(rectify,[],[f16766]) ).
fof(f16766,plain,
! [X2,X1,X3,X0] :
( ( sP82(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP82(X2,X1,X3,X0) ) ),
inference(flattening,[],[f16765]) ).
fof(f16765,plain,
! [X2,X1,X3,X0] :
( ( sP82(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP82(X2,X1,X3,X0) ) ),
inference(nnf_transformation,[],[f14618]) ).
fof(f14618,plain,
! [X2,X1,X3,X0] :
( sP82(X2,X1,X3,X0)
<=> ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP82])]) ).
fof(f34319,plain,
spl647_882,
inference(avatar_split_clause,[],[f23641,f34317]) ).
fof(f34317,plain,
( spl647_882
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| X1 = X2
| ~ sP82(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_882])]) ).
fof(f23641,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X1 = X2
| ~ sP82(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16767]) ).
fof(f34315,plain,
spl647_881,
inference(avatar_split_clause,[],[f23640,f34313]) ).
fof(f34313,plain,
( spl647_881
<=> ! [X0,X3,X2,X1] :
( X2 = X3
| X0 = X3
| ~ sP82(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_881])]) ).
fof(f23640,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X0 = X3
| ~ sP82(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16767]) ).
fof(f34311,plain,
spl647_880,
inference(avatar_split_clause,[],[f23639,f34309]) ).
fof(f34309,plain,
( spl647_880
<=> ! [X2,X0,X1,X3] :
( X2 = X3
| X1 = X2
| ~ sP82(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_880])]) ).
fof(f23639,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X1 = X2
| ~ sP82(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16767]) ).
fof(f34307,plain,
spl647_879,
inference(avatar_split_clause,[],[f23278,f34305]) ).
fof(f34305,plain,
( spl647_879
<=> ! [X4,X0,X3,X2,X1] :
( c_Fun_Oinj__on(X4,X3,X2,X1)
| ~ c_Fun_Obij__betw(X4,X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_879])]) ).
fof(f23278,plain,
! [X2,X3,X0,X1,X4] :
( c_Fun_Oinj__on(X4,X3,X2,X1)
| ~ c_Fun_Obij__betw(X4,X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f13896]) ).
fof(f13896,plain,
! [X0,X1,X2,X3,X4] :
( c_Fun_Oinj__on(X4,X3,X2,X1)
| ~ c_Fun_Obij__betw(X4,X3,X2,X1,X0) ),
inference(ennf_transformation,[],[f9563]) ).
fof(f9563,plain,
! [X0,X1,X2,X3,X4] :
( c_Fun_Obij__betw(X4,X3,X2,X1,X0)
=> c_Fun_Oinj__on(X4,X3,X2,X1) ),
inference(rectify,[],[f4828]) ).
fof(f4828,axiom,
! [X18,X9,X1,X14,X4] :
( c_Fun_Obij__betw(X4,X14,X1,X9,X18)
=> c_Fun_Oinj__on(X4,X14,X1,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34303,plain,
spl647_878,
inference(avatar_split_clause,[],[f22609,f34301]) ).
fof(f34301,plain,
( spl647_878
<=> ! [X0,X3,X2,X1] :
( c_List_Olist_ONil(X2) = X0
| ~ c_List_Olist__all2(X3,X2,X1,c_List_Olist_ONil(X3),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_878])]) ).
fof(f22609,plain,
! [X2,X3,X0,X1] :
( c_List_Olist_ONil(X2) = X0
| ~ c_List_Olist__all2(X3,X2,X1,c_List_Olist_ONil(X3),X0) ),
inference(cnf_transformation,[],[f16296]) ).
fof(f16296,plain,
! [X0,X1,X2,X3] :
( ( c_List_Olist__all2(X3,X2,X1,c_List_Olist_ONil(X3),X0)
| c_List_Olist_ONil(X2) != X0 )
& ( c_List_Olist_ONil(X2) = X0
| ~ c_List_Olist__all2(X3,X2,X1,c_List_Olist_ONil(X3),X0) ) ),
inference(nnf_transformation,[],[f9144]) ).
fof(f9144,plain,
! [X0,X1,X2,X3] :
( c_List_Olist__all2(X3,X2,X1,c_List_Olist_ONil(X3),X0)
<=> c_List_Olist_ONil(X2) = X0 ),
inference(rectify,[],[f4244]) ).
fof(f4244,axiom,
! [X202,X23,X14,X4] :
( c_List_Olist__all2(X4,X14,X23,c_List_Olist_ONil(X4),X202)
<=> c_List_Olist_ONil(X14) = X202 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34299,plain,
spl647_877,
inference(avatar_split_clause,[],[f22607,f34297]) ).
fof(f34297,plain,
( spl647_877
<=> ! [X0,X3,X2,X1] :
( c_List_Olist_ONil(X3) = X0
| ~ c_List_Olist__all2(X3,X2,X1,X0,c_List_Olist_ONil(X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_877])]) ).
fof(f22607,plain,
! [X2,X3,X0,X1] :
( c_List_Olist_ONil(X3) = X0
| ~ c_List_Olist__all2(X3,X2,X1,X0,c_List_Olist_ONil(X2)) ),
inference(cnf_transformation,[],[f16295]) ).
fof(f16295,plain,
! [X0,X1,X2,X3] :
( ( c_List_Olist__all2(X3,X2,X1,X0,c_List_Olist_ONil(X2))
| c_List_Olist_ONil(X3) != X0 )
& ( c_List_Olist_ONil(X3) = X0
| ~ c_List_Olist__all2(X3,X2,X1,X0,c_List_Olist_ONil(X2)) ) ),
inference(nnf_transformation,[],[f9143]) ).
fof(f9143,plain,
! [X0,X1,X2,X3] :
( c_List_Olist__all2(X3,X2,X1,X0,c_List_Olist_ONil(X2))
<=> c_List_Olist_ONil(X3) = X0 ),
inference(rectify,[],[f4243]) ).
fof(f4243,axiom,
! [X203,X23,X14,X4] :
( c_List_Olist__all2(X4,X14,X23,X203,c_List_Olist_ONil(X14))
<=> c_List_Olist_ONil(X4) = X203 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34295,plain,
spl647_876,
inference(avatar_split_clause,[],[f22277,f34293]) ).
fof(f34293,plain,
( spl647_876
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X1,sK435(X0,X1,X2)))
| ~ sP56(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_876])]) ).
fof(f22277,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X1,sK435(X0,X1,X2)))
| ~ sP56(X0,X1,X2) ),
inference(cnf_transformation,[],[f16162]) ).
fof(f34291,plain,
spl647_875,
inference(avatar_split_clause,[],[f21559,f34289]) ).
fof(f34289,plain,
( spl647_875
<=> ! [X0,X3,X2,X1] : hAPP(X1,X0) = c_Nat_Onat_Onat__case(X3,X2,X1,hAPP(c_Nat_OSuc,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_875])]) ).
fof(f21559,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0) = c_Nat_Onat_Onat__case(X3,X2,X1,hAPP(c_Nat_OSuc,X0)),
inference(cnf_transformation,[],[f8276]) ).
fof(f8276,plain,
! [X0,X1,X2,X3] : hAPP(X1,X0) = c_Nat_Onat_Onat__case(X3,X2,X1,hAPP(c_Nat_OSuc,X0)),
inference(rectify,[],[f2269]) ).
fof(f2269,axiom,
! [X50,X135,X95,X4] : c_Nat_Onat_Onat__case(X4,X95,X135,hAPP(c_Nat_OSuc,X50)) = hAPP(X135,X50),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34287,plain,
( spl647_874
| ~ spl647_24
| ~ spl647_208
| ~ spl647_615 ),
inference(avatar_split_clause,[],[f32859,f32298,f30268,f29354,f34284]) ).
fof(f34284,plain,
( spl647_874
<=> c_Int_OPls = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_874])]) ).
fof(f29354,plain,
( spl647_24
<=> class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_24])]) ).
fof(f30268,plain,
( spl647_208
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl647_208])]) ).
fof(f32298,plain,
( spl647_615
<=> ! [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,[spl647_615])]) ).
fof(f32859,plain,
( c_Int_OPls = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Int_OPls)
| ~ spl647_24
| ~ spl647_208
| ~ spl647_615 ),
inference(forward_demodulation,[],[f32858,f30270]) ).
fof(f30270,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls
| ~ spl647_208 ),
inference(avatar_component_clause,[],[f30268]) ).
fof(f32858,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl647_24
| ~ spl647_615 ),
inference(resolution,[],[f32299,f29356]) ).
fof(f29356,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint)
| ~ spl647_24 ),
inference(avatar_component_clause,[],[f29354]) ).
fof(f32299,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)) )
| ~ spl647_615 ),
inference(avatar_component_clause,[],[f32298]) ).
fof(f34282,plain,
spl647_873,
inference(avatar_split_clause,[],[f21558,f34280]) ).
fof(f34280,plain,
( spl647_873
<=> ! [X2,X0,X1,X3] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_fun(X2,tc_HOL_Obool))),X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_873])]) ).
fof(f21558,plain,
! [X2,X3,X0,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_fun(X2,tc_HOL_Obool))),X1),X0)),
inference(cnf_transformation,[],[f8275]) ).
fof(f8275,plain,
! [X0,X1,X2,X3] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X3,tc_fun(X2,tc_HOL_Obool))),X1),X0)),
inference(rectify,[],[f2260]) ).
fof(f2260,axiom,
! [X15,X13,X14,X4] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X4,tc_fun(X14,tc_HOL_Obool))),X13),X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34278,plain,
spl647_872,
inference(avatar_split_clause,[],[f21546,f34276]) ).
fof(f34276,plain,
( spl647_872
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK414(X0,X1,X2)))
| ~ c_List_Olist__ex(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_872])]) ).
fof(f21546,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK414(X0,X1,X2)))
| ~ c_List_Olist__ex(X2,X0,X1) ),
inference(cnf_transformation,[],[f16050]) ).
fof(f16050,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(X0,sK414(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK414(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) )
| ~ c_List_Olist__ex(X2,X0,X1) )
& ( c_List_Olist__ex(X2,X0,X1)
| ! [X4] :
( ~ hBOOL(hAPP(X0,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X1))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK414])],[f16048,f16049]) ).
fof(f16049,plain,
! [X0,X1,X2] :
( ? [X3] :
( hBOOL(hAPP(X0,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
=> ( hBOOL(hAPP(X0,sK414(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK414(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f16048,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( hBOOL(hAPP(X0,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
| ~ c_List_Olist__ex(X2,X0,X1) )
& ( c_List_Olist__ex(X2,X0,X1)
| ! [X4] :
( ~ hBOOL(hAPP(X0,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X1))) ) ) ),
inference(rectify,[],[f16047]) ).
fof(f16047,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( hBOOL(hAPP(X0,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
| ~ c_List_Olist__ex(X2,X0,X1) )
& ( c_List_Olist__ex(X2,X0,X1)
| ! [X3] :
( ~ hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) ) ) ),
inference(nnf_transformation,[],[f8263]) ).
fof(f8263,plain,
! [X0,X1,X2] :
( ? [X3] :
( hBOOL(hAPP(X0,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
<=> c_List_Olist__ex(X2,X0,X1) ),
inference(rectify,[],[f4693]) ).
fof(f4693,axiom,
! [X23,X203,X4] :
( ? [X2] :
( hBOOL(hAPP(X23,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X203))) )
<=> c_List_Olist__ex(X4,X23,X203) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34274,plain,
spl647_871,
inference(avatar_split_clause,[],[f21538,f34272]) ).
fof(f34272,plain,
( spl647_871
<=> ! [X2,X0,X1] :
( c_List_Olist__all(X2,X0,X1)
| ~ hBOOL(hAPP(X0,sK411(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_871])]) ).
fof(f21538,plain,
! [X2,X0,X1] :
( c_List_Olist__all(X2,X0,X1)
| ~ hBOOL(hAPP(X0,sK411(X0,X1,X2))) ),
inference(cnf_transformation,[],[f16041]) ).
fof(f16041,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
| ~ c_List_Olist__all(X2,X0,X1) )
& ( c_List_Olist__all(X2,X0,X1)
| ( ~ hBOOL(hAPP(X0,sK411(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK411(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK411])],[f16039,f16040]) ).
fof(f16040,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X1))) )
=> ( ~ hBOOL(hAPP(X0,sK411(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK411(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f16039,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
| ~ c_List_Olist__all(X2,X0,X1) )
& ( c_List_Olist__all(X2,X0,X1)
| ? [X4] :
( ~ hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X1))) ) ) ),
inference(rectify,[],[f16038]) ).
fof(f16038,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
| ~ c_List_Olist__all(X2,X0,X1) )
& ( c_List_Olist__all(X2,X0,X1)
| ? [X3] :
( ~ hBOOL(hAPP(X0,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) ) ) ),
inference(nnf_transformation,[],[f12629]) ).
fof(f12629,plain,
! [X0,X1,X2] :
( ! [X3] :
( hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
<=> c_List_Olist__all(X2,X0,X1) ),
inference(ennf_transformation,[],[f8261]) ).
fof(f8261,plain,
! [X0,X1,X2] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1)))
=> hBOOL(hAPP(X0,X3)) )
<=> c_List_Olist__all(X2,X0,X1) ),
inference(rectify,[],[f4575]) ).
fof(f4575,axiom,
! [X23,X203,X4] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X203)))
=> hBOOL(hAPP(X23,X2)) )
<=> c_List_Olist__all(X4,X23,X203) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34270,plain,
spl647_870,
inference(avatar_split_clause,[],[f21330,f34268]) ).
fof(f34268,plain,
( spl647_870
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK386(X0,X1,X2)))
| ~ sP45(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_870])]) ).
fof(f21330,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK386(X0,X1,X2)))
| ~ sP45(X0,X1,X2) ),
inference(cnf_transformation,[],[f15882]) ).
fof(f15882,plain,
! [X0,X1,X2] :
( ( sP45(X0,X1,X2)
| ! [X3] :
( ~ hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X3))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X2)) ) )
& ( ( hBOOL(hAPP(X0,sK386(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,sK386(X0,X1,X2)))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),sK386(X0,X1,X2))),X2)) )
| ~ sP45(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK386])],[f15880,f15881]) ).
fof(f15881,plain,
! [X0,X1,X2] :
( ? [X4] :
( hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X4))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X2)) )
=> ( hBOOL(hAPP(X0,sK386(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,sK386(X0,X1,X2)))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),sK386(X0,X1,X2))),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15880,plain,
! [X0,X1,X2] :
( ( sP45(X0,X1,X2)
| ! [X3] :
( ~ hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X3))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X3)),X2)) ) )
& ( ? [X4] :
( hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,X4))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X4)),X2)) )
| ~ sP45(X0,X1,X2) ) ),
inference(rectify,[],[f15879]) ).
fof(f15879,plain,
! [X2,X0,X1] :
( ( sP45(X2,X0,X1)
| ! [X3] :
( ~ hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X3))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X1)) ) )
& ( ? [X3] :
( hBOOL(hAPP(X2,X3))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X3))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X1)) )
| ~ sP45(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f14551]) ).
fof(f34266,plain,
spl647_869,
inference(avatar_split_clause,[],[f21323,f34264]) ).
fof(f34264,plain,
( spl647_869
<=> ! [X2,X0,X1] :
( sP44(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK384(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_869])]) ).
fof(f21323,plain,
! [X2,X0,X1] :
( sP44(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK384(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15876]) ).
fof(f34262,plain,
spl647_868,
inference(avatar_split_clause,[],[f21316,f34260]) ).
fof(f34260,plain,
( spl647_868
<=> ! [X2,X0,X1] :
( sP41(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK382(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_868])]) ).
fof(f21316,plain,
! [X2,X0,X1] :
( sP41(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK382(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15870]) ).
fof(f34258,plain,
spl647_867,
inference(avatar_split_clause,[],[f21310,f34256]) ).
fof(f34256,plain,
( spl647_867
<=> ! [X2,X0,X1] :
( sP42(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK380(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_867])]) ).
fof(f21310,plain,
! [X2,X0,X1] :
( sP42(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK380(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15864]) ).
fof(f34254,plain,
spl647_866,
inference(avatar_split_clause,[],[f21257,f34252]) ).
fof(f34252,plain,
( spl647_866
<=> ! [X2,X0,X1] :
( c_List_Olist__all(X2,X1,hAPP(c_List_Orev(X2),X0))
| ~ c_List_Olist__all(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_866])]) ).
fof(f21257,plain,
! [X2,X0,X1] :
( c_List_Olist__all(X2,X1,hAPP(c_List_Orev(X2),X0))
| ~ c_List_Olist__all(X2,X1,X0) ),
inference(cnf_transformation,[],[f15830]) ).
fof(f15830,plain,
! [X0,X1,X2] :
( ( c_List_Olist__all(X2,X1,hAPP(c_List_Orev(X2),X0))
| ~ c_List_Olist__all(X2,X1,X0) )
& ( c_List_Olist__all(X2,X1,X0)
| ~ c_List_Olist__all(X2,X1,hAPP(c_List_Orev(X2),X0)) ) ),
inference(nnf_transformation,[],[f8166]) ).
fof(f8166,plain,
! [X0,X1,X2] :
( c_List_Olist__all(X2,X1,hAPP(c_List_Orev(X2),X0))
<=> c_List_Olist__all(X2,X1,X0) ),
inference(rectify,[],[f4573]) ).
fof(f4573,axiom,
! [X203,X23,X4] :
( c_List_Olist__all(X4,X23,hAPP(c_List_Orev(X4),X203))
<=> c_List_Olist__all(X4,X23,X203) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34250,plain,
spl647_865,
inference(avatar_split_clause,[],[f21256,f34248]) ).
fof(f34248,plain,
( spl647_865
<=> ! [X2,X0,X1] :
( c_List_Olist__all(X2,X1,X0)
| ~ c_List_Olist__all(X2,X1,hAPP(c_List_Orev(X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_865])]) ).
fof(f21256,plain,
! [X2,X0,X1] :
( c_List_Olist__all(X2,X1,X0)
| ~ c_List_Olist__all(X2,X1,hAPP(c_List_Orev(X2),X0)) ),
inference(cnf_transformation,[],[f15830]) ).
fof(f34246,plain,
spl647_864,
inference(avatar_split_clause,[],[f21255,f34244]) ).
fof(f34244,plain,
( spl647_864
<=> ! [X2,X0,X1] :
( c_List_Olist__ex(X2,X1,hAPP(c_List_Orev(X2),X0))
| ~ c_List_Olist__ex(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_864])]) ).
fof(f21255,plain,
! [X2,X0,X1] :
( c_List_Olist__ex(X2,X1,hAPP(c_List_Orev(X2),X0))
| ~ c_List_Olist__ex(X2,X1,X0) ),
inference(cnf_transformation,[],[f15829]) ).
fof(f15829,plain,
! [X0,X1,X2] :
( ( c_List_Olist__ex(X2,X1,hAPP(c_List_Orev(X2),X0))
| ~ c_List_Olist__ex(X2,X1,X0) )
& ( c_List_Olist__ex(X2,X1,X0)
| ~ c_List_Olist__ex(X2,X1,hAPP(c_List_Orev(X2),X0)) ) ),
inference(nnf_transformation,[],[f8165]) ).
fof(f8165,plain,
! [X0,X1,X2] :
( c_List_Olist__ex(X2,X1,hAPP(c_List_Orev(X2),X0))
<=> c_List_Olist__ex(X2,X1,X0) ),
inference(rectify,[],[f4558]) ).
fof(f4558,axiom,
! [X203,X23,X4] :
( c_List_Olist__ex(X4,X23,hAPP(c_List_Orev(X4),X203))
<=> c_List_Olist__ex(X4,X23,X203) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34242,plain,
spl647_863,
inference(avatar_split_clause,[],[f21254,f34240]) ).
fof(f34240,plain,
( spl647_863
<=> ! [X2,X0,X1] :
( c_List_Olist__ex(X2,X1,X0)
| ~ c_List_Olist__ex(X2,X1,hAPP(c_List_Orev(X2),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_863])]) ).
fof(f21254,plain,
! [X2,X0,X1] :
( c_List_Olist__ex(X2,X1,X0)
| ~ c_List_Olist__ex(X2,X1,hAPP(c_List_Orev(X2),X0)) ),
inference(cnf_transformation,[],[f15829]) ).
fof(f34238,plain,
spl647_862,
inference(avatar_split_clause,[],[f21247,f34236]) ).
fof(f34236,plain,
( spl647_862
<=> ! [X2,X0,X1] :
( sP39(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_862])]) ).
fof(f21247,plain,
! [X2,X0,X1] :
( sP39(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f15826]) ).
fof(f34234,plain,
spl647_861,
inference(avatar_split_clause,[],[f21245,f34232]) ).
fof(f34232,plain,
( spl647_861
<=> ! [X2,X0,X1] :
( sP39(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK376(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_861])]) ).
fof(f21245,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK376(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15824]) ).
fof(f34230,plain,
spl647_860,
inference(avatar_split_clause,[],[f21240,f34228]) ).
fof(f34228,plain,
( spl647_860
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
| ~ sP38(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_860])]) ).
fof(f21240,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
| ~ sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f15819]) ).
fof(f15819,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
| ~ sP38(X0,X1,X2) )
& ( sP38(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))) ) ),
inference(nnf_transformation,[],[f14540]) ).
fof(f14540,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
<=> sP38(X0,X1,X2) ),
inference(definition_folding,[],[f12612,f14539,f14538,f14537]) ).
fof(f14539,plain,
! [X0,X1,X2] :
( sP38(X0,X1,X2)
<=> ( sP37(X2,X1,X0)
& sP36(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP38])]) ).
fof(f12612,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
<=> ( ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X2,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
inference(flattening,[],[f12611]) ).
fof(f12611,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
<=> ( ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X2,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
inference(ennf_transformation,[],[f8161]) ).
fof(f8161,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X3,X4] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X4),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X4)) )
=> hBOOL(hAPP(X2,X4)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> ! [X5,X6] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X5)),X6) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X6),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X6)) )
=> hBOOL(hAPP(X2,X6)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
=> hBOOL(hAPP(X2,X1)) ) ) ),
inference(rectify,[],[f1713]) ).
fof(f1713,axiom,
! [X48,X46,X23] :
( hBOOL(hAPP(X23,c_Divides_Odiv__class_Omod(tc_Int_Oint,X46,X48)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X86,X83] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X86)),X83) = X46
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X83),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),X83)) )
=> hBOOL(hAPP(X23,X83)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))
=> ! [X86,X83] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X86)),X83) = X46
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X83),X48))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X83)) )
=> hBOOL(hAPP(X23,X83)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X48
=> hBOOL(hAPP(X23,X46)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34226,plain,
spl647_859,
inference(avatar_split_clause,[],[f21239,f34224]) ).
fof(f34224,plain,
( spl647_859
<=> ! [X2,X0,X1] :
( sP38(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_859])]) ).
fof(f21239,plain,
! [X2,X0,X1] :
( sP38(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))) ),
inference(cnf_transformation,[],[f15819]) ).
fof(f34222,plain,
spl647_858,
inference(avatar_split_clause,[],[f21238,f34220]) ).
fof(f34220,plain,
( spl647_858
<=> ! [X2,X0,X1] :
( sP36(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK374(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_858])]) ).
fof(f21238,plain,
! [X2,X0,X1] :
( sP36(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK374(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15818]) ).
fof(f34218,plain,
spl647_857,
inference(avatar_split_clause,[],[f21232,f34216]) ).
fof(f34216,plain,
( spl647_857
<=> ! [X2,X0,X1] :
( sP37(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK372(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_857])]) ).
fof(f21232,plain,
! [X2,X0,X1] :
( sP37(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK372(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15813]) ).
fof(f34214,plain,
spl647_856,
inference(avatar_split_clause,[],[f21144,f34212]) ).
fof(f34212,plain,
( spl647_856
<=> ! [X2,X0,X1] :
( c_List_Olist__all(X2,X1,X0)
| ~ hBOOL(hAPP(X1,sK356(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_856])]) ).
fof(f21144,plain,
! [X2,X0,X1] :
( c_List_Olist__all(X2,X1,X0)
| ~ hBOOL(hAPP(X1,sK356(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15741]) ).
fof(f15741,plain,
! [X0,X1,X2] :
( ( c_List_Olist__all(X2,X1,X0)
| ( ~ hBOOL(hAPP(X1,sK356(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK356(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olist__all(X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK356])],[f15739,f15740]) ).
fof(f15740,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
=> ( ~ hBOOL(hAPP(X1,sK356(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK356(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15739,plain,
! [X0,X1,X2] :
( ( c_List_Olist__all(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olist__all(X2,X1,X0) ) ),
inference(rectify,[],[f15738]) ).
fof(f15738,plain,
! [X0,X1,X2] :
( ( c_List_Olist__all(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X3] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olist__all(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f12598]) ).
fof(f12598,plain,
! [X0,X1,X2] :
( c_List_Olist__all(X2,X1,X0)
<=> ! [X3] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
inference(ennf_transformation,[],[f8139]) ).
fof(f8139,plain,
! [X0,X1,X2] :
( c_List_Olist__all(X2,X1,X0)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0)))
=> hBOOL(hAPP(X1,X3)) ) ),
inference(rectify,[],[f4570]) ).
fof(f4570,axiom,
! [X203,X23,X4] :
( c_List_Olist__all(X4,X23,X203)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X203)))
=> hBOOL(hAPP(X23,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34210,plain,
spl647_855,
inference(avatar_split_clause,[],[f21141,f34208]) ).
fof(f34208,plain,
( spl647_855
<=> ! [X2,X0,X1] :
( c_List_Olist__all(X2,X1,X0)
| ~ hBOOL(hAPP(X1,sK355(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_855])]) ).
fof(f21141,plain,
! [X2,X0,X1] :
( c_List_Olist__all(X2,X1,X0)
| ~ hBOOL(hAPP(X1,sK355(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15737]) ).
fof(f15737,plain,
! [X0,X1,X2] :
( ( c_List_Olist__all(X2,X1,X0)
| ( ~ hBOOL(hAPP(X1,sK355(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK355(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olist__all(X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK355])],[f15735,f15736]) ).
fof(f15736,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
=> ( ~ hBOOL(hAPP(X1,sK355(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK355(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15735,plain,
! [X0,X1,X2] :
( ( c_List_Olist__all(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olist__all(X2,X1,X0) ) ),
inference(rectify,[],[f15734]) ).
fof(f15734,plain,
! [X0,X1,X2] :
( ( c_List_Olist__all(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ! [X3] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olist__all(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f12597]) ).
fof(f12597,plain,
! [X0,X1,X2] :
( c_List_Olist__all(X2,X1,X0)
<=> ! [X3] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
inference(ennf_transformation,[],[f8138]) ).
fof(f8138,plain,
! [X0,X1,X2] :
( c_List_Olist__all(X2,X1,X0)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0)))
=> hBOOL(hAPP(X1,X3)) ) ),
inference(rectify,[],[f4576]) ).
fof(f4576,axiom,
! [X203,X23,X4] :
( c_List_Olist__all(X4,X23,X203)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X203)))
=> hBOOL(hAPP(X23,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34206,plain,
spl647_854,
inference(avatar_split_clause,[],[f21128,f34204]) ).
fof(f34204,plain,
( spl647_854
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X1,sK351(X0,X1,X2)))
| ~ c_List_Olist__ex(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_854])]) ).
fof(f21128,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X1,sK351(X0,X1,X2)))
| ~ c_List_Olist__ex(X2,X1,X0) ),
inference(cnf_transformation,[],[f15724]) ).
fof(f15724,plain,
! [X0,X1,X2] :
( ( c_List_Olist__ex(X2,X1,X0)
| ! [X3] :
( ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ( hBOOL(hAPP(X1,sK351(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK351(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olist__ex(X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK351])],[f15722,f15723]) ).
fof(f15723,plain,
! [X0,X1,X2] :
( ? [X4] :
( hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
=> ( hBOOL(hAPP(X1,sK351(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK351(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15722,plain,
! [X0,X1,X2] :
( ( c_List_Olist__ex(X2,X1,X0)
| ! [X3] :
( ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ? [X4] :
( hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olist__ex(X2,X1,X0) ) ),
inference(rectify,[],[f15721]) ).
fof(f15721,plain,
! [X0,X1,X2] :
( ( c_List_Olist__ex(X2,X1,X0)
| ! [X3] :
( ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ? [X3] :
( hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olist__ex(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f8135]) ).
fof(f8135,plain,
! [X0,X1,X2] :
( c_List_Olist__ex(X2,X1,X0)
<=> ? [X3] :
( hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
inference(rectify,[],[f4692]) ).
fof(f4692,axiom,
! [X203,X23,X4] :
( c_List_Olist__ex(X4,X23,X203)
<=> ? [X2] :
( hBOOL(hAPP(X23,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X203))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34202,plain,
spl647_853,
inference(avatar_split_clause,[],[f21125,f34200]) ).
fof(f34200,plain,
( spl647_853
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X1,sK350(X0,X1,X2)))
| ~ c_List_Olist__ex(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_853])]) ).
fof(f21125,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X1,sK350(X0,X1,X2)))
| ~ c_List_Olist__ex(X2,X1,X0) ),
inference(cnf_transformation,[],[f15720]) ).
fof(f15720,plain,
! [X0,X1,X2] :
( ( c_List_Olist__ex(X2,X1,X0)
| ! [X3] :
( ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ( hBOOL(hAPP(X1,sK350(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK350(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olist__ex(X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK350])],[f15718,f15719]) ).
fof(f15719,plain,
! [X0,X1,X2] :
( ? [X4] :
( hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
=> ( hBOOL(hAPP(X1,sK350(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK350(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15718,plain,
! [X0,X1,X2] :
( ( c_List_Olist__ex(X2,X1,X0)
| ! [X3] :
( ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ? [X4] :
( hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olist__ex(X2,X1,X0) ) ),
inference(rectify,[],[f15717]) ).
fof(f15717,plain,
! [X0,X1,X2] :
( ( c_List_Olist__ex(X2,X1,X0)
| ! [X3] :
( ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) )
& ( ? [X3] :
( hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olist__ex(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f8134]) ).
fof(f8134,plain,
! [X0,X1,X2] :
( c_List_Olist__ex(X2,X1,X0)
<=> ? [X3] :
( hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
inference(rectify,[],[f4557]) ).
fof(f4557,axiom,
! [X203,X23,X4] :
( c_List_Olist__ex(X4,X23,X203)
<=> ? [X2] :
( hBOOL(hAPP(X23,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X203))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34198,plain,
spl647_852,
inference(avatar_split_clause,[],[f21117,f34196]) ).
fof(f34196,plain,
( spl647_852
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK349(X0,X1,X2)))
| ~ sP32(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_852])]) ).
fof(f21117,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK349(X0,X1,X2)))
| ~ sP32(X0,X1,X2) ),
inference(cnf_transformation,[],[f15715]) ).
fof(f15715,plain,
! [X0,X1,X2] :
( ( sP32(X0,X1,X2)
| ! [X3] :
( ( sK348(X0,X1,X2,X3) != X3
& hBOOL(hAPP(X0,sK348(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X2),sK348(X0,X1,X2,X3)),hAPP(c_List_Oset(X2),X1))) )
| ~ hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) ) )
& ( ( ! [X6] :
( sK349(X0,X1,X2) = X6
| ~ hBOOL(hAPP(X0,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),hAPP(c_List_Oset(X2),X1))) )
& hBOOL(hAPP(X0,sK349(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK349(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) )
| ~ sP32(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK348,sK349])],[f15712,f15714,f15713]) ).
fof(f15713,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( X3 != X4
& hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X1))) )
=> ( sK348(X0,X1,X2,X3) != X3
& hBOOL(hAPP(X0,sK348(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X2),sK348(X0,X1,X2,X3)),hAPP(c_List_Oset(X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15714,plain,
! [X0,X1,X2] :
( ? [X5] :
( ! [X6] :
( X5 = X6
| ~ hBOOL(hAPP(X0,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),hAPP(c_List_Oset(X2),X1))) )
& hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_List_Oset(X2),X1))) )
=> ( ! [X6] :
( sK349(X0,X1,X2) = X6
| ~ hBOOL(hAPP(X0,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),hAPP(c_List_Oset(X2),X1))) )
& hBOOL(hAPP(X0,sK349(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK349(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15712,plain,
! [X0,X1,X2] :
( ( sP32(X0,X1,X2)
| ! [X3] :
( ? [X4] :
( X3 != X4
& hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X1))) )
| ~ hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) ) )
& ( ? [X5] :
( ! [X6] :
( X5 = X6
| ~ hBOOL(hAPP(X0,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),hAPP(c_List_Oset(X2),X1))) )
& hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_List_Oset(X2),X1))) )
| ~ sP32(X0,X1,X2) ) ),
inference(rectify,[],[f15711]) ).
fof(f15711,plain,
! [X1,X0,X2] :
( ( sP32(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))) ) )
& ( ? [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))) )
| ~ sP32(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f14530]) ).
fof(f14530,plain,
! [X1,X0,X2] :
( sP32(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,[sP32])]) ).
fof(f34194,plain,
spl647_851,
inference(avatar_split_clause,[],[f21109,f34192]) ).
fof(f34192,plain,
( spl647_851
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK347(X0,X1,X2)))
| ~ sP31(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_851])]) ).
fof(f21109,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK347(X0,X1,X2)))
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f15709]) ).
fof(f15709,plain,
! [X0,X1,X2] :
( ( sP31(X0,X1,X2)
| ! [X3] :
( ( sK346(X0,X1,X2,X3) != X3
& hBOOL(hAPP(X0,sK346(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X2),sK346(X0,X1,X2,X3)),hAPP(c_List_Oset(X2),X1))) )
| ~ hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) ) )
& ( ( ! [X6] :
( sK347(X0,X1,X2) = X6
| ~ hBOOL(hAPP(X0,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),hAPP(c_List_Oset(X2),X1))) )
& hBOOL(hAPP(X0,sK347(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK347(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) )
| ~ sP31(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK346,sK347])],[f15706,f15708,f15707]) ).
fof(f15707,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( X3 != X4
& hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X1))) )
=> ( sK346(X0,X1,X2,X3) != X3
& hBOOL(hAPP(X0,sK346(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X2),sK346(X0,X1,X2,X3)),hAPP(c_List_Oset(X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15708,plain,
! [X0,X1,X2] :
( ? [X5] :
( ! [X6] :
( X5 = X6
| ~ hBOOL(hAPP(X0,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),hAPP(c_List_Oset(X2),X1))) )
& hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_List_Oset(X2),X1))) )
=> ( ! [X6] :
( sK347(X0,X1,X2) = X6
| ~ hBOOL(hAPP(X0,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),hAPP(c_List_Oset(X2),X1))) )
& hBOOL(hAPP(X0,sK347(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK347(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15706,plain,
! [X0,X1,X2] :
( ( sP31(X0,X1,X2)
| ! [X3] :
( ? [X4] :
( X3 != X4
& hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X1))) )
| ~ hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) ) )
& ( ? [X5] :
( ! [X6] :
( X5 = X6
| ~ hBOOL(hAPP(X0,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),hAPP(c_List_Oset(X2),X1))) )
& hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(hAPP(c_member(X2),X5),hAPP(c_List_Oset(X2),X1))) )
| ~ sP31(X0,X1,X2) ) ),
inference(rectify,[],[f15705]) ).
fof(f15705,plain,
! [X1,X0,X2] :
( ( sP31(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))) ) )
& ( ? [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))) )
| ~ sP31(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f14528]) ).
fof(f14528,plain,
! [X1,X0,X2] :
( sP31(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,[sP31])]) ).
fof(f34190,plain,
spl647_850,
inference(avatar_split_clause,[],[f21107,f34188]) ).
fof(f34188,plain,
( spl647_850
<=> ! [X2,X0,X1] :
( c_List_Oall__interval__nat(X2,X1,X0)
| ~ hBOOL(hAPP(X2,sK345(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_850])]) ).
fof(f21107,plain,
! [X2,X0,X1] :
( c_List_Oall__interval__nat(X2,X1,X0)
| ~ hBOOL(hAPP(X2,sK345(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15704]) ).
fof(f15704,plain,
! [X0,X1,X2] :
( ( c_List_Oall__interval__nat(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,sK345(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK345(X0,X1,X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) )
| ~ c_List_Oall__interval__nat(X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK345])],[f15702,f15703]) ).
fof(f15703,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) )
=> ( ~ hBOOL(hAPP(X2,sK345(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK345(X0,X1,X2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15702,plain,
! [X0,X1,X2] :
( ( c_List_Oall__interval__nat(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) )
| ~ c_List_Oall__interval__nat(X2,X1,X0) ) ),
inference(rectify,[],[f15701]) ).
fof(f15701,plain,
! [X0,X1,X2] :
( ( c_List_Oall__interval__nat(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) ) )
& ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) )
| ~ c_List_Oall__interval__nat(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f12590]) ).
fof(f12590,plain,
! [X0,X1,X2] :
( c_List_Oall__interval__nat(X2,X1,X0)
<=> ! [X3] :
( hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) ) ),
inference(ennf_transformation,[],[f8131]) ).
fof(f8131,plain,
! [X0,X1,X2] :
( c_List_Oall__interval__nat(X2,X1,X0)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X3),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0)))
=> hBOOL(hAPP(X2,X3)) ) ),
inference(rectify,[],[f4868]) ).
fof(f4868,axiom,
! [X62,X63,X23] :
( c_List_Oall__interval__nat(X23,X63,X62)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X63),X62)))
=> hBOOL(hAPP(X23,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34186,plain,
spl647_849,
inference(avatar_split_clause,[],[f21104,f34184]) ).
fof(f34184,plain,
( spl647_849
<=> ! [X2,X0,X1] :
( c_List_Oall__interval__int(X2,X1,X0)
| ~ hBOOL(hAPP(X2,sK344(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_849])]) ).
fof(f21104,plain,
! [X2,X0,X1] :
( c_List_Oall__interval__int(X2,X1,X0)
| ~ hBOOL(hAPP(X2,sK344(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15700]) ).
fof(f15700,plain,
! [X0,X1,X2] :
( ( c_List_Oall__interval__int(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,sK344(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK344(X0,X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))) )
| ~ c_List_Oall__interval__int(X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK344])],[f15698,f15699]) ).
fof(f15699,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))) )
=> ( ~ hBOOL(hAPP(X2,sK344(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK344(X0,X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15698,plain,
! [X0,X1,X2] :
( ( c_List_Oall__interval__int(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X4),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))) )
| ~ c_List_Oall__interval__int(X2,X1,X0) ) ),
inference(rectify,[],[f15697]) ).
fof(f15697,plain,
! [X0,X1,X2] :
( ( c_List_Oall__interval__int(X2,X1,X0)
| ? [X3] :
( ~ hBOOL(hAPP(X2,X3))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))) ) )
& ( ! [X3] :
( hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))) )
| ~ c_List_Oall__interval__int(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f12589]) ).
fof(f12589,plain,
! [X0,X1,X2] :
( c_List_Oall__interval__int(X2,X1,X0)
<=> ! [X3] :
( hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))) ) ),
inference(ennf_transformation,[],[f8130]) ).
fof(f8130,plain,
! [X0,X1,X2] :
( c_List_Oall__interval__int(X2,X1,X0)
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X3),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0)))
=> hBOOL(hAPP(X2,X3)) ) ),
inference(rectify,[],[f4685]) ).
fof(f4685,axiom,
! [X62,X63,X23] :
( c_List_Oall__interval__int(X23,X63,X62)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X63,X62)))
=> hBOOL(hAPP(X23,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34182,plain,
spl647_848,
inference(avatar_split_clause,[],[f21049,f34180]) ).
fof(f34180,plain,
( spl647_848
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
| ~ sP30(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_848])]) ).
fof(f21049,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
| ~ sP30(X0,X1,X2) ),
inference(cnf_transformation,[],[f15644]) ).
fof(f15644,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1)) )
| ~ sP30(X0,X1,X2) ),
inference(rectify,[],[f15643]) ).
fof(f15643,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) )
| ~ sP30(X2,X1,X0) ),
inference(nnf_transformation,[],[f14526]) ).
fof(f14526,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) )
| ~ sP30(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP30])]) ).
fof(f34178,plain,
spl647_847,
inference(avatar_split_clause,[],[f20575,f34176]) ).
fof(f34176,plain,
( spl647_847
<=> ! [X2,X0,X1] :
( c_Wellfounded_Owf(tc_List_Olist(X2),hAPP(c_List_Olexn(X2,X1),X0))
| ~ c_Wellfounded_Owf(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_847])]) ).
fof(f20575,plain,
! [X2,X0,X1] :
( c_Wellfounded_Owf(tc_List_Olist(X2),hAPP(c_List_Olexn(X2,X1),X0))
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(cnf_transformation,[],[f12095]) ).
fof(f12095,plain,
! [X0,X1,X2] :
( c_Wellfounded_Owf(tc_List_Olist(X2),hAPP(c_List_Olexn(X2,X1),X0))
| ~ c_Wellfounded_Owf(X2,X1) ),
inference(ennf_transformation,[],[f7769]) ).
fof(f7769,plain,
! [X0,X1,X2] :
( c_Wellfounded_Owf(X2,X1)
=> c_Wellfounded_Owf(tc_List_Olist(X2),hAPP(c_List_Olexn(X2,X1),X0)) ),
inference(rectify,[],[f3412]) ).
fof(f3412,axiom,
! [X46,X116,X4] :
( c_Wellfounded_Owf(X4,X116)
=> c_Wellfounded_Owf(tc_List_Olist(X4),hAPP(c_List_Olexn(X4,X116),X46)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34174,plain,
spl647_846,
inference(avatar_split_clause,[],[f20243,f34172]) ).
fof(f34172,plain,
( spl647_846
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,c_List_OtakeWhile(X2,X0,X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_846])]) ).
fof(f20243,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,c_List_OtakeWhile(X2,X0,X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f11682]) ).
fof(f11682,plain,
! [X0,X1,X2] :
( c_List_Olinorder__class_Osorted(X2,c_List_OtakeWhile(X2,X0,X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f11681]) ).
fof(f11681,plain,
! [X0,X1,X2] :
( c_List_Olinorder__class_Osorted(X2,c_List_OtakeWhile(X2,X0,X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7523]) ).
fof(f7523,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_List_Olinorder__class_Osorted(X2,X1)
=> c_List_Olinorder__class_Osorted(X2,c_List_OtakeWhile(X2,X0,X1)) ) ),
inference(rectify,[],[f4473]) ).
fof(f4473,axiom,
! [X23,X203,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_List_Olinorder__class_Osorted(X4,X203)
=> c_List_Olinorder__class_Osorted(X4,c_List_OtakeWhile(X4,X23,X203)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34170,plain,
spl647_845,
inference(avatar_split_clause,[],[f20242,f34168]) ).
fof(f34168,plain,
( spl647_845
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,c_List_Oremove1(X2,X0,X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_845])]) ).
fof(f20242,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X2,c_List_Oremove1(X2,X0,X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f11680]) ).
fof(f11680,plain,
! [X0,X1,X2] :
( c_List_Olinorder__class_Osorted(X2,c_List_Oremove1(X2,X0,X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f11679]) ).
fof(f11679,plain,
! [X0,X1,X2] :
( c_List_Olinorder__class_Osorted(X2,c_List_Oremove1(X2,X0,X1))
| ~ c_List_Olinorder__class_Osorted(X2,X1)
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7522]) ).
fof(f7522,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_List_Olinorder__class_Osorted(X2,X1)
=> c_List_Olinorder__class_Osorted(X2,c_List_Oremove1(X2,X0,X1)) ) ),
inference(rectify,[],[f4407]) ).
fof(f4407,axiom,
! [X26,X201,X20] :
( class_Orderings_Olinorder(X20)
=> ( c_List_Olinorder__class_Osorted(X20,X201)
=> c_List_Olinorder__class_Osorted(X20,c_List_Oremove1(X20,X26,X201)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34166,plain,
spl647_844,
inference(avatar_split_clause,[],[f20215,f34164]) ).
fof(f34164,plain,
( spl647_844
<=> ! [X2,X0,X1] :
( c_List_Olist_ONil(X1) = c_List_Olinorder__class_Osort__key(X1,X2,X0,c_List_Olist_ONil(X1))
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_844])]) ).
fof(f20215,plain,
! [X2,X0,X1] :
( c_List_Olist_ONil(X1) = c_List_Olinorder__class_Osort__key(X1,X2,X0,c_List_Olist_ONil(X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f11647]) ).
fof(f11647,plain,
! [X0,X1,X2] :
( c_List_Olist_ONil(X1) = c_List_Olinorder__class_Osort__key(X1,X2,X0,c_List_Olist_ONil(X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7495]) ).
fof(f7495,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> c_List_Olist_ONil(X1) = c_List_Olinorder__class_Osort__key(X1,X2,X0,c_List_Olist_ONil(X1)) ),
inference(rectify,[],[f4294]) ).
fof(f4294,axiom,
! [X1,X4,X14] :
( class_Orderings_Olinorder(X14)
=> c_List_Olist_ONil(X4) = c_List_Olinorder__class_Osort__key(X4,X14,X1,c_List_Olist_ONil(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34162,plain,
spl647_843,
inference(avatar_split_clause,[],[f20109,f34160]) ).
fof(f34160,plain,
( spl647_843
<=> ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(X2) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),X0)
| ~ class_Orderings_Obot(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_843])]) ).
fof(f20109,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(X2) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),X0)
| ~ class_Orderings_Obot(X2) ),
inference(cnf_transformation,[],[f11498]) ).
fof(f11498,plain,
! [X0,X1,X2] :
( c_Orderings_Obot__class_Obot(X2) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),X0)
| ~ class_Orderings_Obot(X2) ),
inference(ennf_transformation,[],[f7396]) ).
fof(f7396,plain,
! [X0,X1,X2] :
( class_Orderings_Obot(X2)
=> c_Orderings_Obot__class_Obot(X2) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X2)),X0) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X13,X14,X4] :
( class_Orderings_Obot(X4)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X14,X4)),X13) = c_Orderings_Obot__class_Obot(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34158,plain,
spl647_842,
inference(avatar_split_clause,[],[f20072,f34156]) ).
fof(f34156,plain,
( spl647_842
<=> ! [X2,X0,X1] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X0) = c_Orderings_Otop__class_Otop(X2)
| ~ class_Orderings_Otop(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_842])]) ).
fof(f20072,plain,
! [X2,X0,X1] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X0) = c_Orderings_Otop__class_Otop(X2)
| ~ class_Orderings_Otop(X2) ),
inference(cnf_transformation,[],[f11465]) ).
fof(f11465,plain,
! [X0,X1,X2] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X0) = c_Orderings_Otop__class_Otop(X2)
| ~ class_Orderings_Otop(X2) ),
inference(ennf_transformation,[],[f7371]) ).
fof(f7371,plain,
! [X0,X1,X2] :
( class_Orderings_Otop(X2)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X0) = c_Orderings_Otop__class_Otop(X2) ),
inference(rectify,[],[f2082]) ).
fof(f2082,axiom,
! [X13,X14,X4] :
( class_Orderings_Otop(X4)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X14,X4)),X13) = c_Orderings_Otop__class_Otop(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34154,plain,
spl647_841,
inference(avatar_split_clause,[],[f19889,f34152]) ).
fof(f34152,plain,
( spl647_841
<=> ! [X2,X0,X1] :
( c_FunDef_OTHE__default(X1,X0,X2) = X0
| hBOOL(hAPP(X2,sK220(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_841])]) ).
fof(f19889,plain,
! [X2,X0,X1] :
( c_FunDef_OTHE__default(X1,X0,X2) = X0
| hBOOL(hAPP(X2,sK220(X2))) ),
inference(cnf_transformation,[],[f15305]) ).
fof(f34150,plain,
spl647_840,
inference(avatar_split_clause,[],[f19604,f34148]) ).
fof(f34148,plain,
( spl647_840
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Relation_Orel__comp(X2,X2,X1),c_Relation_OId(X2)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_840])]) ).
fof(f19604,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Relation_Orel__comp(X2,X2,X1),c_Relation_OId(X2)),X0) = X0,
inference(cnf_transformation,[],[f6958]) ).
fof(f6958,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Relation_Orel__comp(X2,X2,X1),c_Relation_OId(X2)),X0) = X0,
inference(rectify,[],[f3595]) ).
fof(f3595,axiom,
! [X138,X14,X4] : hAPP(hAPP(c_Relation_Orel__comp(X4,X4,X14),c_Relation_OId(X4)),X138) = X138,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34146,plain,
spl647_839,
inference(avatar_split_clause,[],[f19603,f34144]) ).
fof(f34144,plain,
( spl647_839
<=> ! [X2,X0,X1] : hAPP(hAPP(c_Relation_Orel__comp(X2,X1,X1),X0),c_Relation_OId(X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_839])]) ).
fof(f19603,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Relation_Orel__comp(X2,X1,X1),X0),c_Relation_OId(X1)) = X0,
inference(cnf_transformation,[],[f6957]) ).
fof(f6957,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Relation_Orel__comp(X2,X1,X1),X0),c_Relation_OId(X1)) = X0,
inference(rectify,[],[f3596]) ).
fof(f3596,axiom,
! [X138,X14,X4] : hAPP(hAPP(c_Relation_Orel__comp(X4,X14,X14),X138),c_Relation_OId(X14)) = X138,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34142,plain,
spl647_838,
inference(avatar_split_clause,[],[f19602,f34140]) ).
fof(f34140,plain,
( spl647_838
<=> ! [X2,X0,X1] : hAPP(c_Relation_Oconverse(X2,X1),hAPP(c_Relation_Oconverse(X1,X2),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_838])]) ).
fof(f19602,plain,
! [X2,X0,X1] : hAPP(c_Relation_Oconverse(X2,X1),hAPP(c_Relation_Oconverse(X1,X2),X0)) = X0,
inference(cnf_transformation,[],[f6956]) ).
fof(f6956,plain,
! [X0,X1,X2] : hAPP(c_Relation_Oconverse(X2,X1),hAPP(c_Relation_Oconverse(X1,X2),X0)) = X0,
inference(rectify,[],[f3630]) ).
fof(f3630,axiom,
! [X116,X4,X14] : hAPP(c_Relation_Oconverse(X14,X4),hAPP(c_Relation_Oconverse(X4,X14),X116)) = X116,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34138,plain,
spl647_837,
inference(avatar_split_clause,[],[f19601,f34136]) ).
fof(f34136,plain,
( spl647_837
<=> ! [X2,X0,X1] : hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_837])]) ).
fof(f19601,plain,
! [X2,X0,X1] : hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X0,
inference(cnf_transformation,[],[f6955]) ).
fof(f6955,plain,
! [X0,X1,X2] : hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X0,
inference(rectify,[],[f4036]) ).
fof(f4036,axiom,
! [X201,X19,X20] : hAPP(c_List_Otl(X20),hAPP(hAPP(c_List_Olist_OCons(X20),X19),X201)) = X201,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34134,plain,
spl647_836,
inference(avatar_split_clause,[],[f19600,f34132]) ).
fof(f34132,plain,
( spl647_836
<=> ! [X2,X0,X1] : hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_836])]) ).
fof(f19600,plain,
! [X2,X0,X1] : hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X1,
inference(cnf_transformation,[],[f6954]) ).
fof(f6954,plain,
! [X0,X1,X2] : hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X1,
inference(rectify,[],[f4027]) ).
fof(f4027,axiom,
! [X201,X19,X20] : hAPP(c_List_Ohd(X20),hAPP(hAPP(c_List_Olist_OCons(X20),X19),X201)) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34130,plain,
spl647_835,
inference(avatar_split_clause,[],[f19599,f34128]) ).
fof(f34128,plain,
( spl647_835
<=> ! [X2,X0,X1] : c_List_Olist_ONil(tc_prod(X2,X1)) = c_Enum_Oproduct(X2,X1,c_List_Olist_ONil(X2),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_835])]) ).
fof(f19599,plain,
! [X2,X0,X1] : c_List_Olist_ONil(tc_prod(X2,X1)) = c_Enum_Oproduct(X2,X1,c_List_Olist_ONil(X2),X0),
inference(cnf_transformation,[],[f6953]) ).
fof(f6953,plain,
! [X0,X1,X2] : c_List_Olist_ONil(tc_prod(X2,X1)) = c_Enum_Oproduct(X2,X1,c_List_Olist_ONil(X2),X0),
inference(rectify,[],[f4245]) ).
fof(f4245,axiom,
! [X237,X4,X20] : c_List_Olist_ONil(tc_prod(X20,X4)) = c_Enum_Oproduct(X20,X4,c_List_Olist_ONil(X20),X237),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34126,plain,
spl647_834,
inference(avatar_split_clause,[],[f19597,f34124]) ).
fof(f34124,plain,
( spl647_834
<=> ! [X2,X0,X1] : c_List_Olist_ONil(X2) = hAPP(hAPP(c_List_Olist__update(X2,c_List_Olist_ONil(X2)),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_834])]) ).
fof(f19597,plain,
! [X2,X0,X1] : c_List_Olist_ONil(X2) = hAPP(hAPP(c_List_Olist__update(X2,c_List_Olist_ONil(X2)),X1),X0),
inference(cnf_transformation,[],[f6951]) ).
fof(f6951,plain,
! [X0,X1,X2] : c_List_Olist_ONil(X2) = hAPP(hAPP(c_List_Olist__update(X2,c_List_Olist_ONil(X2)),X1),X0),
inference(rectify,[],[f3904]) ).
fof(f3904,axiom,
! [X21,X55,X20] : c_List_Olist_ONil(X20) = hAPP(hAPP(c_List_Olist__update(X20,c_List_Olist_ONil(X20)),X55),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34122,plain,
spl647_833,
inference(avatar_split_clause,[],[f19596,f34120]) ).
fof(f34120,plain,
( spl647_833
<=> ! [X2,X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Omap(X2,X1),X0),c_List_Olist_ONil(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_833])]) ).
fof(f19596,plain,
! [X2,X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Omap(X2,X1),X0),c_List_Olist_ONil(X2)),
inference(cnf_transformation,[],[f6950]) ).
fof(f6950,plain,
! [X0,X1,X2] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Omap(X2,X1),X0),c_List_Olist_ONil(X2)),
inference(rectify,[],[f4128]) ).
fof(f4128,axiom,
! [X1,X4,X14] : c_List_Olist_ONil(X4) = hAPP(hAPP(c_List_Omap(X14,X4),X1),c_List_Olist_ONil(X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34118,plain,
spl647_832,
inference(avatar_split_clause,[],[f19594,f34116]) ).
fof(f34116,plain,
( spl647_832
<=> ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X2),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_832])]) ).
fof(f19594,plain,
! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X2),X1),X0),
inference(cnf_transformation,[],[f6948]) ).
fof(f6948,plain,
! [X0,X1,X2] : c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X2),X1),X0),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X9,X5,X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X4),X5),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34114,plain,
spl647_831,
inference(avatar_split_clause,[],[f19199,f34112]) ).
fof(f34112,plain,
( spl647_831
<=> ! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != hAPP(c_List_Orev(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_831])]) ).
fof(f19199,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != hAPP(c_List_Orev(X1),X0) ),
inference(cnf_transformation,[],[f15058]) ).
fof(f15058,plain,
! [X0,X1] :
( ( c_List_Olist_ONil(X1) = hAPP(c_List_Orev(X1),X0)
| c_List_Olist_ONil(X1) != X0 )
& ( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != hAPP(c_List_Orev(X1),X0) ) ),
inference(nnf_transformation,[],[f6783]) ).
fof(f6783,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = hAPP(c_List_Orev(X1),X0)
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f4438]) ).
fof(f4438,axiom,
! [X203,X4] :
( c_List_Olist_ONil(X4) = hAPP(c_List_Orev(X4),X203)
<=> c_List_Olist_ONil(X4) = X203 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34110,plain,
spl647_830,
inference(avatar_split_clause,[],[f19197,f34108]) ).
fof(f34108,plain,
( spl647_830
<=> ! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != hAPP(c_List_Orotate1(X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_830])]) ).
fof(f19197,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != hAPP(c_List_Orotate1(X1),X0) ),
inference(cnf_transformation,[],[f15057]) ).
fof(f15057,plain,
! [X0,X1] :
( ( c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),X0)
| c_List_Olist_ONil(X1) != X0 )
& ( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != hAPP(c_List_Orotate1(X1),X0) ) ),
inference(nnf_transformation,[],[f6782]) ).
fof(f6782,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),X0)
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f4006]) ).
fof(f4006,axiom,
! [X203,X4] :
( c_List_Olist_ONil(X4) = hAPP(c_List_Orotate1(X4),X203)
<=> c_List_Olist_ONil(X4) = X203 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34106,plain,
spl647_829,
inference(avatar_split_clause,[],[f19187,f34104]) ).
fof(f19187,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,sK196(X1)))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ),
inference(cnf_transformation,[],[f15046]) ).
fof(f15046,plain,
! [X0,X1] :
( ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ! [X2] : ~ hBOOL(hAPP(X1,X2)) )
& ( hBOOL(hAPP(X1,sK196(X1)))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK196])],[f15044,f15045]) ).
fof(f15045,plain,
! [X1] :
( ? [X3] : hBOOL(hAPP(X1,X3))
=> hBOOL(hAPP(X1,sK196(X1))) ),
introduced(choice_axiom,[]) ).
fof(f15044,plain,
! [X0,X1] :
( ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ! [X2] : ~ hBOOL(hAPP(X1,X2)) )
& ( ? [X3] : hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ) ),
inference(rectify,[],[f15043]) ).
fof(f15043,plain,
! [X0,X1] :
( ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ! [X2] : ~ hBOOL(hAPP(X1,X2)) )
& ( ? [X2] : hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ) ),
inference(nnf_transformation,[],[f6777]) ).
fof(f6777,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
<=> ? [X2] : hBOOL(hAPP(X1,X2)) ),
inference(rectify,[],[f3519]) ).
fof(f3519,axiom,
! [X4,X23] :
( hBOOL(hAPP(X23,c_Hilbert__Choice_OEps(X4,X23)))
<=> ? [X124] : hBOOL(hAPP(X23,X124)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34102,plain,
spl647_828,
inference(avatar_split_clause,[],[f19100,f34100]) ).
fof(f34100,plain,
( spl647_828
<=> ! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK171(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_828])]) ).
fof(f19100,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK171(X0,X1))) ),
inference(cnf_transformation,[],[f14962]) ).
fof(f14962,plain,
! [X0,X1] :
( ( c_Wellfounded_OwfP(X1,X0)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK171(X0,X1))) )
& ( ! [X3] : hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK171])],[f14960,f14961]) ).
fof(f14961,plain,
! [X0,X1] :
( ? [X2] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2))
=> ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK171(X0,X1))) ),
introduced(choice_axiom,[]) ).
fof(f14960,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,[],[f14959]) ).
fof(f14959,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,[],[f6751]) ).
fof(f6751,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
<=> ! [X2] : hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) ),
inference(rectify,[],[f3420]) ).
fof(f3420,axiom,
! [X116,X4] :
( c_Wellfounded_OwfP(X4,X116)
<=> ! [X124] : hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X116),X124)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34098,plain,
spl647_827,
inference(avatar_split_clause,[],[f19085,f34096]) ).
fof(f34096,plain,
( spl647_827
<=> ! [X2,X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ sP4(X0)
| ~ hBOOL(hAPP(hAPP(X0,X2),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_827])]) ).
fof(f19085,plain,
! [X2,X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ sP4(X0)
| ~ hBOOL(hAPP(hAPP(X0,X2),X2)) ),
inference(cnf_transformation,[],[f14949]) ).
fof(f14949,plain,
! [X0,X1] :
( ( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ sP4(X0)
| ! [X2] : ~ hBOOL(hAPP(hAPP(X0,X2),X2)) )
& ( ( sP4(X0)
& hBOOL(hAPP(hAPP(X0,sK168(X0)),sK168(X0))) )
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK168])],[f14947,f14948]) ).
fof(f14948,plain,
! [X0] :
( ? [X3] : hBOOL(hAPP(hAPP(X0,X3),X3))
=> hBOOL(hAPP(hAPP(X0,sK168(X0)),sK168(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14947,plain,
! [X0,X1] :
( ( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ sP4(X0)
| ! [X2] : ~ hBOOL(hAPP(hAPP(X0,X2),X2)) )
& ( ( sP4(X0)
& ? [X3] : hBOOL(hAPP(hAPP(X0,X3),X3)) )
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
inference(rectify,[],[f14946]) ).
fof(f14946,plain,
! [X0,X1] :
( ( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ sP4(X0)
| ! [X4] : ~ hBOOL(hAPP(hAPP(X0,X4),X4)) )
& ( ( sP4(X0)
& ? [X4] : hBOOL(hAPP(hAPP(X0,X4),X4)) )
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
inference(flattening,[],[f14945]) ).
fof(f14945,plain,
! [X0,X1] :
( ( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ sP4(X0)
| ! [X4] : ~ hBOOL(hAPP(hAPP(X0,X4),X4)) )
& ( ( sP4(X0)
& ? [X4] : hBOOL(hAPP(hAPP(X0,X4),X4)) )
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
inference(nnf_transformation,[],[f14483]) ).
fof(f14483,plain,
! [X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
<=> ( sP4(X0)
& ? [X4] : hBOOL(hAPP(hAPP(X0,X4),X4)) ) ),
inference(definition_folding,[],[f6746,f14482]) ).
fof(f6746,plain,
! [X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
<=> ( ! [X2,X3] :
( hBOOL(hAPP(hAPP(X0,X2),X3))
<=> ( hAPP(X0,X2) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(X0,X3),X3))
& hBOOL(hAPP(hAPP(X0,X2),X2)) ) )
& ? [X4] : hBOOL(hAPP(hAPP(X0,X4),X4)) ) ),
inference(rectify,[],[f4752]) ).
fof(f4752,axiom,
! [X138,X4] :
( c_Equiv__Relations_Opart__equivp(X4,X138)
<=> ( ! [X2,X38] :
( hBOOL(hAPP(hAPP(X138,X2),X38))
<=> ( hAPP(X138,X2) = hAPP(X138,X38)
& hBOOL(hAPP(hAPP(X138,X38),X38))
& hBOOL(hAPP(hAPP(X138,X2),X2)) ) )
& ? [X2] : hBOOL(hAPP(hAPP(X138,X2),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34094,plain,
spl647_826,
inference(avatar_split_clause,[],[f19083,f34092]) ).
fof(f34092,plain,
( spl647_826
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(X0,sK168(X0)),sK168(X0)))
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_826])]) ).
fof(f19083,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(X0,sK168(X0)),sK168(X0)))
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(cnf_transformation,[],[f14949]) ).
fof(f34090,plain,
spl647_825,
inference(avatar_split_clause,[],[f19071,f34088]) ).
fof(f34088,plain,
( spl647_825
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(X0,sK165(X0)),sK165(X0)))
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_825])]) ).
fof(f19071,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(X0,sK165(X0)),sK165(X0)))
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(cnf_transformation,[],[f14939]) ).
fof(f14939,plain,
! [X0,X1] :
( ( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ c_Predicate_Otransp(X1,X0)
| ~ c_Predicate_Osymp(X1,X0)
| ! [X2] : ~ hBOOL(hAPP(hAPP(X0,X2),X2)) )
& ( ( c_Predicate_Otransp(X1,X0)
& c_Predicate_Osymp(X1,X0)
& hBOOL(hAPP(hAPP(X0,sK165(X0)),sK165(X0))) )
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK165])],[f14937,f14938]) ).
fof(f14938,plain,
! [X0] :
( ? [X3] : hBOOL(hAPP(hAPP(X0,X3),X3))
=> hBOOL(hAPP(hAPP(X0,sK165(X0)),sK165(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14937,plain,
! [X0,X1] :
( ( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ c_Predicate_Otransp(X1,X0)
| ~ c_Predicate_Osymp(X1,X0)
| ! [X2] : ~ hBOOL(hAPP(hAPP(X0,X2),X2)) )
& ( ( c_Predicate_Otransp(X1,X0)
& c_Predicate_Osymp(X1,X0)
& ? [X3] : hBOOL(hAPP(hAPP(X0,X3),X3)) )
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
inference(rectify,[],[f14936]) ).
fof(f14936,plain,
! [X0,X1] :
( ( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ c_Predicate_Otransp(X1,X0)
| ~ c_Predicate_Osymp(X1,X0)
| ! [X2] : ~ hBOOL(hAPP(hAPP(X0,X2),X2)) )
& ( ( c_Predicate_Otransp(X1,X0)
& c_Predicate_Osymp(X1,X0)
& ? [X2] : hBOOL(hAPP(hAPP(X0,X2),X2)) )
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
inference(flattening,[],[f14935]) ).
fof(f14935,plain,
! [X0,X1] :
( ( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ c_Predicate_Otransp(X1,X0)
| ~ c_Predicate_Osymp(X1,X0)
| ! [X2] : ~ hBOOL(hAPP(hAPP(X0,X2),X2)) )
& ( ( c_Predicate_Otransp(X1,X0)
& c_Predicate_Osymp(X1,X0)
& ? [X2] : hBOOL(hAPP(hAPP(X0,X2),X2)) )
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
inference(nnf_transformation,[],[f6745]) ).
fof(f6745,plain,
! [X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
<=> ( c_Predicate_Otransp(X1,X0)
& c_Predicate_Osymp(X1,X0)
& ? [X2] : hBOOL(hAPP(hAPP(X0,X2),X2)) ) ),
inference(rectify,[],[f4766]) ).
fof(f4766,axiom,
! [X138,X4] :
( c_Equiv__Relations_Opart__equivp(X4,X138)
<=> ( c_Predicate_Otransp(X4,X138)
& c_Predicate_Osymp(X4,X138)
& ? [X2] : hBOOL(hAPP(hAPP(X138,X2),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34086,plain,
spl647_824,
inference(avatar_split_clause,[],[f19051,f34084]) ).
fof(f34084,plain,
( spl647_824
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != sK164(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_824])]) ).
fof(f19051,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != sK164(X0,X1) ),
inference(cnf_transformation,[],[f14926]) ).
fof(f14926,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != sK164(X0,X1)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),sK164(X0,X1)),hAPP(c_Relation_OImage(X1,X1,X0),sK164(X0,X1)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK164])],[f11270,f14925]) ).
fof(f14925,plain,
! [X0,X1] :
( ? [X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Relation_OImage(X1,X1,X0),X2))) )
=> ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != sK164(X0,X1)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),sK164(X0,X1)),hAPP(c_Relation_OImage(X1,X1,X0),sK164(X0,X1)))) ) ),
introduced(choice_axiom,[]) ).
fof(f11270,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ? [X2] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X2
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Relation_OImage(X1,X1,X0),X2))) ) ),
inference(ennf_transformation,[],[f6731]) ).
fof(f6731,plain,
! [X0,X1] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_Relation_OImage(X1,X1,X0),X2)))
=> c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X2 )
=> c_Wellfounded_Owf(X1,X0) ),
inference(rectify,[],[f3514]) ).
fof(f3514,axiom,
! [X138,X4] :
( ! [X40] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X40),hAPP(c_Relation_OImage(X4,X4,X138),X40)))
=> c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = X40 )
=> c_Wellfounded_Owf(X4,X138) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34082,plain,
spl647_823,
inference(avatar_split_clause,[],[f19049,f34080]) ).
fof(f34080,plain,
( spl647_823
<=> ! [X0,X1] :
( hBOOL(hAPP(X1,X0))
| ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,sK163(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_823])]) ).
fof(f19049,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,X0))
| ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,sK163(X1)))) ),
inference(cnf_transformation,[],[f14924]) ).
fof(f14924,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,X0))
| ( ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,sK163(X1))))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK163(X1)),c_Int_OInteg)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK163])],[f11269,f14923]) ).
fof(f14923,plain,
! [X1] :
( ? [X2] :
( ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),c_Int_OInteg)) )
=> ( ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,sK163(X1))))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK163(X1)),c_Int_OInteg)) ) ),
introduced(choice_axiom,[]) ).
fof(f11269,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,X0))
| ? [X2] :
( ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),c_Int_OInteg)) ) ),
inference(ennf_transformation,[],[f6730]) ).
fof(f6730,plain,
! [X0,X1] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X2),c_Int_OInteg))
=> hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,X2))) )
=> hBOOL(hAPP(X1,X0)) ),
inference(rectify,[],[f3441]) ).
fof(f3441,axiom,
! [X13,X23] :
( ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X38),c_Int_OInteg))
=> hBOOL(hAPP(X23,hAPP(c_Int_OAbs__Integ,X38))) )
=> hBOOL(hAPP(X23,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34078,plain,
spl647_822,
inference(avatar_split_clause,[],[f19047,f34076]) ).
fof(f19047,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,X0))
| ~ hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Oof__nat,sK162(X1)))) ),
inference(cnf_transformation,[],[f14922]) ).
fof(f14922,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,X0))
| ( ~ hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Oof__nat,sK162(X1))))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK162(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK162])],[f11268,f14921]) ).
fof(f14921,plain,
! [X1] :
( ? [X2] :
( ~ hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Oof__nat,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) )
=> ( ~ hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Oof__nat,sK162(X1))))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK162(X1)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ),
introduced(choice_axiom,[]) ).
fof(f11268,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,X0))
| ? [X2] :
( ~ hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Oof__nat,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ),
inference(ennf_transformation,[],[f6729]) ).
fof(f6729,plain,
! [X0,X1] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> hBOOL(hAPP(X1,hAPP(c_Code__Numeral_Oof__nat,X2))) )
=> hBOOL(hAPP(X1,X0)) ),
inference(rectify,[],[f4799]) ).
fof(f4799,axiom,
! [X13,X23] :
( ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X38),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
=> hBOOL(hAPP(X23,hAPP(c_Code__Numeral_Oof__nat,X38))) )
=> hBOOL(hAPP(X23,X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34074,plain,
spl647_821,
inference(avatar_split_clause,[],[f18682,f34072]) ).
fof(f34072,plain,
( spl647_821
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(X0,sK138(X0)),sK138(X0)))
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_821])]) ).
fof(f18682,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(X0,sK138(X0)),sK138(X0)))
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(cnf_transformation,[],[f14838]) ).
fof(f14838,plain,
! [X0,X1] :
( ( c_Predicate_Otransp(X1,X0)
& c_Predicate_Osymp(X1,X0)
& hBOOL(hAPP(hAPP(X0,sK138(X0)),sK138(X0))) )
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK138])],[f10866,f14837]) ).
fof(f14837,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(hAPP(X0,X2),X2))
=> hBOOL(hAPP(hAPP(X0,sK138(X0)),sK138(X0))) ),
introduced(choice_axiom,[]) ).
fof(f10866,plain,
! [X0,X1] :
( ( c_Predicate_Otransp(X1,X0)
& c_Predicate_Osymp(X1,X0)
& ? [X2] : hBOOL(hAPP(hAPP(X0,X2),X2)) )
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(flattening,[],[f10865]) ).
fof(f10865,plain,
! [X0,X1] :
( ( c_Predicate_Otransp(X1,X0)
& c_Predicate_Osymp(X1,X0)
& ? [X2] : hBOOL(hAPP(hAPP(X0,X2),X2)) )
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(ennf_transformation,[],[f6439]) ).
fof(f6439,plain,
! [X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
=> ~ ( ? [X2] : hBOOL(hAPP(hAPP(X0,X2),X2))
=> ( c_Predicate_Osymp(X1,X0)
=> ~ c_Predicate_Otransp(X1,X0) ) ) ),
inference(rectify,[],[f4767]) ).
fof(f4767,axiom,
! [X138,X4] :
( c_Equiv__Relations_Opart__equivp(X4,X138)
=> ~ ( ? [X2] : hBOOL(hAPP(hAPP(X138,X2),X2))
=> ( c_Predicate_Osymp(X4,X138)
=> ~ c_Predicate_Otransp(X4,X138) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34070,plain,
spl647_820,
inference(avatar_split_clause,[],[f18673,f34068]) ).
fof(f34068,plain,
( spl647_820
<=> ! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_820])]) ).
fof(f18673,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(cnf_transformation,[],[f10853]) ).
fof(f10853,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(flattening,[],[f10852]) ).
fof(f10852,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(ennf_transformation,[],[f6431]) ).
fof(f6431,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X1)
=> ( c_Nat__Transfer_Ois__nat(X0)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)) ) ),
inference(rectify,[],[f2130]) ).
fof(f2130,axiom,
! [X21,X19] :
( c_Nat__Transfer_Ois__nat(X19)
=> ( c_Nat__Transfer_Ois__nat(X21)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X19),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34066,plain,
spl647_819,
inference(avatar_split_clause,[],[f18672,f34064]) ).
fof(f18672,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(cnf_transformation,[],[f10851]) ).
fof(f10851,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(flattening,[],[f10850]) ).
fof(f10850,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(ennf_transformation,[],[f6430]) ).
fof(f6430,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X1)
=> ( c_Nat__Transfer_Ois__nat(X0)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0)) ) ),
inference(rectify,[],[f2127]) ).
fof(f2127,axiom,
! [X21,X19] :
( c_Nat__Transfer_Ois__nat(X19)
=> ( c_Nat__Transfer_Ois__nat(X21)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X19),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34062,plain,
spl647_818,
inference(avatar_split_clause,[],[f18671,f34060]) ).
fof(f34060,plain,
( spl647_818
<=> ! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_818])]) ).
fof(f18671,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(cnf_transformation,[],[f10849]) ).
fof(f10849,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(flattening,[],[f10848]) ).
fof(f10848,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(ennf_transformation,[],[f6429]) ).
fof(f6429,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X1)
=> ( c_Nat__Transfer_Ois__nat(X0)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)) ) ),
inference(rectify,[],[f2134]) ).
fof(f2134,axiom,
! [X21,X19] :
( c_Nat__Transfer_Ois__nat(X19)
=> ( c_Nat__Transfer_Ois__nat(X21)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X19),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34058,plain,
spl647_817,
inference(avatar_split_clause,[],[f18663,f34056]) ).
fof(f18663,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X0),X1))
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(cnf_transformation,[],[f10837]) ).
fof(f10837,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X0),X1))
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(flattening,[],[f10836]) ).
fof(f10836,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X0),X1))
| ~ c_Nat__Transfer_Onat__set(X1) ),
inference(ennf_transformation,[],[f6422]) ).
fof(f6422,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(X1)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X0),X1))
=> c_Nat__Transfer_Ois__nat(X0) ) ),
inference(rectify,[],[f2938]) ).
fof(f2938,axiom,
! [X13,X9] :
( c_Nat__Transfer_Onat__set(X9)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X13),X9))
=> c_Nat__Transfer_Ois__nat(X13) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34054,plain,
spl647_816,
inference(avatar_split_clause,[],[f18648,f34052]) ).
fof(f34052,plain,
( spl647_816
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ~ hBOOL(hAPP(X0,X2))
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_816])]) ).
fof(f18648,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ~ hBOOL(hAPP(X0,X2))
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f14824]) ).
fof(f34050,plain,
spl647_815,
inference(avatar_split_clause,[],[f18645,f34048]) ).
fof(f34048,plain,
( spl647_815
<=> ! [X0,X1,X3] :
( hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_815])]) ).
fof(f18645,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f14820]) ).
fof(f34046,plain,
spl647_814,
inference(avatar_split_clause,[],[f18580,f34044]) ).
fof(f34044,plain,
( spl647_814
<=> ! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Otl(X1),X0))
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_814])]) ).
fof(f18580,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Otl(X1),X0))
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10751]) ).
fof(f10751,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Otl(X1),X0))
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ class_Orderings_Olinorder(X1) ),
inference(flattening,[],[f10750]) ).
fof(f10750,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Otl(X1),X0))
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6364]) ).
fof(f6364,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> ( c_List_Olinorder__class_Osorted(X1,X0)
=> c_List_Olinorder__class_Osorted(X1,hAPP(c_List_Otl(X1),X0)) ) ),
inference(rectify,[],[f4408]) ).
fof(f4408,axiom,
! [X201,X20] :
( class_Orderings_Olinorder(X20)
=> ( c_List_Olinorder__class_Osorted(X20,X201)
=> c_List_Olinorder__class_Osorted(X20,hAPP(c_List_Otl(X20),X201)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34042,plain,
( spl647_813
| ~ spl647_577
| ~ spl647_727 ),
inference(avatar_split_clause,[],[f33735,f32771,f31911,f34040]) ).
fof(f34040,plain,
( spl647_813
<=> ! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| ~ c_Nat__Transfer_Ois__nat(sK93(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_813])]) ).
fof(f32771,plain,
( spl647_727
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK93(X0)))
| c_Nat__Transfer_Onat__set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_727])]) ).
fof(f33735,plain,
( ! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| ~ c_Nat__Transfer_Ois__nat(sK93(X0)) )
| ~ spl647_577
| ~ spl647_727 ),
inference(resolution,[],[f32772,f31912]) ).
fof(f32772,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK93(X0)))
| c_Nat__Transfer_Onat__set(X0) )
| ~ spl647_727 ),
inference(avatar_component_clause,[],[f32771]) ).
fof(f34038,plain,
spl647_812,
inference(avatar_split_clause,[],[f18557,f34036]) ).
fof(f34036,plain,
( spl647_812
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_812])]) ).
fof(f18557,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(cnf_transformation,[],[f10725]) ).
fof(f10725,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(ennf_transformation,[],[f6341]) ).
fof(f6341,plain,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = X0 ),
inference(rectify,[],[f752]) ).
fof(f752,axiom,
! [X26,X20] :
( class_Groups_Ocomm__monoid__add(X20)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),c_Groups_Ozero__class_Ozero(X20)),X26) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34034,plain,
spl647_811,
inference(avatar_split_clause,[],[f18556,f34032]) ).
fof(f34032,plain,
( spl647_811
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_811])]) ).
fof(f18556,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(cnf_transformation,[],[f10724]) ).
fof(f10724,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ocomm__monoid__add(X1) ),
inference(ennf_transformation,[],[f6340]) ).
fof(f6340,plain,
! [X0,X1] :
( class_Groups_Ocomm__monoid__add(X1)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f755]) ).
fof(f755,axiom,
! [X26,X20] :
( class_Groups_Ocomm__monoid__add(X20)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),X26),c_Groups_Ozero__class_Ozero(X20)) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34030,plain,
spl647_810,
inference(avatar_split_clause,[],[f18552,f34028]) ).
fof(f34028,plain,
( spl647_810
<=> ! [X0,X1] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_810])]) ).
fof(f18552,plain,
! [X0,X1] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f10719]) ).
fof(f10719,plain,
! [X0,X1] :
( hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f6336]) ).
fof(f6336,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(rectify,[],[f1633]) ).
fof(f1633,axiom,
! [X26,X20] :
( class_Divides_Osemiring__div(X20)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X20),X26),c_Groups_Oone__class_Oone(X20)) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34026,plain,
spl647_809,
inference(avatar_split_clause,[],[f18540,f34024]) ).
fof(f34024,plain,
( spl647_809
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_809])]) ).
fof(f18540,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f10706]) ).
fof(f10706,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f6324]) ).
fof(f6324,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
inference(rectify,[],[f553]) ).
fof(f553,axiom,
! [X26,X20] :
( class_Rings_Ocomm__semiring__1(X20)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),c_Groups_Oone__class_Oone(X20)),X26) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34022,plain,
spl647_808,
inference(avatar_split_clause,[],[f18539,f34020]) ).
fof(f34020,plain,
( spl647_808
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_808])]) ).
fof(f18539,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f10705]) ).
fof(f10705,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f6323]) ).
fof(f6323,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = X0 ),
inference(rectify,[],[f750]) ).
fof(f750,axiom,
! [X26,X20] :
( class_Rings_Ocomm__semiring__1(X20)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),c_Groups_Ozero__class_Ozero(X20)),X26) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34018,plain,
spl647_807,
inference(avatar_split_clause,[],[f18538,f34016]) ).
fof(f34016,plain,
( spl647_807
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_807])]) ).
fof(f18538,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f10704]) ).
fof(f10704,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f6322]) ).
fof(f6322,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(rectify,[],[f552]) ).
fof(f552,axiom,
! [X26,X20] :
( class_Rings_Ocomm__semiring__1(X20)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),X26),c_Groups_Oone__class_Oone(X20)) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34014,plain,
spl647_806,
inference(avatar_split_clause,[],[f18537,f34012]) ).
fof(f34012,plain,
( spl647_806
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_806])]) ).
fof(f18537,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f10703]) ).
fof(f10703,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f6321]) ).
fof(f6321,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f749]) ).
fof(f749,axiom,
! [X26,X20] :
( class_Rings_Ocomm__semiring__1(X20)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),X26),c_Groups_Ozero__class_Ozero(X20)) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34010,plain,
spl647_805,
inference(avatar_split_clause,[],[f18536,f34008]) ).
fof(f34008,plain,
( spl647_805
<=> ! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_805])]) ).
fof(f18536,plain,
! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f10702]) ).
fof(f10702,plain,
! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f6320]) ).
fof(f6320,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
inference(rectify,[],[f1752]) ).
fof(f1752,axiom,
! [X19,X20] :
( class_Rings_Ocomm__semiring__1(X20)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X20),X19),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34006,plain,
spl647_804,
inference(avatar_split_clause,[],[f18532,f34004]) ).
fof(f34004,plain,
( spl647_804
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Groups_Ocomm__monoid__mult(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_804])]) ).
fof(f18532,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(cnf_transformation,[],[f10698]) ).
fof(f10698,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(ennf_transformation,[],[f6316]) ).
fof(f6316,plain,
! [X0,X1] :
( class_Groups_Ocomm__monoid__mult(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
inference(rectify,[],[f442]) ).
fof(f442,axiom,
! [X26,X20] :
( class_Groups_Ocomm__monoid__mult(X20)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),c_Groups_Oone__class_Oone(X20)),X26) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f34002,plain,
spl647_803,
inference(avatar_split_clause,[],[f18531,f34000]) ).
fof(f34000,plain,
( spl647_803
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Groups_Ocomm__monoid__mult(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_803])]) ).
fof(f18531,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(cnf_transformation,[],[f10697]) ).
fof(f10697,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Groups_Ocomm__monoid__mult(X1) ),
inference(ennf_transformation,[],[f6315]) ).
fof(f6315,plain,
! [X0,X1] :
( class_Groups_Ocomm__monoid__mult(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(rectify,[],[f440]) ).
fof(f440,axiom,
! [X26,X20] :
( class_Groups_Ocomm__monoid__mult(X20)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),X26),c_Groups_Oone__class_Oone(X20)) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33998,plain,
spl647_802,
inference(avatar_split_clause,[],[f18515,f33996]) ).
fof(f33996,plain,
( spl647_802
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Groups_Omonoid__mult(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_802])]) ).
fof(f18515,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(cnf_transformation,[],[f10682]) ).
fof(f10682,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(ennf_transformation,[],[f6301]) ).
fof(f6301,plain,
! [X0,X1] :
( class_Groups_Omonoid__mult(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
inference(rectify,[],[f443]) ).
fof(f443,axiom,
! [X26,X20] :
( class_Groups_Omonoid__mult(X20)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),c_Groups_Oone__class_Oone(X20)),X26) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33994,plain,
spl647_801,
inference(avatar_split_clause,[],[f18514,f33992]) ).
fof(f33992,plain,
( spl647_801
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Groups_Omonoid__mult(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_801])]) ).
fof(f18514,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(cnf_transformation,[],[f10681]) ).
fof(f10681,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(ennf_transformation,[],[f6300]) ).
fof(f6300,plain,
! [X0,X1] :
( class_Groups_Omonoid__mult(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),X0),c_Groups_Oone__class_Oone(X1)) = X0 ),
inference(rectify,[],[f441]) ).
fof(f441,axiom,
! [X26,X20] :
( class_Groups_Omonoid__mult(X20)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X20),X26),c_Groups_Oone__class_Oone(X20)) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33990,plain,
spl647_800,
inference(avatar_split_clause,[],[f18513,f33988]) ).
fof(f33988,plain,
( spl647_800
<=> ! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ class_Groups_Omonoid__mult(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_800])]) ).
fof(f18513,plain,
! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(cnf_transformation,[],[f10680]) ).
fof(f10680,plain,
! [X0,X1] :
( hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0
| ~ class_Groups_Omonoid__mult(X1) ),
inference(ennf_transformation,[],[f6299]) ).
fof(f6299,plain,
! [X0,X1] :
( class_Groups_Omonoid__mult(X1)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X1),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
inference(rectify,[],[f1912]) ).
fof(f1912,axiom,
! [X26,X20] :
( class_Groups_Omonoid__mult(X20)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X20),X26),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33986,plain,
spl647_799,
inference(avatar_split_clause,[],[f18511,f33984]) ).
fof(f33984,plain,
( spl647_799
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = X0
| ~ class_Groups_Omonoid__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_799])]) ).
fof(f18511,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = X0
| ~ class_Groups_Omonoid__add(X1) ),
inference(cnf_transformation,[],[f10678]) ).
fof(f10678,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = X0
| ~ class_Groups_Omonoid__add(X1) ),
inference(ennf_transformation,[],[f6297]) ).
fof(f6297,plain,
! [X0,X1] :
( class_Groups_Omonoid__add(X1)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),c_Groups_Ozero__class_Ozero(X1)),X0) = X0 ),
inference(rectify,[],[f751]) ).
fof(f751,axiom,
! [X26,X20] :
( class_Groups_Omonoid__add(X20)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),c_Groups_Ozero__class_Ozero(X20)),X26) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33982,plain,
spl647_798,
inference(avatar_split_clause,[],[f18510,f33980]) ).
fof(f33980,plain,
( spl647_798
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Omonoid__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_798])]) ).
fof(f18510,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Omonoid__add(X1) ),
inference(cnf_transformation,[],[f10677]) ).
fof(f10677,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Omonoid__add(X1) ),
inference(ennf_transformation,[],[f6296]) ).
fof(f6296,plain,
! [X0,X1] :
( class_Groups_Omonoid__add(X1)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f754]) ).
fof(f754,axiom,
! [X26,X20] :
( class_Groups_Omonoid__add(X20)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X20),X26),c_Groups_Ozero__class_Ozero(X20)) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33978,plain,
spl647_797,
inference(avatar_split_clause,[],[f18483,f33976]) ).
fof(f33976,plain,
( spl647_797
<=> ! [X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)) = X0
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_797])]) ).
fof(f18483,plain,
! [X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)) = X0
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f10647]) ).
fof(f10647,plain,
! [X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)) = X0
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f6271]) ).
fof(f6271,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)) = X0 ),
inference(rectify,[],[f1417]) ).
fof(f1417,axiom,
! [X19,X20] :
( class_Lattices_Oboolean__algebra(X20)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X20),hAPP(c_Groups_Ouminus__class_Ouminus(X20),X19)) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33974,plain,
spl647_796,
inference(avatar_split_clause,[],[f18477,f33972]) ).
fof(f33972,plain,
( spl647_796
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X0) = X0
| ~ class_Lattices_Obounded__lattice__top(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_796])]) ).
fof(f18477,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X0) = X0
| ~ class_Lattices_Obounded__lattice__top(X1) ),
inference(cnf_transformation,[],[f10641]) ).
fof(f10641,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X0) = X0
| ~ class_Lattices_Obounded__lattice__top(X1) ),
inference(ennf_transformation,[],[f6265]) ).
fof(f6265,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),c_Orderings_Otop__class_Otop(X1)),X0) = X0 ),
inference(rectify,[],[f2099]) ).
fof(f2099,axiom,
! [X19,X20] :
( class_Lattices_Obounded__lattice__top(X20)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20),c_Orderings_Otop__class_Otop(X20)),X19) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33970,plain,
spl647_795,
inference(avatar_split_clause,[],[f18476,f33968]) ).
fof(f33968,plain,
( spl647_795
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X0) = X0
| ~ class_Lattices_Obounded__lattice__bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_795])]) ).
fof(f18476,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X0) = X0
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(cnf_transformation,[],[f10640]) ).
fof(f10640,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X0) = X0
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(ennf_transformation,[],[f6264]) ).
fof(f6264,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X0) = X0 ),
inference(rectify,[],[f142]) ).
fof(f142,axiom,
! [X19,X20] :
( class_Lattices_Obounded__lattice__bot(X20)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20),c_Orderings_Obot__class_Obot(X20)),X19) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33966,plain,
spl647_794,
inference(avatar_split_clause,[],[f18475,f33964]) ).
fof(f33964,plain,
( spl647_794
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),c_Orderings_Otop__class_Otop(X1)) = X0
| ~ class_Lattices_Obounded__lattice__top(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_794])]) ).
fof(f18475,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),c_Orderings_Otop__class_Otop(X1)) = X0
| ~ class_Lattices_Obounded__lattice__top(X1) ),
inference(cnf_transformation,[],[f10639]) ).
fof(f10639,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),c_Orderings_Otop__class_Otop(X1)) = X0
| ~ class_Lattices_Obounded__lattice__top(X1) ),
inference(ennf_transformation,[],[f6263]) ).
fof(f6263,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),c_Orderings_Otop__class_Otop(X1)) = X0 ),
inference(rectify,[],[f2098]) ).
fof(f2098,axiom,
! [X19,X20] :
( class_Lattices_Obounded__lattice__top(X20)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20),X19),c_Orderings_Otop__class_Otop(X20)) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33962,plain,
spl647_793,
inference(avatar_split_clause,[],[f18474,f33960]) ).
fof(f33960,plain,
( spl647_793
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),c_Orderings_Obot__class_Obot(X1)) = X0
| ~ class_Lattices_Obounded__lattice__bot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_793])]) ).
fof(f18474,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),c_Orderings_Obot__class_Obot(X1)) = X0
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(cnf_transformation,[],[f10638]) ).
fof(f10638,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),c_Orderings_Obot__class_Obot(X1)) = X0
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(ennf_transformation,[],[f6262]) ).
fof(f6262,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),c_Orderings_Obot__class_Obot(X1)) = X0 ),
inference(rectify,[],[f143]) ).
fof(f143,axiom,
! [X19,X20] :
( class_Lattices_Obounded__lattice__bot(X20)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20),X19),c_Orderings_Obot__class_Obot(X20)) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33958,plain,
spl647_792,
inference(avatar_split_clause,[],[f18432,f33956]) ).
fof(f33956,plain,
( spl647_792
<=> ! [X0,X1] :
( hAPP(c_Int_Oring__1__class_Oof__int(X1),X0) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)
| ~ class_Int_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_792])]) ).
fof(f18432,plain,
! [X0,X1] :
( hAPP(c_Int_Oring__1__class_Oof__int(X1),X0) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f10601]) ).
fof(f10601,plain,
! [X0,X1] :
( hAPP(c_Int_Oring__1__class_Oof__int(X1),X0) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X0)
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f6226]) ).
fof(f6226,plain,
! [X0,X1] :
( class_Int_Onumber__ring(X1)
=> hAPP(c_Int_Oring__1__class_Oof__int(X1),X0) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X0) ),
inference(rectify,[],[f2026]) ).
fof(f2026,axiom,
! [X53,X20] :
( class_Int_Onumber__ring(X20)
=> hAPP(c_Int_Onumber__class_Onumber__of(X20),X53) = hAPP(c_Int_Oring__1__class_Oof__int(X20),X53) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33954,plain,
spl647_791,
inference(avatar_split_clause,[],[f18395,f33952]) ).
fof(f33952,plain,
( spl647_791
<=> ! [X0,X1] :
( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X0))
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_791])]) ).
fof(f18395,plain,
! [X0,X1] :
( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X0))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f10574]) ).
fof(f10574,plain,
! [X0,X1] :
( c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X0))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(ennf_transformation,[],[f6202]) ).
fof(f6202,plain,
! [X0,X1] :
( class_Rings_Olinordered__idom(X1)
=> c_Groups_Osgn__class_Osgn(X1,X0) = c_Groups_Osgn__class_Osgn(X1,c_Groups_Osgn__class_Osgn(X1,X0)) ),
inference(rectify,[],[f2054]) ).
fof(f2054,axiom,
! [X26,X20] :
( class_Rings_Olinordered__idom(X20)
=> c_Groups_Osgn__class_Osgn(X20,X26) = c_Groups_Osgn__class_Osgn(X20,c_Groups_Osgn__class_Osgn(X20,X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33950,plain,
spl647_790,
inference(avatar_split_clause,[],[f18342,f33948]) ).
fof(f33948,plain,
( spl647_790
<=> ! [X0,X1] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_790])]) ).
fof(f18342,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f10527]) ).
fof(f10527,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f6161]) ).
fof(f6161,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X0),c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f766]) ).
fof(f766,axiom,
! [X26,X20] :
( class_Groups_Ogroup__add(X20)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20),X26),c_Groups_Ozero__class_Ozero(X20)) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33946,plain,
spl647_789,
inference(avatar_split_clause,[],[f18341,f33944]) ).
fof(f33944,plain,
( spl647_789
<=> ! [X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)) = X0
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_789])]) ).
fof(f18341,plain,
! [X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)) = X0
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f10526]) ).
fof(f10526,plain,
! [X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)) = X0
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f6160]) ).
fof(f6160,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X1),hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0)) = X0 ),
inference(rectify,[],[f1420]) ).
fof(f1420,axiom,
! [X26,X20] :
( class_Groups_Ogroup__add(X20)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X20),hAPP(c_Groups_Ouminus__class_Ouminus(X20),X26)) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33942,plain,
spl647_788,
inference(avatar_split_clause,[],[f18340,f33940]) ).
fof(f33940,plain,
( spl647_788
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X0),X0)
| ~ class_Groups_Ogroup__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_788])]) ).
fof(f18340,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X0),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(cnf_transformation,[],[f10525]) ).
fof(f10525,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X0),X0)
| ~ class_Groups_Ogroup__add(X1) ),
inference(ennf_transformation,[],[f6159]) ).
fof(f6159,plain,
! [X0,X1] :
( class_Groups_Ogroup__add(X1)
=> c_Groups_Ozero__class_Ozero(X1) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X1),X0),X0) ),
inference(rectify,[],[f765]) ).
fof(f765,axiom,
! [X26,X20] :
( class_Groups_Ogroup__add(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X20),X26),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33938,plain,
spl647_787,
inference(avatar_split_clause,[],[f17876,f33936]) ).
fof(f33936,plain,
( spl647_787
<=> ! [X0,X1] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_787])]) ).
fof(f33934,plain,
spl647_786,
inference(avatar_split_clause,[],[f17869,f33932]) ).
fof(f33932,plain,
( spl647_786
<=> ! [X0,X1] : hAPP(c_Set_OPow(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_786])]) ).
fof(f17869,plain,
! [X0,X1] : hAPP(c_Set_OPow(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
inference(cnf_transformation,[],[f5761]) ).
fof(f5761,plain,
! [X0,X1] : hAPP(c_Set_OPow(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool)),
inference(rectify,[],[f1964]) ).
fof(f1964,axiom,
! [X9,X4] : c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(c_Set_OPow(X4),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33930,plain,
spl647_785,
inference(avatar_split_clause,[],[f17761,f33928]) ).
fof(f33928,plain,
( spl647_785
<=> ! [X4,X0] :
( hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK105(X0))))
| ~ hBOOL(hAPP(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_785])]) ).
fof(f17761,plain,
! [X0,X4] :
( hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK105(X0))))
| ~ hBOOL(hAPP(X0,X4)) ),
inference(cnf_transformation,[],[f14726]) ).
fof(f33926,plain,
spl647_784,
inference(avatar_split_clause,[],[f17756,f33924]) ).
fof(f33924,plain,
( spl647_784
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK100(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_784])]) ).
fof(f17756,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK100(X0)))) ),
inference(cnf_transformation,[],[f14716]) ).
fof(f33922,plain,
spl647_783,
inference(avatar_split_clause,[],[f17580,f33920]) ).
fof(f33920,plain,
( spl647_783
<=> ! [X0] :
( c_Finite__Set_Ofun__left__comm(X0,tc_List_Olist(X0),c_List_Olinorder__class_Oinsort__key(X0,X0,c_COMBI(X0)))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_783])]) ).
fof(f17580,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm(X0,tc_List_Olist(X0),c_List_Olinorder__class_Oinsort__key(X0,X0,c_COMBI(X0)))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10373]) ).
fof(f10373,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm(X0,tc_List_Olist(X0),c_List_Olinorder__class_Oinsort__key(X0,X0,c_COMBI(X0)))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5545]) ).
fof(f5545,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_Finite__Set_Ofun__left__comm(X0,tc_List_Olist(X0),c_List_Olinorder__class_Oinsort__key(X0,X0,c_COMBI(X0))) ),
inference(rectify,[],[f4089]) ).
fof(f4089,axiom,
! [X4] :
( class_Orderings_Olinorder(X4)
=> c_Finite__Set_Ofun__left__comm(X4,tc_List_Olist(X4),c_List_Olinorder__class_Oinsort__key(X4,X4,c_COMBI(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33918,plain,
( ~ spl647_782
| ~ spl647_338
| ~ spl647_675 ),
inference(avatar_split_clause,[],[f33380,f32549,f30858,f33915]) ).
fof(f33915,plain,
( spl647_782
<=> sP30(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_782])]) ).
fof(f33380,plain,
( ~ sP30(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint))
| ~ spl647_338
| ~ spl647_675 ),
inference(resolution,[],[f32550,f30860]) ).
fof(f33913,plain,
spl647_781,
inference(avatar_split_clause,[],[f17579,f33911]) ).
fof(f33911,plain,
( spl647_781
<=> ! [X0] :
( c_List_Olist_ONil(X0) = c_List_Olinorder__class_Osorted__list__of__set(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_781])]) ).
fof(f17579,plain,
! [X0] :
( c_List_Olist_ONil(X0) = c_List_Olinorder__class_Osorted__list__of__set(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10372]) ).
fof(f10372,plain,
! [X0] :
( c_List_Olist_ONil(X0) = c_List_Olinorder__class_Osorted__list__of__set(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5544]) ).
fof(f5544,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_List_Olist_ONil(X0) = c_List_Olinorder__class_Osorted__list__of__set(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) ),
inference(rectify,[],[f3938]) ).
fof(f3938,axiom,
! [X4] :
( class_Orderings_Olinorder(X4)
=> c_List_Olist_ONil(X4) = c_List_Olinorder__class_Osorted__list__of__set(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33909,plain,
spl647_780,
inference(avatar_split_clause,[],[f17573,f33907]) ).
fof(f33907,plain,
( spl647_780
<=> ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oone__class_Oone(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_780])]) ).
fof(f17573,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oone__class_Oone(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[],[f10366]) ).
fof(f10366,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oone__class_Oone(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(ennf_transformation,[],[f5538]) ).
fof(f5538,plain,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oone__class_Oone(X0))) ),
inference(rectify,[],[f857]) ).
fof(f857,axiom,
! [X20] :
( class_Rings_Olinordered__semidom(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),c_Groups_Ozero__class_Ozero(X20)),c_Groups_Oone__class_Oone(X20))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33905,plain,
spl647_779,
inference(avatar_split_clause,[],[f17572,f33903]) ).
fof(f33903,plain,
( spl647_779
<=> ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oone__class_Oone(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_779])]) ).
fof(f17572,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oone__class_Oone(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[],[f10365]) ).
fof(f10365,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oone__class_Oone(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(ennf_transformation,[],[f5537]) ).
fof(f5537,plain,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X0),c_Groups_Ozero__class_Ozero(X0)),c_Groups_Oone__class_Oone(X0))) ),
inference(rectify,[],[f860]) ).
fof(f860,axiom,
! [X20] :
( class_Rings_Olinordered__semidom(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20),c_Groups_Ozero__class_Ozero(X20)),c_Groups_Oone__class_Oone(X20))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33901,plain,
spl647_778,
inference(avatar_split_clause,[],[f17571,f33899]) ).
fof(f33899,plain,
( spl647_778
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_778])]) ).
fof(f17571,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[],[f10364]) ).
fof(f10364,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(ennf_transformation,[],[f5536]) ).
fof(f5536,plain,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0))) ),
inference(rectify,[],[f858]) ).
fof(f858,axiom,
! [X20] :
( class_Rings_Olinordered__semidom(X20)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),c_Groups_Oone__class_Oone(X20)),c_Groups_Ozero__class_Ozero(X20))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33897,plain,
spl647_777,
inference(avatar_split_clause,[],[f17570,f33895]) ).
fof(f33895,plain,
( spl647_777
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X0),c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_777])]) ).
fof(f17570,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X0),c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(cnf_transformation,[],[f10363]) ).
fof(f10363,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X0),c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0)))
| ~ class_Rings_Olinordered__semidom(X0) ),
inference(ennf_transformation,[],[f5535]) ).
fof(f5535,plain,
! [X0] :
( class_Rings_Olinordered__semidom(X0)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X0),c_Groups_Oone__class_Oone(X0)),c_Groups_Ozero__class_Ozero(X0))) ),
inference(rectify,[],[f859]) ).
fof(f859,axiom,
! [X20] :
( class_Rings_Olinordered__semidom(X20)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20),c_Groups_Oone__class_Oone(X20)),c_Groups_Ozero__class_Ozero(X20))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33893,plain,
spl647_776,
inference(avatar_split_clause,[],[f17567,f33891]) ).
fof(f33891,plain,
( spl647_776
<=> ! [X0] :
( hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Ozero__class_Ozero(X0)),c_Nat_Osemiring__1__class_ONats(X0)))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_776])]) ).
fof(f17567,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Ozero__class_Ozero(X0)),c_Nat_Osemiring__1__class_ONats(X0)))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10360]) ).
fof(f10360,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Ozero__class_Ozero(X0)),c_Nat_Osemiring__1__class_ONats(X0)))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5532]) ).
fof(f5532,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Ozero__class_Ozero(X0)),c_Nat_Osemiring__1__class_ONats(X0))) ),
inference(rectify,[],[f1321]) ).
fof(f1321,axiom,
! [X4] :
( class_Rings_Osemiring__1(X4)
=> hBOOL(hAPP(hAPP(c_member(X4),c_Groups_Ozero__class_Ozero(X4)),c_Nat_Osemiring__1__class_ONats(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33889,plain,
spl647_775,
inference(avatar_split_clause,[],[f17566,f33887]) ).
fof(f33887,plain,
( spl647_775
<=> ! [X0] :
( hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Oone__class_Oone(X0)),c_Nat_Osemiring__1__class_ONats(X0)))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_775])]) ).
fof(f17566,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Oone__class_Oone(X0)),c_Nat_Osemiring__1__class_ONats(X0)))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10359]) ).
fof(f10359,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Oone__class_Oone(X0)),c_Nat_Osemiring__1__class_ONats(X0)))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5531]) ).
fof(f5531,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Oone__class_Oone(X0)),c_Nat_Osemiring__1__class_ONats(X0))) ),
inference(rectify,[],[f1324]) ).
fof(f1324,axiom,
! [X4] :
( class_Rings_Osemiring__1(X4)
=> hBOOL(hAPP(hAPP(c_member(X4),c_Groups_Oone__class_Oone(X4)),c_Nat_Osemiring__1__class_ONats(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33885,plain,
spl647_774,
inference(avatar_split_clause,[],[f17558,f33883]) ).
fof(f33883,plain,
( spl647_774
<=> ! [X0] :
( c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0))
| ~ class_Power_Opower(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_774])]) ).
fof(f17558,plain,
! [X0] :
( c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0))
| ~ class_Power_Opower(X0) ),
inference(cnf_transformation,[],[f10351]) ).
fof(f10351,plain,
! [X0] :
( c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0))
| ~ class_Power_Opower(X0) ),
inference(ennf_transformation,[],[f5523]) ).
fof(f5523,plain,
! [X0] :
( class_Power_Opower(X0)
=> c_Power_Opower__class_Opower(X0) = c_Power_Opower_Opower(X0,c_Groups_Oone__class_Oone(X0),c_Groups_Otimes__class_Otimes(X0)) ),
inference(rectify,[],[f1950]) ).
fof(f1950,axiom,
! [X4] :
( class_Power_Opower(X4)
=> c_Power_Opower__class_Opower(X4) = c_Power_Opower_Opower(X4,c_Groups_Oone__class_Oone(X4),c_Groups_Otimes__class_Otimes(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33881,plain,
spl647_773,
inference(avatar_split_clause,[],[f17555,f33879]) ).
fof(f33879,plain,
( spl647_773
<=> ! [X0] :
( c_Fun_Oinj__on(tc_Nat_Onat,X0,c_Nat_Osemiring__1__class_Oof__nat(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ class_Nat_Osemiring__char__0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_773])]) ).
fof(f17555,plain,
! [X0] :
( c_Fun_Oinj__on(tc_Nat_Onat,X0,c_Nat_Osemiring__1__class_Oof__nat(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ class_Nat_Osemiring__char__0(X0) ),
inference(cnf_transformation,[],[f10348]) ).
fof(f10348,plain,
! [X0] :
( c_Fun_Oinj__on(tc_Nat_Onat,X0,c_Nat_Osemiring__1__class_Oof__nat(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ class_Nat_Osemiring__char__0(X0) ),
inference(ennf_transformation,[],[f5520]) ).
fof(f5520,plain,
! [X0] :
( class_Nat_Osemiring__char__0(X0)
=> c_Fun_Oinj__on(tc_Nat_Onat,X0,c_Nat_Osemiring__1__class_Oof__nat(X0),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(rectify,[],[f3092]) ).
fof(f3092,axiom,
! [X4] :
( class_Nat_Osemiring__char__0(X4)
=> c_Fun_Oinj__on(tc_Nat_Onat,X4,c_Nat_Osemiring__1__class_Oof__nat(X4),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33877,plain,
spl647_772,
inference(avatar_split_clause,[],[f17554,f33875]) ).
fof(f33875,plain,
( spl647_772
<=> ! [X0] :
( c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_772])]) ).
fof(f17554,plain,
! [X0] :
( c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(cnf_transformation,[],[f10347]) ).
fof(f10347,plain,
! [X0] :
( c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(ennf_transformation,[],[f5519]) ).
fof(f5519,plain,
! [X0] :
( class_Complete__Lattice_Ocomplete__lattice(X0)
=> c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OSup__class_OSup(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) ),
inference(rectify,[],[f709]) ).
fof(f709,axiom,
! [X4] :
( class_Complete__Lattice_Ocomplete__lattice(X4)
=> c_Orderings_Obot__class_Obot(X4) = c_Complete__Lattice_OSup__class_OSup(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33871,plain,
spl647_771,
inference(avatar_split_clause,[],[f17553,f33869]) ).
fof(f33869,plain,
( spl647_771
<=> ! [X0] :
( c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_771])]) ).
fof(f17553,plain,
! [X0] :
( c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(cnf_transformation,[],[f10346]) ).
fof(f10346,plain,
! [X0] :
( c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(ennf_transformation,[],[f5518]) ).
fof(f5518,plain,
! [X0] :
( class_Complete__Lattice_Ocomplete__lattice(X0)
=> c_Orderings_Obot__class_Obot(X0) = c_Complete__Lattice_OInf__class_OInf(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(rectify,[],[f2135]) ).
fof(f2135,axiom,
! [X4] :
( class_Complete__Lattice_Ocomplete__lattice(X4)
=> c_Orderings_Obot__class_Obot(X4) = c_Complete__Lattice_OInf__class_OInf(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33867,plain,
spl647_770,
inference(avatar_split_clause,[],[f17552,f33865]) ).
fof(f33865,plain,
( spl647_770
<=> ! [X0] :
( c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OSup__class_OSup(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_770])]) ).
fof(f17552,plain,
! [X0] :
( c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OSup__class_OSup(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(cnf_transformation,[],[f10345]) ).
fof(f10345,plain,
! [X0] :
( c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OSup__class_OSup(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(ennf_transformation,[],[f5517]) ).
fof(f5517,plain,
! [X0] :
( class_Complete__Lattice_Ocomplete__lattice(X0)
=> c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OSup__class_OSup(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool))) ),
inference(rectify,[],[f2083]) ).
fof(f2083,axiom,
! [X4] :
( class_Complete__Lattice_Ocomplete__lattice(X4)
=> c_Orderings_Otop__class_Otop(X4) = c_Complete__Lattice_OSup__class_OSup(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33863,plain,
spl647_769,
inference(avatar_split_clause,[],[f17551,f33861]) ).
fof(f33861,plain,
( spl647_769
<=> ! [X0] :
( c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_769])]) ).
fof(f17551,plain,
! [X0] :
( c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(cnf_transformation,[],[f10344]) ).
fof(f10344,plain,
! [X0] :
( c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))
| ~ class_Complete__Lattice_Ocomplete__lattice(X0) ),
inference(ennf_transformation,[],[f5516]) ).
fof(f5516,plain,
! [X0] :
( class_Complete__Lattice_Ocomplete__lattice(X0)
=> c_Orderings_Otop__class_Otop(X0) = c_Complete__Lattice_OInf__class_OInf(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) ),
inference(rectify,[],[f2145]) ).
fof(f2145,axiom,
! [X4] :
( class_Complete__Lattice_Ocomplete__lattice(X4)
=> c_Orderings_Otop__class_Otop(X4) = c_Complete__Lattice_OInf__class_OInf(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33859,plain,
spl647_768,
inference(avatar_split_clause,[],[f17535,f33857]) ).
fof(f33857,plain,
( spl647_768
<=> ! [X0] :
( hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Ozero__class_Ozero(X0)),c_Int_Oring__1__class_OInts(X0)))
| ~ class_Rings_Oring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_768])]) ).
fof(f17535,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Ozero__class_Ozero(X0)),c_Int_Oring__1__class_OInts(X0)))
| ~ class_Rings_Oring__1(X0) ),
inference(cnf_transformation,[],[f10328]) ).
fof(f10328,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Ozero__class_Ozero(X0)),c_Int_Oring__1__class_OInts(X0)))
| ~ class_Rings_Oring__1(X0) ),
inference(ennf_transformation,[],[f5500]) ).
fof(f5500,plain,
! [X0] :
( class_Rings_Oring__1(X0)
=> hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Ozero__class_Ozero(X0)),c_Int_Oring__1__class_OInts(X0))) ),
inference(rectify,[],[f976]) ).
fof(f976,axiom,
! [X4] :
( class_Rings_Oring__1(X4)
=> hBOOL(hAPP(hAPP(c_member(X4),c_Groups_Ozero__class_Ozero(X4)),c_Int_Oring__1__class_OInts(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33855,plain,
spl647_767,
inference(avatar_split_clause,[],[f17534,f33853]) ).
fof(f33853,plain,
( spl647_767
<=> ! [X0] :
( hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Oone__class_Oone(X0)),c_Int_Oring__1__class_OInts(X0)))
| ~ class_Rings_Oring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_767])]) ).
fof(f17534,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Oone__class_Oone(X0)),c_Int_Oring__1__class_OInts(X0)))
| ~ class_Rings_Oring__1(X0) ),
inference(cnf_transformation,[],[f10327]) ).
fof(f10327,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Oone__class_Oone(X0)),c_Int_Oring__1__class_OInts(X0)))
| ~ class_Rings_Oring__1(X0) ),
inference(ennf_transformation,[],[f5499]) ).
fof(f5499,plain,
! [X0] :
( class_Rings_Oring__1(X0)
=> hBOOL(hAPP(hAPP(c_member(X0),c_Groups_Oone__class_Oone(X0)),c_Int_Oring__1__class_OInts(X0))) ),
inference(rectify,[],[f980]) ).
fof(f980,axiom,
! [X4] :
( class_Rings_Oring__1(X4)
=> hBOOL(hAPP(hAPP(c_member(X4),c_Groups_Oone__class_Oone(X4)),c_Int_Oring__1__class_OInts(X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33851,plain,
spl647_766,
inference(avatar_split_clause,[],[f17402,f33849]) ).
fof(f33849,plain,
( spl647_766
<=> ! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_766])]) ).
fof(f17402,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f5380]) ).
fof(f5380,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(rectify,[],[f470]) ).
fof(f470,axiom,
! [X44] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33847,plain,
spl647_765,
inference(avatar_split_clause,[],[f17400,f33845]) ).
fof(f33845,plain,
( spl647_765
<=> ! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_765])]) ).
fof(f33843,plain,
spl647_764,
inference(avatar_split_clause,[],[f17398,f33841]) ).
fof(f33841,plain,
( spl647_764
<=> ! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X0)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_764])]) ).
fof(f17398,plain,
! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X0)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f5376]) ).
fof(f5376,plain,
! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X0)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)),
inference(rectify,[],[f1415]) ).
fof(f1415,axiom,
! [X53] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X53)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X53)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33839,plain,
spl647_763,
inference(avatar_split_clause,[],[f17397,f33837]) ).
fof(f33837,plain,
( spl647_763
<=> ! [X0] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_763])]) ).
fof(f33835,plain,
spl647_762,
inference(avatar_split_clause,[],[f17394,f33833]) ).
fof(f33833,plain,
( spl647_762
<=> ! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_762])]) ).
fof(f17394,plain,
! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X0),
inference(cnf_transformation,[],[f5372]) ).
fof(f5372,plain,
! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X0),
inference(rectify,[],[f1978]) ).
fof(f1978,axiom,
! [X53] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X53) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X53),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33831,plain,
( spl647_761
| ~ spl647_743 ),
inference(avatar_split_clause,[],[f33791,f32835,f33829]) ).
fof(f33829,plain,
( spl647_761
<=> ! [X0] : sP12(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_761])]) ).
fof(f32835,plain,
( spl647_743
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) != hAPP(c_Int_Onat,X1)
| sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_743])]) ).
fof(f33791,plain,
( ! [X0] : sP12(X0,X0)
| ~ spl647_743 ),
inference(equality_resolution,[],[f32836]) ).
fof(f32836,plain,
( ! [X0,X1] :
( hAPP(c_Int_Onat,X0) != hAPP(c_Int_Onat,X1)
| sP12(X0,X1) )
| ~ spl647_743 ),
inference(avatar_component_clause,[],[f32835]) ).
fof(f33827,plain,
spl647_760,
inference(avatar_split_clause,[],[f17392,f33825]) ).
fof(f33825,plain,
( spl647_760
<=> ! [X0] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X0) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_760])]) ).
fof(f17392,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X0) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),
inference(cnf_transformation,[],[f5370]) ).
fof(f5370,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X0) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),
inference(rectify,[],[f2957]) ).
fof(f2957,axiom,
! [X48] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X48) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X48)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33823,plain,
spl647_759,
inference(avatar_split_clause,[],[f17391,f33821]) ).
fof(f33821,plain,
( spl647_759
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Relation_ODomain(X0,X0),c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_759])]) ).
fof(f17391,plain,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Relation_ODomain(X0,X0),c_Relation_OId(X0)),
inference(cnf_transformation,[],[f5369]) ).
fof(f5369,plain,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Relation_ODomain(X0,X0),c_Relation_OId(X0)),
inference(rectify,[],[f3605]) ).
fof(f3605,axiom,
! [X4] : c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Relation_ODomain(X4,X4),c_Relation_OId(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33819,plain,
spl647_758,
inference(avatar_split_clause,[],[f17390,f33817]) ).
fof(f33817,plain,
( spl647_758
<=> ! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Relation_ORange(X0,X0),c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_758])]) ).
fof(f17390,plain,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Relation_ORange(X0,X0),c_Relation_OId(X0)),
inference(cnf_transformation,[],[f5368]) ).
fof(f5368,plain,
! [X0] : c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Relation_ORange(X0,X0),c_Relation_OId(X0)),
inference(rectify,[],[f3606]) ).
fof(f3606,axiom,
! [X4] : c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Relation_ORange(X4,X4),c_Relation_OId(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33815,plain,
spl647_757,
inference(avatar_split_clause,[],[f17388,f33813]) ).
fof(f33813,plain,
( spl647_757
<=> ! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_757])]) ).
fof(f17388,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f5366]) ).
fof(f5366,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(rectify,[],[f665]) ).
fof(f665,axiom,
! [X44] : hAPP(c_Nat_OSuc,X44) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X44),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33811,plain,
spl647_756,
inference(avatar_split_clause,[],[f17387,f33809]) ).
fof(f33809,plain,
( spl647_756
<=> ! [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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_756])]) ).
fof(f33807,plain,
spl647_755,
inference(avatar_split_clause,[],[f17386,f33805]) ).
fof(f33805,plain,
( spl647_755
<=> ! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_755])]) ).
fof(f17386,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0)),
inference(cnf_transformation,[],[f5364]) ).
fof(f5364,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0)),
inference(rectify,[],[f2773]) ).
fof(f2773,axiom,
! [X68] : hAPP(c_Nat_OSuc,X68) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X68)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33803,plain,
spl647_754,
inference(avatar_split_clause,[],[f17217,f33800]) ).
fof(f17217,plain,
c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
inference(cnf_transformation,[],[f3011]) ).
fof(f3011,axiom,
c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Int_Ointrel),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f33784,plain,
( ~ spl647_753
| ~ spl647_337
| ~ spl647_675 ),
inference(avatar_split_clause,[],[f33379,f32549,f30853,f33781]) ).
fof(f33781,plain,
( spl647_753
<=> sP30(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_753])]) ).
fof(f33379,plain,
( ~ sP30(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless(tc_Int_Oint))
| ~ spl647_337
| ~ spl647_675 ),
inference(resolution,[],[f32550,f30855]) ).
fof(f33759,plain,
( spl647_752
| ~ spl647_349
| ~ spl647_675 ),
inference(avatar_split_clause,[],[f33355,f32549,f30904,f33757]) ).
fof(f33757,plain,
( spl647_752
<=> ! [X0] : ~ sP30(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_752])]) ).
fof(f30904,plain,
( spl647_349
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_349])]) ).
fof(f33355,plain,
( ! [X0] : ~ sP30(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat))
| ~ spl647_349
| ~ spl647_675 ),
inference(resolution,[],[f32550,f30905]) ).
fof(f30905,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0))
| ~ spl647_349 ),
inference(avatar_component_clause,[],[f30904]) ).
fof(f33709,plain,
( spl647_751
| ~ spl647_348
| ~ spl647_675 ),
inference(avatar_split_clause,[],[f33354,f32549,f30900,f33707]) ).
fof(f33707,plain,
( spl647_751
<=> ! [X0] : ~ sP30(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_751])]) ).
fof(f33354,plain,
( ! [X0] : ~ sP30(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint))
| ~ spl647_348
| ~ spl647_675 ),
inference(resolution,[],[f32550,f30901]) ).
fof(f33648,plain,
( spl647_750
| ~ spl647_347
| ~ spl647_675 ),
inference(avatar_split_clause,[],[f33353,f32549,f30896,f33646]) ).
fof(f33646,plain,
( spl647_750
<=> ! [X0] : ~ sP30(X0,X0,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_750])]) ).
fof(f30896,plain,
( spl647_347
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_347])]) ).
fof(f33353,plain,
( ! [X0] : ~ sP30(X0,X0,c_Rings_Odvd__class_Odvd(tc_Nat_Onat))
| ~ spl647_347
| ~ spl647_675 ),
inference(resolution,[],[f32550,f30897]) ).
fof(f30897,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0))
| ~ spl647_347 ),
inference(avatar_component_clause,[],[f30896]) ).
fof(f33513,plain,
( spl647_749
| ~ spl647_306
| ~ spl647_675 ),
inference(avatar_split_clause,[],[f33352,f32549,f30687,f33511]) ).
fof(f33511,plain,
( spl647_749
<=> ! [X0] : ~ sP30(X0,X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_749])]) ).
fof(f33352,plain,
( ! [X0] : ~ sP30(X0,X0,c_fequal)
| ~ spl647_306
| ~ spl647_675 ),
inference(resolution,[],[f32550,f30688]) ).
fof(f32921,plain,
( spl647_747
| ~ spl647_748
| ~ spl647_576
| ~ spl647_633 ),
inference(avatar_split_clause,[],[f32891,f32370,f31907,f32918,f32914]) ).
fof(f32914,plain,
( spl647_747
<=> c_Nat__Transfer_Ois__nat(c_Orderings_Otop__class_Otop(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_747])]) ).
fof(f32918,plain,
( spl647_748
<=> class_Orderings_Otop(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_748])]) ).
fof(f32370,plain,
( spl647_633
<=> ! [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,[spl647_633])]) ).
fof(f32891,plain,
( ~ class_Orderings_Otop(tc_Int_Oint)
| c_Nat__Transfer_Ois__nat(c_Orderings_Otop__class_Otop(tc_Int_Oint))
| ~ spl647_576
| ~ spl647_633 ),
inference(resolution,[],[f32371,f31908]) ).
fof(f32371,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) )
| ~ spl647_633 ),
inference(avatar_component_clause,[],[f32370]) ).
fof(f32851,plain,
( spl647_746
| ~ spl647_372
| ~ spl647_607 ),
inference(avatar_split_clause,[],[f32846,f32265,f30996,f32849]) ).
fof(f32849,plain,
( spl647_746
<=> ! [X0] : ~ class_Finite__Set_Ofinite(tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_746])]) ).
fof(f30996,plain,
( spl647_372
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_372])]) ).
fof(f32265,plain,
( spl647_607
<=> ! [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,[spl647_607])]) ).
fof(f32846,plain,
( ! [X0] : ~ class_Finite__Set_Ofinite(tc_List_Olist(X0))
| ~ spl647_372
| ~ spl647_607 ),
inference(resolution,[],[f32266,f30997]) ).
fof(f30997,plain,
( ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) )
| ~ spl647_372 ),
inference(avatar_component_clause,[],[f30996]) ).
fof(f32266,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))))
| ~ spl647_607 ),
inference(avatar_component_clause,[],[f32265]) ).
fof(f32845,plain,
spl647_745,
inference(avatar_split_clause,[],[f28885,f32843]) ).
fof(f32843,plain,
( spl647_745
<=> ! [X2,X1,X3] : hBOOL(hAPP(hAPP(c_List_Omember(X3),c_List_Oinsert(X3,X2,X1)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_745])]) ).
fof(f28885,plain,
! [X2,X3,X1] : hBOOL(hAPP(hAPP(c_List_Omember(X3),c_List_Oinsert(X3,X2,X1)),X2)),
inference(forward_demodulation,[],[f25722,f27823]) ).
fof(f27823,plain,
! [X2,X0,X1] : hAPP(c_List_Omember(X2),c_List_Oinsert(X2,X1,X0)) = hAPP(c_List_Omember(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)),
inference(forward_demodulation,[],[f24641,f24632]) ).
fof(f24632,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X2),X1),hAPP(c_List_Omember(X2),X0)) = hAPP(c_List_Omember(X2),c_List_Oinsert(X2,X1,X0)),
inference(definition_unfolding,[],[f19655,f17267,f17267]) ).
fof(f19655,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X2),X1),hAPP(c_List_Oset(X2),X0)) = hAPP(c_List_Oset(X2),c_List_Oinsert(X2,X1,X0)),
inference(cnf_transformation,[],[f7009]) ).
fof(f7009,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X1),hAPP(c_List_Oset(X2),X0)) = hAPP(c_List_Oset(X2),c_List_Oinsert(X2,X1,X0)),
inference(rectify,[],[f4520]) ).
fof(f4520,axiom,
! [X203,X13,X4] : hAPP(hAPP(c_Set_Oinsert(X4),X13),hAPP(c_List_Oset(X4),X203)) = hAPP(c_List_Oset(X4),c_List_Oinsert(X4,X13,X203)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f24641,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X2),X1),hAPP(c_List_Omember(X2),X0)) = hAPP(c_List_Omember(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)),
inference(definition_unfolding,[],[f19675,f17267,f17267]) ).
fof(f19675,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Set_Oinsert(X2),X1),hAPP(c_List_Oset(X2),X0)) = hAPP(c_List_Oset(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)),
inference(cnf_transformation,[],[f7029]) ).
fof(f7029,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Set_Oinsert(X2),X1),hAPP(c_List_Oset(X2),X0)) = hAPP(c_List_Oset(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)),
inference(rectify,[],[f3797]) ).
fof(f3797,axiom,
! [X203,X13,X4] : hAPP(c_List_Oset(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X203)) = hAPP(hAPP(c_Set_Oinsert(X4),X13),hAPP(c_List_Oset(X4),X203)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f25722,plain,
! [X2,X3,X1] : hBOOL(hAPP(hAPP(c_List_Omember(X3),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X1)),X2)),
inference(equality_resolution,[],[f22686]) ).
fof(f22686,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_List_Omember(X3),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X1)),X0))
| X0 != X2 ),
inference(cnf_transformation,[],[f16347]) ).
fof(f16347,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_List_Omember(X3),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X1)),X0))
| ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X3),X1),X0))
& X0 != X2 ) )
& ( hBOOL(hAPP(hAPP(c_List_Omember(X3),X1),X0))
| X0 = X2
| ~ hBOOL(hAPP(hAPP(c_List_Omember(X3),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X1)),X0)) ) ),
inference(flattening,[],[f16346]) ).
fof(f16346,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_List_Omember(X3),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X1)),X0))
| ( ~ hBOOL(hAPP(hAPP(c_List_Omember(X3),X1),X0))
& X0 != X2 ) )
& ( hBOOL(hAPP(hAPP(c_List_Omember(X3),X1),X0))
| X0 = X2
| ~ hBOOL(hAPP(hAPP(c_List_Omember(X3),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X1)),X0)) ) ),
inference(nnf_transformation,[],[f9172]) ).
fof(f9172,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_List_Omember(X3),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X1)),X0))
<=> ( hBOOL(hAPP(hAPP(c_List_Omember(X3),X1),X0))
| X0 = X2 ) ),
inference(rectify,[],[f4669]) ).
fof(f4669,axiom,
! [X15,X203,X13,X4] :
( hBOOL(hAPP(hAPP(c_List_Omember(X4),hAPP(hAPP(c_List_Olist_OCons(X4),X13),X203)),X15))
<=> ( hBOOL(hAPP(hAPP(c_List_Omember(X4),X203),X15))
| X13 = X15 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32841,plain,
spl647_744,
inference(avatar_split_clause,[],[f28052,f32839]) ).
fof(f32839,plain,
( spl647_744
<=> ! [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,[spl647_744])]) ).
fof(f28052,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,[],[f20151,f17145]) ).
fof(f20151,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,[],[f11561]) ).
fof(f11561,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,[],[f7434]) ).
fof(f7434,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,[],[f2290]) ).
fof(f2290,axiom,
! [X63,X139,X4] :
( class_Rings_Osemiring__1(X4)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X4,X139,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X63) = X63 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32837,plain,
spl647_743,
inference(avatar_split_clause,[],[f27576,f32835]) ).
fof(f27576,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) != hAPP(c_Int_Onat,X1)
| sP12(X0,X1) ),
inference(forward_demodulation,[],[f27575,f26052]) ).
fof(f27575,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) != hAPP(c_Int_Onat,X1)
| sP12(X0,X1) ),
inference(forward_demodulation,[],[f19329,f26052]) ).
fof(f19329,plain,
! [X0,X1] :
( sP12(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,[],[f15145]) ).
fof(f15145,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)
| ~ sP12(X0,X1) )
& ( sP12(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,[],[f14498]) ).
fof(f14498,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)
<=> sP12(X0,X1) ),
inference(definition_folding,[],[f11291,f14497,f14496]) ).
fof(f14496,plain,
! [X1,X0] :
( sP11(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,[sP11])]) ).
fof(f11291,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,[],[f6830]) ).
fof(f6830,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,[],[f1306]) ).
fof(f1306,axiom,
! [X113,X73] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X73) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X113)
<=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X73)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X113)))
=> X73 = X113 )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X113)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X73) ) ) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X73)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X113)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32833,plain,
spl647_742,
inference(avatar_split_clause,[],[f27574,f32831]) ).
fof(f32831,plain,
( spl647_742
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) = hAPP(c_Int_Onat,X1)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_742])]) ).
fof(f27574,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = hAPP(c_Int_Onat,X1)
| ~ sP12(X0,X1) ),
inference(forward_demodulation,[],[f27573,f26052]) ).
fof(f27573,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X1)
| ~ sP12(X0,X1) ),
inference(forward_demodulation,[],[f19330,f26052]) ).
fof(f19330,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)
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f15145]) ).
fof(f32829,plain,
spl647_741,
inference(avatar_split_clause,[],[f27572,f32827]) ).
fof(f27572,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Int_OPls = X0
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f27571,f17285]) ).
fof(f27571,plain,
! [X0,X1] :
( c_Int_OPls = X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f27570,f17135]) ).
fof(f27570,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)))
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f19323,f17285]) ).
fof(f19323,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)))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f15144]) ).
fof(f15144,plain,
! [X0,X1] :
( ( sP11(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))) ) )
| ~ sP11(X0,X1) ) ),
inference(rectify,[],[f15143]) ).
fof(f15143,plain,
! [X1,X0] :
( ( sP11(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))) ) )
| ~ sP11(X1,X0) ) ),
inference(flattening,[],[f15142]) ).
fof(f15142,plain,
! [X1,X0] :
( ( sP11(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))) ) )
| ~ sP11(X1,X0) ) ),
inference(nnf_transformation,[],[f14496]) ).
fof(f32825,plain,
spl647_740,
inference(avatar_split_clause,[],[f27569,f32823]) ).
fof(f32823,plain,
( spl647_740
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| X0 = X1
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_740])]) ).
fof(f27569,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| X0 = X1
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f19324,f17285]) ).
fof(f19324,plain,
! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f15144]) ).
fof(f32821,plain,
spl647_739,
inference(avatar_split_clause,[],[f27568,f32819]) ).
fof(f32819,plain,
( spl647_739
<=> ! [X0,X1] :
( c_Int_OPls != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_739])]) ).
fof(f27568,plain,
! [X0,X1] :
( c_Int_OPls != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X0,X1) ),
inference(forward_demodulation,[],[f27567,f17135]) ).
fof(f27567,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X0,X1) ),
inference(forward_demodulation,[],[f27566,f17285]) ).
fof(f27566,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ),
inference(forward_demodulation,[],[f19326,f17285]) ).
fof(f19326,plain,
! [X0,X1] :
( sP11(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,[],[f15144]) ).
fof(f32817,plain,
spl647_738,
inference(avatar_split_clause,[],[f27559,f32815]) ).
fof(f32815,plain,
( spl647_738
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X1,X0)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_738])]) ).
fof(f27559,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X1,X0)
| ~ sP12(X0,X1) ),
inference(forward_demodulation,[],[f19318,f17285]) ).
fof(f19318,plain,
! [X0,X1] :
( sP11(X1,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP12(X0,X1) ),
inference(cnf_transformation,[],[f15141]) ).
fof(f32813,plain,
spl647_737,
inference(avatar_split_clause,[],[f27555,f32811]) ).
fof(f32811,plain,
( spl647_737
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP12(X0,X1)
| ~ sP11(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_737])]) ).
fof(f27555,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP12(X0,X1)
| ~ sP11(X1,X0) ),
inference(forward_demodulation,[],[f19321,f17285]) ).
fof(f19321,plain,
! [X0,X1] :
( sP12(X0,X1)
| ~ sP11(X1,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(cnf_transformation,[],[f15141]) ).
fof(f32809,plain,
spl647_736,
inference(avatar_split_clause,[],[f27543,f32807]) ).
fof(f32807,plain,
( spl647_736
<=> ! [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,[spl647_736])]) ).
fof(f27543,plain,
! [X3,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0
| ~ hBOOL(hAPP(X0,X3)) ),
inference(forward_demodulation,[],[f19302,f17793]) ).
fof(f19302,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,[],[f15129]) ).
fof(f32805,plain,
spl647_735,
inference(avatar_split_clause,[],[f27524,f32803]) ).
fof(f32803,plain,
( spl647_735
<=> ! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_735])]) ).
fof(f27524,plain,
! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP9(X0,X1) ),
inference(forward_demodulation,[],[f19274,f17285]) ).
fof(f19274,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
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f15113]) ).
fof(f15113,plain,
! [X0,X1] :
( ( sP9(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 )
| ~ sP9(X0,X1) ) ),
inference(flattening,[],[f15112]) ).
fof(f15112,plain,
! [X0,X1] :
( ( sP9(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 )
| ~ sP9(X0,X1) ) ),
inference(nnf_transformation,[],[f14492]) ).
fof(f32801,plain,
spl647_734,
inference(avatar_split_clause,[],[f27523,f32799]) ).
fof(f32799,plain,
( spl647_734
<=> ! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_734])]) ).
fof(f27523,plain,
! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP9(X0,X1) ),
inference(forward_demodulation,[],[f19275,f17285]) ).
fof(f19275,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
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f15113]) ).
fof(f32797,plain,
spl647_733,
inference(avatar_split_clause,[],[f27522,f32795]) ).
fof(f32795,plain,
( spl647_733
<=> ! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_733])]) ).
fof(f27522,plain,
! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP9(X0,X1) ),
inference(forward_demodulation,[],[f19276,f17285]) ).
fof(f19276,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
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f15113]) ).
fof(f32793,plain,
spl647_732,
inference(avatar_split_clause,[],[f27521,f32791]) ).
fof(f32791,plain,
( spl647_732
<=> ! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_732])]) ).
fof(f27521,plain,
! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP9(X0,X1) ),
inference(forward_demodulation,[],[f19277,f17285]) ).
fof(f19277,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
| ~ sP9(X0,X1) ),
inference(cnf_transformation,[],[f15113]) ).
fof(f32789,plain,
spl647_731,
inference(avatar_split_clause,[],[f26972,f32787]) ).
fof(f32787,plain,
( spl647_731
<=> ! [X0,X1] :
( hAPP(c_fequal,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_731])]) ).
fof(f26972,plain,
! [X0,X1] :
( hAPP(c_fequal,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(forward_demodulation,[],[f18640,f26468]) ).
fof(f18640,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,[],[f10813]) ).
fof(f10813,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,[],[f6406]) ).
fof(f6406,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,[],[f2582]) ).
fof(f2582,axiom,
! [X5,X4] :
( class_Orderings_Oorder(X4)
=> hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X4,X5,X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32785,plain,
spl647_730,
inference(avatar_split_clause,[],[f26605,f32783]) ).
fof(f32783,plain,
( spl647_730
<=> ! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_730])]) ).
fof(f26605,plain,
! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25279,f17145]) ).
fof(f25279,plain,
! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f18189]) ).
fof(f18189,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f10451]) ).
fof(f10451,plain,
! [X0,X1] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(ennf_transformation,[],[f6072]) ).
fof(f6072,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) ) ),
inference(rectify,[],[f1839]) ).
fof(f1839,axiom,
! [X123,X45] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X45
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X123),X45) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X123),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X123),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X45
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X123),X45) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32781,plain,
spl647_729,
inference(avatar_split_clause,[],[f26448,f32779]) ).
fof(f32779,plain,
( spl647_729
<=> ! [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,[spl647_729])]) ).
fof(f26448,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,[],[f17858,f17145]) ).
fof(f17858,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,[],[f5750]) ).
fof(f5750,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,[],[f3887]) ).
fof(f3887,axiom,
! [X201,X20] : c_List_Olist_ONil(X20) = hAPP(hAPP(c_List_Otake(X20),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X201),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32777,plain,
spl647_728,
inference(avatar_split_clause,[],[f26338,f32775]) ).
fof(f32775,plain,
( spl647_728
<=> ! [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,[spl647_728])]) ).
fof(f26338,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,[],[f26337,f17135]) ).
fof(f26337,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,[],[f17673,f17145]) ).
fof(f17673,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,[],[f14666]) ).
fof(f14666,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,[],[f5616]) ).
fof(f5616,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,[],[f1228]) ).
fof(f1228,axiom,
! [X46] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X46)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X46 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32773,plain,
spl647_727,
inference(avatar_split_clause,[],[f26317,f32771]) ).
fof(f26317,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK93(X0)))
| c_Nat__Transfer_Onat__set(X0) ),
inference(forward_demodulation,[],[f17644,f17135]) ).
fof(f17644,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)),sK93(X0))) ),
inference(cnf_transformation,[],[f14644]) ).
fof(f14644,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)),sK93(X0)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK93(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,[sK93])],[f14642,f14643]) ).
fof(f14643,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)),sK93(X0)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK93(X0)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14642,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,[],[f14641]) ).
fof(f14641,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,[],[f10435]) ).
fof(f10435,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,[],[f5602]) ).
fof(f5602,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,[],[f2934]) ).
fof(f2934,axiom,
! [X70] :
( c_Nat__Transfer_Onat__set(X70)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X70))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32769,plain,
spl647_726,
inference(avatar_split_clause,[],[f26217,f32767]) ).
fof(f26217,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f17600,f17145]) ).
fof(f17600,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,[],[f10392]) ).
fof(f10392,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,[],[f5564]) ).
fof(f5564,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0) ),
inference(rectify,[],[f1791]) ).
fof(f1791,axiom,
! [X27] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X27))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X27) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32765,plain,
spl647_725,
inference(avatar_split_clause,[],[f26205,f32763]) ).
fof(f32763,plain,
( spl647_725
<=> ! [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,[spl647_725])]) ).
fof(f26205,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,[],[f17565,f17145]) ).
fof(f17565,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,[],[f10358]) ).
fof(f10358,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,[],[f5530]) ).
fof(f5530,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,[],[f1241]) ).
fof(f1241,axiom,
! [X20] :
( class_Rings_Osemiring__1(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32761,plain,
spl647_724,
inference(avatar_split_clause,[],[f26069,f32759]) ).
fof(f32759,plain,
( spl647_724
<=> ! [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,[spl647_724])]) ).
fof(f26069,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,[],[f26068,f25910]) ).
fof(f26068,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,[],[f17428,f17145]) ).
fof(f17428,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,[],[f5406]) ).
fof(f5406,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,[],[f1901]) ).
fof(f1901,axiom,
! [X44] : 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))),X44),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32757,plain,
spl647_723,
inference(avatar_split_clause,[],[f26057,f32755]) ).
fof(f32755,plain,
( spl647_723
<=> ! [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,[spl647_723])]) ).
fof(f26057,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,[],[f17403,f17135]) ).
fof(f17403,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,[],[f5381]) ).
fof(f5381,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,[],[f1219]) ).
fof(f1219,axiom,
! [X27] : 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),X27))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32753,plain,
spl647_722,
inference(avatar_split_clause,[],[f26054,f32751]) ).
fof(f32751,plain,
( spl647_722
<=> ! [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,[spl647_722])]) ).
fof(f26054,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,[],[f17399,f26052]) ).
fof(f17399,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,[],[f5377]) ).
fof(f5377,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,[],[f4203]) ).
fof(f4203,axiom,
! [X53] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X53)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X53),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32749,plain,
( spl647_721
| ~ spl647_372
| ~ spl647_549 ),
inference(avatar_split_clause,[],[f32165,f31792,f30996,f32747]) ).
fof(f32747,plain,
( spl647_721
<=> ! [X2,X0,X1] :
( sP24(X0,X1,X2)
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_721])]) ).
fof(f31792,plain,
( spl647_549
<=> ! [X2,X0,X1] :
( sP24(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_549])]) ).
fof(f32165,plain,
( ! [X2,X0,X1] :
( sP24(X0,X1,X2)
| ~ class_Finite__Set_Ofinite(X0) )
| ~ spl647_372
| ~ spl647_549 ),
inference(resolution,[],[f31793,f30997]) ).
fof(f31793,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| sP24(X2,X1,X0) )
| ~ spl647_549 ),
inference(avatar_component_clause,[],[f31792]) ).
fof(f32745,plain,
spl647_720,
inference(avatar_split_clause,[],[f26049,f32743]) ).
fof(f32743,plain,
( spl647_720
<=> ! [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,[spl647_720])]) ).
fof(f26049,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,[],[f17383,f17135]) ).
fof(f17383,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,[],[f5361]) ).
fof(f5361,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,[],[f1230]) ).
fof(f1230,axiom,
! [X53] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X53)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32741,plain,
spl647_719,
inference(avatar_split_clause,[],[f26046,f32739]) ).
fof(f32739,plain,
( spl647_719
<=> ! [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,[spl647_719])]) ).
fof(f26046,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,[],[f17381,f17145]) ).
fof(f17381,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,[],[f5359]) ).
fof(f5359,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,[],[f743]) ).
fof(f743,axiom,
! [X44] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32737,plain,
spl647_718,
inference(avatar_split_clause,[],[f26043,f32735]) ).
fof(f32735,plain,
( spl647_718
<=> ! [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,[spl647_718])]) ).
fof(f26043,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,[],[f17378,f17145]) ).
fof(f17378,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,[],[f5356]) ).
fof(f5356,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,[],[f2771]) ).
fof(f2771,axiom,
! [X46] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X46) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X46),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32733,plain,
spl647_717,
inference(avatar_split_clause,[],[f26042,f32731]) ).
fof(f32731,plain,
( spl647_717
<=> ! [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,[spl647_717])]) ).
fof(f26042,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,[],[f17369,f17145]) ).
fof(f17369,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,[],[f5347]) ).
fof(f5347,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,[],[f872]) ).
fof(f872,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32729,plain,
spl647_716,
inference(avatar_split_clause,[],[f26039,f32727]) ).
fof(f32727,plain,
( spl647_716
<=> ! [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,[spl647_716])]) ).
fof(f32725,plain,
spl647_715,
inference(avatar_split_clause,[],[f26038,f32723]) ).
fof(f32723,plain,
( spl647_715
<=> ! [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,[spl647_715])]) ).
fof(f26038,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,[],[f17366,f17145]) ).
fof(f17366,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,[],[f5344]) ).
fof(f5344,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,[],[f790]) ).
fof(f790,axiom,
! [X44] : 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)),X44),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32721,plain,
spl647_714,
inference(avatar_split_clause,[],[f26037,f32719]) ).
fof(f32719,plain,
( spl647_714
<=> ! [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,[spl647_714])]) ).
fof(f26037,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,[],[f17365,f17145]) ).
fof(f17365,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,[],[f5343]) ).
fof(f5343,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,[],[f1096]) ).
fof(f1096,axiom,
! [X44] : 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)),X44),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32717,plain,
spl647_713,
inference(avatar_split_clause,[],[f26036,f32715]) ).
fof(f32715,plain,
( spl647_713
<=> ! [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,[spl647_713])]) ).
fof(f26036,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,[],[f17364,f17145]) ).
fof(f17364,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,[],[f5342]) ).
fof(f5342,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,[],[f795]) ).
fof(f795,axiom,
! [X45] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X45),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32713,plain,
spl647_712,
inference(avatar_split_clause,[],[f26035,f32711]) ).
fof(f32711,plain,
( spl647_712
<=> ! [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,[spl647_712])]) ).
fof(f26035,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,[],[f17363,f17145]) ).
fof(f17363,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,[],[f5341]) ).
fof(f5341,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,[],[f1097]) ).
fof(f1097,axiom,
! [X44] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X44),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32709,plain,
spl647_711,
inference(avatar_split_clause,[],[f25957,f32706]) ).
fof(f32706,plain,
( spl647_711
<=> 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,[spl647_711])]) ).
fof(f25957,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,[],[f17215,f17134]) ).
fof(f17215,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,[],[f1413]) ).
fof(f1413,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32704,plain,
( spl647_710
| ~ spl647_372
| ~ spl647_548 ),
inference(avatar_split_clause,[],[f32150,f31788,f30996,f32702]) ).
fof(f32702,plain,
( spl647_710
<=> ! [X2,X0,X1] :
( sP22(X0,X1,X2)
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_710])]) ).
fof(f31788,plain,
( spl647_548
<=> ! [X2,X0,X1] :
( sP22(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_548])]) ).
fof(f32150,plain,
( ! [X2,X0,X1] :
( sP22(X0,X1,X2)
| ~ class_Finite__Set_Ofinite(X0) )
| ~ spl647_372
| ~ spl647_548 ),
inference(resolution,[],[f31789,f30997]) ).
fof(f31789,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| sP22(X2,X1,X0) )
| ~ spl647_548 ),
inference(avatar_component_clause,[],[f31788]) ).
fof(f32700,plain,
spl647_709,
inference(avatar_split_clause,[],[f25956,f32697]) ).
fof(f32697,plain,
( spl647_709
<=> 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,[spl647_709])]) ).
fof(f25956,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,[],[f17212,f17145]) ).
fof(f17212,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,[],[f2404]) ).
fof(f2404,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32695,plain,
spl647_708,
inference(avatar_split_clause,[],[f25951,f32692]) ).
fof(f32692,plain,
( spl647_708
<=> 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,[spl647_708])]) ).
fof(f25951,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,[],[f17210,f17145]) ).
fof(f17210,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,[],[f2954]) ).
fof(f2954,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32688,plain,
( spl647_707
| ~ spl647_331
| ~ spl647_497
| ~ spl647_706 ),
inference(avatar_split_clause,[],[f32683,f32679,f31581,f30819,f32685]) ).
fof(f32679,plain,
( spl647_706
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_706])]) ).
fof(f32683,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl647_331
| ~ spl647_497
| ~ spl647_706 ),
inference(forward_demodulation,[],[f32681,f32001]) ).
fof(f32681,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))
| ~ spl647_706 ),
inference(avatar_component_clause,[],[f32679]) ).
fof(f32682,plain,
spl647_706,
inference(avatar_split_clause,[],[f25932,f32679]) ).
fof(f25932,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)),
inference(forward_demodulation,[],[f25931,f25909]) ).
fof(f25931,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(forward_demodulation,[],[f24179,f17133]) ).
fof(f24179,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin)),
inference(definition_unfolding,[],[f17191,f24151]) ).
fof(f17191,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,[],[f1390]) ).
fof(f1390,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32676,plain,
spl647_705,
inference(avatar_split_clause,[],[f25930,f32673]) ).
fof(f32673,plain,
( spl647_705
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_705])]) ).
fof(f25930,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)),
inference(forward_demodulation,[],[f25929,f25909]) ).
fof(f25929,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(forward_demodulation,[],[f24178,f17133]) ).
fof(f24178,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin)),
inference(definition_unfolding,[],[f17190,f24151]) ).
fof(f17190,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,[],[f1389]) ).
fof(f1389,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32671,plain,
( spl647_704
| ~ spl647_331
| ~ spl647_497
| ~ spl647_703 ),
inference(avatar_split_clause,[],[f32666,f32662,f31581,f30819,f32668]) ).
fof(f32668,plain,
( spl647_704
<=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_704])]) ).
fof(f32662,plain,
( spl647_703
<=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_703])]) ).
fof(f32666,plain,
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl647_331
| ~ spl647_497
| ~ spl647_703 ),
inference(forward_demodulation,[],[f32664,f32001]) ).
fof(f32664,plain,
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))
| ~ spl647_703 ),
inference(avatar_component_clause,[],[f32662]) ).
fof(f32665,plain,
spl647_703,
inference(avatar_split_clause,[],[f25928,f32662]) ).
fof(f25928,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)),
inference(forward_demodulation,[],[f25927,f25909]) ).
fof(f25927,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(forward_demodulation,[],[f24177,f17133]) ).
fof(f24177,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin)),
inference(definition_unfolding,[],[f17187,f24151]) ).
fof(f17187,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,[],[f1403]) ).
fof(f1403,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32660,plain,
spl647_702,
inference(avatar_split_clause,[],[f25367,f32658]) ).
fof(f32658,plain,
( spl647_702
<=> ! [X0,X3] :
( hBOOL(hAPP(X0,X3))
| ~ sP8(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_702])]) ).
fof(f25367,plain,
! [X3,X0] :
( hBOOL(hAPP(X0,X3))
| ~ sP8(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) ),
inference(equality_resolution,[],[f19179]) ).
fof(f19179,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(X0,X3))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3) != X1
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f15041]) ).
fof(f32656,plain,
( spl647_701
| ~ spl647_391
| ~ spl647_541 ),
inference(avatar_split_clause,[],[f32120,f31760,f31080,f32654]) ).
fof(f32654,plain,
( spl647_701
<=> ! [X0,X1] : ~ sP8(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_701])]) ).
fof(f31080,plain,
( spl647_391
<=> ! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_391])]) ).
fof(f31760,plain,
( spl647_541
<=> ! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP8(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_541])]) ).
fof(f32120,plain,
( ! [X0,X1] : ~ sP8(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1)
| ~ spl647_391
| ~ spl647_541 ),
inference(resolution,[],[f31761,f31081]) ).
fof(f31081,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0))
| ~ spl647_391 ),
inference(avatar_component_clause,[],[f31080]) ).
fof(f31761,plain,
( ! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP8(X1,X0) )
| ~ spl647_541 ),
inference(avatar_component_clause,[],[f31760]) ).
fof(f32652,plain,
spl647_700,
inference(avatar_split_clause,[],[f25296,f32650]) ).
fof(f32650,plain,
( spl647_700
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_700])]) ).
fof(f25296,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(equality_resolution,[],[f18319]) ).
fof(f18319,plain,
! [X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) = X0
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f14746]) ).
fof(f32648,plain,
spl647_699,
inference(avatar_split_clause,[],[f24295,f32646]) ).
fof(f32646,plain,
( spl647_699
<=> ! [X0,X1] : c_Int_OBit0(X0) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_699])]) ).
fof(f24295,plain,
! [X0,X1] : c_Int_OBit0(X0) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin),
inference(definition_unfolding,[],[f17777,f24151]) ).
fof(f17777,plain,
! [X0,X1] : c_Int_OBit0(X0) != c_Int_OBit1(X1),
inference(cnf_transformation,[],[f5669]) ).
fof(f5669,plain,
! [X0,X1] : c_Int_OBit0(X0) != c_Int_OBit1(X1),
inference(rectify,[],[f1458]) ).
fof(f1458,axiom,
! [X56,X53] : c_Int_OBit1(X53) != c_Int_OBit0(X56),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32644,plain,
spl647_698,
inference(avatar_split_clause,[],[f24216,f32642]) ).
fof(f32642,plain,
( spl647_698
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_List_Omember(X0),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_698])]) ).
fof(f24216,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_List_Omember(X0),c_List_Olist_ONil(X0)),
inference(definition_unfolding,[],[f17377,f17267]) ).
fof(f17377,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,[],[f5355]) ).
fof(f5355,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,[],[f3901]) ).
fof(f3901,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32640,plain,
( spl647_697
| ~ spl647_597
| ~ spl647_696 ),
inference(avatar_split_clause,[],[f32636,f32633,f31997,f32638]) ).
fof(f32638,plain,
( spl647_697
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,sK109(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_697])]) ).
fof(f32633,plain,
( spl647_696
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_696])]) ).
fof(f32636,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,sK109(X0)))
| ~ spl647_597
| ~ spl647_696 ),
inference(forward_demodulation,[],[f32634,f31998]) ).
fof(f32634,plain,
( ! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0)))
| ~ spl647_696 ),
inference(avatar_component_clause,[],[f32633]) ).
fof(f32635,plain,
spl647_696,
inference(avatar_split_clause,[],[f24201,f32633]) ).
fof(f24201,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0))),
inference(definition_unfolding,[],[f17263,f17371]) ).
fof(f17263,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X0),
inference(cnf_transformation,[],[f5241]) ).
fof(f5241,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X0),
inference(rectify,[],[f2060]) ).
fof(f2060,axiom,
! [X134] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X134),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32631,plain,
spl647_695,
inference(avatar_split_clause,[],[f23539,f32629]) ).
fof(f32629,plain,
( spl647_695
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,X3))
| ~ sP77(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_695])]) ).
fof(f23539,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X1,X3))
| ~ sP77(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16684]) ).
fof(f16684,plain,
! [X0,X1,X2,X3,X4] :
( ( sP77(X0,X1,X2,X3,X4)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X2,X1),X6) != X0
| ~ hBOOL(hAPP(X1,X3))
| ( hBOOL(hAPP(X1,sK566(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK566(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),sK568(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),sK567(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK567(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK568(X0,X1,X2,X3,X4))) = X4 )
| ~ sP77(X0,X1,X2,X3,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK566,sK567,sK568])],[f16681,f16683,f16682]) ).
fof(f16682,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,sK566(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK566(X1,X2,X5)),hAPP(c_List_Oset(X2),X5))) ) ),
introduced(choice_axiom,[]) ).
fof(f16683,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),sK568(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),sK567(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK567(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK568(X0,X1,X2,X3,X4))) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f16681,plain,
! [X0,X1,X2,X3,X4] :
( ( sP77(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 )
| ~ sP77(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16680]) ).
fof(f16680,plain,
! [X2,X1,X4,X3,X0] :
( ( sP77(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 )
| ~ sP77(X2,X1,X4,X3,X0) ) ),
inference(nnf_transformation,[],[f14608]) ).
fof(f14608,plain,
! [X2,X1,X4,X3,X0] :
( sP77(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,[sP77])]) ).
fof(f32627,plain,
spl647_694,
inference(avatar_split_clause,[],[f23531,f32625]) ).
fof(f32625,plain,
( spl647_694
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,X3))
| ~ sP76(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_694])]) ).
fof(f23531,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X1,X3))
| ~ sP76(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16678]) ).
fof(f16678,plain,
! [X0,X1,X2,X3,X4] :
( ( sP76(X0,X1,X2,X3,X4)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X2,X1),X6) != X0
| ~ hBOOL(hAPP(X1,X3))
| ( hBOOL(hAPP(X1,sK563(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK563(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),sK565(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),sK564(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK564(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK565(X0,X1,X2,X3,X4))) = X4 )
| ~ sP76(X0,X1,X2,X3,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK563,sK564,sK565])],[f16675,f16677,f16676]) ).
fof(f16676,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,sK563(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK563(X1,X2,X5)),hAPP(c_List_Oset(X2),X5))) ) ),
introduced(choice_axiom,[]) ).
fof(f16677,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),sK565(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),sK564(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK564(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK565(X0,X1,X2,X3,X4))) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f16675,plain,
! [X0,X1,X2,X3,X4] :
( ( sP76(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 )
| ~ sP76(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16674]) ).
fof(f16674,plain,
! [X0,X3,X4,X1,X2] :
( ( sP76(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 )
| ~ sP76(X0,X3,X4,X1,X2) ) ),
inference(nnf_transformation,[],[f14606]) ).
fof(f14606,plain,
! [X0,X3,X4,X1,X2] :
( sP76(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,[sP76])]) ).
fof(f32623,plain,
spl647_693,
inference(avatar_split_clause,[],[f22896,f32621]) ).
fof(f32621,plain,
( spl647_693
<=> ! [X4,X0,X3,X2,X1] : hAPP(c_Fun_Ofun__upd(X4,X3,X2,X1,X0),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_693])]) ).
fof(f22896,plain,
! [X2,X3,X0,X1,X4] : hAPP(c_Fun_Ofun__upd(X4,X3,X2,X1,X0),X1) = X0,
inference(cnf_transformation,[],[f9230]) ).
fof(f9230,plain,
! [X0,X1,X2,X3,X4] : hAPP(c_Fun_Ofun__upd(X4,X3,X2,X1,X0),X1) = X0,
inference(rectify,[],[f2924]) ).
fof(f2924,axiom,
! [X15,X13,X1,X4,X14] : hAPP(c_Fun_Ofun__upd(X14,X4,X1,X13,X15),X13) = X15,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32619,plain,
spl647_692,
inference(avatar_split_clause,[],[f22893,f32617]) ).
fof(f32617,plain,
( spl647_692
<=> ! [X0,X3,X2,X1] :
( sP70(X0,X1,X2,X3)
| ~ sP71(X0,X1,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_692])]) ).
fof(f22893,plain,
! [X2,X3,X0,X1] :
( sP70(X0,X1,X2,X3)
| ~ sP71(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f16497]) ).
fof(f16497,plain,
! [X0,X1,X2,X3] :
( ( sP70(X0,X1,X2,X3)
| ~ sP71(X0,X1,X3,X2) )
& ( sP71(X0,X1,X3,X2)
| ~ sP70(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f14598]) ).
fof(f14598,plain,
! [X0,X1,X2,X3] :
( sP70(X0,X1,X2,X3)
<=> sP71(X0,X1,X3,X2) ),
inference(definition_folding,[],[f9228,f14597,f14596]) ).
fof(f14597,plain,
! [X0,X1,X3,X2] :
( sP71(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,[sP71])]) ).
fof(f9228,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,[],[f68]) ).
fof(f68,axiom,
! [X23,X18,X9,X4] :
( ? [X2] :
( hBOOL(hAPP(X23,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X9),X18))) )
<=> ( ? [X2] :
( hBOOL(hAPP(X23,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),X18)) )
| ? [X2] :
( hBOOL(hAPP(X23,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32615,plain,
( spl647_691
| ~ spl647_366
| ~ spl647_540 ),
inference(avatar_split_clause,[],[f32087,f31756,f30972,f32613]) ).
fof(f32613,plain,
( spl647_691
<=> ! [X0,X1] : sP8(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_691])]) ).
fof(f30972,plain,
( spl647_366
<=> ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_366])]) ).
fof(f32087,plain,
( ! [X0,X1] : sP8(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),X1)
| ~ spl647_366
| ~ spl647_540 ),
inference(resolution,[],[f31757,f30973]) ).
fof(f30973,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0))
| ~ spl647_366 ),
inference(avatar_component_clause,[],[f30972]) ).
fof(f32611,plain,
spl647_690,
inference(avatar_split_clause,[],[f22892,f32609]) ).
fof(f32609,plain,
( spl647_690
<=> ! [X0,X3,X2,X1] :
( sP71(X0,X1,X3,X2)
| ~ sP70(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_690])]) ).
fof(f22892,plain,
! [X2,X3,X0,X1] :
( sP71(X0,X1,X3,X2)
| ~ sP70(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16497]) ).
fof(f32607,plain,
spl647_689,
inference(avatar_split_clause,[],[f22593,f32605]) ).
fof(f32605,plain,
( spl647_689
<=> ! [X0,X3,X2,X1] :
( sP60(X2,X0,X3,X1)
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_689])]) ).
fof(f22593,plain,
! [X2,X3,X0,X1] :
( sP60(X2,X0,X3,X1)
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16277]) ).
fof(f16277,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
| ~ sP60(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)) )
& ( ( sP60(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,[],[f16276]) ).
fof(f16276,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
| ~ sP60(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)) )
& ( ( sP60(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,[],[f14579]) ).
fof(f14579,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
<=> ( sP60(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,[],[f13555,f14578]) ).
fof(f14578,plain,
! [X2,X0,X3,X1] :
( sP60(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,[sP60])]) ).
fof(f13555,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,[],[f9138]) ).
fof(f9138,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,[],[f4706]) ).
fof(f4706,axiom,
! [X33,X34,X138,X4] :
( c_Wellfounded_Omax__extp(X4,X138,X34,X33)
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),X34))
=> ? [X43] :
( hBOOL(hAPP(hAPP(X138,X2),X43))
& hBOOL(hAPP(hAPP(c_member(X4),X43),X33)) ) )
& c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) != X33
& hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X33))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32603,plain,
spl647_688,
inference(avatar_split_clause,[],[f22584,f32601]) ).
fof(f32601,plain,
( spl647_688
<=> ! [X0,X3,X2,X1] :
( sP59(X2,X0,X3,X1)
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_688])]) ).
fof(f22584,plain,
! [X2,X3,X0,X1] :
( sP59(X2,X0,X3,X1)
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16270]) ).
fof(f16270,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
| ~ sP59(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)) )
& ( ( sP59(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,[],[f16269]) ).
fof(f16269,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
| ~ sP59(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)) )
& ( ( sP59(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,[],[f14577]) ).
fof(f14577,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
<=> ( sP59(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,[],[f13554,f14576]) ).
fof(f14576,plain,
! [X2,X0,X3,X1] :
( sP59(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,[sP59])]) ).
fof(f13554,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,[],[f9137]) ).
fof(f9137,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,[],[f3108]) ).
fof(f3108,axiom,
! [X33,X34,X138,X4] :
( c_Wellfounded_Omax__extp(X4,X138,X34,X33)
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),X34))
=> ? [X43] :
( hBOOL(hAPP(hAPP(X138,X2),X43))
& hBOOL(hAPP(hAPP(c_member(X4),X43),X33)) ) )
& c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) != X33
& hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X33))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X34)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32599,plain,
spl647_687,
inference(avatar_split_clause,[],[f22582,f32597]) ).
fof(f32597,plain,
( spl647_687
<=> ! [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,[spl647_687])]) ).
fof(f22582,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16270]) ).
fof(f32595,plain,
spl647_686,
inference(avatar_split_clause,[],[f22581,f32593]) ).
fof(f32593,plain,
( spl647_686
<=> ! [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,[spl647_686])]) ).
fof(f22581,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16270]) ).
fof(f32591,plain,
spl647_685,
inference(avatar_split_clause,[],[f21556,f32589]) ).
fof(f32589,plain,
( spl647_685
<=> ! [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,[spl647_685])]) ).
fof(f21556,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,[],[f8273]) ).
fof(f8273,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,[],[f219]) ).
fof(f219,axiom,
! [X17,X1,X14,X4] : c_Nitpick_Ofold__graph_H(X4,X14,X1,X17,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32587,plain,
spl647_684,
inference(avatar_split_clause,[],[f21555,f32585]) ).
fof(f32585,plain,
( spl647_684
<=> ! [X2,X0,X1,X3] : c_Fun_Ofun__upd(X3,X2,X1,X0,hAPP(X1,X0)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_684])]) ).
fof(f21555,plain,
! [X2,X3,X0,X1] : c_Fun_Ofun__upd(X3,X2,X1,X0,hAPP(X1,X0)) = X1,
inference(cnf_transformation,[],[f8272]) ).
fof(f8272,plain,
! [X0,X1,X2,X3] : c_Fun_Ofun__upd(X3,X2,X1,X0,hAPP(X1,X0)) = X1,
inference(rectify,[],[f2919]) ).
fof(f2919,axiom,
! [X13,X1,X14,X4] : c_Fun_Ofun__upd(X4,X14,X1,X13,hAPP(X1,X13)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32583,plain,
spl647_683,
inference(avatar_split_clause,[],[f21554,f32581]) ).
fof(f32581,plain,
( spl647_683
<=> ! [X2,X0,X1,X3] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_683])]) ).
fof(f21554,plain,
! [X2,X3,X0,X1] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0,
inference(cnf_transformation,[],[f8271]) ).
fof(f8271,plain,
! [X0,X1,X2,X3] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0,
inference(rectify,[],[f4062]) ).
fof(f4062,axiom,
! [X5,X1,X14,X4] : hAPP(c_List_Ofoldl(X4,X14,X1,X5),c_List_Olist_ONil(X14)) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32579,plain,
spl647_682,
inference(avatar_split_clause,[],[f21553,f32577]) ).
fof(f32577,plain,
( spl647_682
<=> ! [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,[spl647_682])]) ).
fof(f21553,plain,
! [X2,X3,X0,X1] : hAPP(c_List_Olist_Olist__case(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X1,
inference(cnf_transformation,[],[f8270]) ).
fof(f8270,plain,
! [X0,X1,X2,X3] : hAPP(c_List_Olist_Olist__case(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X1,
inference(rectify,[],[f3933]) ).
fof(f3933,axiom,
! [X135,X95,X14,X4] : hAPP(c_List_Olist_Olist__case(X4,X14,X95,X135),c_List_Olist_ONil(X14)) = X95,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32575,plain,
spl647_681,
inference(avatar_split_clause,[],[f21258,f32573]) ).
fof(f32573,plain,
( spl647_681
<=> ! [X2,X0,X1] :
( X0 = X1
| ~ c_Fun_Obij__betw(X2,X2,c_Fun_Oid(X2),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_681])]) ).
fof(f21258,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_Fun_Obij__betw(X2,X2,c_Fun_Oid(X2),X1,X0) ),
inference(cnf_transformation,[],[f15831]) ).
fof(f15831,plain,
! [X0,X1,X2] :
( ( c_Fun_Obij__betw(X2,X2,c_Fun_Oid(X2),X1,X0)
| X0 != X1 )
& ( X0 = X1
| ~ c_Fun_Obij__betw(X2,X2,c_Fun_Oid(X2),X1,X0) ) ),
inference(nnf_transformation,[],[f8167]) ).
fof(f8167,plain,
! [X0,X1,X2] :
( c_Fun_Obij__betw(X2,X2,c_Fun_Oid(X2),X1,X0)
<=> X0 = X1 ),
inference(rectify,[],[f4820]) ).
fof(f4820,axiom,
! [X18,X9,X4] :
( c_Fun_Obij__betw(X4,X4,c_Fun_Oid(X4),X9,X18)
<=> X9 = X18 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32571,plain,
( spl647_680
| ~ spl647_372
| ~ spl647_540 ),
inference(avatar_split_clause,[],[f32085,f31756,f30996,f32569]) ).
fof(f32569,plain,
( spl647_680
<=> ! [X0,X1] :
( sP8(c_Finite__Set_Ofinite(X0),X1)
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_680])]) ).
fof(f32085,plain,
( ! [X0,X1] :
( sP8(c_Finite__Set_Ofinite(X0),X1)
| ~ class_Finite__Set_Ofinite(X0) )
| ~ spl647_372
| ~ spl647_540 ),
inference(resolution,[],[f31757,f30997]) ).
fof(f32567,plain,
spl647_679,
inference(avatar_split_clause,[],[f21209,f32565]) ).
fof(f32565,plain,
( spl647_679
<=> ! [X2,X0,X1] :
( c_List_Olist__all(tc_Int_Oint,X2,c_List_Oupto(X1,X0))
| ~ c_List_Oall__interval__int(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_679])]) ).
fof(f21209,plain,
! [X2,X0,X1] :
( c_List_Olist__all(tc_Int_Oint,X2,c_List_Oupto(X1,X0))
| ~ c_List_Oall__interval__int(X2,X1,X0) ),
inference(cnf_transformation,[],[f15795]) ).
fof(f15795,plain,
! [X0,X1,X2] :
( ( c_List_Olist__all(tc_Int_Oint,X2,c_List_Oupto(X1,X0))
| ~ c_List_Oall__interval__int(X2,X1,X0) )
& ( c_List_Oall__interval__int(X2,X1,X0)
| ~ c_List_Olist__all(tc_Int_Oint,X2,c_List_Oupto(X1,X0)) ) ),
inference(nnf_transformation,[],[f8155]) ).
fof(f8155,plain,
! [X0,X1,X2] :
( c_List_Olist__all(tc_Int_Oint,X2,c_List_Oupto(X1,X0))
<=> c_List_Oall__interval__int(X2,X1,X0) ),
inference(rectify,[],[f4683]) ).
fof(f4683,axiom,
! [X62,X63,X23] :
( c_List_Olist__all(tc_Int_Oint,X23,c_List_Oupto(X63,X62))
<=> c_List_Oall__interval__int(X23,X63,X62) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32563,plain,
spl647_678,
inference(avatar_split_clause,[],[f21208,f32561]) ).
fof(f32561,plain,
( spl647_678
<=> ! [X2,X0,X1] :
( c_List_Oall__interval__int(X2,X1,X0)
| ~ c_List_Olist__all(tc_Int_Oint,X2,c_List_Oupto(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_678])]) ).
fof(f21208,plain,
! [X2,X0,X1] :
( c_List_Oall__interval__int(X2,X1,X0)
| ~ c_List_Olist__all(tc_Int_Oint,X2,c_List_Oupto(X1,X0)) ),
inference(cnf_transformation,[],[f15795]) ).
fof(f32559,plain,
spl647_677,
inference(avatar_split_clause,[],[f21194,f32557]) ).
fof(f32557,plain,
( spl647_677
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP35(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_677])]) ).
fof(f21194,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP35(X1,X0,X2) ),
inference(cnf_transformation,[],[f15780]) ).
fof(f15780,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP35(X1,X0,X2) )
& ( sP35(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ) ),
inference(nnf_transformation,[],[f14536]) ).
fof(f14536,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
<=> sP35(X1,X0,X2) ),
inference(definition_folding,[],[f12605,f14535,f14534]) ).
fof(f14534,plain,
! [X0,X1] :
( sP34(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,[sP34])]) ).
fof(f12605,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,[],[f8149]) ).
fof(f8149,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,[],[f2398]) ).
fof(f2398,axiom,
! [X152,X46,X47] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X47,X46),X152))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X46
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X46))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X152)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X46),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X152))) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X46))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X152)),X46))
& 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),X152))) ) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X46
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X152) )
& 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),X152)),X46)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X152)) = X47 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32555,plain,
spl647_676,
inference(avatar_split_clause,[],[f21193,f32553]) ).
fof(f32553,plain,
( spl647_676
<=> ! [X2,X0,X1] :
( sP35(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_676])]) ).
fof(f21193,plain,
! [X2,X0,X1] :
( sP35(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ),
inference(cnf_transformation,[],[f15780]) ).
fof(f32551,plain,
spl647_675,
inference(avatar_split_clause,[],[f21050,f32549]) ).
fof(f21050,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP30(X0,X1,X2) ),
inference(cnf_transformation,[],[f15644]) ).
fof(f32547,plain,
spl647_674,
inference(avatar_split_clause,[],[f20715,f32545]) ).
fof(f32545,plain,
( spl647_674
<=> ! [X0,X1] :
( sK265(X0,X1) != sK266(X0,X1)
| ~ sP25(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_674])]) ).
fof(f20715,plain,
! [X0,X1] :
( sK265(X0,X1) != sK266(X0,X1)
| ~ sP25(X0,X1) ),
inference(cnf_transformation,[],[f15526]) ).
fof(f32543,plain,
spl647_673,
inference(avatar_split_clause,[],[f19593,f32541]) ).
fof(f32541,plain,
( spl647_673
<=> ! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_673])]) ).
fof(f19593,plain,
! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0,
inference(cnf_transformation,[],[f6947]) ).
fof(f6947,plain,
! [X0,X1,X2] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0,
inference(rectify,[],[f3451]) ).
fof(f3451,axiom,
! [X0,X4,X14] : hAPP(c_Fun_Ocomp(X14,X14,X4,c_Fun_Oid(X14)),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32539,plain,
spl647_672,
inference(avatar_split_clause,[],[f19592,f32537]) ).
fof(f32537,plain,
( spl647_672
<=> ! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_672])]) ).
fof(f19592,plain,
! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0,
inference(cnf_transformation,[],[f6946]) ).
fof(f6946,plain,
! [X0,X1,X2] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0,
inference(rectify,[],[f3450]) ).
fof(f3450,axiom,
! [X1,X14,X4] : hAPP(c_Fun_Ocomp(X4,X14,X4,X1),c_Fun_Oid(X4)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32535,plain,
spl647_671,
inference(avatar_split_clause,[],[f19590,f32533]) ).
fof(f32533,plain,
( spl647_671
<=> ! [X2,X0,X1] : hAPP(c_New__DSequence_Opos__single(X2,X1),X0) = hAPP(c_Lazy__Sequence_Osingle(X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_671])]) ).
fof(f19590,plain,
! [X2,X0,X1] : hAPP(c_New__DSequence_Opos__single(X2,X1),X0) = hAPP(c_Lazy__Sequence_Osingle(X2),X1),
inference(cnf_transformation,[],[f6944]) ).
fof(f6944,plain,
! [X0,X1,X2] : hAPP(c_New__DSequence_Opos__single(X2,X1),X0) = hAPP(c_Lazy__Sequence_Osingle(X2),X1),
inference(rectify,[],[f4603]) ).
fof(f4603,axiom,
! [X246,X19,X20] : hAPP(c_New__DSequence_Opos__single(X20,X19),X246) = hAPP(c_Lazy__Sequence_Osingle(X20),X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32531,plain,
spl647_670,
inference(avatar_split_clause,[],[f19589,f32529]) ).
fof(f32529,plain,
( spl647_670
<=> ! [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,[spl647_670])]) ).
fof(f19589,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,[],[f6943]) ).
fof(f6943,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,[],[f20]) ).
fof(f20,axiom,
! [X13,X1,X4] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32524,plain,
spl647_669,
inference(avatar_split_clause,[],[f19570,f32522]) ).
fof(f19570,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(X0,sK218(X0,X1)))
| ~ hBOOL(hAPP(X0,X3)) ),
inference(cnf_transformation,[],[f15302]) ).
fof(f15302,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(X0,sK218(X0,X1)))
& hBOOL(hAPP(hAPP(c_member(X1),sK218(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) )
| ! [X3] : ~ hBOOL(hAPP(X0,X3)) )
& ( hBOOL(hAPP(X0,sK219(X0)))
| ! [X5] :
( ~ hBOOL(hAPP(X0,X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK218,sK219])],[f15299,f15301,f15300]) ).
fof(f15300,plain,
! [X0,X1] :
( ? [X2] :
( hBOOL(hAPP(X0,X2))
& hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) )
=> ( hBOOL(hAPP(X0,sK218(X0,X1)))
& hBOOL(hAPP(hAPP(c_member(X1),sK218(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ) ),
introduced(choice_axiom,[]) ).
fof(f15301,plain,
! [X0] :
( ? [X4] : hBOOL(hAPP(X0,X4))
=> hBOOL(hAPP(X0,sK219(X0))) ),
introduced(choice_axiom,[]) ).
fof(f15299,plain,
! [X0,X1] :
( ( ? [X2] :
( hBOOL(hAPP(X0,X2))
& hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) )
| ! [X3] : ~ hBOOL(hAPP(X0,X3)) )
& ( ? [X4] : hBOOL(hAPP(X0,X4))
| ! [X5] :
( ~ hBOOL(hAPP(X0,X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ) ) ),
inference(rectify,[],[f15298]) ).
fof(f15298,plain,
! [X0,X1] :
( ( ? [X2] :
( hBOOL(hAPP(X0,X2))
& hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) )
| ! [X3] : ~ hBOOL(hAPP(X0,X3)) )
& ( ? [X3] : hBOOL(hAPP(X0,X3))
| ! [X2] :
( ~ hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ) ) ),
inference(nnf_transformation,[],[f6924]) ).
fof(f6924,plain,
! [X0,X1] :
( ? [X2] :
( hBOOL(hAPP(X0,X2))
& hBOOL(hAPP(hAPP(c_member(X1),X2),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) )
<=> ? [X3] : hBOOL(hAPP(X0,X3)) ),
inference(rectify,[],[f4695]) ).
fof(f4695,axiom,
! [X23,X4] :
( ? [X2] :
( hBOOL(hAPP(X23,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))) )
<=> ? [X124] : hBOOL(hAPP(X23,X124)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32520,plain,
spl647_668,
inference(avatar_split_clause,[],[f19261,f32518]) ).
fof(f32518,plain,
( spl647_668
<=> ! [X0,X1] :
( c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Otrans(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_668])]) ).
fof(f19261,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Otrans(X1,X0) ),
inference(cnf_transformation,[],[f15105]) ).
fof(f15105,plain,
! [X0,X1] :
( ( c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Otrans(X1,X0) )
& ( c_Relation_Otrans(X1,X0)
| ~ c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
inference(nnf_transformation,[],[f6810]) ).
fof(f6810,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
<=> c_Relation_Otrans(X1,X0) ),
inference(rectify,[],[f4716]) ).
fof(f4716,axiom,
! [X116,X4] :
( c_Relation_Otrans(X4,hAPP(c_Relation_Oconverse(X4,X4),X116))
<=> c_Relation_Otrans(X4,X116) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32516,plain,
spl647_667,
inference(avatar_split_clause,[],[f19260,f32514]) ).
fof(f32514,plain,
( spl647_667
<=> ! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| ~ c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_667])]) ).
fof(f19260,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| ~ c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ),
inference(cnf_transformation,[],[f15105]) ).
fof(f32512,plain,
spl647_666,
inference(avatar_split_clause,[],[f19259,f32510]) ).
fof(f32510,plain,
( spl647_666
<=> ! [X0,X1] :
( c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Osym(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_666])]) ).
fof(f19259,plain,
! [X0,X1] :
( c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Osym(X1,X0) ),
inference(cnf_transformation,[],[f15104]) ).
fof(f15104,plain,
! [X0,X1] :
( ( c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Osym(X1,X0) )
& ( c_Relation_Osym(X1,X0)
| ~ c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
inference(nnf_transformation,[],[f6809]) ).
fof(f6809,plain,
! [X0,X1] :
( c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
<=> c_Relation_Osym(X1,X0) ),
inference(rectify,[],[f4756]) ).
fof(f4756,axiom,
! [X116,X4] :
( c_Relation_Osym(X4,hAPP(c_Relation_Oconverse(X4,X4),X116))
<=> c_Relation_Osym(X4,X116) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32508,plain,
spl647_665,
inference(avatar_split_clause,[],[f19258,f32506]) ).
fof(f32506,plain,
( spl647_665
<=> ! [X0,X1] :
( c_Relation_Osym(X1,X0)
| ~ c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_665])]) ).
fof(f19258,plain,
! [X0,X1] :
( c_Relation_Osym(X1,X0)
| ~ c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ),
inference(cnf_transformation,[],[f15104]) ).
fof(f32504,plain,
spl647_664,
inference(avatar_split_clause,[],[f19257,f32502]) ).
fof(f32502,plain,
( spl647_664
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Oantisym(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_664])]) ).
fof(f19257,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Oantisym(X1,X0) ),
inference(cnf_transformation,[],[f15103]) ).
fof(f15103,plain,
! [X0,X1] :
( ( c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Oantisym(X1,X0) )
& ( c_Relation_Oantisym(X1,X0)
| ~ c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
inference(nnf_transformation,[],[f6808]) ).
fof(f6808,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
<=> c_Relation_Oantisym(X1,X0) ),
inference(rectify,[],[f4731]) ).
fof(f4731,axiom,
! [X116,X4] :
( c_Relation_Oantisym(X4,hAPP(c_Relation_Oconverse(X4,X4),X116))
<=> c_Relation_Oantisym(X4,X116) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32500,plain,
spl647_663,
inference(avatar_split_clause,[],[f19256,f32498]) ).
fof(f32498,plain,
( spl647_663
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| ~ c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_663])]) ).
fof(f19256,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| ~ c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ),
inference(cnf_transformation,[],[f15103]) ).
fof(f32496,plain,
spl647_662,
inference(avatar_split_clause,[],[f19255,f32494]) ).
fof(f32494,plain,
( spl647_662
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_662])]) ).
fof(f19255,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ),
inference(cnf_transformation,[],[f15102]) ).
fof(f15102,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,[],[f6807]) ).
fof(f6807,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
<=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f3624]) ).
fof(f3624,axiom,
! [X116,X4] :
( c_Wellfounded_Oacyclic(X4,hAPP(c_Relation_Oconverse(X4,X4),X116))
<=> c_Wellfounded_Oacyclic(X4,X116) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32492,plain,
spl647_661,
inference(avatar_split_clause,[],[f19254,f32490]) ).
fof(f32490,plain,
( spl647_661
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_661])]) ).
fof(f19254,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ),
inference(cnf_transformation,[],[f15102]) ).
fof(f32488,plain,
spl647_660,
inference(avatar_split_clause,[],[f19212,f32486]) ).
fof(f32486,plain,
( spl647_660
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Oof__nat,X0) != hAPP(c_Code__Numeral_Oof__nat,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_660])]) ).
fof(f19212,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Oof__nat,X0) != hAPP(c_Code__Numeral_Oof__nat,X1) ),
inference(cnf_transformation,[],[f15067]) ).
fof(f15067,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,[],[f6789]) ).
fof(f6789,plain,
! [X0,X1] :
( hAPP(c_Code__Numeral_Oof__nat,X0) = hAPP(c_Code__Numeral_Oof__nat,X1)
<=> X0 = X1 ),
inference(rectify,[],[f4172]) ).
fof(f4172,axiom,
! [X47,X46] :
( hAPP(c_Code__Numeral_Oof__nat,X46) = hAPP(c_Code__Numeral_Oof__nat,X47)
<=> X46 = X47 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32481,plain,
spl647_659,
inference(avatar_split_clause,[],[f19208,f32479]) ).
fof(f32479,plain,
( spl647_659
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Onat__of,X0) != hAPP(c_Code__Numeral_Onat__of,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_659])]) ).
fof(f19208,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Onat__of,X0) != hAPP(c_Code__Numeral_Onat__of,X1) ),
inference(cnf_transformation,[],[f15065]) ).
fof(f15065,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,[],[f6787]) ).
fof(f6787,plain,
! [X0,X1] :
( hAPP(c_Code__Numeral_Onat__of,X0) = hAPP(c_Code__Numeral_Onat__of,X1)
<=> X0 = X1 ),
inference(rectify,[],[f4197]) ).
fof(f4197,axiom,
! [X15,X13] :
( hAPP(c_Code__Numeral_Onat__of,X13) = hAPP(c_Code__Numeral_Onat__of,X15)
<=> X13 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32477,plain,
spl647_658,
inference(avatar_split_clause,[],[f19206,f32475]) ).
fof(f32475,plain,
( spl647_658
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Int_ORep__Integ,X0) != hAPP(c_Int_ORep__Integ,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_658])]) ).
fof(f19206,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Int_ORep__Integ,X0) != hAPP(c_Int_ORep__Integ,X1) ),
inference(cnf_transformation,[],[f15064]) ).
fof(f15064,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,[],[f6786]) ).
fof(f6786,plain,
! [X0,X1] :
( hAPP(c_Int_ORep__Integ,X0) = hAPP(c_Int_ORep__Integ,X1)
<=> X0 = X1 ),
inference(rectify,[],[f2746]) ).
fof(f2746,axiom,
! [X15,X13] :
( hAPP(c_Int_ORep__Integ,X13) = hAPP(c_Int_ORep__Integ,X15)
<=> X13 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32473,plain,
spl647_657,
inference(avatar_split_clause,[],[f19163,f32471]) ).
fof(f32471,plain,
( spl647_657
<=> ! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != c_List_Oremdups(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_657])]) ).
fof(f19163,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != c_List_Oremdups(X1,X0) ),
inference(cnf_transformation,[],[f15023]) ).
fof(f15023,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,[],[f6770]) ).
fof(f6770,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = c_List_Oremdups(X1,X0)
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f4280]) ).
fof(f4280,axiom,
! [X13,X4] :
( c_List_Olist_ONil(X4) = c_List_Oremdups(X4,X13)
<=> c_List_Olist_ONil(X4) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32469,plain,
spl647_656,
inference(avatar_split_clause,[],[f19151,f32467]) ).
fof(f32467,plain,
( spl647_656
<=> ! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| c_List_Oremdups(X1,X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_656])]) ).
fof(f19151,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| c_List_Oremdups(X1,X0) != X0 ),
inference(cnf_transformation,[],[f15009]) ).
fof(f15009,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,[],[f6766]) ).
fof(f6766,plain,
! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
<=> hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(rectify,[],[f4271]) ).
fof(f4271,axiom,
! [X203,X4] :
( c_List_Oremdups(X4,X203) = X203
<=> hBOOL(hAPP(c_List_Odistinct(X4),X203)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32465,plain,
spl647_655,
inference(avatar_split_clause,[],[f19108,f32463]) ).
fof(f32463,plain,
( spl647_655
<=> ! [X0,X1] :
( c_Relation_Osym(X1,X0)
| hAPP(c_Relation_Oconverse(X1,X1),X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_655])]) ).
fof(f19108,plain,
! [X0,X1] :
( c_Relation_Osym(X1,X0)
| hAPP(c_Relation_Oconverse(X1,X1),X0) != X0 ),
inference(cnf_transformation,[],[f14971]) ).
fof(f14971,plain,
! [X0,X1] :
( ( c_Relation_Osym(X1,X0)
| hAPP(c_Relation_Oconverse(X1,X1),X0) != X0 )
& ( hAPP(c_Relation_Oconverse(X1,X1),X0) = X0
| ~ c_Relation_Osym(X1,X0) ) ),
inference(nnf_transformation,[],[f6754]) ).
fof(f6754,plain,
! [X0,X1] :
( c_Relation_Osym(X1,X0)
<=> hAPP(c_Relation_Oconverse(X1,X1),X0) = X0 ),
inference(rectify,[],[f4757]) ).
fof(f4757,axiom,
! [X116,X4] :
( c_Relation_Osym(X4,X116)
<=> hAPP(c_Relation_Oconverse(X4,X4),X116) = X116 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32461,plain,
spl647_654,
inference(avatar_split_clause,[],[f19107,f32459]) ).
fof(f32459,plain,
( spl647_654
<=> ! [X0,X1] :
( hAPP(c_Relation_Oconverse(X1,X1),X0) = X0
| ~ c_Relation_Osym(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_654])]) ).
fof(f19107,plain,
! [X0,X1] :
( hAPP(c_Relation_Oconverse(X1,X1),X0) = X0
| ~ c_Relation_Osym(X1,X0) ),
inference(cnf_transformation,[],[f14971]) ).
fof(f32457,plain,
spl647_653,
inference(avatar_split_clause,[],[f19106,f32455]) ).
fof(f32455,plain,
( spl647_653
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| sK173(X0,X1) != sK174(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_653])]) ).
fof(f19106,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| sK173(X0,X1) != sK174(X0,X1) ),
inference(cnf_transformation,[],[f14970]) ).
fof(f14970,plain,
! [X0,X1] :
( ( c_Relation_Oantisym(X1,X0)
| ( sK173(X0,X1) != sK174(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK174(X0,X1)),sK173(X0,X1))),X0))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK173(X0,X1)),sK174(X0,X1))),X0)) ) )
& ( ! [X4,X5] :
( 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(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X0)) )
| ~ c_Relation_Oantisym(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK173,sK174])],[f14968,f14969]) ).
fof(f14969,plain,
! [X0,X1] :
( ? [X2,X3] :
( X2 != X3
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X0))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X0)) )
=> ( sK173(X0,X1) != sK174(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK174(X0,X1)),sK173(X0,X1))),X0))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK173(X0,X1)),sK174(X0,X1))),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14968,plain,
! [X0,X1] :
( ( c_Relation_Oantisym(X1,X0)
| ? [X2,X3] :
( X2 != X3
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X0))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X0)) ) )
& ( ! [X4,X5] :
( 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(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X5)),X0)) )
| ~ c_Relation_Oantisym(X1,X0) ) ),
inference(rectify,[],[f14967]) ).
fof(f14967,plain,
! [X0,X1] :
( ( c_Relation_Oantisym(X1,X0)
| ? [X2,X3] :
( X2 != X3
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X0))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X0)) ) )
& ( ! [X2,X3] :
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X0)) )
| ~ c_Relation_Oantisym(X1,X0) ) ),
inference(nnf_transformation,[],[f11278]) ).
fof(f11278,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
<=> ! [X2,X3] :
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X0)) ) ),
inference(flattening,[],[f11277]) ).
fof(f11277,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
<=> ! [X2,X3] :
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X0)) ) ),
inference(ennf_transformation,[],[f6753]) ).
fof(f6753,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
<=> ! [X2,X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),X0))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X0))
=> X2 = X3 ) ) ),
inference(rectify,[],[f4735]) ).
fof(f4735,axiom,
! [X116,X4] :
( c_Relation_Oantisym(X4,X116)
<=> ! [X2,X38] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X38)),X116))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X38),X2)),X116))
=> X2 = X38 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32453,plain,
spl647_652,
inference(avatar_split_clause,[],[f19052,f32451]) ).
fof(f19052,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(cnf_transformation,[],[f11271]) ).
fof(f11271,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ! [X2] : ~ hBOOL(hAPP(X1,X2)) ),
inference(ennf_transformation,[],[f6732]) ).
fof(f6732,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(X1,X2))
=> hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ),
inference(rectify,[],[f3515]) ).
fof(f3515,axiom,
! [X4,X195] :
( ? [X2] : hBOOL(hAPP(X195,X2))
=> hBOOL(hAPP(X195,c_Hilbert__Choice_OEps(X4,X195))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32449,plain,
spl647_651,
inference(avatar_split_clause,[],[f18757,f32447]) ).
fof(f32447,plain,
( spl647_651
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_651])]) ).
fof(f18757,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ),
inference(cnf_transformation,[],[f10934]) ).
fof(f10934,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ),
inference(ennf_transformation,[],[f6498]) ).
fof(f6498,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Nat_OSuc,X1)
=> X0 = X1 ),
inference(rectify,[],[f478]) ).
fof(f478,axiom,
! [X21,X19] :
( hAPP(c_Nat_OSuc,X19) = hAPP(c_Nat_OSuc,X21)
=> X19 = X21 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32445,plain,
spl647_650,
inference(avatar_split_clause,[],[f18746,f32443]) ).
fof(f32443,plain,
( spl647_650
<=> ! [X0,X1] :
( sK145(X0,X1) != sK146(X0,X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_650])]) ).
fof(f18746,plain,
! [X0,X1] :
( sK145(X0,X1) != sK146(X0,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f14856]) ).
fof(f14856,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),sK145(X0,X1))),hAPP(c_List_Oset(X0),sK146(X0,X1)))
& sK145(X0,X1) != sK146(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),sK146(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1)))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),sK145(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK145,sK146])],[f14853,f14855,f14854]) ).
fof(f14854,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),sK145(X0,X1))),hAPP(c_List_Oset(X0),X3))
& sK145(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)),sK145(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f14855,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),sK145(X0,X1))),hAPP(c_List_Oset(X0),X3))
& sK145(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),sK145(X0,X1))),hAPP(c_List_Oset(X0),sK146(X0,X1)))
& sK145(X0,X1) != sK146(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),sK146(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f14853,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,[],[f14852]) ).
fof(f14852,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,[],[f14478]) ).
fof(f14478,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(f32436,plain,
spl647_649,
inference(avatar_split_clause,[],[f18730,f32434]) ).
fof(f32434,plain,
( spl647_649
<=> ! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_649])]) ).
fof(f18730,plain,
! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(cnf_transformation,[],[f10912]) ).
fof(f10912,plain,
! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(ennf_transformation,[],[f6479]) ).
fof(f6479,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
=> c_List_Oremdups(X1,X0) = X0 ),
inference(rectify,[],[f4273]) ).
fof(f4273,axiom,
! [X201,X20] :
( hBOOL(hAPP(c_List_Odistinct(X20),X201))
=> c_List_Oremdups(X20,X201) = X201 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32432,plain,
spl647_648,
inference(avatar_split_clause,[],[f18708,f32430]) ).
fof(f32430,plain,
( spl647_648
<=> ! [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,[spl647_648])]) ).
fof(f18708,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,[],[f10891]) ).
fof(f10891,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,[],[f6461]) ).
fof(f6461,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,[],[f3372]) ).
fof(f3372,axiom,
! [X116,X4] :
( c_Wellfounded_Owf(X4,X116)
=> c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Omax__ext(X4,X116)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32428,plain,
spl647_647,
inference(avatar_split_clause,[],[f18707,f32426]) ).
fof(f32426,plain,
( spl647_647
<=> ! [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,[spl647_647])]) ).
fof(f18707,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,[],[f10890]) ).
fof(f10890,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,[],[f6460]) ).
fof(f6460,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,[],[f3364]) ).
fof(f3364,axiom,
! [X116,X4] :
( c_Wellfounded_Owf(X4,X116)
=> c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Omin__ext(X4,X116)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32424,plain,
spl647_646,
inference(avatar_split_clause,[],[f18626,f32422]) ).
fof(f32422,plain,
( spl647_646
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_646])]) ).
fof(f18626,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10794]) ).
fof(f10794,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6392]) ).
fof(f6392,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0 ),
inference(rectify,[],[f325]) ).
fof(f325,axiom,
! [X19,X20] :
( class_Lattices_Olattice(X20)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20),X19),X19) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32420,plain,
spl647_645,
inference(avatar_split_clause,[],[f18625,f32418]) ).
fof(f32418,plain,
( spl647_645
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_645])]) ).
fof(f18625,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10793]) ).
fof(f10793,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6391]) ).
fof(f6391,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0 ),
inference(rectify,[],[f417]) ).
fof(f417,axiom,
! [X19,X20] :
( class_Lattices_Olattice(X20)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20),X19),X19) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32416,plain,
spl647_644,
inference(avatar_split_clause,[],[f18620,f32414]) ).
fof(f32414,plain,
( spl647_644
<=> ! [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,[spl647_644])]) ).
fof(f18620,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(cnf_transformation,[],[f10788]) ).
fof(f10788,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(ennf_transformation,[],[f6386]) ).
fof(f6386,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0 ),
inference(rectify,[],[f304]) ).
fof(f304,axiom,
! [X19,X20] :
( class_Lattices_Osemilattice__inf(X20)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X20),X19),X19) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32412,plain,
spl647_643,
inference(avatar_split_clause,[],[f18618,f32410]) ).
fof(f32410,plain,
( spl647_643
<=> ! [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,[spl647_643])]) ).
fof(f18618,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(cnf_transformation,[],[f10786]) ).
fof(f10786,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(ennf_transformation,[],[f6384]) ).
fof(f6384,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0 ),
inference(rectify,[],[f151]) ).
fof(f151,axiom,
! [X26,X20] :
( class_Lattices_Osemilattice__sup(X20)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X20),X26),X26) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32408,plain,
spl647_642,
inference(avatar_split_clause,[],[f18579,f32406]) ).
fof(f32406,plain,
( spl647_642
<=> ! [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,[spl647_642])]) ).
fof(f18579,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,[],[f10749]) ).
fof(f10749,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,[],[f10748]) ).
fof(f10748,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,[],[f6363]) ).
fof(f6363,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,[],[f4414]) ).
fof(f4414,axiom,
! [X56,X20] :
( class_Orderings_Olinorder(X20)
=> ( c_List_Olinorder__class_Osorted(X20,X56)
=> c_List_Olinorder__class_Osorted(X20,c_List_Oremdups(X20,X56)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32404,plain,
spl647_641,
inference(avatar_split_clause,[],[f18565,f32402]) ).
fof(f32402,plain,
( spl647_641
<=> ! [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,[spl647_641])]) ).
fof(f18565,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,[],[f10734]) ).
fof(f10734,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,[],[f6349]) ).
fof(f6349,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,[],[f4402]) ).
fof(f4402,axiom,
! [X203,X4] :
( class_Orderings_Olinorder(X4)
=> c_List_Olinorder__class_Osorted(X4,c_List_Olinorder__class_Osort__key(X4,X4,c_COMBI(X4),X203)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32400,plain,
spl647_640,
inference(avatar_split_clause,[],[f18563,f32398]) ).
fof(f32398,plain,
( spl647_640
<=> ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_640])]) ).
fof(f18563,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10732]) ).
fof(f10732,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6347]) ).
fof(f6347,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0 ),
inference(rectify,[],[f1054]) ).
fof(f1054,axiom,
! [X19,X20] :
( class_Orderings_Olinorder(X20)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X20),X19),X19) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32396,plain,
spl647_639,
inference(avatar_split_clause,[],[f18561,f32394]) ).
fof(f32394,plain,
( spl647_639
<=> ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_639])]) ).
fof(f18561,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10730]) ).
fof(f10730,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6345]) ).
fof(f6345,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0 ),
inference(rectify,[],[f2452]) ).
fof(f2452,axiom,
! [X19,X20] :
( class_Orderings_Olinorder(X20)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X20),X19),X19) = X19 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32392,plain,
spl647_638,
inference(avatar_split_clause,[],[f18551,f32390]) ).
fof(f32390,plain,
( spl647_638
<=> ! [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,[spl647_638])]) ).
fof(f18551,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,[],[f10718]) ).
fof(f10718,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,[],[f6335]) ).
fof(f6335,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,[],[f1590]) ).
fof(f1590,axiom,
! [X26,X20] :
( class_Divides_Osemiring__div(X20)
=> c_Groups_Ozero__class_Ozero(X20) = c_Divides_Odiv__class_Omod(X20,c_Groups_Ozero__class_Ozero(X20),X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32388,plain,
spl647_637,
inference(avatar_split_clause,[],[f18550,f32386]) ).
fof(f32386,plain,
( spl647_637
<=> ! [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,[spl647_637])]) ).
fof(f18550,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,[],[f10717]) ).
fof(f10717,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,[],[f6334]) ).
fof(f6334,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,[],[f1639]) ).
fof(f1639,axiom,
! [X26,X20] :
( class_Divides_Osemiring__div(X20)
=> c_Groups_Ozero__class_Ozero(X20) = c_Divides_Odiv__class_Omod(X20,X26,c_Groups_Oone__class_Oone(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32384,plain,
spl647_636,
inference(avatar_split_clause,[],[f18535,f32382]) ).
fof(f32382,plain,
( spl647_636
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_636])]) ).
fof(f18535,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f10701]) ).
fof(f10701,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f6319]) ).
fof(f6319,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),c_Groups_Oone__class_Oone(X1)),X0)) ),
inference(rectify,[],[f4899]) ).
fof(f4899,axiom,
! [X26,X20] :
( class_Rings_Ocomm__semiring__1(X20)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X20),c_Groups_Oone__class_Oone(X20)),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32380,plain,
spl647_635,
inference(avatar_split_clause,[],[f18534,f32378]) ).
fof(f32378,plain,
( spl647_635
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_635])]) ).
fof(f18534,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f10700]) ).
fof(f10700,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1)))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f6318]) ).
fof(f6318,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),c_Groups_Ozero__class_Ozero(X1))) ),
inference(rectify,[],[f4877]) ).
fof(f4877,axiom,
! [X26,X20] :
( class_Rings_Ocomm__semiring__1(X20)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X20),X26),c_Groups_Ozero__class_Ozero(X20))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32376,plain,
spl647_634,
inference(avatar_split_clause,[],[f18507,f32374]) ).
fof(f32374,plain,
( spl647_634
<=> ! [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,[spl647_634])]) ).
fof(f18507,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,[],[f10673]) ).
fof(f10673,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,[],[f6293]) ).
fof(f6293,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,[],[f121]) ).
fof(f121,axiom,
! [X19,X20] :
( class_Orderings_Obot(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),c_Orderings_Obot__class_Obot(X20)),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32372,plain,
spl647_633,
inference(avatar_split_clause,[],[f18473,f32370]) ).
fof(f18473,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,[],[f10637]) ).
fof(f10637,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,[],[f6261]) ).
fof(f6261,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,[],[f2094]) ).
fof(f2094,axiom,
! [X19,X20] :
( class_Orderings_Otop(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),X19),c_Orderings_Otop__class_Otop(X20))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32368,plain,
spl647_632,
inference(avatar_split_clause,[],[f18285,f32366]) ).
fof(f32366,plain,
( spl647_632
<=> ! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_632])]) ).
fof(f18285,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ),
inference(cnf_transformation,[],[f6118]) ).
fof(f6118,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ),
inference(rectify,[],[f5223]) ).
fof(f5223,axiom,
! [X31,X23] :
( hBOOL(X31)
| ~ hBOOL(X23)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X23),X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32364,plain,
spl647_631,
inference(avatar_split_clause,[],[f18284,f32362]) ).
fof(f32362,plain,
( spl647_631
<=> ! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_631])]) ).
fof(f18284,plain,
! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ),
inference(cnf_transformation,[],[f6117]) ).
fof(f6117,plain,
! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ),
inference(rectify,[],[f5220]) ).
fof(f5220,axiom,
! [X31,X23] :
( hBOOL(X31)
| hBOOL(X23)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X23),X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32360,plain,
spl647_630,
inference(avatar_split_clause,[],[f18278,f32358]) ).
fof(f32358,plain,
( spl647_630
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_630])]) ).
fof(f18278,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6111]) ).
fof(f6111,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(rectify,[],[f5215]) ).
fof(f5215,axiom,
! [X31,X23] :
( hBOOL(hAPP(hAPP(c_fconj,X23),X31))
| ~ hBOOL(X31)
| ~ hBOOL(X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32356,plain,
spl647_629,
inference(avatar_split_clause,[],[f17868,f32354]) ).
fof(f32354,plain,
( spl647_629
<=> ! [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,[spl647_629])]) ).
fof(f17868,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,[],[f5760]) ).
fof(f5760,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,[],[f1746]) ).
fof(f1746,axiom,
! [X44,X45] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X45,X44)),X45)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32352,plain,
spl647_628,
inference(avatar_split_clause,[],[f17866,f32350]) ).
fof(f32350,plain,
( spl647_628
<=> ! [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,[spl647_628])]) ).
fof(f17866,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5758]) ).
fof(f5758,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f2153]) ).
fof(f2153,axiom,
! [X13,X4] : hBOOL(hAPP(hAPP(c_member(X4),X13),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32348,plain,
spl647_627,
inference(avatar_split_clause,[],[f17864,f32346]) ).
fof(f32346,plain,
( spl647_627
<=> ! [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,[spl647_627])]) ).
fof(f17864,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(cnf_transformation,[],[f5756]) ).
fof(f5756,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(rectify,[],[f320]) ).
fof(f320,axiom,
! [X9,X4] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X9),X9) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32344,plain,
spl647_626,
inference(avatar_split_clause,[],[f17863,f32342]) ).
fof(f32342,plain,
( spl647_626
<=> ! [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,[spl647_626])]) ).
fof(f17863,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(cnf_transformation,[],[f5755]) ).
fof(f5755,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(rectify,[],[f49]) ).
fof(f49,axiom,
! [X9,X4] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X9),X9) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32340,plain,
spl647_625,
inference(avatar_split_clause,[],[f17862,f32338]) ).
fof(f32338,plain,
( spl647_625
<=> ! [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,[spl647_625])]) ).
fof(f17862,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,[],[f5754]) ).
fof(f5754,plain,
! [X0,X1] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X0)) = X0,
inference(rectify,[],[f1963]) ).
fof(f1963,axiom,
! [X9,X4] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_OPow(X4),X9)) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32336,plain,
spl647_624,
inference(avatar_split_clause,[],[f17861,f32334]) ).
fof(f32334,plain,
( spl647_624
<=> ! [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,[spl647_624])]) ).
fof(f17861,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5753]) ).
fof(f5753,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f3886]) ).
fof(f3886,axiom,
! [X44,X20] : c_List_Olist_ONil(X20) = hAPP(hAPP(c_List_Otake(X20),X44),c_List_Olist_ONil(X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32332,plain,
spl647_623,
inference(avatar_split_clause,[],[f17860,f32330]) ).
fof(f32330,plain,
( spl647_623
<=> ! [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,[spl647_623])]) ).
fof(f17860,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Odrop(X1),X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5752]) ).
fof(f5752,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Odrop(X1),X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f4007]) ).
fof(f4007,axiom,
! [X44,X20] : c_List_Olist_ONil(X20) = hAPP(hAPP(c_List_Odrop(X20),X44),c_List_Olist_ONil(X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32328,plain,
spl647_622,
inference(avatar_split_clause,[],[f17856,f32326]) ).
fof(f32326,plain,
( spl647_622
<=> ! [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,[spl647_622])]) ).
fof(f17856,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5748]) ).
fof(f5748,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f124]) ).
fof(f124,axiom,
! [X11,X4] : ~ hBOOL(hAPP(hAPP(c_member(X4),X11),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32324,plain,
spl647_621,
inference(avatar_split_clause,[],[f17643,f32322]) ).
fof(f32322,plain,
( spl647_621
<=> ! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK93(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_621])]) ).
fof(f17643,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK93(X0)),X0)) ),
inference(cnf_transformation,[],[f14644]) ).
fof(f32320,plain,
spl647_620,
inference(avatar_split_clause,[],[f17564,f32318]) ).
fof(f32318,plain,
( spl647_620
<=> ! [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,[spl647_620])]) ).
fof(f17564,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,[],[f10357]) ).
fof(f10357,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,[],[f5529]) ).
fof(f5529,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,[],[f1249]) ).
fof(f1249,axiom,
! [X20] :
( class_Rings_Osemiring__1(X20)
=> c_Groups_Oone__class_Oone(X20) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X20),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32316,plain,
spl647_619,
inference(avatar_split_clause,[],[f17560,f32314]) ).
fof(f32314,plain,
( spl647_619
<=> ! [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,[spl647_619])]) ).
fof(f17560,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,[],[f10353]) ).
fof(f10353,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,[],[f5525]) ).
fof(f5525,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,[],[f3896]) ).
fof(f3896,axiom,
! [X20] :
( class_Groups_Omonoid__add(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(c_List_Omonoid__add__class_Olistsum(X20),c_List_Olist_ONil(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32312,plain,
spl647_618,
inference(avatar_split_clause,[],[f17550,f32310]) ).
fof(f32310,plain,
( spl647_618
<=> ! [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,[spl647_618])]) ).
fof(f17550,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,[],[f10343]) ).
fof(f10343,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,[],[f5515]) ).
fof(f5515,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,[],[f2108]) ).
fof(f2108,axiom,
! [X20] :
( class_Lattices_Oboolean__algebra(X20)
=> c_Orderings_Obot__class_Obot(X20) = hAPP(c_Groups_Ouminus__class_Ouminus(X20),c_Orderings_Otop__class_Otop(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32308,plain,
spl647_617,
inference(avatar_split_clause,[],[f17549,f32306]) ).
fof(f32306,plain,
( spl647_617
<=> ! [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,[spl647_617])]) ).
fof(f17549,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,[],[f10342]) ).
fof(f10342,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,[],[f5514]) ).
fof(f5514,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,[],[f2109]) ).
fof(f2109,axiom,
! [X20] :
( class_Lattices_Oboolean__algebra(X20)
=> c_Orderings_Otop__class_Otop(X20) = hAPP(c_Groups_Ouminus__class_Ouminus(X20),c_Orderings_Obot__class_Obot(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32304,plain,
spl647_616,
inference(avatar_split_clause,[],[f17537,f32302]) ).
fof(f32302,plain,
( spl647_616
<=> ! [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,[spl647_616])]) ).
fof(f17537,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,[],[f10330]) ).
fof(f10330,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,[],[f5502]) ).
fof(f5502,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,[],[f1345]) ).
fof(f1345,axiom,
! [X20] :
( class_Rings_Olinordered__idom(X20)
=> c_Groups_Oone__class_Oone(X20) = hAPP(c_Groups_Oabs__class_Oabs(X20),c_Groups_Oone__class_Oone(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32300,plain,
spl647_615,
inference(avatar_split_clause,[],[f17536,f32298]) ).
fof(f17536,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,[],[f10329]) ).
fof(f10329,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,[],[f5501]) ).
fof(f5501,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,[],[f1340]) ).
fof(f1340,axiom,
! [X20] :
( class_Groups_Oordered__ab__group__add__abs(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(c_Groups_Oabs__class_Oabs(X20),c_Groups_Ozero__class_Ozero(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32296,plain,
spl647_614,
inference(avatar_split_clause,[],[f17532,f32294]) ).
fof(f32294,plain,
( spl647_614
<=> ! [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,[spl647_614])]) ).
fof(f17532,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,[],[f10325]) ).
fof(f10325,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,[],[f5497]) ).
fof(f5497,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,[],[f2037]) ).
fof(f2037,axiom,
! [X20] :
( class_Rings_Oring__1(X20)
=> c_Groups_Oone__class_Oone(X20) = hAPP(c_Int_Oring__1__class_Oof__int(X20),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32292,plain,
spl647_613,
inference(avatar_split_clause,[],[f17531,f32290]) ).
fof(f32290,plain,
( spl647_613
<=> ! [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,[spl647_613])]) ).
fof(f17531,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,[],[f10324]) ).
fof(f10324,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,[],[f5496]) ).
fof(f5496,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,[],[f1431]) ).
fof(f1431,axiom,
! [X20] :
( class_Groups_Ogroup__add(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(c_Groups_Ouminus__class_Ouminus(X20),c_Groups_Ozero__class_Ozero(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32288,plain,
spl647_612,
inference(avatar_split_clause,[],[f17376,f32286]) ).
fof(f32286,plain,
( spl647_612
<=> ! [X0] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X0) = c_Lazy__Sequence_Osmall__lazy_H(X0,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_612])]) ).
fof(f17376,plain,
! [X0] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X0) = c_Lazy__Sequence_Osmall__lazy_H(X0,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f5354]) ).
fof(f5354,plain,
! [X0] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X0) = c_Lazy__Sequence_Osmall__lazy_H(X0,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)),
inference(rectify,[],[f4658]) ).
fof(f4658,axiom,
! [X30] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X30) = c_Lazy__Sequence_Osmall__lazy_H(X30,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32284,plain,
spl647_611,
inference(avatar_split_clause,[],[f17375,f32282]) ).
fof(f32282,plain,
( spl647_611
<=> ! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_611])]) ).
fof(f17375,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)),
inference(cnf_transformation,[],[f5353]) ).
fof(f5353,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)),
inference(rectify,[],[f4149]) ).
fof(f4149,axiom,
! [X4] : c_Fun_Oid(tc_List_Olist(X4)) = hAPP(c_List_Omap(X4,X4),c_COMBI(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32280,plain,
spl647_610,
inference(avatar_split_clause,[],[f17374,f32278]) ).
fof(f32278,plain,
( spl647_610
<=> ! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_610])]) ).
fof(f17374,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)),
inference(cnf_transformation,[],[f5352]) ).
fof(f5352,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)),
inference(rectify,[],[f4117]) ).
fof(f4117,axiom,
! [X4] : c_Fun_Oid(tc_List_Olist(X4)) = hAPP(c_List_Omap(X4,X4),c_Fun_Oid(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32276,plain,
( ~ spl647_608
| spl647_609
| ~ spl647_222
| ~ spl647_434 ),
inference(avatar_split_clause,[],[f31513,f31278,f30331,f32273,f32269]) ).
fof(f32269,plain,
( spl647_608
<=> c_Relation_Osym(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_608])]) ).
fof(f32273,plain,
( spl647_609
<=> c_Relation_Osym(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_609])]) ).
fof(f30331,plain,
( spl647_222
<=> c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_222])]) ).
fof(f31278,plain,
( spl647_434
<=> ! [X0,X1] :
( c_Relation_Osym(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Relation_Osym(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_434])]) ).
fof(f31513,plain,
( c_Relation_Osym(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ c_Relation_Osym(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl647_222
| ~ spl647_434 ),
inference(superposition,[],[f31279,f30333]) ).
fof(f30333,plain,
( c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl647_222 ),
inference(avatar_component_clause,[],[f30331]) ).
fof(f31279,plain,
( ! [X0,X1] :
( c_Relation_Osym(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Relation_Osym(X1,X0) )
| ~ spl647_434 ),
inference(avatar_component_clause,[],[f31278]) ).
fof(f32267,plain,
spl647_607,
inference(avatar_split_clause,[],[f17360,f32265]) ).
fof(f17360,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,[],[f5338]) ).
fof(f5338,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,[],[f3774]) ).
fof(f3774,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32263,plain,
spl647_606,
inference(avatar_split_clause,[],[f17214,f32260]) ).
fof(f32260,plain,
( spl647_606
<=> 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,[spl647_606])]) ).
fof(f17214,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,[],[f3088]) ).
fof(f3088,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32258,plain,
spl647_605,
inference(avatar_split_clause,[],[f17209,f32255]) ).
fof(f32255,plain,
( spl647_605
<=> 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,[spl647_605])]) ).
fof(f17209,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,[],[f4179]) ).
fof(f4179,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32253,plain,
spl647_604,
inference(avatar_split_clause,[],[f17208,f32250]) ).
fof(f32250,plain,
( spl647_604
<=> 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,[spl647_604])]) ).
fof(f17208,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,[],[f2092]) ).
fof(f2092,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32248,plain,
spl647_603,
inference(avatar_split_clause,[],[f17206,f32245]) ).
fof(f32245,plain,
( spl647_603
<=> 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,[spl647_603])]) ).
fof(f17206,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,[],[f4204]) ).
fof(f4204,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32220,plain,
( ~ spl647_602
| spl647_327
| ~ spl647_577 ),
inference(avatar_split_clause,[],[f32210,f31911,f30799,f32217]) ).
fof(f32217,plain,
( spl647_602
<=> c_Nat__Transfer_Ois__nat(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_602])]) ).
fof(f32210,plain,
( ~ c_Nat__Transfer_Ois__nat(c_Int_OMin)
| spl647_327
| ~ spl647_577 ),
inference(resolution,[],[f31912,f30801]) ).
fof(f32190,plain,
( ~ spl647_129
| ~ spl647_268
| spl647_601 ),
inference(avatar_split_clause,[],[f32164,f32059,f30535,f29879]) ).
fof(f29879,plain,
( spl647_129
<=> class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_129])]) ).
fof(f30535,plain,
( spl647_268
<=> ! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_268])]) ).
fof(f32059,plain,
( spl647_601
<=> c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_601])]) ).
fof(f32164,plain,
( ~ class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral)
| ~ spl647_268
| spl647_601 ),
inference(resolution,[],[f32060,f30536]) ).
fof(f30536,plain,
( ! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) )
| ~ spl647_268 ),
inference(avatar_component_clause,[],[f30535]) ).
fof(f32060,plain,
( ~ c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| spl647_601 ),
inference(avatar_component_clause,[],[f32059]) ).
fof(f32062,plain,
( ~ spl647_600
| spl647_601
| ~ spl647_334
| ~ spl647_415 ),
inference(avatar_split_clause,[],[f31510,f31200,f30837,f32059,f32055]) ).
fof(f32055,plain,
( spl647_600
<=> class_Int_Onumber__ring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_600])]) ).
fof(f30837,plain,
( spl647_334
<=> 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,[spl647_334])]) ).
fof(f31200,plain,
( spl647_415
<=> ! [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,[spl647_415])]) ).
fof(f31510,plain,
( c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| ~ class_Int_Onumber__ring(tc_Code__Numeral_Ocode__numeral)
| ~ spl647_334
| ~ spl647_415 ),
inference(superposition,[],[f31201,f30839]) ).
fof(f30839,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)
| ~ spl647_334 ),
inference(avatar_component_clause,[],[f30837]) ).
fof(f31201,plain,
( ! [X0] :
( c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) )
| ~ spl647_415 ),
inference(avatar_component_clause,[],[f31200]) ).
fof(f32036,plain,
( spl647_599
| ~ spl647_243
| ~ spl647_403 ),
inference(avatar_split_clause,[],[f31501,f31152,f30422,f32034]) ).
fof(f32034,plain,
( spl647_599
<=> ! [X0] : sP6(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_599])]) ).
fof(f30422,plain,
( spl647_243
<=> ! [X0] : sP6(hAPP(c_Int_Onat,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_243])]) ).
fof(f31152,plain,
( spl647_403
<=> ! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_403])]) ).
fof(f31501,plain,
( ! [X0] : sP6(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ spl647_243
| ~ spl647_403 ),
inference(superposition,[],[f30423,f31153]) ).
fof(f31153,plain,
( ! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0
| ~ spl647_403 ),
inference(avatar_component_clause,[],[f31152]) ).
fof(f30423,plain,
( ! [X0] : sP6(hAPP(c_Int_Onat,X0),X0)
| ~ spl647_243 ),
inference(avatar_component_clause,[],[f30422]) ).
fof(f32020,plain,
( spl647_598
| ~ spl647_244
| ~ spl647_403 ),
inference(avatar_split_clause,[],[f31500,f31152,f30426,f32018]) ).
fof(f32018,plain,
( spl647_598
<=> ! [X0] : sP7(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_598])]) ).
fof(f30426,plain,
( spl647_244
<=> ! [X1] : sP7(hAPP(c_Int_Onat,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_244])]) ).
fof(f31500,plain,
( ! [X0] : sP7(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ spl647_244
| ~ spl647_403 ),
inference(superposition,[],[f30427,f31153]) ).
fof(f30427,plain,
( ! [X1] : sP7(hAPP(c_Int_Onat,X1),X1)
| ~ spl647_244 ),
inference(avatar_component_clause,[],[f30426]) ).
fof(f31999,plain,
( spl647_597
| ~ spl647_271
| ~ spl647_345 ),
inference(avatar_split_clause,[],[f31099,f30888,f30547,f31997]) ).
fof(f30547,plain,
( spl647_271
<=> ! [X0] : hAPP(c_Code__Numeral_Oof__nat,sK109(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_271])]) ).
fof(f31099,plain,
( ! [X0] : hAPP(c_Code__Numeral_Onat__of,X0) = sK109(X0)
| ~ spl647_271
| ~ spl647_345 ),
inference(superposition,[],[f30889,f30548]) ).
fof(f30548,plain,
( ! [X0] : hAPP(c_Code__Numeral_Oof__nat,sK109(X0)) = X0
| ~ spl647_271 ),
inference(avatar_component_clause,[],[f30547]) ).
fof(f31991,plain,
spl647_596,
inference(avatar_split_clause,[],[f28923,f31989]) ).
fof(f31989,plain,
( spl647_596
<=> ! [X2,X1,X3] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(c_fequal,X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_596])]) ).
fof(f28923,plain,
! [X2,X3,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(c_fequal,X1)),X1)),
inference(forward_demodulation,[],[f25732,f26468]) ).
fof(f25732,plain,
! [X2,X3,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X1)),
inference(equality_resolution,[],[f22752]) ).
fof(f22752,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f16393]) ).
fof(f31987,plain,
spl647_595,
inference(avatar_split_clause,[],[f27913,f31985]) ).
fof(f31985,plain,
( spl647_595
<=> ! [X0,X1] : c_List_Olast(X1,c_List_Oinsert(X1,X0,c_List_Olist_ONil(X1))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_595])]) ).
fof(f27913,plain,
! [X0,X1] : c_List_Olast(X1,c_List_Oinsert(X1,X0,c_List_Olist_ONil(X1))) = X0,
inference(forward_demodulation,[],[f25443,f17921]) ).
fof(f25443,plain,
! [X0,X1] : c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1))) = X0,
inference(equality_resolution,[],[f19853]) ).
fof(f19853,plain,
! [X2,X0,X1] :
( c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2)) = X0
| c_List_Olist_ONil(X1) != X2 ),
inference(cnf_transformation,[],[f11307]) ).
fof(f11307,plain,
! [X0,X1,X2] :
( ( c_List_Olast(X1,X2) = c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2))
| c_List_Olist_ONil(X1) = X2 )
& ( c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2)) = X0
| c_List_Olist_ONil(X1) != X2 ) ),
inference(ennf_transformation,[],[f7205]) ).
fof(f7205,plain,
! [X0,X1,X2] :
( ( c_List_Olist_ONil(X1) != X2
=> c_List_Olast(X1,X2) = c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2)) )
& ( c_List_Olist_ONil(X1) = X2
=> c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2)) = X0 ) ),
inference(rectify,[],[f4104]) ).
fof(f4104,axiom,
! [X19,X20,X201] :
( ( c_List_Olist_ONil(X20) != X201
=> c_List_Olast(X20,X201) = c_List_Olast(X20,hAPP(hAPP(c_List_Olist_OCons(X20),X19),X201)) )
& ( c_List_Olist_ONil(X20) = X201
=> c_List_Olast(X20,hAPP(hAPP(c_List_Olist_OCons(X20),X19),X201)) = X19 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31983,plain,
spl647_594,
inference(avatar_split_clause,[],[f27807,f31981]) ).
fof(f31981,plain,
( spl647_594
<=> ! [X2,X0,X1] : hAPP(c_Finite__Set_Ofold1(X2,X1),hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_594])]) ).
fof(f27807,plain,
! [X2,X0,X1] : hAPP(c_Finite__Set_Ofold1(X2,X1),hAPP(c_fequal,X0)) = X0,
inference(forward_demodulation,[],[f19630,f26468]) ).
fof(f19630,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,[],[f6984]) ).
fof(f6984,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,[],[f22]) ).
fof(f22,axiom,
! [X5,X1,X4] : hAPP(c_Finite__Set_Ofold1(X4,X1),hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31979,plain,
( spl647_593
| ~ spl647_223
| ~ spl647_275 ),
inference(avatar_split_clause,[],[f30755,f30563,f30336,f31977]) ).
fof(f31977,plain,
( spl647_593
<=> ! [X0] : c_Fun_Oinj__on(tc_Int_Oint,tc_Int_Oint,c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_593])]) ).
fof(f30336,plain,
( spl647_223
<=> c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_223])]) ).
fof(f30563,plain,
( spl647_275
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_275])]) ).
fof(f30755,plain,
( ! [X0] : c_Fun_Oinj__on(tc_Int_Oint,tc_Int_Oint,c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)
| ~ spl647_223
| ~ spl647_275 ),
inference(superposition,[],[f30564,f30338]) ).
fof(f30338,plain,
( c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint)
| ~ spl647_223 ),
inference(avatar_component_clause,[],[f30336]) ).
fof(f30564,plain,
( ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0)
| ~ spl647_275 ),
inference(avatar_component_clause,[],[f30563]) ).
fof(f31975,plain,
spl647_592,
inference(avatar_split_clause,[],[f27798,f31973]) ).
fof(f31973,plain,
( spl647_592
<=> ! [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,[spl647_592])]) ).
fof(f27798,plain,
! [X2,X0,X1] : hAPP(c_Nat_Onat_Onat__rec(X2,X1,X0),c_HOL_Obool_Obool__size(c_fTrue)) = X1,
inference(forward_demodulation,[],[f19587,f17145]) ).
fof(f19587,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,[],[f6941]) ).
fof(f6941,plain,
! [X0,X1,X2] : hAPP(c_Nat_Onat_Onat__rec(X2,X1,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rectify,[],[f2287]) ).
fof(f2287,axiom,
! [X135,X95,X4] : hAPP(c_Nat_Onat_Onat__rec(X4,X95,X135),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X95,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31971,plain,
spl647_591,
inference(avatar_split_clause,[],[f27694,f31968]) ).
fof(f31968,plain,
( spl647_591
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_591])]) ).
fof(f27694,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f27693,f26605]) ).
fof(f27693,plain,
! [X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_HOL_Obool_Obool__size(c_fTrue)))),
inference(forward_demodulation,[],[f25432,f17145]) ).
fof(f25432,plain,
! [X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(equality_resolution,[],[f19471]) ).
fof(f19471,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f15225]) ).
fof(f15225,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ~ 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) = 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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))) ) ),
inference(flattening,[],[f15224]) ).
fof(f15224,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ~ 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) = 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),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))) ) ),
inference(nnf_transformation,[],[f6887]) ).
fof(f6887,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ) ),
inference(rectify,[],[f1903]) ).
fof(f1903,axiom,
! [X46,X13] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X13),X46)))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X46
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31966,plain,
spl647_590,
inference(avatar_split_clause,[],[f26969,f31964]) ).
fof(f31964,plain,
( spl647_590
<=> ! [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,[spl647_590])]) ).
fof(f26969,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(forward_demodulation,[],[f18628,f26468]) ).
fof(f18628,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,[],[f10796]) ).
fof(f10796,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,[],[f6394]) ).
fof(f6394,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,[],[f446]) ).
fof(f446,axiom,
! [X13,X4] :
( class_Lattices_Olattice(X4)
=> c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X13),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31962,plain,
spl647_589,
inference(avatar_split_clause,[],[f26968,f31960]) ).
fof(f31960,plain,
( spl647_589
<=> ! [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,[spl647_589])]) ).
fof(f26968,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(forward_demodulation,[],[f18627,f26468]) ).
fof(f18627,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,[],[f10795]) ).
fof(f10795,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,[],[f6393]) ).
fof(f6393,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,[],[f380]) ).
fof(f380,axiom,
! [X13,X4] :
( class_Lattices_Olattice(X4)
=> c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X13),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31958,plain,
spl647_588,
inference(avatar_split_clause,[],[f26959,f31956]) ).
fof(f31956,plain,
( spl647_588
<=> ! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_588])]) ).
fof(f26959,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(forward_demodulation,[],[f18568,f26468]) ).
fof(f18568,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,[],[f10737]) ).
fof(f10737,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,[],[f6352]) ).
fof(f6352,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,[],[f2495]) ).
fof(f2495,axiom,
! [X13,X4] :
( class_Orderings_Olinorder(X4)
=> c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Set_Oinsert(X4),X13),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31954,plain,
spl647_587,
inference(avatar_split_clause,[],[f26958,f31952]) ).
fof(f31952,plain,
( spl647_587
<=> ! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_587])]) ).
fof(f26958,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(forward_demodulation,[],[f18567,f26468]) ).
fof(f18567,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,[],[f10736]) ).
fof(f10736,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,[],[f6351]) ).
fof(f6351,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,[],[f1174]) ).
fof(f1174,axiom,
! [X13,X4] :
( class_Orderings_Olinorder(X4)
=> c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X13),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31950,plain,
spl647_586,
inference(avatar_split_clause,[],[f26957,f31948]) ).
fof(f31948,plain,
( spl647_586
<=> ! [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,[spl647_586])]) ).
fof(f26957,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,[],[f18566,f17921]) ).
fof(f18566,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,[],[f10735]) ).
fof(f10735,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,[],[f6350]) ).
fof(f6350,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,[],[f4400]) ).
fof(f4400,axiom,
! [X19,X20] :
( class_Orderings_Olinorder(X20)
=> c_List_Olinorder__class_Osorted(X20,hAPP(hAPP(c_List_Olist_OCons(X20),X19),c_List_Olist_ONil(X20))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31946,plain,
spl647_585,
inference(avatar_split_clause,[],[f26929,f31944]) ).
fof(f31944,plain,
( spl647_585
<=> ! [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,[spl647_585])]) ).
fof(f26929,plain,
! [X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(forward_demodulation,[],[f18490,f26468]) ).
fof(f18490,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,[],[f10654]) ).
fof(f10654,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,[],[f6278]) ).
fof(f6278,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,[],[f710]) ).
fof(f710,axiom,
! [X5,X4] :
( class_Complete__Lattice_Ocomplete__lattice(X4)
=> c_Complete__Lattice_OSup__class_OSup(X4,hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31942,plain,
spl647_584,
inference(avatar_split_clause,[],[f26928,f31940]) ).
fof(f31940,plain,
( spl647_584
<=> ! [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,[spl647_584])]) ).
fof(f26928,plain,
! [X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(forward_demodulation,[],[f18489,f26468]) ).
fof(f18489,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,[],[f10653]) ).
fof(f10653,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,[],[f6277]) ).
fof(f6277,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,[],[f2144]) ).
fof(f2144,axiom,
! [X5,X4] :
( class_Complete__Lattice_Ocomplete__lattice(X4)
=> c_Complete__Lattice_OInf__class_OInf(X4,hAPP(hAPP(c_Set_Oinsert(X4),X5),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31938,plain,
spl647_583,
inference(avatar_split_clause,[],[f26821,f31936]) ).
fof(f31936,plain,
( spl647_583
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Int_OPls)
| ~ class_Int_Oring__char__0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_583])]) ).
fof(f26821,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Int_OPls)
| ~ class_Int_Oring__char__0(X1) ),
inference(forward_demodulation,[],[f25294,f17135]) ).
fof(f25294,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Int_Oring__char__0(X1) ),
inference(equality_resolution,[],[f18312]) ).
fof(f18312,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ class_Int_Oring__char__0(X1) ),
inference(cnf_transformation,[],[f14744]) ).
fof(f31934,plain,
spl647_582,
inference(avatar_split_clause,[],[f26447,f31932]) ).
fof(f31932,plain,
( spl647_582
<=> ! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_582])]) ).
fof(f26447,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f17841,f17145]) ).
fof(f17841,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f5733]) ).
fof(f5733,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f3998]) ).
fof(f3998,axiom,
! [X201,X20] : hAPP(hAPP(c_List_Odrop(X20),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X201) = X201,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31930,plain,
spl647_581,
inference(avatar_split_clause,[],[f26446,f31928]) ).
fof(f31928,plain,
( spl647_581
<=> ! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X0),c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_581])]) ).
fof(f26446,plain,
! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X0),c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)),
inference(forward_demodulation,[],[f17834,f17145]) ).
fof(f17834,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X0),c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)),
inference(cnf_transformation,[],[f5726]) ).
fof(f5726,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X1,X0),c_Lazy__Sequence_Olazy__sequence_OEmpty(X1)),
inference(rectify,[],[f4678]) ).
fof(f4678,axiom,
! [X92,X4] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X4,X92),c_Lazy__Sequence_Olazy__sequence_OEmpty(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31926,plain,
spl647_580,
inference(avatar_split_clause,[],[f26361,f31924]) ).
fof(f31924,plain,
( spl647_580
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_580])]) ).
fof(f26361,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f26360,f17285]) ).
fof(f26360,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,[],[f17684,f17285]) ).
fof(f17684,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,[],[f14674]) ).
fof(f14674,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,[],[f5621]) ).
fof(f5621,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,[],[f1523]) ).
fof(f1523,axiom,
! [X59] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X59))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X59))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31922,plain,
spl647_579,
inference(avatar_split_clause,[],[f26359,f31920]) ).
fof(f31920,plain,
( spl647_579
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_579])]) ).
fof(f26359,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0))) ),
inference(forward_demodulation,[],[f26358,f17285]) ).
fof(f26358,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,[],[f17685,f17285]) ).
fof(f17685,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,[],[f14674]) ).
fof(f31918,plain,
~ spl647_578,
inference(avatar_split_clause,[],[f26328,f31915]) ).
fof(f31915,plain,
( spl647_578
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_578])]) ).
fof(f26328,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),
inference(forward_demodulation,[],[f26327,f25911]) ).
fof(f26327,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Code__Numeral_Oof__nat,c_HOL_Obool_Obool__size(c_fTrue)))),
inference(forward_demodulation,[],[f25261,f17145]) ).
fof(f25261,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(equality_resolution,[],[f17670]) ).
fof(f17670,plain,
! [X0] :
( hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0)) ),
inference(cnf_transformation,[],[f14664]) ).
fof(f31913,plain,
spl647_577,
inference(avatar_split_clause,[],[f26320,f31911]) ).
fof(f26320,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,[],[f17645,f17135]) ).
fof(f17645,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,[],[f14645]) ).
fof(f14645,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,[],[f5603]) ).
fof(f5603,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,[],[f2141]) ).
fof(f2141,axiom,
! [X13] :
( c_Nat__Transfer_Ois__nat(X13)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31909,plain,
spl647_576,
inference(avatar_split_clause,[],[f26319,f31907]) ).
fof(f26319,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,[],[f17646,f17135]) ).
fof(f17646,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,[],[f14645]) ).
fof(f31905,plain,
spl647_575,
inference(avatar_split_clause,[],[f26195,f31903]) ).
fof(f31903,plain,
( spl647_575
<=> ! [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,[spl647_575])]) ).
fof(f26195,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,[],[f17533,f17135]) ).
fof(f17533,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,[],[f10326]) ).
fof(f10326,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,[],[f5498]) ).
fof(f5498,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,[],[f2031]) ).
fof(f2031,axiom,
! [X20] :
( class_Rings_Oring__1(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(c_Int_Oring__1__class_Oof__int(X20),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31901,plain,
spl647_574,
inference(avatar_split_clause,[],[f26056,f31899]) ).
fof(f31899,plain,
( spl647_574
<=> ! [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,[spl647_574])]) ).
fof(f26056,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,[],[f26055,f25910]) ).
fof(f26055,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,[],[f17401,f17145]) ).
fof(f17401,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,[],[f5379]) ).
fof(f5379,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,[],[f1760]) ).
fof(f1760,axiom,
! [X45] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X45),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X45,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31897,plain,
spl647_573,
inference(avatar_split_clause,[],[f26031,f31895]) ).
fof(f26031,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f17356,f17145]) ).
fof(f17356,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,[],[f5334]) ).
fof(f5334,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f781]) ).
fof(f781,axiom,
! [X44] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44) = X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31893,plain,
( ~ spl647_131
| spl647_572
| ~ spl647_226
| ~ spl647_268 ),
inference(avatar_split_clause,[],[f30753,f30535,f30351,f31890,f29889]) ).
fof(f29889,plain,
( spl647_131
<=> class_Rings_Osemiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_131])]) ).
fof(f31890,plain,
( spl647_572
<=> c_Int_Oiszero(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_572])]) ).
fof(f30351,plain,
( spl647_226
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_226])]) ).
fof(f30753,plain,
( c_Int_Oiszero(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue))
| ~ class_Rings_Osemiring__1(tc_Nat_Onat)
| ~ spl647_226
| ~ spl647_268 ),
inference(superposition,[],[f30536,f30353]) ).
fof(f30353,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue)
| ~ spl647_226 ),
inference(avatar_component_clause,[],[f30351]) ).
fof(f31888,plain,
spl647_571,
inference(avatar_split_clause,[],[f26029,f31886]) ).
fof(f31886,plain,
( spl647_571
<=> ! [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,[spl647_571])]) ).
fof(f26029,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f17354,f17145]) ).
fof(f17354,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,[],[f5332]) ).
fof(f5332,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f2470]) ).
fof(f2470,axiom,
! [X44] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44) = X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31884,plain,
spl647_570,
inference(avatar_split_clause,[],[f26028,f31882]) ).
fof(f31882,plain,
( spl647_570
<=> ! [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,[spl647_570])]) ).
fof(f26028,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17351,f17145]) ).
fof(f17351,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,[],[f5329]) ).
fof(f5329,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f782]) ).
fof(f782,axiom,
! [X45] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X45),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X45,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31880,plain,
spl647_569,
inference(avatar_split_clause,[],[f26026,f31878]) ).
fof(f31878,plain,
( spl647_569
<=> ! [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,[spl647_569])]) ).
fof(f26026,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17349,f17145]) ).
fof(f17349,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,[],[f5327]) ).
fof(f5327,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f789]) ).
fof(f789,axiom,
! [X45] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X45,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31876,plain,
spl647_568,
inference(avatar_split_clause,[],[f26025,f31874]) ).
fof(f31874,plain,
( spl647_568
<=> ! [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,[spl647_568])]) ).
fof(f26025,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17348,f17145]) ).
fof(f17348,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,[],[f5326]) ).
fof(f5326,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f2469]) ).
fof(f2469,axiom,
! [X44] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X44),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31872,plain,
spl647_567,
inference(avatar_split_clause,[],[f26023,f31870]) ).
fof(f31870,plain,
( spl647_567
<=> ! [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,[spl647_567])]) ).
fof(f26023,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0),
inference(forward_demodulation,[],[f17337,f17145]) ).
fof(f17337,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,[],[f5315]) ).
fof(f5315,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0),
inference(rectify,[],[f788]) ).
fof(f788,axiom,
! [X45] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X45),X45),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31868,plain,
spl647_566,
inference(avatar_split_clause,[],[f26022,f31866]) ).
fof(f31866,plain,
( spl647_566
<=> ! [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,[spl647_566])]) ).
fof(f26022,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,[],[f17336,f17145]) ).
fof(f17336,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,[],[f5314]) ).
fof(f5314,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,[],[f3897]) ).
fof(f3897,axiom,
! [X20] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X20)),c_List_Olist_ONil(X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31864,plain,
spl647_565,
inference(avatar_split_clause,[],[f26021,f31862]) ).
fof(f31862,plain,
( spl647_565
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_565])]) ).
fof(f26021,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X0)),
inference(forward_demodulation,[],[f17335,f17145]) ).
fof(f17335,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X0)),
inference(cnf_transformation,[],[f5313]) ).
fof(f5313,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X0)),
inference(rectify,[],[f4677]) ).
fof(f4677,axiom,
! [X20] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X20)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31859,plain,
spl647_564,
inference(avatar_split_clause,[],[f25922,f31856]) ).
fof(f31856,plain,
( spl647_564
<=> c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_564])]) ).
fof(f25922,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)))),
inference(forward_demodulation,[],[f25921,f25909]) ).
fof(f25921,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))),
inference(forward_demodulation,[],[f24174,f17133]) ).
fof(f24174,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin)))),
inference(definition_unfolding,[],[f17176,f24151]) ).
fof(f17176,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,[],[f2117]) ).
fof(f2117,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31854,plain,
spl647_563,
inference(avatar_split_clause,[],[f25710,f31852]) ).
fof(f31852,plain,
( spl647_563
<=> ! [X2,X1,X3] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_563])]) ).
fof(f25710,plain,
! [X2,X3,X1] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X2)),
inference(equality_resolution,[],[f22615]) ).
fof(f22615,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
| X0 != X2 ),
inference(cnf_transformation,[],[f16300]) ).
fof(f31850,plain,
spl647_562,
inference(avatar_split_clause,[],[f25597,f31848]) ).
fof(f31848,plain,
( spl647_562
<=> ! [X2,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_562])]) ).
fof(f25597,plain,
! [X2,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X1)),
inference(equality_resolution,[],[f21355]) ).
fof(f21355,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0)) ),
inference(cnf_transformation,[],[f15899]) ).
fof(f15899,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0))
| X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0)) )
& ( ( X0 != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0)) ) ),
inference(flattening,[],[f15898]) ).
fof(f15898,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0))
| X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0)) )
& ( ( X0 != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0)) ) ),
inference(nnf_transformation,[],[f8189]) ).
fof(f8189,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0))
<=> ( X0 != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0)) ) ),
inference(rectify,[],[f246]) ).
fof(f246,axiom,
! [X18,X9,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X9),X18))
<=> ( X9 != X18
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X9),X18)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31843,plain,
spl647_561,
inference(avatar_split_clause,[],[f25596,f31841]) ).
fof(f25596,plain,
! [X2,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X1))),
inference(equality_resolution,[],[f21353]) ).
fof(f21353,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
| X0 != X1 ),
inference(cnf_transformation,[],[f15897]) ).
fof(f15897,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
| X0 != X1 )
& ( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0))) ) ),
inference(nnf_transformation,[],[f8188]) ).
fof(f8188,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
<=> X0 = X1 ),
inference(rectify,[],[f150]) ).
fof(f150,axiom,
! [X15,X13,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),X13),hAPP(c_fequal,X15)))
<=> X13 = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31839,plain,
spl647_560,
inference(avatar_split_clause,[],[f25501,f31837]) ).
fof(f31837,plain,
( spl647_560
<=> ! [X2,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_560])]) ).
fof(f25501,plain,
! [X2,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f20529]) ).
fof(f20529,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),X1))
| X0 != X1
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f15465]) ).
fof(f15465,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0)) )
| X0 != X1 ) )
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f15464]) ).
fof(f15464,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0)) )
| X0 != X1 ) )
| ~ class_Orderings_Oorder(X2) ),
inference(nnf_transformation,[],[f12059]) ).
fof(f12059,plain,
! [X0,X1,X2] :
( ( X0 = X1
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0)) ) )
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f7740]) ).
fof(f7740,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( X0 = X1
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0)) ) ) ),
inference(rectify,[],[f57]) ).
fof(f57,axiom,
! [X15,X13,X4] :
( class_Orderings_Oorder(X4)
=> ( X13 = X15
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X15),X13))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X13),X15)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31835,plain,
spl647_559,
inference(avatar_split_clause,[],[f25497,f31833]) ).
fof(f31833,plain,
( spl647_559
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_559])]) ).
fof(f25497,plain,
! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f20513]) ).
fof(f20513,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f12032]) ).
fof(f12032,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f12031]) ).
fof(f12031,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f7726]) ).
fof(f7726,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
=> X0 != X1 ) ),
inference(rectify,[],[f203]) ).
fof(f203,axiom,
! [X21,X19,X20] :
( class_Orderings_Oorder(X20)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20),X19),X21))
=> X19 != X21 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31831,plain,
spl647_558,
inference(avatar_split_clause,[],[f25488,f31829]) ).
fof(f31829,plain,
( spl647_558
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_558])]) ).
fof(f25488,plain,
! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(equality_resolution,[],[f20370]) ).
fof(f20370,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f15414]) ).
fof(f15414,plain,
! [X0,X1,X2] :
( ( ( X0 != X1
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| X0 = X1 ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f15413]) ).
fof(f15413,plain,
! [X0,X1,X2] :
( ( ( X0 != X1
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| X0 = X1 ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(nnf_transformation,[],[f11885]) ).
fof(f11885,plain,
! [X0,X1,X2] :
( ( X0 != X1
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0)) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7625]) ).
fof(f7625,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( X0 != X1
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0)) ) ) ),
inference(rectify,[],[f195]) ).
fof(f195,axiom,
! [X15,X13,X4] :
( class_Orderings_Olinorder(X4)
=> ( X13 != X15
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X15),X13))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X13),X15)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31827,plain,
spl647_557,
inference(avatar_split_clause,[],[f25306,f31825]) ).
fof(f31825,plain,
( spl647_557
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_557])]) ).
fof(f25306,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(equality_resolution,[],[f18411]) ).
fof(f18411,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f14768]) ).
fof(f31823,plain,
spl647_556,
inference(avatar_split_clause,[],[f24303,f31821]) ).
fof(f31821,plain,
( spl647_556
<=> ! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_556])]) ).
fof(f24303,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X0)),
inference(definition_unfolding,[],[f17794,f17312]) ).
fof(f17312,plain,
! [X0] : c_Wellfounded_Omeasure(X0) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0),c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f5290]) ).
fof(f5290,plain,
! [X0] : c_Wellfounded_Omeasure(X0) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0),c_Wellfounded_Oless__than),
inference(rectify,[],[f2800]) ).
fof(f2800,axiom,
! [X4] : c_Wellfounded_Omeasure(X4) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X4),c_Wellfounded_Oless__than),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17794,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X0)),
inference(cnf_transformation,[],[f5686]) ).
fof(f5686,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X0)),
inference(rectify,[],[f3361]) ).
fof(f3361,axiom,
! [X1,X4] : c_Wellfounded_Owf(X4,hAPP(c_Wellfounded_Omeasure(X4),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31819,plain,
spl647_555,
inference(avatar_split_clause,[],[f24297,f31817]) ).
fof(f24297,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))),
inference(definition_unfolding,[],[f17782,f17880]) ).
fof(f17782,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X0)),
inference(cnf_transformation,[],[f5674]) ).
fof(f5674,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X0)),
inference(rectify,[],[f4401]) ).
fof(f4401,axiom,
! [X54,X55] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X55,X54)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31815,plain,
spl647_554,
inference(avatar_split_clause,[],[f24197,f31813]) ).
fof(f31813,plain,
( spl647_554
<=> ! [X0] : c_Int_OPls != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_554])]) ).
fof(f24197,plain,
! [X0] : c_Int_OPls != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin),
inference(definition_unfolding,[],[f17254,f24151]) ).
fof(f17254,plain,
! [X0] : c_Int_OPls != c_Int_OBit1(X0),
inference(cnf_transformation,[],[f5232]) ).
fof(f5232,plain,
! [X0] : c_Int_OPls != c_Int_OBit1(X0),
inference(rectify,[],[f1354]) ).
fof(f1354,axiom,
! [X56] : c_Int_OPls != c_Int_OBit1(X56),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31811,plain,
spl647_553,
inference(avatar_split_clause,[],[f24168,f31808]) ).
fof(f31808,plain,
( spl647_553
<=> c_Int_OMin = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OMin)),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_553])]) ).
fof(f24168,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OMin)),c_Int_OMin),
inference(definition_unfolding,[],[f17131,f24151]) ).
fof(f17131,plain,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
inference(cnf_transformation,[],[f1959]) ).
fof(f1959,axiom,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31806,plain,
spl647_552,
inference(avatar_split_clause,[],[f21549,f31804]) ).
fof(f31804,plain,
( spl647_552
<=> ! [X2,X0,X1,X3] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X2,X1,X0,c_Lazy__Sequence_Olazy__sequence_OEmpty(X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_552])]) ).
fof(f21549,plain,
! [X2,X3,X0,X1] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X2,X1,X0,c_Lazy__Sequence_Olazy__sequence_OEmpty(X2)) = X1,
inference(cnf_transformation,[],[f8266]) ).
fof(f8266,plain,
! [X0,X1,X2,X3] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X3,X2,X1,X0,c_Lazy__Sequence_Olazy__sequence_OEmpty(X2)) = X1,
inference(rectify,[],[f4800]) ).
fof(f4800,axiom,
! [X135,X95,X14,X4] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(X4,X14,X95,X135,c_Lazy__Sequence_Olazy__sequence_OEmpty(X14)) = X95,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31802,plain,
spl647_551,
inference(avatar_split_clause,[],[f21548,f31800]) ).
fof(f31800,plain,
( spl647_551
<=> ! [X2,X0,X1,X3] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_551])]) ).
fof(f21548,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1,
inference(cnf_transformation,[],[f8265]) ).
fof(f8265,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1,
inference(rectify,[],[f5205]) ).
fof(f5205,axiom,
! [X280,X279,X4,X20] : hAPP(hAPP(c_COMBK(X20,X4),X279),X280) = X279,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31798,plain,
spl647_550,
inference(avatar_split_clause,[],[f21090,f31796]) ).
fof(f31796,plain,
( spl647_550
<=> ! [X2,X0,X1] :
( X1 = X2
| ~ c_List_Olist__all2(X0,X0,c_fequal,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_550])]) ).
fof(f21090,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ c_List_Olist__all2(X0,X0,c_fequal,X2,X1) ),
inference(cnf_transformation,[],[f15684]) ).
fof(f15684,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,[],[f8124]) ).
fof(f8124,plain,
! [X0,X1,X2] :
( X1 = X2
<=> c_List_Olist__all2(X0,X0,c_fequal,X2,X1) ),
inference(rectify,[],[f4241]) ).
fof(f4241,axiom,
! [X4,X202,X203] :
( X202 = X203
<=> c_List_Olist__all2(X4,X4,c_fequal,X203,X202) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31794,plain,
spl647_549,
inference(avatar_split_clause,[],[f20700,f31792]) ).
fof(f20700,plain,
! [X2,X0,X1] :
( sP24(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(cnf_transformation,[],[f14517]) ).
fof(f14517,plain,
! [X0,X1,X2] :
( sP24(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(definition_folding,[],[f12224,f14516,f14515]) ).
fof(f14516,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)
<=> sP23(X0,X1,X2) )
| ~ sP24(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).
fof(f12224,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,[],[f12223]) ).
fof(f12223,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,[],[f7863]) ).
fof(f7863,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,[],[f865]) ).
fof(f865,axiom,
! [X1,X9,X4] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X9))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X9) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ? [X2] :
( ! [X43] :
( hBOOL(hAPP(hAPP(c_member(X4),X43),X9))
=> ( X2 != X43
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X1,X43) ) )
& hAPP(X1,X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(X4),X2),X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31790,plain,
spl647_548,
inference(avatar_split_clause,[],[f20688,f31788]) ).
fof(f20688,plain,
! [X2,X0,X1] :
( sP22(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(cnf_transformation,[],[f14514]) ).
fof(f14514,plain,
! [X0,X1,X2] :
( sP22(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(definition_folding,[],[f12221,f14513,f14512]) ).
fof(f14513,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)
<=> sP21(X0,X1,X2) )
| ~ sP22(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
fof(f12221,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,[],[f12220]) ).
fof(f12220,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,[],[f7861]) ).
fof(f7861,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,[],[f887]) ).
fof(f887,axiom,
! [X1,X9,X4] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X9))
=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X9)
<=> ? [X2] :
( ! [X43] :
( hBOOL(hAPP(hAPP(c_member(X4),X43),X9))
=> ( X2 != X43
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X1,X43) ) )
& hAPP(X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(X4),X2),X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31786,plain,
spl647_547,
inference(avatar_split_clause,[],[f20562,f31784]) ).
fof(f31784,plain,
( spl647_547
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_547])]) ).
fof(f20562,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(cnf_transformation,[],[f12079]) ).
fof(f12079,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(ennf_transformation,[],[f7758]) ).
fof(f7758,plain,
! [X0,X1,X2] :
( c_Equiv__Relations_Oequivp(X2,X1)
=> hBOOL(hAPP(hAPP(X1,X0),X0)) ),
inference(rectify,[],[f3028]) ).
fof(f3028,axiom,
! [X13,X138,X4] :
( c_Equiv__Relations_Oequivp(X4,X138)
=> hBOOL(hAPP(hAPP(X138,X13),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31782,plain,
spl647_546,
inference(avatar_split_clause,[],[f20561,f31780]) ).
fof(f31780,plain,
( spl647_546
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_546])]) ).
fof(f20561,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ),
inference(cnf_transformation,[],[f12078]) ).
fof(f12078,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ),
inference(ennf_transformation,[],[f7757]) ).
fof(f7757,plain,
! [X0,X1,X2] :
( c_Predicate_Oreflp(X2,X1)
=> hBOOL(hAPP(hAPP(X1,X0),X0)) ),
inference(rectify,[],[f3304]) ).
fof(f3304,axiom,
! [X13,X116,X4] :
( c_Predicate_Oreflp(X4,X116)
=> hBOOL(hAPP(hAPP(X116,X13),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31778,plain,
spl647_545,
inference(avatar_split_clause,[],[f19588,f31776]) ).
fof(f31776,plain,
( spl647_545
<=> ! [X2,X0,X1] : c_Predicate_Oconversep(X2,X1,c_Predicate_Oconversep(X1,X2,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_545])]) ).
fof(f19588,plain,
! [X2,X0,X1] : c_Predicate_Oconversep(X2,X1,c_Predicate_Oconversep(X1,X2,X0)) = X0,
inference(cnf_transformation,[],[f6942]) ).
fof(f6942,plain,
! [X0,X1,X2] : c_Predicate_Oconversep(X2,X1,c_Predicate_Oconversep(X1,X2,X0)) = X0,
inference(rectify,[],[f4609]) ).
fof(f4609,axiom,
! [X116,X4,X14] : c_Predicate_Oconversep(X14,X4,c_Predicate_Oconversep(X4,X14,X116)) = X116,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31774,plain,
spl647_544,
inference(avatar_split_clause,[],[f19586,f31772]) ).
fof(f31772,plain,
( spl647_544
<=> ! [X2,X0,X1] : hAPP(c_New__DSequence_Oneg__single(X2,X1),X0) = c_Lazy__Sequence_Ohb__single(X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_544])]) ).
fof(f19586,plain,
! [X2,X0,X1] : hAPP(c_New__DSequence_Oneg__single(X2,X1),X0) = c_Lazy__Sequence_Ohb__single(X2,X1),
inference(cnf_transformation,[],[f6940]) ).
fof(f6940,plain,
! [X0,X1,X2] : hAPP(c_New__DSequence_Oneg__single(X2,X1),X0) = c_Lazy__Sequence_Ohb__single(X2,X1),
inference(rectify,[],[f4595]) ).
fof(f4595,axiom,
! [X246,X19,X20] : hAPP(c_New__DSequence_Oneg__single(X20,X19),X246) = c_Lazy__Sequence_Ohb__single(X20,X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31770,plain,
spl647_543,
inference(avatar_split_clause,[],[f19583,f31768]) ).
fof(f31768,plain,
( spl647_543
<=> ! [X2,X0,X1] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) = c_Lazy__Sequence_Omap(X2,X1,X0,c_Lazy__Sequence_Olazy__sequence_OEmpty(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_543])]) ).
fof(f19583,plain,
! [X2,X0,X1] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) = c_Lazy__Sequence_Omap(X2,X1,X0,c_Lazy__Sequence_Olazy__sequence_OEmpty(X2)),
inference(cnf_transformation,[],[f6937]) ).
fof(f6937,plain,
! [X0,X1,X2] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X1) = c_Lazy__Sequence_Omap(X2,X1,X0,c_Lazy__Sequence_Olazy__sequence_OEmpty(X2)),
inference(rectify,[],[f4873]) ).
fof(f4873,axiom,
! [X1,X4,X14] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X4) = c_Lazy__Sequence_Omap(X14,X4,X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31766,plain,
spl647_542,
inference(avatar_split_clause,[],[f19581,f31764]) ).
fof(f31764,plain,
( spl647_542
<=> ! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_542])]) ).
fof(f19581,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[],[f6935]) ).
fof(f6935,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2),
inference(rectify,[],[f3883]) ).
fof(f3883,axiom,
! [X215,X117,X20] : c_List_Olist_ONil(X20) != hAPP(hAPP(c_List_Olist_OCons(X20),X117),X215),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31762,plain,
spl647_541,
inference(avatar_split_clause,[],[f19186,f31760]) ).
fof(f19186,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP8(X1,X0) ),
inference(cnf_transformation,[],[f15042]) ).
fof(f15042,plain,
! [X0,X1] :
( ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP8(X1,X0) )
& ( sP8(X1,X0)
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ) ),
inference(nnf_transformation,[],[f14491]) ).
fof(f14491,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
<=> sP8(X1,X0) ),
inference(definition_folding,[],[f11289,f14490]) ).
fof(f11289,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,[],[f6776]) ).
fof(f6776,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,[],[f1827]) ).
fof(f1827,axiom,
! [X63,X23] :
( hBOOL(hAPP(X23,hAPP(c_Int_Onat,X63)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X63),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(X23,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X109] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X109) = X63
=> hBOOL(hAPP(X23,X109)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31758,plain,
spl647_540,
inference(avatar_split_clause,[],[f19185,f31756]) ).
fof(f19185,plain,
! [X0,X1] :
( sP8(X1,X0)
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ),
inference(cnf_transformation,[],[f15042]) ).
fof(f31754,plain,
spl647_539,
inference(avatar_split_clause,[],[f19099,f31752]) ).
fof(f31752,plain,
( spl647_539
<=> ! [X0,X1,X3] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_539])]) ).
fof(f19099,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ),
inference(cnf_transformation,[],[f14962]) ).
fof(f31750,plain,
spl647_538,
inference(avatar_split_clause,[],[f18706,f31748]) ).
fof(f31748,plain,
( spl647_538
<=> ! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_538])]) ).
fof(f18706,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10889]) ).
fof(f10889,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6459]) ).
fof(f6459,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0)) ),
inference(rectify,[],[f3423]) ).
fof(f3423,axiom,
! [X138,X4] :
( c_Wellfounded_Owf(X4,X138)
=> c_Wellfounded_OwfP(X4,c_FunDef_Oin__rel(X4,X4,X138)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31746,plain,
spl647_537,
inference(avatar_split_clause,[],[f18698,f31744]) ).
fof(f31744,plain,
( spl647_537
<=> ! [X0,X1] :
( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olistrel(X1,X0))
| ~ c_Relation_Otrans(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_537])]) ).
fof(f18698,plain,
! [X0,X1] :
( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olistrel(X1,X0))
| ~ c_Relation_Otrans(X1,X0) ),
inference(cnf_transformation,[],[f10880]) ).
fof(f10880,plain,
! [X0,X1] :
( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olistrel(X1,X0))
| ~ c_Relation_Otrans(X1,X0) ),
inference(ennf_transformation,[],[f6451]) ).
fof(f6451,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
=> c_Relation_Otrans(tc_List_Olist(X1),c_List_Olistrel(X1,X0)) ),
inference(rectify,[],[f4715]) ).
fof(f4715,axiom,
! [X116,X4] :
( c_Relation_Otrans(X4,X116)
=> c_Relation_Otrans(tc_List_Olist(X4),c_List_Olistrel(X4,X116)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31742,plain,
spl647_536,
inference(avatar_split_clause,[],[f18697,f31740]) ).
fof(f31740,plain,
( spl647_536
<=> ! [X0,X1] :
( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olexord(X1,X0))
| ~ c_Relation_Otrans(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_536])]) ).
fof(f18697,plain,
! [X0,X1] :
( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olexord(X1,X0))
| ~ c_Relation_Otrans(X1,X0) ),
inference(cnf_transformation,[],[f10879]) ).
fof(f10879,plain,
! [X0,X1] :
( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olexord(X1,X0))
| ~ c_Relation_Otrans(X1,X0) ),
inference(ennf_transformation,[],[f6450]) ).
fof(f6450,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
=> c_Relation_Otrans(tc_List_Olist(X1),c_List_Olexord(X1,X0)) ),
inference(rectify,[],[f4717]) ).
fof(f4717,axiom,
! [X116,X4] :
( c_Relation_Otrans(X4,X116)
=> c_Relation_Otrans(tc_List_Olist(X4),c_List_Olexord(X4,X116)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31738,plain,
spl647_535,
inference(avatar_split_clause,[],[f18694,f31736]) ).
fof(f31736,plain,
( spl647_535
<=> ! [X0,X1] :
( c_Relation_Osym(tc_List_Olist(X1),c_List_Olistrel(X1,X0))
| ~ c_Relation_Osym(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_535])]) ).
fof(f18694,plain,
! [X0,X1] :
( c_Relation_Osym(tc_List_Olist(X1),c_List_Olistrel(X1,X0))
| ~ c_Relation_Osym(X1,X0) ),
inference(cnf_transformation,[],[f10875]) ).
fof(f10875,plain,
! [X0,X1] :
( c_Relation_Osym(tc_List_Olist(X1),c_List_Olistrel(X1,X0))
| ~ c_Relation_Osym(X1,X0) ),
inference(ennf_transformation,[],[f6447]) ).
fof(f6447,plain,
! [X0,X1] :
( c_Relation_Osym(X1,X0)
=> c_Relation_Osym(tc_List_Olist(X1),c_List_Olistrel(X1,X0)) ),
inference(rectify,[],[f4758]) ).
fof(f4758,axiom,
! [X116,X4] :
( c_Relation_Osym(X4,X116)
=> c_Relation_Osym(tc_List_Olist(X4),c_List_Olistrel(X4,X116)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31734,plain,
spl647_534,
inference(avatar_split_clause,[],[f18670,f31732]) ).
fof(f31732,plain,
( spl647_534
<=> ! [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,[spl647_534])]) ).
fof(f18670,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,[],[f10847]) ).
fof(f10847,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,[],[f10846]) ).
fof(f10846,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,[],[f6428]) ).
fof(f6428,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,[],[f2133]) ).
fof(f2133,axiom,
! [X21,X19] :
( c_Nat__Transfer_Ois__nat(X19)
=> ( c_Nat__Transfer_Ois__nat(X21)
=> c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X19,X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31730,plain,
spl647_533,
inference(avatar_split_clause,[],[f18666,f31728]) ).
fof(f31728,plain,
( spl647_533
<=> ! [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,[spl647_533])]) ).
fof(f18666,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,[],[f10841]) ).
fof(f10841,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,[],[f6425]) ).
fof(f6425,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,[],[f2136]) ).
fof(f2136,axiom,
! [X44,X19] :
( c_Nat__Transfer_Ois__nat(X19)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X19),X44)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31726,plain,
spl647_532,
inference(avatar_split_clause,[],[f18637,f31724]) ).
fof(f31724,plain,
( spl647_532
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_532])]) ).
fof(f18637,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10810]) ).
fof(f10810,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6403]) ).
fof(f6403,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0)) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X19,X20] :
( class_Orderings_Opreorder(X20)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X20),X19),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31722,plain,
( spl647_531
| ~ spl647_194
| ~ spl647_435 ),
inference(avatar_split_clause,[],[f31514,f31282,f30205,f31719]) ).
fof(f31719,plain,
( spl647_531
<=> c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_531])]) ).
fof(f30205,plain,
( spl647_194
<=> c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_194])]) ).
fof(f31282,plain,
( spl647_435
<=> ! [X0,X1] :
( c_Transitive__Closure_Otrancl(X1,X0) = X0
| ~ c_Relation_Otrans(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_435])]) ).
fof(f31514,plain,
( c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl647_194
| ~ spl647_435 ),
inference(resolution,[],[f31283,f30207]) ).
fof(f30207,plain,
( c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl647_194 ),
inference(avatar_component_clause,[],[f30205]) ).
fof(f31283,plain,
( ! [X0,X1] :
( ~ c_Relation_Otrans(X1,X0)
| c_Transitive__Closure_Otrancl(X1,X0) = X0 )
| ~ spl647_435 ),
inference(avatar_component_clause,[],[f31282]) ).
fof(f31717,plain,
spl647_530,
inference(avatar_split_clause,[],[f18636,f31715]) ).
fof(f31715,plain,
( spl647_530
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_530])]) ).
fof(f18636,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10809]) ).
fof(f10809,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6402]) ).
fof(f6402,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0)) ),
inference(rectify,[],[f193]) ).
fof(f193,axiom,
! [X19,X20] :
( class_Orderings_Opreorder(X20)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X20),X19),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31713,plain,
spl647_529,
inference(avatar_split_clause,[],[f18604,f31711]) ).
fof(f31711,plain,
( spl647_529
<=> ! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_529])]) ).
fof(f18604,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f14801]) ).
fof(f14801,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,[],[f14476]) ).
fof(f14476,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(f31709,plain,
spl647_528,
inference(avatar_split_clause,[],[f18603,f31707]) ).
fof(f31707,plain,
( spl647_528
<=> ! [X0,X1] :
( sP0(X1,X0)
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_528])]) ).
fof(f18603,plain,
! [X0,X1] :
( sP0(X1,X0)
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f14801]) ).
fof(f31705,plain,
spl647_527,
inference(avatar_split_clause,[],[f18549,f31703]) ).
fof(f31703,plain,
( spl647_527
<=> ! [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,[spl647_527])]) ).
fof(f18549,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,[],[f10716]) ).
fof(f10716,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,[],[f6333]) ).
fof(f6333,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f1591]) ).
fof(f1591,axiom,
! [X26,X20] :
( class_Divides_Osemiring__div(X20)
=> c_Divides_Odiv__class_Omod(X20,X26,c_Groups_Ozero__class_Ozero(X20)) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31701,plain,
spl647_526,
inference(avatar_split_clause,[],[f18548,f31699]) ).
fof(f31699,plain,
( spl647_526
<=> ! [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,[spl647_526])]) ).
fof(f18548,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,[],[f10715]) ).
fof(f10715,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,[],[f6332]) ).
fof(f6332,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0) ),
inference(rectify,[],[f1592]) ).
fof(f1592,axiom,
! [X26,X20] :
( class_Divides_Osemiring__div(X20)
=> c_Groups_Ozero__class_Ozero(X20) = c_Divides_Odiv__class_Omod(X20,X26,X26) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31697,plain,
spl647_525,
inference(avatar_split_clause,[],[f18533,f31695]) ).
fof(f31695,plain,
( spl647_525
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_525])]) ).
fof(f18533,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f10699]) ).
fof(f10699,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f6317]) ).
fof(f6317,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0)) ),
inference(rectify,[],[f4927]) ).
fof(f4927,axiom,
! [X26,X20] :
( class_Rings_Ocomm__semiring__1(X20)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X20),X26),X26)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31693,plain,
spl647_524,
inference(avatar_split_clause,[],[f18523,f31691]) ).
fof(f31691,plain,
( spl647_524
<=> ! [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,[spl647_524])]) ).
fof(f18523,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Int_Oiszero(X1,X0)
| ~ class_Rings_Osemiring__1(X1) ),
inference(cnf_transformation,[],[f14787]) ).
fof(f14787,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,[],[f10691]) ).
fof(f10691,plain,
! [X0,X1] :
( ( c_Int_Oiszero(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Rings_Osemiring__1(X1) ),
inference(ennf_transformation,[],[f6309]) ).
fof(f6309,plain,
! [X0,X1] :
( class_Rings_Osemiring__1(X1)
=> ( c_Int_Oiszero(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f1643]) ).
fof(f1643,axiom,
! [X17,X4] :
( class_Rings_Osemiring__1(X4)
=> ( c_Int_Oiszero(X4,X17)
<=> c_Groups_Ozero__class_Ozero(X4) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31689,plain,
spl647_523,
inference(avatar_split_clause,[],[f18288,f31687]) ).
fof(f31687,plain,
( spl647_523
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_523])]) ).
fof(f18288,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ),
inference(cnf_transformation,[],[f6121]) ).
fof(f6121,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ),
inference(rectify,[],[f5209]) ).
fof(f5209,axiom,
! [X15,X13] :
( X13 = X15
| ~ hBOOL(hAPP(hAPP(c_fequal,X13),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31685,plain,
spl647_522,
inference(avatar_split_clause,[],[f17854,f31683]) ).
fof(f17854,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X0)),
inference(cnf_transformation,[],[f5746]) ).
fof(f5746,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X0)),
inference(rectify,[],[f46]) ).
fof(f46,axiom,
! [X9,X4] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X9),X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31681,plain,
spl647_521,
inference(avatar_split_clause,[],[f17853,f31679]) ).
fof(f31679,plain,
( spl647_521
<=> ! [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,[spl647_521])]) ).
fof(f17853,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,[],[f5745]) ).
fof(f5745,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,[],[f2739]) ).
fof(f2739,axiom,
! [X68,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X97),X68))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31677,plain,
spl647_520,
inference(avatar_split_clause,[],[f17852,f31675]) ).
fof(f31675,plain,
( spl647_520
<=> ! [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,[spl647_520])]) ).
fof(f17852,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,[],[f5744]) ).
fof(f5744,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,[],[f2810]) ).
fof(f2810,axiom,
! [X68,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X97),X68))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31673,plain,
spl647_519,
inference(avatar_split_clause,[],[f17851,f31671]) ).
fof(f31671,plain,
( spl647_519
<=> ! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_519])]) ).
fof(f17851,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(cnf_transformation,[],[f5743]) ).
fof(f5743,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(rectify,[],[f2906]) ).
fof(f2906,axiom,
! [X158,X4] : hAPP(c_Set_Oimage(X4,X4,c_COMBI(X4)),X158) = X158,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31669,plain,
spl647_518,
inference(avatar_split_clause,[],[f17850,f31667]) ).
fof(f31667,plain,
( spl647_518
<=> ! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_518])]) ).
fof(f17850,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(cnf_transformation,[],[f5742]) ).
fof(f5742,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(rectify,[],[f3310]) ).
fof(f3310,axiom,
! [X158,X4] : hAPP(c_Set_Oimage(X4,X4,c_Fun_Oid(X4)),X158) = X158,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31665,plain,
spl647_517,
inference(avatar_split_clause,[],[f17849,f31663]) ).
fof(f31663,plain,
( spl647_517
<=> ! [X0,X1] : hAPP(c_Relation_OImage(X1,X1,c_Relation_OId(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_517])]) ).
fof(f17849,plain,
! [X0,X1] : hAPP(c_Relation_OImage(X1,X1,c_Relation_OId(X1)),X0) = X0,
inference(cnf_transformation,[],[f5741]) ).
fof(f5741,plain,
! [X0,X1] : hAPP(c_Relation_OImage(X1,X1,c_Relation_OId(X1)),X0) = X0,
inference(rectify,[],[f3597]) ).
fof(f3597,axiom,
! [X9,X4] : hAPP(c_Relation_OImage(X4,X4,c_Relation_OId(X4)),X9) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31661,plain,
spl647_516,
inference(avatar_split_clause,[],[f17848,f31659]) ).
fof(f31659,plain,
( spl647_516
<=> ! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_516])]) ).
fof(f17848,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(cnf_transformation,[],[f5740]) ).
fof(f5740,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(rectify,[],[f3132]) ).
fof(f3132,axiom,
! [X158,X4] : hAPP(c_Set_Ovimage(X4,X4,c_COMBI(X4)),X158) = X158,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31657,plain,
spl647_515,
inference(avatar_split_clause,[],[f17847,f31655]) ).
fof(f31655,plain,
( spl647_515
<=> ! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_515])]) ).
fof(f17847,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(cnf_transformation,[],[f5739]) ).
fof(f5739,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(rectify,[],[f3307]) ).
fof(f3307,axiom,
! [X9,X4] : hAPP(c_Set_Ovimage(X4,X4,c_Fun_Oid(X4)),X9) = X9,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31653,plain,
spl647_514,
inference(avatar_split_clause,[],[f17844,f31651]) ).
fof(f31651,plain,
( spl647_514
<=> ! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_514])]) ).
fof(f17844,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0,
inference(cnf_transformation,[],[f5736]) ).
fof(f5736,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0,
inference(rectify,[],[f3964]) ).
fof(f3964,axiom,
! [X200,X20] : hAPP(hAPP(c_List_Oappend(X20),c_List_Olist_ONil(X20)),X200) = X200,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31649,plain,
spl647_513,
inference(avatar_split_clause,[],[f17843,f31647]) ).
fof(f31647,plain,
( spl647_513
<=> ! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_513])]) ).
fof(f17843,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0,
inference(cnf_transformation,[],[f5735]) ).
fof(f5735,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0,
inference(rectify,[],[f3962]) ).
fof(f3962,axiom,
! [X201,X20] : hAPP(hAPP(c_List_Oappend(X20),X201),c_List_Olist_ONil(X20)) = X201,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31645,plain,
spl647_512,
inference(avatar_split_clause,[],[f17842,f31643]) ).
fof(f31643,plain,
( spl647_512
<=> ! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_512])]) ).
fof(f17842,plain,
! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0,
inference(cnf_transformation,[],[f5734]) ).
fof(f5734,plain,
! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0,
inference(rectify,[],[f4451]) ).
fof(f4451,axiom,
! [X201,X20] : hAPP(c_List_Orev(X20),hAPP(c_List_Orev(X20),X201)) = X201,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31641,plain,
spl647_511,
inference(avatar_split_clause,[],[f17837,f31639]) ).
fof(f31639,plain,
( spl647_511
<=> ! [X0,X1] : c_List_Oremdups(X1,X0) = c_List_Oremdups(X1,c_List_Oremdups(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_511])]) ).
fof(f17837,plain,
! [X0,X1] : c_List_Oremdups(X1,X0) = c_List_Oremdups(X1,c_List_Oremdups(X1,X0)),
inference(cnf_transformation,[],[f5729]) ).
fof(f5729,plain,
! [X0,X1] : c_List_Oremdups(X1,X0) = c_List_Oremdups(X1,c_List_Oremdups(X1,X0)),
inference(rectify,[],[f4276]) ).
fof(f4276,axiom,
! [X201,X20] : c_List_Oremdups(X20,X201) = c_List_Oremdups(X20,c_List_Oremdups(X20,X201)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31637,plain,
( ~ spl647_26
| ~ spl647_510
| ~ spl647_263
| ~ spl647_414 ),
inference(avatar_split_clause,[],[f31509,f31196,f30515,f31634,f29364]) ).
fof(f31634,plain,
( spl647_510
<=> c_Int_Oiszero(tc_Int_Oint,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_510])]) ).
fof(f31196,plain,
( spl647_414
<=> ! [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,[spl647_414])]) ).
fof(f31509,plain,
( ~ c_Int_Oiszero(tc_Int_Oint,c_Int_OMin)
| ~ class_Int_Onumber__ring(tc_Int_Oint)
| ~ spl647_263
| ~ spl647_414 ),
inference(superposition,[],[f31197,f30516]) ).
fof(f31197,plain,
( ! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) )
| ~ spl647_414 ),
inference(avatar_component_clause,[],[f31196]) ).
fof(f31632,plain,
spl647_509,
inference(avatar_split_clause,[],[f17836,f31630]) ).
fof(f31630,plain,
( spl647_509
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_509])]) ).
fof(f17836,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5728]) ).
fof(f5728,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f4331]) ).
fof(f4331,axiom,
! [X23,X4] : c_List_Olist_ONil(X4) = hAPP(c_List_Ofilter(X4,X23),c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31628,plain,
spl647_508,
inference(avatar_split_clause,[],[f17640,f31626]) ).
fof(f31626,plain,
( spl647_508
<=> ! [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,[spl647_508])]) ).
fof(f17640,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,[],[f10433]) ).
fof(f10433,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,[],[f10432]) ).
fof(f10432,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,[],[f5600]) ).
fof(f5600,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,[],[f1095]) ).
fof(f1095,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31624,plain,
spl647_507,
inference(avatar_split_clause,[],[f17639,f31622]) ).
fof(f31622,plain,
( spl647_507
<=> ! [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,[spl647_507])]) ).
fof(f17639,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,[],[f10431]) ).
fof(f10431,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,[],[f10430]) ).
fof(f10430,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,[],[f5599]) ).
fof(f5599,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,[],[f2450]) ).
fof(f2450,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31620,plain,
spl647_506,
inference(avatar_split_clause,[],[f17587,f31618]) ).
fof(f31618,plain,
( spl647_506
<=> ! [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,[spl647_506])]) ).
fof(f17587,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,[],[f10380]) ).
fof(f10380,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,[],[f5552]) ).
fof(f5552,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,[],[f1130]) ).
fof(f1130,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31616,plain,
spl647_505,
inference(avatar_split_clause,[],[f17586,f31614]) ).
fof(f31614,plain,
( spl647_505
<=> ! [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,[spl647_505])]) ).
fof(f17586,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,[],[f10379]) ).
fof(f10379,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,[],[f5551]) ).
fof(f5551,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,[],[f2485]) ).
fof(f2485,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31612,plain,
spl647_504,
inference(avatar_split_clause,[],[f17541,f31610]) ).
fof(f31610,plain,
( spl647_504
<=> ! [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,[spl647_504])]) ).
fof(f17541,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,[],[f10334]) ).
fof(f10334,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,[],[f5506]) ).
fof(f5506,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,[],[f1282]) ).
fof(f1282,axiom,
! [X20] :
( class_Int_Onumber__ring(X20)
=> c_Groups_Ozero__class_Ozero(X20) = hAPP(c_Int_Onumber__class_Onumber__of(X20),c_Int_OPls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31608,plain,
spl647_503,
inference(avatar_split_clause,[],[f17530,f31606]) ).
fof(f31606,plain,
( spl647_503
<=> ! [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,[spl647_503])]) ).
fof(f17530,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,[],[f10323]) ).
fof(f10323,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,[],[f5495]) ).
fof(f5495,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,[],[f2057]) ).
fof(f2057,axiom,
! [X20] :
( class_Groups_Osgn__if(X20)
=> c_Groups_Ozero__class_Ozero(X20) = c_Groups_Osgn__class_Osgn(X20,c_Groups_Ozero__class_Ozero(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31604,plain,
spl647_502,
inference(avatar_split_clause,[],[f17359,f31602]) ).
fof(f31602,plain,
( spl647_502
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_502])]) ).
fof(f17359,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))),
inference(cnf_transformation,[],[f5337]) ).
fof(f5337,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))),
inference(rectify,[],[f467]) ).
fof(f467,axiom,
! [X44] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),hAPP(c_Nat_OSuc,X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31600,plain,
spl647_501,
inference(avatar_split_clause,[],[f17358,f31598]) ).
fof(f31598,plain,
( spl647_501
<=> ! [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,[spl647_501])]) ).
fof(f17358,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,[],[f5336]) ).
fof(f5336,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f502]) ).
fof(f502,axiom,
! [X44] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X44) = X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31596,plain,
spl647_500,
inference(avatar_split_clause,[],[f17357,f31594]) ).
fof(f31594,plain,
( spl647_500
<=> ! [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,[spl647_500])]) ).
fof(f17357,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,[],[f5335]) ).
fof(f5335,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
inference(rectify,[],[f1161]) ).
fof(f1161,axiom,
! [X27] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X27) = X27,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31591,plain,
spl647_499,
inference(avatar_split_clause,[],[f17353,f31589]) ).
fof(f31589,plain,
( spl647_499
<=> ! [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,[spl647_499])]) ).
fof(f17353,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,[],[f5331]) ).
fof(f5331,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(rectify,[],[f504]) ).
fof(f504,axiom,
! [X44] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31587,plain,
spl647_498,
inference(avatar_split_clause,[],[f17352,f31585]) ).
fof(f31585,plain,
( spl647_498
<=> ! [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,[spl647_498])]) ).
fof(f17352,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,[],[f5330]) ).
fof(f5330,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
inference(rectify,[],[f1162]) ).
fof(f1162,axiom,
! [X27] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X27),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X27,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31583,plain,
spl647_497,
inference(avatar_split_clause,[],[f17347,f31581]) ).
fof(f17347,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,[],[f5325]) ).
fof(f5325,plain,
! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = X0,
inference(rectify,[],[f1414]) ).
fof(f1414,axiom,
! [X27] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X27)) = X27,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31579,plain,
spl647_496,
inference(avatar_split_clause,[],[f17346,f31577]) ).
fof(f31577,plain,
( spl647_496
<=> ! [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,[spl647_496])]) ).
fof(f17346,plain,
! [X0] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)) = X0,
inference(cnf_transformation,[],[f5324]) ).
fof(f5324,plain,
! [X0] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)) = X0,
inference(rectify,[],[f2405]) ).
fof(f2405,axiom,
! [X68] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X68)) = X68,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31575,plain,
spl647_495,
inference(avatar_split_clause,[],[f17344,f31573]) ).
fof(f31573,plain,
( spl647_495
<=> ! [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,[spl647_495])]) ).
fof(f17344,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,[],[f5322]) ).
fof(f5322,plain,
! [X0] : c_List_Olist_ONil(tc_List_Olist(X0)) = c_List_Otranspose(X0,c_List_Olist_ONil(tc_List_Olist(X0))),
inference(rectify,[],[f4330]) ).
fof(f4330,axiom,
! [X20] : c_List_Olist_ONil(tc_List_Olist(X20)) = c_List_Otranspose(X20,c_List_Olist_ONil(tc_List_Olist(X20))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31571,plain,
spl647_494,
inference(avatar_split_clause,[],[f17343,f31569]) ).
fof(f17343,plain,
! [X0] : c_Int_OBit0(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0),
inference(cnf_transformation,[],[f5321]) ).
fof(f5321,plain,
! [X0] : c_Int_OBit0(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0),
inference(rectify,[],[f1459]) ).
fof(f1459,axiom,
! [X53] : c_Int_OBit0(X53) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),X53),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31567,plain,
spl647_493,
inference(avatar_split_clause,[],[f17342,f31565]) ).
fof(f31565,plain,
( spl647_493
<=> ! [X0] : c_Relation_OId(X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_493])]) ).
fof(f17342,plain,
! [X0] : c_Relation_OId(X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Relation_OId(X0)),
inference(cnf_transformation,[],[f5320]) ).
fof(f5320,plain,
! [X0] : c_Relation_OId(X0) = hAPP(c_Relation_Oconverse(X0,X0),c_Relation_OId(X0)),
inference(rectify,[],[f3623]) ).
fof(f3623,axiom,
! [X4] : c_Relation_OId(X4) = hAPP(c_Relation_Oconverse(X4,X4),c_Relation_OId(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31562,plain,
spl647_492,
inference(avatar_split_clause,[],[f17334,f31560]) ).
fof(f31560,plain,
( spl647_492
<=> ! [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,[spl647_492])]) ).
fof(f17334,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X0)),
inference(cnf_transformation,[],[f5312]) ).
fof(f5312,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X0)),
inference(rectify,[],[f525]) ).
fof(f525,axiom,
! [X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X44)),X44)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31558,plain,
spl647_491,
inference(avatar_split_clause,[],[f17333,f31556]) ).
fof(f31556,plain,
( spl647_491
<=> ! [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,[spl647_491])]) ).
fof(f17333,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,[],[f5311]) ).
fof(f5311,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,[],[f2079]) ).
fof(f2079,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31554,plain,
spl647_490,
inference(avatar_split_clause,[],[f17205,f31551]) ).
fof(f31551,plain,
( spl647_490
<=> 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,[spl647_490])]) ).
fof(f17205,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,[],[f4200]) ).
fof(f4200,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31548,plain,
spl647_489,
inference(avatar_split_clause,[],[f17204,f31545]) ).
fof(f31545,plain,
( spl647_489
<=> 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,[spl647_489])]) ).
fof(f17204,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,[],[f3093]) ).
fof(f3093,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31536,plain,
( spl647_488
| spl647_221
| ~ spl647_392 ),
inference(avatar_split_clause,[],[f31118,f31084,f30326,f31533]) ).
fof(f31533,plain,
( spl647_488
<=> sP11(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_488])]) ).
fof(f30326,plain,
( spl647_221
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_221])]) ).
fof(f31118,plain,
( sP11(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| spl647_221
| ~ spl647_392 ),
inference(resolution,[],[f31085,f30328]) ).
fof(f30328,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| spl647_221 ),
inference(avatar_component_clause,[],[f30326]) ).
fof(f31524,plain,
( ~ spl647_487
| ~ spl647_312
| ~ spl647_385 ),
inference(avatar_split_clause,[],[f31112,f31050,f30715,f31521]) ).
fof(f31521,plain,
( spl647_487
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_487])]) ).
fof(f30715,plain,
( spl647_312
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_312])]) ).
fof(f31112,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_HOL_Obool_Obool__size(c_fTrue)
| ~ spl647_312
| ~ spl647_385 ),
inference(superposition,[],[f30716,f31052]) ).
fof(f30716,plain,
( ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0)
| ~ spl647_312 ),
inference(avatar_component_clause,[],[f30715]) ).
fof(f31506,plain,
( ~ spl647_486
| ~ spl647_372
| spl647_397 ),
inference(avatar_split_clause,[],[f31490,f31126,f30996,f31503]) ).
fof(f31503,plain,
( spl647_486
<=> class_Finite__Set_Ofinite(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_486])]) ).
fof(f31126,plain,
( spl647_397
<=> 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,[spl647_397])]) ).
fof(f31490,plain,
( ~ class_Finite__Set_Ofinite(tc_Nat_Onat)
| ~ spl647_372
| spl647_397 ),
inference(resolution,[],[f31128,f30997]) ).
fof(f31128,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| spl647_397 ),
inference(avatar_component_clause,[],[f31126]) ).
fof(f31497,plain,
( ~ spl647_485
| ~ spl647_372
| spl647_396 ),
inference(avatar_split_clause,[],[f31489,f31121,f30996,f31494]) ).
fof(f31494,plain,
( spl647_485
<=> class_Finite__Set_Ofinite(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_485])]) ).
fof(f31121,plain,
( spl647_396
<=> 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,[spl647_396])]) ).
fof(f31489,plain,
( ~ class_Finite__Set_Ofinite(tc_Int_Oint)
| ~ spl647_372
| spl647_396 ),
inference(resolution,[],[f31123,f30997]) ).
fof(f31123,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool))))
| spl647_396 ),
inference(avatar_component_clause,[],[f31121]) ).
fof(f31488,plain,
spl647_484,
inference(avatar_split_clause,[],[f28487,f31486]) ).
fof(f31486,plain,
( spl647_484
<=> ! [X2,X1] :
( ~ sP43(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,c_Int_OPls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_484])]) ).
fof(f28487,plain,
! [X2,X1] :
( ~ sP43(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,c_Int_OPls)) ),
inference(forward_demodulation,[],[f28486,f17135]) ).
fof(f28486,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,c_Int_OPls))
| ~ sP43(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(forward_demodulation,[],[f25587,f17135]) ).
fof(f25587,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP43(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(equality_resolution,[],[f21300]) ).
fof(f21300,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ sP43(X0,X1,X2) ),
inference(cnf_transformation,[],[f15858]) ).
fof(f15858,plain,
! [X0,X1,X2] :
( ( sP43(X0,X1,X2)
| ~ sP42(X2,X1,X0)
| ~ sP41(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP42(X2,X1,X0)
& sP41(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP43(X0,X1,X2) ) ),
inference(flattening,[],[f15857]) ).
fof(f15857,plain,
! [X0,X1,X2] :
( ( sP43(X0,X1,X2)
| ~ sP42(X2,X1,X0)
| ~ sP41(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP42(X2,X1,X0)
& sP41(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP43(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14547]) ).
fof(f31484,plain,
spl647_483,
inference(avatar_split_clause,[],[f28461,f31482]) ).
fof(f31482,plain,
( spl647_483
<=> ! [X2,X1] :
( ~ sP38(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_483])]) ).
fof(f28461,plain,
! [X2,X1] :
( ~ sP38(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,X1)) ),
inference(forward_demodulation,[],[f25562,f17135]) ).
fof(f25562,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,X1))
| ~ sP38(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(equality_resolution,[],[f21222]) ).
fof(f21222,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f15808]) ).
fof(f15808,plain,
! [X0,X1,X2] :
( ( sP38(X0,X1,X2)
| ~ sP37(X2,X1,X0)
| ~ sP36(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP37(X2,X1,X0)
& sP36(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP38(X0,X1,X2) ) ),
inference(flattening,[],[f15807]) ).
fof(f15807,plain,
! [X0,X1,X2] :
( ( sP38(X0,X1,X2)
| ~ sP37(X2,X1,X0)
| ~ sP36(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP37(X2,X1,X0)
& sP36(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP38(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14539]) ).
fof(f31480,plain,
spl647_482,
inference(avatar_split_clause,[],[f27797,f31478]) ).
fof(f31478,plain,
( spl647_482
<=> ! [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,[spl647_482])]) ).
fof(f27797,plain,
! [X2,X0,X1] : c_Nat_Onat_Onat__case(X2,X1,X0,c_HOL_Obool_Obool__size(c_fTrue)) = X1,
inference(forward_demodulation,[],[f19579,f17145]) ).
fof(f19579,plain,
! [X2,X0,X1] : c_Nat_Onat_Onat__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(cnf_transformation,[],[f6933]) ).
fof(f6933,plain,
! [X0,X1,X2] : c_Nat_Onat_Onat__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rectify,[],[f2268]) ).
fof(f2268,axiom,
! [X135,X95,X4] : c_Nat_Onat_Onat__case(X4,X95,X135,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X95,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31476,plain,
spl647_481,
inference(avatar_split_clause,[],[f26132,f31474]) ).
fof(f31474,plain,
( spl647_481
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_481])]) ).
fof(f26132,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Int_OPls),
inference(forward_demodulation,[],[f17500,f17135]) ).
fof(f17500,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,[],[f5478]) ).
fof(f5478,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,[],[f1576]) ).
fof(f1576,axiom,
! [X26] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X26,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X26
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X26),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31472,plain,
( spl647_480
| ~ spl647_243
| ~ spl647_333 ),
inference(avatar_split_clause,[],[f31093,f30832,f30422,f31469]) ).
fof(f31469,plain,
( spl647_480
<=> sP6(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_480])]) ).
fof(f30832,plain,
( spl647_333
<=> 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,[spl647_333])]) ).
fof(f31093,plain,
( sP6(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl647_243
| ~ spl647_333 ),
inference(superposition,[],[f30423,f30834]) ).
fof(f30834,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl647_333 ),
inference(avatar_component_clause,[],[f30832]) ).
fof(f31467,plain,
spl647_479,
inference(avatar_split_clause,[],[f26052,f31465]) ).
fof(f31465,plain,
( spl647_479
<=> ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_479])]) ).
fof(f31463,plain,
spl647_478,
inference(avatar_split_clause,[],[f26048,f31461]) ).
fof(f26048,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)),
inference(forward_demodulation,[],[f26047,f25910]) ).
fof(f26047,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),X0)),
inference(forward_demodulation,[],[f17382,f17145]) ).
fof(f17382,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0)),
inference(cnf_transformation,[],[f5360]) ).
fof(f5360,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0)),
inference(rectify,[],[f4878]) ).
fof(f4878,axiom,
! [X53] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X53)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31459,plain,
spl647_477,
inference(avatar_split_clause,[],[f26041,f31457]) ).
fof(f31457,plain,
( spl647_477
<=> ! [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,[spl647_477])]) ).
fof(f26041,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,[],[f26040,f25910]) ).
fof(f26040,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,[],[f17368,f17145]) ).
fof(f17368,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,[],[f5346]) ).
fof(f5346,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,[],[f1769]) ).
fof(f1769,axiom,
! [X45] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X45,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31455,plain,
spl647_476,
inference(avatar_split_clause,[],[f26032,f31453]) ).
fof(f26032,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OPls),X0),
inference(forward_demodulation,[],[f17361,f17135]) ).
fof(f17361,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,[],[f5339]) ).
fof(f5339,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,[],[f1617]) ).
fof(f1617,axiom,
! [X25] : 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)),X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31451,plain,
spl647_475,
inference(avatar_split_clause,[],[f26019,f31449]) ).
fof(f26019,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,[],[f17326,f17145]) ).
fof(f17326,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,[],[f5304]) ).
fof(f5304,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,[],[f786]) ).
fof(f786,axiom,
! [X44] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X44)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31447,plain,
spl647_474,
inference(avatar_split_clause,[],[f26013,f31445]) ).
fof(f31445,plain,
( spl647_474
<=> ! [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,[spl647_474])]) ).
fof(f26013,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f17307,f17145]) ).
fof(f17307,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,[],[f5285]) ).
fof(f5285,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rectify,[],[f741]) ).
fof(f741,axiom,
! [X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31443,plain,
spl647_473,
inference(avatar_split_clause,[],[f25947,f31440]) ).
fof(f25947,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,[],[f17202,f17135]) ).
fof(f17202,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,[],[f1211]) ).
fof(f1211,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31438,plain,
spl647_472,
inference(avatar_split_clause,[],[f25946,f31435]) ).
fof(f25946,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,[],[f17201,f17135]) ).
fof(f17201,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,[],[f1144]) ).
fof(f1144,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31433,plain,
spl647_471,
inference(avatar_split_clause,[],[f25940,f31430]) ).
fof(f31430,plain,
( spl647_471
<=> 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,[spl647_471])]) ).
fof(f25940,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,[],[f17196,f17145]) ).
fof(f17196,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,[],[f2024]) ).
fof(f2024,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31428,plain,
spl647_470,
inference(avatar_split_clause,[],[f25705,f31426]) ).
fof(f31426,plain,
( spl647_470
<=> ! [X2,X1,X3] : c_List_Olist__all2(X3,X2,X1,c_List_Olist_ONil(X3),c_List_Olist_ONil(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_470])]) ).
fof(f25705,plain,
! [X2,X3,X1] : c_List_Olist__all2(X3,X2,X1,c_List_Olist_ONil(X3),c_List_Olist_ONil(X2)),
inference(equality_resolution,[],[f22608]) ).
fof(f22608,plain,
! [X2,X3,X0,X1] :
( c_List_Olist__all2(X3,X2,X1,X0,c_List_Olist_ONil(X2))
| c_List_Olist_ONil(X3) != X0 ),
inference(cnf_transformation,[],[f16295]) ).
fof(f31424,plain,
( spl647_469
| ~ spl647_244
| ~ spl647_333 ),
inference(avatar_split_clause,[],[f31092,f30832,f30426,f31421]) ).
fof(f31421,plain,
( spl647_469
<=> sP7(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_469])]) ).
fof(f31092,plain,
( sP7(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl647_244
| ~ spl647_333 ),
inference(superposition,[],[f30427,f30834]) ).
fof(f31419,plain,
spl647_468,
inference(avatar_split_clause,[],[f25703,f31417]) ).
fof(f31417,plain,
( spl647_468
<=> ! [X2,X1,X3] : ~ c_Wellfounded_Omax__extp(X3,X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_468])]) ).
fof(f25703,plain,
! [X2,X3,X1] : ~ c_Wellfounded_Omax__extp(X3,X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),
inference(equality_resolution,[],[f22583]) ).
fof(f22583,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) != X0
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16270]) ).
fof(f31415,plain,
spl647_467,
inference(avatar_split_clause,[],[f25370,f31413]) ).
fof(f31413,plain,
( spl647_467
<=> ! [X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_467])]) ).
fof(f25370,plain,
! [X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)),
inference(equality_resolution,[],[f19198]) ).
fof(f19198,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),X0)
| c_List_Olist_ONil(X1) != X0 ),
inference(cnf_transformation,[],[f15057]) ).
fof(f31411,plain,
spl647_466,
inference(avatar_split_clause,[],[f24311,f31409]) ).
fof(f31409,plain,
( spl647_466
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Omember(X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_466])]) ).
fof(f24311,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Omember(X1),X0))),
inference(definition_unfolding,[],[f17829,f17267]) ).
fof(f17829,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X0))),
inference(cnf_transformation,[],[f5721]) ).
fof(f5721,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X0))),
inference(rectify,[],[f3783]) ).
fof(f3783,axiom,
! [X203,X4] : hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_List_Oset(X4),X203))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31407,plain,
spl647_465,
inference(avatar_split_clause,[],[f24169,f31404]) ).
fof(f31404,plain,
( spl647_465
<=> c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_465])]) ).
fof(f24169,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin),
inference(definition_unfolding,[],[f17132,f17339]) ).
fof(f17132,plain,
c_Int_OPls = c_Int_Osucc(c_Int_OMin),
inference(cnf_transformation,[],[f1985]) ).
fof(f1985,axiom,
c_Int_OPls = c_Int_Osucc(c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31402,plain,
spl647_464,
inference(avatar_split_clause,[],[f23221,f31400]) ).
fof(f31400,plain,
( spl647_464
<=> ! [X2,X4,X0,X3,X1] :
( sP73(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_464])]) ).
fof(f23221,plain,
! [X2,X3,X0,X1,X4] :
( sP73(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ),
inference(cnf_transformation,[],[f14601]) ).
fof(f14601,plain,
! [X0,X1,X2,X3,X4] :
( sP73(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ),
inference(definition_folding,[],[f13821,f14600,f14599]) ).
fof(f14600,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)))
<=> sP72(X0,X1,X4,X2,X3) )
| ~ sP73(X3,X2,X4,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP73])]) ).
fof(f13821,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,[],[f9501]) ).
fof(f9501,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,[],[f2597]) ).
fof(f2597,axiom,
! [X10,X11,X12,X5,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,X5,X12)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X11,X10)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X10))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X10))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),X5)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),X10))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X11),X5)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X5),X12)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31398,plain,
spl647_463,
inference(avatar_split_clause,[],[f21302,f31396]) ).
fof(f31396,plain,
( spl647_463
<=> ! [X2,X0,X1] :
( sP42(X2,X1,X0)
| ~ sP43(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_463])]) ).
fof(f21302,plain,
! [X2,X0,X1] :
( sP42(X2,X1,X0)
| ~ sP43(X0,X1,X2) ),
inference(cnf_transformation,[],[f15858]) ).
fof(f31394,plain,
spl647_462,
inference(avatar_split_clause,[],[f21301,f31392]) ).
fof(f31392,plain,
( spl647_462
<=> ! [X2,X0,X1] :
( sP41(X2,X1,X0)
| ~ sP43(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_462])]) ).
fof(f21301,plain,
! [X2,X0,X1] :
( sP41(X2,X1,X0)
| ~ sP43(X0,X1,X2) ),
inference(cnf_transformation,[],[f15858]) ).
fof(f31390,plain,
spl647_461,
inference(avatar_split_clause,[],[f21224,f31388]) ).
fof(f31388,plain,
( spl647_461
<=> ! [X2,X0,X1] :
( sP37(X2,X1,X0)
| ~ sP38(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_461])]) ).
fof(f21224,plain,
! [X2,X0,X1] :
( sP37(X2,X1,X0)
| ~ sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f15808]) ).
fof(f31386,plain,
spl647_460,
inference(avatar_split_clause,[],[f21223,f31384]) ).
fof(f31384,plain,
( spl647_460
<=> ! [X2,X0,X1] :
( sP36(X2,X1,X0)
| ~ sP38(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_460])]) ).
fof(f21223,plain,
! [X2,X0,X1] :
( sP36(X2,X1,X0)
| ~ sP38(X0,X1,X2) ),
inference(cnf_transformation,[],[f15808]) ).
fof(f31382,plain,
spl647_459,
inference(avatar_split_clause,[],[f21167,f31380]) ).
fof(f31380,plain,
( spl647_459
<=> ! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP33(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_459])]) ).
fof(f21167,plain,
! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP33(X0,X2,X1) ),
inference(cnf_transformation,[],[f15764]) ).
fof(f15764,plain,
! [X0,X1,X2] :
( ( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP33(X0,X2,X1) )
& ( sP33(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14533]) ).
fof(f14533,plain,
! [X0,X1,X2] :
( c_Relation_Orefl__on(X2,X1,X0)
<=> sP33(X0,X2,X1) ),
inference(definition_folding,[],[f12602,f14532]) ).
fof(f14532,plain,
! [X0,X2,X1] :
( sP33(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,[sP33])]) ).
fof(f12602,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,[],[f8144]) ).
fof(f8144,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,[],[f3427]) ).
fof(f3427,axiom,
! [X116,X9,X4] :
( c_Relation_Orefl__on(X4,X9,X116)
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),X9))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X2)),X116)) )
& ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X2),X116))
=> 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)),X9)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X9))),X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31378,plain,
( spl647_458
| ~ spl647_228
| ~ spl647_300 ),
inference(avatar_split_clause,[],[f30774,f30663,f30361,f31375]) ).
fof(f31375,plain,
( spl647_458
<=> sP5(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_458])]) ).
fof(f30361,plain,
( spl647_228
<=> c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_228])]) ).
fof(f30663,plain,
( spl647_300
<=> ! [X0,X1] :
( sP5(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_300])]) ).
fof(f30774,plain,
( sP5(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl647_228
| ~ spl647_300 ),
inference(resolution,[],[f30664,f30363]) ).
fof(f30363,plain,
( c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl647_228 ),
inference(avatar_component_clause,[],[f30361]) ).
fof(f30664,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,X0)
| sP5(X1,X0) )
| ~ spl647_300 ),
inference(avatar_component_clause,[],[f30663]) ).
fof(f31373,plain,
spl647_457,
inference(avatar_split_clause,[],[f21166,f31371]) ).
fof(f31371,plain,
( spl647_457
<=> ! [X2,X0,X1] :
( sP33(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_457])]) ).
fof(f21166,plain,
! [X2,X0,X1] :
( sP33(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f15764]) ).
fof(f31369,plain,
spl647_456,
inference(avatar_split_clause,[],[f21123,f31367]) ).
fof(f31367,plain,
( spl647_456
<=> ! [X2,X0,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| ~ sP32(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_456])]) ).
fof(f21123,plain,
! [X2,X0,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| ~ sP32(X1,X0,X2) ),
inference(cnf_transformation,[],[f15716]) ).
fof(f15716,plain,
! [X0,X1,X2] :
( ( c_List_Olist__ex1(X2,X1,X0)
| ~ sP32(X1,X0,X2) )
& ( sP32(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14531]) ).
fof(f14531,plain,
! [X0,X1,X2] :
( c_List_Olist__ex1(X2,X1,X0)
<=> sP32(X1,X0,X2) ),
inference(definition_folding,[],[f12594,f14530]) ).
fof(f12594,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,[],[f12593]) ).
fof(f12593,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,[],[f8133]) ).
fof(f8133,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,[],[f4582]) ).
fof(f4582,axiom,
! [X203,X23,X4] :
( c_List_Olist__ex1(X4,X23,X203)
<=> ? [X2] :
( ! [X38] :
( ( hBOOL(hAPP(X23,X38))
& hBOOL(hAPP(hAPP(c_member(X4),X38),hAPP(c_List_Oset(X4),X203))) )
=> X2 = X38 )
& hBOOL(hAPP(X23,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X203))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31365,plain,
spl647_455,
inference(avatar_split_clause,[],[f21122,f31363]) ).
fof(f31363,plain,
( spl647_455
<=> ! [X2,X0,X1] :
( sP32(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_455])]) ).
fof(f21122,plain,
! [X2,X0,X1] :
( sP32(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ),
inference(cnf_transformation,[],[f15716]) ).
fof(f31361,plain,
spl647_454,
inference(avatar_split_clause,[],[f21115,f31359]) ).
fof(f31359,plain,
( spl647_454
<=> ! [X2,X0,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| ~ sP31(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_454])]) ).
fof(f21115,plain,
! [X2,X0,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| ~ sP31(X1,X0,X2) ),
inference(cnf_transformation,[],[f15710]) ).
fof(f15710,plain,
! [X0,X1,X2] :
( ( c_List_Olist__ex1(X2,X1,X0)
| ~ sP31(X1,X0,X2) )
& ( sP31(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14529]) ).
fof(f14529,plain,
! [X0,X1,X2] :
( c_List_Olist__ex1(X2,X1,X0)
<=> sP31(X1,X0,X2) ),
inference(definition_folding,[],[f12592,f14528]) ).
fof(f12592,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,[],[f12591]) ).
fof(f12591,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,[],[f8132]) ).
fof(f8132,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,[],[f4671]) ).
fof(f4671,axiom,
! [X203,X23,X4] :
( c_List_Olist__ex1(X4,X23,X203)
<=> ? [X2] :
( ! [X38] :
( ( hBOOL(hAPP(X23,X38))
& hBOOL(hAPP(hAPP(c_member(X4),X38),hAPP(c_List_Oset(X4),X203))) )
=> X2 = X38 )
& hBOOL(hAPP(X23,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X203))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31357,plain,
spl647_453,
inference(avatar_split_clause,[],[f21114,f31355]) ).
fof(f31355,plain,
( spl647_453
<=> ! [X2,X0,X1] :
( sP31(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_453])]) ).
fof(f21114,plain,
! [X2,X0,X1] :
( sP31(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ),
inference(cnf_transformation,[],[f15710]) ).
fof(f31353,plain,
spl647_452,
inference(avatar_split_clause,[],[f20607,f31351]) ).
fof(f31351,plain,
( spl647_452
<=> ! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ c_Equiv__Relations_Oequiv(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_452])]) ).
fof(f20607,plain,
! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ c_Equiv__Relations_Oequiv(X2,X1,X0) ),
inference(cnf_transformation,[],[f12134]) ).
fof(f12134,plain,
! [X0,X1,X2] :
( ( c_Relation_Otrans(X2,X0)
& c_Relation_Osym(X2,X0)
& c_Relation_Orefl__on(X2,X1,X0) )
| ~ c_Equiv__Relations_Oequiv(X2,X1,X0) ),
inference(flattening,[],[f12133]) ).
fof(f12133,plain,
! [X0,X1,X2] :
( ( c_Relation_Otrans(X2,X0)
& c_Relation_Osym(X2,X0)
& c_Relation_Orefl__on(X2,X1,X0) )
| ~ c_Equiv__Relations_Oequiv(X2,X1,X0) ),
inference(ennf_transformation,[],[f7801]) ).
fof(f7801,plain,
! [X0,X1,X2] :
( c_Equiv__Relations_Oequiv(X2,X1,X0)
=> ~ ( c_Relation_Orefl__on(X2,X1,X0)
=> ( c_Relation_Osym(X2,X0)
=> ~ c_Relation_Otrans(X2,X0) ) ) ),
inference(rectify,[],[f4762]) ).
fof(f4762,axiom,
! [X116,X9,X4] :
( c_Equiv__Relations_Oequiv(X4,X9,X116)
=> ~ ( c_Relation_Orefl__on(X4,X9,X116)
=> ( c_Relation_Osym(X4,X116)
=> ~ c_Relation_Otrans(X4,X116) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31349,plain,
spl647_451,
inference(avatar_split_clause,[],[f19580,f31347]) ).
fof(f31347,plain,
( spl647_451
<=> ! [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,[spl647_451])]) ).
fof(f19580,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,[],[f6934]) ).
fof(f6934,plain,
! [X0,X1,X2] : c_Fun_Oinj__on(X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(rectify,[],[f3041]) ).
fof(f3041,axiom,
! [X1,X14,X4] : c_Fun_Oinj__on(X4,X14,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31345,plain,
spl647_450,
inference(avatar_split_clause,[],[f19578,f31343]) ).
fof(f31343,plain,
( spl647_450
<=> ! [X2,X0,X1] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_450])]) ).
fof(f19578,plain,
! [X2,X0,X1] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X1,
inference(cnf_transformation,[],[f6932]) ).
fof(f6932,plain,
! [X0,X1,X2] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X1,
inference(rectify,[],[f2249]) ).
fof(f2249,axiom,
! [X135,X95,X4] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X4,X95,X135,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X95,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31341,plain,
spl647_449,
inference(avatar_split_clause,[],[f19577,f31339]) ).
fof(f31339,plain,
( spl647_449
<=> ! [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,[spl647_449])]) ).
fof(f19577,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,[],[f6931]) ).
fof(f6931,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,[],[f2114]) ).
fof(f2114,axiom,
! [X135,X95,X4] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X4,X95,X135,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X95,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31337,plain,
spl647_448,
inference(avatar_split_clause,[],[f19575,f31335]) ).
fof(f31335,plain,
( spl647_448
<=> ! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2) != X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_448])]) ).
fof(f19575,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2) != X2,
inference(cnf_transformation,[],[f6929]) ).
fof(f6929,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2) != X2,
inference(rectify,[],[f3726]) ).
fof(f3726,axiom,
! [X19,X20,X201] : hAPP(hAPP(c_List_Olist_OCons(X20),X19),X201) != X201,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31333,plain,
( spl647_447
| ~ spl647_228
| ~ spl647_299 ),
inference(avatar_split_clause,[],[f30771,f30659,f30361,f31330]) ).
fof(f31330,plain,
( spl647_447
<=> c_Wellfounded_Oacyclic(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_447])]) ).
fof(f30659,plain,
( spl647_299
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_299])]) ).
fof(f30771,plain,
( c_Wellfounded_Oacyclic(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl647_228
| ~ spl647_299 ),
inference(resolution,[],[f30660,f30363]) ).
fof(f30660,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,X0)
| c_Wellfounded_Oacyclic(X1,X0) )
| ~ spl647_299 ),
inference(avatar_component_clause,[],[f30659]) ).
fof(f31328,plain,
spl647_446,
inference(avatar_split_clause,[],[f19150,f31326]) ).
fof(f31326,plain,
( spl647_446
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_446])]) ).
fof(f19150,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f15008]) ).
fof(f15008,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onat,X1) = X0
| ~ sP7(X0,X1) )
& ( sP7(X0,X1)
| hAPP(c_Int_Onat,X1) != X0 ) ),
inference(nnf_transformation,[],[f14489]) ).
fof(f14489,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
<=> sP7(X0,X1) ),
inference(definition_folding,[],[f11284,f14488]) ).
fof(f11284,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,[],[f6765]) ).
fof(f6765,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,[],[f1824]) ).
fof(f1824,axiom,
! [X47,X59] :
( hAPP(c_Int_Onat,X59) = X47
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X59))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X47 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X59))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X47) = X59 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31324,plain,
spl647_445,
inference(avatar_split_clause,[],[f19142,f31322]) ).
fof(f31322,plain,
( spl647_445
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| ~ sP6(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_445])]) ).
fof(f19142,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| ~ sP6(X1,X0) ),
inference(cnf_transformation,[],[f15005]) ).
fof(f15005,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onat,X0) = X1
| ~ sP6(X1,X0) )
& ( sP6(X1,X0)
| hAPP(c_Int_Onat,X0) != X1 ) ),
inference(nnf_transformation,[],[f14487]) ).
fof(f14487,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
<=> sP6(X1,X0) ),
inference(definition_folding,[],[f11283,f14486]) ).
fof(f11283,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,[],[f6764]) ).
fof(f6764,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,[],[f1825]) ).
fof(f1825,axiom,
! [X59,X47] :
( hAPP(c_Int_Onat,X59) = X47
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X59))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X47 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X59))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X47) = X59 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31320,plain,
spl647_444,
inference(avatar_split_clause,[],[f19131,f31318]) ).
fof(f31318,plain,
( spl647_444
<=> ! [X0,X1] :
( X0 = X1
| c_Int_OBit0(X0) != c_Int_OBit0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_444])]) ).
fof(f19131,plain,
! [X0,X1] :
( X0 = X1
| c_Int_OBit0(X0) != c_Int_OBit0(X1) ),
inference(cnf_transformation,[],[f15000]) ).
fof(f15000,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,[],[f6762]) ).
fof(f6762,plain,
! [X0,X1] :
( c_Int_OBit0(X0) = c_Int_OBit0(X1)
<=> X0 = X1 ),
inference(rectify,[],[f1416]) ).
fof(f1416,axiom,
! [X97,X48] :
( c_Int_OBit0(X48) = c_Int_OBit0(X97)
<=> X48 = X97 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31316,plain,
spl647_443,
inference(avatar_split_clause,[],[f19022,f31314]) ).
fof(f31314,plain,
( spl647_443
<=> ! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_443])]) ).
fof(f19022,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f11242]) ).
fof(f11242,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(flattening,[],[f11241]) ).
fof(f11241,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6713]) ).
fof(f6713,plain,
! [X0,X1] :
( ( class_Enum_Oenum(X0)
& class_Enum_Oenum(X1) )
=> class_Enum_Oenum(tc_fun(X1,X0)) ),
inference(rectify,[],[f5002]) ).
fof(f5002,axiom,
! [X278,X277] :
( ( class_Enum_Oenum(X278)
& class_Enum_Oenum(X277) )
=> class_Enum_Oenum(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31312,plain,
spl647_442,
inference(avatar_split_clause,[],[f19021,f31310]) ).
fof(f31310,plain,
( spl647_442
<=> ! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_442])]) ).
fof(f19021,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f11240]) ).
fof(f11240,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(flattening,[],[f11239]) ).
fof(f11239,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6712]) ).
fof(f6712,plain,
! [X0,X1] :
( ( class_Enum_Oenum(X0)
& class_Enum_Oenum(X1) )
=> class_Enum_Oenum(tc_prod(X1,X0)) ),
inference(rectify,[],[f5153]) ).
fof(f5153,axiom,
! [X278,X277] :
( ( class_Enum_Oenum(X278)
& class_Enum_Oenum(X277) )
=> class_Enum_Oenum(tc_prod(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31308,plain,
spl647_441,
inference(avatar_split_clause,[],[f19020,f31306]) ).
fof(f31306,plain,
( spl647_441
<=> ! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_441])]) ).
fof(f19020,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f11238]) ).
fof(f11238,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(flattening,[],[f11237]) ).
fof(f11237,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6711]) ).
fof(f6711,plain,
! [X0,X1] :
( ( class_Enum_Oenum(X0)
& class_Enum_Oenum(X1) )
=> class_Enum_Oenum(tc_sum(X1,X0)) ),
inference(rectify,[],[f5145]) ).
fof(f5145,axiom,
! [X278,X277] :
( ( class_Enum_Oenum(X278)
& class_Enum_Oenum(X277) )
=> class_Enum_Oenum(tc_sum(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31304,plain,
spl647_440,
inference(avatar_split_clause,[],[f19019,f31302]) ).
fof(f31302,plain,
( spl647_440
<=> ! [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,[spl647_440])]) ).
fof(f19019,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11236]) ).
fof(f11236,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11235]) ).
fof(f11235,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6710]) ).
fof(f6710,plain,
! [X0,X1] :
( ( class_Finite__Set_Ofinite(X0)
& class_Finite__Set_Ofinite(X1) )
=> class_Finite__Set_Ofinite(tc_fun(X1,X0)) ),
inference(rectify,[],[f4994]) ).
fof(f4994,axiom,
! [X278,X277] :
( ( class_Finite__Set_Ofinite(X278)
& class_Finite__Set_Ofinite(X277) )
=> class_Finite__Set_Ofinite(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31300,plain,
spl647_439,
inference(avatar_split_clause,[],[f19018,f31298]) ).
fof(f31298,plain,
( spl647_439
<=> ! [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,[spl647_439])]) ).
fof(f19018,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11234]) ).
fof(f11234,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11233]) ).
fof(f11233,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6709]) ).
fof(f6709,plain,
! [X0,X1] :
( ( class_Finite__Set_Ofinite(X0)
& class_Finite__Set_Ofinite(X1) )
=> class_Finite__Set_Ofinite(tc_prod(X1,X0)) ),
inference(rectify,[],[f5152]) ).
fof(f5152,axiom,
! [X278,X277] :
( ( class_Finite__Set_Ofinite(X278)
& class_Finite__Set_Ofinite(X277) )
=> class_Finite__Set_Ofinite(tc_prod(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31296,plain,
spl647_438,
inference(avatar_split_clause,[],[f19017,f31294]) ).
fof(f31294,plain,
( spl647_438
<=> ! [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,[spl647_438])]) ).
fof(f19017,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11232]) ).
fof(f11232,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11231]) ).
fof(f11231,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6708]) ).
fof(f6708,plain,
! [X0,X1] :
( ( class_Finite__Set_Ofinite(X0)
& class_Finite__Set_Ofinite(X1) )
=> class_Finite__Set_Ofinite(tc_sum(X1,X0)) ),
inference(rectify,[],[f5144]) ).
fof(f5144,axiom,
! [X278,X277] :
( ( class_Finite__Set_Ofinite(X278)
& class_Finite__Set_Ofinite(X277) )
=> class_Finite__Set_Ofinite(tc_sum(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31292,plain,
spl647_437,
inference(avatar_split_clause,[],[f19016,f31290]) ).
fof(f31290,plain,
( spl647_437
<=> ! [X0,X1] :
( class_Lazy__Sequence_Osmall__lazy(tc_prod(X1,X0))
| ~ class_Lazy__Sequence_Osmall__lazy(X0)
| ~ class_Lazy__Sequence_Osmall__lazy(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_437])]) ).
fof(f19016,plain,
! [X0,X1] :
( class_Lazy__Sequence_Osmall__lazy(tc_prod(X1,X0))
| ~ class_Lazy__Sequence_Osmall__lazy(X0)
| ~ class_Lazy__Sequence_Osmall__lazy(X1) ),
inference(cnf_transformation,[],[f11230]) ).
fof(f11230,plain,
! [X0,X1] :
( class_Lazy__Sequence_Osmall__lazy(tc_prod(X1,X0))
| ~ class_Lazy__Sequence_Osmall__lazy(X0)
| ~ class_Lazy__Sequence_Osmall__lazy(X1) ),
inference(flattening,[],[f11229]) ).
fof(f11229,plain,
! [X0,X1] :
( class_Lazy__Sequence_Osmall__lazy(tc_prod(X1,X0))
| ~ class_Lazy__Sequence_Osmall__lazy(X0)
| ~ class_Lazy__Sequence_Osmall__lazy(X1) ),
inference(ennf_transformation,[],[f6707]) ).
fof(f6707,plain,
! [X0,X1] :
( ( class_Lazy__Sequence_Osmall__lazy(X0)
& class_Lazy__Sequence_Osmall__lazy(X1) )
=> class_Lazy__Sequence_Osmall__lazy(tc_prod(X1,X0)) ),
inference(rectify,[],[f5151]) ).
fof(f5151,axiom,
! [X278,X277] :
( ( class_Lazy__Sequence_Osmall__lazy(X278)
& class_Lazy__Sequence_Osmall__lazy(X277) )
=> class_Lazy__Sequence_Osmall__lazy(tc_prod(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31288,plain,
spl647_436,
inference(avatar_split_clause,[],[f18703,f31286]) ).
fof(f31286,plain,
( spl647_436
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_436])]) ).
fof(f18703,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10886]) ).
fof(f10886,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6456]) ).
fof(f6456,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Owf(X1,c_Transitive__Closure_Otrancl(X1,X0)) ),
inference(rectify,[],[f3542]) ).
fof(f3542,axiom,
! [X116,X4] :
( c_Wellfounded_Owf(X4,X116)
=> c_Wellfounded_Owf(X4,c_Transitive__Closure_Otrancl(X4,X116)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31284,plain,
spl647_435,
inference(avatar_split_clause,[],[f18696,f31282]) ).
fof(f18696,plain,
! [X0,X1] :
( c_Transitive__Closure_Otrancl(X1,X0) = X0
| ~ c_Relation_Otrans(X1,X0) ),
inference(cnf_transformation,[],[f10878]) ).
fof(f10878,plain,
! [X0,X1] :
( c_Transitive__Closure_Otrancl(X1,X0) = X0
| ~ c_Relation_Otrans(X1,X0) ),
inference(ennf_transformation,[],[f6449]) ).
fof(f6449,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
=> c_Transitive__Closure_Otrancl(X1,X0) = X0 ),
inference(rectify,[],[f4719]) ).
fof(f4719,axiom,
! [X116,X4] :
( c_Relation_Otrans(X4,X116)
=> c_Transitive__Closure_Otrancl(X4,X116) = X116 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31280,plain,
spl647_434,
inference(avatar_split_clause,[],[f18692,f31278]) ).
fof(f18692,plain,
! [X0,X1] :
( c_Relation_Osym(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Relation_Osym(X1,X0) ),
inference(cnf_transformation,[],[f10873]) ).
fof(f10873,plain,
! [X0,X1] :
( c_Relation_Osym(X1,c_Transitive__Closure_Otrancl(X1,X0))
| ~ c_Relation_Osym(X1,X0) ),
inference(ennf_transformation,[],[f6445]) ).
fof(f6445,plain,
! [X0,X1] :
( c_Relation_Osym(X1,X0)
=> c_Relation_Osym(X1,c_Transitive__Closure_Otrancl(X1,X0)) ),
inference(rectify,[],[f4753]) ).
fof(f4753,axiom,
! [X116,X4] :
( c_Relation_Osym(X4,X116)
=> c_Relation_Osym(X4,c_Transitive__Closure_Otrancl(X4,X116)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31276,plain,
spl647_433,
inference(avatar_split_clause,[],[f18669,f31274]) ).
fof(f31274,plain,
( spl647_433
<=> ! [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,[spl647_433])]) ).
fof(f18669,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,[],[f10845]) ).
fof(f10845,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,[],[f10844]) ).
fof(f10844,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,[],[f6427]) ).
fof(f6427,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,[],[f2137]) ).
fof(f2137,axiom,
! [X21,X19] :
( c_Nat__Transfer_Ois__nat(X19)
=> ( c_Nat__Transfer_Ois__nat(X21)
=> c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X19,X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31272,plain,
spl647_432,
inference(avatar_split_clause,[],[f18350,f31270]) ).
fof(f31270,plain,
( spl647_432
<=> ! [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,[spl647_432])]) ).
fof(f18350,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,[],[f10533]) ).
fof(f10533,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,[],[f6167]) ).
fof(f6167,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,[],[f3042]) ).
fof(f3042,axiom,
! [X9,X4] :
( class_Groups_Oordered__ab__group__add(X4)
=> c_Fun_Oinj__on(X4,X4,c_Groups_Ouminus__class_Ouminus(X4),X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31268,plain,
spl647_431,
inference(avatar_split_clause,[],[f18287,f31266]) ).
fof(f31266,plain,
( spl647_431
<=> ! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_431])]) ).
fof(f18287,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(cnf_transformation,[],[f6120]) ).
fof(f6120,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(rectify,[],[f5216]) ).
fof(f5216,axiom,
! [X31,X23] :
( hBOOL(X23)
| ~ hBOOL(hAPP(hAPP(c_fconj,X23),X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31264,plain,
spl647_430,
inference(avatar_split_clause,[],[f18286,f31262]) ).
fof(f31262,plain,
( spl647_430
<=> ! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_430])]) ).
fof(f18286,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(cnf_transformation,[],[f6119]) ).
fof(f6119,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(rectify,[],[f5217]) ).
fof(f5217,axiom,
! [X31,X23] :
( hBOOL(X31)
| ~ hBOOL(hAPP(hAPP(c_fconj,X23),X31)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31260,plain,
spl647_429,
inference(avatar_split_clause,[],[f18282,f31258]) ).
fof(f18282,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ),
inference(cnf_transformation,[],[f6115]) ).
fof(f6115,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ),
inference(rectify,[],[f5221]) ).
fof(f5221,axiom,
! [X31,X23] :
( hBOOL(hAPP(hAPP(c_fimplies,X23),X31))
| hBOOL(X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31256,plain,
spl647_428,
inference(avatar_split_clause,[],[f18281,f31254]) ).
fof(f18281,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6114]) ).
fof(f6114,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5222]) ).
fof(f5222,axiom,
! [X23,X31] :
( hBOOL(hAPP(hAPP(c_fimplies,X23),X31))
| ~ hBOOL(X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31252,plain,
spl647_427,
inference(avatar_split_clause,[],[f18280,f31250]) ).
fof(f18280,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6113]) ).
fof(f6113,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5218]) ).
fof(f5218,axiom,
! [X31,X23] :
( hBOOL(hAPP(hAPP(c_fdisj,X23),X31))
| ~ hBOOL(X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31247,plain,
spl647_426,
inference(avatar_split_clause,[],[f18279,f31245]) ).
fof(f18279,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6112]) ).
fof(f6112,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5219]) ).
fof(f5219,axiom,
! [X23,X31] :
( hBOOL(hAPP(hAPP(c_fdisj,X23),X31))
| ~ hBOOL(X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31243,plain,
spl647_425,
inference(avatar_split_clause,[],[f17833,f31241]) ).
fof(f31241,plain,
( spl647_425
<=> ! [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,[spl647_425])]) ).
fof(f17833,plain,
! [X0,X1] : c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X0),
inference(cnf_transformation,[],[f5725]) ).
fof(f5725,plain,
! [X0,X1] : c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X0),
inference(rectify,[],[f4434]) ).
fof(f4434,axiom,
! [X9,X4] : c_Fun_Oinj__on(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Orev(X4),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31239,plain,
spl647_424,
inference(avatar_split_clause,[],[f17831,f31237]) ).
fof(f31237,plain,
( spl647_424
<=> ! [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,[spl647_424])]) ).
fof(f17831,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,[],[f5723]) ).
fof(f5723,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,[],[f3]) ).
fof(f3,axiom,
! [X5,X4] : c_Hoare__Mirabelle_Ohoare__derivs(X4,X5,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31235,plain,
spl647_423,
inference(avatar_split_clause,[],[f17828,f31233]) ).
fof(f31233,plain,
( spl647_423
<=> ! [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,[spl647_423])]) ).
fof(f17828,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,[],[f5720]) ).
fof(f5720,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f2543]) ).
fof(f2543,axiom,
! [X68,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X97,X68))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31231,plain,
spl647_422,
inference(avatar_split_clause,[],[f17827,f31229]) ).
fof(f31229,plain,
( spl647_422
<=> ! [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,[spl647_422])]) ).
fof(f17827,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,[],[f5719]) ).
fof(f5719,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f2651]) ).
fof(f2651,axiom,
! [X68,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X97,X68))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31227,plain,
spl647_421,
inference(avatar_split_clause,[],[f17826,f31225]) ).
fof(f31225,plain,
( spl647_421
<=> ! [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,[spl647_421])]) ).
fof(f17826,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,[],[f5718]) ).
fof(f5718,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f2652]) ).
fof(f2652,axiom,
! [X68,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X97,X68))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31223,plain,
spl647_420,
inference(avatar_split_clause,[],[f17825,f31221]) ).
fof(f31221,plain,
( spl647_420
<=> ! [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,[spl647_420])]) ).
fof(f17825,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,[],[f5717]) ).
fof(f5717,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f2618]) ).
fof(f2618,axiom,
! [X68,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X97,X68))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31219,plain,
spl647_419,
inference(avatar_split_clause,[],[f17824,f31217]) ).
fof(f31217,plain,
( spl647_419
<=> ! [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,[spl647_419])]) ).
fof(f17824,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,[],[f5716]) ).
fof(f5716,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f2653]) ).
fof(f2653,axiom,
! [X68,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X97,X68))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31215,plain,
spl647_418,
inference(avatar_split_clause,[],[f17823,f31213]) ).
fof(f31213,plain,
( spl647_418
<=> ! [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,[spl647_418])]) ).
fof(f17823,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,[],[f5715]) ).
fof(f5715,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f2642]) ).
fof(f2642,axiom,
! [X68,X97] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X97,X68))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31211,plain,
spl647_417,
inference(avatar_split_clause,[],[f17822,f31209]) ).
fof(f31209,plain,
( spl647_417
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_417])]) ).
fof(f17822,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5714]) ).
fof(f5714,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4482]) ).
fof(f4482,axiom,
! [X23,X4] : c_List_Olist_ONil(X4) = c_List_OtakeWhile(X4,X23,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31206,plain,
spl647_416,
inference(avatar_split_clause,[],[f17821,f31204]) ).
fof(f31204,plain,
( spl647_416
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_416])]) ).
fof(f17821,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5713]) ).
fof(f5713,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f3890]) ).
fof(f3890,axiom,
! [X19,X20] : c_List_Olist_ONil(X20) = c_List_Oremove1(X20,X19,c_List_Olist_ONil(X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31202,plain,
spl647_415,
inference(avatar_split_clause,[],[f17539,f31200]) ).
fof(f17539,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,[],[f10332]) ).
fof(f10332,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,[],[f5504]) ).
fof(f5504,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls)) ),
inference(rectify,[],[f1702]) ).
fof(f1702,axiom,
! [X20] :
( class_Int_Onumber__ring(X20)
=> c_Int_Oiszero(X20,hAPP(c_Int_Onumber__class_Onumber__of(X20),c_Int_OPls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31198,plain,
spl647_414,
inference(avatar_split_clause,[],[f17538,f31196]) ).
fof(f17538,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,[],[f10331]) ).
fof(f10331,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,[],[f5503]) ).
fof(f5503,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin)) ),
inference(rectify,[],[f1984]) ).
fof(f1984,axiom,
! [X20] :
( class_Int_Onumber__ring(X20)
=> ~ c_Int_Oiszero(X20,hAPP(c_Int_Onumber__class_Onumber__of(X20),c_Int_OMin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31194,plain,
spl647_413,
inference(avatar_split_clause,[],[f17332,f31192]) ).
fof(f31192,plain,
( spl647_413
<=> ! [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,[spl647_413])]) ).
fof(f17332,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,[],[f5310]) ).
fof(f5310,plain,
! [X0] : c_Relation_Orefl__on(X0,c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),c_Relation_OId(X0)),
inference(rectify,[],[f3607]) ).
fof(f3607,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31190,plain,
spl647_412,
inference(avatar_split_clause,[],[f17331,f31188]) ).
fof(f31188,plain,
( spl647_412
<=> ! [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,[spl647_412])]) ).
fof(f17331,plain,
! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f5309]) ).
fof(f5309,plain,
! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f3358]) ).
fof(f3358,axiom,
! [X4] : c_Wellfounded_Owf(X4,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31186,plain,
spl647_411,
inference(avatar_split_clause,[],[f17330,f31184]) ).
fof(f31184,plain,
( spl647_411
<=> ! [X0] : c_Relation_Oantisym(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_411])]) ).
fof(f17330,plain,
! [X0] : c_Relation_Oantisym(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f5308]) ).
fof(f5308,plain,
! [X0] : c_Relation_Oantisym(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f4732]) ).
fof(f4732,axiom,
! [X4] : c_Relation_Oantisym(X4,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31182,plain,
spl647_410,
inference(avatar_split_clause,[],[f17328,f31180]) ).
fof(f31180,plain,
( spl647_410
<=> ! [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,[spl647_410])]) ).
fof(f17328,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5306]) ).
fof(f5306,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(rectify,[],[f189]) ).
fof(f189,axiom,
! [X4] : hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31178,plain,
spl647_409,
inference(avatar_split_clause,[],[f17325,f31176]) ).
fof(f31176,plain,
( spl647_409
<=> ! [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,[spl647_409])]) ).
fof(f17325,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0))),
inference(cnf_transformation,[],[f5303]) ).
fof(f5303,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0))),
inference(rectify,[],[f2403]) ).
fof(f2403,axiom,
! [X48] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X48))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31174,plain,
spl647_408,
inference(avatar_split_clause,[],[f17324,f31172]) ).
fof(f31172,plain,
( spl647_408
<=> ! [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,[spl647_408])]) ).
fof(f17324,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0))),
inference(cnf_transformation,[],[f5302]) ).
fof(f5302,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0))),
inference(rectify,[],[f2738]) ).
fof(f2738,axiom,
! [X48] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X48))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31170,plain,
spl647_407,
inference(avatar_split_clause,[],[f17323,f31168]) ).
fof(f31168,plain,
( spl647_407
<=> ! [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,[spl647_407])]) ).
fof(f17323,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,[],[f5301]) ).
fof(f5301,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,[],[f2935]) ).
fof(f2935,axiom,
! [X22] : 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)),X22)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31166,plain,
spl647_406,
inference(avatar_split_clause,[],[f17322,f31164]) ).
fof(f31164,plain,
( spl647_406
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_406])]) ).
fof(f17322,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(cnf_transformation,[],[f5300]) ).
fof(f5300,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(rectify,[],[f1275]) ).
fof(f1275,axiom,
! [X53] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),c_Int_OPls) = X53,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31162,plain,
spl647_405,
inference(avatar_split_clause,[],[f17321,f31160]) ).
fof(f31160,plain,
( spl647_405
<=> ! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_405])]) ).
fof(f31158,plain,
spl647_404,
inference(avatar_split_clause,[],[f17320,f31156]) ).
fof(f31156,plain,
( spl647_404
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_404])]) ).
fof(f17320,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0,
inference(cnf_transformation,[],[f5298]) ).
fof(f5298,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0,
inference(rectify,[],[f1276]) ).
fof(f1276,axiom,
! [X53] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X53) = X53,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31154,plain,
spl647_403,
inference(avatar_split_clause,[],[f17319,f31152]) ).
fof(f17319,plain,
! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0,
inference(cnf_transformation,[],[f5297]) ).
fof(f5297,plain,
! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0,
inference(rectify,[],[f1749]) ).
fof(f1749,axiom,
! [X44] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44)) = X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31150,plain,
spl647_402,
inference(avatar_split_clause,[],[f17316,f31148]) ).
fof(f31148,plain,
( spl647_402
<=> ! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_402])]) ).
fof(f17316,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5294]) ).
fof(f5294,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)),
inference(rectify,[],[f4436]) ).
fof(f4436,axiom,
! [X20] : c_List_Olist_ONil(X20) = hAPP(c_List_Orev(X20),c_List_Olist_ONil(X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31146,plain,
spl647_401,
inference(avatar_split_clause,[],[f17315,f31144]) ).
fof(f31144,plain,
( spl647_401
<=> ! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_401])]) ).
fof(f17315,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5293]) ).
fof(f5293,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)),
inference(rectify,[],[f4045]) ).
fof(f4045,axiom,
! [X20] : c_List_Olist_ONil(X20) = hAPP(c_List_Otl(X20),c_List_Olist_ONil(X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31142,plain,
spl647_400,
inference(avatar_split_clause,[],[f17313,f31140]) ).
fof(f31140,plain,
( spl647_400
<=> ! [X0] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X0) = c_Lazy__Sequence_Oflat(X0,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_400])]) ).
fof(f17313,plain,
! [X0] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X0) = c_Lazy__Sequence_Oflat(X0,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(X0))),
inference(cnf_transformation,[],[f5291]) ).
fof(f5291,plain,
! [X0] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X0) = c_Lazy__Sequence_Oflat(X0,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(X0))),
inference(rectify,[],[f4867]) ).
fof(f4867,axiom,
! [X20] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X20) = c_Lazy__Sequence_Oflat(X20,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(X20))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31138,plain,
spl647_399,
inference(avatar_split_clause,[],[f17310,f31136]) ).
fof(f31136,plain,
( spl647_399
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_399])]) ).
fof(f17310,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0),
inference(cnf_transformation,[],[f5288]) ).
fof(f5288,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0),
inference(rectify,[],[f1277]) ).
fof(f1277,axiom,
! [X87] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X87),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31134,plain,
spl647_398,
inference(avatar_split_clause,[],[f17188,f31131]) ).
fof(f31131,plain,
( spl647_398
<=> 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,[spl647_398])]) ).
fof(f17188,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,[],[f1226]) ).
fof(f1226,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31129,plain,
~ spl647_397,
inference(avatar_split_clause,[],[f17184,f31126]) ).
fof(f17184,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,[],[f2422]) ).
fof(f2422,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31124,plain,
~ spl647_396,
inference(avatar_split_clause,[],[f17183,f31121]) ).
fof(f17183,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,[],[f2626]) ).
fof(f2626,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31111,plain,
( spl647_395
| ~ spl647_320 ),
inference(avatar_split_clause,[],[f30786,f30748,f31108]) ).
fof(f31108,plain,
( spl647_395
<=> sP11(c_Int_OPls,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_395])]) ).
fof(f30748,plain,
( spl647_320
<=> ! [X1] :
( c_Int_OPls != X1
| sP11(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_320])]) ).
fof(f30786,plain,
( sP11(c_Int_OPls,c_Int_OPls)
| ~ spl647_320 ),
inference(equality_resolution,[],[f30749]) ).
fof(f30749,plain,
( ! [X1] :
( c_Int_OPls != X1
| sP11(X1,X1) )
| ~ spl647_320 ),
inference(avatar_component_clause,[],[f30748]) ).
fof(f31098,plain,
( spl647_394
| ~ spl647_196
| ~ spl647_300 ),
inference(avatar_split_clause,[],[f30773,f30663,f30215,f31095]) ).
fof(f31095,plain,
( spl647_394
<=> sP5(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_394])]) ).
fof(f30215,plain,
( spl647_196
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_196])]) ).
fof(f30773,plain,
( sP5(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl647_196
| ~ spl647_300 ),
inference(resolution,[],[f30664,f30217]) ).
fof(f30217,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl647_196 ),
inference(avatar_component_clause,[],[f30215]) ).
fof(f31091,plain,
( spl647_393
| ~ spl647_195
| ~ spl647_300 ),
inference(avatar_split_clause,[],[f30772,f30663,f30210,f31088]) ).
fof(f31088,plain,
( spl647_393
<=> sP5(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_393])]) ).
fof(f30210,plain,
( spl647_195
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_195])]) ).
fof(f30772,plain,
( sP5(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl647_195
| ~ spl647_300 ),
inference(resolution,[],[f30664,f30212]) ).
fof(f30212,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl647_195 ),
inference(avatar_component_clause,[],[f30210]) ).
fof(f31086,plain,
spl647_392,
inference(avatar_split_clause,[],[f27565,f31084]) ).
fof(f27565,plain,
! [X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X1,X1) ),
inference(forward_demodulation,[],[f25405,f17285]) ).
fof(f25405,plain,
! [X1] :
( sP11(X1,X1)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(equality_resolution,[],[f19327]) ).
fof(f19327,plain,
! [X0,X1] :
( sP11(X0,X1)
| X0 != X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(cnf_transformation,[],[f15144]) ).
fof(f31082,plain,
spl647_391,
inference(avatar_split_clause,[],[f26439,f31080]) ).
fof(f26439,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0)),
inference(forward_demodulation,[],[f17816,f24216]) ).
fof(f17816,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X1),c_List_Olist_ONil(X1)),X0)),
inference(cnf_transformation,[],[f5708]) ).
fof(f5708,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X1),c_List_Olist_ONil(X1)),X0)),
inference(rectify,[],[f4667]) ).
fof(f4667,axiom,
! [X21,X20] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X20),c_List_Olist_ONil(X20)),X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31078,plain,
spl647_390,
inference(avatar_split_clause,[],[f25936,f31075]) ).
fof(f31075,plain,
( spl647_390
<=> 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,[spl647_390])]) ).
fof(f25936,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,[],[f25935,f17135]) ).
fof(f25935,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17193,f17145]) ).
fof(f17193,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1227]) ).
fof(f1227,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31073,plain,
spl647_389,
inference(avatar_split_clause,[],[f25919,f31070]) ).
fof(f31070,plain,
( spl647_389
<=> 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,[spl647_389])]) ).
fof(f25919,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17174,f17145]) ).
fof(f17174,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,[],[f1288]) ).
fof(f1288,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31068,plain,
spl647_388,
inference(avatar_split_clause,[],[f25918,f31065]) ).
fof(f31065,plain,
( spl647_388
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_388])]) ).
fof(f25918,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
inference(forward_demodulation,[],[f17173,f17145]) ).
fof(f17173,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
inference(cnf_transformation,[],[f4580]) ).
fof(f4580,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31063,plain,
spl647_387,
inference(avatar_split_clause,[],[f25917,f31060]) ).
fof(f31060,plain,
( spl647_387
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_387])]) ).
fof(f25917,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
inference(forward_demodulation,[],[f17172,f17145]) ).
fof(f17172,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
inference(cnf_transformation,[],[f4581]) ).
fof(f4581,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31058,plain,
spl647_386,
inference(avatar_split_clause,[],[f25911,f31055]) ).
fof(f31055,plain,
( spl647_386
<=> 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,[spl647_386])]) ).
fof(f31053,plain,
spl647_385,
inference(avatar_split_clause,[],[f25910,f31050]) ).
fof(f31048,plain,
( spl647_384
| ~ spl647_196
| ~ spl647_299 ),
inference(avatar_split_clause,[],[f30770,f30659,f30215,f31045]) ).
fof(f31045,plain,
( spl647_384
<=> c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_384])]) ).
fof(f30770,plain,
( c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl647_196
| ~ spl647_299 ),
inference(resolution,[],[f30660,f30217]) ).
fof(f31043,plain,
spl647_383,
inference(avatar_split_clause,[],[f25380,f31041]) ).
fof(f25380,plain,
! [X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)),
inference(equality_resolution,[],[f19230]) ).
fof(f19230,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f15077]) ).
fof(f31039,plain,
spl647_382,
inference(avatar_split_clause,[],[f24264,f31037]) ).
fof(f31037,plain,
( spl647_382
<=> ! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Omember(tc_Int_Oint),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_382])]) ).
fof(f24264,plain,
! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Omember(tc_Int_Oint),X0)) ),
inference(definition_unfolding,[],[f17641,f17267]) ).
fof(f17641,plain,
! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ),
inference(cnf_transformation,[],[f10434]) ).
fof(f10434,plain,
! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ),
inference(ennf_transformation,[],[f10131]) ).
fof(f10131,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0))
=> c_List_Onat__list(X0) ),
inference(unused_predicate_definition_removal,[],[f5601]) ).
fof(f5601,plain,
! [X0] :
( c_List_Onat__list(X0)
<=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ),
inference(rectify,[],[f3831]) ).
fof(f3831,axiom,
! [X97] :
( c_List_Onat__list(X97)
<=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X97)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31035,plain,
spl647_381,
inference(avatar_split_clause,[],[f21828,f31033]) ).
fof(f31033,plain,
( spl647_381
<=> ! [X0,X3,X2,X1] :
( sP53(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_381])]) ).
fof(f21828,plain,
! [X2,X3,X0,X1] :
( sP53(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f14566]) ).
fof(f14566,plain,
! [X0,X1,X2,X3] :
( sP53(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f12686,f14565,f14564]) ).
fof(f14564,plain,
! [X2,X0,X3,X1] :
( sP52(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,[sP52])]) ).
fof(f14565,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)))
<=> sP52(X2,X0,X3,X1) )
| ~ sP53(X1,X3,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP53])]) ).
fof(f12686,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,[],[f8536]) ).
fof(f8536,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,[],[f837]) ).
fof(f837,axiom,
! [X12,X11,X5,X4] :
( class_Rings_Olinordered__ring__strict(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X5),X11)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X12),X11)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X5))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X5),X12))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31031,plain,
spl647_380,
inference(avatar_split_clause,[],[f21819,f31029]) ).
fof(f31029,plain,
( spl647_380
<=> ! [X0,X3,X2,X1] :
( sP51(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_380])]) ).
fof(f21819,plain,
! [X2,X3,X0,X1] :
( sP51(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f14563]) ).
fof(f14563,plain,
! [X0,X1,X2,X3] :
( sP51(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f12685,f14562,f14561]) ).
fof(f14561,plain,
! [X1,X0,X3,X2] :
( sP50(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,[sP50])]) ).
fof(f14562,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)))
<=> sP50(X1,X0,X3,X2) )
| ~ sP51(X2,X3,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP51])]) ).
fof(f12685,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,[],[f8535]) ).
fof(f8535,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,[],[f838]) ).
fof(f838,axiom,
! [X12,X5,X11,X4] :
( class_Rings_Olinordered__ring__strict(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X5)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X11),X12)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X12),X5))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X11),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X5),X12))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X11)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31027,plain,
spl647_379,
inference(avatar_split_clause,[],[f20609,f31025]) ).
fof(f20609,plain,
! [X2,X0,X1] :
( c_Relation_Otrans(X2,X0)
| ~ c_Equiv__Relations_Oequiv(X2,X1,X0) ),
inference(cnf_transformation,[],[f12134]) ).
fof(f31023,plain,
spl647_378,
inference(avatar_split_clause,[],[f20608,f31021]) ).
fof(f20608,plain,
! [X2,X0,X1] :
( c_Relation_Osym(X2,X0)
| ~ c_Equiv__Relations_Oequiv(X2,X1,X0) ),
inference(cnf_transformation,[],[f12134]) ).
fof(f31019,plain,
spl647_377,
inference(avatar_split_clause,[],[f20385,f31017]) ).
fof(f31017,plain,
( spl647_377
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X1)
| ~ sP19(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_377])]) ).
fof(f20385,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X1)
| ~ sP19(X0,X1,X2) ),
inference(cnf_transformation,[],[f15428]) ).
fof(f15428,plain,
! [X0,X1,X2] :
( ( sP19(X0,X1,X2)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK239(X0,X1,X2)),sK240(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK240(X0,X1,X2)),hAPP(c_List_Oset(X0),X1)))
& hBOOL(hAPP(hAPP(c_member(X0),sK239(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) )
| ~ sP19(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK239,sK240])],[f15425,f15427,f15426]) ).
fof(f15426,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),sK239(X0,X1,X2)),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X1))) )
& hBOOL(hAPP(hAPP(c_member(X0),sK239(X0,X1,X2)),hAPP(c_List_Oset(X0),X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15427,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK239(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),sK239(X0,X1,X2)),sK240(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK240(X0,X1,X2)),hAPP(c_List_Oset(X0),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15425,plain,
! [X0,X1,X2] :
( ( sP19(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) )
| ~ sP19(X0,X1,X2) ) ),
inference(rectify,[],[f15424]) ).
fof(f15424,plain,
! [X2,X0,X1] :
( ( sP19(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) )
| ~ sP19(X2,X0,X1) ) ),
inference(flattening,[],[f15423]) ).
fof(f15423,plain,
! [X2,X0,X1] :
( ( sP19(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) )
| ~ sP19(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f14509]) ).
fof(f14509,plain,
! [X2,X0,X1] :
( sP19(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,[sP19])]) ).
fof(f31015,plain,
spl647_376,
inference(avatar_split_clause,[],[f20384,f31013]) ).
fof(f31013,plain,
( spl647_376
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X2)
| ~ sP19(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_376])]) ).
fof(f20384,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X2)
| ~ sP19(X0,X1,X2) ),
inference(cnf_transformation,[],[f15428]) ).
fof(f31011,plain,
spl647_375,
inference(avatar_split_clause,[],[f19573,f31009]) ).
fof(f31009,plain,
( spl647_375
<=> ! [X2,X0,X1] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X2) != c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_375])]) ).
fof(f19573,plain,
! [X2,X0,X1] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X2) != c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X1,X0),
inference(cnf_transformation,[],[f6927]) ).
fof(f6927,plain,
! [X0,X1,X2] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X2) != c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X1,X0),
inference(rectify,[],[f4680]) ).
fof(f4680,axiom,
! [X259,X117,X20] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X20) != c_Lazy__Sequence_Olazy__sequence_OInsert(X20,X117,X259),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31007,plain,
spl647_374,
inference(avatar_split_clause,[],[f18665,f31005]) ).
fof(f31005,plain,
( spl647_374
<=> ! [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,[spl647_374])]) ).
fof(f18665,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,[],[f10840]) ).
fof(f10840,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,[],[f6424]) ).
fof(f6424,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,[],[f2937]) ).
fof(f2937,axiom,
! [X15,X13] :
( c_Nat__Transfer_Ois__nat(X13)
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X13,X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31003,plain,
( spl647_373
| ~ spl647_195
| ~ spl647_299 ),
inference(avatar_split_clause,[],[f30769,f30659,f30210,f31000]) ).
fof(f31000,plain,
( spl647_373
<=> c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_373])]) ).
fof(f30769,plain,
( c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl647_195
| ~ spl647_299 ),
inference(resolution,[],[f30660,f30212]) ).
fof(f30998,plain,
spl647_372,
inference(avatar_split_clause,[],[f18643,f30996]) ).
fof(f18643,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f10816]) ).
fof(f10816,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6409]) ).
fof(f6409,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(X1)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(rectify,[],[f194]) ).
fof(f194,axiom,
! [X9,X4] :
( class_Finite__Set_Ofinite(X4)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X9)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30994,plain,
spl647_371,
inference(avatar_split_clause,[],[f17815,f30992]) ).
fof(f30992,plain,
( spl647_371
<=> ! [X0,X1] : c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_371])]) ).
fof(f17815,plain,
! [X0,X1] : c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X0,X0),
inference(cnf_transformation,[],[f5707]) ).
fof(f5707,plain,
! [X0,X1] : c_Fun_Obij__betw(X1,X1,c_Fun_Oid(X1),X0,X0),
inference(rectify,[],[f4807]) ).
fof(f4807,axiom,
! [X9,X4] : c_Fun_Obij__betw(X4,X4,c_Fun_Oid(X4),X9,X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30990,plain,
spl647_370,
inference(avatar_split_clause,[],[f17813,f30988]) ).
fof(f30988,plain,
( spl647_370
<=> ! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_370])]) ).
fof(f17813,plain,
! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5705]) ).
fof(f5705,plain,
! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(rectify,[],[f3892]) ).
fof(f3892,axiom,
! [X116,X4] : c_List_Olistrelp(X4,X116,c_List_Olist_ONil(X4),c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30986,plain,
spl647_369,
inference(avatar_split_clause,[],[f17812,f30984]) ).
fof(f30984,plain,
( spl647_369
<=> ! [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,[spl647_369])]) ).
fof(f17812,plain,
! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(cnf_transformation,[],[f5704]) ).
fof(f5704,plain,
! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(rectify,[],[f3646]) ).
fof(f3646,axiom,
! [X116,X4] : c_Relation_Ototal__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X116),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30982,plain,
spl647_368,
inference(avatar_split_clause,[],[f17810,f30980]) ).
fof(f30980,plain,
( spl647_368
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Olistsp(X1,X0),c_List_Olist_ONil(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_368])]) ).
fof(f17810,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Olistsp(X1,X0),c_List_Olist_ONil(X1))),
inference(cnf_transformation,[],[f5702]) ).
fof(f5702,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Olistsp(X1,X0),c_List_Olist_ONil(X1))),
inference(rectify,[],[f4223]) ).
fof(f4223,axiom,
! [X9,X4] : hBOOL(hAPP(c_List_Olistsp(X4,X9),c_List_Olist_ONil(X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30978,plain,
spl647_367,
inference(avatar_split_clause,[],[f17809,f30976]) ).
fof(f30976,plain,
( spl647_367
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_367])]) ).
fof(f17809,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X0))),
inference(cnf_transformation,[],[f5701]) ).
fof(f5701,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X0))),
inference(rectify,[],[f4269]) ).
fof(f4269,axiom,
! [X201,X20] : hBOOL(hAPP(c_List_Odistinct(X20),c_List_Oremdups(X20,X201))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30974,plain,
spl647_366,
inference(avatar_split_clause,[],[f17808,f30972]) ).
fof(f17808,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)),
inference(cnf_transformation,[],[f5700]) ).
fof(f5700,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)),
inference(rectify,[],[f2121]) ).
fof(f2121,axiom,
! [X13,X4] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30970,plain,
spl647_365,
inference(avatar_split_clause,[],[f17806,f30968]) ).
fof(f30968,plain,
( spl647_365
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_365])]) ).
fof(f17806,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))),
inference(cnf_transformation,[],[f5698]) ).
fof(f5698,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))),
inference(rectify,[],[f3859]) ).
fof(f3859,axiom,
! [X54,X55] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X55,X54))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30966,plain,
spl647_364,
inference(avatar_split_clause,[],[f17805,f30964]) ).
fof(f30964,plain,
( spl647_364
<=> ! [X0,X1] : c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_364])]) ).
fof(f17805,plain,
! [X0,X1] : c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),X0) = X0,
inference(cnf_transformation,[],[f5697]) ).
fof(f5697,plain,
! [X0,X1] : c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),X0) = X0,
inference(rectify,[],[f4679]) ).
fof(f4679,axiom,
! [X253,X20] : c_Lazy__Sequence_Oappend(X20,c_Lazy__Sequence_Olazy__sequence_OEmpty(X20),X253) = X253,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30962,plain,
spl647_363,
inference(avatar_split_clause,[],[f17804,f30960]) ).
fof(f30960,plain,
( spl647_363
<=> ! [X0,X1] : c_List_Osplice(X1,c_List_Olist_ONil(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_363])]) ).
fof(f17804,plain,
! [X0,X1] : c_List_Osplice(X1,c_List_Olist_ONil(X1),X0) = X0,
inference(cnf_transformation,[],[f5696]) ).
fof(f5696,plain,
! [X0,X1] : c_List_Osplice(X1,c_List_Olist_ONil(X1),X0) = X0,
inference(rectify,[],[f4601]) ).
fof(f4601,axiom,
! [X200,X20] : c_List_Osplice(X20,c_List_Olist_ONil(X20),X200) = X200,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30958,plain,
( spl647_362
| ~ spl647_201
| ~ spl647_298 ),
inference(avatar_split_clause,[],[f30768,f30655,f30236,f30956]) ).
fof(f30956,plain,
( spl647_362
<=> ! [X0] : c_Predicate_Otransp(X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_362])]) ).
fof(f30236,plain,
( spl647_201
<=> ! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_201])]) ).
fof(f30655,plain,
( spl647_298
<=> ! [X0,X1] :
( c_Predicate_Otransp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_298])]) ).
fof(f30768,plain,
( ! [X0] : c_Predicate_Otransp(X0,c_fequal)
| ~ spl647_201
| ~ spl647_298 ),
inference(resolution,[],[f30656,f30237]) ).
fof(f30237,plain,
( ! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal)
| ~ spl647_201 ),
inference(avatar_component_clause,[],[f30236]) ).
fof(f30656,plain,
( ! [X0,X1] :
( ~ c_Equiv__Relations_Oequivp(X1,X0)
| c_Predicate_Otransp(X1,X0) )
| ~ spl647_298 ),
inference(avatar_component_clause,[],[f30655]) ).
fof(f30954,plain,
spl647_361,
inference(avatar_split_clause,[],[f17803,f30952]) ).
fof(f30952,plain,
( spl647_361
<=> ! [X0,X1] : c_List_Osplice(X1,X0,c_List_Olist_ONil(X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_361])]) ).
fof(f17803,plain,
! [X0,X1] : c_List_Osplice(X1,X0,c_List_Olist_ONil(X1)) = X0,
inference(cnf_transformation,[],[f5695]) ).
fof(f5695,plain,
! [X0,X1] : c_List_Osplice(X1,X0,c_List_Olist_ONil(X1)) = X0,
inference(rectify,[],[f4600]) ).
fof(f4600,axiom,
! [X201,X20] : c_List_Osplice(X20,X201,c_List_Olist_ONil(X20)) = X201,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30950,plain,
spl647_360,
inference(avatar_split_clause,[],[f17802,f30948]) ).
fof(f30948,plain,
( spl647_360
<=> ! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_360])]) ).
fof(f17802,plain,
! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0,
inference(cnf_transformation,[],[f5694]) ).
fof(f5694,plain,
! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0,
inference(rectify,[],[f3356]) ).
fof(f3356,axiom,
! [X13,X4] : c_HOL_OThe(X4,hAPP(c_fequal,X13)) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30946,plain,
spl647_359,
inference(avatar_split_clause,[],[f17801,f30944]) ).
fof(f30944,plain,
( spl647_359
<=> ! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_359])]) ).
fof(f17801,plain,
! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0,
inference(cnf_transformation,[],[f5693]) ).
fof(f5693,plain,
! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0,
inference(rectify,[],[f3517]) ).
fof(f3517,axiom,
! [X13,X4] : c_Hilbert__Choice_OEps(X4,hAPP(c_fequal,X13)) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30942,plain,
spl647_358,
inference(avatar_split_clause,[],[f17800,f30940]) ).
fof(f30940,plain,
( spl647_358
<=> ! [X0,X1] : hAPP(c_New__DSequence_Opos__empty(X1),X0) = c_Lazy__Sequence_Oempty(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_358])]) ).
fof(f17800,plain,
! [X0,X1] : hAPP(c_New__DSequence_Opos__empty(X1),X0) = c_Lazy__Sequence_Oempty(X1),
inference(cnf_transformation,[],[f5692]) ).
fof(f5692,plain,
! [X0,X1] : hAPP(c_New__DSequence_Opos__empty(X1),X0) = c_Lazy__Sequence_Oempty(X1),
inference(rectify,[],[f4588]) ).
fof(f4588,axiom,
! [X246,X20] : hAPP(c_New__DSequence_Opos__empty(X20),X246) = c_Lazy__Sequence_Oempty(X20),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30938,plain,
spl647_357,
inference(avatar_split_clause,[],[f17651,f30936]) ).
fof(f30936,plain,
( spl647_357
<=> ! [X0] :
( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_357])]) ).
fof(f17651,plain,
! [X0] :
( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) ),
inference(cnf_transformation,[],[f14648]) ).
fof(f14648,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,[],[f5606]) ).
fof(f5606,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
<=> c_Int_OPls = X0 ),
inference(rectify,[],[f1455]) ).
fof(f1455,axiom,
! [X97] :
( c_Int_OPls = c_Int_OBit0(X97)
<=> c_Int_OPls = X97 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30934,plain,
spl647_356,
inference(avatar_split_clause,[],[f17585,f30932]) ).
fof(f30932,plain,
( spl647_356
<=> ! [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,[spl647_356])]) ).
fof(f17585,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,[],[f10378]) ).
fof(f10378,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,[],[f5550]) ).
fof(f5550,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,[],[f379]) ).
fof(f379,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30930,plain,
spl647_355,
inference(avatar_split_clause,[],[f17584,f30928]) ).
fof(f30928,plain,
( spl647_355
<=> ! [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,[spl647_355])]) ).
fof(f17584,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,[],[f10377]) ).
fof(f10377,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,[],[f5549]) ).
fof(f5549,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,[],[f45]) ).
fof(f45,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30926,plain,
spl647_354,
inference(avatar_split_clause,[],[f17578,f30924]) ).
fof(f30924,plain,
( spl647_354
<=> ! [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,[spl647_354])]) ).
fof(f17578,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10371]) ).
fof(f10371,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5543]) ).
fof(f5543,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0)) ),
inference(rectify,[],[f1100]) ).
fof(f1100,axiom,
! [X4] :
( class_Orderings_Olinorder(X4)
=> c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Orderings_Oord__class_Omin(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30922,plain,
spl647_353,
inference(avatar_split_clause,[],[f17577,f30920]) ).
fof(f30920,plain,
( spl647_353
<=> ! [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,[spl647_353])]) ).
fof(f17577,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10370]) ).
fof(f10370,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5542]) ).
fof(f5542,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0)) ),
inference(rectify,[],[f2436]) ).
fof(f2436,axiom,
! [X4] :
( class_Orderings_Olinorder(X4)
=> c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Orderings_Oord__class_Omax(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30918,plain,
spl647_352,
inference(avatar_split_clause,[],[f17559,f30916]) ).
fof(f30916,plain,
( spl647_352
<=> ! [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,[spl647_352])]) ).
fof(f17559,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,[],[f10352]) ).
fof(f10352,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,[],[f5524]) ).
fof(f5524,plain,
! [X0] :
( class_Groups_Oab__semigroup__mult(X0)
=> c_Finite__Set_Ofun__left__comm(X0,X0,c_Groups_Otimes__class_Otimes(X0)) ),
inference(rectify,[],[f444]) ).
fof(f444,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30914,plain,
spl647_351,
inference(avatar_split_clause,[],[f17556,f30912]) ).
fof(f30912,plain,
( spl647_351
<=> ! [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,[spl647_351])]) ).
fof(f17556,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(cnf_transformation,[],[f10349]) ).
fof(f10349,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(ennf_transformation,[],[f5521]) ).
fof(f5521,plain,
! [X0] :
( class_Rings_Ozero__neq__one(X0)
=> c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) ),
inference(rectify,[],[f767]) ).
fof(f767,axiom,
! [X20] :
( class_Rings_Ozero__neq__one(X20)
=> c_Groups_Oone__class_Oone(X20) != c_Groups_Ozero__class_Ozero(X20) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30910,plain,
spl647_350,
inference(avatar_split_clause,[],[f17306,f30908]) ).
fof(f30908,plain,
( spl647_350
<=> ! [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,[spl647_350])]) ).
fof(f17306,plain,
! [X0] : c_Finite__Set_Ofun__left__comm__idem(X0,tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0)),
inference(cnf_transformation,[],[f5284]) ).
fof(f5284,plain,
! [X0] : c_Finite__Set_Ofun__left__comm__idem(X0,tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0)),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X4] : c_Finite__Set_Ofun__left__comm__idem(X4,tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30906,plain,
spl647_349,
inference(avatar_split_clause,[],[f17305,f30904]) ).
fof(f17305,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f5283]) ).
fof(f5283,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f498]) ).
fof(f498,axiom,
! [X44] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X44),X44)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30902,plain,
spl647_348,
inference(avatar_split_clause,[],[f17304,f30900]) ).
fof(f17304,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)),
inference(cnf_transformation,[],[f5282]) ).
fof(f5282,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)),
inference(rectify,[],[f1164]) ).
fof(f1164,axiom,
! [X87] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X87),X87)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30898,plain,
spl647_347,
inference(avatar_split_clause,[],[f17303,f30896]) ).
fof(f17303,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f5281]) ).
fof(f5281,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f4876]) ).
fof(f4876,axiom,
! [X19] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X19),X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30894,plain,
spl647_346,
inference(avatar_split_clause,[],[f17301,f30892]) ).
fof(f30892,plain,
( spl647_346
<=> ! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_346])]) ).
fof(f17301,plain,
! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0,
inference(cnf_transformation,[],[f5279]) ).
fof(f5279,plain,
! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0,
inference(rectify,[],[f4195]) ).
fof(f4195,axiom,
! [X53] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X53)) = X53,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30890,plain,
spl647_345,
inference(avatar_split_clause,[],[f17300,f30888]) ).
fof(f17300,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0,
inference(cnf_transformation,[],[f5278]) ).
fof(f5278,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0,
inference(rectify,[],[f4194]) ).
fof(f4194,axiom,
! [X44] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X44)) = X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30886,plain,
spl647_344,
inference(avatar_split_clause,[],[f17299,f30884]) ).
fof(f30884,plain,
( spl647_344
<=> ! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_344])]) ).
fof(f17299,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0,
inference(cnf_transformation,[],[f5277]) ).
fof(f5277,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0,
inference(rectify,[],[f2991]) ).
fof(f2991,axiom,
! [X13] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X13)) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30882,plain,
spl647_343,
inference(avatar_split_clause,[],[f17295,f30880]) ).
fof(f30880,plain,
( spl647_343
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(X0,c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_343])]) ).
fof(f17295,plain,
! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(X0,c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5273]) ).
fof(f5273,plain,
! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(X0,c_List_Olist_ONil(X0)),
inference(rectify,[],[f4277]) ).
fof(f4277,axiom,
! [X20] : c_List_Olist_ONil(X20) = c_List_Oremdups(X20,c_List_Olist_ONil(X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30878,plain,
spl647_342,
inference(avatar_split_clause,[],[f17293,f30876]) ).
fof(f30876,plain,
( spl647_342
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Quickcheck_Obeyond(X0,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_342])]) ).
fof(f17293,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Quickcheck_Obeyond(X0,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(cnf_transformation,[],[f5271]) ).
fof(f5271,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Quickcheck_Obeyond(X0,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(rectify,[],[f4802]) ).
fof(f4802,axiom,
! [X53] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Quickcheck_Obeyond(X53,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30874,plain,
( spl647_341
| ~ spl647_242
| ~ spl647_322 ),
inference(avatar_split_clause,[],[f30825,f30765,f30418,f30871]) ).
fof(f30871,plain,
( spl647_341
<=> sP4(c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_341])]) ).
fof(f30418,plain,
( spl647_242
<=> ! [X0,X1] :
( sP4(X0)
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_242])]) ).
fof(f30765,plain,
( spl647_322
<=> ! [X0] : c_Equiv__Relations_Opart__equivp(X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_322])]) ).
fof(f30825,plain,
( sP4(c_fequal)
| ~ spl647_242
| ~ spl647_322 ),
inference(resolution,[],[f30766,f30419]) ).
fof(f30419,plain,
( ! [X0,X1] :
( ~ c_Equiv__Relations_Opart__equivp(X1,X0)
| sP4(X0) )
| ~ spl647_242 ),
inference(avatar_component_clause,[],[f30418]) ).
fof(f30766,plain,
( ! [X0] : c_Equiv__Relations_Opart__equivp(X0,c_fequal)
| ~ spl647_322 ),
inference(avatar_component_clause,[],[f30765]) ).
fof(f30869,plain,
spl647_340,
inference(avatar_split_clause,[],[f17290,f30867]) ).
fof(f30867,plain,
( spl647_340
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_340])]) ).
fof(f17290,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f5268]) ).
fof(f5268,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f485]) ).
fof(f485,axiom,
! [X44] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X44),X44)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30865,plain,
spl647_339,
inference(avatar_split_clause,[],[f17289,f30863]) ).
fof(f30863,plain,
( spl647_339
<=> ! [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,[spl647_339])]) ).
fof(f17289,plain,
! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(cnf_transformation,[],[f5267]) ).
fof(f5267,plain,
! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(rectify,[],[f1270]) ).
fof(f1270,axiom,
! [X44] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X44))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30861,plain,
spl647_338,
inference(avatar_split_clause,[],[f17181,f30858]) ).
fof(f17181,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f1967]) ).
fof(f1967,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30856,plain,
spl647_337,
inference(avatar_split_clause,[],[f17179,f30853]) ).
fof(f17179,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f1970]) ).
fof(f1970,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30851,plain,
( spl647_336
| ~ spl647_263
| ~ spl647_335 ),
inference(avatar_split_clause,[],[f30846,f30842,f30515,f30848]) ).
fof(f30842,plain,
( spl647_335
<=> 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,[spl647_335])]) ).
fof(f30846,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))
| ~ spl647_263
| ~ spl647_335 ),
inference(forward_demodulation,[],[f30844,f30516]) ).
fof(f30844,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)))
| ~ spl647_335 ),
inference(avatar_component_clause,[],[f30842]) ).
fof(f30845,plain,
spl647_335,
inference(avatar_split_clause,[],[f17178,f30842]) ).
fof(f17178,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
inference(cnf_transformation,[],[f1979]) ).
fof(f1979,axiom,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30840,plain,
spl647_334,
inference(avatar_split_clause,[],[f17168,f30837]) ).
fof(f17168,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,[],[f1547]) ).
fof(f1547,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30835,plain,
spl647_333,
inference(avatar_split_clause,[],[f17165,f30832]) ).
fof(f17165,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f1788]) ).
fof(f1788,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30830,plain,
spl647_332,
inference(avatar_split_clause,[],[f17164,f30827]) ).
fof(f30827,plain,
( spl647_332
<=> 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,[spl647_332])]) ).
fof(f17164,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,[],[f4174]) ).
fof(f4174,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30822,plain,
spl647_331,
inference(avatar_split_clause,[],[f17162,f30819]) ).
fof(f17162,plain,
c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f1977]) ).
fof(f1977,axiom,
c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30817,plain,
spl647_330,
inference(avatar_split_clause,[],[f17161,f30814]) ).
fof(f30814,plain,
( spl647_330
<=> 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,[spl647_330])]) ).
fof(f17161,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,[],[f2660]) ).
fof(f2660,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30812,plain,
spl647_329,
inference(avatar_split_clause,[],[f17160,f30809]) ).
fof(f30809,plain,
( spl647_329
<=> 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,[spl647_329])]) ).
fof(f17160,plain,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f2627]) ).
fof(f2627,axiom,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30807,plain,
spl647_328,
inference(avatar_split_clause,[],[f17159,f30804]) ).
fof(f30804,plain,
( spl647_328
<=> 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,[spl647_328])]) ).
fof(f17159,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f2629]) ).
fof(f2629,axiom,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30802,plain,
~ spl647_327,
inference(avatar_split_clause,[],[f17158,f30799]) ).
fof(f17158,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f1966]) ).
fof(f1966,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30797,plain,
~ spl647_326,
inference(avatar_split_clause,[],[f17156,f30794]) ).
fof(f17156,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f1971]) ).
fof(f1971,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30791,plain,
~ spl647_325,
inference(avatar_split_clause,[],[f17154,f30788]) ).
fof(f30788,plain,
( spl647_325
<=> 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,[spl647_325])]) ).
fof(f17154,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(cnf_transformation,[],[f1271]) ).
fof(f1271,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30785,plain,
( spl647_324
| ~ spl647_201
| ~ spl647_297 ),
inference(avatar_split_clause,[],[f30763,f30651,f30236,f30783]) ).
fof(f30783,plain,
( spl647_324
<=> ! [X0] : c_Predicate_Osymp(X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_324])]) ).
fof(f30651,plain,
( spl647_297
<=> ! [X0,X1] :
( c_Predicate_Osymp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_297])]) ).
fof(f30763,plain,
( ! [X0] : c_Predicate_Osymp(X0,c_fequal)
| ~ spl647_201
| ~ spl647_297 ),
inference(resolution,[],[f30652,f30237]) ).
fof(f30652,plain,
( ! [X0,X1] :
( ~ c_Equiv__Relations_Oequivp(X1,X0)
| c_Predicate_Osymp(X1,X0) )
| ~ spl647_297 ),
inference(avatar_component_clause,[],[f30651]) ).
fof(f30778,plain,
( spl647_323
| ~ spl647_201
| ~ spl647_296 ),
inference(avatar_split_clause,[],[f30762,f30647,f30236,f30776]) ).
fof(f30776,plain,
( spl647_323
<=> ! [X0] : c_Predicate_Oreflp(X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_323])]) ).
fof(f30647,plain,
( spl647_296
<=> ! [X0,X1] :
( c_Predicate_Oreflp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_296])]) ).
fof(f30762,plain,
( ! [X0] : c_Predicate_Oreflp(X0,c_fequal)
| ~ spl647_201
| ~ spl647_296 ),
inference(resolution,[],[f30648,f30237]) ).
fof(f30648,plain,
( ! [X0,X1] :
( ~ c_Equiv__Relations_Oequivp(X1,X0)
| c_Predicate_Oreflp(X1,X0) )
| ~ spl647_296 ),
inference(avatar_component_clause,[],[f30647]) ).
fof(f30767,plain,
( spl647_322
| ~ spl647_201
| ~ spl647_295 ),
inference(avatar_split_clause,[],[f30761,f30643,f30236,f30765]) ).
fof(f30643,plain,
( spl647_295
<=> ! [X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_295])]) ).
fof(f30761,plain,
( ! [X0] : c_Equiv__Relations_Opart__equivp(X0,c_fequal)
| ~ spl647_201
| ~ spl647_295 ),
inference(resolution,[],[f30644,f30237]) ).
fof(f30644,plain,
( ! [X0,X1] :
( ~ c_Equiv__Relations_Oequivp(X1,X0)
| c_Equiv__Relations_Opart__equivp(X1,X0) )
| ~ spl647_295 ),
inference(avatar_component_clause,[],[f30643]) ).
fof(f30760,plain,
( ~ spl647_130
| spl647_321
| ~ spl647_208
| ~ spl647_268 ),
inference(avatar_split_clause,[],[f30752,f30535,f30268,f30757,f29884]) ).
fof(f29884,plain,
( spl647_130
<=> class_Rings_Osemiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_130])]) ).
fof(f30757,plain,
( spl647_321
<=> c_Int_Oiszero(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_321])]) ).
fof(f30752,plain,
( c_Int_Oiszero(tc_Int_Oint,c_Int_OPls)
| ~ class_Rings_Osemiring__1(tc_Int_Oint)
| ~ spl647_208
| ~ spl647_268 ),
inference(superposition,[],[f30536,f30270]) ).
fof(f30750,plain,
spl647_320,
inference(avatar_split_clause,[],[f27564,f30748]) ).
fof(f27564,plain,
! [X1] :
( c_Int_OPls != X1
| sP11(X1,X1) ),
inference(forward_demodulation,[],[f27563,f17135]) ).
fof(f27563,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
| sP11(X1,X1) ),
inference(forward_demodulation,[],[f25404,f17285]) ).
fof(f25404,plain,
! [X1] :
( sP11(X1,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ),
inference(equality_resolution,[],[f19328]) ).
fof(f19328,plain,
! [X0,X1] :
( sP11(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,[],[f15144]) ).
fof(f30746,plain,
spl647_319,
inference(avatar_split_clause,[],[f26601,f30744]) ).
fof(f30744,plain,
( spl647_319
<=> ! [X0] : c_Nitpick_Onat__gcd(X0,c_HOL_Obool_Obool__size(c_fTrue)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_319])]) ).
fof(f26601,plain,
! [X0] : c_Nitpick_Onat__gcd(X0,c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f25277,f17145]) ).
fof(f25277,plain,
! [X0] : c_Nitpick_Onat__gcd(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(equality_resolution,[],[f18185]) ).
fof(f18185,plain,
! [X0,X1] :
( c_Nitpick_Onat__gcd(X0,X1) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f10449]) ).
fof(f30742,plain,
spl647_318,
inference(avatar_split_clause,[],[f26143,f30739]) ).
fof(f30739,plain,
( spl647_318
<=> c_Int_OPls = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_318])]) ).
fof(f26143,plain,
c_Int_OPls = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(forward_demodulation,[],[f25254,f17135]) ).
fof(f25254,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(equality_resolution,[],[f17502]) ).
fof(f17502,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,[],[f10310]) ).
fof(f10310,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,[],[f5479]) ).
fof(f5479,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,[],[f1895]) ).
fof(f1895,axiom,
! [X53] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X53
=> ( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X53,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,X53) = 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),X53),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,X53,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,X53) = 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),X53),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) = X53
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X53) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30737,plain,
spl647_317,
inference(avatar_split_clause,[],[f26131,f30735]) ).
fof(f30735,plain,
( spl647_317
<=> ! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_317])]) ).
fof(f26131,plain,
! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(forward_demodulation,[],[f17501,f17135]) ).
fof(f17501,plain,
! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f5478]) ).
fof(f30733,plain,
spl647_316,
inference(avatar_split_clause,[],[f26034,f30731]) ).
fof(f30731,plain,
( spl647_316
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_316])]) ).
fof(f26034,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin),
inference(forward_demodulation,[],[f26033,f17135]) ).
fof(f26033,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,[],[f17362,f17285]) ).
fof(f17362,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,[],[f5340]) ).
fof(f5340,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,[],[f2001]) ).
fof(f2001,axiom,
! [X26] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X26,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30729,plain,
spl647_315,
inference(avatar_split_clause,[],[f26024,f30727]) ).
fof(f30727,plain,
( spl647_315
<=> ! [X0] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_315])]) ).
fof(f26024,plain,
! [X0] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) = X0,
inference(forward_demodulation,[],[f17345,f17285]) ).
fof(f17345,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0),
inference(cnf_transformation,[],[f5323]) ).
fof(f5323,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0),
inference(rectify,[],[f2027]) ).
fof(f2027,axiom,
! [X87] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X87) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X87),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30725,plain,
spl647_314,
inference(avatar_split_clause,[],[f26016,f30723]) ).
fof(f30723,plain,
( spl647_314
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OPls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_314])]) ).
fof(f26016,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OPls,X0),
inference(forward_demodulation,[],[f17311,f17135]) ).
fof(f17311,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,[],[f5289]) ).
fof(f5289,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,[],[f1618]) ).
fof(f1618,axiom,
! [X25] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30721,plain,
spl647_313,
inference(avatar_split_clause,[],[f26012,f30719]) ).
fof(f30719,plain,
( spl647_313
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_313])]) ).
fof(f26012,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(forward_demodulation,[],[f17294,f17135]) ).
fof(f17294,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f5272]) ).
fof(f5272,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(rectify,[],[f1619]) ).
fof(f1619,axiom,
! [X26] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X26,X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30717,plain,
spl647_312,
inference(avatar_split_clause,[],[f26005,f30715]) ).
fof(f26005,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0),
inference(forward_demodulation,[],[f17272,f17145]) ).
fof(f17272,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X0),
inference(cnf_transformation,[],[f5250]) ).
fof(f5250,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X0),
inference(rectify,[],[f772]) ).
fof(f772,axiom,
! [X79] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X79),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30713,plain,
~ spl647_311,
inference(avatar_split_clause,[],[f25943,f30710]) ).
fof(f30710,plain,
( spl647_311
<=> c_Int_OPls = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_311])]) ).
fof(f25943,plain,
c_Int_OPls != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
inference(forward_demodulation,[],[f17199,f25912]) ).
fof(f25912,plain,
c_Int_OPls = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(forward_demodulation,[],[f17169,f17135]) ).
fof(f17169,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,[],[f1289]) ).
fof(f1289,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17199,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,[],[f1976]) ).
fof(f1976,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30708,plain,
spl647_310,
inference(avatar_split_clause,[],[f25914,f30705]) ).
fof(f30705,plain,
( spl647_310
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_310])]) ).
fof(f25914,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OPls),
inference(forward_demodulation,[],[f25913,f17145]) ).
fof(f25913,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(forward_demodulation,[],[f17170,f17135]) ).
fof(f17170,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f1766]) ).
fof(f1766,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30703,plain,
spl647_309,
inference(avatar_split_clause,[],[f25908,f30700]) ).
fof(f25908,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Nat_Onat_Onat__size(c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17153,f17145]) ).
fof(f17153,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,[],[f2209]) ).
fof(f2209,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30698,plain,
spl647_308,
inference(avatar_split_clause,[],[f25907,f30695]) ).
fof(f30695,plain,
( spl647_308
<=> 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,[spl647_308])]) ).
fof(f25907,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,[],[f17152,f17145]) ).
fof(f17152,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,[],[f2020]) ).
fof(f2020,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/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30693,plain,
spl647_307,
inference(avatar_split_clause,[],[f25544,f30691]) ).
fof(f30691,plain,
( spl647_307
<=> ! [X2,X0] : c_List_Olist__all2(X0,X0,c_fequal,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_307])]) ).
fof(f25544,plain,
! [X2,X0] : c_List_Olist__all2(X0,X0,c_fequal,X2,X2),
inference(equality_resolution,[],[f21089]) ).
fof(f21089,plain,
! [X2,X0,X1] :
( c_List_Olist__all2(X0,X0,c_fequal,X2,X1)
| X1 != X2 ),
inference(cnf_transformation,[],[f15684]) ).
fof(f30689,plain,
spl647_306,
inference(avatar_split_clause,[],[f25286,f30687]) ).
fof(f25286,plain,
! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_resolution,[],[f18283]) ).
fof(f18283,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f6116]) ).
fof(f6116,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
| X0 != X1 ),
inference(rectify,[],[f5210]) ).
fof(f5210,axiom,
! [X15,X13] :
( hBOOL(hAPP(hAPP(c_fequal,X13),X15))
| X13 != X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30685,plain,
spl647_305,
inference(avatar_split_clause,[],[f25270,f30683]) ).
fof(f30683,plain,
( spl647_305
<=> ! [X1] : c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_305])]) ).
fof(f25270,plain,
! [X1] : c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X1),
inference(equality_resolution,[],[f18173]) ).
fof(f18173,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f10444]) ).
fof(f30681,plain,
spl647_304,
inference(avatar_split_clause,[],[f20390,f30679]) ).
fof(f30679,plain,
( spl647_304
<=> ! [X2,X0,X1] :
( sP20(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_304])]) ).
fof(f20390,plain,
! [X2,X0,X1] :
( sP20(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f14511]) ).
fof(f14511,plain,
! [X0,X1,X2] :
( sP20(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(definition_folding,[],[f11891,f14510,f14509]) ).
fof(f14510,plain,
! [X1,X0,X2] :
( ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Oappend(X2),X1),X0))
<=> sP19(X2,X0,X1) )
| ~ sP20(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).
fof(f11891,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,[],[f7631]) ).
fof(f7631,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,[],[f4424]) ).
fof(f4424,axiom,
! [X202,X203,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Oappend(X4),X203),X202))
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X203)))
=> ! [X43] :
( hBOOL(hAPP(hAPP(c_member(X4),X43),hAPP(c_List_Oset(X4),X202)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X2),X43)) ) )
& c_List_Olinorder__class_Osorted(X4,X202)
& c_List_Olinorder__class_Osorted(X4,X203) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30677,plain,
spl647_303,
inference(avatar_split_clause,[],[f19939,f30675]) ).
fof(f30675,plain,
( spl647_303
<=> ! [X2,X0,X1] :
( sP18(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_303])]) ).
fof(f19939,plain,
! [X2,X0,X1] :
( sP18(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f14508]) ).
fof(f14508,plain,
! [X0,X1,X2] :
( sP18(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f11352,f14507,f14506]) ).
fof(f14506,plain,
! [X0,X2,X1] :
( sP17(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,[sP17])]) ).
fof(f14507,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)))
<=> sP17(X0,X2,X1) )
| ~ sP18(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f11352,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,[],[f7275]) ).
fof(f7275,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,[],[f828]) ).
fof(f828,axiom,
! [X12,X5,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),X5),X12)),c_Groups_Ozero__class_Ozero(X4)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X5),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),c_Groups_Ozero__class_Ozero(X4)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30673,plain,
spl647_302,
inference(avatar_split_clause,[],[f19930,f30671]) ).
fof(f30671,plain,
( spl647_302
<=> ! [X2,X0,X1] :
( sP16(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_302])]) ).
fof(f19930,plain,
! [X2,X0,X1] :
( sP16(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f14505]) ).
fof(f14505,plain,
! [X0,X1,X2] :
( sP16(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f11351,f14504,f14503]) ).
fof(f14503,plain,
! [X2,X0,X1] :
( sP15(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,[sP15])]) ).
fof(f14504,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)))
<=> sP15(X2,X0,X1) )
| ~ sP16(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f11351,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,[],[f7274]) ).
fof(f7274,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,[],[f829]) ).
fof(f829,axiom,
! [X12,X5,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),X5),X12)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X12),c_Groups_Ozero__class_Ozero(X4)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X5),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X12))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X5)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30669,plain,
spl647_301,
inference(avatar_split_clause,[],[f19128,f30667]) ).
fof(f30667,plain,
( spl647_301
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ sP5(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_301])]) ).
fof(f19128,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ sP5(X1,X0) ),
inference(cnf_transformation,[],[f14998]) ).
fof(f14998,plain,
! [X0,X1] :
( ( c_Wellfounded_Owf(X1,X0)
| ~ sP5(X1,X0) )
& ( sP5(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
inference(nnf_transformation,[],[f14485]) ).
fof(f14485,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> sP5(X1,X0) ),
inference(definition_folding,[],[f11282,f14484]) ).
fof(f11282,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,[],[f6760]) ).
fof(f6760,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,[],[f3541]) ).
fof(f3541,axiom,
! [X116,X4] :
( c_Wellfounded_Owf(X4,X116)
<=> ! [X196] :
( ? [X2] : hBOOL(hAPP(hAPP(c_member(X4),X2),X196))
=> ? [X2] :
( ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X38),X2)),X116))
=> ~ hBOOL(hAPP(hAPP(c_member(X4),X38),X196)) )
& hBOOL(hAPP(hAPP(c_member(X4),X2),X196)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30665,plain,
spl647_300,
inference(avatar_split_clause,[],[f19127,f30663]) ).
fof(f19127,plain,
! [X0,X1] :
( sP5(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f14998]) ).
fof(f30661,plain,
spl647_299,
inference(avatar_split_clause,[],[f18702,f30659]) ).
fof(f18702,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10885]) ).
fof(f10885,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6455]) ).
fof(f6455,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f3429]) ).
fof(f3429,axiom,
! [X116,X4] :
( c_Wellfounded_Owf(X4,X116)
=> c_Wellfounded_Oacyclic(X4,X116) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30657,plain,
spl647_298,
inference(avatar_split_clause,[],[f18689,f30655]) ).
fof(f18689,plain,
! [X0,X1] :
( c_Predicate_Otransp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ),
inference(cnf_transformation,[],[f10870]) ).
fof(f10870,plain,
! [X0,X1] :
( ( c_Predicate_Otransp(X1,X0)
& c_Predicate_Osymp(X1,X0)
& c_Predicate_Oreflp(X1,X0) )
| ~ c_Equiv__Relations_Oequivp(X1,X0) ),
inference(flattening,[],[f10869]) ).
fof(f10869,plain,
! [X0,X1] :
( ( c_Predicate_Otransp(X1,X0)
& c_Predicate_Osymp(X1,X0)
& c_Predicate_Oreflp(X1,X0) )
| ~ c_Equiv__Relations_Oequivp(X1,X0) ),
inference(ennf_transformation,[],[f6442]) ).
fof(f6442,plain,
! [X0,X1] :
( c_Equiv__Relations_Oequivp(X1,X0)
=> ~ ( c_Predicate_Oreflp(X1,X0)
=> ( c_Predicate_Osymp(X1,X0)
=> ~ c_Predicate_Otransp(X1,X0) ) ) ),
inference(rectify,[],[f4738]) ).
fof(f4738,axiom,
! [X138,X4] :
( c_Equiv__Relations_Oequivp(X4,X138)
=> ~ ( c_Predicate_Oreflp(X4,X138)
=> ( c_Predicate_Osymp(X4,X138)
=> ~ c_Predicate_Otransp(X4,X138) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30653,plain,
spl647_297,
inference(avatar_split_clause,[],[f18688,f30651]) ).
fof(f18688,plain,
! [X0,X1] :
( c_Predicate_Osymp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ),
inference(cnf_transformation,[],[f10870]) ).
fof(f30649,plain,
spl647_296,
inference(avatar_split_clause,[],[f18687,f30647]) ).
fof(f18687,plain,
! [X0,X1] :
( c_Predicate_Oreflp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ),
inference(cnf_transformation,[],[f10870]) ).
fof(f30645,plain,
spl647_295,
inference(avatar_split_clause,[],[f18686,f30643]) ).
fof(f18686,plain,
! [X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ),
inference(cnf_transformation,[],[f10868]) ).
fof(f10868,plain,
! [X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ),
inference(ennf_transformation,[],[f6441]) ).
fof(f6441,plain,
! [X0,X1] :
( c_Equiv__Relations_Oequivp(X1,X0)
=> c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(rectify,[],[f4747]) ).
fof(f4747,axiom,
! [X138,X4] :
( c_Equiv__Relations_Oequivp(X4,X138)
=> c_Equiv__Relations_Opart__equivp(X4,X138) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30641,plain,
spl647_294,
inference(avatar_split_clause,[],[f18684,f30639]) ).
fof(f30639,plain,
( spl647_294
<=> ! [X0,X1] :
( c_Predicate_Otransp(X1,X0)
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_294])]) ).
fof(f18684,plain,
! [X0,X1] :
( c_Predicate_Otransp(X1,X0)
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(cnf_transformation,[],[f14838]) ).
fof(f30637,plain,
spl647_293,
inference(avatar_split_clause,[],[f18683,f30635]) ).
fof(f30635,plain,
( spl647_293
<=> ! [X0,X1] :
( c_Predicate_Osymp(X1,X0)
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_293])]) ).
fof(f18683,plain,
! [X0,X1] :
( c_Predicate_Osymp(X1,X0)
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(cnf_transformation,[],[f14838]) ).
fof(f30633,plain,
spl647_292,
inference(avatar_split_clause,[],[f18639,f30631]) ).
fof(f30631,plain,
( spl647_292
<=> ! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_292])]) ).
fof(f18639,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f10812]) ).
fof(f10812,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f6405]) ).
fof(f6405,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> class_Orderings_Oorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f4996]) ).
fof(f4996,axiom,
! [X277,X278] :
( class_Orderings_Oorder(X278)
=> class_Orderings_Oorder(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30629,plain,
spl647_291,
inference(avatar_split_clause,[],[f18638,f30627]) ).
fof(f30627,plain,
( spl647_291
<=> ! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_291])]) ).
fof(f18638,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(cnf_transformation,[],[f10811]) ).
fof(f10811,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(ennf_transformation,[],[f6404]) ).
fof(f6404,plain,
! [X0,X1] :
( class_Orderings_Oord(X1)
=> class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(rectify,[],[f4998]) ).
fof(f4998,axiom,
! [X277,X278] :
( class_Orderings_Oord(X278)
=> class_Orderings_Oord(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30625,plain,
spl647_290,
inference(avatar_split_clause,[],[f18635,f30623]) ).
fof(f30623,plain,
( spl647_290
<=> ! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_290])]) ).
fof(f18635,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10808]) ).
fof(f10808,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6401]) ).
fof(f6401,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> class_Orderings_Opreorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f4993]) ).
fof(f4993,axiom,
! [X277,X278] :
( class_Orderings_Opreorder(X278)
=> class_Orderings_Opreorder(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30621,plain,
spl647_289,
inference(avatar_split_clause,[],[f18634,f30619]) ).
fof(f30619,plain,
( spl647_289
<=> ! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_289])]) ).
fof(f18634,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(cnf_transformation,[],[f10807]) ).
fof(f10807,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(ennf_transformation,[],[f6400]) ).
fof(f6400,plain,
! [X0,X1] :
( class_Groups_Ominus(X1)
=> class_Groups_Ominus(tc_fun(X0,X1)) ),
inference(rectify,[],[f5001]) ).
fof(f5001,axiom,
! [X277,X278] :
( class_Groups_Ominus(X278)
=> class_Groups_Ominus(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30617,plain,
spl647_288,
inference(avatar_split_clause,[],[f18624,f30615]) ).
fof(f30615,plain,
( spl647_288
<=> ! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_288])]) ).
fof(f18624,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10792]) ).
fof(f10792,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6390]) ).
fof(f6390,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Olattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4995]) ).
fof(f4995,axiom,
! [X277,X278] :
( class_Lattices_Olattice(X278)
=> class_Lattices_Olattice(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30613,plain,
spl647_287,
inference(avatar_split_clause,[],[f18623,f30611]) ).
fof(f30611,plain,
( spl647_287
<=> ! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_287])]) ).
fof(f18623,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10791]) ).
fof(f10791,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6389]) ).
fof(f6389,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__inf(tc_fun(X0,X1)) ),
inference(rectify,[],[f4990]) ).
fof(f4990,axiom,
! [X277,X278] :
( class_Lattices_Olattice(X278)
=> class_Lattices_Osemilattice__inf(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30609,plain,
spl647_286,
inference(avatar_split_clause,[],[f18622,f30607]) ).
fof(f30607,plain,
( spl647_286
<=> ! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_286])]) ).
fof(f18622,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10790]) ).
fof(f10790,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6388]) ).
fof(f6388,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__sup(tc_fun(X0,X1)) ),
inference(rectify,[],[f4989]) ).
fof(f4989,axiom,
! [X277,X278] :
( class_Lattices_Olattice(X278)
=> class_Lattices_Osemilattice__sup(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30605,plain,
spl647_285,
inference(avatar_split_clause,[],[f18617,f30603]) ).
fof(f30603,plain,
( spl647_285
<=> ! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_285])]) ).
fof(f18617,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(cnf_transformation,[],[f10785]) ).
fof(f10785,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(ennf_transformation,[],[f6383]) ).
fof(f6383,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(X1)
=> class_Lattices_Odistrib__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4991]) ).
fof(f4991,axiom,
! [X277,X278] :
( class_Lattices_Odistrib__lattice(X278)
=> class_Lattices_Odistrib__lattice(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30601,plain,
spl647_284,
inference(avatar_split_clause,[],[f18506,f30599]) ).
fof(f30599,plain,
( spl647_284
<=> ! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_284])]) ).
fof(f18506,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(cnf_transformation,[],[f10672]) ).
fof(f10672,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(ennf_transformation,[],[f6292]) ).
fof(f6292,plain,
! [X0,X1] :
( class_Orderings_Obot(X1)
=> class_Orderings_Obot(tc_fun(X0,X1)) ),
inference(rectify,[],[f4999]) ).
fof(f4999,axiom,
! [X277,X278] :
( class_Orderings_Obot(X278)
=> class_Orderings_Obot(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30597,plain,
spl647_283,
inference(avatar_split_clause,[],[f18503,f30595]) ).
fof(f30595,plain,
( spl647_283
<=> ! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_283])]) ).
fof(f18503,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(cnf_transformation,[],[f10669]) ).
fof(f10669,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(ennf_transformation,[],[f6289]) ).
fof(f6289,plain,
! [X0,X1] :
( class_Groups_Ouminus(X1)
=> class_Groups_Ouminus(tc_fun(X0,X1)) ),
inference(rectify,[],[f5000]) ).
fof(f5000,axiom,
! [X277,X278] :
( class_Groups_Ouminus(X278)
=> class_Groups_Ouminus(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30593,plain,
spl647_282,
inference(avatar_split_clause,[],[f18488,f30591]) ).
fof(f30591,plain,
( spl647_282
<=> ! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_282])]) ).
fof(f18488,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(cnf_transformation,[],[f10652]) ).
fof(f10652,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(ennf_transformation,[],[f6276]) ).
fof(f6276,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(X1)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4986]) ).
fof(f4986,axiom,
! [X277,X278] :
( class_Complete__Lattice_Ocomplete__lattice(X278)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30589,plain,
spl647_281,
inference(avatar_split_clause,[],[f18482,f30587]) ).
fof(f30587,plain,
( spl647_281
<=> ! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_281])]) ).
fof(f18482,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f10646]) ).
fof(f10646,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f6270]) ).
fof(f6270,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
inference(rectify,[],[f4992]) ).
fof(f4992,axiom,
! [X277,X278] :
( class_Lattices_Oboolean__algebra(X278)
=> class_Lattices_Oboolean__algebra(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30585,plain,
spl647_280,
inference(avatar_split_clause,[],[f18472,f30583]) ).
fof(f30583,plain,
( spl647_280
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_280])]) ).
fof(f18472,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10636]) ).
fof(f10636,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6260]) ).
fof(f6260,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice__top(tc_fun(X0,X1)) ),
inference(rectify,[],[f4987]) ).
fof(f4987,axiom,
! [X277,X278] :
( class_Lattices_Obounded__lattice(X278)
=> class_Lattices_Obounded__lattice__top(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30581,plain,
spl647_279,
inference(avatar_split_clause,[],[f18471,f30579]) ).
fof(f30579,plain,
( spl647_279
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_279])]) ).
fof(f18471,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10635]) ).
fof(f10635,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6259]) ).
fof(f6259,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1)) ),
inference(rectify,[],[f4988]) ).
fof(f4988,axiom,
! [X277,X278] :
( class_Lattices_Obounded__lattice(X278)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30577,plain,
spl647_278,
inference(avatar_split_clause,[],[f18470,f30575]) ).
fof(f30575,plain,
( spl647_278
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_278])]) ).
fof(f18470,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10634]) ).
fof(f10634,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6258]) ).
fof(f6258,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4985]) ).
fof(f4985,axiom,
! [X277,X278] :
( class_Lattices_Obounded__lattice(X278)
=> class_Lattices_Obounded__lattice(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30573,plain,
spl647_277,
inference(avatar_split_clause,[],[f18469,f30571]) ).
fof(f30571,plain,
( spl647_277
<=> ! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_277])]) ).
fof(f18469,plain,
! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ),
inference(cnf_transformation,[],[f10633]) ).
fof(f10633,plain,
! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ),
inference(ennf_transformation,[],[f6257]) ).
fof(f6257,plain,
! [X0,X1] :
( class_Orderings_Otop(X1)
=> class_Orderings_Otop(tc_fun(X0,X1)) ),
inference(rectify,[],[f4997]) ).
fof(f4997,axiom,
! [X277,X278] :
( class_Orderings_Otop(X278)
=> class_Orderings_Otop(tc_fun(X277,X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30569,plain,
spl647_276,
inference(avatar_split_clause,[],[f17798,f30567]) ).
fof(f30567,plain,
( spl647_276
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_276])]) ).
fof(f17798,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0),
inference(cnf_transformation,[],[f5690]) ).
fof(f5690,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0),
inference(rectify,[],[f3044]) ).
fof(f3044,axiom,
! [X9,X4] : c_Fun_Oinj__on(X4,X4,c_COMBI(X4),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30565,plain,
spl647_275,
inference(avatar_split_clause,[],[f17797,f30563]) ).
fof(f17797,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0),
inference(cnf_transformation,[],[f5689]) ).
fof(f5689,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0),
inference(rectify,[],[f3301]) ).
fof(f3301,axiom,
! [X9,X4] : c_Fun_Oinj__on(X4,X4,c_Fun_Oid(X4),X9),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30561,plain,
spl647_274,
inference(avatar_split_clause,[],[f17793,f30559]) ).
fof(f30557,plain,
spl647_273,
inference(avatar_split_clause,[],[f17792,f30555]) ).
fof(f30555,plain,
( spl647_273
<=> ! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_273])]) ).
fof(f17792,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f5684]) ).
fof(f5684,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(rectify,[],[f5204]) ).
fof(f5204,axiom,
! [X279,X20] : hAPP(c_COMBI(X20),X279) = X279,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30553,plain,
spl647_272,
inference(avatar_split_clause,[],[f17790,f30551]) ).
fof(f30551,plain,
( spl647_272
<=> ! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_272])]) ).
fof(f17790,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0,
inference(cnf_transformation,[],[f5682]) ).
fof(f5682,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0,
inference(rectify,[],[f3303]) ).
fof(f3303,axiom,
! [X183,X20] : hAPP(c_Fun_Oid(X20),X183) = X183,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30549,plain,
spl647_271,
inference(avatar_split_clause,[],[f17768,f30547]) ).
fof(f17768,plain,
! [X0] : hAPP(c_Code__Numeral_Oof__nat,sK109(X0)) = X0,
inference(cnf_transformation,[],[f14735]) ).
fof(f14735,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK109(X0)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
& hAPP(c_Code__Numeral_Oof__nat,sK109(X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK109])],[f10442,f14734]) ).
fof(f14734,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
& hAPP(c_Code__Numeral_Oof__nat,X1) = X0 )
=> ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK109(X0)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
& hAPP(c_Code__Numeral_Oof__nat,sK109(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f10442,plain,
! [X0] :
? [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
& hAPP(c_Code__Numeral_Oof__nat,X1) = X0 ),
inference(ennf_transformation,[],[f5661]) ).
fof(f5661,plain,
! [X0] :
~ ! [X1] :
( hAPP(c_Code__Numeral_Oof__nat,X1) = X0
=> ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X1),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
inference(rectify,[],[f4798]) ).
fof(f4798,axiom,
! [X13] :
~ ! [X38] :
( hAPP(c_Code__Numeral_Oof__nat,X38) = X13
=> ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X38),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30545,plain,
spl647_270,
inference(avatar_split_clause,[],[f17766,f30543]) ).
fof(f30543,plain,
( spl647_270
<=> ! [X0] : hAPP(c_Int_OAbs__Integ,sK108(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_270])]) ).
fof(f17766,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,sK108(X0)) = X0,
inference(cnf_transformation,[],[f14733]) ).
fof(f30541,plain,
spl647_269,
inference(avatar_split_clause,[],[f17575,f30539]) ).
fof(f30539,plain,
( spl647_269
<=> ! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_269])]) ).
fof(f17575,plain,
! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10368]) ).
fof(f10368,plain,
! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5540]) ).
fof(f5540,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0)) ),
inference(rectify,[],[f4411]) ).
fof(f4411,axiom,
! [X20] :
( class_Orderings_Olinorder(X20)
=> c_List_Olinorder__class_Osorted(X20,c_List_Olist_ONil(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30537,plain,
spl647_268,
inference(avatar_split_clause,[],[f17563,f30535]) ).
fof(f17563,plain,
! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10356]) ).
fof(f10356,plain,
! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5528]) ).
fof(f5528,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f1642]) ).
fof(f1642,axiom,
! [X20] :
( class_Rings_Osemiring__1(X20)
=> c_Int_Oiszero(X20,c_Groups_Ozero__class_Ozero(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30533,plain,
spl647_267,
inference(avatar_split_clause,[],[f17562,f30531]) ).
fof(f30531,plain,
( spl647_267
<=> ! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_267])]) ).
fof(f17562,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10355]) ).
fof(f10355,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5527]) ).
fof(f5527,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f1645]) ).
fof(f1645,axiom,
! [X20] :
( class_Rings_Osemiring__1(X20)
=> ~ c_Int_Oiszero(X20,c_Groups_Oone__class_Oone(X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30529,plain,
spl647_266,
inference(avatar_split_clause,[],[f17527,f30527]) ).
fof(f30527,plain,
( spl647_266
<=> ! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_266])]) ).
fof(f17527,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ),
inference(cnf_transformation,[],[f5491]) ).
fof(f5491,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ),
inference(rectify,[],[f5213]) ).
fof(f5213,axiom,
! [X23] :
( ~ hBOOL(X23)
| ~ hBOOL(hAPP(c_fNot,X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30525,plain,
spl647_265,
inference(avatar_split_clause,[],[f17526,f30523]) ).
fof(f30523,plain,
( spl647_265
<=> ! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_265])]) ).
fof(f17526,plain,
! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f5490]) ).
fof(f5490,plain,
! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f5214]) ).
fof(f5214,axiom,
! [X23] :
( hBOOL(hAPP(c_fNot,X23))
| hBOOL(X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30521,plain,
spl647_264,
inference(avatar_split_clause,[],[f17286,f30519]) ).
fof(f30519,plain,
( spl647_264
<=> ! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_264])]) ).
fof(f17286,plain,
! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))),
inference(cnf_transformation,[],[f5264]) ).
fof(f5264,plain,
! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))),
inference(rectify,[],[f3878]) ).
fof(f3878,axiom,
! [X20] : hBOOL(hAPP(c_List_Odistinct(X20),c_List_Olist_ONil(X20))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30517,plain,
spl647_263,
inference(avatar_split_clause,[],[f17285,f30515]) ).
fof(f30513,plain,
spl647_262,
inference(avatar_split_clause,[],[f17284,f30511]) ).
fof(f30511,plain,
( spl647_262
<=> ! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_262])]) ).
fof(f17284,plain,
! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f5262]) ).
fof(f5262,plain,
! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0,
inference(rectify,[],[f2421]) ).
fof(f2421,axiom,
! [X44] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X44) = X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30509,plain,
spl647_261,
inference(avatar_split_clause,[],[f17278,f30507]) ).
fof(f30507,plain,
( spl647_261
<=> ! [X0] : c_fequal = c_Predicate_Oconversep(X0,X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_261])]) ).
fof(f17278,plain,
! [X0] : c_fequal = c_Predicate_Oconversep(X0,X0,c_fequal),
inference(cnf_transformation,[],[f5256]) ).
fof(f5256,plain,
! [X0] : c_fequal = c_Predicate_Oconversep(X0,X0,c_fequal),
inference(rectify,[],[f4608]) ).
fof(f4608,axiom,
! [X4] : c_fequal = c_Predicate_Oconversep(X4,X4,c_fequal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30505,plain,
spl647_260,
inference(avatar_split_clause,[],[f17150,f30502]) ).
fof(f30502,plain,
( spl647_260
<=> c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_260])]) ).
fof(f17150,plain,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
inference(cnf_transformation,[],[f1466]) ).
fof(f1466,axiom,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30500,plain,
( ~ spl647_259
| spl647_258 ),
inference(avatar_split_clause,[],[f30495,f30491,f30497]) ).
fof(f30491,plain,
( spl647_258
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_258])]) ).
fof(f30495,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(c_fequal,v_t),hAPP(c_fequal,v_t))
| spl647_258 ),
inference(forward_demodulation,[],[f30493,f26468]) ).
fof(f30493,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
| spl647_258 ),
inference(avatar_component_clause,[],[f30491]) ).
fof(f30494,plain,
~ spl647_258,
inference(avatar_split_clause,[],[f16932,f30491]) ).
fof(f16932,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5226]) ).
fof(f5226,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(flattening,[],[f5225]) ).
fof(f5225,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(negated_conjecture,[],[f5224]) ).
fof(f5224,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),v_t),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30488,plain,
spl647_257,
inference(avatar_split_clause,[],[f28499,f30486]) ).
fof(f30486,plain,
( spl647_257
<=> ! [X0,X1] : sP44(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_257])]) ).
fof(f28499,plain,
! [X0,X1] : sP44(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25590,f17145]) ).
fof(f25590,plain,
! [X0,X1] : sP44(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f21320]) ).
fof(f21320,plain,
! [X2,X0,X1] :
( sP44(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f15876]) ).
fof(f30484,plain,
spl647_256,
inference(avatar_split_clause,[],[f28473,f30482]) ).
fof(f30482,plain,
( spl647_256
<=> ! [X0,X1] : sP39(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_256])]) ).
fof(f28473,plain,
! [X0,X1] : sP39(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25565,f17145]) ).
fof(f25565,plain,
! [X0,X1] : sP39(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f21242]) ).
fof(f21242,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f15824]) ).
fof(f30480,plain,
spl647_255,
inference(avatar_split_clause,[],[f27628,f30477]) ).
fof(f30477,plain,
( spl647_255
<=> sP14(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_255])]) ).
fof(f27628,plain,
sP14(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f27627,f25910]) ).
fof(f27627,plain,
sP14(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f25423,f17145]) ).
fof(f25423,plain,
sP14(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f25422]) ).
fof(f25422,plain,
! [X1] :
( sP14(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f19415]) ).
fof(f19415,plain,
! [X0,X1] :
( sP14(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f15194]) ).
fof(f30475,plain,
spl647_254,
inference(avatar_split_clause,[],[f27626,f30472]) ).
fof(f30472,plain,
( spl647_254
<=> sP14(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_254])]) ).
fof(f27626,plain,
sP14(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f27625,f25910]) ).
fof(f27625,plain,
sP14(hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25421,f17145]) ).
fof(f25421,plain,
sP14(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f25420]) ).
fof(f25420,plain,
! [X1] :
( sP14(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f19416]) ).
fof(f19416,plain,
! [X0,X1] :
( sP14(X0,X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f15194]) ).
fof(f30470,plain,
spl647_253,
inference(avatar_split_clause,[],[f27608,f30467]) ).
fof(f30467,plain,
( spl647_253
<=> sP13(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_253])]) ).
fof(f27608,plain,
sP13(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f27607,f25910]) ).
fof(f27607,plain,
sP13(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f25419,f17145]) ).
fof(f25419,plain,
sP13(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f25418]) ).
fof(f25418,plain,
! [X1] :
( sP13(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f19407]) ).
fof(f19407,plain,
! [X0,X1] :
( sP13(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f15191]) ).
fof(f30465,plain,
spl647_252,
inference(avatar_split_clause,[],[f27606,f30462]) ).
fof(f30462,plain,
( spl647_252
<=> sP13(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_252])]) ).
fof(f27606,plain,
sP13(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f27605,f25910]) ).
fof(f27605,plain,
sP13(hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25417,f17145]) ).
fof(f25417,plain,
sP13(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f25416]) ).
fof(f25416,plain,
! [X1] :
( sP13(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f19408]) ).
fof(f19408,plain,
! [X0,X1] :
( sP13(X0,X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f15191]) ).
fof(f30460,plain,
spl647_251,
inference(avatar_split_clause,[],[f26149,f30457]) ).
fof(f30457,plain,
( spl647_251
<=> c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_251])]) ).
fof(f26149,plain,
c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls),
inference(forward_demodulation,[],[f25255,f17135]) ).
fof(f25255,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(equality_resolution,[],[f17505]) ).
fof(f17505,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,[],[f10311]) ).
fof(f10311,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,[],[f5480]) ).
fof(f5480,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,[],[f2069]) ).
fof(f2069,axiom,
! [X55] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X55
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
=> 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,X55) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X55))
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X55) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X55
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X55) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30455,plain,
spl647_250,
inference(avatar_split_clause,[],[f25906,f30452]) ).
fof(f30452,plain,
( spl647_250
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_250])]) ).
fof(f25906,plain,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17147,f17145]) ).
fof(f17147,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f953]) ).
fof(f953,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30450,plain,
spl647_249,
inference(avatar_split_clause,[],[f25905,f30447]) ).
fof(f30447,plain,
( spl647_249
<=> c_HOL_Obool_Obool__size(c_fTrue) = c_HOL_Obool_Obool__size(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_249])]) ).
fof(f25905,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_HOL_Obool_Obool__size(c_fFalse),
inference(forward_demodulation,[],[f17146,f17145]) ).
fof(f17146,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
inference(cnf_transformation,[],[f3715]) ).
fof(f3715,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30445,plain,
spl647_248,
inference(avatar_split_clause,[],[f25833,f30443]) ).
fof(f30443,plain,
( spl647_248
<=> ! [X2,X3] : sP82(X3,X2,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_248])]) ).
fof(f25833,plain,
! [X2,X3] : sP82(X3,X2,X2,X3),
inference(equality_resolution,[],[f25832]) ).
fof(f25832,plain,
! [X2,X3,X1] :
( sP82(X3,X1,X2,X3)
| X1 != X2 ),
inference(equality_resolution,[],[f23643]) ).
fof(f23643,plain,
! [X2,X3,X0,X1] :
( sP82(X0,X1,X2,X3)
| X0 != X3
| X1 != X2 ),
inference(cnf_transformation,[],[f16767]) ).
fof(f30441,plain,
spl647_247,
inference(avatar_split_clause,[],[f25831,f30439]) ).
fof(f30439,plain,
( spl647_247
<=> ! [X1,X3] : sP82(X1,X1,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_247])]) ).
fof(f25831,plain,
! [X3,X1] : sP82(X1,X1,X3,X3),
inference(equality_resolution,[],[f25830]) ).
fof(f25830,plain,
! [X2,X3,X1] :
( sP82(X1,X1,X2,X3)
| X2 != X3 ),
inference(equality_resolution,[],[f23644]) ).
fof(f23644,plain,
! [X2,X3,X0,X1] :
( sP82(X0,X1,X2,X3)
| X0 != X1
| X2 != X3 ),
inference(cnf_transformation,[],[f16767]) ).
fof(f30437,plain,
spl647_246,
inference(avatar_split_clause,[],[f25606,f30435]) ).
fof(f30435,plain,
( spl647_246
<=> ! [X0,X1] : sP48(X0,X1,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_246])]) ).
fof(f25606,plain,
! [X0,X1] : sP48(X0,X1,c_List_Olist_ONil(X1)),
inference(equality_resolution,[],[f21400]) ).
fof(f21400,plain,
! [X2,X0,X1] :
( sP48(X0,X1,X2)
| c_List_Olist_ONil(X1) != X2 ),
inference(cnf_transformation,[],[f15939]) ).
fof(f15939,plain,
! [X0,X1,X2] :
( ( sP48(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)),sK398(X0,X1,X2)),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),sK397(X0,X1,X2)),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),sK397(X0,X1,X2)),sK398(X0,X1,X2)) = X2 )
| c_List_Olist_ONil(X1) = X2
| ~ sP48(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK397,sK398])],[f15937,f15938]) ).
fof(f15938,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)),sK398(X0,X1,X2)),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),sK397(X0,X1,X2)),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),sK397(X0,X1,X2)),sK398(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f15937,plain,
! [X0,X1,X2] :
( ( sP48(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
| ~ sP48(X0,X1,X2) ) ),
inference(rectify,[],[f15936]) ).
fof(f15936,plain,
! [X0,X2,X1] :
( ( sP48(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
| ~ sP48(X0,X2,X1) ) ),
inference(flattening,[],[f15935]) ).
fof(f15935,plain,
! [X0,X2,X1] :
( ( sP48(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
| ~ sP48(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f14557]) ).
fof(f14557,plain,
! [X0,X2,X1] :
( sP48(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,[sP48])]) ).
fof(f30433,plain,
spl647_245,
inference(avatar_split_clause,[],[f25391,f30430]) ).
fof(f30430,plain,
( spl647_245
<=> sP9(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_245])]) ).
fof(f25391,plain,
sP9(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(equality_resolution,[],[f25390]) ).
fof(f25390,plain,
! [X1] :
( sP9(c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ),
inference(equality_resolution,[],[f19278]) ).
fof(f19278,plain,
! [X0,X1] :
( sP9(X0,X1)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ),
inference(cnf_transformation,[],[f15113]) ).
fof(f30428,plain,
spl647_244,
inference(avatar_split_clause,[],[f25358,f30426]) ).
fof(f25358,plain,
! [X1] : sP7(hAPP(c_Int_Onat,X1),X1),
inference(equality_resolution,[],[f19149]) ).
fof(f19149,plain,
! [X0,X1] :
( sP7(X0,X1)
| hAPP(c_Int_Onat,X1) != X0 ),
inference(cnf_transformation,[],[f15008]) ).
fof(f30424,plain,
spl647_243,
inference(avatar_split_clause,[],[f25353,f30422]) ).
fof(f25353,plain,
! [X0] : sP6(hAPP(c_Int_Onat,X0),X0),
inference(equality_resolution,[],[f19141]) ).
fof(f19141,plain,
! [X0,X1] :
( sP6(X1,X0)
| hAPP(c_Int_Onat,X0) != X1 ),
inference(cnf_transformation,[],[f15005]) ).
fof(f30420,plain,
spl647_242,
inference(avatar_split_clause,[],[f19084,f30418]) ).
fof(f19084,plain,
! [X0,X1] :
( sP4(X0)
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(cnf_transformation,[],[f14949]) ).
fof(f30416,plain,
spl647_241,
inference(avatar_split_clause,[],[f18611,f30414]) ).
fof(f30414,plain,
( spl647_241
<=> ! [X0,X1] :
( sP1(X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_241])]) ).
fof(f18611,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f14477]) ).
fof(f14477,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(definition_folding,[],[f10782,f14476,f14475]) ).
fof(f10782,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,[],[f6380]) ).
fof(f6380,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,[],[f4514]) ).
fof(f4514,axiom,
! [X5,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_List_Olinorder__class_Osorted(X4,X5)
<=> ( ? [X208,X2] :
( c_List_Olinorder__class_Osorted(X4,X208)
& ! [X43] :
( hBOOL(hAPP(hAPP(c_member(X4),X43),hAPP(c_List_Oset(X4),X208)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X2),X43)) )
& hAPP(hAPP(c_List_Olist_OCons(X4),X2),X208) = X5 )
| c_List_Olist_ONil(X4) = X5 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30412,plain,
spl647_240,
inference(avatar_split_clause,[],[f17789,f30410]) ).
fof(f30410,plain,
( spl647_240
<=> ! [X0,X1] : c_List_Olist__all(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_240])]) ).
fof(f17789,plain,
! [X0,X1] : c_List_Olist__all(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5681]) ).
fof(f5681,plain,
! [X0,X1] : c_List_Olist__all(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4564]) ).
fof(f4564,axiom,
! [X23,X4] : c_List_Olist__all(X4,X23,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30408,plain,
spl647_239,
inference(avatar_split_clause,[],[f17786,f30406]) ).
fof(f30406,plain,
( spl647_239
<=> ! [X0,X1] : c_Relation_Otrans(X1,c_Transitive__Closure_Otrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_239])]) ).
fof(f17786,plain,
! [X0,X1] : c_Relation_Otrans(X1,c_Transitive__Closure_Otrancl(X1,X0)),
inference(cnf_transformation,[],[f5678]) ).
fof(f5678,plain,
! [X0,X1] : c_Relation_Otrans(X1,c_Transitive__Closure_Otrancl(X1,X0)),
inference(rectify,[],[f4720]) ).
fof(f4720,axiom,
! [X116,X4] : c_Relation_Otrans(X4,c_Transitive__Closure_Otrancl(X4,X116)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30404,plain,
spl647_238,
inference(avatar_split_clause,[],[f17781,f30402]) ).
fof(f30402,plain,
( spl647_238
<=> ! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_238])]) ).
fof(f17781,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)),
inference(cnf_transformation,[],[f5673]) ).
fof(f5673,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)),
inference(rectify,[],[f4405]) ).
fof(f4405,axiom,
! [X54,X55] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X55,X54)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30400,plain,
spl647_237,
inference(avatar_split_clause,[],[f17780,f30398]) ).
fof(f30398,plain,
( spl647_237
<=> ! [X0,X1] : ~ c_List_Olist__ex(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_237])]) ).
fof(f17780,plain,
! [X0,X1] : ~ c_List_Olist__ex(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5672]) ).
fof(f5672,plain,
! [X0,X1] : ~ c_List_Olist__ex(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4555]) ).
fof(f4555,axiom,
! [X23,X4] : ~ c_List_Olist__ex(X4,X23,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30396,plain,
spl647_236,
inference(avatar_split_clause,[],[f17779,f30394]) ).
fof(f30394,plain,
( spl647_236
<=> ! [X0,X1] : ~ c_List_Olist__ex1(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_236])]) ).
fof(f17779,plain,
! [X0,X1] : ~ c_List_Olist__ex1(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5671]) ).
fof(f5671,plain,
! [X0,X1] : ~ c_List_Olist__ex1(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4579]) ).
fof(f4579,axiom,
! [X23,X4] : ~ c_List_Olist__ex1(X4,X23,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30392,plain,
spl647_235,
inference(avatar_split_clause,[],[f17590,f30390]) ).
fof(f30390,plain,
( spl647_235
<=> ! [X0] :
( class_Enum_Oenum(tc_Option_Ooption(X0))
| ~ class_Enum_Oenum(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_235])]) ).
fof(f17590,plain,
! [X0] :
( class_Enum_Oenum(tc_Option_Ooption(X0))
| ~ class_Enum_Oenum(X0) ),
inference(cnf_transformation,[],[f10383]) ).
fof(f10383,plain,
! [X0] :
( class_Enum_Oenum(tc_Option_Ooption(X0))
| ~ class_Enum_Oenum(X0) ),
inference(ennf_transformation,[],[f5555]) ).
fof(f5555,plain,
! [X0] :
( class_Enum_Oenum(X0)
=> class_Enum_Oenum(tc_Option_Ooption(X0)) ),
inference(rectify,[],[f5148]) ).
fof(f5148,axiom,
! [X278] :
( class_Enum_Oenum(X278)
=> class_Enum_Oenum(tc_Option_Ooption(X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30388,plain,
spl647_234,
inference(avatar_split_clause,[],[f17588,f30386]) ).
fof(f30386,plain,
( spl647_234
<=> ! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_234])]) ).
fof(f17588,plain,
! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(cnf_transformation,[],[f10381]) ).
fof(f10381,plain,
! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(ennf_transformation,[],[f5553]) ).
fof(f5553,plain,
! [X0] :
( class_Finite__Set_Ofinite(X0)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X0)) ),
inference(rectify,[],[f5147]) ).
fof(f5147,axiom,
! [X278] :
( class_Finite__Set_Ofinite(X278)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30384,plain,
spl647_233,
inference(avatar_split_clause,[],[f17583,f30382]) ).
fof(f30382,plain,
( spl647_233
<=> ! [X0] :
( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X0))
| ~ class_Lazy__Sequence_Osmall__lazy(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_233])]) ).
fof(f17583,plain,
! [X0] :
( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X0))
| ~ class_Lazy__Sequence_Osmall__lazy(X0) ),
inference(cnf_transformation,[],[f10376]) ).
fof(f10376,plain,
! [X0] :
( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X0))
| ~ class_Lazy__Sequence_Osmall__lazy(X0) ),
inference(ennf_transformation,[],[f5548]) ).
fof(f5548,plain,
! [X0] :
( class_Lazy__Sequence_Osmall__lazy(X0)
=> class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X0)) ),
inference(rectify,[],[f5142]) ).
fof(f5142,axiom,
! [X278] :
( class_Lazy__Sequence_Osmall__lazy(X278)
=> class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X278)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30380,plain,
spl647_232,
inference(avatar_split_clause,[],[f17271,f30378]) ).
fof(f30378,plain,
( spl647_232
<=> ! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_232])]) ).
fof(f17271,plain,
! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0),
inference(cnf_transformation,[],[f5249]) ).
fof(f5249,plain,
! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0),
inference(rectify,[],[f3091]) ).
fof(f3091,axiom,
! [X103] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X103),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30376,plain,
spl647_231,
inference(avatar_split_clause,[],[f17270,f30374]) ).
fof(f30374,plain,
( spl647_231
<=> ! [X0] : c_Relation_Osingle__valued(X0,X0,c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_231])]) ).
fof(f17270,plain,
! [X0] : c_Relation_Osingle__valued(X0,X0,c_Relation_OId(X0)),
inference(cnf_transformation,[],[f5248]) ).
fof(f5248,plain,
! [X0] : c_Relation_Osingle__valued(X0,X0,c_Relation_OId(X0)),
inference(rectify,[],[f3659]) ).
fof(f3659,axiom,
! [X4] : c_Relation_Osingle__valued(X4,X4,c_Relation_OId(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30372,plain,
spl647_230,
inference(avatar_split_clause,[],[f17269,f30370]) ).
fof(f30370,plain,
( spl647_230
<=> ! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_230])]) ).
fof(f17269,plain,
! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f5247]) ).
fof(f5247,plain,
! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(rectify,[],[f2128]) ).
fof(f2128,axiom,
! [X27] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30368,plain,
spl647_229,
inference(avatar_split_clause,[],[f17265,f30366]) ).
fof(f30366,plain,
( spl647_229
<=> ! [X0] : hAPP(c_Nat_OSuc,X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl647_229])]) ).
fof(f17265,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(cnf_transformation,[],[f5243]) ).
fof(f5243,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(rectify,[],[f481]) ).
fof(f481,axiom,
! [X44] : hAPP(c_Nat_OSuc,X44) != X44,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30364,plain,
spl647_228,
inference(avatar_split_clause,[],[f17149,f30361]) ).
fof(f17149,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f3371]) ).
fof(f3371,axiom,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30359,plain,
spl647_227,
inference(avatar_split_clause,[],[f17148,f30356]) ).
fof(f30356,plain,
( spl647_227
<=> c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_227])]) ).
fof(f17148,plain,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
inference(cnf_transformation,[],[f2931]) ).
fof(f2931,axiom,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30354,plain,
spl647_226,
inference(avatar_split_clause,[],[f17145,f30351]) ).
fof(f30349,plain,
spl647_225,
inference(avatar_split_clause,[],[f17143,f30346]) ).
fof(f30346,plain,
( spl647_225
<=> c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_225])]) ).
fof(f17143,plain,
c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),
inference(cnf_transformation,[],[f1134]) ).
fof(f1134,axiom,
c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30344,plain,
spl647_224,
inference(avatar_split_clause,[],[f17142,f30341]) ).
fof(f30341,plain,
( spl647_224
<=> c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_224])]) ).
fof(f17142,plain,
c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),
inference(cnf_transformation,[],[f2451]) ).
fof(f2451,axiom,
c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30339,plain,
spl647_223,
inference(avatar_split_clause,[],[f17141,f30336]) ).
fof(f17141,plain,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
inference(cnf_transformation,[],[f3311]) ).
fof(f3311,axiom,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30334,plain,
spl647_222,
inference(avatar_split_clause,[],[f17139,f30331]) ).
fof(f17139,plain,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f3543]) ).
fof(f3543,axiom,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30329,plain,
~ spl647_221,
inference(avatar_split_clause,[],[f17137,f30326]) ).
fof(f17137,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f1280]) ).
fof(f1280,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30323,plain,
spl647_220,
inference(avatar_split_clause,[],[f27478,f30320]) ).
fof(f30320,plain,
( spl647_220
<=> sP7(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_220])]) ).
fof(f27478,plain,
sP7(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls),
inference(forward_demodulation,[],[f27477,f25936]) ).
fof(f27477,plain,
sP7(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f25355,f17145]) ).
fof(f25355,plain,
sP7(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f25354]) ).
fof(f25354,plain,
! [X1] :
( sP7(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f19148]) ).
fof(f19148,plain,
! [X0,X1] :
( sP7(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1 ),
inference(cnf_transformation,[],[f15007]) ).
fof(f30318,plain,
spl647_219,
inference(avatar_split_clause,[],[f27470,f30315]) ).
fof(f30315,plain,
( spl647_219
<=> sP6(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_219])]) ).
fof(f27470,plain,
sP6(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls),
inference(forward_demodulation,[],[f27469,f25936]) ).
fof(f27469,plain,
sP6(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f25350,f17145]) ).
fof(f25350,plain,
sP6(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f25349]) ).
fof(f25349,plain,
! [X1] :
( sP6(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f19140]) ).
fof(f19140,plain,
! [X0,X1] :
( sP6(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1 ),
inference(cnf_transformation,[],[f15004]) ).
fof(f30313,plain,
~ spl647_218,
inference(avatar_split_clause,[],[f25904,f30310]) ).
fof(f30310,plain,
( spl647_218
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_218])]) ).
fof(f25904,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)),
inference(forward_demodulation,[],[f17138,f17135]) ).
fof(f17138,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(cnf_transformation,[],[f1279]) ).
fof(f1279,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30308,plain,
~ spl647_217,
inference(avatar_split_clause,[],[f25903,f30305]) ).
fof(f30305,plain,
( spl647_217
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl647_217])]) ).
fof(f25903,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Int_OPls,
inference(forward_demodulation,[],[f17136,f17135]) ).
fof(f17136,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f1208]) ).
fof(f1208,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30303,plain,
spl647_216,
inference(avatar_split_clause,[],[f25316,f30301]) ).
fof(f30301,plain,
( spl647_216
<=> ! [X0] : sP0(X0,c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_216])]) ).
fof(f25316,plain,
! [X0] : sP0(X0,c_List_Olist_ONil(X0)),
inference(equality_resolution,[],[f18608]) ).
fof(f18608,plain,
! [X0,X1] :
( sP0(X0,X1)
| c_List_Olist_ONil(X0) != X1 ),
inference(cnf_transformation,[],[f14807]) ).
fof(f30299,plain,
spl647_215,
inference(avatar_split_clause,[],[f17776,f30297]) ).
fof(f30297,plain,
( spl647_215
<=> ! [X0,X1] : class_Nat_Osize(tc_prod(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_215])]) ).
fof(f17776,plain,
! [X0,X1] : class_Nat_Osize(tc_prod(X1,X0)),
inference(cnf_transformation,[],[f5668]) ).
fof(f5668,plain,
! [X0,X1] : class_Nat_Osize(tc_prod(X1,X0)),
inference(rectify,[],[f5154]) ).
fof(f5154,axiom,
! [X278,X277] : class_Nat_Osize(tc_prod(X277,X278)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30295,plain,
spl647_214,
inference(avatar_split_clause,[],[f17775,f30293]) ).
fof(f30293,plain,
( spl647_214
<=> ! [X0,X1] : class_Nat_Osize(tc_sum(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_214])]) ).
fof(f17775,plain,
! [X0,X1] : class_Nat_Osize(tc_sum(X1,X0)),
inference(cnf_transformation,[],[f5667]) ).
fof(f5667,plain,
! [X0,X1] : class_Nat_Osize(tc_sum(X1,X0)),
inference(rectify,[],[f5146]) ).
fof(f5146,axiom,
! [X278,X277] : class_Nat_Osize(tc_sum(X277,X278)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30291,plain,
spl647_213,
inference(avatar_split_clause,[],[f17774,f30289]) ).
fof(f30289,plain,
( spl647_213
<=> ! [X0,X1] : class_Nat_Osize(tc_Nitpick_Opair__box(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_213])]) ).
fof(f17774,plain,
! [X0,X1] : class_Nat_Osize(tc_Nitpick_Opair__box(X1,X0)),
inference(cnf_transformation,[],[f5666]) ).
fof(f5666,plain,
! [X0,X1] : class_Nat_Osize(tc_Nitpick_Opair__box(X1,X0)),
inference(rectify,[],[f5150]) ).
fof(f5150,axiom,
! [X278,X277] : class_Nat_Osize(tc_Nitpick_Opair__box(X277,X278)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30287,plain,
spl647_212,
inference(avatar_split_clause,[],[f17262,f30285]) ).
fof(f30285,plain,
( spl647_212
<=> ! [X0] : c_Relation_Otrans(X0,c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_212])]) ).
fof(f17262,plain,
! [X0] : c_Relation_Otrans(X0,c_Relation_OId(X0)),
inference(cnf_transformation,[],[f5240]) ).
fof(f5240,plain,
! [X0] : c_Relation_Otrans(X0,c_Relation_OId(X0)),
inference(rectify,[],[f4718]) ).
fof(f4718,axiom,
! [X4] : c_Relation_Otrans(X4,c_Relation_OId(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30283,plain,
spl647_211,
inference(avatar_split_clause,[],[f17261,f30281]) ).
fof(f30281,plain,
( spl647_211
<=> ! [X0] : c_Relation_Osym(X0,c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_211])]) ).
fof(f17261,plain,
! [X0] : c_Relation_Osym(X0,c_Relation_OId(X0)),
inference(cnf_transformation,[],[f5239]) ).
fof(f5239,plain,
! [X0] : c_Relation_Osym(X0,c_Relation_OId(X0)),
inference(rectify,[],[f4755]) ).
fof(f4755,axiom,
! [X4] : c_Relation_Osym(X4,c_Relation_OId(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30279,plain,
spl647_210,
inference(avatar_split_clause,[],[f17260,f30277]) ).
fof(f30277,plain,
( spl647_210
<=> ! [X0] : c_Relation_Oantisym(X0,c_Relation_OId(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_210])]) ).
fof(f17260,plain,
! [X0] : c_Relation_Oantisym(X0,c_Relation_OId(X0)),
inference(cnf_transformation,[],[f5238]) ).
fof(f5238,plain,
! [X0] : c_Relation_Oantisym(X0,c_Relation_OId(X0)),
inference(rectify,[],[f4729]) ).
fof(f4729,axiom,
! [X4] : c_Relation_Oantisym(X4,c_Relation_OId(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30275,plain,
spl647_209,
inference(avatar_split_clause,[],[f17256,f30273]) ).
fof(f30273,plain,
( spl647_209
<=> ! [X0] : c_Int_OMin != c_Int_OBit0(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_209])]) ).
fof(f17256,plain,
! [X0] : c_Int_OMin != c_Int_OBit0(X0),
inference(cnf_transformation,[],[f5234]) ).
fof(f5234,plain,
! [X0] : c_Int_OMin != c_Int_OBit0(X0),
inference(rectify,[],[f1960]) ).
fof(f1960,axiom,
! [X56] : c_Int_OBit0(X56) != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30271,plain,
spl647_208,
inference(avatar_split_clause,[],[f17135,f30268]) ).
fof(f30266,plain,
spl647_207,
inference(avatar_split_clause,[],[f17134,f30263]) ).
fof(f30263,plain,
( spl647_207
<=> c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral ),
introduced(avatar_definition,[new_symbols(naming,[spl647_207])]) ).
fof(f30261,plain,
spl647_206,
inference(avatar_split_clause,[],[f17133,f30258]) ).
fof(f30258,plain,
( spl647_206
<=> c_Int_OPls = c_Int_OBit0(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_206])]) ).
fof(f30256,plain,
spl647_205,
inference(avatar_split_clause,[],[f17129,f30253]) ).
fof(f30253,plain,
( spl647_205
<=> c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_205])]) ).
fof(f17129,plain,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f4173]) ).
fof(f4173,axiom,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30251,plain,
spl647_204,
inference(avatar_split_clause,[],[f27527,f30249]) ).
fof(f30249,plain,
( spl647_204
<=> ! [X0] : sP10(X0,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_204])]) ).
fof(f27527,plain,
! [X0] : sP10(X0,c_Int_OPls),
inference(forward_demodulation,[],[f25396,f17135]) ).
fof(f25396,plain,
! [X0] : sP10(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(equality_resolution,[],[f19292]) ).
fof(f19292,plain,
! [X0,X1] :
( sP10(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ),
inference(cnf_transformation,[],[f15121]) ).
fof(f15121,plain,
! [X0,X1] :
( ( sP10(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
| ~ sP10(X0,X1) ) ),
inference(rectify,[],[f15120]) ).
fof(f15120,plain,
! [X1,X0] :
( ( sP10(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
| ~ sP10(X1,X0) ) ),
inference(flattening,[],[f15119]) ).
fof(f15119,plain,
! [X1,X0] :
( ( sP10(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
| ~ sP10(X1,X0) ) ),
inference(nnf_transformation,[],[f14494]) ).
fof(f30247,plain,
spl647_203,
inference(avatar_split_clause,[],[f27520,f30244]) ).
fof(f30244,plain,
( spl647_203
<=> sP9(c_Int_OMin,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_203])]) ).
fof(f27520,plain,
sP9(c_Int_OMin,c_Int_OMin),
inference(forward_demodulation,[],[f25389,f17285]) ).
fof(f25389,plain,
sP9(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
inference(equality_resolution,[],[f25388]) ).
fof(f25388,plain,
! [X1] :
( sP9(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X1)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 ),
inference(equality_resolution,[],[f19279]) ).
fof(f19279,plain,
! [X0,X1] :
( sP9(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,[],[f15113]) ).
fof(f30242,plain,
spl647_202,
inference(avatar_split_clause,[],[f17771,f30240]) ).
fof(f30240,plain,
( spl647_202
<=> ! [X0,X1] : c_FunDef_Ois__measure(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_202])]) ).
fof(f17771,plain,
! [X0,X1] : c_FunDef_Ois__measure(X1,X0),
inference(cnf_transformation,[],[f5663]) ).
fof(f5663,plain,
! [X0,X1] : c_FunDef_Ois__measure(X1,X0),
inference(rectify,[],[f4568]) ).
fof(f4568,axiom,
! [X5,X4] : c_FunDef_Ois__measure(X4,X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30238,plain,
spl647_201,
inference(avatar_split_clause,[],[f17253,f30236]) ).
fof(f17253,plain,
! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal),
inference(cnf_transformation,[],[f5231]) ).
fof(f5231,plain,
! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal),
inference(rectify,[],[f3030]) ).
fof(f3030,axiom,
! [X4] : c_Equiv__Relations_Oequivp(X4,c_fequal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30234,plain,
spl647_200,
inference(avatar_split_clause,[],[f17252,f30232]) ).
fof(f30232,plain,
( spl647_200
<=> ! [X0] : class_Nat_Osize(tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_200])]) ).
fof(f17252,plain,
! [X0] : class_Nat_Osize(tc_List_Olist(X0)),
inference(cnf_transformation,[],[f5230]) ).
fof(f5230,plain,
! [X0] : class_Nat_Osize(tc_List_Olist(X0)),
inference(rectify,[],[f5143]) ).
fof(f5143,axiom,
! [X278] : class_Nat_Osize(tc_List_Olist(X278)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30230,plain,
spl647_199,
inference(avatar_split_clause,[],[f17251,f30228]) ).
fof(f30228,plain,
( spl647_199
<=> ! [X0] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_199])]) ).
fof(f17251,plain,
! [X0] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)),
inference(cnf_transformation,[],[f5229]) ).
fof(f5229,plain,
! [X0] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)),
inference(rectify,[],[f5203]) ).
fof(f5203,axiom,
! [X278] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X278)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30226,plain,
spl647_198,
inference(avatar_split_clause,[],[f17250,f30224]) ).
fof(f30224,plain,
( spl647_198
<=> ! [X0] : class_Nat_Osize(tc_Option_Ooption(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_198])]) ).
fof(f17250,plain,
! [X0] : class_Nat_Osize(tc_Option_Ooption(X0)),
inference(cnf_transformation,[],[f5228]) ).
fof(f5228,plain,
! [X0] : class_Nat_Osize(tc_Option_Ooption(X0)),
inference(rectify,[],[f5149]) ).
fof(f5149,axiom,
! [X278] : class_Nat_Osize(tc_Option_Ooption(X278)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30222,plain,
spl647_197,
inference(avatar_split_clause,[],[f17249,f30220]) ).
fof(f30220,plain,
( spl647_197
<=> ! [X0] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_197])]) ).
fof(f17249,plain,
! [X0] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X0)),
inference(cnf_transformation,[],[f5227]) ).
fof(f5227,plain,
! [X0] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X0)),
inference(rectify,[],[f5160]) ).
fof(f5160,axiom,
! [X278] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X278)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30218,plain,
spl647_196,
inference(avatar_split_clause,[],[f17128,f30215]) ).
fof(f17128,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f3357]) ).
fof(f3357,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30213,plain,
spl647_195,
inference(avatar_split_clause,[],[f17127,f30210]) ).
fof(f17127,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f3415]) ).
fof(f3415,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30208,plain,
spl647_194,
inference(avatar_split_clause,[],[f17126,f30205]) ).
fof(f17126,plain,
c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f4709]) ).
fof(f4709,axiom,
c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30203,plain,
( spl647_193
| ~ spl647_192 ),
inference(avatar_split_clause,[],[f30198,f30194,f30200]) ).
fof(f30200,plain,
( spl647_193
<=> c_Nat__Transfer_Ois__nat(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_193])]) ).
fof(f30194,plain,
( spl647_192
<=> c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_192])]) ).
fof(f30198,plain,
( c_Nat__Transfer_Ois__nat(c_Int_OPls)
| ~ spl647_192 ),
inference(forward_demodulation,[],[f30196,f17135]) ).
fof(f30196,plain,
( c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl647_192 ),
inference(avatar_component_clause,[],[f30194]) ).
fof(f30197,plain,
spl647_192,
inference(avatar_split_clause,[],[f17125,f30194]) ).
fof(f17125,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f2125]) ).
fof(f2125,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30192,plain,
spl647_191,
inference(avatar_split_clause,[],[f17124,f30189]) ).
fof(f30189,plain,
( spl647_191
<=> c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_191])]) ).
fof(f17124,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f2129]) ).
fof(f2129,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30187,plain,
~ spl647_190,
inference(avatar_split_clause,[],[f17122,f30184]) ).
fof(f30184,plain,
( spl647_190
<=> c_Int_OPls = c_Int_OMin ),
introduced(avatar_definition,[new_symbols(naming,[spl647_190])]) ).
fof(f17122,plain,
c_Int_OPls != c_Int_OMin,
inference(cnf_transformation,[],[f1956]) ).
fof(f1956,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30182,plain,
spl647_189,
inference(avatar_split_clause,[],[f17121,f30179]) ).
fof(f30179,plain,
( spl647_189
<=> hBOOL(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_189])]) ).
fof(f17121,plain,
hBOOL(c_fTrue),
inference(cnf_transformation,[],[f5212]) ).
fof(f5212,axiom,
hBOOL(c_fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30177,plain,
spl647_188,
inference(avatar_split_clause,[],[f17120,f30174]) ).
fof(f30174,plain,
( spl647_188
<=> class_Nat_Osize(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_188])]) ).
fof(f17120,plain,
class_Nat_Osize(tc_HOL_Obool),
inference(cnf_transformation,[],[f5141]) ).
fof(f5141,axiom,
class_Nat_Osize(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30172,plain,
spl647_187,
inference(avatar_split_clause,[],[f17119,f30169]) ).
fof(f30169,plain,
( spl647_187
<=> class_Nat_Osize(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_187])]) ).
fof(f17119,plain,
class_Nat_Osize(tc_Nat_Onat),
inference(cnf_transformation,[],[f5123]) ).
fof(f5123,axiom,
class_Nat_Osize(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30167,plain,
spl647_186,
inference(avatar_split_clause,[],[f17118,f30164]) ).
fof(f30164,plain,
( spl647_186
<=> class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_186])]) ).
fof(f17118,plain,
class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5202]) ).
fof(f5202,axiom,
class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30162,plain,
spl647_185,
inference(avatar_split_clause,[],[f17117,f30159]) ).
fof(f30159,plain,
( spl647_185
<=> class_Nat_Osize(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_185])]) ).
fof(f17117,plain,
class_Nat_Osize(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5158]) ).
fof(f5158,axiom,
class_Nat_Osize(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30157,plain,
spl647_184,
inference(avatar_split_clause,[],[f17116,f30154]) ).
fof(f30154,plain,
( spl647_184
<=> class_Nat_Osize(tc_Code__Evaluation_Oterm) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_184])]) ).
fof(f17116,plain,
class_Nat_Osize(tc_Code__Evaluation_Oterm),
inference(cnf_transformation,[],[f5159]) ).
fof(f5159,axiom,
class_Nat_Osize(tc_Code__Evaluation_Oterm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30152,plain,
spl647_183,
inference(avatar_split_clause,[],[f17115,f30149]) ).
fof(f30149,plain,
( spl647_183
<=> class_Enum_Oenum(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_183])]) ).
fof(f17115,plain,
class_Enum_Oenum(tc_HOL_Obool),
inference(cnf_transformation,[],[f5140]) ).
fof(f5140,axiom,
class_Enum_Oenum(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30147,plain,
spl647_182,
inference(avatar_split_clause,[],[f17114,f30144]) ).
fof(f30144,plain,
( spl647_182
<=> class_Enum_Oenum(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_182])]) ).
fof(f17114,plain,
class_Enum_Oenum(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5157]) ).
fof(f5157,axiom,
class_Enum_Oenum(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30142,plain,
spl647_181,
inference(avatar_split_clause,[],[f17113,f30139]) ).
fof(f30139,plain,
( spl647_181
<=> class_Finite__Set_Ofinite(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_181])]) ).
fof(f17113,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(cnf_transformation,[],[f5132]) ).
fof(f5132,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30137,plain,
spl647_180,
inference(avatar_split_clause,[],[f17112,f30134]) ).
fof(f30134,plain,
( spl647_180
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_180])]) ).
fof(f17112,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5156]) ).
fof(f5156,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30132,plain,
spl647_179,
inference(avatar_split_clause,[],[f17111,f30129]) ).
fof(f30129,plain,
( spl647_179
<=> class_Orderings_Oorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_179])]) ).
fof(f17111,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f5134]) ).
fof(f5134,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30127,plain,
spl647_178,
inference(avatar_split_clause,[],[f17110,f30124]) ).
fof(f30124,plain,
( spl647_178
<=> class_Orderings_Oorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_178])]) ).
fof(f17110,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5113]) ).
fof(f5113,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30122,plain,
spl647_177,
inference(avatar_split_clause,[],[f17109,f30119]) ).
fof(f30119,plain,
( spl647_177
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_177])]) ).
fof(f17109,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5058]) ).
fof(f5058,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30117,plain,
spl647_176,
inference(avatar_split_clause,[],[f17108,f30114]) ).
fof(f30114,plain,
( spl647_176
<=> class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_176])]) ).
fof(f17108,plain,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5193]) ).
fof(f5193,axiom,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30112,plain,
spl647_175,
inference(avatar_split_clause,[],[f17107,f30109]) ).
fof(f30109,plain,
( spl647_175
<=> class_Orderings_Oord(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_175])]) ).
fof(f17107,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f5136]) ).
fof(f5136,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30107,plain,
spl647_174,
inference(avatar_split_clause,[],[f17106,f30104]) ).
fof(f30104,plain,
( spl647_174
<=> class_Orderings_Oord(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_174])]) ).
fof(f17106,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f5115]) ).
fof(f5115,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30102,plain,
spl647_173,
inference(avatar_split_clause,[],[f17105,f30099]) ).
fof(f30099,plain,
( spl647_173
<=> class_Orderings_Oord(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_173])]) ).
fof(f17105,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(cnf_transformation,[],[f5062]) ).
fof(f5062,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30097,plain,
spl647_172,
inference(avatar_split_clause,[],[f17104,f30094]) ).
fof(f30094,plain,
( spl647_172
<=> class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_172])]) ).
fof(f17104,plain,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5195]) ).
fof(f5195,axiom,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30092,plain,
spl647_171,
inference(avatar_split_clause,[],[f17103,f30089]) ).
fof(f30089,plain,
( spl647_171
<=> class_Orderings_Opreorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_171])]) ).
fof(f17103,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f5131]) ).
fof(f5131,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30087,plain,
spl647_170,
inference(avatar_split_clause,[],[f17102,f30084]) ).
fof(f30084,plain,
( spl647_170
<=> class_Orderings_Opreorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_170])]) ).
fof(f17102,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5105]) ).
fof(f5105,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30082,plain,
spl647_169,
inference(avatar_split_clause,[],[f17101,f30079]) ).
fof(f30079,plain,
( spl647_169
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_169])]) ).
fof(f17101,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5046]) ).
fof(f5046,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30077,plain,
spl647_168,
inference(avatar_split_clause,[],[f17100,f30074]) ).
fof(f30074,plain,
( spl647_168
<=> class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_168])]) ).
fof(f17100,plain,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5186]) ).
fof(f5186,axiom,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30072,plain,
spl647_167,
inference(avatar_split_clause,[],[f17099,f30069]) ).
fof(f30069,plain,
( spl647_167
<=> class_Groups_Ominus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_167])]) ).
fof(f17099,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(cnf_transformation,[],[f5139]) ).
fof(f5139,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30067,plain,
spl647_166,
inference(avatar_split_clause,[],[f17098,f30064]) ).
fof(f30064,plain,
( spl647_166
<=> class_Groups_Ominus(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_166])]) ).
fof(f17098,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(cnf_transformation,[],[f5117]) ).
fof(f5117,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30062,plain,
spl647_165,
inference(avatar_split_clause,[],[f17097,f30059]) ).
fof(f30059,plain,
( spl647_165
<=> class_Groups_Ominus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_165])]) ).
fof(f17097,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(cnf_transformation,[],[f5067]) ).
fof(f5067,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30057,plain,
spl647_164,
inference(avatar_split_clause,[],[f17096,f30054]) ).
fof(f30054,plain,
( spl647_164
<=> class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_164])]) ).
fof(f17096,plain,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5196]) ).
fof(f5196,axiom,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30052,plain,
spl647_163,
inference(avatar_split_clause,[],[f17095,f30049]) ).
fof(f30049,plain,
( spl647_163
<=> class_Lattices_Olattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_163])]) ).
fof(f17095,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5133]) ).
fof(f5133,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30047,plain,
spl647_162,
inference(avatar_split_clause,[],[f17094,f30044]) ).
fof(f30044,plain,
( spl647_162
<=> class_Lattices_Olattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_162])]) ).
fof(f17094,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f5111]) ).
fof(f5111,axiom,
class_Lattices_Olattice(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30042,plain,
spl647_161,
inference(avatar_split_clause,[],[f17093,f30039]) ).
fof(f30039,plain,
( spl647_161
<=> class_Lattices_Olattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_161])]) ).
fof(f17093,plain,
class_Lattices_Olattice(tc_Int_Oint),
inference(cnf_transformation,[],[f5053]) ).
fof(f5053,axiom,
class_Lattices_Olattice(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30037,plain,
spl647_160,
inference(avatar_split_clause,[],[f17092,f30034]) ).
fof(f30034,plain,
( spl647_160
<=> class_Lattices_Osemilattice__inf(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_160])]) ).
fof(f17092,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(cnf_transformation,[],[f5128]) ).
fof(f5128,axiom,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30032,plain,
spl647_159,
inference(avatar_split_clause,[],[f17091,f30029]) ).
fof(f30029,plain,
( spl647_159
<=> class_Lattices_Osemilattice__inf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_159])]) ).
fof(f17091,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(cnf_transformation,[],[f5090]) ).
fof(f5090,axiom,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30027,plain,
spl647_158,
inference(avatar_split_clause,[],[f17090,f30024]) ).
fof(f30024,plain,
( spl647_158
<=> class_Lattices_Osemilattice__inf(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_158])]) ).
fof(f17090,plain,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
inference(cnf_transformation,[],[f5027]) ).
fof(f5027,axiom,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30022,plain,
spl647_157,
inference(avatar_split_clause,[],[f17089,f30019]) ).
fof(f30019,plain,
( spl647_157
<=> class_Lattices_Osemilattice__sup(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_157])]) ).
fof(f17089,plain,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
inference(cnf_transformation,[],[f5127]) ).
fof(f5127,axiom,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30017,plain,
spl647_156,
inference(avatar_split_clause,[],[f17088,f30014]) ).
fof(f30014,plain,
( spl647_156
<=> class_Lattices_Osemilattice__sup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_156])]) ).
fof(f17088,plain,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
inference(cnf_transformation,[],[f5089]) ).
fof(f5089,axiom,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30012,plain,
spl647_155,
inference(avatar_split_clause,[],[f17087,f30009]) ).
fof(f30009,plain,
( spl647_155
<=> class_Lattices_Osemilattice__sup(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_155])]) ).
fof(f17087,plain,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
inference(cnf_transformation,[],[f5026]) ).
fof(f5026,axiom,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30007,plain,
spl647_154,
inference(avatar_split_clause,[],[f17086,f30004]) ).
fof(f30004,plain,
( spl647_154
<=> class_Lattices_Odistrib__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_154])]) ).
fof(f17086,plain,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5129]) ).
fof(f5129,axiom,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30002,plain,
spl647_153,
inference(avatar_split_clause,[],[f17085,f29999]) ).
fof(f29999,plain,
( spl647_153
<=> class_Lattices_Odistrib__lattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_153])]) ).
fof(f17085,plain,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f5091]) ).
fof(f5091,axiom,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29997,plain,
spl647_152,
inference(avatar_split_clause,[],[f17084,f29994]) ).
fof(f29994,plain,
( spl647_152
<=> class_Lattices_Odistrib__lattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_152])]) ).
fof(f17084,plain,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
inference(cnf_transformation,[],[f5028]) ).
fof(f5028,axiom,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29992,plain,
spl647_151,
inference(avatar_split_clause,[],[f17083,f29989]) ).
fof(f29989,plain,
( spl647_151
<=> class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_151])]) ).
fof(f17083,plain,
class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
inference(cnf_transformation,[],[f5025]) ).
fof(f5025,axiom,
class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29987,plain,
spl647_150,
inference(avatar_split_clause,[],[f17082,f29984]) ).
fof(f29984,plain,
( spl647_150
<=> class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_150])]) ).
fof(f17082,plain,
class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5155]) ).
fof(f5155,axiom,
class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29982,plain,
spl647_149,
inference(avatar_split_clause,[],[f17081,f29979]) ).
fof(f29979,plain,
( spl647_149
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_149])]) ).
fof(f17081,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5106]) ).
fof(f5106,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29977,plain,
spl647_148,
inference(avatar_split_clause,[],[f17080,f29974]) ).
fof(f29974,plain,
( spl647_148
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_148])]) ).
fof(f17080,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5047]) ).
fof(f5047,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29972,plain,
spl647_147,
inference(avatar_split_clause,[],[f17079,f29969]) ).
fof(f29969,plain,
( spl647_147
<=> class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_147])]) ).
fof(f17079,plain,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5187]) ).
fof(f5187,axiom,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29967,plain,
spl647_146,
inference(avatar_split_clause,[],[f17078,f29964]) ).
fof(f29964,plain,
( spl647_146
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_146])]) ).
fof(f17078,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5097]) ).
fof(f5097,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29962,plain,
spl647_145,
inference(avatar_split_clause,[],[f17077,f29959]) ).
fof(f29959,plain,
( spl647_145
<=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_145])]) ).
fof(f17077,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5035]) ).
fof(f5035,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29957,plain,
spl647_144,
inference(avatar_split_clause,[],[f17076,f29954]) ).
fof(f29954,plain,
( spl647_144
<=> class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_144])]) ).
fof(f17076,plain,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5179]) ).
fof(f5179,axiom,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29952,plain,
spl647_143,
inference(avatar_split_clause,[],[f17075,f29949]) ).
fof(f29949,plain,
( spl647_143
<=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_143])]) ).
fof(f17075,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(cnf_transformation,[],[f5100]) ).
fof(f5100,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29947,plain,
spl647_142,
inference(avatar_split_clause,[],[f17074,f29944]) ).
fof(f29944,plain,
( spl647_142
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_142])]) ).
fof(f17074,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f5040]) ).
fof(f5040,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29942,plain,
spl647_141,
inference(avatar_split_clause,[],[f17073,f29939]) ).
fof(f29939,plain,
( spl647_141
<=> class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_141])]) ).
fof(f17073,plain,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5182]) ).
fof(f5182,axiom,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29937,plain,
spl647_140,
inference(avatar_split_clause,[],[f17072,f29934]) ).
fof(f29934,plain,
( spl647_140
<=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_140])]) ).
fof(f17072,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f5098]) ).
fof(f5098,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29932,plain,
spl647_139,
inference(avatar_split_clause,[],[f17071,f29929]) ).
fof(f29929,plain,
( spl647_139
<=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_139])]) ).
fof(f17071,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5038]) ).
fof(f5038,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29927,plain,
spl647_138,
inference(avatar_split_clause,[],[f17070,f29924]) ).
fof(f29924,plain,
( spl647_138
<=> class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_138])]) ).
fof(f17070,plain,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5180]) ).
fof(f5180,axiom,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29922,plain,
spl647_137,
inference(avatar_split_clause,[],[f17069,f29919]) ).
fof(f29919,plain,
( spl647_137
<=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_137])]) ).
fof(f17069,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5093]) ).
fof(f5093,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29917,plain,
spl647_136,
inference(avatar_split_clause,[],[f17068,f29914]) ).
fof(f29914,plain,
( spl647_136
<=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_136])]) ).
fof(f17068,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5030]) ).
fof(f5030,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29912,plain,
spl647_135,
inference(avatar_split_clause,[],[f17067,f29909]) ).
fof(f29909,plain,
( spl647_135
<=> class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_135])]) ).
fof(f17067,plain,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5175]) ).
fof(f5175,axiom,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29907,plain,
spl647_134,
inference(avatar_split_clause,[],[f17066,f29904]) ).
fof(f29904,plain,
( spl647_134
<=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_134])]) ).
fof(f17066,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f5088]) ).
fof(f5088,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29902,plain,
spl647_133,
inference(avatar_split_clause,[],[f17065,f29899]) ).
fof(f29899,plain,
( spl647_133
<=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_133])]) ).
fof(f17065,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(cnf_transformation,[],[f5024]) ).
fof(f5024,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29897,plain,
spl647_132,
inference(avatar_split_clause,[],[f17064,f29894]) ).
fof(f29894,plain,
( spl647_132
<=> class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_132])]) ).
fof(f17064,plain,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5173]) ).
fof(f5173,axiom,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29892,plain,
spl647_131,
inference(avatar_split_clause,[],[f17063,f29889]) ).
fof(f17063,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f5109]) ).
fof(f5109,axiom,
class_Rings_Osemiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29887,plain,
spl647_130,
inference(avatar_split_clause,[],[f17062,f29884]) ).
fof(f17062,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5051]) ).
fof(f5051,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29882,plain,
spl647_129,
inference(avatar_split_clause,[],[f17061,f29879]) ).
fof(f17061,plain,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5190]) ).
fof(f5190,axiom,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29877,plain,
spl647_128,
inference(avatar_split_clause,[],[f17060,f29874]) ).
fof(f29874,plain,
( spl647_128
<=> class_Int_Onumber(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_128])]) ).
fof(f17060,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(cnf_transformation,[],[f5120]) ).
fof(f5120,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29872,plain,
spl647_127,
inference(avatar_split_clause,[],[f17059,f29869]) ).
fof(f29869,plain,
( spl647_127
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_127])]) ).
fof(f17059,plain,
class_Int_Onumber(tc_Int_Oint),
inference(cnf_transformation,[],[f5072]) ).
fof(f5072,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29867,plain,
spl647_126,
inference(avatar_split_clause,[],[f17058,f29864]) ).
fof(f29864,plain,
( spl647_126
<=> class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_126])]) ).
fof(f17058,plain,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5199]) ).
fof(f5199,axiom,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29862,plain,
spl647_125,
inference(avatar_split_clause,[],[f17057,f29859]) ).
fof(f29859,plain,
( spl647_125
<=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_125])]) ).
fof(f17057,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f5080]) ).
fof(f5080,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29857,plain,
spl647_124,
inference(avatar_split_clause,[],[f17056,f29854]) ).
fof(f29854,plain,
( spl647_124
<=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_124])]) ).
fof(f17056,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5009]) ).
fof(f5009,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29852,plain,
spl647_123,
inference(avatar_split_clause,[],[f17055,f29849]) ).
fof(f29849,plain,
( spl647_123
<=> class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_123])]) ).
fof(f17055,plain,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5165]) ).
fof(f5165,axiom,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29847,plain,
spl647_122,
inference(avatar_split_clause,[],[f17054,f29844]) ).
fof(f29844,plain,
( spl647_122
<=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_122])]) ).
fof(f17054,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5082]) ).
fof(f5082,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29842,plain,
spl647_121,
inference(avatar_split_clause,[],[f17053,f29839]) ).
fof(f29839,plain,
( spl647_121
<=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_121])]) ).
fof(f17053,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5012]) ).
fof(f5012,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29837,plain,
spl647_120,
inference(avatar_split_clause,[],[f17052,f29834]) ).
fof(f29834,plain,
( spl647_120
<=> class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_120])]) ).
fof(f17052,plain,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5167]) ).
fof(f5167,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29832,plain,
spl647_119,
inference(avatar_split_clause,[],[f17051,f29829]) ).
fof(f29829,plain,
( spl647_119
<=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_119])]) ).
fof(f17051,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5107]) ).
fof(f5107,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29827,plain,
spl647_118,
inference(avatar_split_clause,[],[f17050,f29824]) ).
fof(f29824,plain,
( spl647_118
<=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_118])]) ).
fof(f17050,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5048]) ).
fof(f5048,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29822,plain,
spl647_117,
inference(avatar_split_clause,[],[f17049,f29819]) ).
fof(f29819,plain,
( spl647_117
<=> class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_117])]) ).
fof(f17049,plain,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5188]) ).
fof(f5188,axiom,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29817,plain,
spl647_116,
inference(avatar_split_clause,[],[f17048,f29814]) ).
fof(f29814,plain,
( spl647_116
<=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_116])]) ).
fof(f17048,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5108]) ).
fof(f5108,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29812,plain,
spl647_115,
inference(avatar_split_clause,[],[f17047,f29809]) ).
fof(f29809,plain,
( spl647_115
<=> class_Groups_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_115])]) ).
fof(f17047,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5050]) ).
fof(f5050,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29807,plain,
spl647_114,
inference(avatar_split_clause,[],[f17046,f29804]) ).
fof(f29804,plain,
( spl647_114
<=> class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_114])]) ).
fof(f17046,plain,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5189]) ).
fof(f5189,axiom,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29802,plain,
spl647_113,
inference(avatar_split_clause,[],[f17045,f29799]) ).
fof(f29799,plain,
( spl647_113
<=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_113])]) ).
fof(f17045,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5092]) ).
fof(f5092,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29797,plain,
spl647_112,
inference(avatar_split_clause,[],[f17044,f29794]) ).
fof(f29794,plain,
( spl647_112
<=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_112])]) ).
fof(f17044,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5029]) ).
fof(f5029,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29792,plain,
spl647_111,
inference(avatar_split_clause,[],[f17043,f29789]) ).
fof(f29789,plain,
( spl647_111
<=> class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_111])]) ).
fof(f17043,plain,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5174]) ).
fof(f5174,axiom,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29787,plain,
spl647_110,
inference(avatar_split_clause,[],[f17042,f29784]) ).
fof(f29784,plain,
( spl647_110
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_110])]) ).
fof(f17042,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[],[f5077]) ).
fof(f5077,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29782,plain,
spl647_109,
inference(avatar_split_clause,[],[f17041,f29779]) ).
fof(f29779,plain,
( spl647_109
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_109])]) ).
fof(f17041,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[],[f5005]) ).
fof(f5005,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29777,plain,
spl647_108,
inference(avatar_split_clause,[],[f17040,f29774]) ).
fof(f29774,plain,
( spl647_108
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_108])]) ).
fof(f17040,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5162]) ).
fof(f5162,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29772,plain,
spl647_107,
inference(avatar_split_clause,[],[f17039,f29769]) ).
fof(f29769,plain,
( spl647_107
<=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_107])]) ).
fof(f17039,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f5110]) ).
fof(f5110,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29767,plain,
spl647_106,
inference(avatar_split_clause,[],[f17038,f29764]) ).
fof(f29764,plain,
( spl647_106
<=> class_Rings_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_106])]) ).
fof(f17038,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5052]) ).
fof(f5052,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29762,plain,
spl647_105,
inference(avatar_split_clause,[],[f17037,f29759]) ).
fof(f29759,plain,
( spl647_105
<=> class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_105])]) ).
fof(f17037,plain,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5191]) ).
fof(f5191,axiom,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29757,plain,
spl647_104,
inference(avatar_split_clause,[],[f17036,f29754]) ).
fof(f29754,plain,
( spl647_104
<=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_104])]) ).
fof(f17036,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5081]) ).
fof(f5081,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29752,plain,
spl647_103,
inference(avatar_split_clause,[],[f17035,f29749]) ).
fof(f29749,plain,
( spl647_103
<=> class_Power_Opower(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_103])]) ).
fof(f17035,plain,
class_Power_Opower(tc_Nat_Onat),
inference(cnf_transformation,[],[f5118]) ).
fof(f5118,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29747,plain,
spl647_102,
inference(avatar_split_clause,[],[f17034,f29744]) ).
fof(f29744,plain,
( spl647_102
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_102])]) ).
fof(f17034,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5076]) ).
fof(f5076,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29742,plain,
spl647_101,
inference(avatar_split_clause,[],[f17033,f29739]) ).
fof(f29739,plain,
( spl647_101
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_101])]) ).
fof(f17033,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5004]) ).
fof(f5004,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29737,plain,
spl647_100,
inference(avatar_split_clause,[],[f17032,f29734]) ).
fof(f29734,plain,
( spl647_100
<=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_100])]) ).
fof(f17032,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5010]) ).
fof(f5010,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29732,plain,
spl647_99,
inference(avatar_split_clause,[],[f17031,f29729]) ).
fof(f29729,plain,
( spl647_99
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_99])]) ).
fof(f17031,plain,
class_Power_Opower(tc_Int_Oint),
inference(cnf_transformation,[],[f5068]) ).
fof(f5068,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29727,plain,
spl647_98,
inference(avatar_split_clause,[],[f17030,f29724]) ).
fof(f29724,plain,
( spl647_98
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_98])]) ).
fof(f17030,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5161]) ).
fof(f5161,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29722,plain,
spl647_97,
inference(avatar_split_clause,[],[f17029,f29719]) ).
fof(f29719,plain,
( spl647_97
<=> class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_97])]) ).
fof(f17029,plain,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5197]) ).
fof(f5197,axiom,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29717,plain,
spl647_96,
inference(avatar_split_clause,[],[f17028,f29714]) ).
fof(f29714,plain,
( spl647_96
<=> class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_96])]) ).
fof(f17028,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5166]) ).
fof(f5166,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29712,plain,
spl647_95,
inference(avatar_split_clause,[],[f17027,f29709]) ).
fof(f29709,plain,
( spl647_95
<=> class_Rings_Odvd(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_95])]) ).
fof(f17027,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(cnf_transformation,[],[f5122]) ).
fof(f5122,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29707,plain,
spl647_94,
inference(avatar_split_clause,[],[f17026,f29704]) ).
fof(f29704,plain,
( spl647_94
<=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_94])]) ).
fof(f17026,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5084]) ).
fof(f5084,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29702,plain,
spl647_93,
inference(avatar_split_clause,[],[f17025,f29699]) ).
fof(f29699,plain,
( spl647_93
<=> class_Rings_Odvd(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_93])]) ).
fof(f17025,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(cnf_transformation,[],[f5074]) ).
fof(f5074,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29697,plain,
spl647_92,
inference(avatar_split_clause,[],[f17024,f29694]) ).
fof(f29694,plain,
( spl647_92
<=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_92])]) ).
fof(f17024,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5016]) ).
fof(f5016,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29692,plain,
spl647_91,
inference(avatar_split_clause,[],[f17023,f29689]) ).
fof(f29689,plain,
( spl647_91
<=> class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_91])]) ).
fof(f17023,plain,
class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5201]) ).
fof(f5201,axiom,
class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29687,plain,
spl647_90,
inference(avatar_split_clause,[],[f17022,f29684]) ).
fof(f29684,plain,
( spl647_90
<=> class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_90])]) ).
fof(f17022,plain,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5169]) ).
fof(f5169,axiom,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29682,plain,
spl647_89,
inference(avatar_split_clause,[],[f17021,f29679]) ).
fof(f29679,plain,
( spl647_89
<=> class_Orderings_Obot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_89])]) ).
fof(f17021,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(cnf_transformation,[],[f5137]) ).
fof(f5137,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29677,plain,
spl647_88,
inference(avatar_split_clause,[],[f17020,f29674]) ).
fof(f29674,plain,
( spl647_88
<=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_88])]) ).
fof(f17020,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5095]) ).
fof(f5095,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29672,plain,
spl647_87,
inference(avatar_split_clause,[],[f17019,f29669]) ).
fof(f29669,plain,
( spl647_87
<=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_87])]) ).
fof(f17019,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(cnf_transformation,[],[f5096]) ).
fof(f5096,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29667,plain,
spl647_86,
inference(avatar_split_clause,[],[f17018,f29664]) ).
fof(f29664,plain,
( spl647_86
<=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_86])]) ).
fof(f17018,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5086]) ).
fof(f5086,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29662,plain,
spl647_85,
inference(avatar_split_clause,[],[f17017,f29659]) ).
fof(f29659,plain,
( spl647_85
<=> class_Orderings_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_85])]) ).
fof(f17017,plain,
class_Orderings_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f5116]) ).
fof(f5116,axiom,
class_Orderings_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29657,plain,
spl647_84,
inference(avatar_split_clause,[],[f17016,f29654]) ).
fof(f29654,plain,
( spl647_84
<=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_84])]) ).
fof(f17016,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5022]) ).
fof(f5022,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29652,plain,
spl647_83,
inference(avatar_split_clause,[],[f17015,f29649]) ).
fof(f29649,plain,
( spl647_83
<=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_83])]) ).
fof(f17015,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5032]) ).
fof(f5032,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29647,plain,
spl647_82,
inference(avatar_split_clause,[],[f17014,f29644]) ).
fof(f29644,plain,
( spl647_82
<=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_82])]) ).
fof(f17014,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5034]) ).
fof(f5034,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29642,plain,
spl647_81,
inference(avatar_split_clause,[],[f17013,f29639]) ).
fof(f29639,plain,
( spl647_81
<=> class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_81])]) ).
fof(f17013,plain,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5171]) ).
fof(f5171,axiom,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29637,plain,
spl647_80,
inference(avatar_split_clause,[],[f17012,f29634]) ).
fof(f29634,plain,
( spl647_80
<=> class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_80])]) ).
fof(f17012,plain,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5177]) ).
fof(f5177,axiom,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29632,plain,
spl647_79,
inference(avatar_split_clause,[],[f17011,f29629]) ).
fof(f29629,plain,
( spl647_79
<=> class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_79])]) ).
fof(f17011,plain,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5178]) ).
fof(f5178,axiom,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29627,plain,
spl647_78,
inference(avatar_split_clause,[],[f17010,f29624]) ).
fof(f29624,plain,
( spl647_78
<=> class_Groups_Ouminus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_78])]) ).
fof(f17010,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(cnf_transformation,[],[f5138]) ).
fof(f5138,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29622,plain,
spl647_77,
inference(avatar_split_clause,[],[f17009,f29619]) ).
fof(f29619,plain,
( spl647_77
<=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_77])]) ).
fof(f17009,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(cnf_transformation,[],[f5104]) ).
fof(f5104,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29617,plain,
spl647_76,
inference(avatar_split_clause,[],[f17008,f29614]) ).
fof(f29614,plain,
( spl647_76
<=> class_Rings_Omult__zero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_76])]) ).
fof(f17008,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(cnf_transformation,[],[f5112]) ).
fof(f5112,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29612,plain,
spl647_75,
inference(avatar_split_clause,[],[f17007,f29609]) ).
fof(f29609,plain,
( spl647_75
<=> class_Rings_Osemiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_75])]) ).
fof(f17007,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5114]) ).
fof(f5114,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29607,plain,
spl647_74,
inference(avatar_split_clause,[],[f17006,f29604]) ).
fof(f29604,plain,
( spl647_74
<=> class_Rings_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_74])]) ).
fof(f17006,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5061]) ).
fof(f5061,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29602,plain,
spl647_73,
inference(avatar_split_clause,[],[f17005,f29599]) ).
fof(f29599,plain,
( spl647_73
<=> class_Groups_Ouminus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_73])]) ).
fof(f17005,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(cnf_transformation,[],[f5063]) ).
fof(f5063,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29597,plain,
spl647_72,
inference(avatar_split_clause,[],[f17004,f29594]) ).
fof(f29594,plain,
( spl647_72
<=> class_Rings_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_72])]) ).
fof(f17004,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(cnf_transformation,[],[f5056]) ).
fof(f5056,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29592,plain,
spl647_71,
inference(avatar_split_clause,[],[f17003,f29589]) ).
fof(f29589,plain,
( spl647_71
<=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_71])]) ).
fof(f17003,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(cnf_transformation,[],[f5044]) ).
fof(f5044,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29587,plain,
spl647_70,
inference(avatar_split_clause,[],[f17002,f29584]) ).
fof(f29584,plain,
( spl647_70
<=> class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_70])]) ).
fof(f17002,plain,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5192]) ).
fof(f5192,axiom,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29582,plain,
spl647_69,
inference(avatar_split_clause,[],[f17001,f29579]) ).
fof(f29579,plain,
( spl647_69
<=> class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_69])]) ).
fof(f17001,plain,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5185]) ).
fof(f5185,axiom,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29577,plain,
spl647_68,
inference(avatar_split_clause,[],[f17000,f29574]) ).
fof(f29574,plain,
( spl647_68
<=> class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_68])]) ).
fof(f17000,plain,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5194]) ).
fof(f5194,axiom,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29572,plain,
spl647_67,
inference(avatar_split_clause,[],[f16999,f29569]) ).
fof(f29569,plain,
( spl647_67
<=> class_Nat_Osemiring__char__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_67])]) ).
fof(f16999,plain,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f5103]) ).
fof(f5103,axiom,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29567,plain,
spl647_66,
inference(avatar_split_clause,[],[f16998,f29564]) ).
fof(f29564,plain,
( spl647_66
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_66])]) ).
fof(f16998,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5079]) ).
fof(f5079,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29562,plain,
spl647_65,
inference(avatar_split_clause,[],[f16997,f29559]) ).
fof(f29559,plain,
( spl647_65
<=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_65])]) ).
fof(f16997,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5087]) ).
fof(f5087,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29557,plain,
spl647_64,
inference(avatar_split_clause,[],[f16996,f29554]) ).
fof(f29554,plain,
( spl647_64
<=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_64])]) ).
fof(f16996,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5094]) ).
fof(f5094,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29552,plain,
spl647_63,
inference(avatar_split_clause,[],[f16995,f29549]) ).
fof(f29549,plain,
( spl647_63
<=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_63])]) ).
fof(f16995,plain,
class_Nat_Osemiring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5042]) ).
fof(f5042,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29547,plain,
spl647_62,
inference(avatar_split_clause,[],[f16994,f29544]) ).
fof(f29544,plain,
( spl647_62
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_62])]) ).
fof(f16994,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5008]) ).
fof(f5008,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29542,plain,
spl647_61,
inference(avatar_split_clause,[],[f16993,f29539]) ).
fof(f29539,plain,
( spl647_61
<=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_61])]) ).
fof(f16993,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5031]) ).
fof(f5031,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29537,plain,
spl647_60,
inference(avatar_split_clause,[],[f16992,f29534]) ).
fof(f29534,plain,
( spl647_60
<=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_60])]) ).
fof(f16992,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5023]) ).
fof(f5023,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29532,plain,
spl647_59,
inference(avatar_split_clause,[],[f16991,f29529]) ).
fof(f29529,plain,
( spl647_59
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_59])]) ).
fof(f16991,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5164]) ).
fof(f5164,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29527,plain,
spl647_58,
inference(avatar_split_clause,[],[f16990,f29524]) ).
fof(f29524,plain,
( spl647_58
<=> class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_58])]) ).
fof(f16990,plain,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5172]) ).
fof(f5172,axiom,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29522,plain,
spl647_57,
inference(avatar_split_clause,[],[f16989,f29519]) ).
fof(f29519,plain,
( spl647_57
<=> class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_57])]) ).
fof(f16989,plain,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5176]) ).
fof(f5176,axiom,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29517,plain,
spl647_56,
inference(avatar_split_clause,[],[f16988,f29514]) ).
fof(f29514,plain,
( spl647_56
<=> class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_56])]) ).
fof(f16988,plain,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5184]) ).
fof(f5184,axiom,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29512,plain,
spl647_55,
inference(avatar_split_clause,[],[f16987,f29509]) ).
fof(f29509,plain,
( spl647_55
<=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_55])]) ).
fof(f16987,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5101]) ).
fof(f5101,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29507,plain,
spl647_54,
inference(avatar_split_clause,[],[f16986,f29504]) ).
fof(f29504,plain,
( spl647_54
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_54])]) ).
fof(f16986,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5083]) ).
fof(f5083,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29502,plain,
spl647_53,
inference(avatar_split_clause,[],[f16985,f29499]) ).
fof(f29499,plain,
( spl647_53
<=> class_Groups_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_53])]) ).
fof(f16985,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f5119]) ).
fof(f5119,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29497,plain,
spl647_52,
inference(avatar_split_clause,[],[f16984,f29494]) ).
fof(f29494,plain,
( spl647_52
<=> class_Groups_Osemigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_52])]) ).
fof(f16984,plain,
class_Groups_Osemigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5099]) ).
fof(f5099,axiom,
class_Groups_Osemigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29492,plain,
spl647_51,
inference(avatar_split_clause,[],[f16983,f29489]) ).
fof(f29489,plain,
( spl647_51
<=> class_Groups_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_51])]) ).
fof(f16983,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f5121]) ).
fof(f5121,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29487,plain,
spl647_50,
inference(avatar_split_clause,[],[f16982,f29484]) ).
fof(f29484,plain,
( spl647_50
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_50])]) ).
fof(f16982,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f5078]) ).
fof(f5078,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29482,plain,
spl647_49,
inference(avatar_split_clause,[],[f16981,f29479]) ).
fof(f29479,plain,
( spl647_49
<=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_49])]) ).
fof(f16981,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5085]) ).
fof(f5085,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29477,plain,
spl647_48,
inference(avatar_split_clause,[],[f16980,f29474]) ).
fof(f29474,plain,
( spl647_48
<=> class_Groups_Osemigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_48])]) ).
fof(f16980,plain,
class_Groups_Osemigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5039]) ).
fof(f5039,axiom,
class_Groups_Osemigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29472,plain,
spl647_47,
inference(avatar_split_clause,[],[f16979,f29469]) ).
fof(f29469,plain,
( spl647_47
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_47])]) ).
fof(f16979,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5006]) ).
fof(f5006,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29467,plain,
spl647_46,
inference(avatar_split_clause,[],[f16978,f29464]) ).
fof(f29464,plain,
( spl647_46
<=> class_Groups_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_46])]) ).
fof(f16978,plain,
class_Groups_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f5073]) ).
fof(f5073,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29462,plain,
spl647_45,
inference(avatar_split_clause,[],[f16977,f29459]) ).
fof(f29459,plain,
( spl647_45
<=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_45])]) ).
fof(f16977,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5019]) ).
fof(f5019,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29457,plain,
spl647_44,
inference(avatar_split_clause,[],[f16976,f29454]) ).
fof(f29454,plain,
( spl647_44
<=> class_Groups_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_44])]) ).
fof(f16976,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f5069]) ).
fof(f5069,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29452,plain,
spl647_43,
inference(avatar_split_clause,[],[f16975,f29449]) ).
fof(f29449,plain,
( spl647_43
<=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_43])]) ).
fof(f16975,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5041]) ).
fof(f5041,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29447,plain,
spl647_42,
inference(avatar_split_clause,[],[f16974,f29444]) ).
fof(f29444,plain,
( spl647_42
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_42])]) ).
fof(f16974,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5014]) ).
fof(f5014,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29442,plain,
spl647_41,
inference(avatar_split_clause,[],[f16973,f29439]) ).
fof(f29439,plain,
( spl647_41
<=> class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_41])]) ).
fof(f16973,plain,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5200]) ).
fof(f5200,axiom,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29437,plain,
spl647_40,
inference(avatar_split_clause,[],[f16972,f29434]) ).
fof(f29434,plain,
( spl647_40
<=> class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_40])]) ).
fof(f16972,plain,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5183]) ).
fof(f5183,axiom,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29432,plain,
spl647_39,
inference(avatar_split_clause,[],[f16971,f29429]) ).
fof(f29429,plain,
( spl647_39
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_39])]) ).
fof(f16971,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5168]) ).
fof(f5168,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29427,plain,
spl647_38,
inference(avatar_split_clause,[],[f16970,f29424]) ).
fof(f29424,plain,
( spl647_38
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_38])]) ).
fof(f16970,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5163]) ).
fof(f5163,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29422,plain,
spl647_37,
inference(avatar_split_clause,[],[f16969,f29419]) ).
fof(f29419,plain,
( spl647_37
<=> class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_37])]) ).
fof(f16969,plain,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5198]) ).
fof(f5198,axiom,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29417,plain,
spl647_36,
inference(avatar_split_clause,[],[f16968,f29414]) ).
fof(f29414,plain,
( spl647_36
<=> class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_36])]) ).
fof(f16968,plain,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5181]) ).
fof(f5181,axiom,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29412,plain,
spl647_35,
inference(avatar_split_clause,[],[f16967,f29409]) ).
fof(f29409,plain,
( spl647_35
<=> class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_35])]) ).
fof(f16967,plain,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5170]) ).
fof(f5170,axiom,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29407,plain,
spl647_34,
inference(avatar_split_clause,[],[f16966,f29404]) ).
fof(f29404,plain,
( spl647_34
<=> class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_34])]) ).
fof(f16966,plain,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5124]) ).
fof(f5124,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29402,plain,
spl647_33,
inference(avatar_split_clause,[],[f16965,f29399]) ).
fof(f29399,plain,
( spl647_33
<=> class_Lattices_Oboolean__algebra(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_33])]) ).
fof(f16965,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(cnf_transformation,[],[f5130]) ).
fof(f5130,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29397,plain,
spl647_32,
inference(avatar_split_clause,[],[f16964,f29394]) ).
fof(f29394,plain,
( spl647_32
<=> class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_32])]) ).
fof(f16964,plain,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
inference(cnf_transformation,[],[f5126]) ).
fof(f5126,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29392,plain,
spl647_31,
inference(avatar_split_clause,[],[f16963,f29389]) ).
fof(f29389,plain,
( spl647_31
<=> class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_31])]) ).
fof(f16963,plain,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
inference(cnf_transformation,[],[f5125]) ).
fof(f5125,axiom,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29387,plain,
spl647_30,
inference(avatar_split_clause,[],[f16962,f29384]) ).
fof(f29384,plain,
( spl647_30
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_30])]) ).
fof(f16962,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(cnf_transformation,[],[f5075]) ).
fof(f5075,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29382,plain,
spl647_29,
inference(avatar_split_clause,[],[f16961,f29379]) ).
fof(f29379,plain,
( spl647_29
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_29])]) ).
fof(f16961,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(cnf_transformation,[],[f5003]) ).
fof(f5003,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29377,plain,
spl647_28,
inference(avatar_split_clause,[],[f16960,f29374]) ).
fof(f29374,plain,
( spl647_28
<=> class_Lattices_Obounded__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_28])]) ).
fof(f16960,plain,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f4984]) ).
fof(f4984,axiom,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29372,plain,
spl647_27,
inference(avatar_split_clause,[],[f16959,f29369]) ).
fof(f29369,plain,
( spl647_27
<=> class_Orderings_Otop(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_27])]) ).
fof(f16959,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(cnf_transformation,[],[f5135]) ).
fof(f5135,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29367,plain,
spl647_26,
inference(avatar_split_clause,[],[f16958,f29364]) ).
fof(f16958,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5060]) ).
fof(f5060,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29362,plain,
spl647_25,
inference(avatar_split_clause,[],[f16957,f29359]) ).
fof(f29359,plain,
( spl647_25
<=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_25])]) ).
fof(f16957,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(cnf_transformation,[],[f5037]) ).
fof(f5037,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29357,plain,
spl647_24,
inference(avatar_split_clause,[],[f16956,f29354]) ).
fof(f16956,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f5011]) ).
fof(f5011,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29352,plain,
spl647_23,
inference(avatar_split_clause,[],[f16955,f29349]) ).
fof(f29349,plain,
( spl647_23
<=> class_Rings_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_23])]) ).
fof(f16955,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5066]) ).
fof(f5066,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29347,plain,
spl647_22,
inference(avatar_split_clause,[],[f16954,f29344]) ).
fof(f29344,plain,
( spl647_22
<=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_22])]) ).
fof(f16954,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5021]) ).
fof(f5021,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29342,plain,
spl647_21,
inference(avatar_split_clause,[],[f16953,f29339]) ).
fof(f29339,plain,
( spl647_21
<=> class_Groups_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_21])]) ).
fof(f16953,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5054]) ).
fof(f5054,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29337,plain,
spl647_20,
inference(avatar_split_clause,[],[f16952,f29334]) ).
fof(f29334,plain,
( spl647_20
<=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_20])]) ).
fof(f16952,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5013]) ).
fof(f5013,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29332,plain,
spl647_19,
inference(avatar_split_clause,[],[f16951,f29329]) ).
fof(f29329,plain,
( spl647_19
<=> class_Groups_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_19])]) ).
fof(f16951,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5043]) ).
fof(f5043,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29327,plain,
spl647_18,
inference(avatar_split_clause,[],[f16950,f29324]) ).
fof(f29324,plain,
( spl647_18
<=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_18])]) ).
fof(f16950,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5017]) ).
fof(f5017,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29322,plain,
spl647_17,
inference(avatar_split_clause,[],[f16949,f29319]) ).
fof(f29319,plain,
( spl647_17
<=> class_Rings_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_17])]) ).
fof(f16949,plain,
class_Rings_Oring(tc_Int_Oint),
inference(cnf_transformation,[],[f5070]) ).
fof(f5070,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29317,plain,
spl647_16,
inference(avatar_split_clause,[],[f16948,f29314]) ).
fof(f29314,plain,
( spl647_16
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_16])]) ).
fof(f16948,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5059]) ).
fof(f5059,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29312,plain,
spl647_15,
inference(avatar_split_clause,[],[f16947,f29309]) ).
fof(f29309,plain,
( spl647_15
<=> class_Rings_Oordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_15])]) ).
fof(f16947,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5045]) ).
fof(f5045,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29307,plain,
spl647_14,
inference(avatar_split_clause,[],[f16946,f29304]) ).
fof(f29304,plain,
( spl647_14
<=> class_Divides_Oring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_14])]) ).
fof(f16946,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f5055]) ).
fof(f5055,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29302,plain,
spl647_13,
inference(avatar_split_clause,[],[f16945,f29299]) ).
fof(f29299,plain,
( spl647_13
<=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_13])]) ).
fof(f16945,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5049]) ).
fof(f5049,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29297,plain,
spl647_12,
inference(avatar_split_clause,[],[f16944,f29294]) ).
fof(f29294,plain,
( spl647_12
<=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_12])]) ).
fof(f16944,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5036]) ).
fof(f5036,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29292,plain,
spl647_11,
inference(avatar_split_clause,[],[f16943,f29289]) ).
fof(f29289,plain,
( spl647_11
<=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_11])]) ).
fof(f16943,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5015]) ).
fof(f5015,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29287,plain,
spl647_10,
inference(avatar_split_clause,[],[f16942,f29284]) ).
fof(f29284,plain,
( spl647_10
<=> class_Rings_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_10])]) ).
fof(f16942,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(cnf_transformation,[],[f5071]) ).
fof(f5071,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29282,plain,
spl647_9,
inference(avatar_split_clause,[],[f16941,f29279]) ).
fof(f29279,plain,
( spl647_9
<=> class_Rings_Ocomm__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_9])]) ).
fof(f16941,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5057]) ).
fof(f5057,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29277,plain,
spl647_8,
inference(avatar_split_clause,[],[f16940,f29274]) ).
fof(f29274,plain,
( spl647_8
<=> class_Groups_Osgn__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_8])]) ).
fof(f16940,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(cnf_transformation,[],[f5064]) ).
fof(f5064,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29272,plain,
spl647_7,
inference(avatar_split_clause,[],[f16939,f29269]) ).
fof(f29269,plain,
( spl647_7
<=> class_Orderings_Owellorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_7])]) ).
fof(f16939,plain,
class_Orderings_Owellorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5102]) ).
fof(f5102,axiom,
class_Orderings_Owellorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29267,plain,
spl647_6,
inference(avatar_split_clause,[],[f16938,f29264]) ).
fof(f29264,plain,
( spl647_6
<=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_6])]) ).
fof(f16938,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5018]) ).
fof(f5018,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29262,plain,
spl647_5,
inference(avatar_split_clause,[],[f16937,f29259]) ).
fof(f29259,plain,
( spl647_5
<=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_5])]) ).
fof(f16937,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5020]) ).
fof(f5020,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29257,plain,
spl647_4,
inference(avatar_split_clause,[],[f16936,f29254]) ).
fof(f29254,plain,
( spl647_4
<=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_4])]) ).
fof(f16936,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5007]) ).
fof(f5007,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29252,plain,
spl647_3,
inference(avatar_split_clause,[],[f16935,f29249]) ).
fof(f29249,plain,
( spl647_3
<=> class_Groups_Oabs__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_3])]) ).
fof(f16935,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(cnf_transformation,[],[f5065]) ).
fof(f5065,axiom,
class_Groups_Oabs__if(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29247,plain,
spl647_2,
inference(avatar_split_clause,[],[f16934,f29244]) ).
fof(f29244,plain,
( spl647_2
<=> class_Rings_Oordered__ring__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_2])]) ).
fof(f16934,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f5033]) ).
fof(f5033,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29242,plain,
~ spl647_1,
inference(avatar_split_clause,[],[f16933,f29239]) ).
fof(f29239,plain,
( spl647_1
<=> hBOOL(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl647_1])]) ).
fof(f16933,plain,
~ hBOOL(c_fFalse),
inference(cnf_transformation,[],[f5211]) ).
fof(f5211,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW394+1 : TPTP v8.2.0. Released v5.2.0.
% 0.11/0.12 % Command : run_vampire %s %d SAT
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 04:54:39 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.18/0.35 Running first-order model finding
% 0.18/0.35 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc_sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.47/0.66 % (25439)Running in auto input_syntax mode. Trying TPTP
% 0.47/0.66 % (25446)ott-4_1:1_sil=4000:sp=reverse_arity:lcm=predicate:newcnf=on:i=115:bce=on:fd=off:fs=off:fsr=off_0 on theBenchmark for (2999ds/115Mi)
% 0.47/0.68 % (25439)Running in auto input_syntax mode. Trying TPTP
% 0.47/0.68 % (25444)ott+21_1:1_sil=4000:i=104:fsd=on:fd=off:newcnf=on_0 on theBenchmark for (2999ds/104Mi)
% 0.47/0.68 % (25439)Running in auto input_syntax mode. Trying TPTP
% 0.47/0.68 % (25443)fmb+10_1:1_sil=256000:fmbss=23:fmbes=contour:newcnf=on:fmbsr=1.14:i=152523:nm=2:gsp=on:rp=on_0 on theBenchmark for (2999ds/152523Mi)
% 0.47/0.68 % (25439)Running in auto input_syntax mode. Trying TPTP
% 0.47/0.68 % (25445)ott+11_8:59_sil=16000:sp=occurrence:lsd=20:abs=on:i=146:aac=none:nm=16:fdi=10:rawr=on:nicw=on_0 on theBenchmark for (2999ds/146Mi)
% 0.47/0.68 % (25439)Running in auto input_syntax mode. Trying TPTP
% 0.47/0.68 % (25442)fmb+10_1:1_sil=256000:fmbes=contour:i=214858:bce=on_0 on theBenchmark for (2999ds/214858Mi)
% 0.47/0.68 % (25439)Running in auto input_syntax mode. Trying TPTP
% 0.47/0.68 % (25440)fmb+10_1:1_sil=256000:i=98885:tgt=full:fmbsr=1.3:fmbss=10_0 on theBenchmark for (2999ds/98885Mi)
% 0.47/0.68 % (25439)Running in auto input_syntax mode. Trying TPTP
% 0.47/0.68 % (25441)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency:i=99418_0 on theBenchmark for (2999ds/99418Mi)
% 0.47/0.69 % (25446)Instruction limit reached!
% 0.47/0.69 % (25446)------------------------------
% 0.47/0.69 % (25446)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.47/0.69 % (25446)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.47/0.69 % (25446)Termination reason: Time limit
% 0.47/0.69 % (25446)Termination phase: NewCNF
% 0.47/0.69
% 0.47/0.69 % (25446)Memory used [KB]: 12152
% 0.47/0.69 % (25446)Time elapsed: 0.037 s
% 0.47/0.69 % (25446)Instructions burned: 115 (million)
% 0.47/0.73 % (25439)Running in auto input_syntax mode. Trying TPTP
% 0.47/0.73 % (25447)dis+11_1:3_bsr=unit_only:sil=2000:rp=on:newcnf=on:i=404:kws=precedence:lsd=100_0 on theBenchmark for (2999ds/404Mi)
% 0.52/0.74 % (25444)Instruction limit reached!
% 0.52/0.74 % (25444)------------------------------
% 0.52/0.74 % (25444)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.52/0.74 % (25444)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.52/0.74 % (25444)Termination reason: Time limit
% 0.52/0.74 % (25444)Termination phase: NewCNF
% 0.52/0.74
% 0.52/0.74 % (25444)Memory used [KB]: 11668
% 0.52/0.74 % (25444)Time elapsed: 0.062 s
% 0.52/0.74 % (25444)Instructions burned: 105 (million)
% 0.52/0.76 % (25445)Instruction limit reached!
% 0.52/0.76 % (25445)------------------------------
% 0.52/0.76 % (25445)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.52/0.76 % (25445)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.52/0.76 % (25445)Termination reason: Time limit
% 0.52/0.76 % (25445)Termination phase: Preprocessing 3
% 0.52/0.76
% 0.52/0.76 % (25445)Memory used [KB]: 11945
% 0.52/0.76 % (25445)Time elapsed: 0.080 s
% 0.52/0.76 % (25445)Instructions burned: 146 (million)
% 0.52/0.79 % (25439)Running in auto input_syntax mode. Trying TPTP
% 0.52/0.79 % (25448)ott-21_1:1_sil=4000:sp=const_frequency:i=175:fsr=off:fs=off:av=off_0 on theBenchmark for (2998ds/175Mi)
% 0.78/0.80 % (25439)Running in auto input_syntax mode. Trying TPTP
% 0.78/0.80 % (25449)ott+33_1:1_to=lpo:sil=8000:sp=weighted_frequency:rp=on:i=270:nm=3:fsr=off:sac=on_0 on theBenchmark for (2998ds/270Mi)
% 0.78/0.84 % (25447)Instruction limit reached!
% 0.78/0.84 % (25447)------------------------------
% 0.78/0.84 % (25447)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.78/0.84 % (25447)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.78/0.84 % (25447)Termination reason: Time limit
% 0.78/0.84 % (25447)Termination phase: Property scanning
% 0.78/0.84
% 0.78/0.84 % (25447)Memory used [KB]: 14906
% 0.78/0.84 % (25447)Time elapsed: 0.109 s
% 0.78/0.84 % (25447)Instructions burned: 408 (million)
% 0.78/0.84 % (25448)Instruction limit reached!
% 0.78/0.84 % (25448)------------------------------
% 0.78/0.84 % (25448)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.78/0.84 % (25448)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.78/0.84 % (25448)Termination reason: Time limit
% 0.78/0.84 % (25448)Termination phase: Preprocessing 3
% 0.78/0.84
% 0.78/0.84 % (25448)Memory used [KB]: 12595
% 0.78/0.84 % (25448)Time elapsed: 0.059 s
% 0.78/0.84 % (25448)Instructions burned: 175 (million)
% 1.04/0.87 % (25439)Running in auto input_syntax mode. Trying TPTP
% 1.04/0.87 % (25450)ott+4_1:1_sil=2000:i=900:bd=off:fsr=off_0 on theBenchmark for (2997ds/900Mi)
% 1.04/0.88 % (25439)Running in auto input_syntax mode. Trying TPTP
% 1.04/0.88 % (25451)fmb+10_1:1_sil=8000:fde=unused:fmbes=contour:i=7859:nm=2:fmbswr=0_0 on theBenchmark for (2997ds/7859Mi)
% 1.04/0.89 % (25449)Instruction limit reached!
% 1.04/0.89 % (25449)------------------------------
% 1.04/0.89 % (25449)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.04/0.89 % (25449)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.04/0.89 % (25449)Termination reason: Time limit
% 1.04/0.89 % (25449)Termination phase: Property scanning
% 1.04/0.89
% 1.04/0.89 % (25449)Memory used [KB]: 14456
% 1.04/0.89 % (25449)Time elapsed: 0.088 s
% 1.04/0.89 % (25449)Instructions burned: 270 (million)
% 1.16/0.93 % (25439)Running in auto input_syntax mode. Trying TPTP
% 1.16/0.93 % (25452)ott+11_1:2_anc=none:sil=2000:sp=const_max:spb=units:s2a=on:i=2145:s2at=5.0:awrs=converge:awrsf=170:rawr=on:gs=on:fsr=off_0 on theBenchmark for (2997ds/2145Mi)
% 1.16/1.11 % (25450)Instruction limit reached!
% 1.16/1.11 % (25450)------------------------------
% 1.16/1.11 % (25450)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.16/1.11 % (25450)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.16/1.11 % (25450)Termination reason: Time limit
% 1.16/1.11 % (25450)Termination phase: Saturation
% 1.16/1.11
% 1.16/1.11 % (25450)Memory used [KB]: 17058
% 1.16/1.11 % (25450)Time elapsed: 0.240 s
% 1.16/1.11 % (25450)Instructions burned: 902 (million)
% 1.16/1.14 % (25439)Running in auto input_syntax mode. Trying TPTP
% 1.16/1.14 % (25453)ott-30_1:1024_sil=4000:alpa=true:newcnf=on:i=1187:bs=unit_only:ins=1:amm=off_0 on theBenchmark for (2995ds/1187Mi)
% 6.29/1.50 % (25453)Instruction limit reached!
% 6.29/1.50 % (25453)------------------------------
% 6.29/1.50 % (25453)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 6.29/1.50 % (25453)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 6.29/1.50 % (25453)Termination reason: Time limit
% 6.29/1.50 % (25453)Termination phase: Saturation
% 6.29/1.50
% 6.29/1.50 % (25453)Memory used [KB]: 21216
% 6.29/1.50 % (25453)Time elapsed: 0.361 s
% 6.29/1.50 % (25453)Instructions burned: 1190 (million)
% 6.71/1.54 % (25439)Running in auto input_syntax mode. Trying TPTP
% 6.71/1.54 % (25454)fmb+10_1:1_sil=32000:i=23580:newcnf=on_0 on theBenchmark for (2991ds/23580Mi)
% 6.71/1.61 % (25452)Instruction limit reached!
% 6.71/1.61 % (25452)------------------------------
% 6.71/1.61 % (25452)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 6.71/1.61 % (25452)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 6.71/1.61 % (25452)Termination reason: Time limit
% 6.71/1.61 % (25452)Termination phase: Saturation
% 6.71/1.61
% 6.71/1.61 % (25452)Memory used [KB]: 30298
% 6.71/1.61 % (25452)Time elapsed: 0.684 s
% 6.71/1.61 % (25452)Instructions burned: 2146 (million)
% 7.24/1.64 % (25439)Running in auto input_syntax mode. Trying TPTP
% 7.24/1.64 % (25455)fmb+10_1:1_sil=32000:fmbss=17:fmbsr=2.0:i=2892_0 on theBenchmark for (2990ds/2892Mi)
% 8.74/1.88 % (25441)First to succeed.
% 9.36/1.94 % (25441)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-25439"
% 9.36/1.95 % (25439)Running in auto input_syntax mode. Trying TPTP
% 9.36/1.95 % (25441)Refutation found. Thanks to Tanya!
% 9.36/1.95 % SZS status Theorem for theBenchmark
% 9.36/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 9.69/1.99 % (25441)------------------------------
% 9.69/1.99 % (25441)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 9.69/1.99 % (25441)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 9.69/1.99 % (25441)Termination reason: Refutation
% 9.69/1.99
% 9.69/1.99 % (25441)Memory used [KB]: 34293
% 9.69/1.99 % (25441)Time elapsed: 1.260 s
% 9.69/1.99 % (25441)Instructions burned: 3810 (million)
% 9.69/1.99 % (25441)------------------------------
% 9.69/1.99 % (25441)------------------------------
% 9.69/1.99 % (25439)Success in time 1.372 s
%------------------------------------------------------------------------------