TSTP Solution File: SWW298+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW298+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 17:30:32 EDT 2024
% Result : Theorem 12.44s 2.54s
% Output : Refutation 13.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2443
% Syntax : Number of formulae : 7167 (2841 unt; 0 def)
% Number of atoms : 16425 (4304 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 14182 (4924 ~;4656 |;1863 &)
% (1766 <=>; 973 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 1464 (1462 usr;1271 prp; 0-6 aty)
% Number of functors : 342 ( 342 usr; 35 con; 0-5 aty)
% Number of variables : 11281 (10768 !; 513 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f45591,plain,
$false,
inference(avatar_sat_refutation,[],[f29299,f29304,f29309,f29314,f29319,f29324,f29329,f29334,f29339,f29344,f29349,f29354,f29359,f29364,f29369,f29374,f29379,f29384,f29389,f29394,f29399,f29404,f29409,f29414,f29419,f29424,f29429,f29434,f29439,f29444,f29449,f29454,f29459,f29464,f29469,f29474,f29479,f29484,f29489,f29494,f29499,f29504,f29509,f29514,f29519,f29524,f29529,f29534,f29539,f29544,f29549,f29554,f29559,f29564,f29569,f29574,f29579,f29584,f29589,f29594,f29599,f29604,f29609,f29614,f29619,f29624,f29629,f29634,f29639,f29644,f29649,f29654,f29659,f29664,f29669,f29674,f29679,f29684,f29689,f29694,f29699,f29704,f29709,f29714,f29719,f29724,f29729,f29734,f29739,f29744,f29749,f29754,f29759,f29764,f29769,f29774,f29779,f29784,f29789,f29794,f29799,f29804,f29809,f29814,f29819,f29824,f29829,f29834,f29839,f29844,f29849,f29854,f29859,f29864,f29869,f29874,f29879,f29884,f29889,f29894,f29899,f29904,f29909,f29914,f29919,f29924,f29929,f29934,f29939,f29944,f29949,f29954,f29959,f29964,f29969,f29974,f29979,f29984,f29989,f29994,f29999,f30004,f30009,f30014,f30019,f30024,f30029,f30034,f30039,f30044,f30049,f30054,f30059,f30064,f30069,f30074,f30079,f30084,f30089,f30094,f30099,f30104,f30109,f30114,f30119,f30124,f30129,f30134,f30139,f30144,f30149,f30154,f30159,f30164,f30169,f30174,f30179,f30184,f30189,f30194,f30199,f30204,f30209,f30214,f30219,f30224,f30229,f30234,f30239,f30244,f30249,f30254,f30259,f30264,f30270,f30275,f30280,f30285,f30289,f30293,f30297,f30301,f30305,f30309,f30314,f30318,f30323,f30328,f30333,f30338,f30343,f30347,f30351,f30355,f30359,f30363,f30368,f30373,f30378,f30383,f30389,f30394,f30399,f30404,f30409,f30414,f30419,f30423,f30427,f30431,f30435,f30439,f30443,f30447,f30451,f30455,f30459,f30463,f30467,f30471,f30475,f30479,f30484,f30488,f30492,f30496,f30501,f30506,f30511,f30516,f30521,f30526,f30531,f30535,f30539,f30544,f30548,f30552,f30556,f30560,f30564,f30568,f30572,f30576,f30580,f30584,f30588,f30592,f30596,f30600,f30604,f30608,f30612,f30616,f30620,f30624,f30628,f30632,f30636,f30640,f30644,f30648,f30652,f30656,f30660,f30664,f30668,f30672,f30676,f30680,f30684,f30688,f30692,f30696,f30700,f30704,f30708,f30712,f30716,f30720,f30724,f30728,f30733,f30738,f30743,f30748,f30752,f30756,f30760,f30764,f30768,f30772,f30777,f30781,f30785,f30795,f30800,f30820,f30826,f30832,f30837,f30842,f30847,f30852,f30857,f30862,f30867,f30872,f30877,f30883,f30888,f30893,f30897,f30901,f30905,f30909,f30913,f30917,f30921,f30925,f30929,f30933,f30937,f30941,f30945,f30949,f30953,f30957,f30961,f30965,f30969,f30973,f30977,f30981,f30985,f30989,f30993,f30997,f31001,f31005,f31009,f31013,f31017,f31021,f31025,f31030,f31034,f31038,f31042,f31046,f31050,f31054,f31058,f31062,f31066,f31070,f31075,f31079,f31084,f31089,f31094,f31099,f31104,f31109,f31113,f31117,f31122,f31129,f31135,f31154,f31159,f31164,f31168,f31172,f31176,f31180,f31184,f31188,f31192,f31196,f31200,f31204,f31208,f31212,f31216,f31220,f31224,f31228,f31232,f31236,f31241,f31245,f31249,f31253,f31257,f31261,f31265,f31269,f31273,f31277,f31282,f31286,f31290,f31294,f31298,f31302,f31306,f31310,f31314,f31318,f31322,f31326,f31330,f31334,f31338,f31342,f31346,f31350,f31354,f31358,f31363,f31367,f31371,f31375,f31379,f31383,f31387,f31391,f31395,f31399,f31403,f31408,f31412,f31416,f31421,f31425,f31429,f31433,f31437,f31442,f31447,f31452,f31457,f31461,f31465,f31469,f31473,f31477,f31481,f31485,f31489,f31493,f31497,f31502,f31515,f31526,f31538,f31543,f31554,f31559,f31563,f31567,f31572,f31576,f31580,f31584,f31588,f31593,f31597,f31601,f31605,f31609,f31613,f31617,f31621,f31625,f31629,f31634,f31638,f31642,f31646,f31650,f31654,f31658,f31662,f31666,f31670,f31675,f31679,f31683,f31687,f31691,f31695,f31699,f31703,f31707,f31711,f31715,f31719,f31723,f31727,f31731,f31735,f31739,f31743,f31747,f31751,f31755,f31759,f31763,f31767,f31771,f31775,f31779,f31783,f31787,f31791,f31795,f31799,f31804,f31808,f31812,f31816,f31820,f31824,f31828,f31832,f31836,f31841,f31845,f31849,f31854,f31859,f31863,f31867,f31871,f31875,f31879,f31883,f31887,f31891,f31895,f31899,f31903,f31908,f31912,f31916,f31920,f31924,f31928,f31932,f31936,f31940,f31944,f31948,f31952,f31956,f31960,f31965,f31969,f31973,f31977,f31981,f31985,f31995,f32023,f32064,f32214,f32240,f32245,f32250,f32255,f32259,f32263,f32267,f32274,f32278,f32282,f32286,f32290,f32294,f32298,f32302,f32306,f32310,f32314,f32318,f32322,f32326,f32330,f32334,f32338,f32342,f32346,f32350,f32354,f32358,f32362,f32366,f32370,f32374,f32378,f32382,f32386,f32390,f32394,f32398,f32402,f32406,f32410,f32414,f32418,f32422,f32426,f32430,f32434,f32438,f32442,f32446,f32450,f32454,f32458,f32462,f32466,f32470,f32474,f32478,f32482,f32486,f32490,f32494,f32498,f32502,f32506,f32510,f32514,f32518,f32522,f32526,f32530,f32534,f32538,f32542,f32546,f32550,f32554,f32558,f32562,f32566,f32570,f32574,f32578,f32582,f32586,f32590,f32594,f32598,f32602,f32606,f32610,f32614,f32618,f32622,f32626,f32630,f32634,f32638,f32642,f32646,f32651,f32657,f32662,f32668,f32674,f32681,f32686,f32691,f32695,f32699,f32703,f32707,f32711,f32715,f32719,f32723,f32727,f32731,f32735,f32740,f32744,f32748,f32752,f32756,f32760,f32764,f32768,f32772,f32776,f32780,f32785,f32789,f32793,f32797,f32801,f32805,f32809,f32813,f32817,f32821,f32825,f32829,f32833,f32842,f32883,f32916,f33484,f33606,f33713,f33739,f33758,f33762,f33766,f33770,f33774,f33778,f33782,f33786,f33790,f33794,f33798,f33802,f33806,f33810,f33814,f33818,f33822,f33828,f33832,f33836,f33840,f33844,f33848,f33852,f33856,f33860,f33864,f33868,f33872,f33876,f33880,f33884,f33888,f33892,f33896,f33900,f33904,f33908,f33913,f33917,f33921,f33925,f33929,f33933,f33937,f33941,f33945,f33949,f33953,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,f34283,f34287,f34291,f34295,f34299,f34303,f34308,f34314,f34323,f34329,f34333,f34337,f34341,f34345,f34349,f34353,f34357,f34362,f34371,f34375,f34379,f34383,f34387,f34392,f34397,f34401,f34405,f34409,f34413,f34417,f34421,f34425,f34429,f34433,f34437,f34441,f34445,f34449,f34453,f34457,f34461,f34465,f34469,f34473,f34477,f34481,f34485,f34489,f34493,f34497,f34501,f34505,f34509,f34513,f34517,f34521,f34526,f34530,f34534,f34538,f34542,f34546,f34550,f34554,f34558,f34562,f34566,f34570,f34628,f34670,f35044,f35085,f35369,f35766,f36236,f36608,f36936,f37098,f37404,f37612,f37625,f37629,f37633,f37637,f37641,f37645,f37649,f37653,f37657,f37665,f37669,f37673,f37677,f37681,f37685,f37689,f37693,f37697,f37701,f37705,f37709,f37714,f37719,f37723,f37727,f37731,f37735,f37739,f37743,f37747,f37751,f37755,f37759,f37763,f37767,f37771,f37775,f37779,f37783,f37787,f37791,f37799,f37803,f37807,f37811,f37815,f37819,f37823,f37827,f37831,f37835,f37844,f37848,f37852,f37856,f37860,f37864,f37868,f37872,f37876,f37880,f37885,f37889,f37893,f37897,f37901,f37905,f37909,f37913,f37917,f37921,f37925,f37933,f37937,f37941,f37945,f37949,f37953,f37957,f37961,f37965,f37969,f37973,f37977,f37982,f37986,f37990,f37994,f37998,f38002,f38006,f38010,f38014,f38019,f38023,f38027,f38031,f38036,f38040,f38044,f38048,f38052,f38056,f38060,f38069,f38074,f38078,f38082,f38086,f38090,f38094,f38098,f38102,f38111,f38115,f38119,f38123,f38127,f38131,f38135,f38139,f38143,f38147,f38152,f38156,f38160,f38164,f38168,f38172,f38176,f38180,f38185,f38456,f38640,f39017,f39283,f39404,f39405,f39898,f40158,f40826,f40878,f40892,f40896,f40900,f40904,f40908,f40912,f40916,f40920,f40924,f40928,f40933,f40937,f40941,f40945,f40949,f40953,f40957,f40961,f40965,f40969,f40973,f40977,f40981,f40985,f40989,f40993,f40997,f41001,f41005,f41009,f41013,f41018,f41022,f41026,f41030,f41034,f41038,f41042,f41046,f41050,f41054,f41058,f41065,f41069,f41073,f41077,f41081,f41085,f41089,f41093,f41097,f41101,f41106,f41110,f41114,f41118,f41122,f41126,f41130,f41134,f41138,f41142,f41146,f41152,f41156,f41160,f41164,f41168,f41172,f41176,f41180,f41184,f41188,f41192,f41196,f41200,f41204,f41208,f41212,f41216,f41220,f41224,f41228,f41232,f41237,f41241,f41245,f41249,f41253,f41257,f41261,f41265,f41269,f41273,f41277,f41281,f41285,f41289,f41293,f41297,f41301,f41305,f41309,f41313,f41317,f41321,f41325,f41329,f41333,f41337,f41341,f41345,f41349,f41353,f41357,f41372,f41378,f41398,f41402,f41406,f41410,f41414,f41418,f41422,f41436,f41440,f41444,f41448,f41452,f41456,f41460,f41464,f41468,f41472,f41487,f41491,f41495,f41499,f41503,f41570,f42151,f42728,f42785,f42883,f45021,f45142,f45460,f45467,f45471,f45475,f45479,f45483,f45487,f45491,f45495,f45499,f45503,f45508,f45512,f45516,f45520,f45524,f45528,f45532,f45536,f45540,f45544,f45548,f45553,f45557,f45561,f45565,f45569,f45573,f45577,f45581,f45585,f45589,f45590]) ).
fof(f45590,plain,
( spl635_1
| ~ spl635_663
| ~ spl635_1250 ),
inference(avatar_split_clause,[],[f45549,f45505,f32540,f29296]) ).
fof(f29296,plain,
( spl635_1
<=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK89) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1])]) ).
fof(f32540,plain,
( spl635_663
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_663])]) ).
fof(f45505,plain,
( spl635_1250
<=> c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),sK89) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1250])]) ).
fof(f45549,plain,
( c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK89)
| ~ spl635_663
| ~ spl635_1250 ),
inference(resolution,[],[f45507,f32541]) ).
fof(f32541,plain,
( ! [X2,X0,X1] :
( ~ c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0)
| c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0) )
| ~ spl635_663 ),
inference(avatar_component_clause,[],[f32540]) ).
fof(f45507,plain,
( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),sK89)
| ~ spl635_1250 ),
inference(avatar_component_clause,[],[f45505]) ).
fof(f45589,plain,
spl635_1270,
inference(avatar_split_clause,[],[f18418,f45587]) ).
fof(f45587,plain,
( spl635_1270
<=> ! [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,[spl635_1270])]) ).
fof(f18418,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,[],[f10566]) ).
fof(f10566,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,[],[f6188]) ).
fof(f6188,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,[],[f1049]) ).
fof(f1049,axiom,
! [X33,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hAPP(c_Groups_Oabs__class_Oabs(X5),X33) = hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__cancel) ).
fof(f45585,plain,
spl635_1269,
inference(avatar_split_clause,[],[f18417,f45583]) ).
fof(f45583,plain,
( spl635_1269
<=> ! [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,[spl635_1269])]) ).
fof(f18417,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,[],[f10565]) ).
fof(f10565,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,[],[f6187]) ).
fof(f6187,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,[],[f1039]) ).
fof(f1039,axiom,
! [X33,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hAPP(c_Groups_Oabs__class_Oabs(X5),X33) = hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__idempotent) ).
fof(f45581,plain,
spl635_1268,
inference(avatar_split_clause,[],[f18402,f45579]) ).
fof(f45579,plain,
( spl635_1268
<=> ! [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,[spl635_1268])]) ).
fof(f18402,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,[],[f10551]) ).
fof(f10551,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,[],[f6175]) ).
fof(f6175,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,[],[f345]) ).
fof(f345,axiom,
! [X4,X5] :
( class_Rings_Oring__1(X5)
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X4) = hAPP(c_Int_Oring__1__class_Oof__int(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__of__nat__eq) ).
fof(f45577,plain,
spl635_1267,
inference(avatar_split_clause,[],[f18382,f45575]) ).
fof(f45575,plain,
( spl635_1267
<=> ! [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,[spl635_1267])]) ).
fof(f18382,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,[],[f10537]) ).
fof(f10537,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,[],[f6161]) ).
fof(f6161,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,[],[f483]) ).
fof(f483,axiom,
! [X33,X5] :
( class_Groups_Ogroup__add(X5)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),c_Groups_Ozero__class_Ozero(X5)),X33) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0) ).
fof(f45573,plain,
spl635_1266,
inference(avatar_split_clause,[],[f18381,f45571]) ).
fof(f45571,plain,
( spl635_1266
<=> ! [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,[spl635_1266])]) ).
fof(f18381,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,[],[f10536]) ).
fof(f10536,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,[],[f6160]) ).
fof(f6160,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,[],[f486]) ).
fof(f486,axiom,
! [X33,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X33)),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_left__minus) ).
fof(f45569,plain,
spl635_1265,
inference(avatar_split_clause,[],[f18380,f45567]) ).
fof(f45567,plain,
( spl635_1265
<=> ! [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,[spl635_1265])]) ).
fof(f18380,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,[],[f10535]) ).
fof(f10535,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,[],[f6159]) ).
fof(f6159,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,[],[f484]) ).
fof(f484,axiom,
! [X33,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X33),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_right__minus) ).
fof(f45565,plain,
spl635_1264,
inference(avatar_split_clause,[],[f18352,f45563]) ).
fof(f45563,plain,
( spl635_1264
<=> ! [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,[spl635_1264])]) ).
fof(f18352,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,[],[f10516]) ).
fof(f10516,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,[],[f6142]) ).
fof(f6142,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,[],[f487]) ).
fof(f487,axiom,
! [X33,X5] :
( class_Groups_Oab__group__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X33)),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ab__left__minus) ).
fof(f45561,plain,
spl635_1263,
inference(avatar_split_clause,[],[f18327,f45559]) ).
fof(f45559,plain,
( spl635_1263
<=> ! [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,[spl635_1263])]) ).
fof(f18327,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,[],[f6120]) ).
fof(f6120,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,[],[f158]) ).
fof(f158,axiom,
! [X4,X24] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X24))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
fof(f45557,plain,
spl635_1262,
inference(avatar_split_clause,[],[f18326,f45555]) ).
fof(f45555,plain,
( spl635_1262
<=> ! [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,[spl635_1262])]) ).
fof(f18326,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,[],[f6119]) ).
fof(f6119,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,[],[f332]) ).
fof(f332,axiom,
! [X59,X31] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X59),X31))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X31),X59)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__linear) ).
fof(f45553,plain,
spl635_1261,
inference(avatar_split_clause,[],[f18308,f45551]) ).
fof(f45551,plain,
( spl635_1261
<=> ! [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,[spl635_1261])]) ).
fof(f18308,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,[],[f10497]) ).
fof(f10497,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,[],[f10496]) ).
fof(f10496,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,[],[f6105]) ).
fof(f6105,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,[],[f1472]) ).
fof(f1472,axiom,
! [X42,X34] :
( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X42),X34))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X34),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
=> c_Random_Olog(X34,X42) = 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(X34,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X42),X34))) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X42),X34))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),X34),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Olog(X34,X42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_log_Osimps) ).
fof(f45548,plain,
spl635_1260,
inference(avatar_split_clause,[],[f18210,f45546]) ).
fof(f45546,plain,
( spl635_1260
<=> ! [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,[spl635_1260])]) ).
fof(f18210,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,[],[f10449]) ).
fof(f10449,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,[],[f6061]) ).
fof(f6061,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,[],[f1483]) ).
fof(f1483,axiom,
! [X40,X67] :
( ( X40 != X67
=> c_Random_Oinc__shift(X67,X40) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X40),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) )
& ( X40 = X67
=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X67,X40) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inc__shift__def) ).
fof(f45544,plain,
spl635_1259,
inference(avatar_split_clause,[],[f17986,f45542]) ).
fof(f45542,plain,
( spl635_1259
<=> ! [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,[spl635_1259])]) ).
fof(f17986,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,[],[f5838]) ).
fof(f5838,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,[],[f737]) ).
fof(f737,axiom,
! [X4,X24] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X4)),hAPP(c_Nat_OSuc,X24))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__less__Suc) ).
fof(f45540,plain,
spl635_1258,
inference(avatar_split_clause,[],[f17985,f45538]) ).
fof(f45538,plain,
( spl635_1258
<=> ! [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,[spl635_1258])]) ).
fof(f17985,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,[],[f5837]) ).
fof(f5837,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,[],[f750]) ).
fof(f750,axiom,
! [X24,X42] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X42)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc2) ).
fof(f45536,plain,
spl635_1257,
inference(avatar_split_clause,[],[f17984,f45534]) ).
fof(f45534,plain,
( spl635_1257
<=> ! [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,[spl635_1257])]) ).
fof(f17984,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,[],[f5836]) ).
fof(f5836,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,[],[f749]) ).
fof(f749,axiom,
! [X24,X42] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X42),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X24)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__Suc1) ).
fof(f45532,plain,
spl635_1256,
inference(avatar_split_clause,[],[f17983,f45530]) ).
fof(f45530,plain,
( spl635_1256
<=> ! [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,[spl635_1256])]) ).
fof(f17983,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,[],[f5835]) ).
fof(f5835,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,[],[f4569]) ).
fof(f4569,axiom,
! [X247,X5] : c_List_Otranspose(X5,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),X247)) = c_List_Otranspose(X5,X247),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Osimps_I2_J) ).
fof(f45528,plain,
spl635_1255,
inference(avatar_split_clause,[],[f17980,f45526]) ).
fof(f45526,plain,
( spl635_1255
<=> ! [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,[spl635_1255])]) ).
fof(f17980,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,[],[f5832]) ).
fof(f5832,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,[],[f2073]) ).
fof(f2073,axiom,
! [X75,X77] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X75),X77) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X77,X75)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__greaterThanAtMost) ).
fof(f45524,plain,
spl635_1254,
inference(avatar_split_clause,[],[f17977,f45522]) ).
fof(f45522,plain,
( spl635_1254
<=> ! [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,[spl635_1254])]) ).
fof(f17977,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,[],[f5829]) ).
fof(f5829,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,[],[f4683]) ).
fof(f4683,axiom,
! [X208,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X208) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Orev(X5),X208)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__rev) ).
fof(f45520,plain,
spl635_1253,
inference(avatar_split_clause,[],[f17976,f45518]) ).
fof(f45518,plain,
( spl635_1253
<=> ! [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,[spl635_1253])]) ).
fof(f17976,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,[],[f5828]) ).
fof(f5828,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,[],[f4288]) ).
fof(f4288,axiom,
! [X208,X5] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),X208) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),hAPP(c_List_Orotate1(X5),X208)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__rotate1) ).
fof(f45516,plain,
spl635_1252,
inference(avatar_split_clause,[],[f17707,f45514]) ).
fof(f45514,plain,
( spl635_1252
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK97(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1252])]) ).
fof(f17707,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),sK97(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f14717]) ).
fof(f14717,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),sK97(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK97(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),sK98(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,[sK97,sK98])],[f14714,f14716,f14715]) ).
fof(f14715,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),sK97(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK97(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14716,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),sK98(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14714,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,[],[f14713]) ).
fof(f14713,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,[],[f10443]) ).
fof(f10443,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,[],[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__eq(tc_Nat_Onat),X2),X1)) ) ),
inference(rectify,[],[f2247]) ).
fof(f2247,axiom,
! [X149] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X149))
<=> ? [X37] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X2),X37)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
fof(f45512,plain,
spl635_1251,
inference(avatar_split_clause,[],[f17706,f45510]) ).
fof(f45510,plain,
( spl635_1251
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK97(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1251])]) ).
fof(f17706,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK97(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f14717]) ).
fof(f45508,plain,
( spl635_1250
| ~ spl635_2
| ~ spl635_1239 ),
inference(avatar_split_clause,[],[f45461,f45458,f29301,f45505]) ).
fof(f29301,plain,
( spl635_2
<=> hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK89),v_ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_2])]) ).
fof(f45458,plain,
( spl635_1239
<=> ! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1239])]) ).
fof(f45461,plain,
( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),sK89)
| ~ spl635_2
| ~ spl635_1239 ),
inference(resolution,[],[f45459,f29303]) ).
fof(f29303,plain,
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK89),v_ts))
| ~ spl635_2 ),
inference(avatar_component_clause,[],[f29301]) ).
fof(f45459,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts))
| c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),X0) )
| ~ spl635_1239 ),
inference(avatar_component_clause,[],[f45458]) ).
fof(f45503,plain,
spl635_1249,
inference(avatar_split_clause,[],[f17704,f45501]) ).
fof(f45501,plain,
( spl635_1249
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK95(X0,X1)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1249])]) ).
fof(f17704,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK95(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f14712]) ).
fof(f14712,plain,
! [X0] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| ! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK95(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK95(X0,X1)),X0)) ) )
& ( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),sK96(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,[sK95,sK96])],[f14709,f14711,f14710]) ).
fof(f14710,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),sK95(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK95(X0,X1)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14711,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),sK96(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X4),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14709,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,[],[f14708]) ).
fof(f14708,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,[],[f10442]) ).
fof(f10442,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,[],[f5611]) ).
fof(f5611,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,[],[f2240]) ).
fof(f2240,axiom,
! [X149] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X149))
<=> ? [X37] :
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),X149))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X37)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
fof(f45499,plain,
spl635_1248,
inference(avatar_split_clause,[],[f17703,f45497]) ).
fof(f45497,plain,
( spl635_1248
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK95(X0,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1248])]) ).
fof(f17703,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),X0))
| hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK95(X0,X1)),X0)) ),
inference(cnf_transformation,[],[f14712]) ).
fof(f45495,plain,
spl635_1247,
inference(avatar_split_clause,[],[f17677,f45493]) ).
fof(f45493,plain,
( spl635_1247
<=> ! [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,[spl635_1247])]) ).
fof(f17677,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,[],[f10435]) ).
fof(f10435,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,[],[f10434]) ).
fof(f10434,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,[],[f5597]) ).
fof(f5597,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,[],[f1124]) ).
fof(f1124,axiom,
! [X5] :
( ( class_Rings_Olinordered__idom(X5)
& class_Int_Onumber__ring(X5) )
=> c_Groups_Oone__class_Oone(X5) = hAPP(c_Groups_Oabs__class_Oabs(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OMin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__minus__one) ).
fof(f45491,plain,
spl635_1246,
inference(avatar_split_clause,[],[f17621,f45489]) ).
fof(f45489,plain,
( spl635_1246
<=> ! [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,[spl635_1246])]) ).
fof(f17621,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,[],[f10381]) ).
fof(f10381,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,[],[f5546]) ).
fof(f5546,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,[],[f1745]) ).
fof(f1745,axiom,
! [X8] :
( class_Orderings_Olinorder(X8)
=> c_Orderings_Oord__class_Omin(X8) = c_Orderings_Oord_Omax(X8,hAPP(c_COMBC(X8,X8,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dual__max) ).
fof(f45487,plain,
spl635_1245,
inference(avatar_split_clause,[],[f17620,f45485]) ).
fof(f45485,plain,
( spl635_1245
<=> ! [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,[spl635_1245])]) ).
fof(f17620,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,[],[f10380]) ).
fof(f10380,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,[],[f5545]) ).
fof(f5545,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,[],[f1732]) ).
fof(f1732,axiom,
! [X8] :
( class_Orderings_Olinorder(X8)
=> c_Orderings_Oord__class_Omax(X8) = c_Orderings_Oord_Omin(X8,hAPP(c_COMBC(X8,X8,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dual__min) ).
fof(f45483,plain,
spl635_1244,
inference(avatar_split_clause,[],[f17475,f45481]) ).
fof(f45481,plain,
( spl635_1244
<=> ! [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,[spl635_1244])]) ).
fof(f17475,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,[],[f5413]) ).
fof(f5413,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,[],[f2052]) ).
fof(f2052,axiom,
! [X39] : 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)),X39)) = X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__set__return__embed) ).
fof(f45479,plain,
spl635_1243,
inference(avatar_split_clause,[],[f17474,f45477]) ).
fof(f45477,plain,
( spl635_1243
<=> ! [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,[spl635_1243])]) ).
fof(f17474,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,[],[f5412]) ).
fof(f5412,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,[],[f3147]) ).
fof(f3147,axiom,
! [X8] : hAPP(c_Set_OPow(X8),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__UNIV) ).
fof(f45475,plain,
spl635_1242,
inference(avatar_split_clause,[],[f17470,f45473]) ).
fof(f45473,plain,
( spl635_1242
<=> ! [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,[spl635_1242])]) ).
fof(f17470,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,[],[f5408]) ).
fof(f5408,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,[],[f2745]) ).
fof(f2745,axiom,
! [X8] : c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = hAPP(c_Relation_OField(X8),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X8),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__empty) ).
fof(f45471,plain,
spl635_1241,
inference(avatar_split_clause,[],[f17469,f45469]) ).
fof(f45469,plain,
( spl635_1241
<=> ! [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,[spl635_1241])]) ).
fof(f17469,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,[],[f5407]) ).
fof(f5407,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,[],[f3164]) ).
fof(f3164,axiom,
! [X8] : c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__UNIV__eq) ).
fof(f45467,plain,
spl635_1240,
inference(avatar_split_clause,[],[f17468,f45465]) ).
fof(f45465,plain,
( spl635_1240
<=> ! [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,[spl635_1240])]) ).
fof(f17468,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,[],[f5406]) ).
fof(f5406,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,[],[f3165]) ).
fof(f3165,axiom,
! [X8] : c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Compl__empty__eq) ).
fof(f45460,plain,
spl635_1239,
inference(avatar_split_clause,[],[f16973,f45458]) ).
fof(f16973,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts)) ),
inference(cnf_transformation,[],[f10315]) ).
fof(f10315,plain,
! [X0] :
( c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts)) ),
inference(ennf_transformation,[],[f5228]) ).
fof(f5228,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),X0) ),
inference(rectify,[],[f5224]) ).
fof(f5224,axiom,
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_n),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(f45142,plain,
( spl635_1238
| ~ spl635_933
| spl635_1233 ),
inference(avatar_split_clause,[],[f44845,f42725,f34548,f45140]) ).
fof(f45140,plain,
( spl635_1238
<=> ! [X0,X1] : sP38(X0,X1,sK106(v_ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1238])]) ).
fof(f34548,plain,
( spl635_933
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP38(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_933])]) ).
fof(f42725,plain,
( spl635_1233
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK106(v_ts)),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1233])]) ).
fof(f44845,plain,
( ! [X0,X1] : sP38(X0,X1,sK106(v_ts))
| ~ spl635_933
| spl635_1233 ),
inference(resolution,[],[f42727,f34549]) ).
fof(f34549,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP38(X0,X1,X2) )
| ~ spl635_933 ),
inference(avatar_component_clause,[],[f34548]) ).
fof(f42727,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK106(v_ts)),c_Int_OPls))
| spl635_1233 ),
inference(avatar_component_clause,[],[f42725]) ).
fof(f45021,plain,
( spl635_1237
| ~ spl635_936
| spl635_1233 ),
inference(avatar_split_clause,[],[f44844,f42725,f34560,f45019]) ).
fof(f45019,plain,
( spl635_1237
<=> ! [X0,X1] : sP43(X0,X1,sK106(v_ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1237])]) ).
fof(f34560,plain,
( spl635_936
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP43(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_936])]) ).
fof(f44844,plain,
( ! [X0,X1] : sP43(X0,X1,sK106(v_ts))
| ~ spl635_936
| spl635_1233 ),
inference(resolution,[],[f42727,f34561]) ).
fof(f34561,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP43(X0,X1,X2) )
| ~ spl635_936 ),
inference(avatar_component_clause,[],[f34560]) ).
fof(f42883,plain,
( ~ spl635_1235
| spl635_1236
| ~ spl635_530
| ~ spl635_1232 ),
inference(avatar_split_clause,[],[f42258,f42148,f31761,f42880,f42876]) ).
fof(f42876,plain,
( spl635_1235
<=> sP8(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK106(v_ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1235])]) ).
fof(f42880,plain,
( spl635_1236
<=> hBOOL(sK106(v_ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1236])]) ).
fof(f31761,plain,
( spl635_530
<=> ! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP8(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_530])]) ).
fof(f42148,plain,
( spl635_1232
<=> sK106(v_ts) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,sK106(v_ts))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1232])]) ).
fof(f42258,plain,
( hBOOL(sK106(v_ts))
| ~ sP8(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK106(v_ts))
| ~ spl635_530
| ~ spl635_1232 ),
inference(superposition,[],[f31762,f42150]) ).
fof(f42150,plain,
( sK106(v_ts) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,sK106(v_ts)))
| ~ spl635_1232 ),
inference(avatar_component_clause,[],[f42148]) ).
fof(f31762,plain,
( ! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP8(X1,X0) )
| ~ spl635_530 ),
inference(avatar_component_clause,[],[f31761]) ).
fof(f42785,plain,
( spl635_1234
| ~ spl635_951
| ~ spl635_1232 ),
inference(avatar_split_clause,[],[f42252,f42148,f37623,f42782]) ).
fof(f42782,plain,
( spl635_1234
<=> sK106(v_ts) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),sK106(v_ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1234])]) ).
fof(f37623,plain,
( spl635_951
<=> ! [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,[spl635_951])]) ).
fof(f42252,plain,
( sK106(v_ts) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),sK106(v_ts))
| ~ spl635_951
| ~ spl635_1232 ),
inference(superposition,[],[f37624,f42150]) ).
fof(f37624,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))
| ~ spl635_951 ),
inference(avatar_component_clause,[],[f37623]) ).
fof(f42728,plain,
( ~ spl635_1233
| ~ spl635_706
| ~ spl635_1232 ),
inference(avatar_split_clause,[],[f42249,f42148,f32725,f42725]) ).
fof(f32725,plain,
( spl635_706
<=> ! [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,[spl635_706])]) ).
fof(f42249,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK106(v_ts)),c_Int_OPls))
| ~ spl635_706
| ~ spl635_1232 ),
inference(superposition,[],[f32726,f42150]) ).
fof(f32726,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))
| ~ spl635_706 ),
inference(avatar_component_clause,[],[f32725]) ).
fof(f42151,plain,
( spl635_1232
| ~ spl635_1052
| spl635_1123 ),
inference(avatar_split_clause,[],[f41059,f41015,f38050,f42148]) ).
fof(f38050,plain,
( spl635_1052
<=> ! [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,[spl635_1052])]) ).
fof(f41015,plain,
( spl635_1123
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,sK106(v_ts))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1123])]) ).
fof(f41059,plain,
( sK106(v_ts) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,sK106(v_ts)))
| ~ spl635_1052
| spl635_1123 ),
inference(resolution,[],[f41017,f38051]) ).
fof(f38051,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 )
| ~ spl635_1052 ),
inference(avatar_component_clause,[],[f38050]) ).
fof(f41017,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,sK106(v_ts)))
| spl635_1123 ),
inference(avatar_component_clause,[],[f41015]) ).
fof(f41570,plain,
( spl635_1231
| ~ spl635_816
| ~ spl635_1089 ),
inference(avatar_split_clause,[],[f41475,f40156,f34060,f41568]) ).
fof(f41568,plain,
( spl635_1231
<=> ! [X0] :
( ~ class_Enum_Oenum(X0)
| hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X0),sK194(c_Enum_Oenum__class_Oenum__ex(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1231])]) ).
fof(f34060,plain,
( spl635_816
<=> ! [X0,X1] :
( hBOOL(hAPP(X1,sK194(X1)))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_816])]) ).
fof(f40156,plain,
( spl635_1089
<=> ! [X0,X1] :
( ~ class_Enum_Oenum(X0)
| hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X0),c_Hilbert__Choice_OEps(X1,c_Enum_Oenum__class_Oenum__ex(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1089])]) ).
fof(f41475,plain,
( ! [X0] :
( ~ class_Enum_Oenum(X0)
| hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X0),sK194(c_Enum_Oenum__class_Oenum__ex(X0)))) )
| ~ spl635_816
| ~ spl635_1089 ),
inference(resolution,[],[f40157,f34061]) ).
fof(f34061,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| hBOOL(hAPP(X1,sK194(X1))) )
| ~ spl635_816 ),
inference(avatar_component_clause,[],[f34060]) ).
fof(f40157,plain,
( ! [X0,X1] :
( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X0),c_Hilbert__Choice_OEps(X1,c_Enum_Oenum__class_Oenum__ex(X0))))
| ~ class_Enum_Oenum(X0) )
| ~ spl635_1089 ),
inference(avatar_component_clause,[],[f40156]) ).
fof(f41503,plain,
spl635_1230,
inference(avatar_split_clause,[],[f28967,f41501]) ).
fof(f41501,plain,
( spl635_1230
<=> ! [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,[spl635_1230])]) ).
fof(f28967,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,[],[f25761,f17957]) ).
fof(f17957,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,[],[f5809]) ).
fof(f5809,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,[],[f4762]) ).
fof(f4762,axiom,
! [X13,X5] : hAPP(hAPP(c_List_Olist_OCons(X5),X13),c_List_Olist_ONil(X5)) = c_List_Oinsert(X5,X13,c_List_Olist_ONil(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__Nil) ).
fof(f25761,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,[],[f22785]) ).
fof(f22785,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,[],[f16430]) ).
fof(f16430,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,[],[f16429]) ).
fof(f16429,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,[],[f9201]) ).
fof(f9201,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,[],[f4424]) ).
fof(f4424,axiom,
! [X209,X30,X210,X8] :
( hAPP(hAPP(c_List_Oappend(X8),X210),hAPP(hAPP(c_List_Olist_OCons(X8),X30),c_List_Olist_ONil(X8))) = X209
<=> ( c_List_Olast(X8,X209) = X30
& c_List_Obutlast(X8,X209) = X210
& c_List_Olist_ONil(X8) != X209 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snoc__eq__iff__butlast) ).
fof(f41499,plain,
spl635_1229,
inference(avatar_split_clause,[],[f28793,f41497]) ).
fof(f41497,plain,
( spl635_1229
<=> ! [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,[spl635_1229])]) ).
fof(f28793,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,[],[f22277,f26500]) ).
fof(f26500,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,[],[f18026,f17832]) ).
fof(f17832,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(cnf_transformation,[],[f5684]) ).
fof(f5684,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(rectify,[],[f3373]) ).
fof(f3373,axiom,
! [X29,X8] : hAPP(c_Set_OCollect(X8),X29) = X29,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(f18026,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,[],[f5878]) ).
fof(f5878,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,[],[f3398]) ).
fof(f3398,axiom,
! [X17,X8] : hAPP(hAPP(c_Set_Oinsert(X8),X17),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X8),hAPP(c_fequal,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__conv2) ).
fof(f22277,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,[],[f16192]) ).
fof(f16192,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,[],[f16191]) ).
fof(f16191,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,[],[f13223]) ).
fof(f13223,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,[],[f8867]) ).
fof(f8867,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,[],[f2351]) ).
fof(f2351,axiom,
! [X23,X47,X17,X8] :
( class_Orderings_Oorder(X8)
=> ( c_SetInterval_Oord__class_OatLeastAtMost(X8,X17,X47) = hAPP(hAPP(c_Set_Oinsert(X8),X23),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))
<=> ( X23 = X47
& X17 = X47 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton__iff) ).
fof(f41495,plain,
spl635_1228,
inference(avatar_split_clause,[],[f28792,f41493]) ).
fof(f41493,plain,
( spl635_1228
<=> ! [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,[spl635_1228])]) ).
fof(f28792,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,[],[f22278,f26500]) ).
fof(f22278,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,[],[f16192]) ).
fof(f41491,plain,
spl635_1227,
inference(avatar_split_clause,[],[f28635,f41489]) ).
fof(f41489,plain,
( spl635_1227
<=> ! [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,[spl635_1227])]) ).
fof(f28635,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,[],[f21643,f17187]) ).
fof(f17187,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
inference(cnf_transformation,[],[f1766]) ).
fof(f1766,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I1_J) ).
fof(f21643,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,[],[f8307]) ).
fof(f8307,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,[],[f1784]) ).
fof(f1784,axiom,
! [X34,X33,X8,X5] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(X5,X8)),c_Nitpick_Opair__box_OPairBox(X5,X8,X33,X34)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Osize_I2_J) ).
fof(f41487,plain,
spl635_1226,
inference(avatar_split_clause,[],[f28501,f41485]) ).
fof(f41485,plain,
( spl635_1226
<=> ! [X2,X1] :
( ~ sP36(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,[spl635_1226])]) ).
fof(f28501,plain,
! [X2,X1] :
( ~ sP36(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,[],[f28500,f17187]) ).
fof(f28500,plain,
! [X2,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| ~ sP36(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2) ),
inference(forward_demodulation,[],[f25588,f17187]) ).
fof(f25588,plain,
! [X2,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X1)
| ~ sP36(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1,X2) ),
inference(equality_resolution,[],[f21265]) ).
fof(f21265,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
| ~ sP36(X0,X1,X2) ),
inference(cnf_transformation,[],[f15829]) ).
fof(f15829,plain,
! [X0,X1,X2] :
( ( sP36(X0,X1,X2)
| ( ~ sP35(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(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 )
| ~ sP36(X0,X1,X2) ) ),
inference(rectify,[],[f15828]) ).
fof(f15828,plain,
! [X1,X0,X2] :
( ( sP36(X1,X0,X2)
| ( ~ sP35(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(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 )
| ~ sP36(X1,X0,X2) ) ),
inference(flattening,[],[f15827]) ).
fof(f15827,plain,
! [X1,X0,X2] :
( ( sP36(X1,X0,X2)
| ( ~ sP35(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(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 )
| ~ sP36(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f14589]) ).
fof(f14589,plain,
! [X1,X0,X2] :
( sP36(X1,X0,X2)
<=> ( ( sP35(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,[sP36])]) ).
fof(f41472,plain,
spl635_1225,
inference(avatar_split_clause,[],[f28272,f41470]) ).
fof(f41470,plain,
( spl635_1225
<=> ! [X2,X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,sK258(X0,X1,X2))
| ~ sP24(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1225])]) ).
fof(f28272,plain,
! [X2,X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,sK258(X0,X1,X2))
| ~ sP24(X0,X1,X2) ),
inference(forward_demodulation,[],[f28271,f25953]) ).
fof(f25953,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17216,f17187]) ).
fof(f17216,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f404]) ).
fof(f404,axiom,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(f28271,plain,
! [X2,X0,X1] :
( hAPP(X0,sK258(X0,X1,X2)) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))
| ~ sP24(X0,X1,X2) ),
inference(forward_demodulation,[],[f20785,f17187]) ).
fof(f20785,plain,
! [X2,X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(X0,sK258(X0,X1,X2))
| ~ sP24(X0,X1,X2) ),
inference(cnf_transformation,[],[f15571]) ).
fof(f15571,plain,
! [X0,X1,X2] :
( ( sP24(X0,X1,X2)
| ! [X3] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(X0,sK257(X0,X1,X2,X3))
& sK257(X0,X1,X2,X3) != X3
& hBOOL(hAPP(hAPP(c_member(X2),sK257(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)
| sK258(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,sK258(X0,X1,X2))
& hBOOL(hAPP(hAPP(c_member(X2),sK258(X0,X1,X2)),X1)) )
| ~ sP24(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK257,sK258])],[f15568,f15570,f15569]) ).
fof(f15569,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,sK257(X0,X1,X2,X3))
& sK257(X0,X1,X2,X3) != X3
& hBOOL(hAPP(hAPP(c_member(X2),sK257(X0,X1,X2,X3)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15570,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(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(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)
| sK258(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,sK258(X0,X1,X2))
& hBOOL(hAPP(hAPP(c_member(X2),sK258(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15568,plain,
! [X0,X1,X2] :
( ( sP24(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(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(X0,X5)
& hBOOL(hAPP(hAPP(c_member(X2),X5),X1)) )
| ~ sP24(X0,X1,X2) ) ),
inference(rectify,[],[f15567]) ).
fof(f15567,plain,
! [X0,X1,X2] :
( ( sP24(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)) )
| ~ sP24(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14569]) ).
fof(f14569,plain,
! [X0,X1,X2] :
( sP24(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,[sP24])]) ).
fof(f41468,plain,
spl635_1224,
inference(avatar_split_clause,[],[f28133,f41466]) ).
fof(f41466,plain,
( spl635_1224
<=> ! [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,[spl635_1224])]) ).
fof(f28133,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,[],[f20318,f26528]) ).
fof(f26528,plain,
! [X0,X1] : hAPP(c_fequal,X0) = hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0),
inference(forward_demodulation,[],[f26527,f26500]) ).
fof(f26527,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,[],[f18115,f17832]) ).
fof(f18115,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,[],[f5967]) ).
fof(f5967,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,[],[f3397]) ).
fof(f3397,axiom,
! [X17,X8] : hAPP(hAPP(c_Set_Oinsert(X8),X17),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X8),hAPP(hAPP(c_COMBC(X8,X8,tc_HOL_Obool),c_fequal),X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singleton__conv) ).
fof(f20318,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,[],[f11722]) ).
fof(f11722,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,[],[f7538]) ).
fof(f7538,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,[],[f4652]) ).
fof(f4652,axiom,
! [X210,X0,X8] :
( class_Orderings_Olinorder(X8)
=> c_List_Olinorder__class_Osorted(X8,hAPP(c_List_Ofilter(X8,hAPP(hAPP(c_COMBC(X8,X8,tc_HOL_Obool),c_fequal),hAPP(X0,X210))),X210)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__same) ).
fof(f41464,plain,
spl635_1223,
inference(avatar_split_clause,[],[f27777,f41462]) ).
fof(f41462,plain,
( spl635_1223
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1223])]) ).
fof(f27777,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1) ),
inference(forward_demodulation,[],[f27776,f17327]) ).
fof(f17327,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(cnf_transformation,[],[f5265]) ).
fof(f5265,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(rectify,[],[f482]) ).
fof(f482,axiom,
! [X40] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X40) = X40,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(f27776,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),X0))
| c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1) ),
inference(forward_demodulation,[],[f27775,f17327]) ).
fof(f27775,plain,
! [X0,X1] :
( c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f27774,f17176]) ).
fof(f17176,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
inference(cnf_transformation,[],[f1058]) ).
fof(f1058,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(f27774,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f27773,f17327]) ).
fof(f27773,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f19559,f17327]) ).
fof(f19559,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f15291]) ).
fof(f15291,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ),
inference(nnf_transformation,[],[f6912]) ).
fof(f6912,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) ),
inference(rectify,[],[f1956]) ).
fof(f1956,axiom,
! [X35,X30] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X35)))
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X35),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdvd__iff__zmod__eq__0__number__of) ).
fof(f41460,plain,
spl635_1222,
inference(avatar_split_clause,[],[f27772,f41458]) ).
fof(f41458,plain,
( spl635_1222
<=> ! [X0,X1] :
( c_Int_OPls != c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1222])]) ).
fof(f27772,plain,
! [X0,X1] :
( c_Int_OPls != c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(forward_demodulation,[],[f27771,f17176]) ).
fof(f27771,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(forward_demodulation,[],[f27770,f17327]) ).
fof(f27770,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),X1)
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0)) ),
inference(forward_demodulation,[],[f27769,f17327]) ).
fof(f27769,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) ),
inference(forward_demodulation,[],[f27768,f17327]) ).
fof(f27768,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),X0))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) ),
inference(forward_demodulation,[],[f19560,f17327]) ).
fof(f19560,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)) ),
inference(cnf_transformation,[],[f15291]) ).
fof(f41456,plain,
spl635_1221,
inference(avatar_split_clause,[],[f27602,f41454]) ).
fof(f41454,plain,
( spl635_1221
<=> ! [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,[spl635_1221])]) ).
fof(f27602,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,[],[f27601,f17327]) ).
fof(f27601,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,[],[f19384,f17176]) ).
fof(f19384,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,[],[f15193]) ).
fof(f15193,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,[],[f15192]) ).
fof(f15192,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,[],[f14549]) ).
fof(f14549,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(f41452,plain,
spl635_1220,
inference(avatar_split_clause,[],[f27599,f41450]) ).
fof(f41450,plain,
( spl635_1220
<=> ! [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,[spl635_1220])]) ).
fof(f27599,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,[],[f27598,f17327]) ).
fof(f27598,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,[],[f27597,f17176]) ).
fof(f27597,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,[],[f19377,f17327]) ).
fof(f19377,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,[],[f15191]) ).
fof(f15191,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,[],[f15190]) ).
fof(f15190,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,[],[f6845]) ).
fof(f6845,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,[],[f450]) ).
fof(f450,axiom,
! [X70,X27] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X70)
<=> ( 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),X70)))
& hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X70)) = X27 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__iff__number__of) ).
fof(f41448,plain,
spl635_1219,
inference(avatar_split_clause,[],[f27584,f41446]) ).
fof(f41446,plain,
( spl635_1219
<=> ! [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,[spl635_1219])]) ).
fof(f27584,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,[],[f27583,f17187]) ).
fof(f27583,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,[],[f19358,f17187]) ).
fof(f19358,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,[],[f15175]) ).
fof(f15175,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,[],[f15174]) ).
fof(f15174,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,[],[f6837]) ).
fof(f6837,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,[],[f638]) ).
fof(f638,axiom,
! [X15,X27] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X15)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X15
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X27 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(f41444,plain,
spl635_1218,
inference(avatar_split_clause,[],[f27582,f41442]) ).
fof(f41442,plain,
( spl635_1218
<=> ! [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,[spl635_1218])]) ).
fof(f27582,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,[],[f27581,f17187]) ).
fof(f27581,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,[],[f19359,f17187]) ).
fof(f19359,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,[],[f15175]) ).
fof(f41440,plain,
spl635_1217,
inference(avatar_split_clause,[],[f26959,f41438]) ).
fof(f41438,plain,
( spl635_1217
<=> ! [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,[spl635_1217])]) ).
fof(f26959,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,[],[f26958]) ).
fof(f26958,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,[],[f26957,f17362]) ).
fof(f17362,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(cnf_transformation,[],[f5300]) ).
fof(f5300,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(rectify,[],[f1064]) ).
fof(f1064,axiom,
! [X40] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X40),c_Int_OPls) = X40,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).
fof(f26957,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,[],[f18504,f18014]) ).
fof(f18014,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,[],[f5866]) ).
fof(f5866,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,[],[f817]) ).
fof(f817,axiom,
! [X59,X31] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X31),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X31),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X59)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(f18504,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,[],[f14835]) ).
fof(f14835,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,[],[f10639]) ).
fof(f10639,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,[],[f6253]) ).
fof(f6253,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,[],[f1157]) ).
fof(f1157,axiom,
! [X30,X8] :
( class_Int_Onumber__ring(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = hAPP(c_Int_Onumber__class_Onumber__of(X8),X30)
<=> c_Int_Oiszero(X8,hAPP(c_Int_Onumber__class_Onumber__of(X8),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__special_I3_J) ).
fof(f41436,plain,
spl635_1216,
inference(avatar_split_clause,[],[f26640,f41434]) ).
fof(f41434,plain,
( spl635_1216
<=> ! [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,[spl635_1216])]) ).
fof(f26640,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,[],[f18230,f17187]) ).
fof(f18230,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,[],[f10458]) ).
fof(f10458,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,[],[f6070]) ).
fof(f6070,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,[],[f4501]) ).
fof(f4501,axiom,
! [X5,X4] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X4
=> c_List_Olist_ONil(tc_List_Olist(X5)) = c_Enum_On__lists(X5,X4,c_List_Olist_ONil(X5)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X4
=> hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),c_List_Olist_ONil(tc_List_Olist(X5))) = c_Enum_On__lists(X5,X4,c_List_Olist_ONil(X5)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__lists__Nil) ).
fof(f41422,plain,
spl635_1215,
inference(avatar_split_clause,[],[f26500,f41420]) ).
fof(f41420,plain,
( spl635_1215
<=> ! [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,[spl635_1215])]) ).
fof(f41418,plain,
spl635_1214,
inference(avatar_split_clause,[],[f26368,f41416]) ).
fof(f41416,plain,
( spl635_1214
<=> ! [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,[spl635_1214])]) ).
fof(f26368,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,[],[f26367,f17187]) ).
fof(f26367,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,[],[f17710,f17176]) ).
fof(f17710,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,[],[f14719]) ).
fof(f14719,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,[],[f5614]) ).
fof(f5614,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,[],[f408]) ).
fof(f408,axiom,
! [X14] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X14)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__0__iff) ).
fof(f41414,plain,
spl635_1213,
inference(avatar_split_clause,[],[f26260,f41412]) ).
fof(f41412,plain,
( spl635_1213
<=> ! [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,[spl635_1213])]) ).
fof(f26260,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,[],[f26259,f17176]) ).
fof(f26259,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,[],[f17646,f17187]) ).
fof(f17646,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,[],[f10406]) ).
fof(f10406,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,[],[f5570]) ).
fof(f5570,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,[],[f409]) ).
fof(f409,axiom,
! [X31] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X31),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__0) ).
fof(f41410,plain,
spl635_1212,
inference(avatar_split_clause,[],[f26223,f41408]) ).
fof(f41408,plain,
( spl635_1212
<=> ! [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,[spl635_1212])]) ).
fof(f26223,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,[],[f17562,f17176]) ).
fof(f17562,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,[],[f10325]) ).
fof(f10325,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,[],[f5487]) ).
fof(f5487,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,[],[f1127]) ).
fof(f1127,axiom,
! [X42] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X42),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X42) = X42 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X42),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X42) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__def) ).
fof(f41406,plain,
spl635_1211,
inference(avatar_split_clause,[],[f26111,f41404]) ).
fof(f41404,plain,
( spl635_1211
<=> ! [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,[spl635_1211])]) ).
fof(f26111,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,[],[f26110,f25953]) ).
fof(f26110,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,[],[f17481,f17187]) ).
fof(f17481,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,[],[f5419]) ).
fof(f5419,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,[],[f1485]) ).
fof(f1485,axiom,
! [X106] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,X106)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(X106)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osize_I2_J) ).
fof(f41402,plain,
spl635_1210,
inference(avatar_split_clause,[],[f26108,f41400]) ).
fof(f41400,plain,
( spl635_1210
<=> ! [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,[spl635_1210])]) ).
fof(f26108,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,[],[f17476,f17176]) ).
fof(f17476,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,[],[f5414]) ).
fof(f5414,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,[],[f784]) ).
fof(f784,axiom,
! [X4] : 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),X4))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_negative__zle__0) ).
fof(f41398,plain,
spl635_1209,
inference(avatar_split_clause,[],[f26100,f41396]) ).
fof(f41396,plain,
( spl635_1209
<=> ! [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,[spl635_1209])]) ).
fof(f26100,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,[],[f26099,f17428]) ).
fof(f17428,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,[],[f5366]) ).
fof(f5366,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,[],[f648]) ).
fof(f648,axiom,
! [X4] : hAPP(c_Nat_OSuc,X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(f26099,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,[],[f26098,f25953]) ).
fof(f26098,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,[],[f24269,f17187]) ).
fof(f24269,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,[],[f17466,f17412]) ).
fof(f17412,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,[],[f5350]) ).
fof(f5350,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,[],[f1816]) ).
fof(f1816,axiom,
! [X40] : c_Code__Numeral_OSuc__code__numeral(X40) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X40))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__code__numeral__def) ).
fof(f17466,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,[],[f5404]) ).
fof(f5404,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,[],[f1471]) ).
fof(f1471,axiom,
! [X100] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(X100)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(X100)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osize_I2_J) ).
fof(f41378,plain,
( spl635_1208
| ~ spl635_328
| ~ spl635_486
| ~ spl635_1207 ),
inference(avatar_split_clause,[],[f41373,f41369,f31582,f30869,f41375]) ).
fof(f41375,plain,
( spl635_1208
<=> 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,[spl635_1208])]) ).
fof(f30869,plain,
( spl635_328
<=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin ),
introduced(avatar_definition,[new_symbols(naming,[spl635_328])]) ).
fof(f31582,plain,
( spl635_486
<=> ! [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,[spl635_486])]) ).
fof(f41369,plain,
( spl635_1207
<=> 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,[spl635_1207])]) ).
fof(f41373,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)))
| ~ spl635_328
| ~ spl635_486
| ~ spl635_1207 ),
inference(forward_demodulation,[],[f41371,f31991]) ).
fof(f31991,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)
| ~ spl635_328
| ~ spl635_486 ),
inference(superposition,[],[f31583,f30871]) ).
fof(f30871,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin
| ~ spl635_328 ),
inference(avatar_component_clause,[],[f30869]) ).
fof(f31583,plain,
( ! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = X0
| ~ spl635_486 ),
inference(avatar_component_clause,[],[f31582]) ).
fof(f41371,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))
| ~ spl635_1207 ),
inference(avatar_component_clause,[],[f41369]) ).
fof(f41372,plain,
spl635_1207,
inference(avatar_split_clause,[],[f25996,f41369]) ).
fof(f25996,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,[],[f25995,f25953]) ).
fof(f25995,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,[],[f25994,f17187]) ).
fof(f25994,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,[],[f25993,f25942]) ).
fof(f25942,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,[],[f24210,f17174]) ).
fof(f17174,plain,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
inference(cnf_transformation,[],[f1242]) ).
fof(f1242,axiom,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__Pls) ).
fof(f24210,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,[],[f17204,f24179]) ).
fof(f24179,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,[],[f17322,f17386]) ).
fof(f17386,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(cnf_transformation,[],[f5324]) ).
fof(f5324,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(rectify,[],[f907]) ).
fof(f907,axiom,
! [X40] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X40),c_Int_OMin) = c_Int_Osucc(X40),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__bin__simps_I2_J) ).
fof(f17322,plain,
! [X0] : c_Int_OBit1(X0) = c_Int_Osucc(c_Int_OBit0(X0)),
inference(cnf_transformation,[],[f5260]) ).
fof(f5260,plain,
! [X0] : c_Int_OBit1(X0) = c_Int_Osucc(c_Int_OBit0(X0)),
inference(rectify,[],[f1274]) ).
fof(f1274,axiom,
! [X40] : c_Int_OBit1(X40) = c_Int_Osucc(c_Int_OBit0(X40)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Bit0) ).
fof(f17204,plain,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin),
inference(cnf_transformation,[],[f1204]) ).
fof(f1204,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',fact_minus__Min) ).
fof(f25993,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,[],[f24219,f17174]) ).
fof(f24219,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,[],[f17260,f24179]) ).
fof(f17260,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,[],[f1296]) ).
fof(f1296,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',fact_numeral__2__eq__2) ).
fof(f41357,plain,
spl635_1206,
inference(avatar_split_clause,[],[f25623,f41355]) ).
fof(f41355,plain,
( spl635_1206
<=> ! [X4,X0,X2] :
( hBOOL(hAPP(X0,X4))
| ~ sP48(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1206])]) ).
fof(f25623,plain,
! [X2,X0,X4] :
( hBOOL(hAPP(X0,X4))
| ~ sP48(X0,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4),X2) ),
inference(equality_resolution,[],[f21429]) ).
fof(f21429,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(X0,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),X4) != X1
| ~ sP48(X0,X1,X2) ),
inference(cnf_transformation,[],[f15949]) ).
fof(f15949,plain,
! [X0,X1,X2] :
( ( sP48(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK386(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),sK386(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)) ) )
| ~ sP48(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK386])],[f15947,f15948]) ).
fof(f15948,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,sK386(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),sK386(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f15947,plain,
! [X0,X1,X2] :
( ( sP48(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)) ) )
| ~ sP48(X0,X1,X2) ) ),
inference(rectify,[],[f15946]) ).
fof(f15946,plain,
! [X2,X1,X0] :
( ( sP48(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)) ) )
| ~ sP48(X2,X1,X0) ) ),
inference(flattening,[],[f15945]) ).
fof(f15945,plain,
! [X2,X1,X0] :
( ( sP48(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)) ) )
| ~ sP48(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14609]) ).
fof(f14609,plain,
! [X2,X1,X0] :
( sP48(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,[sP48])]) ).
fof(f41353,plain,
spl635_1205,
inference(avatar_split_clause,[],[f25622,f41351]) ).
fof(f41351,plain,
( spl635_1205
<=> ! [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,[spl635_1205])]) ).
fof(f25622,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,[],[f21421]) ).
fof(f21421,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,[],[f15943]) ).
fof(f15943,plain,
! [X0,X1,X2] :
( ( sP47(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK385(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),sK385(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,[sK385])],[f15941,f15942]) ).
fof(f15942,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,sK385(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X2),sK385(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f15941,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,[],[f15940]) ).
fof(f15940,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,[],[f15939]) ).
fof(f15939,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,[],[f14607]) ).
fof(f14607,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(f41349,plain,
spl635_1204,
inference(avatar_split_clause,[],[f25320,f41347]) ).
fof(f41347,plain,
( spl635_1204
<=> ! [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,[spl635_1204])]) ).
fof(f25320,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,[],[f18360]) ).
fof(f18360,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,[],[f14801]) ).
fof(f14801,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,[],[f10523]) ).
fof(f10523,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,[],[f6147]) ).
fof(f6147,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,[],[f593]) ).
fof(f593,axiom,
! [X17,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X17),X17)
<=> c_Groups_Ozero__class_Ozero(X8) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__zero__sym) ).
fof(f41345,plain,
spl635_1203,
inference(avatar_split_clause,[],[f25311,f41343]) ).
fof(f41343,plain,
( spl635_1203
<=> ! [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,[spl635_1203])]) ).
fof(f25311,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,[],[f18336]) ).
fof(f18336,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,[],[f14792]) ).
fof(f14792,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,[],[f14791]) ).
fof(f14791,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,[],[f10504]) ).
fof(f10504,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,[],[f6133]) ).
fof(f6133,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,[],[f707]) ).
fof(f707,axiom,
! [X30,X8] :
( class_Rings_Oring__1__no__zero__divisors(X8)
=> ( c_Groups_Oone__class_Oone(X8) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X30),X30)
<=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X8),c_Groups_Oone__class_Oone(X8)) = X30
| c_Groups_Oone__class_Oone(X8) = X30 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_square__eq__1__iff) ).
fof(f41341,plain,
spl635_1202,
inference(avatar_split_clause,[],[f24628,f41339]) ).
fof(f41339,plain,
( spl635_1202
<=> ! [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,[spl635_1202])]) ).
fof(f24628,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,[],[f19368,f17309]) ).
fof(f17309,plain,
! [X0] : c_List_Oset(X0) = c_List_Omember(X0),
inference(cnf_transformation,[],[f5247]) ).
fof(f5247,plain,
! [X0] : c_List_Oset(X0) = c_List_Omember(X0),
inference(rectify,[],[f4881]) ).
fof(f4881,axiom,
! [X8] : c_List_Oset(X8) = c_List_Omember(X8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_member__set) ).
fof(f19368,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,[],[f15186]) ).
fof(f15186,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,[],[f6841]) ).
fof(f6841,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,[],[f4117]) ).
fof(f4117,axiom,
! [X210,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = hAPP(c_List_Oset(X8),X210)
<=> c_List_Olist_ONil(X8) = X210 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__empty) ).
fof(f41337,plain,
spl635_1201,
inference(avatar_split_clause,[],[f24244,f41335]) ).
fof(f41335,plain,
( spl635_1201
<=> ! [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,[spl635_1201])]) ).
fof(f24244,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,[],[f17310,f17386,f17380]) ).
fof(f17380,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,[],[f1192]) ).
fof(f1192,axiom,
! [X40] : c_Int_Opred(X40) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X40),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Min) ).
fof(f17310,plain,
! [X0] : c_Int_Osucc(c_Int_Opred(X0)) = X0,
inference(cnf_transformation,[],[f5248]) ).
fof(f5248,plain,
! [X0] : c_Int_Osucc(c_Int_Opred(X0)) = X0,
inference(rectify,[],[f1176]) ).
fof(f1176,axiom,
! [X13] : c_Int_Osucc(c_Int_Opred(X13)) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__pred) ).
fof(f41333,plain,
spl635_1200,
inference(avatar_split_clause,[],[f24020,f41331]) ).
fof(f41331,plain,
( spl635_1200
<=> ! [X3,X4,X0,X5,X2,X1] :
( X4 = X5
| X1 = X2
| ~ sP87(X0,X1,X2,X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1200])]) ).
fof(f24020,plain,
! [X2,X3,X0,X1,X4,X5] :
( X4 = X5
| X1 = X2
| ~ sP87(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f16908]) ).
fof(f16908,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,[],[f16907]) ).
fof(f16907,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,[],[f16906]) ).
fof(f16906,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,[],[f14680]) ).
fof(f14680,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(f41329,plain,
spl635_1199,
inference(avatar_split_clause,[],[f24012,f41327]) ).
fof(f41327,plain,
( spl635_1199
<=> ! [X3,X4,X0,X5,X2,X1] :
( X4 = X5
| X2 = X3
| ~ sP86(X0,X1,X2,X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1199])]) ).
fof(f24012,plain,
! [X2,X3,X0,X1,X4,X5] :
( X4 = X5
| X2 = X3
| ~ sP86(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f16904]) ).
fof(f16904,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,[],[f16903]) ).
fof(f16903,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,[],[f16902]) ).
fof(f16902,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,[],[f14678]) ).
fof(f14678,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(f41325,plain,
spl635_1198,
inference(avatar_split_clause,[],[f23900,f41323]) ).
fof(f41323,plain,
( spl635_1198
<=> ! [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,[spl635_1198])]) ).
fof(f23900,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,[],[f14338]) ).
fof(f14338,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,[],[f9926]) ).
fof(f9926,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Typedef_Otype__definition(X5,X4,X3,X2,X1)
=> hAPP(X2,hAPP(X3,X0)) = X0 ),
inference(rectify,[],[f3261]) ).
fof(f3261,axiom,
! [X30,X39,X181,X182,X25,X8] :
( c_Typedef_Otype__definition(X8,X25,X182,X181,X39)
=> hAPP(X181,hAPP(X182,X30)) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
fof(f41321,plain,
spl635_1197,
inference(avatar_split_clause,[],[f23573,f41319]) ).
fof(f41319,plain,
( spl635_1197
<=> ! [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,[spl635_1197])]) ).
fof(f23573,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X2,X1) = X0
| c_Fun_Ofun__upd(X4,X3,X2,X1,X0) != X2 ),
inference(cnf_transformation,[],[f16717]) ).
fof(f16717,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,[],[f9731]) ).
fof(f9731,plain,
! [X0,X1,X2,X3,X4] :
( c_Fun_Ofun__upd(X4,X3,X2,X1,X0) = X2
<=> hAPP(X2,X1) = X0 ),
inference(rectify,[],[f2671]) ).
fof(f2671,axiom,
! [X35,X30,X1,X25,X8] :
( c_Fun_Ofun__upd(X8,X25,X1,X30,X35) = X1
<=> hAPP(X1,X30) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__idem__iff) ).
fof(f41317,plain,
spl635_1196,
inference(avatar_split_clause,[],[f23293,f41315]) ).
fof(f41315,plain,
( spl635_1196
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0))
| ~ sP73(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1196])]) ).
fof(f23293,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0))
| ~ sP73(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16612]) ).
fof(f16612,plain,
! [X0,X1,X2,X3,X4] :
( ( sP73(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)) ) )
| ~ sP73(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16611]) ).
fof(f16611,plain,
! [X0,X1,X4,X2,X3] :
( ( sP73(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)) ) )
| ~ sP73(X0,X1,X4,X2,X3) ) ),
inference(flattening,[],[f16610]) ).
fof(f16610,plain,
! [X0,X1,X4,X2,X3] :
( ( sP73(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)) ) )
| ~ sP73(X0,X1,X4,X2,X3) ) ),
inference(nnf_transformation,[],[f14653]) ).
fof(f14653,plain,
! [X0,X1,X4,X2,X3] :
( sP73(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,[sP73])]) ).
fof(f41313,plain,
spl635_1195,
inference(avatar_split_clause,[],[f23242,f41311]) ).
fof(f41311,plain,
( spl635_1195
<=> ! [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,[spl635_1195])]) ).
fof(f23242,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,[],[f13840]) ).
fof(f13840,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,[],[f9481]) ).
fof(f9481,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,[],[f4452]) ).
fof(f4452,axiom,
! [X210,X17,X1,X8,X25] :
( class_Orderings_Olinorder(X25)
=> c_List_Olist_ONil(X8) != hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(X8,X25,X1),X17),X210) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insort__not__Nil) ).
fof(f41309,plain,
spl635_1194,
inference(avatar_split_clause,[],[f22968,f41307]) ).
fof(f41307,plain,
( spl635_1194
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,sK513(X0,X1,X2,X3)))
| ~ sP71(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1194])]) ).
fof(f22968,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X0,sK513(X0,X1,X2,X3)))
| ~ sP71(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16557]) ).
fof(f16557,plain,
! [X0,X1,X2,X3] :
( ( sP71(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,sK513(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X3),sK513(X0,X1,X2,X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) )
| ~ sP71(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK513])],[f16555,f16556]) ).
fof(f16556,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,sK513(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X3),sK513(X0,X1,X2,X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f16555,plain,
! [X0,X1,X2,X3] :
( ( sP71(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))) )
| ~ sP71(X0,X1,X2,X3) ) ),
inference(rectify,[],[f16554]) ).
fof(f16554,plain,
! [X0,X1,X2,X3] :
( ( sP71(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))) )
| ~ sP71(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f14650]) ).
fof(f14650,plain,
! [X0,X1,X2,X3] :
( sP71(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,[sP71])]) ).
fof(f41305,plain,
spl635_1193,
inference(avatar_split_clause,[],[f22955,f41303]) ).
fof(f41303,plain,
( spl635_1193
<=> ! [X0,X3,X2,X1] :
( sP70(X0,X1,X3,X2)
| ~ hBOOL(hAPP(X0,sK509(X0,X1,X2,X3))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1193])]) ).
fof(f22955,plain,
! [X2,X3,X0,X1] :
( sP70(X0,X1,X3,X2)
| ~ hBOOL(hAPP(X0,sK509(X0,X1,X2,X3))) ),
inference(cnf_transformation,[],[f16542]) ).
fof(f16542,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))) )
| ~ sP70(X0,X1,X3,X2) )
& ( sP70(X0,X1,X3,X2)
| ( ~ hBOOL(hAPP(X0,sK509(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X3),sK509(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,[sK509])],[f16540,f16541]) ).
fof(f16541,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,sK509(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X3),sK509(X0,X1,X2,X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f16540,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))) )
| ~ sP70(X0,X1,X3,X2) )
& ( sP70(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,[],[f16539]) ).
fof(f16539,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))) )
| ~ sP70(X0,X1,X3,X2) )
& ( sP70(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,[],[f14649]) ).
fof(f14649,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))) )
<=> sP70(X0,X1,X3,X2) ),
inference(definition_folding,[],[f13647,f14648]) ).
fof(f14648,plain,
! [X0,X1,X3,X2] :
( sP70(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,[sP70])]) ).
fof(f13647,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,[],[f9247]) ).
fof(f9247,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,[],[f2110]) ).
fof(f2110,axiom,
! [X29,X38,X39,X8] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X39),X38)))
=> hBOOL(hAPP(X29,X2)) )
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X38))
=> hBOOL(hAPP(X29,X2)) )
& ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X39))
=> hBOOL(hAPP(X29,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ball__Un) ).
fof(f41301,plain,
spl635_1192,
inference(avatar_split_clause,[],[f22713,f41299]) ).
fof(f41299,plain,
( spl635_1192
<=> ! [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,[spl635_1192])]) ).
fof(f22713,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,[],[f16373]) ).
fof(f16373,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,[],[f16372]) ).
fof(f16372,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,[],[f9172]) ).
fof(f9172,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,[],[f4816]) ).
fof(f4816,axiom,
! [X210,X30,X29,X8] :
( c_List_Olist__all(X8,X29,hAPP(hAPP(c_List_Olist_OCons(X8),X30),X210))
<=> ( c_List_Olist__all(X8,X29,X210)
& hBOOL(hAPP(X29,X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__simps_I1_J) ).
fof(f41297,plain,
spl635_1191,
inference(avatar_split_clause,[],[f22712,f41295]) ).
fof(f41295,plain,
( spl635_1191
<=> ! [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,[spl635_1191])]) ).
fof(f22712,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,[],[f16373]) ).
fof(f41293,plain,
spl635_1190,
inference(avatar_split_clause,[],[f22710,f41291]) ).
fof(f41291,plain,
( spl635_1190
<=> ! [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,[spl635_1190])]) ).
fof(f22710,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,[],[f16371]) ).
fof(f16371,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,[],[f16370]) ).
fof(f16370,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,[],[f9171]) ).
fof(f9171,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,[],[f4814]) ).
fof(f4814,axiom,
! [X209,X210,X29,X8] :
( c_List_Olist__all(X8,X29,hAPP(hAPP(c_List_Oappend(X8),X210),X209))
<=> ( c_List_Olist__all(X8,X29,X209)
& c_List_Olist__all(X8,X29,X210) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__append) ).
fof(f41289,plain,
spl635_1189,
inference(avatar_split_clause,[],[f22709,f41287]) ).
fof(f41287,plain,
( spl635_1189
<=> ! [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,[spl635_1189])]) ).
fof(f22709,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,[],[f16371]) ).
fof(f41285,plain,
spl635_1188,
inference(avatar_split_clause,[],[f22708,f41283]) ).
fof(f41283,plain,
( spl635_1188
<=> ! [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,[spl635_1188])]) ).
fof(f22708,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,[],[f16369]) ).
fof(f16369,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,[],[f16368]) ).
fof(f16368,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,[],[f9170]) ).
fof(f9170,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,[],[f4806]) ).
fof(f4806,axiom,
! [X210,X30,X29,X8] :
( c_List_Olist__ex(X8,X29,hAPP(hAPP(c_List_Olist_OCons(X8),X30),X210))
<=> ( c_List_Olist__ex(X8,X29,X210)
| hBOOL(hAPP(X29,X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__simps_I1_J) ).
fof(f41281,plain,
spl635_1187,
inference(avatar_split_clause,[],[f22707,f41279]) ).
fof(f41279,plain,
( spl635_1187
<=> ! [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,[spl635_1187])]) ).
fof(f22707,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,[],[f16369]) ).
fof(f41277,plain,
spl635_1186,
inference(avatar_split_clause,[],[f22705,f41275]) ).
fof(f41275,plain,
( spl635_1186
<=> ! [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,[spl635_1186])]) ).
fof(f22705,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,[],[f16367]) ).
fof(f16367,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,[],[f16366]) ).
fof(f16366,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,[],[f9169]) ).
fof(f9169,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,[],[f4805]) ).
fof(f4805,axiom,
! [X209,X210,X29,X8] :
( c_List_Olist__ex(X8,X29,hAPP(hAPP(c_List_Oappend(X8),X210),X209))
<=> ( c_List_Olist__ex(X8,X29,X209)
| c_List_Olist__ex(X8,X29,X210) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__append) ).
fof(f41273,plain,
spl635_1185,
inference(avatar_split_clause,[],[f22704,f41271]) ).
fof(f41271,plain,
( spl635_1185
<=> ! [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,[spl635_1185])]) ).
fof(f22704,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,[],[f16367]) ).
fof(f41269,plain,
spl635_1184,
inference(avatar_split_clause,[],[f22699,f41267]) ).
fof(f41267,plain,
( spl635_1184
<=> ! [X0,X3,X2,X1] :
( sP62(X0,X1,X2,X3)
| ~ c_List_Olist__ex1(X2,X1,X0)
| hBOOL(hAPP(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1184])]) ).
fof(f22699,plain,
! [X2,X3,X0,X1] :
( sP62(X0,X1,X2,X3)
| ~ c_List_Olist__ex1(X2,X1,X0)
| hBOOL(hAPP(X1,X3)) ),
inference(cnf_transformation,[],[f16364]) ).
fof(f16364,plain,
! [X0,X1,X2,X3] :
( ( sP62(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)) ) )
| ~ sP62(X0,X1,X2,X3) ) ),
inference(rectify,[],[f16363]) ).
fof(f16363,plain,
! [X0,X2,X3,X1] :
( ( sP62(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)) ) )
| ~ sP62(X0,X2,X3,X1) ) ),
inference(flattening,[],[f16362]) ).
fof(f16362,plain,
! [X0,X2,X3,X1] :
( ( sP62(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)) ) )
| ~ sP62(X0,X2,X3,X1) ) ),
inference(nnf_transformation,[],[f14634]) ).
fof(f14634,plain,
! [X0,X2,X3,X1] :
( sP62(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,[sP62])]) ).
fof(f41265,plain,
spl635_1183,
inference(avatar_split_clause,[],[f22696,f41263]) ).
fof(f41263,plain,
( spl635_1183
<=> ! [X0,X3,X2,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| hBOOL(hAPP(X1,X3))
| ~ sP62(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1183])]) ).
fof(f22696,plain,
! [X2,X3,X0,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| hBOOL(hAPP(X1,X3))
| ~ sP62(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16364]) ).
fof(f41261,plain,
spl635_1182,
inference(avatar_split_clause,[],[f22694,f41259]) ).
fof(f41259,plain,
( spl635_1182
<=> ! [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,[spl635_1182])]) ).
fof(f22694,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
| ~ hBOOL(hAPP(X1,X0)) ),
inference(cnf_transformation,[],[f16361]) ).
fof(f16361,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,[],[f16360]) ).
fof(f16360,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,[],[f9167]) ).
fof(f9167,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
<=> ( hBOOL(hAPP(X1,X0))
| X0 = X2 ) ),
inference(rectify,[],[f2243]) ).
fof(f2243,axiom,
! [X30,X39,X35,X8] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X8),X35),X39),X30))
<=> ( hBOOL(hAPP(X39,X30))
| X30 = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).
fof(f41257,plain,
spl635_1181,
inference(avatar_split_clause,[],[f22684,f41255]) ).
fof(f41255,plain,
( spl635_1181
<=> ! [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,[spl635_1181])]) ).
fof(f22684,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(c_Predicate_ORangeP(X3,X2,X1),X0))
| ~ hBOOL(hAPP(hAPP(X1,X4),X0)) ),
inference(cnf_transformation,[],[f16355]) ).
fof(f16355,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,sK492(X0,X1)),X0))
| ~ hBOOL(hAPP(c_Predicate_ORangeP(X3,X2,X1),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK492])],[f16353,f16354]) ).
fof(f16354,plain,
! [X0,X1] :
( ? [X5] : hBOOL(hAPP(hAPP(X1,X5),X0))
=> hBOOL(hAPP(hAPP(X1,sK492(X0,X1)),X0)) ),
introduced(choice_axiom,[]) ).
fof(f16353,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,[],[f16352]) ).
fof(f16352,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,[],[f9163]) ).
fof(f9163,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Predicate_ORangeP(X3,X2,X1),X0))
<=> ? [X4] : hBOOL(hAPP(hAPP(X1,X4),X0)) ),
inference(rectify,[],[f3534]) ).
fof(f3534,axiom,
! [X153,X98,X25,X8] :
( hBOOL(hAPP(c_Predicate_ORangeP(X8,X25,X98),X153))
<=> ? [X114] : hBOOL(hAPP(hAPP(X98,X114),X153)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
fof(f41253,plain,
spl635_1180,
inference(avatar_split_clause,[],[f22682,f41251]) ).
fof(f41251,plain,
( spl635_1180
<=> ! [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,[spl635_1180])]) ).
fof(f22682,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(c_Predicate_ODomainP(X3,X2,X1),X0))
| ~ hBOOL(hAPP(hAPP(X1,X0),X4)) ),
inference(cnf_transformation,[],[f16351]) ).
fof(f16351,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),sK491(X0,X1)))
| ~ hBOOL(hAPP(c_Predicate_ODomainP(X3,X2,X1),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK491])],[f16349,f16350]) ).
fof(f16350,plain,
! [X0,X1] :
( ? [X5] : hBOOL(hAPP(hAPP(X1,X0),X5))
=> hBOOL(hAPP(hAPP(X1,X0),sK491(X0,X1))) ),
introduced(choice_axiom,[]) ).
fof(f16349,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,[],[f16348]) ).
fof(f16348,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,[],[f9162]) ).
fof(f9162,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Predicate_ODomainP(X3,X2,X1),X0))
<=> ? [X4] : hBOOL(hAPP(hAPP(X1,X0),X4)) ),
inference(rectify,[],[f3566]) ).
fof(f3566,axiom,
! [X112,X98,X25,X8] :
( hBOOL(hAPP(c_Predicate_ODomainP(X8,X25,X98),X112))
<=> ? [X65] : hBOOL(hAPP(hAPP(X98,X112),X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).
fof(f41249,plain,
spl635_1179,
inference(avatar_split_clause,[],[f22603,f41247]) ).
fof(f41247,plain,
( spl635_1179
<=> ! [X0,X3,X2,X1] :
( c_Fun_Oinj__on(X2,X3,X1,X0)
| ~ c_Orderings_Oorder__class_Ostrict__mono(X2,X3,X1)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Oorder(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1179])]) ).
fof(f22603,plain,
! [X2,X3,X0,X1] :
( c_Fun_Oinj__on(X2,X3,X1,X0)
| ~ c_Orderings_Oorder__class_Ostrict__mono(X2,X3,X1)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Oorder(X3) ),
inference(cnf_transformation,[],[f13600]) ).
fof(f13600,plain,
! [X0,X1,X2,X3] :
( c_Fun_Oinj__on(X2,X3,X1,X0)
| ~ c_Orderings_Oorder__class_Ostrict__mono(X2,X3,X1)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Oorder(X3) ),
inference(flattening,[],[f13599]) ).
fof(f13599,plain,
! [X0,X1,X2,X3] :
( c_Fun_Oinj__on(X2,X3,X1,X0)
| ~ c_Orderings_Oorder__class_Ostrict__mono(X2,X3,X1)
| ~ class_Orderings_Olinorder(X2)
| ~ class_Orderings_Oorder(X3) ),
inference(ennf_transformation,[],[f9134]) ).
fof(f9134,plain,
! [X0,X1,X2,X3] :
( ( class_Orderings_Olinorder(X2)
& class_Orderings_Oorder(X3) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(X2,X3,X1)
=> c_Fun_Oinj__on(X2,X3,X1,X0) ) ),
inference(rectify,[],[f3060]) ).
fof(f3060,axiom,
! [X39,X1,X8,X25] :
( ( class_Orderings_Olinorder(X8)
& class_Orderings_Oorder(X25) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(X8,X25,X1)
=> c_Fun_Oinj__on(X8,X25,X1,X39) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__mono__imp__inj__on) ).
fof(f41245,plain,
spl635_1178,
inference(avatar_split_clause,[],[f21646,f41243]) ).
fof(f41243,plain,
( spl635_1178
<=> ! [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,[spl635_1178])]) ).
fof(f21646,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,[],[f8310]) ).
fof(f8310,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,[],[f1599]) ).
fof(f1599,axiom,
! [X34,X33,X8,X5] : hAPP(c_Product__Type_Ofst(X5,X8),hAPP(hAPP(c_Product__Type_OPair(X5,X8),X33),X34)) = X33,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fst__conv) ).
fof(f41241,plain,
spl635_1177,
inference(avatar_split_clause,[],[f21645,f41239]) ).
fof(f41239,plain,
( spl635_1177
<=> ! [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,[spl635_1177])]) ).
fof(f21645,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,[],[f8309]) ).
fof(f8309,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,[],[f1601]) ).
fof(f1601,axiom,
! [X34,X33,X5,X8] : hAPP(c_Product__Type_Osnd(X8,X5),hAPP(hAPP(c_Product__Type_OPair(X8,X5),X33),X34)) = X34,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_snd__conv) ).
fof(f41237,plain,
( ~ spl635_1176
| ~ spl635_665
| ~ spl635_1090 ),
inference(avatar_split_clause,[],[f40882,f40823,f32548,f41234]) ).
fof(f41234,plain,
( spl635_1176
<=> sP31(sK106(v_ts),c_Int_OPls,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1176])]) ).
fof(f32548,plain,
( spl635_665
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP31(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_665])]) ).
fof(f40823,plain,
( spl635_1090
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK106(v_ts))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1090])]) ).
fof(f40882,plain,
( ~ sP31(sK106(v_ts),c_Int_OPls,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint))
| ~ spl635_665
| ~ spl635_1090 ),
inference(resolution,[],[f40825,f32549]) ).
fof(f32549,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP31(X0,X1,X2) )
| ~ spl635_665 ),
inference(avatar_component_clause,[],[f32548]) ).
fof(f40825,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK106(v_ts)))
| ~ spl635_1090 ),
inference(avatar_component_clause,[],[f40823]) ).
fof(f41232,plain,
spl635_1175,
inference(avatar_split_clause,[],[f21644,f41230]) ).
fof(f41230,plain,
( spl635_1175
<=> ! [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,[spl635_1175])]) ).
fof(f21644,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,[],[f8308]) ).
fof(f8308,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,[],[f3839]) ).
fof(f3839,axiom,
! [X53,X1,X8,X25] : hAPP(hAPP(c_Finite__Set_Ofold(X25,X8,X1),X53),c_Orderings_Obot__class_Obot(tc_fun(X25,tc_HOL_Obool))) = X53,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__empty) ).
fof(f41228,plain,
spl635_1174,
inference(avatar_split_clause,[],[f21435,f41226]) ).
fof(f41226,plain,
( spl635_1174
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
| ~ sP48(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1174])]) ).
fof(f21435,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
| ~ sP48(X2,X1,X0) ),
inference(cnf_transformation,[],[f15950]) ).
fof(f15950,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
| ~ sP48(X2,X1,X0) )
& ( sP48(X2,X1,X0)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0))) ) ),
inference(nnf_transformation,[],[f14610]) ).
fof(f14610,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0)))
<=> sP48(X2,X1,X0) ),
inference(definition_folding,[],[f12688,f14609]) ).
fof(f12688,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,[],[f8215]) ).
fof(f8215,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,[],[f551]) ).
fof(f551,axiom,
! [X47,X17,X29] :
( hBOOL(hAPP(X29,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),X47)))
<=> ~ ( ? [X74] :
( ~ hBOOL(hAPP(X29,X74))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X74) = X17 )
| ( ~ hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X47)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split__asm) ).
fof(f41224,plain,
spl635_1173,
inference(avatar_split_clause,[],[f21434,f41222]) ).
fof(f41222,plain,
( spl635_1173
<=> ! [X2,X0,X1] :
( sP48(X2,X1,X0)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1173])]) ).
fof(f21434,plain,
! [X2,X0,X1] :
( sP48(X2,X1,X0)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),X0))) ),
inference(cnf_transformation,[],[f15950]) ).
fof(f41220,plain,
spl635_1172,
inference(avatar_split_clause,[],[f21427,f41218]) ).
fof(f41218,plain,
( spl635_1172
<=> ! [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,[spl635_1172])]) ).
fof(f21427,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,[],[f15944]) ).
fof(f15944,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,[],[f14608]) ).
fof(f14608,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,[],[f12687,f14607]) ).
fof(f12687,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,[],[f8214]) ).
fof(f8214,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,[],[f550]) ).
fof(f550,axiom,
! [X47,X17,X29] :
( hBOOL(hAPP(X29,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X17),X47)))
<=> ( ! [X74] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X47),X74) = X17
=> hBOOL(hAPP(X29,X74)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X17),X47))
=> hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__diff__split) ).
fof(f41216,plain,
spl635_1171,
inference(avatar_split_clause,[],[f21426,f41214]) ).
fof(f41214,plain,
( spl635_1171
<=> ! [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,[spl635_1171])]) ).
fof(f21426,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,[],[f15944]) ).
fof(f41212,plain,
spl635_1170,
inference(avatar_split_clause,[],[f21419,f41210]) ).
fof(f41210,plain,
( spl635_1170
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
| ~ sP46(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1170])]) ).
fof(f21419,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
| ~ sP46(X2,X0,X1) ),
inference(cnf_transformation,[],[f15938]) ).
fof(f15938,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
| ( ~ sP46(X2,X0,X1)
& ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) )
& ( sP46(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,[],[f15937]) ).
fof(f15937,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
| ( ~ sP46(X2,X0,X1)
& ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) )
& ( sP46(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,[],[f14606]) ).
fof(f14606,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
<=> ( sP46(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,[],[f8213,f14605]) ).
fof(f14605,plain,
! [X2,X0,X1] :
( sP46(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,[sP46])]) ).
fof(f8213,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,[],[f1018]) ).
fof(f1018,axiom,
! [X15,X27,X29] :
( hBOOL(hAPP(X29,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X27),X15)))
<=> ( ? [X93] :
( hBOOL(hAPP(X29,X93))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X27),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),hAPP(c_Nat_OSuc,X93))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X15),X93)),X27)) )
| ( hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X15 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div_H) ).
fof(f41208,plain,
spl635_1169,
inference(avatar_split_clause,[],[f21409,f41206]) ).
fof(f41206,plain,
( spl635_1169
<=> ! [X2,X0,X1] :
( sP45(X2,X1,X0)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1169])]) ).
fof(f21409,plain,
! [X2,X0,X1] :
( sP45(X2,X1,X0)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0))) ),
inference(cnf_transformation,[],[f15932]) ).
fof(f15932,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
| ~ sP45(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP45(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,[],[f15931]) ).
fof(f15931,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
| ~ sP45(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP45(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,[],[f14604]) ).
fof(f14604,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X1),X0)))
<=> ( sP45(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,[],[f12686,f14603]) ).
fof(f14603,plain,
! [X2,X1,X0] :
( sP45(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,[sP45])]) ).
fof(f12686,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,[],[f12685]) ).
fof(f12685,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,[],[f8212]) ).
fof(f8212,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,[],[f1011]) ).
fof(f1011,axiom,
! [X48,X15,X29] :
( hBOOL(hAPP(X29,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X15),X48)))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X48
=> ! [X85,X36] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X48))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X85)),X36) = X15
=> hBOOL(hAPP(X29,X85)) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X48
=> hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__div) ).
fof(f41204,plain,
spl635_1168,
inference(avatar_split_clause,[],[f21402,f41202]) ).
fof(f41202,plain,
( spl635_1168
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)))
| ~ sP44(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1168])]) ).
fof(f21402,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)))
| ~ sP44(X0,X1,X2) ),
inference(cnf_transformation,[],[f15925]) ).
fof(f15925,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)))
| ~ sP44(X0,X1,X2) )
& ( sP44(X0,X1,X2)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0))) ) ),
inference(nnf_transformation,[],[f14602]) ).
fof(f14602,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)))
<=> sP44(X0,X1,X2) ),
inference(definition_folding,[],[f12684,f14601,f14600,f14599]) ).
fof(f14599,plain,
! [X2,X1,X0] :
( sP42(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,[sP42])]) ).
fof(f14600,plain,
! [X2,X1,X0] :
( sP43(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,[sP43])]) ).
fof(f14601,plain,
! [X0,X1,X2] :
( sP44(X0,X1,X2)
<=> ( sP43(X2,X1,X0)
& sP42(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,[sP44])]) ).
fof(f12684,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,[],[f8211]) ).
fof(f8211,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,[],[f897]) ).
fof(f897,axiom,
! [X48,X15,X29] :
( hBOOL(hAPP(X29,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15),X48)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X85] :
( ? [X36] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X85)),X36) = X15
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X36),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),X36)) )
=> hBOOL(hAPP(X29,X85)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))
=> ! [X85] :
( ? [X36] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X85)),X36) = X15
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X48))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36)) )
=> hBOOL(hAPP(X29,X85)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X48
=> hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__zdiv) ).
fof(f41200,plain,
spl635_1167,
inference(avatar_split_clause,[],[f21401,f41198]) ).
fof(f41198,plain,
( spl635_1167
<=> ! [X2,X0,X1] :
( sP44(X0,X1,X2)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1167])]) ).
fof(f21401,plain,
! [X2,X0,X1] :
( sP44(X0,X1,X2)
| ~ hBOOL(hAPP(X2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0))) ),
inference(cnf_transformation,[],[f15925]) ).
fof(f41196,plain,
spl635_1166,
inference(avatar_split_clause,[],[f21370,f41194]) ).
fof(f41194,plain,
( spl635_1166
<=> ! [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,[spl635_1166])]) ).
fof(f21370,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,[],[f15900]) ).
fof(f15900,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,[],[f15899]) ).
fof(f15899,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,[],[f8205]) ).
fof(f8205,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,[],[f4234]) ).
fof(f4234,axiom,
! [X209,X210,X8] :
( c_List_Olist_ONil(X8) = hAPP(hAPP(c_List_Oappend(X8),X210),X209)
<=> ( c_List_Olist_ONil(X8) = X209
& c_List_Olist_ONil(X8) = X210 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__is__Nil__conv) ).
fof(f41192,plain,
( spl635_1165
| ~ spl635_1071
| ~ spl635_1090 ),
inference(avatar_split_clause,[],[f40879,f40823,f38137,f41190]) ).
fof(f41190,plain,
( spl635_1165
<=> ! [X0] : c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,sK106(v_ts),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1165])]) ).
fof(f38137,plain,
( spl635_1071
<=> ! [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,[spl635_1071])]) ).
fof(f40879,plain,
( ! [X0] : c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,sK106(v_ts),X0))
| ~ spl635_1071
| ~ spl635_1090 ),
inference(resolution,[],[f40825,f38138]) ).
fof(f38138,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)) )
| ~ spl635_1071 ),
inference(avatar_component_clause,[],[f38137]) ).
fof(f41188,plain,
spl635_1164,
inference(avatar_split_clause,[],[f21369,f41186]) ).
fof(f41186,plain,
( spl635_1164
<=> ! [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,[spl635_1164])]) ).
fof(f21369,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,[],[f15900]) ).
fof(f41184,plain,
spl635_1163,
inference(avatar_split_clause,[],[f21347,f41182]) ).
fof(f41182,plain,
( spl635_1163
<=> ! [X2,X0,X1] :
( hAPP(c_Finite__Set_Ocard(X0),sK375(X0,X1,X2)) = X1
| ~ sP41(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1163])]) ).
fof(f21347,plain,
! [X2,X0,X1] :
( hAPP(c_Finite__Set_Ocard(X0),sK375(X0,X1,X2)) = X1
| ~ sP41(X0,X1,X2) ),
inference(cnf_transformation,[],[f15889]) ).
fof(f15889,plain,
! [X0,X1,X2] :
( ( sP41(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)) = sK375(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& hAPP(c_Finite__Set_Ocard(X0),sK375(X0,X1,X2)) = X1
& ~ hBOOL(hAPP(hAPP(c_member(X0),sK374(X0,X1,X2)),sK375(X0,X1,X2)))
& hAPP(hAPP(c_Set_Oinsert(X0),sK374(X0,X1,X2)),sK375(X0,X1,X2)) = X2 )
| ~ sP41(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK374,sK375])],[f15887,f15888]) ).
fof(f15888,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)) = sK375(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& hAPP(c_Finite__Set_Ocard(X0),sK375(X0,X1,X2)) = X1
& ~ hBOOL(hAPP(hAPP(c_member(X0),sK374(X0,X1,X2)),sK375(X0,X1,X2)))
& hAPP(hAPP(c_Set_Oinsert(X0),sK374(X0,X1,X2)),sK375(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f15887,plain,
! [X0,X1,X2] :
( ( sP41(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 )
| ~ sP41(X0,X1,X2) ) ),
inference(rectify,[],[f15886]) ).
fof(f15886,plain,
! [X2,X0,X1] :
( ( sP41(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 )
| ~ sP41(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f14597]) ).
fof(f14597,plain,
! [X2,X0,X1] :
( sP41(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,[sP41])]) ).
fof(f41180,plain,
spl635_1162,
inference(avatar_split_clause,[],[f21283,f41178]) ).
fof(f41178,plain,
( spl635_1162
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_List_Olistsp(X2,X1),X0))
| ~ hBOOL(hAPP(X1,sK362(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1162])]) ).
fof(f21283,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_List_Olistsp(X2,X1),X0))
| ~ hBOOL(hAPP(X1,sK362(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15836]) ).
fof(f15836,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_List_Olistsp(X2,X1),X0))
| ( ~ hBOOL(hAPP(X1,sK362(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK362(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,[sK362])],[f15834,f15835]) ).
fof(f15835,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,sK362(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK362(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15834,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,[],[f15833]) ).
fof(f15833,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,[],[f12673]) ).
fof(f12673,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,[],[f8179]) ).
fof(f8179,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,[],[f4459]) ).
fof(f4459,axiom,
! [X210,X39,X8] :
( hBOOL(hAPP(c_List_Olistsp(X8,X39),X210))
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(c_List_Oset(X8),X210)))
=> hBOOL(hAPP(X39,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_in__listsp__conv__set) ).
fof(f41176,plain,
spl635_1161,
inference(avatar_split_clause,[],[f21263,f41174]) ).
fof(f41174,plain,
( spl635_1161
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Predicate_OPowp(X2,X1),X0))
| ~ hBOOL(hAPP(X1,sK361(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1161])]) ).
fof(f21263,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Predicate_OPowp(X2,X1),X0))
| ~ hBOOL(hAPP(X1,sK361(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15826]) ).
fof(f15826,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Predicate_OPowp(X2,X1),X0))
| ( ~ hBOOL(hAPP(X1,sK361(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK361(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,[sK361])],[f15824,f15825]) ).
fof(f15825,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0)) )
=> ( ~ hBOOL(hAPP(X1,sK361(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK361(X0,X1,X2)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f15824,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,[],[f15823]) ).
fof(f15823,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,[],[f12671]) ).
fof(f12671,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,[],[f8177]) ).
fof(f8177,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,[],[f1838]) ).
fof(f1838,axiom,
! [X38,X39,X8] :
( hBOOL(hAPP(c_Predicate_OPowp(X8,X39),X38))
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X38))
=> hBOOL(hAPP(X39,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__def) ).
fof(f41172,plain,
spl635_1160,
inference(avatar_split_clause,[],[f21260,f41170]) ).
fof(f41170,plain,
( spl635_1160
<=> ! [X2,X0,X1] :
( c_List_OtakeWhile(X2,X1,X0) = X0
| ~ hBOOL(hAPP(X1,sK360(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1160])]) ).
fof(f21260,plain,
! [X2,X0,X1] :
( c_List_OtakeWhile(X2,X1,X0) = X0
| ~ hBOOL(hAPP(X1,sK360(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15822]) ).
fof(f15822,plain,
! [X0,X1,X2] :
( ( c_List_OtakeWhile(X2,X1,X0) = X0
| ( ~ hBOOL(hAPP(X1,sK360(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK360(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,[sK360])],[f15820,f15821]) ).
fof(f15821,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,sK360(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK360(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15820,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,[],[f15819]) ).
fof(f15819,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,[],[f12670]) ).
fof(f12670,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,[],[f8176]) ).
fof(f8176,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,[],[f4706]) ).
fof(f4706,axiom,
! [X210,X29,X8] :
( c_List_OtakeWhile(X8,X29,X210) = X210
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(c_List_Oset(X8),X210)))
=> hBOOL(hAPP(X29,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile__eq__all__conv) ).
fof(f41168,plain,
spl635_1159,
inference(avatar_split_clause,[],[f21243,f41166]) ).
fof(f41166,plain,
( spl635_1159
<=> ! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| sK355(X0,X1,X2) != sK356(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1159])]) ).
fof(f21243,plain,
! [X2,X0,X1] :
( c_Relation_Osingle__valued(X2,X1,X0)
| sK355(X0,X1,X2) != sK356(X0,X1,X2) ),
inference(cnf_transformation,[],[f15805]) ).
fof(f15805,plain,
! [X0,X1,X2] :
( ( c_Relation_Osingle__valued(X2,X1,X0)
| ( sK355(X0,X1,X2) != sK356(X0,X1,X2)
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),sK354(X0,X1,X2)),sK356(X0,X1,X2))),X0))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),sK354(X0,X1,X2)),sK355(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,[sK354,sK355,sK356])],[f15802,f15804,f15803]) ).
fof(f15803,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] :
( sK355(X0,X1,X2) != X5
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),sK354(X0,X1,X2)),X5)),X0)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),sK354(X0,X1,X2)),sK355(X0,X1,X2))),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f15804,plain,
! [X0,X1,X2] :
( ? [X5] :
( sK355(X0,X1,X2) != X5
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),sK354(X0,X1,X2)),X5)),X0)) )
=> ( sK355(X0,X1,X2) != sK356(X0,X1,X2)
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),sK354(X0,X1,X2)),sK356(X0,X1,X2))),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f15802,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,[],[f15801]) ).
fof(f15801,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,[],[f12667]) ).
fof(f12667,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,[],[f8172]) ).
fof(f8172,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,[],[f3799]) ).
fof(f3799,axiom,
! [X98,X25,X8] :
( c_Relation_Osingle__valued(X8,X25,X98)
<=> ! [X2,X45] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X25)),hAPP(hAPP(c_Product__Type_OPair(X8,X25),X2),X45)),X98))
=> ! [X69] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X25)),hAPP(hAPP(c_Product__Type_OPair(X8,X25),X2),X69)),X98))
=> X45 = X69 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__def) ).
fof(f41164,plain,
spl635_1158,
inference(avatar_split_clause,[],[f21224,f41162]) ).
fof(f41162,plain,
( spl635_1158
<=> ! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| sK349(X0,X1,X2) != sK350(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1158])]) ).
fof(f21224,plain,
! [X2,X0,X1] :
( c_Relation_Ototal__on(X2,X1,X0)
| sK349(X0,X1,X2) != sK350(X0,X1,X2) ),
inference(cnf_transformation,[],[f15786]) ).
fof(f15786,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),sK350(X0,X1,X2)),sK349(X0,X1,X2))),X0))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK349(X0,X1,X2)),sK350(X0,X1,X2))),X0))
& sK349(X0,X1,X2) != sK350(X0,X1,X2)
& hBOOL(hAPP(hAPP(c_member(X2),sK350(X0,X1,X2)),X1))
& hBOOL(hAPP(hAPP(c_member(X2),sK349(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,[sK349,sK350])],[f15783,f15785,f15784]) ).
fof(f15784,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),sK349(X0,X1,X2))),X0))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK349(X0,X1,X2)),X4)),X0))
& sK349(X0,X1,X2) != X4
& hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& hBOOL(hAPP(hAPP(c_member(X2),sK349(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15785,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X4),sK349(X0,X1,X2))),X0))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK349(X0,X1,X2)),X4)),X0))
& sK349(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),sK350(X0,X1,X2)),sK349(X0,X1,X2))),X0))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK349(X0,X1,X2)),sK350(X0,X1,X2))),X0))
& sK349(X0,X1,X2) != sK350(X0,X1,X2)
& hBOOL(hAPP(hAPP(c_member(X2),sK350(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15783,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,[],[f15782]) ).
fof(f15782,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,[],[f12663]) ).
fof(f12663,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,[],[f12662]) ).
fof(f12662,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,[],[f8167]) ).
fof(f8167,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,[],[f3800]) ).
fof(f3800,axiom,
! [X98,X39,X8] :
( c_Relation_Ototal__on(X8,X39,X98)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X39))
=> ! [X142] :
( hBOOL(hAPP(hAPP(c_member(X8),X142),X39))
=> ( X2 != X142
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X142),X2)),X98))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X2),X142)),X98)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__def) ).
fof(f41160,plain,
spl635_1157,
inference(avatar_split_clause,[],[f20773,f41158]) ).
fof(f41158,plain,
( spl635_1157
<=> ! [X2,X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,sK255(X0,X1,X2))
| ~ sP22(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1157])]) ).
fof(f20773,plain,
! [X2,X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,sK255(X0,X1,X2))
| ~ sP22(X0,X1,X2) ),
inference(cnf_transformation,[],[f15560]) ).
fof(f15560,plain,
! [X0,X1,X2] :
( ( sP22(X0,X1,X2)
| ! [X3] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(X0,sK254(X0,X1,X2,X3))
& sK254(X0,X1,X2,X3) != X3
& hBOOL(hAPP(hAPP(c_member(X2),sK254(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)
| sK255(X0,X1,X2) = X6
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1)) )
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,sK255(X0,X1,X2))
& hBOOL(hAPP(hAPP(c_member(X2),sK255(X0,X1,X2)),X1)) )
| ~ sP22(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK254,sK255])],[f15557,f15559,f15558]) ).
fof(f15558,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,sK254(X0,X1,X2,X3))
& sK254(X0,X1,X2,X3) != X3
& hBOOL(hAPP(hAPP(c_member(X2),sK254(X0,X1,X2,X3)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15559,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)
| sK255(X0,X1,X2) = X6
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1)) )
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,sK255(X0,X1,X2))
& hBOOL(hAPP(hAPP(c_member(X2),sK255(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15557,plain,
! [X0,X1,X2] :
( ( sP22(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)) )
| ~ sP22(X0,X1,X2) ) ),
inference(rectify,[],[f15556]) ).
fof(f15556,plain,
! [X0,X1,X2] :
( ( sP22(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)) )
| ~ sP22(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14566]) ).
fof(f14566,plain,
! [X0,X1,X2] :
( sP22(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,[sP22])]) ).
fof(f41156,plain,
spl635_1156,
inference(avatar_split_clause,[],[f20708,f41154]) ).
fof(f41154,plain,
( spl635_1156
<=> ! [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,[spl635_1156])]) ).
fof(f20708,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,[],[f12207]) ).
fof(f12207,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,[],[f7841]) ).
fof(f7841,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,[],[f4714]) ).
fof(f4714,axiom,
! [X29,X210,X8] :
( hBOOL(hAPP(c_List_Odistinct(X8),X210))
=> hBOOL(hAPP(c_List_Odistinct(X8),c_List_OtakeWhile(X8,X29,X210))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__takeWhile) ).
fof(f41152,plain,
spl635_1155,
inference(avatar_split_clause,[],[f20707,f41150]) ).
fof(f41150,plain,
( spl635_1155
<=> ! [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,[spl635_1155])]) ).
fof(f20707,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,[],[f12206]) ).
fof(f12206,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,[],[f7840]) ).
fof(f7840,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,[],[f4434]) ).
fof(f4434,axiom,
! [X13,X208,X5] :
( hBOOL(hAPP(c_List_Odistinct(X5),X208))
=> hBOOL(hAPP(c_List_Odistinct(X5),c_List_Oremove1(X5,X13,X208))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remove1) ).
fof(f41146,plain,
spl635_1154,
inference(avatar_split_clause,[],[f20704,f41144]) ).
fof(f41144,plain,
( spl635_1154
<=> ! [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,[spl635_1154])]) ).
fof(f20704,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,[],[f12203]) ).
fof(f12203,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,[],[f7837]) ).
fof(f7837,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,[],[f4758]) ).
fof(f4758,axiom,
! [X13,X208,X5] :
( hBOOL(hAPP(c_List_Odistinct(X5),X208))
=> hBOOL(hAPP(c_List_Odistinct(X5),c_List_Oinsert(X5,X13,X208))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__insert) ).
fof(f41142,plain,
spl635_1153,
inference(avatar_split_clause,[],[f20482,f41140]) ).
fof(f41140,plain,
( spl635_1153
<=> ! [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,[spl635_1153])]) ).
fof(f20482,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,[],[f15494]) ).
fof(f15494,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),sK239(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK239(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,[sK239])],[f15492,f15493]) ).
fof(f15493,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),sK239(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK239(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15492,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,[],[f15491]) ).
fof(f15491,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,[],[f15490]) ).
fof(f15490,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,[],[f11955]) ).
fof(f11955,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,[],[f7663]) ).
fof(f7663,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,[],[f4653]) ).
fof(f4653,axiom,
! [X210,X30,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_List_Olinorder__class_Osorted(X8,hAPP(hAPP(c_List_Olist_OCons(X8),X30),X210))
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(c_List_Oset(X8),X210)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X2)) )
& c_List_Olinorder__class_Osorted(X8,X210) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__Cons) ).
fof(f41138,plain,
spl635_1152,
inference(avatar_split_clause,[],[f20336,f41136]) ).
fof(f41136,plain,
( spl635_1152
<=> ! [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,[spl635_1152])]) ).
fof(f20336,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,[],[f11749]) ).
fof(f11749,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,[],[f11748]) ).
fof(f11748,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,[],[f7556]) ).
fof(f7556,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,[],[f4636]) ).
fof(f4636,axiom,
! [X4,X208,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_List_Olinorder__class_Osorted(X5,X208)
=> c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Otake(X5),X4),X208)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__take) ).
fof(f41134,plain,
spl635_1151,
inference(avatar_split_clause,[],[f20335,f41132]) ).
fof(f41132,plain,
( spl635_1151
<=> ! [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,[spl635_1151])]) ).
fof(f20335,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,[],[f11747]) ).
fof(f11747,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,[],[f11746]) ).
fof(f11746,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,[],[f7555]) ).
fof(f7555,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,[],[f4637]) ).
fof(f4637,axiom,
! [X4,X208,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_List_Olinorder__class_Osorted(X5,X208)
=> c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Odrop(X5),X4),X208)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__drop) ).
fof(f41130,plain,
spl635_1150,
inference(avatar_split_clause,[],[f19692,f41128]) ).
fof(f41128,plain,
( spl635_1150
<=> ! [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,[spl635_1150])]) ).
fof(f19692,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,[],[f6987]) ).
fof(f6987,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,[],[f4136]) ).
fof(f4136,axiom,
! [X207,X8,X5] : hAPP(hAPP(c_List_Ozip(X5,X8),c_List_Olist_ONil(X5)),X207) = c_List_Olist_ONil(tc_prod(X5,X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip__Nil) ).
fof(f41126,plain,
spl635_1149,
inference(avatar_split_clause,[],[f19691,f41124]) ).
fof(f41124,plain,
( spl635_1149
<=> ! [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,[spl635_1149])]) ).
fof(f19691,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,[],[f6986]) ).
fof(f6986,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,[],[f4759]) ).
fof(f4759,axiom,
! [X208,X13,X5] : c_List_Oinsert(X5,X13,c_List_Oremdups(X5,X208)) = c_List_Oremdups(X5,c_List_Oinsert(X5,X13,X208)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__remdups) ).
fof(f41122,plain,
spl635_1148,
inference(avatar_split_clause,[],[f19689,f41120]) ).
fof(f41120,plain,
( spl635_1148
<=> ! [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,[spl635_1148])]) ).
fof(f19689,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,[],[f6984]) ).
fof(f6984,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,[],[f4137]) ).
fof(f4137,axiom,
! [X208,X8,X5] : c_List_Olist_ONil(tc_prod(X5,X8)) = hAPP(hAPP(c_List_Ozip(X5,X8),X208),c_List_Olist_ONil(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zip_Osimps_I1_J) ).
fof(f41118,plain,
spl635_1147,
inference(avatar_split_clause,[],[f19652,f41116]) ).
fof(f41116,plain,
( spl635_1147
<=> ! [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,[spl635_1147])]) ).
fof(f19652,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,[],[f11343]) ).
fof(f11343,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,[],[f11342]) ).
fof(f11342,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,[],[f6947]) ).
fof(f6947,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,[],[f2757]) ).
fof(f2757,axiom,
! [X39,X8] :
~ ? [X165] : hAPP(c_Set_OPow(X8),X39) = hAPP(c_Set_Oimage(X8,tc_fun(X8,tc_HOL_Obool),X165),X39),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Cantors__paradox) ).
fof(f41114,plain,
spl635_1146,
inference(avatar_split_clause,[],[f19394,f41112]) ).
fof(f41112,plain,
( spl635_1146
<=> ! [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,[spl635_1146])]) ).
fof(f19394,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,[],[f15199]) ).
fof(f15199,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,[],[f15198]) ).
fof(f15198,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,[],[f6847]) ).
fof(f6847,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,[],[f385]) ).
fof(f385,axiom,
! [X15,X27] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X27),X15) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X15
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X27 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(f41110,plain,
spl635_1145,
inference(avatar_split_clause,[],[f19393,f41108]) ).
fof(f41108,plain,
( spl635_1145
<=> ! [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,[spl635_1145])]) ).
fof(f19393,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,[],[f15199]) ).
fof(f41106,plain,
( spl635_1144
| ~ spl635_386
| spl635_1123 ),
inference(avatar_split_clause,[],[f41060,f41015,f31115,f41103]) ).
fof(f41103,plain,
( spl635_1144
<=> sP11(sK106(v_ts),sK106(v_ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1144])]) ).
fof(f31115,plain,
( spl635_386
<=> ! [X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_386])]) ).
fof(f41060,plain,
( sP11(sK106(v_ts),sK106(v_ts))
| ~ spl635_386
| spl635_1123 ),
inference(resolution,[],[f41017,f31116]) ).
fof(f31116,plain,
( ! [X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X1,X1) )
| ~ spl635_386 ),
inference(avatar_component_clause,[],[f31115]) ).
fof(f41101,plain,
spl635_1143,
inference(avatar_split_clause,[],[f19338,f41099]) ).
fof(f41099,plain,
( spl635_1143
<=> ! [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,[spl635_1143])]) ).
fof(f19338,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,[],[f15165]) ).
fof(f15165,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,[],[f6833]) ).
fof(f6833,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orev(X1),X0)))
<=> hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(rectify,[],[f4665]) ).
fof(f4665,axiom,
! [X210,X8] :
( hBOOL(hAPP(c_List_Odistinct(X8),hAPP(c_List_Orev(X8),X210)))
<=> hBOOL(hAPP(c_List_Odistinct(X8),X210)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__rev) ).
fof(f41097,plain,
spl635_1142,
inference(avatar_split_clause,[],[f19337,f41095]) ).
fof(f41095,plain,
( spl635_1142
<=> ! [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,[spl635_1142])]) ).
fof(f19337,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,[],[f15165]) ).
fof(f41093,plain,
spl635_1141,
inference(avatar_split_clause,[],[f19336,f41091]) ).
fof(f41091,plain,
( spl635_1141
<=> ! [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,[spl635_1141])]) ).
fof(f19336,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,[],[f15164]) ).
fof(f15164,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,[],[f6832]) ).
fof(f6832,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Orotate1(X1),X0)))
<=> hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(rectify,[],[f4335]) ).
fof(f4335,axiom,
! [X210,X8] :
( hBOOL(hAPP(c_List_Odistinct(X8),hAPP(c_List_Orotate1(X8),X210)))
<=> hBOOL(hAPP(c_List_Odistinct(X8),X210)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct1__rotate) ).
fof(f41089,plain,
spl635_1140,
inference(avatar_split_clause,[],[f19335,f41087]) ).
fof(f41087,plain,
( spl635_1140
<=> ! [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,[spl635_1140])]) ).
fof(f19335,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,[],[f15164]) ).
fof(f41085,plain,
spl635_1139,
inference(avatar_split_clause,[],[f19267,f41083]) ).
fof(f41083,plain,
( spl635_1139
<=> ! [X0,X1] :
( c_List_Otranspose(X1,X0) = c_List_Olist_ONil(tc_List_Olist(X1))
| c_List_Olist_ONil(X1) != sK197(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1139])]) ).
fof(f19267,plain,
! [X0,X1] :
( c_List_Otranspose(X1,X0) = c_List_Olist_ONil(tc_List_Olist(X1))
| c_List_Olist_ONil(X1) != sK197(X0,X1) ),
inference(cnf_transformation,[],[f15116]) ).
fof(f15116,plain,
! [X0,X1] :
( ( c_List_Otranspose(X1,X0) = c_List_Olist_ONil(tc_List_Olist(X1))
| ( c_List_Olist_ONil(X1) != sK197(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),sK197(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,[sK197])],[f15114,f15115]) ).
fof(f15115,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) != sK197(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),sK197(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15114,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,[],[f15113]) ).
fof(f15113,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,[],[f11330]) ).
fof(f11330,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,[],[f6800]) ).
fof(f6800,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,[],[f4576]) ).
fof(f4576,axiom,
! [X210,X8] :
( c_List_Olist_ONil(tc_List_Olist(X8)) = c_List_Otranspose(X8,X210)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X8)),X2),hAPP(c_List_Oset(tc_List_Olist(X8)),X210)))
=> c_List_Olist_ONil(X8) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose__empty) ).
fof(f41081,plain,
spl635_1138,
inference(avatar_split_clause,[],[f19179,f41079]) ).
fof(f41079,plain,
( spl635_1138
<=> ! [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,[spl635_1138])]) ).
fof(f19179,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,[],[f15036]) ).
fof(f15036,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,[],[f6772]) ).
fof(f6772,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,[],[f3492]) ).
fof(f3492,axiom,
! [X122,X8] :
( c_Wellfounded_Owf(X8,X122)
<=> c_Wellfounded_Owf(X8,hAPP(hAPP(c_Relation_Orel__comp(X8,X8,X8),X122),X122)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__comp__self) ).
fof(f41077,plain,
spl635_1137,
inference(avatar_split_clause,[],[f19178,f41075]) ).
fof(f41075,plain,
( spl635_1137
<=> ! [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,[spl635_1137])]) ).
fof(f19178,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,[],[f15036]) ).
fof(f41073,plain,
spl635_1136,
inference(avatar_split_clause,[],[f18912,f41071]) ).
fof(f41071,plain,
( spl635_1136
<=> ! [X5,X0,X1] :
( hBOOL(hAPP(X0,sK153(X0,X1)))
| ~ hBOOL(hAPP(X0,X5))
| ~ sP3(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1136])]) ).
fof(f18912,plain,
! [X0,X1,X5] :
( hBOOL(hAPP(X0,sK153(X0,X1)))
| ~ hBOOL(hAPP(X0,X5))
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f14929]) ).
fof(f14929,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(X0,sK152(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,sK153(X0,X1)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK153(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,[sK152,sK153])],[f14926,f14928,f14927]) ).
fof(f14927,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X0,sK152(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14928,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,sK153(X0,X1)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK153(X0,X1)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f14926,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,[],[f14925]) ).
fof(f14925,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,[],[f14532]) ).
fof(f14532,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(f41069,plain,
spl635_1135,
inference(avatar_split_clause,[],[f18865,f41067]) ).
fof(f41067,plain,
( spl635_1135
<=> ! [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,[spl635_1135])]) ).
fof(f18865,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,[],[f11026]) ).
fof(f11026,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,[],[f11025]) ).
fof(f11025,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,[],[f6556]) ).
fof(f6556,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,[],[f3574]) ).
fof(f3574,axiom,
! [X98,X8] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(X8,X8)),X98))
=> ( c_Wellfounded_Oacyclic(X8,X98)
=> c_Wellfounded_Owf(X8,X98) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__acyclic__wf) ).
fof(f41065,plain,
spl635_1134,
inference(avatar_split_clause,[],[f18830,f41063]) ).
fof(f41063,plain,
( spl635_1134
<=> ! [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,[spl635_1134])]) ).
fof(f18830,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,[],[f10987]) ).
fof(f10987,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,[],[f6522]) ).
fof(f6522,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,[],[f4200]) ).
fof(f4200,axiom,
! [X42,X41] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X41),X42))
=> c_List_Olist_ONil(tc_Int_Oint) = c_List_Oupto(X42,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upto__empty) ).
fof(f41058,plain,
spl635_1133,
inference(avatar_split_clause,[],[f18787,f41056]) ).
fof(f41056,plain,
( spl635_1133
<=> ! [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,[spl635_1133])]) ).
fof(f18787,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,[],[f10945]) ).
fof(f10945,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,[],[f6491]) ).
fof(f6491,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
=> hBOOL(hAPP(c_List_Odistinct(X1),hAPP(c_List_Otl(X1),X0))) ),
inference(rectify,[],[f4328]) ).
fof(f4328,axiom,
! [X208,X5] :
( hBOOL(hAPP(c_List_Odistinct(X5),X208))
=> hBOOL(hAPP(c_List_Odistinct(X5),hAPP(c_List_Otl(X5),X208))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__tl) ).
fof(f41054,plain,
spl635_1132,
inference(avatar_split_clause,[],[f18706,f41052]) ).
fof(f41052,plain,
( spl635_1132
<=> ! [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,[spl635_1132])]) ).
fof(f18706,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,[],[f10852]) ).
fof(f10852,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,[],[f10851]) ).
fof(f10851,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,[],[f6424]) ).
fof(f6424,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,[],[f2154]) ).
fof(f2154,axiom,
! [X38,X39] :
( c_Nat__Transfer_Onat__set(X39)
=> ( c_Nat__Transfer_Onat__set(X38)
=> c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X39),X38)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J) ).
fof(f41050,plain,
spl635_1131,
inference(avatar_split_clause,[],[f18705,f41048]) ).
fof(f41048,plain,
( spl635_1131
<=> ! [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,[spl635_1131])]) ).
fof(f18705,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,[],[f10850]) ).
fof(f10850,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,[],[f10849]) ).
fof(f10849,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,[],[f6423]) ).
fof(f6423,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,[],[f2840]) ).
fof(f2840,axiom,
! [X38,X39] :
( c_Nat__Transfer_Onat__set(X39)
=> ( c_Nat__Transfer_Onat__set(X38)
=> c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),X39),X38)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J) ).
fof(f41046,plain,
spl635_1130,
inference(avatar_split_clause,[],[f18570,f41044]) ).
fof(f41044,plain,
( spl635_1130
<=> ! [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,[spl635_1130])]) ).
fof(f18570,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,[],[f10713]) ).
fof(f10713,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,[],[f6315]) ).
fof(f6315,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,[],[f247]) ).
fof(f247,axiom,
! [X4,X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X4))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0__le__iff) ).
fof(f41042,plain,
spl635_1129,
inference(avatar_split_clause,[],[f18569,f41040]) ).
fof(f41040,plain,
( spl635_1129
<=> ! [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,[spl635_1129])]) ).
fof(f18569,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,[],[f10712]) ).
fof(f10712,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,[],[f6314]) ).
fof(f6314,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,[],[f249]) ).
fof(f249,axiom,
! [X24,X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),X24)),c_Groups_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__less__0__iff) ).
fof(f41038,plain,
spl635_1128,
inference(avatar_split_clause,[],[f18563,f41036]) ).
fof(f41036,plain,
( spl635_1128
<=> ! [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,[spl635_1128])]) ).
fof(f18563,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,[],[f10706]) ).
fof(f10706,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,[],[f6309]) ).
fof(f6309,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,[],[f2610]) ).
fof(f2610,axiom,
! [X15,X8] :
( class_Rings_Osemiring__1(X8)
=> hBOOL(hAPP(hAPP(c_member(X8),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X15)),c_Nat_Osemiring__1__class_ONats(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__in__Nats) ).
fof(f41034,plain,
spl635_1127,
inference(avatar_split_clause,[],[f18472,f41032]) ).
fof(f41032,plain,
( spl635_1127
<=> ! [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,[spl635_1127])]) ).
fof(f18472,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,[],[f10611]) ).
fof(f10611,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,[],[f6226]) ).
fof(f6226,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,[],[f2596]) ).
fof(f2596,axiom,
! [X52,X8] :
( class_Int_Onumber__ring(X8)
=> hBOOL(hAPP(hAPP(c_member(X8),hAPP(c_Int_Onumber__class_Onumber__of(X8),X52)),c_Int_Oring__1__class_OInts(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__number__of) ).
fof(f41030,plain,
spl635_1126,
inference(avatar_split_clause,[],[f18471,f41028]) ).
fof(f41028,plain,
( spl635_1126
<=> ! [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,[spl635_1126])]) ).
fof(f18471,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,[],[f10610]) ).
fof(f10610,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,[],[f6225]) ).
fof(f6225,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,[],[f1098]) ).
fof(f1098,axiom,
! [X33,X5] :
( class_Int_Onumber__ring(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OPls)),X33) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0) ).
fof(f41026,plain,
spl635_1125,
inference(avatar_split_clause,[],[f18470,f41024]) ).
fof(f41024,plain,
( spl635_1125
<=> ! [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,[spl635_1125])]) ).
fof(f18470,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,[],[f10609]) ).
fof(f10609,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,[],[f6224]) ).
fof(f6224,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,[],[f1099]) ).
fof(f1099,axiom,
! [X33,X5] :
( class_Int_Onumber__ring(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X33),hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OPls)) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__numeral__0__right) ).
fof(f41022,plain,
spl635_1124,
inference(avatar_split_clause,[],[f18426,f41020]) ).
fof(f41020,plain,
( spl635_1124
<=> ! [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,[spl635_1124])]) ).
fof(f18426,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,[],[f14816]) ).
fof(f14816,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,[],[f10578]) ).
fof(f10578,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,[],[f6196]) ).
fof(f6196,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,[],[f1043]) ).
fof(f1043,axiom,
! [X17,X8] :
( class_Groups_Oordered__ab__group__add__abs(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = hAPP(c_Groups_Oabs__class_Oabs(X8),X17)
<=> c_Groups_Ozero__class_Ozero(X8) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__eq__0) ).
fof(f41018,plain,
( ~ spl635_1123
| ~ spl635_889
| ~ spl635_1090 ),
inference(avatar_split_clause,[],[f40880,f40823,f34369,f41015]) ).
fof(f34369,plain,
( spl635_889
<=> ! [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,[spl635_889])]) ).
fof(f40880,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,sK106(v_ts)))
| ~ spl635_889
| ~ spl635_1090 ),
inference(resolution,[],[f40825,f34370]) ).
fof(f34370,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)) )
| ~ spl635_889 ),
inference(avatar_component_clause,[],[f34369]) ).
fof(f41013,plain,
spl635_1122,
inference(avatar_split_clause,[],[f18416,f41011]) ).
fof(f41011,plain,
( spl635_1122
<=> ! [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,[spl635_1122])]) ).
fof(f18416,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,[],[f10564]) ).
fof(f10564,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,[],[f6186]) ).
fof(f6186,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,[],[f1068]) ).
fof(f1068,axiom,
! [X33,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),hAPP(c_Groups_Oabs__class_Oabs(X5),X33))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__zero) ).
fof(f41009,plain,
spl635_1121,
inference(avatar_split_clause,[],[f18415,f41007]) ).
fof(f41007,plain,
( spl635_1121
<=> ! [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,[spl635_1121])]) ).
fof(f18415,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,[],[f10563]) ).
fof(f10563,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,[],[f6185]) ).
fof(f6185,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,[],[f1071]) ).
fof(f1071,axiom,
! [X33,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),hAPP(c_Groups_Oabs__class_Oabs(X5),X33)),c_Groups_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__not__less__zero) ).
fof(f41005,plain,
spl635_1120,
inference(avatar_split_clause,[],[f18401,f41003]) ).
fof(f41003,plain,
( spl635_1120
<=> ! [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,[spl635_1120])]) ).
fof(f18401,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,[],[f10550]) ).
fof(f10550,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,[],[f6174]) ).
fof(f6174,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,[],[f2600]) ).
fof(f2600,axiom,
! [X15,X8] :
( class_Rings_Oring__1(X8)
=> hBOOL(hAPP(hAPP(c_member(X8),hAPP(c_Nat_Osemiring__1__class_Oof__nat(X8),X15)),c_Int_Oring__1__class_OInts(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__of__nat) ).
fof(f41001,plain,
spl635_1119,
inference(avatar_split_clause,[],[f18400,f40999]) ).
fof(f40999,plain,
( spl635_1119
<=> ! [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,[spl635_1119])]) ).
fof(f18400,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,[],[f10549]) ).
fof(f10549,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,[],[f6173]) ).
fof(f6173,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,[],[f2601]) ).
fof(f2601,axiom,
! [X53,X8] :
( class_Rings_Oring__1(X8)
=> hBOOL(hAPP(hAPP(c_member(X8),hAPP(c_Int_Oring__1__class_Oof__int(X8),X53)),c_Int_Oring__1__class_OInts(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__of__int) ).
fof(f40997,plain,
spl635_1118,
inference(avatar_split_clause,[],[f18383,f40995]) ).
fof(f40995,plain,
( spl635_1118
<=> ! [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,[spl635_1118])]) ).
fof(f18383,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,[],[f14810]) ).
fof(f14810,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,[],[f10538]) ).
fof(f10538,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,[],[f6162]) ).
fof(f6162,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,[],[f574]) ).
fof(f574,axiom,
! [X17,X8] :
( class_Groups_Ogroup__add(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = hAPP(c_Groups_Ouminus__class_Ouminus(X8),X17)
<=> c_Groups_Ozero__class_Ozero(X8) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(f40993,plain,
spl635_1117,
inference(avatar_split_clause,[],[f18309,f40991]) ).
fof(f40991,plain,
( spl635_1117
<=> ! [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,[spl635_1117])]) ).
fof(f18309,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,[],[f10497]) ).
fof(f40989,plain,
spl635_1116,
inference(avatar_split_clause,[],[f18272,f40987]) ).
fof(f40987,plain,
( spl635_1116
<=> ! [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,[spl635_1116])]) ).
fof(f18272,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,[],[f10478]) ).
fof(f10478,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,[],[f6090]) ).
fof(f6090,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,[],[f4203]) ).
fof(f4203,axiom,
! [X41,X42] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X42),X41))
=> c_List_Olist_ONil(tc_Int_Oint) = c_List_Oupto(X42,X41) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X42),X41))
=> c_List_Oupto(X42,X41) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),X42),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X42),c_Groups_Oone__class_Oone(tc_Int_Oint)),X41)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upto_Osimps) ).
fof(f40985,plain,
spl635_1115,
inference(avatar_split_clause,[],[f18265,f40983]) ).
fof(f40983,plain,
( spl635_1115
<=> ! [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,[spl635_1115])]) ).
fof(f18265,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,[],[f10475]) ).
fof(f10475,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,[],[f6087]) ).
fof(f6087,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,[],[f1089]) ).
fof(f1089,axiom,
! [X4,X24] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X4))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X4) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X4),X4) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X24),X4))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X4) = X24 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__if) ).
fof(f40981,plain,
spl635_1114,
inference(avatar_split_clause,[],[f18261,f40979]) ).
fof(f40979,plain,
( spl635_1114
<=> ! [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,[spl635_1114])]) ).
fof(f18261,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,[],[f10473]) ).
fof(f10473,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,[],[f6085]) ).
fof(f6085,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,[],[f4785]) ).
fof(f4785,axiom,
! [X42,X49] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X49),X42))
=> c_Lazy__Sequence_Osmall__lazy_H(X49,X42) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),X42),c_Lazy__Sequence_Osmall__lazy_H(X49,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X42),c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X49),X42))
=> c_Lazy__Sequence_Osmall__lazy_H(X49,X42) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy_H_Osimps) ).
fof(f40977,plain,
spl635_1113,
inference(avatar_split_clause,[],[f18260,f40975]) ).
fof(f40975,plain,
( spl635_1113
<=> ! [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,[spl635_1113])]) ).
fof(f18260,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,[],[f10472]) ).
fof(f10472,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,[],[f6084]) ).
fof(f6084,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,[],[f1824]) ).
fof(f1824,axiom,
! [X46,X40] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X40),X46))
=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Quickcheck_Obeyond(X40,X46) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),X40),X46))
=> c_Quickcheck_Obeyond(X40,X46) = X46 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_beyond__def) ).
fof(f40973,plain,
spl635_1112,
inference(avatar_split_clause,[],[f17969,f40971]) ).
fof(f40971,plain,
( spl635_1112
<=> ! [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,[spl635_1112])]) ).
fof(f17969,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,[],[f5821]) ).
fof(f5821,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,[],[f3086]) ).
fof(f3086,axiom,
! [X149,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),X149),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__add__nat) ).
fof(f40969,plain,
spl635_1111,
inference(avatar_split_clause,[],[f17967,f40967]) ).
fof(f40967,plain,
( spl635_1111
<=> ! [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,[spl635_1111])]) ).
fof(f17967,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,[],[f5819]) ).
fof(f5819,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,[],[f4868]) ).
fof(f4868,axiom,
! [X122,X8] : c_Predicate_Opred__comp(X8,X8,X8,c_fequal,c_Predicate_Opred__comp(X8,X8,X8,X122,c_fequal)) = X122,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__comp__r) ).
fof(f40965,plain,
spl635_1110,
inference(avatar_split_clause,[],[f17965,f40963]) ).
fof(f40963,plain,
( spl635_1110
<=> ! [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,[spl635_1110])]) ).
fof(f17965,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,[],[f5817]) ).
fof(f5817,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,[],[f2319]) ).
fof(f2319,axiom,
! [X38,X8] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))),X38) = X38,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty__left) ).
fof(f40961,plain,
spl635_1109,
inference(avatar_split_clause,[],[f17964,f40959]) ).
fof(f40959,plain,
( spl635_1109
<=> ! [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,[spl635_1109])]) ).
fof(f17964,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,[],[f5816]) ).
fof(f5816,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,[],[f3125]) ).
fof(f3125,axiom,
! [X38,X8] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))),X38) = X38,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UNIV__left) ).
fof(f40957,plain,
spl635_1108,
inference(avatar_split_clause,[],[f17963,f40955]) ).
fof(f40955,plain,
( spl635_1108
<=> ! [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,[spl635_1108])]) ).
fof(f17963,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,[],[f5815]) ).
fof(f5815,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,[],[f493]) ).
fof(f493,axiom,
! [X24,X4] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X24)),X4) = X24,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse) ).
fof(f40953,plain,
spl635_1107,
inference(avatar_split_clause,[],[f17962,f40951]) ).
fof(f40951,plain,
( spl635_1107
<=> ! [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,[spl635_1107])]) ).
fof(f17962,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,[],[f5814]) ).
fof(f5814,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,[],[f494]) ).
fof(f494,axiom,
! [X4,X24] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X4)),X4) = X24,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__add__inverse2) ).
fof(f40949,plain,
spl635_1106,
inference(avatar_split_clause,[],[f17961,f40947]) ).
fof(f40947,plain,
( spl635_1106
<=> ! [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,[spl635_1106])]) ).
fof(f17961,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,[],[f5813]) ).
fof(f5813,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,[],[f2306]) ).
fof(f2306,axiom,
! [X39,X8] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X39),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__empty) ).
fof(f40945,plain,
spl635_1105,
inference(avatar_split_clause,[],[f17960,f40943]) ).
fof(f40943,plain,
( spl635_1105
<=> ! [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,[spl635_1105])]) ).
fof(f17960,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,[],[f5812]) ).
fof(f5812,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,[],[f2318]) ).
fof(f2318,axiom,
! [X39,X8] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X39),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__empty__right) ).
fof(f40941,plain,
spl635_1104,
inference(avatar_split_clause,[],[f17959,f40939]) ).
fof(f40939,plain,
( spl635_1104
<=> ! [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,[spl635_1104])]) ).
fof(f17959,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,[],[f5811]) ).
fof(f5811,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,[],[f3124]) ).
fof(f3124,axiom,
! [X39,X8] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X39),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) = X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__UNIV__right) ).
fof(f40937,plain,
spl635_1103,
inference(avatar_split_clause,[],[f17958,f40935]) ).
fof(f40935,plain,
( spl635_1103
<=> ! [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,[spl635_1103])]) ).
fof(f17958,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,[],[f5810]) ).
fof(f5810,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,[],[f845]) ).
fof(f845,axiom,
! [X39,X8] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(X8,tc_HOL_Obool)),X39)) = X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__complement) ).
fof(f40933,plain,
( spl635_1102
| ~ spl635_563
| ~ spl635_1090 ),
inference(avatar_split_clause,[],[f40881,f40823,f31897,f40930]) ).
fof(f40930,plain,
( spl635_1102
<=> c_Nat__Transfer_Ois__nat(sK106(v_ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1102])]) ).
fof(f31897,plain,
( spl635_563
<=> ! [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,[spl635_563])]) ).
fof(f40881,plain,
( c_Nat__Transfer_Ois__nat(sK106(v_ts))
| ~ spl635_563
| ~ spl635_1090 ),
inference(resolution,[],[f40825,f31898]) ).
fof(f31898,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| c_Nat__Transfer_Ois__nat(X0) )
| ~ spl635_563 ),
inference(avatar_component_clause,[],[f31897]) ).
fof(f40928,plain,
spl635_1101,
inference(avatar_split_clause,[],[f17957,f40926]) ).
fof(f40926,plain,
( spl635_1101
<=> ! [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,[spl635_1101])]) ).
fof(f40924,plain,
spl635_1100,
inference(avatar_split_clause,[],[f17956,f40922]) ).
fof(f40922,plain,
( spl635_1100
<=> ! [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,[spl635_1100])]) ).
fof(f17956,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,[],[f5808]) ).
fof(f5808,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,[],[f172]) ).
fof(f172,axiom,
! [X4,X24] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X4) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__commute) ).
fof(f40920,plain,
spl635_1099,
inference(avatar_split_clause,[],[f17955,f40918]) ).
fof(f40918,plain,
( spl635_1099
<=> ! [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,[spl635_1099])]) ).
fof(f17955,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,[],[f5807]) ).
fof(f5807,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,[],[f334]) ).
fof(f334,axiom,
! [X59,X31] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X31),X59) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X59),X31),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__commute) ).
fof(f40916,plain,
spl635_1098,
inference(avatar_split_clause,[],[f17954,f40914]) ).
fof(f40914,plain,
( spl635_1098
<=> ! [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,[spl635_1098])]) ).
fof(f17954,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,[],[f5806]) ).
fof(f5806,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,[],[f807]) ).
fof(f807,axiom,
! [X4,X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X24) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
fof(f40912,plain,
spl635_1097,
inference(avatar_split_clause,[],[f17953,f40910]) ).
fof(f40910,plain,
( spl635_1097
<=> ! [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,[spl635_1097])]) ).
fof(f17953,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,[],[f5805]) ).
fof(f5805,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,[],[f473]) ).
fof(f473,axiom,
! [X59,X31] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X31),X59) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X59),X31),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(f40908,plain,
spl635_1096,
inference(avatar_split_clause,[],[f17948,f40906]) ).
fof(f40906,plain,
( spl635_1096
<=> ! [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,[spl635_1096])]) ).
fof(f17948,plain,
! [X0,X1] : hAPP(c_Relation_OField(X1),X0) = hAPP(c_Relation_OField(X1),hAPP(c_Relation_Oconverse(X1,X1),X0)),
inference(cnf_transformation,[],[f5800]) ).
fof(f5800,plain,
! [X0,X1] : hAPP(c_Relation_OField(X1),X0) = hAPP(c_Relation_OField(X1),hAPP(c_Relation_Oconverse(X1,X1),X0)),
inference(rectify,[],[f3771]) ).
fof(f3771,axiom,
! [X98,X8] : hAPP(c_Relation_OField(X8),X98) = hAPP(c_Relation_OField(X8),hAPP(c_Relation_Oconverse(X8,X8),X98)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Field__converse) ).
fof(f40904,plain,
spl635_1095,
inference(avatar_split_clause,[],[f17947,f40902]) ).
fof(f40902,plain,
( spl635_1095
<=> ! [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,[spl635_1095])]) ).
fof(f17947,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,[],[f5799]) ).
fof(f5799,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,[],[f2305]) ).
fof(f2305,axiom,
! [X39,X8] : c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X39),X39),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Diff__cancel) ).
fof(f40900,plain,
spl635_1094,
inference(avatar_split_clause,[],[f17463,f40898]) ).
fof(f40898,plain,
( spl635_1094
<=> ! [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,[spl635_1094])]) ).
fof(f17463,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,[],[f3562]) ).
fof(f3562,axiom,
! [X8] : c_Wellfounded_OwfP(X8,hAPP(c_COMBK(tc_fun(X8,tc_HOL_Obool),X8),hAPP(c_COMBK(tc_HOL_Obool,X8),c_fFalse))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__empty) ).
fof(f40896,plain,
spl635_1093,
inference(avatar_split_clause,[],[f17462,f40894]) ).
fof(f40894,plain,
( spl635_1093
<=> ! [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,[spl635_1093])]) ).
fof(f17462,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,[],[f3225]) ).
fof(f3225,axiom,
! [X30] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,X30)),c_Int_OInteg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ) ).
fof(f40892,plain,
spl635_1092,
inference(avatar_split_clause,[],[f17459,f40890]) ).
fof(f40890,plain,
( spl635_1092
<=> ! [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,[spl635_1092])]) ).
fof(f17459,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,[],[f5397]) ).
fof(f5397,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,[],[f3377]) ).
fof(f3377,axiom,
! [X8] : c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X8),hAPP(c_COMBK(tc_HOL_Obool,X8),c_fFalse)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__def) ).
fof(f40878,plain,
spl635_1091,
inference(avatar_split_clause,[],[f17458,f40876]) ).
fof(f40876,plain,
( spl635_1091
<=> ! [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,[spl635_1091])]) ).
fof(f17458,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,[],[f5396]) ).
fof(f5396,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,[],[f3381]) ).
fof(f3381,axiom,
! [X8] : c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X8),hAPP(c_COMBK(tc_HOL_Obool,X8),c_fTrue)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__def) ).
fof(f40826,plain,
( spl635_1090
| ~ spl635_1044
| ~ spl635_1063 ),
inference(avatar_split_clause,[],[f40512,f38100,f38016,f40823]) ).
fof(f38016,plain,
( spl635_1044
<=> hBOOL(hAPP(v_ts,hAPP(c_Int_Onat,sK106(v_ts)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1044])]) ).
fof(f38100,plain,
( spl635_1063
<=> ! [X4,X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK106(X0)))
| ~ hBOOL(hAPP(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1063])]) ).
fof(f40512,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK106(v_ts)))
| ~ spl635_1044
| ~ spl635_1063 ),
inference(resolution,[],[f38101,f38018]) ).
fof(f38018,plain,
( hBOOL(hAPP(v_ts,hAPP(c_Int_Onat,sK106(v_ts))))
| ~ spl635_1044 ),
inference(avatar_component_clause,[],[f38016]) ).
fof(f38101,plain,
( ! [X0,X4] :
( ~ hBOOL(hAPP(X0,X4))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK106(X0))) )
| ~ spl635_1063 ),
inference(avatar_component_clause,[],[f38100]) ).
fof(f40158,plain,
( spl635_1089
| ~ spl635_640
| ~ spl635_1033 ),
inference(avatar_split_clause,[],[f38065,f37971,f32448,f40156]) ).
fof(f32448,plain,
( spl635_640
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ~ hBOOL(hAPP(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_640])]) ).
fof(f37971,plain,
( spl635_1033
<=> ! [X0] :
( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X0),v_ts))
| ~ class_Enum_Oenum(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1033])]) ).
fof(f38065,plain,
( ! [X0,X1] :
( ~ class_Enum_Oenum(X0)
| hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X0),c_Hilbert__Choice_OEps(X1,c_Enum_Oenum__class_Oenum__ex(X0)))) )
| ~ spl635_640
| ~ spl635_1033 ),
inference(resolution,[],[f37972,f32449]) ).
fof(f32449,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) )
| ~ spl635_640 ),
inference(avatar_component_clause,[],[f32448]) ).
fof(f37972,plain,
( ! [X0] :
( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X0),v_ts))
| ~ class_Enum_Oenum(X0) )
| ~ spl635_1033 ),
inference(avatar_component_clause,[],[f37971]) ).
fof(f39898,plain,
( spl635_1086
| spl635_1088
| ~ spl635_1003
| ~ spl635_1033 ),
inference(avatar_split_clause,[],[f39265,f37971,f37846,f39895,f39277]) ).
fof(f39277,plain,
( spl635_1086
<=> ! [X0] : ~ class_Enum_Oenum(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1086])]) ).
fof(f39895,plain,
( spl635_1088
<=> hBOOL(hAPP(v_ts,sK142(v_ts))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1088])]) ).
fof(f37846,plain,
( spl635_1003
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,sK142(X0)))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1003])]) ).
fof(f39265,plain,
( ! [X0] :
( hBOOL(hAPP(v_ts,sK142(v_ts)))
| ~ class_Enum_Oenum(X0) )
| ~ spl635_1003
| ~ spl635_1033 ),
inference(duplicate_literal_removal,[],[f39252]) ).
fof(f39252,plain,
( ! [X0] :
( hBOOL(hAPP(v_ts,sK142(v_ts)))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X0) )
| ~ spl635_1003
| ~ spl635_1033 ),
inference(resolution,[],[f37847,f37972]) ).
fof(f37847,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| hBOOL(hAPP(X0,sK142(X0)))
| ~ class_Enum_Oenum(X1) )
| ~ spl635_1003 ),
inference(avatar_component_clause,[],[f37846]) ).
fof(f39405,plain,
( ~ spl635_185
| ~ spl635_1086 ),
inference(avatar_contradiction_clause,[],[f39402]) ).
fof(f39402,plain,
( $false
| ~ spl635_185
| ~ spl635_1086 ),
inference(resolution,[],[f39278,f30218]) ).
fof(f30218,plain,
( class_Enum_Oenum(tc_HOL_Obool)
| ~ spl635_185 ),
inference(avatar_component_clause,[],[f30216]) ).
fof(f30216,plain,
( spl635_185
<=> class_Enum_Oenum(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_185])]) ).
fof(f39278,plain,
( ! [X0] : ~ class_Enum_Oenum(X0)
| ~ spl635_1086 ),
inference(avatar_component_clause,[],[f39277]) ).
fof(f39404,plain,
( ~ spl635_184
| ~ spl635_1086 ),
inference(avatar_contradiction_clause,[],[f39403]) ).
fof(f39403,plain,
( $false
| ~ spl635_184
| ~ spl635_1086 ),
inference(resolution,[],[f39278,f30213]) ).
fof(f30213,plain,
( class_Enum_Oenum(tc_Product__Type_Ounit)
| ~ spl635_184 ),
inference(avatar_component_clause,[],[f30211]) ).
fof(f30211,plain,
( spl635_184
<=> class_Enum_Oenum(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_184])]) ).
fof(f39283,plain,
( spl635_1086
| spl635_1087
| ~ spl635_1001
| ~ spl635_1033 ),
inference(avatar_split_clause,[],[f39189,f37971,f37833,f39280,f39277]) ).
fof(f39280,plain,
( spl635_1087
<=> hBOOL(hAPP(v_ts,sK140(v_ts))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1087])]) ).
fof(f37833,plain,
( spl635_1001
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,sK140(X0)))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1001])]) ).
fof(f39189,plain,
( ! [X0] :
( hBOOL(hAPP(v_ts,sK140(v_ts)))
| ~ class_Enum_Oenum(X0) )
| ~ spl635_1001
| ~ spl635_1033 ),
inference(duplicate_literal_removal,[],[f39176]) ).
fof(f39176,plain,
( ! [X0] :
( hBOOL(hAPP(v_ts,sK140(v_ts)))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X0) )
| ~ spl635_1001
| ~ spl635_1033 ),
inference(resolution,[],[f37834,f37972]) ).
fof(f37834,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| hBOOL(hAPP(X0,sK140(X0)))
| ~ class_Enum_Oenum(X1) )
| ~ spl635_1001 ),
inference(avatar_component_clause,[],[f37833]) ).
fof(f39017,plain,
( spl635_1085
| ~ spl635_982
| ~ spl635_1044 ),
inference(avatar_split_clause,[],[f38810,f38016,f37753,f39015]) ).
fof(f39015,plain,
( spl635_1085
<=> ! [X0] :
( hBOOL(hAPP(v_ts,c_Orderings_Oord__class_OLeast(X0,v_ts)))
| ~ class_Orderings_Owellorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1085])]) ).
fof(f37753,plain,
( spl635_982
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Orderings_Oord__class_OLeast(X1,X0)))
| ~ hBOOL(hAPP(X0,X2))
| ~ class_Orderings_Owellorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_982])]) ).
fof(f38810,plain,
( ! [X0] :
( hBOOL(hAPP(v_ts,c_Orderings_Oord__class_OLeast(X0,v_ts)))
| ~ class_Orderings_Owellorder(X0) )
| ~ spl635_982
| ~ spl635_1044 ),
inference(resolution,[],[f37754,f38018]) ).
fof(f37754,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X0,c_Orderings_Oord__class_OLeast(X1,X0)))
| ~ class_Orderings_Owellorder(X1) )
| ~ spl635_982 ),
inference(avatar_component_clause,[],[f37753]) ).
fof(f38640,plain,
( spl635_1084
| ~ spl635_658
| ~ spl635_1033 ),
inference(avatar_split_clause,[],[f38064,f37971,f32520,f38638]) ).
fof(f38638,plain,
( spl635_1084
<=> ! [X0,X1] :
( ~ class_Enum_Oenum(X0)
| hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X0),sK216(c_Enum_Oenum__class_Oenum__ex(X0),X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1084])]) ).
fof(f32520,plain,
( spl635_658
<=> ! [X0,X1,X3] :
( hBOOL(hAPP(X0,sK216(X0,X1)))
| ~ hBOOL(hAPP(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_658])]) ).
fof(f38064,plain,
( ! [X0,X1] :
( ~ class_Enum_Oenum(X0)
| hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X0),sK216(c_Enum_Oenum__class_Oenum__ex(X0),X1))) )
| ~ spl635_658
| ~ spl635_1033 ),
inference(resolution,[],[f37972,f32521]) ).
fof(f32521,plain,
( ! [X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X3))
| hBOOL(hAPP(X0,sK216(X0,X1))) )
| ~ spl635_658 ),
inference(avatar_component_clause,[],[f32520]) ).
fof(f38456,plain,
( spl635_1083
| ~ spl635_804
| ~ spl635_1033 ),
inference(avatar_split_clause,[],[f38062,f37971,f34012,f38454]) ).
fof(f38454,plain,
( spl635_1083
<=> ! [X0,X1] :
( ~ class_Enum_Oenum(X0)
| hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),c_Enum_Oenum__class_Oenum__ex(X0)))
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1083])]) ).
fof(f34012,plain,
( spl635_804
<=> ! [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,[spl635_804])]) ).
fof(f38062,plain,
( ! [X0,X1] :
( ~ class_Enum_Oenum(X0)
| hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),c_Enum_Oenum__class_Oenum__ex(X0)))
| ~ class_Enum_Oenum(X1) )
| ~ spl635_804
| ~ spl635_1033 ),
inference(resolution,[],[f37972,f34013]) ).
fof(f34013,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ~ class_Enum_Oenum(X1) )
| ~ spl635_804 ),
inference(avatar_component_clause,[],[f34012]) ).
fof(f38185,plain,
spl635_1082,
inference(avatar_split_clause,[],[f28987,f38183]) ).
fof(f38183,plain,
( spl635_1082
<=> ! [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,[spl635_1082])]) ).
fof(f28987,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(c_fequal,X1)),X0))
| X0 = X1 ),
inference(forward_demodulation,[],[f22829,f26500]) ).
fof(f22829,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,[],[f16454]) ).
fof(f16454,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,[],[f9210]) ).
fof(f9210,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,[],[f3201]) ).
fof(f3201,axiom,
! [X47,X17,X1,X8] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,X1,hAPP(hAPP(c_Set_Oinsert(X8),X17),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))),X47))
<=> X17 = X47 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1Set__sing) ).
fof(f38180,plain,
spl635_1081,
inference(avatar_split_clause,[],[f28540,f38178]) ).
fof(f38178,plain,
( spl635_1081
<=> ! [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,[spl635_1081])]) ).
fof(f28540,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,[],[f25596,f17187]) ).
fof(f25596,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,[],[f21328]) ).
fof(f21328,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,[],[f15876]) ).
fof(f15876,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
| ~ sP40(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP40(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,[],[f15875]) ).
fof(f15875,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
| ~ sP40(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP40(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,[],[f14596]) ).
fof(f14596,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
<=> ( sP40(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(definition_folding,[],[f12681,f14595]) ).
fof(f14595,plain,
! [X2,X1,X0] :
( sP40(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,[sP40])]) ).
fof(f12681,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,[],[f12680]) ).
fof(f12680,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,[],[f8189]) ).
fof(f8189,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,[],[f1143]) ).
fof(f1143,axiom,
! [X48,X15,X29] :
( hBOOL(hAPP(X29,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X15,X48)))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X48
=> ! [X85,X36] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),X48))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X48),X85)),X36) = X15
=> hBOOL(hAPP(X29,X36)) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X48
=> hBOOL(hAPP(X29,X15)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__mod) ).
fof(f38176,plain,
spl635_1080,
inference(avatar_split_clause,[],[f28432,f38174]) ).
fof(f38174,plain,
( spl635_1080
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1080])]) ).
fof(f28432,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
| X0 = X1 ),
inference(forward_demodulation,[],[f21065,f26500]) ).
fof(f21065,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,[],[f12548]) ).
fof(f12548,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,[],[f8088]) ).
fof(f8088,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,[],[f2471]) ).
fof(f2471,axiom,
! [X17,X47,X8] :
( hBOOL(hAPP(hAPP(c_member(X8),X47),hAPP(hAPP(c_Set_Oinsert(X8),X17),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))))
=> X17 = X47 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_singletonE) ).
fof(f38172,plain,
spl635_1079,
inference(avatar_split_clause,[],[f27740,f38170]) ).
fof(f38170,plain,
( spl635_1079
<=> ! [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,[spl635_1079])]) ).
fof(f27740,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,[],[f25456,f24258]) ).
fof(f24258,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,[],[f17413,f17386]) ).
fof(f17413,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,[],[f5351]) ).
fof(f5351,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,[],[f1008]) ).
fof(f1008,axiom,
! [X40] : c_Int_Osucc(X40) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X40),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__def) ).
fof(f25456,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,[],[f19543]) ).
fof(f19543,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,[],[f15281]) ).
fof(f15281,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,[],[f15280]) ).
fof(f15280,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,[],[f6905]) ).
fof(f6905,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,[],[f663]) ).
fof(f663,axiom,
! [X53,X52] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X52),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X53),c_Groups_Oone__class_Oone(tc_Int_Oint))))
<=> ( X52 = X53
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X52),X53)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__add1__eq) ).
fof(f38168,plain,
spl635_1078,
inference(avatar_split_clause,[],[f27696,f38166]) ).
fof(f38166,plain,
( spl635_1078
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1078])]) ).
fof(f27696,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| sP15(X0,X1) ),
inference(forward_demodulation,[],[f27695,f25953]) ).
fof(f27695,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))
| sP15(X0,X1) ),
inference(forward_demodulation,[],[f19490,f17187]) ).
fof(f19490,plain,
! [X0,X1] :
( sP15(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,[],[f15252]) ).
fof(f15252,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)
| ~ sP15(X0,X1) )
& ( sP15(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,[],[f14556]) ).
fof(f14556,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)
<=> sP15(X0,X1) ),
inference(definition_folding,[],[f6882,f14555]) ).
fof(f14555,plain,
! [X0,X1] :
( sP15(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,[sP15])]) ).
fof(f6882,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,[],[f746]) ).
fof(f746,axiom,
! [X15,X27] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X15)
<=> ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X15
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X27 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X15
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__1) ).
fof(f38164,plain,
spl635_1077,
inference(avatar_split_clause,[],[f27694,f38162]) ).
fof(f38162,plain,
( spl635_1077
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1077])]) ).
fof(f27694,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ~ sP15(X0,X1) ),
inference(forward_demodulation,[],[f27693,f25953]) ).
fof(f27693,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))
| ~ sP15(X0,X1) ),
inference(forward_demodulation,[],[f19491,f17187]) ).
fof(f19491,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)
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f15252]) ).
fof(f38160,plain,
spl635_1076,
inference(avatar_split_clause,[],[f27676,f38158]) ).
fof(f38158,plain,
( spl635_1076
<=> ! [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,[spl635_1076])]) ).
fof(f27676,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,[],[f27675,f25953]) ).
fof(f27675,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,[],[f19482,f17187]) ).
fof(f19482,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,[],[f15249]) ).
fof(f15249,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,[],[f14554]) ).
fof(f14554,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,[],[f6881,f14553]) ).
fof(f14553,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(f6881,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,[],[f745]) ).
fof(f745,axiom,
! [X15,X27] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X27),X15)
<=> ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X15
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X27 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X15
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__is__add) ).
fof(f38156,plain,
spl635_1075,
inference(avatar_split_clause,[],[f27674,f38154]) ).
fof(f38154,plain,
( spl635_1075
<=> ! [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,[spl635_1075])]) ).
fof(f27674,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,[],[f27673,f25953]) ).
fof(f27673,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,[],[f19483,f17187]) ).
fof(f19483,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,[],[f15249]) ).
fof(f38152,plain,
( spl635_1074
| ~ spl635_529
| ~ spl635_1044 ),
inference(avatar_split_clause,[],[f38103,f38016,f31757,f38149]) ).
fof(f38149,plain,
( spl635_1074
<=> sP8(v_ts,sK106(v_ts)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1074])]) ).
fof(f31757,plain,
( spl635_529
<=> ! [X0,X1] :
( sP8(X1,X0)
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_529])]) ).
fof(f38103,plain,
( sP8(v_ts,sK106(v_ts))
| ~ spl635_529
| ~ spl635_1044 ),
inference(resolution,[],[f38018,f31758]) ).
fof(f31758,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| sP8(X1,X0) )
| ~ spl635_529 ),
inference(avatar_component_clause,[],[f31757]) ).
fof(f38147,plain,
spl635_1073,
inference(avatar_split_clause,[],[f27554,f38145]) ).
fof(f38145,plain,
( spl635_1073
<=> ! [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,[spl635_1073])]) ).
fof(f27554,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,[],[f19329,f17187]) ).
fof(f19329,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,[],[f15161]) ).
fof(f15161,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,[],[f6829]) ).
fof(f6829,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,[],[f4132]) ).
fof(f4132,axiom,
! [X210,X8] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X210)
<=> c_List_Olist_ONil(X8) = X210 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_length__0__conv) ).
fof(f38143,plain,
spl635_1072,
inference(avatar_split_clause,[],[f27547,f38141]) ).
fof(f38141,plain,
( spl635_1072
<=> ! [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,[spl635_1072])]) ).
fof(f27547,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,[],[f25393,f17187]) ).
fof(f25393,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,[],[f19258]) ).
fof(f19258,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,[],[f15109]) ).
fof(f15109,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),sK196(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,[sK196])],[f15107,f15108]) ).
fof(f15108,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),sK196(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f15107,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,[],[f15106]) ).
fof(f15106,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,[],[f6796]) ).
fof(f6796,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,[],[f1088]) ).
fof(f1088,axiom,
! [X72,X27] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X27,X72)
<=> ? [X93] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X72),X93) = X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__eq__0__iff) ).
fof(f38139,plain,
spl635_1071,
inference(avatar_split_clause,[],[f27237,f38137]) ).
fof(f27237,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,[],[f18948,f17176]) ).
fof(f18948,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,[],[f11117]) ).
fof(f11117,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,[],[f6619]) ).
fof(f6619,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,[],[f2086]) ).
fof(f2086,axiom,
! [X35,X30] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30))
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X30,X35)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__function__closures) ).
fof(f38135,plain,
spl635_1070,
inference(avatar_split_clause,[],[f27067,f38133]) ).
fof(f38133,plain,
( spl635_1070
<=> ! [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,[spl635_1070])]) ).
fof(f27067,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,[],[f18871,f17187]) ).
fof(f18871,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,[],[f11032]) ).
fof(f11032,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,[],[f6561]) ).
fof(f6561,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,[],[f637]) ).
fof(f637,axiom,
! [X4,X24] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X4) = X24
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
fof(f38131,plain,
spl635_1069,
inference(avatar_split_clause,[],[f26983,f38129]) ).
fof(f38129,plain,
( spl635_1069
<=> ! [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,[spl635_1069])]) ).
fof(f26983,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,[],[f18590,f17187]) ).
fof(f18590,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,[],[f10732]) ).
fof(f10732,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,[],[f6334]) ).
fof(f6334,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,[],[f402]) ).
fof(f402,axiom,
! [X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) ).
fof(f38127,plain,
spl635_1068,
inference(avatar_split_clause,[],[f26964,f38125]) ).
fof(f38125,plain,
( spl635_1068
<=> ! [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,[spl635_1068])]) ).
fof(f26964,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,[],[f18552,f17187]) ).
fof(f18552,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,[],[f10694]) ).
fof(f10694,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,[],[f6298]) ).
fof(f6298,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,[],[f403]) ).
fof(f403,axiom,
! [X33,X5] :
( class_Power_Opower(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),X33),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__0) ).
fof(f38123,plain,
spl635_1067,
inference(avatar_split_clause,[],[f26854,f38121]) ).
fof(f38121,plain,
( spl635_1067
<=> ! [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,[spl635_1067])]) ).
fof(f26854,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,[],[f18348,f17176]) ).
fof(f18348,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,[],[f14797]) ).
fof(f14797,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,[],[f10514]) ).
fof(f10514,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,[],[f6140]) ).
fof(f6140,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,[],[f343]) ).
fof(f343,axiom,
! [X53,X8] :
( class_Int_Oring__char__0(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = hAPP(c_Int_Oring__1__class_Oof__int(X8),X53)
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X53 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__eq__0__iff) ).
fof(f38119,plain,
spl635_1066,
inference(avatar_split_clause,[],[f26720,f38117]) ).
fof(f38117,plain,
( spl635_1066
<=> ! [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,[spl635_1066])]) ).
fof(f26720,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,[],[f18270,f17176]) ).
fof(f18270,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,[],[f10477]) ).
fof(f10477,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,[],[f6089]) ).
fof(f6089,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,[],[f831]) ).
fof(f831,axiom,
! [X13,X12] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),X13))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Nat__Transfer_Otsub(X13,X12) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X12),X13))
=> c_Nat__Transfer_Otsub(X13,X12) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X13),X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tsub__def) ).
fof(f38115,plain,
spl635_1065,
inference(avatar_split_clause,[],[f26643,f38113]) ).
fof(f38113,plain,
( spl635_1065
<=> ! [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,[spl635_1065])]) ).
fof(f26643,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,[],[f18234,f17187]) ).
fof(f18234,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,[],[f10460]) ).
fof(f10460,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,[],[f6072]) ).
fof(f6072,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,[],[f3108]) ).
fof(f3108,axiom,
! [X39,X8] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X39))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X8),X39) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X39))
=> hAPP(c_Finite__Set_Ocard(X8),X39) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,X8,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,X8),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X39) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__def) ).
fof(f38111,plain,
spl635_1064,
inference(avatar_split_clause,[],[f26528,f38109]) ).
fof(f38109,plain,
( spl635_1064
<=> ! [X0,X1] : hAPP(c_fequal,X0) = hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1064])]) ).
fof(f38102,plain,
spl635_1063,
inference(avatar_split_clause,[],[f26470,f38100]) ).
fof(f26470,plain,
! [X0,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK106(X0)))
| ~ hBOOL(hAPP(X0,X4)) ),
inference(forward_demodulation,[],[f17801,f17176]) ).
fof(f17801,plain,
! [X0,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK106(X0)))
| ~ hBOOL(hAPP(X0,X4)) ),
inference(cnf_transformation,[],[f14781]) ).
fof(f14781,plain,
! [X0] :
( ( hBOOL(hAPP(X0,sK105(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,sK106(X0))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK106(X0))) )
| ! [X4] : ~ hBOOL(hAPP(X0,X4)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK105,sK106])],[f14778,f14780,f14779]) ).
fof(f14779,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP(X0,X1))
=> hBOOL(hAPP(X0,sK105(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14780,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,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(f14778,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,[],[f14777]) ).
fof(f14777,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,[],[f394]) ).
fof(f394,axiom,
! [X29] :
( ? [X65] : hBOOL(hAPP(X29,X65))
<=> ? [X2] :
( hBOOL(hAPP(X29,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',fact_ex__nat) ).
fof(f38098,plain,
spl635_1062,
inference(avatar_split_clause,[],[f26465,f38096]) ).
fof(f38096,plain,
( spl635_1062
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK101(X0)))
| hBOOL(hAPP(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1062])]) ).
fof(f26465,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK101(X0)))
| hBOOL(hAPP(X0,X1)) ),
inference(forward_demodulation,[],[f17796,f17176]) ).
fof(f17796,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)),sK101(X0))) ),
inference(cnf_transformation,[],[f14771]) ).
fof(f14771,plain,
! [X0] :
( ( ! [X1] : hBOOL(hAPP(X0,X1))
| ( ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK101(X0))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK101(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,sK102(X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK101,sK102])],[f14768,f14770,f14769]) ).
fof(f14769,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,sK101(X0))))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK101(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f14770,plain,
! [X0] :
( ? [X4] : ~ hBOOL(hAPP(X0,X4))
=> ~ hBOOL(hAPP(X0,sK102(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14768,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,[],[f14767]) ).
fof(f14767,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,[],[f10445]) ).
fof(f10445,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,[],[f393]) ).
fof(f393,axiom,
! [X29] :
( ! [X65] : hBOOL(hAPP(X29,X65))
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
=> hBOOL(hAPP(X29,hAPP(c_Int_Onat,X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat) ).
fof(f38094,plain,
spl635_1061,
inference(avatar_split_clause,[],[f26420,f38092]) ).
fof(f38092,plain,
( spl635_1061
<=> ! [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,[spl635_1061])]) ).
fof(f26420,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,[],[f26419,f25953]) ).
fof(f26419,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,[],[f26418,f17187]) ).
fof(f26418,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,[],[f17775,f17187]) ).
fof(f17775,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,[],[f14757]) ).
fof(f14757,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,[],[f119]) ).
fof(f119,axiom,
! [X15] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__Suc0) ).
fof(f38090,plain,
spl635_1060,
inference(avatar_split_clause,[],[f26401,f38088]) ).
fof(f38088,plain,
( spl635_1060
<=> ! [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,[spl635_1060])]) ).
fof(f26401,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,[],[f26400,f17187]) ).
fof(f26400,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,[],[f17747,f17187]) ).
fof(f17747,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,[],[f14740]) ).
fof(f14740,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,[],[f36]) ).
fof(f36,axiom,
! [X15] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X15),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
fof(f38086,plain,
spl635_1059,
inference(avatar_split_clause,[],[f26374,f38084]) ).
fof(f38084,plain,
( spl635_1059
<=> ! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) != sK99(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,[spl635_1059])]) ).
fof(f26374,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) != sK99(X0)
| c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X0) ),
inference(forward_demodulation,[],[f26373,f17187]) ).
fof(f26373,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) != sK99(X0) ),
inference(forward_demodulation,[],[f17716,f17187]) ).
fof(f17716,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) != sK99(X0) ),
inference(cnf_transformation,[],[f14724]) ).
fof(f14724,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) != sK99(X0)
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK99(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,[sK99])],[f14722,f14723]) ).
fof(f14723,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) != sK99(X0)
& hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK99(X0)),hAPP(c_List_Oset(tc_Nat_Onat),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f14722,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,[],[f14721]) ).
fof(f14721,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,[],[f10444]) ).
fof(f10444,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,[],[f5616]) ).
fof(f5616,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,[],[f4191]) ).
fof(f4191,axiom,
! [X219] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),X219)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),X2),hAPP(c_List_Oset(tc_Nat_Onat),X219)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__eq__0__nat__iff__nat) ).
fof(f38082,plain,
spl635_1058,
inference(avatar_split_clause,[],[f26364,f38080]) ).
fof(f38080,plain,
( spl635_1058
<=> ! [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,[spl635_1058])]) ).
fof(f26364,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,[],[f26363,f25943]) ).
fof(f25943,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,[],[f17207,f17187]) ).
fof(f17207,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,[],[f1795]) ).
fof(f1795,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',fact_zero__code__numeral__def) ).
fof(f26363,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,[],[f17708,f17187]) ).
fof(f17708,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,[],[f14718]) ).
fof(f14718,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,[],[f5613]) ).
fof(f5613,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,[],[f1791]) ).
fof(f1791,axiom,
! [X14] :
( hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X14
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X14)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral__not__eq__zero) ).
fof(f38078,plain,
spl635_1057,
inference(avatar_split_clause,[],[f26249,f38076]) ).
fof(f38076,plain,
( spl635_1057
<=> ! [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,[spl635_1057])]) ).
fof(f26249,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,[],[f26248,f17187]) ).
fof(f26248,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,[],[f17637,f17187]) ).
fof(f17637,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,[],[f10396]) ).
fof(f10396,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,[],[f5561]) ).
fof(f5561,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,[],[f47]) ).
fof(f47,axiom,
! [X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X4
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
fof(f38074,plain,
spl635_1056,
inference(avatar_split_clause,[],[f26245,f38072]) ).
fof(f38072,plain,
( spl635_1056
<=> ! [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,[spl635_1056])]) ).
fof(f26245,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,[],[f17635,f17176]) ).
fof(f17635,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,[],[f10394]) ).
fof(f10394,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,[],[f5559]) ).
fof(f5559,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,[],[f862]) ).
fof(f862,axiom,
! [X33] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X33
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X33),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__self) ).
fof(f38069,plain,
( spl635_1055
| ~ spl635_328
| ~ spl635_486
| ~ spl635_1054 ),
inference(avatar_split_clause,[],[f38061,f38058,f31582,f30869,f38067]) ).
fof(f38067,plain,
( spl635_1055
<=> ! [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,[spl635_1055])]) ).
fof(f38058,plain,
( spl635_1054
<=> ! [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,[spl635_1054])]) ).
fof(f38061,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) )
| ~ spl635_328
| ~ spl635_486
| ~ spl635_1054 ),
inference(forward_demodulation,[],[f38059,f31991]) ).
fof(f38059,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) )
| ~ spl635_1054 ),
inference(avatar_component_clause,[],[f38058]) ).
fof(f38060,plain,
spl635_1054,
inference(avatar_split_clause,[],[f26232,f38058]) ).
fof(f26232,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,[],[f26231,f25942]) ).
fof(f26231,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,[],[f24300,f17174]) ).
fof(f24300,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,[],[f17582,f24179]) ).
fof(f17582,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,[],[f10342]) ).
fof(f10342,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,[],[f5507]) ).
fof(f5507,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,[],[f1197]) ).
fof(f1197,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OBit1(c_Int_OPls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).
fof(f38056,plain,
spl635_1053,
inference(avatar_split_clause,[],[f26199,f38054]) ).
fof(f38054,plain,
( spl635_1053
<=> ! [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,[spl635_1053])]) ).
fof(f26199,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,[],[f26198,f17327]) ).
fof(f26198,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,[],[f26197,f17176]) ).
fof(f26197,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,[],[f17551,f26085]) ).
fof(f26085,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X0),
inference(forward_demodulation,[],[f17435,f17327]) ).
fof(f17435,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,[],[f818]) ).
fof(f818,axiom,
! [X67] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X67) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X67)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__number__of__def) ).
fof(f17551,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,[],[f10320]) ).
fof(f10320,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,[],[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_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,[],[f896]) ).
fof(f896,axiom,
! [X67] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X67)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X67) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X67)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X67)))
=> 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),X67)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__nat__number__of) ).
fof(f38052,plain,
spl635_1052,
inference(avatar_split_clause,[],[f26196,f38050]) ).
fof(f26196,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,[],[f26195,f17327]) ).
fof(f26195,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,[],[f26194,f17327]) ).
fof(f26194,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,[],[f17552,f26085]) ).
fof(f17552,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,[],[f10320]) ).
fof(f38048,plain,
spl635_1051,
inference(avatar_split_clause,[],[f26193,f38046]) ).
fof(f38046,plain,
( spl635_1051
<=> ! [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,[spl635_1051])]) ).
fof(f26193,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,[],[f26192,f17327]) ).
fof(f26192,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,[],[f17549,f26085]) ).
fof(f17549,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,[],[f10319]) ).
fof(f10319,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,[],[f5481]) ).
fof(f5481,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,[],[f901]) ).
fof(f901,axiom,
! [X67] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X67)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X67)) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X67)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X67)))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X67)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__nat__number__of) ).
fof(f38044,plain,
spl635_1050,
inference(avatar_split_clause,[],[f26096,f38042]) ).
fof(f38042,plain,
( spl635_1050
<=> ! [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,[spl635_1050])]) ).
fof(f26096,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,[],[f17457,f17176]) ).
fof(f17457,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_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)),
inference(cnf_transformation,[],[f5395]) ).
fof(f5395,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_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)),
inference(rectify,[],[f2055]) ).
fof(f2055,axiom,
! [X75] : hAPP(c_Int_Onat,X75) = 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)),X75)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atLeastZeroLessThan__int) ).
fof(f38040,plain,
spl635_1049,
inference(avatar_split_clause,[],[f26093,f38038]) ).
fof(f38038,plain,
( spl635_1049
<=> ! [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,[spl635_1049])]) ).
fof(f26093,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,[],[f17447,f17187]) ).
fof(f17447,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,[],[f5385]) ).
fof(f5385,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,[],[f787]) ).
fof(f787,axiom,
! [X4] : 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),X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zminus__int) ).
fof(f38036,plain,
spl635_1048,
inference(avatar_split_clause,[],[f26009,f38033]) ).
fof(f38033,plain,
( spl635_1048
<=> 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,[spl635_1048])]) ).
fof(f26009,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,[],[f26008,f25996]) ).
fof(f26008,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,[],[f26007,f25942]) ).
fof(f26007,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,[],[f24223,f17174]) ).
fof(f24223,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,[],[f17265,f24179]) ).
fof(f17265,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,[],[f3208]) ).
fof(f3208,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',fact_card__UNIV__bool) ).
fof(f38031,plain,
spl635_1047,
inference(avatar_split_clause,[],[f25858,f38029]) ).
fof(f38029,plain,
( spl635_1047
<=> ! [X4,X0,X2] : sP82(X0,hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0),X2,c_List_Olist_ONil(X2),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1047])]) ).
fof(f25858,plain,
! [X2,X0,X4] : sP82(X0,hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0),X2,c_List_Olist_ONil(X2),X4),
inference(equality_resolution,[],[f25857]) ).
fof(f25857,plain,
! [X2,X3,X0,X4] :
( sP82(X0,hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0),X2,X3,X4)
| c_List_Olist_ONil(X2) != X3 ),
inference(equality_resolution,[],[f23674]) ).
fof(f23674,plain,
! [X2,X3,X0,X1,X4] :
( sP82(X0,X1,X2,X3,X4)
| hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0) != X1
| c_List_Olist_ONil(X2) != X3 ),
inference(cnf_transformation,[],[f16790]) ).
fof(f16790,plain,
! [X0,X1,X2,X3,X4] :
( ( sP82(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),sK583(X0,X1,X2,X3,X4)),X1) = X0
& hAPP(hAPP(c_List_Olist_OCons(X2),X4),sK583(X0,X1,X2,X3,X4)) = X3 )
| ( hAPP(hAPP(c_List_Olist_OCons(X2),X4),X0) = X1
& c_List_Olist_ONil(X2) = X3 )
| ~ sP82(X0,X1,X2,X3,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK583])],[f16788,f16789]) ).
fof(f16789,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),sK583(X0,X1,X2,X3,X4)),X1) = X0
& hAPP(hAPP(c_List_Olist_OCons(X2),X4),sK583(X0,X1,X2,X3,X4)) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f16788,plain,
! [X0,X1,X2,X3,X4] :
( ( sP82(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 )
| ~ sP82(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16787]) ).
fof(f16787,plain,
! [X0,X2,X4,X3,X1] :
( ( sP82(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 )
| ~ sP82(X0,X2,X4,X3,X1) ) ),
inference(flattening,[],[f16786]) ).
fof(f16786,plain,
! [X0,X2,X4,X3,X1] :
( ( sP82(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 )
| ~ sP82(X0,X2,X4,X3,X1) ) ),
inference(nnf_transformation,[],[f14670]) ).
fof(f14670,plain,
! [X0,X2,X4,X3,X1] :
( sP82(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,[sP82])]) ).
fof(f38027,plain,
spl635_1046,
inference(avatar_split_clause,[],[f25854,f38025]) ).
fof(f38025,plain,
( spl635_1046
<=> ! [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,[spl635_1046])]) ).
fof(f25854,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,[],[f25853]) ).
fof(f25853,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,[],[f23666]) ).
fof(f23666,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,[],[f16784]) ).
fof(f16784,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),sK582(X0,X1,X2,X3,X4)),X1) = X0
& hAPP(hAPP(c_List_Olist_OCons(X2),X4),sK582(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,[sK582])],[f16782,f16783]) ).
fof(f16783,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),sK582(X0,X1,X2,X3,X4)),X1) = X0
& hAPP(hAPP(c_List_Olist_OCons(X2),X4),sK582(X0,X1,X2,X3,X4)) = X3 ) ),
introduced(choice_axiom,[]) ).
fof(f16782,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,[],[f16781]) ).
fof(f16781,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,[],[f16780]) ).
fof(f16780,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,[],[f14668]) ).
fof(f14668,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(f38023,plain,
spl635_1045,
inference(avatar_split_clause,[],[f25474,f38021]) ).
fof(f38021,plain,
( spl635_1045
<=> ! [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,[spl635_1045])]) ).
fof(f25474,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,[],[f19975]) ).
fof(f19975,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,[],[f15368]) ).
fof(f15368,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,[],[f15367]) ).
fof(f15367,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,[],[f11367]) ).
fof(f11367,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,[],[f7275]) ).
fof(f7275,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,[],[f179]) ).
fof(f179,axiom,
! [X47,X17,X8] :
( class_Rings_Oring__no__zero__divisors(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X17),X47)
<=> ( c_Groups_Ozero__class_Ozero(X8) = X47
| c_Groups_Ozero__class_Ozero(X8) = X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__eq__0__iff) ).
fof(f38019,plain,
( spl635_1044
| ~ spl635_770
| ~ spl635_950 ),
inference(avatar_split_clause,[],[f37659,f37609,f33874,f38016]) ).
fof(f33874,plain,
( spl635_770
<=> ! [X4,X0] :
( hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK106(X0))))
| ~ hBOOL(hAPP(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_770])]) ).
fof(f37609,plain,
( spl635_950
<=> hBOOL(hAPP(v_ts,sK89)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_950])]) ).
fof(f37659,plain,
( hBOOL(hAPP(v_ts,hAPP(c_Int_Onat,sK106(v_ts))))
| ~ spl635_770
| ~ spl635_950 ),
inference(resolution,[],[f37611,f33875]) ).
fof(f33875,plain,
( ! [X0,X4] :
( ~ hBOOL(hAPP(X0,X4))
| hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK106(X0)))) )
| ~ spl635_770 ),
inference(avatar_component_clause,[],[f33874]) ).
fof(f37611,plain,
( hBOOL(hAPP(v_ts,sK89))
| ~ spl635_950 ),
inference(avatar_component_clause,[],[f37609]) ).
fof(f38014,plain,
spl635_1043,
inference(avatar_split_clause,[],[f25473,f38012]) ).
fof(f38012,plain,
( spl635_1043
<=> ! [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,[spl635_1043])]) ).
fof(f25473,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,[],[f19976]) ).
fof(f19976,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,[],[f15368]) ).
fof(f38010,plain,
spl635_1042,
inference(avatar_split_clause,[],[f24964,f38008]) ).
fof(f38008,plain,
( spl635_1042
<=> ! [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,[spl635_1042])]) ).
fof(f24964,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,[],[f21640,f19665]) ).
fof(f19665,plain,
! [X2,X0,X1] : c_Product__Type_Oprod_Oprod__case(X2,X1,X0) = c_Product__Type_Ointernal__split(X2,X1,X0),
inference(cnf_transformation,[],[f6960]) ).
fof(f6960,plain,
! [X0,X1,X2] : c_Product__Type_Oprod_Oprod__case(X2,X1,X0) = c_Product__Type_Ointernal__split(X2,X1,X0),
inference(rectify,[],[f1764]) ).
fof(f1764,axiom,
! [X109,X25,X8] : c_Product__Type_Oprod_Oprod__case(X8,X25,X109) = c_Product__Type_Ointernal__split(X8,X25,X109),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_internal__split__def) ).
fof(f21640,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,[],[f8304]) ).
fof(f8304,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,[],[f1836]) ).
fof(f1836,axiom,
! [X1,X109,X25,X8] : c_Product__Type_Ocurry(X8,X25,X109,hAPP(c_Product__Type_Oprod_Oprod__case(X8,X25,X109),X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_curry__split) ).
fof(f38006,plain,
spl635_1041,
inference(avatar_split_clause,[],[f24963,f38004]) ).
fof(f38004,plain,
( spl635_1041
<=> ! [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,[spl635_1041])]) ).
fof(f24963,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,[],[f21639,f19665]) ).
fof(f21639,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,[],[f8303]) ).
fof(f8303,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,[],[f1835]) ).
fof(f1835,axiom,
! [X1,X109,X25,X8] : hAPP(c_Product__Type_Oprod_Oprod__case(X8,X25,X109),c_Product__Type_Ocurry(X8,X25,X109,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__curry) ).
fof(f38002,plain,
spl635_1040,
inference(avatar_split_clause,[],[f24377,f38000]) ).
fof(f38000,plain,
( spl635_1040
<=> ! [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,[spl635_1040])]) ).
fof(f24377,plain,
! [X0,X1] : hAPP(c_List_Omember(X1),X0) = hAPP(c_List_Omember(X1),hAPP(c_List_Orev(X1),X0)),
inference(definition_unfolding,[],[f17927,f17309,f17309]) ).
fof(f17927,plain,
! [X0,X1] : hAPP(c_List_Oset(X1),X0) = hAPP(c_List_Oset(X1),hAPP(c_List_Orev(X1),X0)),
inference(cnf_transformation,[],[f5779]) ).
fof(f5779,plain,
! [X0,X1] : hAPP(c_List_Oset(X1),X0) = hAPP(c_List_Oset(X1),hAPP(c_List_Orev(X1),X0)),
inference(rectify,[],[f4676]) ).
fof(f4676,axiom,
! [X210,X8] : hAPP(c_List_Oset(X8),X210) = hAPP(c_List_Oset(X8),hAPP(c_List_Orev(X8),X210)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rev) ).
fof(f37998,plain,
spl635_1039,
inference(avatar_split_clause,[],[f24376,f37996]) ).
fof(f37996,plain,
( spl635_1039
<=> ! [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,[spl635_1039])]) ).
fof(f24376,plain,
! [X0,X1] : hAPP(c_List_Omember(X1),X0) = hAPP(c_List_Omember(X1),hAPP(c_List_Orotate1(X1),X0)),
inference(definition_unfolding,[],[f17926,f17309,f17309]) ).
fof(f17926,plain,
! [X0,X1] : hAPP(c_List_Oset(X1),X0) = hAPP(c_List_Oset(X1),hAPP(c_List_Orotate1(X1),X0)),
inference(cnf_transformation,[],[f5778]) ).
fof(f5778,plain,
! [X0,X1] : hAPP(c_List_Oset(X1),X0) = hAPP(c_List_Oset(X1),hAPP(c_List_Orotate1(X1),X0)),
inference(rectify,[],[f4276]) ).
fof(f4276,axiom,
! [X210,X8] : hAPP(c_List_Oset(X8),X210) = hAPP(c_List_Oset(X8),hAPP(c_List_Orotate1(X8),X210)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__rotate1) ).
fof(f37994,plain,
spl635_1038,
inference(avatar_split_clause,[],[f24360,f37992]) ).
fof(f37992,plain,
( spl635_1038
<=> ! [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,[spl635_1038])]) ).
fof(f24360,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,[],[f17868,f17908]) ).
fof(f17908,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,[],[f5760]) ).
fof(f5760,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,[],[f1781]) ).
fof(f1781,axiom,
! [X15,X27] : c_Divides_Odivmod__nat(X27,X15) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(X27,X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__def) ).
fof(f17868,plain,
! [X0,X1] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),c_Divides_Odivmod__nat(X1,X0))),
inference(cnf_transformation,[],[f5720]) ).
fof(f5720,plain,
! [X0,X1] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X1,X0),c_Divides_Odivmod__nat(X1,X0))),
inference(rectify,[],[f1597]) ).
fof(f1597,axiom,
! [X4,X24] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X24,X4),c_Divides_Odivmod__nat(X24,X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).
fof(f37990,plain,
spl635_1037,
inference(avatar_split_clause,[],[f24349,f37988]) ).
fof(f37988,plain,
( spl635_1037
<=> ! [X0,X1] : c_Relation_Otrans(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X0),c_Transitive__Closure_Ortrancl(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1037])]) ).
fof(f24349,plain,
! [X0,X1] : c_Relation_Otrans(X1,hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X0),c_Transitive__Closure_Ortrancl(X1,X0))),
inference(definition_unfolding,[],[f17825,f17973]) ).
fof(f17973,plain,
! [X0,X1] : c_Transitive__Closure_Otrancl(X1,X0) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X0),c_Transitive__Closure_Ortrancl(X1,X0)),
inference(cnf_transformation,[],[f5825]) ).
fof(f5825,plain,
! [X0,X1] : c_Transitive__Closure_Otrancl(X1,X0) = hAPP(hAPP(c_Relation_Orel__comp(X1,X1,X1),X0),c_Transitive__Closure_Ortrancl(X1,X0)),
inference(rectify,[],[f3708]) ).
fof(f3708,axiom,
! [X98,X8] : c_Transitive__Closure_Otrancl(X8,X98) = hAPP(hAPP(c_Relation_Orel__comp(X8,X8,X8),X98),c_Transitive__Closure_Ortrancl(X8,X98)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trancl__unfold__left) ).
fof(f17825,plain,
! [X0,X1] : c_Relation_Otrans(X1,c_Transitive__Closure_Otrancl(X1,X0)),
inference(cnf_transformation,[],[f5677]) ).
fof(f5677,plain,
! [X0,X1] : c_Relation_Otrans(X1,c_Transitive__Closure_Otrancl(X1,X0)),
inference(rectify,[],[f4915]) ).
fof(f4915,axiom,
! [X98,X8] : c_Relation_Otrans(X8,c_Transitive__Closure_Otrancl(X8,X98)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__trancl) ).
fof(f37986,plain,
spl635_1036,
inference(avatar_split_clause,[],[f24314,f37984]) ).
fof(f37984,plain,
( spl635_1036
<=> ! [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,[spl635_1036])]) ).
fof(f24314,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,[],[f17690,f24179]) ).
fof(f17690,plain,
! [X0] :
( c_Int_OMin = X0
| c_Int_OMin != c_Int_OBit1(X0) ),
inference(cnf_transformation,[],[f14702]) ).
fof(f14702,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,[],[f5605]) ).
fof(f5605,plain,
! [X0] :
( c_Int_OMin = c_Int_OBit1(X0)
<=> c_Int_OMin = X0 ),
inference(rectify,[],[f1174]) ).
fof(f1174,axiom,
! [X77] :
( c_Int_OMin = c_Int_OBit1(X77)
<=> c_Int_OMin = X77 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).
fof(f37982,plain,
spl635_1035,
inference(avatar_split_clause,[],[f24206,f37979]) ).
fof(f37979,plain,
( spl635_1035
<=> c_Wellfounded_Oless__than = hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Wellfounded_Opred__nat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1035])]) ).
fof(f24206,plain,
c_Wellfounded_Oless__than = hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Wellfounded_Opred__nat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)),
inference(definition_unfolding,[],[f17181,f17973]) ).
fof(f17181,plain,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f3681]) ).
fof(f3681,axiom,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__than__def) ).
fof(f37977,plain,
spl635_1034,
inference(avatar_split_clause,[],[f23576,f37975]) ).
fof(f37975,plain,
( spl635_1034
<=> ! [X4,X0,X3,X2,X1] :
( X0 = X2
| c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) != c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1034])]) ).
fof(f23576,plain,
! [X2,X3,X0,X1,X4] :
( X0 = X2
| c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) != c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) ),
inference(cnf_transformation,[],[f16719]) ).
fof(f16719,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) = c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) != c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) ) ),
inference(flattening,[],[f16718]) ).
fof(f16718,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) = c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) != c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) ) ),
inference(nnf_transformation,[],[f9732]) ).
fof(f9732,plain,
! [X0,X1,X2,X3,X4] :
( c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) = c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0)
<=> ( X0 = X2
& X1 = X3 ) ),
inference(rectify,[],[f4871]) ).
fof(f4871,axiom,
! [X257,X124,X258,X17,X8] :
( c_Lazy__Sequence_Olazy__sequence_OInsert(X8,X17,X258) = c_Lazy__Sequence_Olazy__sequence_OInsert(X8,X124,X257)
<=> ( X257 = X258
& X17 = X124 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Oinject) ).
fof(f37973,plain,
( spl635_1033
| ~ spl635_804
| ~ spl635_950 ),
inference(avatar_split_clause,[],[f37658,f37609,f34012,f37971]) ).
fof(f37658,plain,
( ! [X0] :
( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X0),v_ts))
| ~ class_Enum_Oenum(X0) )
| ~ spl635_804
| ~ spl635_950 ),
inference(resolution,[],[f37611,f34013]) ).
fof(f37969,plain,
spl635_1032,
inference(avatar_split_clause,[],[f23575,f37967]) ).
fof(f37967,plain,
( spl635_1032
<=> ! [X2,X4,X0,X3,X1] :
( X1 = X3
| c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) != c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1032])]) ).
fof(f23575,plain,
! [X2,X3,X0,X1,X4] :
( X1 = X3
| c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X3,X2) != c_Lazy__Sequence_Olazy__sequence_OInsert(X4,X1,X0) ),
inference(cnf_transformation,[],[f16719]) ).
fof(f37965,plain,
spl635_1031,
inference(avatar_split_clause,[],[f22856,f37963]) ).
fof(f37963,plain,
( spl635_1031
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ sP67(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1031])]) ).
fof(f22856,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ~ sP67(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16470]) ).
fof(f16470,plain,
! [X0,X1,X2,X3] :
( ( sP67(X0,X1,X2,X3)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ( ( ~ sP66(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))
& ( ( sP66(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)) ) )
| ~ sP67(X0,X1,X2,X3) ) ),
inference(rectify,[],[f16469]) ).
fof(f16469,plain,
! [X0,X1,X3,X2] :
( ( sP67(X0,X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ( ( ~ sP66(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))
& ( ( sP66(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)) ) )
| ~ sP67(X0,X1,X3,X2) ) ),
inference(flattening,[],[f16468]) ).
fof(f16468,plain,
! [X0,X1,X3,X2] :
( ( sP67(X0,X1,X3,X2)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
| ( ( ~ sP66(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))
& ( ( sP66(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)) ) )
| ~ sP67(X0,X1,X3,X2) ) ),
inference(nnf_transformation,[],[f14642]) ).
fof(f14642,plain,
! [X0,X1,X3,X2] :
( sP67(X0,X1,X3,X2)
<=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1),X0))
& ( ( sP66(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,[sP67])]) ).
fof(f37961,plain,
spl635_1030,
inference(avatar_split_clause,[],[f22349,f37959]) ).
fof(f37959,plain,
( spl635_1030
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X0),sK433(X0,X1,X2)))
| ~ sP57(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1030])]) ).
fof(f22349,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X0),sK433(X0,X1,X2)))
| ~ sP57(X0,X1,X2) ),
inference(cnf_transformation,[],[f16212]) ).
fof(f16212,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X0),sK432(X0,X1,X2)),sK433(X0,X1,X2))))
& hBOOL(hAPP(X1,sK433(X0,X1,X2)))
& ~ hBOOL(hAPP(hAPP(c_member(X0),sK432(X0,X1,X2)),sK433(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK432(X0,X1,X2)),X2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X0),sK433(X0,X1,X2))) )
| ~ sP57(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK432,sK433])],[f16210,f16211]) ).
fof(f16211,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),sK432(X0,X1,X2)),sK433(X0,X1,X2))))
& hBOOL(hAPP(X1,sK433(X0,X1,X2)))
& ~ hBOOL(hAPP(hAPP(c_member(X0),sK432(X0,X1,X2)),sK433(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK432(X0,X1,X2)),X2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X0),sK433(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f16210,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)) )
| ~ sP57(X0,X1,X2) ),
inference(rectify,[],[f16209]) ).
fof(f16209,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)) )
| ~ sP57(X3,X0,X1) ),
inference(nnf_transformation,[],[f14624]) ).
fof(f14624,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)) )
| ~ sP57(X3,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP57])]) ).
fof(f37957,plain,
spl635_1029,
inference(avatar_split_clause,[],[f22302,f37955]) ).
fof(f37955,plain,
( spl635_1029
<=> ! [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,[spl635_1029])]) ).
fof(f22302,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,[],[f13250]) ).
fof(f13250,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,[],[f8884]) ).
fof(f8884,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,[],[f3488]) ).
fof(f3488,axiom,
! [X1,X25,X98,X8] :
( c_Wellfounded_Owf(X8,X98)
=> c_Wellfounded_Owf(X25,hAPP(hAPP(c_Relation_Oinv__image(X8,X25),X98),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__inv__image) ).
fof(f37953,plain,
spl635_1028,
inference(avatar_split_clause,[],[f22300,f37951]) ).
fof(f37951,plain,
( spl635_1028
<=> ! [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,[spl635_1028])]) ).
fof(f22300,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,[],[f13247]) ).
fof(f13247,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,[],[f8882]) ).
fof(f8882,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,[],[f4906]) ).
fof(f4906,axiom,
! [X1,X25,X98,X8] :
( c_Relation_Otrans(X8,X98)
=> c_Relation_Otrans(X25,hAPP(hAPP(c_Relation_Oinv__image(X8,X25),X98),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__inv__image) ).
fof(f37949,plain,
spl635_1027,
inference(avatar_split_clause,[],[f22298,f37947]) ).
fof(f37947,plain,
( spl635_1027
<=> ! [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,[spl635_1027])]) ).
fof(f22298,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,[],[f13244]) ).
fof(f13244,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,[],[f8880]) ).
fof(f8880,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,[],[f4951]) ).
fof(f4951,axiom,
! [X1,X25,X98,X8] :
( c_Relation_Osym(X8,X98)
=> c_Relation_Osym(X25,hAPP(hAPP(c_Relation_Oinv__image(X8,X25),X98),X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__inv__image) ).
fof(f37945,plain,
spl635_1026,
inference(avatar_split_clause,[],[f21641,f37943]) ).
fof(f37943,plain,
( spl635_1026
<=> ! [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,[spl635_1026])]) ).
fof(f21641,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,[],[f8305]) ).
fof(f8305,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,[],[f3113]) ).
fof(f3113,axiom,
! [X53,X1,X25,X8] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(X8,X25,X1,X53,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))),X53)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_Oequations_I1_J) ).
fof(f37941,plain,
spl635_1025,
inference(avatar_split_clause,[],[f21375,f37939]) ).
fof(f37939,plain,
( spl635_1025
<=> ! [X2,X0,X1] :
( X0 = X1
| hAPP(c_List_Orev(X2),X0) != hAPP(c_List_Orev(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1025])]) ).
fof(f21375,plain,
! [X2,X0,X1] :
( X0 = X1
| hAPP(c_List_Orev(X2),X0) != hAPP(c_List_Orev(X2),X1) ),
inference(cnf_transformation,[],[f15903]) ).
fof(f15903,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,[],[f8207]) ).
fof(f8207,plain,
! [X0,X1,X2] :
( hAPP(c_List_Orev(X2),X0) = hAPP(c_List_Orev(X2),X1)
<=> X0 = X1 ),
inference(rectify,[],[f4679]) ).
fof(f4679,axiom,
! [X209,X210,X8] :
( hAPP(c_List_Orev(X8),X210) = hAPP(c_List_Orev(X8),X209)
<=> X209 = X210 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__is__rev__conv) ).
fof(f37937,plain,
spl635_1024,
inference(avatar_split_clause,[],[f21364,f37935]) ).
fof(f37935,plain,
( spl635_1024
<=> ! [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,[spl635_1024])]) ).
fof(f21364,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,[],[f15896]) ).
fof(f15896,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,[],[f8202]) ).
fof(f8202,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,[],[f3767]) ).
fof(f3767,axiom,
! [X98,X39,X8] :
( c_Relation_Orefl__on(X8,X39,hAPP(c_Relation_Oconverse(X8,X8),X98))
<=> c_Relation_Orefl__on(X8,X39,X98) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__converse) ).
fof(f37933,plain,
spl635_1023,
inference(avatar_split_clause,[],[f21363,f37931]) ).
fof(f37931,plain,
( spl635_1023
<=> ! [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,[spl635_1023])]) ).
fof(f21363,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,[],[f15896]) ).
fof(f37925,plain,
spl635_1022,
inference(avatar_split_clause,[],[f21362,f37923]) ).
fof(f37923,plain,
( spl635_1022
<=> ! [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,[spl635_1022])]) ).
fof(f21362,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,[],[f15895]) ).
fof(f15895,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,[],[f8201]) ).
fof(f8201,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,[],[f3797]) ).
fof(f3797,axiom,
! [X98,X39,X8] :
( c_Relation_Ototal__on(X8,X39,hAPP(c_Relation_Oconverse(X8,X8),X98))
<=> c_Relation_Ototal__on(X8,X39,X98) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__converse) ).
fof(f37921,plain,
spl635_1021,
inference(avatar_split_clause,[],[f21361,f37919]) ).
fof(f37919,plain,
( spl635_1021
<=> ! [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,[spl635_1021])]) ).
fof(f21361,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,[],[f15895]) ).
fof(f37917,plain,
spl635_1020,
inference(avatar_split_clause,[],[f21355,f37915]) ).
fof(f37915,plain,
( spl635_1020
<=> ! [X2,X0,X1] :
( c_List_Olist_ONil(X2) = X1
| hAPP(hAPP(c_List_Oappend(X2),X1),X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1020])]) ).
fof(f21355,plain,
! [X2,X0,X1] :
( c_List_Olist_ONil(X2) = X1
| hAPP(hAPP(c_List_Oappend(X2),X1),X0) != X0 ),
inference(cnf_transformation,[],[f15892]) ).
fof(f15892,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_List_Oappend(X2),X1),X0) = X0
| c_List_Olist_ONil(X2) != X1 )
& ( c_List_Olist_ONil(X2) = X1
| hAPP(hAPP(c_List_Oappend(X2),X1),X0) != X0 ) ),
inference(nnf_transformation,[],[f8198]) ).
fof(f8198,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_List_Oappend(X2),X1),X0) = X0
<=> c_List_Olist_ONil(X2) = X1 ),
inference(rectify,[],[f4232]) ).
fof(f4232,axiom,
! [X209,X210,X8] :
( hAPP(hAPP(c_List_Oappend(X8),X210),X209) = X209
<=> c_List_Olist_ONil(X8) = X210 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv2) ).
fof(f37913,plain,
spl635_1019,
inference(avatar_split_clause,[],[f21353,f37911]) ).
fof(f37911,plain,
( spl635_1019
<=> ! [X2,X0,X1] :
( c_List_Olist_ONil(X2) = X0
| hAPP(hAPP(c_List_Oappend(X2),X1),X0) != X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1019])]) ).
fof(f21353,plain,
! [X2,X0,X1] :
( c_List_Olist_ONil(X2) = X0
| hAPP(hAPP(c_List_Oappend(X2),X1),X0) != X1 ),
inference(cnf_transformation,[],[f15891]) ).
fof(f15891,plain,
! [X0,X1,X2] :
( ( hAPP(hAPP(c_List_Oappend(X2),X1),X0) = X1
| c_List_Olist_ONil(X2) != X0 )
& ( c_List_Olist_ONil(X2) = X0
| hAPP(hAPP(c_List_Oappend(X2),X1),X0) != X1 ) ),
inference(nnf_transformation,[],[f8197]) ).
fof(f8197,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_List_Oappend(X2),X1),X0) = X1
<=> c_List_Olist_ONil(X2) = X0 ),
inference(rectify,[],[f4233]) ).
fof(f4233,axiom,
! [X209,X210,X8] :
( hAPP(hAPP(c_List_Oappend(X8),X210),X209) = X210
<=> c_List_Olist_ONil(X8) = X209 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__self__conv) ).
fof(f37909,plain,
spl635_1018,
inference(avatar_split_clause,[],[f21352,f37907]) ).
fof(f37907,plain,
( spl635_1018
<=> ! [X2,X0,X1] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Finite__Set_Ocard(X2),X1)
| ~ sP41(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1018])]) ).
fof(f21352,plain,
! [X2,X0,X1] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Finite__Set_Ocard(X2),X1)
| ~ sP41(X2,X0,X1) ),
inference(cnf_transformation,[],[f15890]) ).
fof(f15890,plain,
! [X0,X1,X2] :
( ( hAPP(c_Nat_OSuc,X0) = hAPP(c_Finite__Set_Ocard(X2),X1)
| ~ sP41(X2,X0,X1) )
& ( sP41(X2,X0,X1)
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Finite__Set_Ocard(X2),X1) ) ),
inference(nnf_transformation,[],[f14598]) ).
fof(f14598,plain,
! [X0,X1,X2] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Finite__Set_Ocard(X2),X1)
<=> sP41(X2,X0,X1) ),
inference(definition_folding,[],[f12683,f14597]) ).
fof(f12683,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,[],[f8196]) ).
fof(f8196,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,[],[f2577]) ).
fof(f2577,axiom,
! [X48,X39,X8] :
( hAPP(c_Nat_OSuc,X48) = hAPP(c_Finite__Set_Ocard(X8),X39)
<=> ? [X115,X155] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X48
=> c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = X155 )
& hAPP(c_Finite__Set_Ocard(X8),X155) = X48
& ~ hBOOL(hAPP(hAPP(c_member(X8),X115),X155))
& hAPP(hAPP(c_Set_Oinsert(X8),X115),X155) = X39 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__Suc__eq) ).
fof(f37905,plain,
spl635_1017,
inference(avatar_split_clause,[],[f21351,f37903]) ).
fof(f37903,plain,
( spl635_1017
<=> ! [X2,X0,X1] :
( sP41(X2,X0,X1)
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Finite__Set_Ocard(X2),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1017])]) ).
fof(f21351,plain,
! [X2,X0,X1] :
( sP41(X2,X0,X1)
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Finite__Set_Ocard(X2),X1) ),
inference(cnf_transformation,[],[f15890]) ).
fof(f37901,plain,
spl635_1016,
inference(avatar_split_clause,[],[f21120,f37899]) ).
fof(f37899,plain,
( spl635_1016
<=> ! [X2,X0,X1] :
( c_Orderings_Oorder__class_Omono(X1,X2,X0)
| ~ c_Orderings_Oorder__class_Ostrict__mono(X1,X2,X0)
| ~ class_Orderings_Oorder(X1)
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1016])]) ).
fof(f21120,plain,
! [X2,X0,X1] :
( c_Orderings_Oorder__class_Omono(X1,X2,X0)
| ~ c_Orderings_Oorder__class_Ostrict__mono(X1,X2,X0)
| ~ class_Orderings_Oorder(X1)
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f12614]) ).
fof(f12614,plain,
! [X0,X1,X2] :
( c_Orderings_Oorder__class_Omono(X1,X2,X0)
| ~ c_Orderings_Oorder__class_Ostrict__mono(X1,X2,X0)
| ~ class_Orderings_Oorder(X1)
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f12613]) ).
fof(f12613,plain,
! [X0,X1,X2] :
( c_Orderings_Oorder__class_Omono(X1,X2,X0)
| ~ c_Orderings_Oorder__class_Ostrict__mono(X1,X2,X0)
| ~ class_Orderings_Oorder(X1)
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f8128]) ).
fof(f8128,plain,
! [X0,X1,X2] :
( ( class_Orderings_Oorder(X1)
& class_Orderings_Oorder(X2) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(X1,X2,X0)
=> c_Orderings_Oorder__class_Omono(X1,X2,X0) ) ),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X1,X8,X25] :
( ( class_Orderings_Oorder(X8)
& class_Orderings_Oorder(X25) )
=> ( c_Orderings_Oorder__class_Ostrict__mono(X8,X25,X1)
=> c_Orderings_Oorder__class_Omono(X8,X25,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_strict__mono__mono) ).
fof(f37897,plain,
spl635_1015,
inference(avatar_split_clause,[],[f19688,f37895]) ).
fof(f37895,plain,
( spl635_1015
<=> ! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1015])]) ).
fof(f19688,plain,
! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X1),X0))),
inference(cnf_transformation,[],[f6983]) ).
fof(f6983,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Set_Oinsert(X2),X1),X0))),
inference(rectify,[],[f2437]) ).
fof(f2437,axiom,
! [X38,X17,X8] : hBOOL(hAPP(hAPP(c_member(X8),X17),hAPP(hAPP(c_Set_Oinsert(X8),X17),X38))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).
fof(f37893,plain,
spl635_1014,
inference(avatar_split_clause,[],[f19687,f37891]) ).
fof(f37891,plain,
( spl635_1014
<=> ! [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,[spl635_1014])]) ).
fof(f19687,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,[],[f6982]) ).
fof(f6982,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,[],[f1756]) ).
fof(f1756,axiom,
! [X34,X33,X5] : hAPP(hAPP(c_Nitpick_Ofrac(X5),X33),X34) = c_Nitpick_OAbs__Frac(X5,c_Nitpick_Onorm__frac(X33,X34)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Ofrac__def) ).
fof(f37889,plain,
spl635_1013,
inference(avatar_split_clause,[],[f19686,f37887]) ).
fof(f37887,plain,
( spl635_1013
<=> ! [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,[spl635_1013])]) ).
fof(f19686,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,[],[f6981]) ).
fof(f6981,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,[],[f3308]) ).
fof(f3308,axiom,
! [X39,X1,X8] : hAPP(c_Finite__Set_Ofold1(X8,X1),X39) = c_HOL_OThe(X8,c_Finite__Set_Ofold1Set(X8,X1,X39)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__def) ).
fof(f37885,plain,
( spl635_1012
| ~ spl635_816
| ~ spl635_981 ),
inference(avatar_split_clause,[],[f37836,f37749,f34060,f37882]) ).
fof(f37882,plain,
( spl635_1012
<=> hBOOL(hAPP(v_ts,sK194(v_ts))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1012])]) ).
fof(f37749,plain,
( spl635_981
<=> ! [X0] : hBOOL(hAPP(v_ts,c_Hilbert__Choice_OEps(X0,v_ts))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_981])]) ).
fof(f37836,plain,
( hBOOL(hAPP(v_ts,sK194(v_ts)))
| ~ spl635_816
| ~ spl635_981 ),
inference(resolution,[],[f37750,f34061]) ).
fof(f37750,plain,
( ! [X0] : hBOOL(hAPP(v_ts,c_Hilbert__Choice_OEps(X0,v_ts)))
| ~ spl635_981 ),
inference(avatar_component_clause,[],[f37749]) ).
fof(f37880,plain,
spl635_1011,
inference(avatar_split_clause,[],[f19452,f37878]) ).
fof(f37878,plain,
( spl635_1011
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X0))
| ~ sP13(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1011])]) ).
fof(f19452,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X0))
| ~ sP13(X0,X1) ),
inference(cnf_transformation,[],[f15231]) ).
fof(f15231,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X0))
| ~ sP13(X0,X1) )
& ( sP13(X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X0)) ) ),
inference(nnf_transformation,[],[f14552]) ).
fof(f14552,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X0))
<=> sP13(X0,X1) ),
inference(definition_folding,[],[f11332,f14551]) ).
fof(f14551,plain,
! [X0,X1] :
( sP13(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)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)))
| ~ 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,[sP13])]) ).
fof(f11332,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),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)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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,[],[f6870]) ).
fof(f6870,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),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))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))) ) ) ),
inference(rectify,[],[f1933]) ).
fof(f1933,axiom,
! [X27,X53] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X53)),X27))
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X53))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X27 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X53))
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X53),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__iff) ).
fof(f37876,plain,
spl635_1010,
inference(avatar_split_clause,[],[f19451,f37874]) ).
fof(f37874,plain,
( spl635_1010
<=> ! [X0,X1] :
( sP13(X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1010])]) ).
fof(f19451,plain,
! [X0,X1] :
( sP13(X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X0)) ),
inference(cnf_transformation,[],[f15231]) ).
fof(f37872,plain,
spl635_1009,
inference(avatar_split_clause,[],[f19372,f37870]) ).
fof(f37870,plain,
( spl635_1009
<=> ! [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,[spl635_1009])]) ).
fof(f19372,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,[],[f15188]) ).
fof(f15188,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,[],[f6843]) ).
fof(f6843,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,[],[f287]) ).
fof(f287,axiom,
! [X15,X27] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27)
<=> X15 = X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__int__eq) ).
fof(f37868,plain,
spl635_1008,
inference(avatar_split_clause,[],[f19346,f37866]) ).
fof(f37866,plain,
( spl635_1008
<=> ! [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,[spl635_1008])]) ).
fof(f19346,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,[],[f15168]) ).
fof(f15168,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,[],[f14545]) ).
fof(f14545,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,[],[f6834,f14544]) ).
fof(f14544,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(f6834,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,[],[f1002]) ).
fof(f1002,axiom,
! [X15,X27] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X27),X15)
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X15
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X27 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X15
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X27 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__eq__1__iff) ).
fof(f37864,plain,
spl635_1007,
inference(avatar_split_clause,[],[f19345,f37862]) ).
fof(f37862,plain,
( spl635_1007
<=> ! [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,[spl635_1007])]) ).
fof(f19345,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,[],[f15168]) ).
fof(f37860,plain,
spl635_1006,
inference(avatar_split_clause,[],[f19218,f37858]) ).
fof(f37858,plain,
( spl635_1006
<=> ! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| sK187(X0,X1) != sK188(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1006])]) ).
fof(f19218,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| sK187(X0,X1) != sK188(X0,X1) ),
inference(cnf_transformation,[],[f15069]) ).
fof(f15069,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])],[f15066,f15068,f15067]) ).
fof(f15067,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(f15068,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(f15066,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,[],[f15065]) ).
fof(f15065,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,[],[f11326]) ).
fof(f11326,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,[],[f11325]) ).
fof(f11325,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,[],[f6782]) ).
fof(f6782,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,[],[f4341]) ).
fof(f4341,axiom,
! [X210,X8] :
( hBOOL(hAPP(c_List_Odistinct(X8),X210))
<=> ! [X85] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X85),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X210)))
=> ! [X36] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X36),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X210)))
=> ( X36 != X85
=> hAPP(hAPP(c_List_Onth(X8),X210),X85) != hAPP(hAPP(c_List_Onth(X8),X210),X36) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__conv__nth) ).
fof(f37856,plain,
spl635_1005,
inference(avatar_split_clause,[],[f19182,f37854]) ).
fof(f37854,plain,
( spl635_1005
<=> ! [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,[spl635_1005])]) ).
fof(f19182,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X0)))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f15045]) ).
fof(f15045,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])],[f15043,f15044]) ).
fof(f15044,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(f15043,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,[],[f15042]) ).
fof(f15042,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,[],[f6774]) ).
fof(f6774,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> ! [X2] : hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X0))) ),
inference(rectify,[],[f3511]) ).
fof(f3511,axiom,
! [X98,X8] :
( c_Wellfounded_Owf(X8,X98)
<=> ! [X2] : hBOOL(hAPP(hAPP(c_member(X8),X2),c_Wellfounded_Oacc(X8,X98))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acc__iff) ).
fof(f37852,plain,
spl635_1004,
inference(avatar_split_clause,[],[f18733,f37850]) ).
fof(f37850,plain,
( spl635_1004
<=> ! [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,[spl635_1004])]) ).
fof(f18733,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,[],[f10891]) ).
fof(f10891,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,[],[f10890]) ).
fof(f10890,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,[],[f6446]) ).
fof(f6446,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,[],[f4935]) ).
fof(f4935,axiom,
! [X122,X8] :
( c_Predicate_Oreflp(X8,X122)
=> ( c_Predicate_Osymp(X8,X122)
=> ( c_Predicate_Otransp(X8,X122)
=> c_Equiv__Relations_Oequivp(X8,X122) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivpI) ).
fof(f37848,plain,
spl635_1003,
inference(avatar_split_clause,[],[f18704,f37846]) ).
fof(f18704,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,sK142(X0)))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f14893]) ).
fof(f14893,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(X0,sK142(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,[sK142])],[f14891,f14892]) ).
fof(f14892,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X0,sK142(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14891,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,[],[f14890]) ).
fof(f14890,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,[],[f10848]) ).
fof(f10848,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,[],[f6422]) ).
fof(f6422,plain,
! [X0,X1] :
( class_Enum_Oenum(X1)
=> ( ? [X2] : hBOOL(hAPP(X0,X2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0)) ) ),
inference(rectify,[],[f4777]) ).
fof(f4777,axiom,
! [X29,X8] :
( class_Enum_Oenum(X8)
=> ( ? [X65] : hBOOL(hAPP(X29,X65))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X8),X29)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exists__code) ).
fof(f37844,plain,
spl635_1002,
inference(avatar_split_clause,[],[f18701,f37842]) ).
fof(f37842,plain,
( spl635_1002
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ~ hBOOL(hAPP(X0,sK141(X0)))
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1002])]) ).
fof(f18701,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ~ hBOOL(hAPP(X0,sK141(X0)))
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f14889]) ).
fof(f14889,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,sK141(X0))) ) )
| ~ class_Enum_Oenum(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK141])],[f14887,f14888]) ).
fof(f14888,plain,
! [X0] :
( ? [X3] : ~ hBOOL(hAPP(X0,X3))
=> ~ hBOOL(hAPP(X0,sK141(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14887,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,[],[f14886]) ).
fof(f14886,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,[],[f10847]) ).
fof(f10847,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,[],[f6421]) ).
fof(f6421,plain,
! [X0,X1] :
( class_Enum_Oenum(X1)
=> ( ! [X2] : hBOOL(hAPP(X0,X2))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0)) ) ),
inference(rectify,[],[f4798]) ).
fof(f4798,axiom,
! [X29,X8] :
( class_Enum_Oenum(X8)
=> ( ! [X65] : hBOOL(hAPP(X29,X65))
<=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X8),X29)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__code) ).
fof(f37835,plain,
spl635_1001,
inference(avatar_split_clause,[],[f18699,f37833]) ).
fof(f18699,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,sK140(X0)))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f14885]) ).
fof(f14885,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
| ! [X2] : ~ hBOOL(hAPP(X0,X2)) )
& ( hBOOL(hAPP(X0,sK140(X0)))
| ~ hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0)) ) )
| ~ class_Enum_Oenum(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK140])],[f14883,f14884]) ).
fof(f14884,plain,
! [X0] :
( ? [X3] : hBOOL(hAPP(X0,X3))
=> hBOOL(hAPP(X0,sK140(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14883,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,[],[f14882]) ).
fof(f14882,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,[],[f10846]) ).
fof(f10846,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,[],[f6420]) ).
fof(f6420,plain,
! [X0,X1] :
( class_Enum_Oenum(X1)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X1),X0))
<=> ? [X2] : hBOOL(hAPP(X0,X2)) ) ),
inference(rectify,[],[f4776]) ).
fof(f4776,axiom,
! [X29,X8] :
( class_Enum_Oenum(X8)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(X8),X29))
<=> ? [X65] : hBOOL(hAPP(X29,X65)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__ex) ).
fof(f37831,plain,
spl635_1000,
inference(avatar_split_clause,[],[f18698,f37829]) ).
fof(f37829,plain,
( spl635_1000
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ~ hBOOL(hAPP(X0,sK139(X0)))
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_1000])]) ).
fof(f18698,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ~ hBOOL(hAPP(X0,sK139(X0)))
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f14881]) ).
fof(f14881,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
| ~ hBOOL(hAPP(X0,sK139(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,[sK139])],[f14879,f14880]) ).
fof(f14880,plain,
! [X0] :
( ? [X2] : ~ hBOOL(hAPP(X0,X2))
=> ~ hBOOL(hAPP(X0,sK139(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14879,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,[],[f14878]) ).
fof(f14878,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,[],[f10845]) ).
fof(f10845,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,[],[f6419]) ).
fof(f6419,plain,
! [X0,X1] :
( class_Enum_Oenum(X1)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X1),X0))
<=> ! [X2] : hBOOL(hAPP(X0,X2)) ) ),
inference(rectify,[],[f4797]) ).
fof(f4797,axiom,
! [X29,X8] :
( class_Enum_Oenum(X8)
=> ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(X8),X29))
<=> ! [X65] : hBOOL(hAPP(X29,X65)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__all) ).
fof(f37827,plain,
spl635_999,
inference(avatar_split_clause,[],[f18651,f37825]) ).
fof(f37825,plain,
( spl635_999
<=> ! [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,[spl635_999])]) ).
fof(f18651,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X0,sK126(X0,X1))
| c_List_Olist_ONil(X0) = X1
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f14860]) ).
fof(f14860,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])],[f14857,f14859,f14858]) ).
fof(f14858,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(f14859,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(f14857,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,[],[f14856]) ).
fof(f14856,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,[],[f14855]) ).
fof(f14855,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,[],[f14527]) ).
fof(f14527,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(f37823,plain,
spl635_998,
inference(avatar_split_clause,[],[f18641,f37821]) ).
fof(f37821,plain,
( spl635_998
<=> ! [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,[spl635_998])]) ).
fof(f18641,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,[],[f14851]) ).
fof(f14851,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])],[f10799,f14850]) ).
fof(f14850,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(f10799,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,[],[f10798]) ).
fof(f10798,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,[],[f6382]) ).
fof(f6382,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,[],[f4790]) ).
fof(f4790,axiom,
! [X39,X8] :
( class_Orderings_Olinorder(X8)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X39))
=> ? [X2] :
( ! [X45] :
( ( hBOOL(hAPP(c_List_Odistinct(X8),X45))
& c_List_Olinorder__class_Osorted(X8,X45)
& hAPP(c_List_Oset(X8),X45) = X39 )
=> X2 = X45 )
& hBOOL(hAPP(c_List_Odistinct(X8),X2))
& c_List_Olinorder__class_Osorted(X8,X2)
& hAPP(c_List_Oset(X8),X2) = X39 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__sorted__distinct__unique) ).
fof(f37819,plain,
spl635_997,
inference(avatar_split_clause,[],[f18631,f37817]) ).
fof(f37817,plain,
( spl635_997
<=> ! [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,[spl635_997])]) ).
fof(f18631,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,[],[f10783]) ).
fof(f10783,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,[],[f10782]) ).
fof(f10782,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,[],[f6374]) ).
fof(f6374,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,[],[f4657]) ).
fof(f4657,axiom,
! [X39,X8] :
( class_Orderings_Olinorder(X8)
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X39))
=> ( hBOOL(hAPP(c_List_Odistinct(X8),c_List_Olinorder__class_Osorted__list__of__set(X8,X39)))
& c_List_Olinorder__class_Osorted(X8,c_List_Olinorder__class_Osorted__list__of__set(X8,X39))
& hAPP(c_List_Oset(X8),c_List_Olinorder__class_Osorted__list__of__set(X8,X39)) = X39 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set) ).
fof(f37815,plain,
spl635_996,
inference(avatar_split_clause,[],[f18594,f37813]) ).
fof(f37813,plain,
( spl635_996
<=> ! [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,[spl635_996])]) ).
fof(f18594,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,[],[f10736]) ).
fof(f10736,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,[],[f6338]) ).
fof(f6338,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,[],[f317]) ).
fof(f317,axiom,
! [X33,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) ).
fof(f37811,plain,
spl635_995,
inference(avatar_split_clause,[],[f18593,f37809]) ).
fof(f37809,plain,
( spl635_995
<=> ! [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,[spl635_995])]) ).
fof(f18593,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,[],[f10735]) ).
fof(f10735,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,[],[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),c_Groups_Ozero__class_Ozero(X1)),X0) ),
inference(rectify,[],[f849]) ).
fof(f849,axiom,
! [X33,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5),c_Groups_Ozero__class_Ozero(X5)),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__0) ).
fof(f37807,plain,
spl635_994,
inference(avatar_split_clause,[],[f18592,f37805]) ).
fof(f37805,plain,
( spl635_994
<=> ! [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,[spl635_994])]) ).
fof(f18592,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,[],[f10734]) ).
fof(f10734,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,[],[f6336]) ).
fof(f6336,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,[],[f316]) ).
fof(f316,axiom,
! [X33,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X33),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) ).
fof(f37803,plain,
spl635_993,
inference(avatar_split_clause,[],[f18591,f37801]) ).
fof(f37801,plain,
( spl635_993
<=> ! [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,[spl635_993])]) ).
fof(f18591,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,[],[f10733]) ).
fof(f10733,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,[],[f6335]) ).
fof(f6335,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,[],[f850]) ).
fof(f850,axiom,
! [X33,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5),X33),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__0) ).
fof(f37799,plain,
spl635_992,
inference(avatar_split_clause,[],[f18560,f37797]) ).
fof(f37797,plain,
( spl635_992
<=> ! [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,[spl635_992])]) ).
fof(f18560,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,[],[f10703]) ).
fof(f10703,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,[],[f6306]) ).
fof(f6306,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,[],[f378]) ).
fof(f378,axiom,
! [X4,X5] :
( class_Groups_Omonoid__mult(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(hAPP(c_Power_Opower__class_Opower(X5),c_Groups_Oone__class_Oone(X5)),X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one) ).
fof(f37791,plain,
spl635_991,
inference(avatar_split_clause,[],[f18549,f37789]) ).
fof(f37789,plain,
( spl635_991
<=> ! [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,[spl635_991])]) ).
fof(f18549,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,[],[f10691]) ).
fof(f10691,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,[],[f6295]) ).
fof(f6295,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,[],[f177]) ).
fof(f177,axiom,
! [X33,X5] :
( class_Rings_Omult__zero(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Ozero__class_Ozero(X5)),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__left) ).
fof(f37787,plain,
spl635_990,
inference(avatar_split_clause,[],[f18548,f37785]) ).
fof(f37785,plain,
( spl635_990
<=> ! [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,[spl635_990])]) ).
fof(f18548,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,[],[f10690]) ).
fof(f10690,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,[],[f6294]) ).
fof(f6294,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,[],[f178]) ).
fof(f178,axiom,
! [X33,X5] :
( class_Rings_Omult__zero(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X33),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__zero__right) ).
fof(f37783,plain,
spl635_989,
inference(avatar_split_clause,[],[f18518,f37781]) ).
fof(f37781,plain,
( spl635_989
<=> ! [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,[spl635_989])]) ).
fof(f18518,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,[],[f10652]) ).
fof(f10652,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,[],[f6266]) ).
fof(f6266,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,[],[f2911]) ).
fof(f2911,axiom,
! [X13,X5] :
( class_Lattices_Obounded__lattice__bot(X5)
=> c_Orderings_Obot__class_Obot(X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Orderings_Obot__class_Obot(X5)),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__bot__left) ).
fof(f37779,plain,
spl635_988,
inference(avatar_split_clause,[],[f18517,f37777]) ).
fof(f37777,plain,
( spl635_988
<=> ! [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,[spl635_988])]) ).
fof(f18517,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,[],[f10651]) ).
fof(f10651,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,[],[f6265]) ).
fof(f6265,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,[],[f2912]) ).
fof(f2912,axiom,
! [X13,X5] :
( class_Lattices_Obounded__lattice__bot(X5)
=> c_Orderings_Obot__class_Obot(X5) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X13),c_Orderings_Obot__class_Obot(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__bot__right) ).
fof(f37775,plain,
spl635_987,
inference(avatar_split_clause,[],[f18516,f37773]) ).
fof(f37773,plain,
( spl635_987
<=> ! [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,[spl635_987])]) ).
fof(f18516,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,[],[f10650]) ).
fof(f10650,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,[],[f6264]) ).
fof(f6264,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,[],[f3151]) ).
fof(f3151,axiom,
! [X13,X5] :
( class_Lattices_Obounded__lattice__top(X5)
=> c_Orderings_Otop__class_Otop(X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Orderings_Otop__class_Otop(X5)),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__top__left) ).
fof(f37771,plain,
spl635_986,
inference(avatar_split_clause,[],[f18515,f37769]) ).
fof(f37769,plain,
( spl635_986
<=> ! [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,[spl635_986])]) ).
fof(f18515,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,[],[f10649]) ).
fof(f10649,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,[],[f6263]) ).
fof(f6263,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,[],[f3150]) ).
fof(f3150,axiom,
! [X13,X5] :
( class_Lattices_Obounded__lattice__top(X5)
=> c_Orderings_Otop__class_Otop(X5) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X13),c_Orderings_Otop__class_Otop(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__top__right) ).
fof(f37767,plain,
spl635_985,
inference(avatar_split_clause,[],[f18447,f37765]) ).
fof(f37765,plain,
( spl635_985
<=> ! [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,[spl635_985])]) ).
fof(f18447,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,[],[f14821]) ).
fof(f14821,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,[],[f10597]) ).
fof(f10597,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,[],[f6212]) ).
fof(f6212,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,[],[f693]) ).
fof(f693,axiom,
! [X17,X8] :
( class_Rings_Olinordered__idom(X8)
=> ( c_Groups_Ozero__class_Ozero(X8) = c_Groups_Osgn__class_Osgn(X8,X17)
<=> c_Groups_Ozero__class_Ozero(X8) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__0__0) ).
fof(f37763,plain,
spl635_984,
inference(avatar_split_clause,[],[f18414,f37761]) ).
fof(f37761,plain,
( spl635_984
<=> ! [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,[spl635_984])]) ).
fof(f18414,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,[],[f10562]) ).
fof(f10562,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,[],[f6184]) ).
fof(f6184,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,[],[f1040]) ).
fof(f1040,axiom,
! [X33,X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X33),hAPP(c_Groups_Oabs__class_Oabs(X5),X33))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__ge__self) ).
fof(f37759,plain,
spl635_983,
inference(avatar_split_clause,[],[f18355,f37757]) ).
fof(f37757,plain,
( spl635_983
<=> ! [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,[spl635_983])]) ).
fof(f18355,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,[],[f14799]) ).
fof(f14799,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,[],[f10521]) ).
fof(f10521,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,[],[f6145]) ).
fof(f6145,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,[],[f573]) ).
fof(f573,axiom,
! [X17,X8] :
( class_Groups_Olinordered__ab__group__add(X8)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X8),X17) = X17
<=> c_Groups_Ozero__class_Ozero(X8) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
fof(f37755,plain,
spl635_982,
inference(avatar_split_clause,[],[f18344,f37753]) ).
fof(f18344,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,c_Orderings_Oord__class_OLeast(X1,X0)))
| ~ hBOOL(hAPP(X0,X2))
| ~ class_Orderings_Owellorder(X1) ),
inference(cnf_transformation,[],[f10509]) ).
fof(f10509,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,c_Orderings_Oord__class_OLeast(X1,X0)))
| ! [X2] : ~ hBOOL(hAPP(X0,X2))
| ~ class_Orderings_Owellorder(X1) ),
inference(flattening,[],[f10508]) ).
fof(f10508,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,c_Orderings_Oord__class_OLeast(X1,X0)))
| ! [X2] : ~ hBOOL(hAPP(X0,X2))
| ~ class_Orderings_Owellorder(X1) ),
inference(ennf_transformation,[],[f6137]) ).
fof(f6137,plain,
! [X0,X1] :
( class_Orderings_Owellorder(X1)
=> ( ? [X2] : hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X0,c_Orderings_Oord__class_OLeast(X1,X0))) ) ),
inference(rectify,[],[f2564]) ).
fof(f2564,axiom,
! [X29,X8] :
( class_Orderings_Owellorder(X8)
=> ( ? [X65] : hBOOL(hAPP(X29,X65))
=> hBOOL(hAPP(X29,c_Orderings_Oord__class_OLeast(X8,X29))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastI__ex) ).
fof(f37751,plain,
( spl635_981
| ~ spl635_640
| ~ spl635_950 ),
inference(avatar_split_clause,[],[f37661,f37609,f32448,f37749]) ).
fof(f37661,plain,
( ! [X0] : hBOOL(hAPP(v_ts,c_Hilbert__Choice_OEps(X0,v_ts)))
| ~ spl635_640
| ~ spl635_950 ),
inference(resolution,[],[f37611,f32449]) ).
fof(f37747,plain,
spl635_980,
inference(avatar_split_clause,[],[f18259,f37745]) ).
fof(f37745,plain,
( spl635_980
<=> ! [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,[spl635_980])]) ).
fof(f18259,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,[],[f10472]) ).
fof(f37743,plain,
spl635_979,
inference(avatar_split_clause,[],[f17945,f37741]) ).
fof(f37741,plain,
( spl635_979
<=> ! [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,[spl635_979])]) ).
fof(f17945,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X0),hAPP(c_Set_OPow(X1),X0))),
inference(cnf_transformation,[],[f5797]) ).
fof(f5797,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(tc_fun(X1,tc_HOL_Obool)),X0),hAPP(c_Set_OPow(X1),X0))),
inference(rectify,[],[f2762]) ).
fof(f2762,axiom,
! [X39,X8] : hBOOL(hAPP(hAPP(c_member(tc_fun(X8,tc_HOL_Obool)),X39),hAPP(c_Set_OPow(X8),X39))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__top) ).
fof(f37739,plain,
spl635_978,
inference(avatar_split_clause,[],[f17944,f37737]) ).
fof(f37737,plain,
( spl635_978
<=> ! [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,[spl635_978])]) ).
fof(f17944,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,[],[f5796]) ).
fof(f5796,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,[],[f2299]) ).
fof(f2299,axiom,
! [X39,X8] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))),X39)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__subsetI) ).
fof(f37735,plain,
spl635_977,
inference(avatar_split_clause,[],[f17943,f37733]) ).
fof(f37733,plain,
( spl635_977
<=> ! [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,[spl635_977])]) ).
fof(f17943,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,[],[f5795]) ).
fof(f5795,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,[],[f626]) ).
fof(f626,axiom,
! [X4,X24] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X4)),X24)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__le__self) ).
fof(f37731,plain,
spl635_976,
inference(avatar_split_clause,[],[f17942,f37729]) ).
fof(f37729,plain,
( spl635_976
<=> ! [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,[spl635_976])]) ).
fof(f17942,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,[],[f5794]) ).
fof(f5794,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,[],[f934]) ).
fof(f934,axiom,
! [X4,X24] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X4)),X24)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__dividend) ).
fof(f37727,plain,
spl635_975,
inference(avatar_split_clause,[],[f17941,f37725]) ).
fof(f37725,plain,
( spl635_975
<=> ! [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,[spl635_975])]) ).
fof(f17941,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,[],[f5793]) ).
fof(f5793,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,[],[f3142]) ).
fof(f3142,axiom,
! [X39,X8] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X39),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__UNIV) ).
fof(f37723,plain,
spl635_974,
inference(avatar_split_clause,[],[f17940,f37721]) ).
fof(f37721,plain,
( spl635_974
<=> ! [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,[spl635_974])]) ).
fof(f17940,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,[],[f5792]) ).
fof(f5792,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,[],[f664]) ).
fof(f664,axiom,
! [X24,X4] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
fof(f37719,plain,
spl635_973,
inference(avatar_split_clause,[],[f17939,f37717]) ).
fof(f37717,plain,
( spl635_973
<=> ! [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,[spl635_973])]) ).
fof(f17939,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,[],[f5791]) ).
fof(f5791,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,[],[f665]) ).
fof(f665,axiom,
! [X24,X4] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X4),X24))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
fof(f37714,plain,
spl635_972,
inference(avatar_split_clause,[],[f17938,f37712]) ).
fof(f37712,plain,
( spl635_972
<=> ! [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,[spl635_972])]) ).
fof(f17938,plain,
! [X0,X1] : c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0)) = X0,
inference(cnf_transformation,[],[f5790]) ).
fof(f5790,plain,
! [X0,X1] : c_HOL_OThe(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0)) = X0,
inference(rectify,[],[f1787]) ).
fof(f1787,axiom,
! [X17,X8] : c_HOL_OThe(X8,hAPP(hAPP(c_COMBC(X8,X8,tc_HOL_Obool),c_fequal),X17)) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__eq__trivial) ).
fof(f37709,plain,
spl635_971,
inference(avatar_split_clause,[],[f17937,f37707]) ).
fof(f37707,plain,
( spl635_971
<=> ! [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,[spl635_971])]) ).
fof(f17937,plain,
! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0)) = X0,
inference(cnf_transformation,[],[f5789]) ).
fof(f5789,plain,
! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(hAPP(c_COMBC(X1,X1,tc_HOL_Obool),c_fequal),X0)) = X0,
inference(rectify,[],[f3659]) ).
fof(f3659,axiom,
! [X30,X8] : c_Hilbert__Choice_OEps(X8,hAPP(hAPP(c_COMBC(X8,X8,tc_HOL_Obool),c_fequal),X30)) = X30,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__trivial) ).
fof(f37705,plain,
( spl635_970
| ~ spl635_658
| ~ spl635_950 ),
inference(avatar_split_clause,[],[f37660,f37609,f32520,f37703]) ).
fof(f37703,plain,
( spl635_970
<=> ! [X0] : hBOOL(hAPP(v_ts,sK216(v_ts,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_970])]) ).
fof(f37660,plain,
( ! [X0] : hBOOL(hAPP(v_ts,sK216(v_ts,X0)))
| ~ spl635_658
| ~ spl635_950 ),
inference(resolution,[],[f37611,f32521]) ).
fof(f37701,plain,
spl635_969,
inference(avatar_split_clause,[],[f17936,f37699]) ).
fof(f37699,plain,
( spl635_969
<=> ! [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,[spl635_969])]) ).
fof(f17936,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,[],[f5788]) ).
fof(f5788,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,[],[f3810]) ).
fof(f3810,axiom,
! [X122,X8] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(X8,X8),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X122) = X122,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__pow__1) ).
fof(f37697,plain,
spl635_968,
inference(avatar_split_clause,[],[f17935,f37695]) ).
fof(f37695,plain,
( spl635_968
<=> ! [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,[spl635_968])]) ).
fof(f17935,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,[],[f5787]) ).
fof(f5787,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,[],[f1990]) ).
fof(f1990,axiom,
! [X75,X77] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X77),hAPP(c_Nat_OSuc,X75)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X77,X75),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).
fof(f37693,plain,
spl635_967,
inference(avatar_split_clause,[],[f17934,f37691]) ).
fof(f37691,plain,
( spl635_967
<=> ! [X0,X1] : c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X0)) = c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_967])]) ).
fof(f17934,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X0)) = c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(cnf_transformation,[],[f5786]) ).
fof(f5786,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(tc_List_Olist(X1),c_List_Olistrel1(X1,X0)) = c_List_Olistrel(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(rectify,[],[f4029]) ).
fof(f4029,axiom,
! [X98,X8] : c_Transitive__Closure_Ortrancl(tc_List_Olist(X8),c_List_Olistrel1(X8,X98)) = c_List_Olistrel(X8,c_Transitive__Closure_Ortrancl(X8,X98)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).
fof(f37689,plain,
spl635_966,
inference(avatar_split_clause,[],[f17928,f37687]) ).
fof(f37687,plain,
( spl635_966
<=> ! [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,[spl635_966])]) ).
fof(f17928,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,[],[f5780]) ).
fof(f5780,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,[],[f2170]) ).
fof(f2170,axiom,
! [X75,X77] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X77,X75) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,X77)),X75),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastSucLessThan__greaterThanLessThan) ).
fof(f37685,plain,
spl635_965,
inference(avatar_split_clause,[],[f17925,f37683]) ).
fof(f37683,plain,
( spl635_965
<=> ! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Ortrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_965])]) ).
fof(f17925,plain,
! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Ortrancl(X1,X0)),
inference(cnf_transformation,[],[f5777]) ).
fof(f5777,plain,
! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Relation_ODomain(X1,X1),c_Transitive__Closure_Ortrancl(X1,X0)),
inference(rectify,[],[f3730]) ).
fof(f3730,axiom,
! [X122,X8] : c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) = hAPP(c_Relation_ODomain(X8,X8),c_Transitive__Closure_Ortrancl(X8,X122)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Domain__rtrancl) ).
fof(f37681,plain,
spl635_964,
inference(avatar_split_clause,[],[f17924,f37679]) ).
fof(f37679,plain,
( spl635_964
<=> ! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Ortrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_964])]) ).
fof(f17924,plain,
! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Ortrancl(X1,X0)),
inference(cnf_transformation,[],[f5776]) ).
fof(f5776,plain,
! [X0,X1] : c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)) = hAPP(c_Relation_ORange(X1,X1),c_Transitive__Closure_Ortrancl(X1,X0)),
inference(rectify,[],[f3722]) ).
fof(f3722,axiom,
! [X122,X8] : c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)) = hAPP(c_Relation_ORange(X8,X8),c_Transitive__Closure_Ortrancl(X8,X122)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Range__rtrancl) ).
fof(f37677,plain,
spl635_963,
inference(avatar_split_clause,[],[f17920,f37675]) ).
fof(f37675,plain,
( spl635_963
<=> ! [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,[spl635_963])]) ).
fof(f17920,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,[],[f5772]) ).
fof(f5772,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,[],[f659]) ).
fof(f659,axiom,
! [X42,X41] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X41),X42)),X42)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
fof(f37673,plain,
spl635_962,
inference(avatar_split_clause,[],[f17919,f37671]) ).
fof(f37671,plain,
( spl635_962
<=> ! [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,[spl635_962])]) ).
fof(f17919,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,[],[f5771]) ).
fof(f5771,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,[],[f660]) ).
fof(f660,axiom,
! [X41,X42] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X42),X41)),X42)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
fof(f37669,plain,
spl635_961,
inference(avatar_split_clause,[],[f17918,f37667]) ).
fof(f37667,plain,
( spl635_961
<=> ! [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,[spl635_961])]) ).
fof(f17918,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,[],[f5770]) ).
fof(f5770,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,[],[f2321]) ).
fof(f2321,axiom,
! [X39,X8] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8,tc_HOL_Obool)),X39),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__psubset__empty) ).
fof(f37665,plain,
spl635_960,
inference(avatar_split_clause,[],[f17808,f37663]) ).
fof(f37663,plain,
( spl635_960
<=> ! [X0] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK109(X0)),c_Int_OInteg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_960])]) ).
fof(f17808,plain,
! [X0] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK109(X0)),c_Int_OInteg)),
inference(cnf_transformation,[],[f14788]) ).
fof(f14788,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK109(X0)),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,sK109(X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK109])],[f10447,f14787]) ).
fof(f14787,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)),sK109(X0)),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,sK109(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f10447,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,[],[f3571]) ).
fof(f3571,axiom,
! [X30] :
~ ! [X45] :
( hAPP(c_Int_OAbs__Integ,X45) = X30
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X45),c_Int_OInteg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Abs__Integ__cases) ).
fof(f37657,plain,
spl635_959,
inference(avatar_split_clause,[],[f17806,f37655]) ).
fof(f37655,plain,
( spl635_959
<=> ! [X2,X0] :
( hBOOL(hAPP(X0,sK107(X0)))
| ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_959])]) ).
fof(f17806,plain,
! [X2,X0] :
( hBOOL(hAPP(X0,sK107(X0)))
| ~ hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
inference(cnf_transformation,[],[f14786]) ).
fof(f14786,plain,
! [X0] :
( ( ( hBOOL(hAPP(X0,sK107(X0)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK107(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),sK108(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,[sK107,sK108])],[f14783,f14785,f14784]) ).
fof(f14784,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,sK107(X0)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK107(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f14785,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),sK108(X0)))) ),
introduced(choice_axiom,[]) ).
fof(f14783,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,[],[f14782]) ).
fof(f14782,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,[],[f324]) ).
fof(f324,axiom,
! [X29] :
( ? [X2] :
( hBOOL(hAPP(X29,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(X29,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).
fof(f37653,plain,
spl635_958,
inference(avatar_split_clause,[],[f17799,f37651]) ).
fof(f37651,plain,
( spl635_958
<=> ! [X0,X3] :
( hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
| ~ hBOOL(hAPP(X0,sK104(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_958])]) ).
fof(f17799,plain,
! [X3,X0] :
( hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
| ~ hBOOL(hAPP(X0,sK104(X0))) ),
inference(cnf_transformation,[],[f14776]) ).
fof(f14776,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),sK103(X0)))) )
& ( ! [X3] : hBOOL(hAPP(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)))
| ( ~ hBOOL(hAPP(X0,sK104(X0)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK104(X0))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK103,sK104])],[f14773,f14775,f14774]) ).
fof(f14774,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),sK103(X0)))) ),
introduced(choice_axiom,[]) ).
fof(f14775,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,sK104(X0)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK104(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f14773,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,[],[f14772]) ).
fof(f14772,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,[],[f10446]) ).
fof(f10446,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,[],[f323]) ).
fof(f323,axiom,
! [X29] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
=> hBOOL(hAPP(X29,X2)) )
<=> ! [X2] : hBOOL(hAPP(X29,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).
fof(f37649,plain,
spl635_957,
inference(avatar_split_clause,[],[f17745,f37647]) ).
fof(f37647,plain,
( spl635_957
<=> ! [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,[spl635_957])]) ).
fof(f17745,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,[],[f14739]) ).
fof(f14739,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,[],[f1898]) ).
fof(f1898,axiom,
! [X27] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X27),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
fof(f37645,plain,
spl635_956,
inference(avatar_split_clause,[],[f17600,f37643]) ).
fof(f37643,plain,
( spl635_956
<=> ! [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,[spl635_956])]) ).
fof(f17600,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,[],[f10360]) ).
fof(f10360,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,[],[f5525]) ).
fof(f5525,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,[],[f4371]) ).
fof(f4371,axiom,
! [X8] :
( class_Groups_Omonoid__add(X8)
=> c_List_Omonoid__add__class_Olistsum(X8) = c_List_Ofoldl(X8,X8,c_Groups_Oplus__class_Oplus(X8),c_Groups_Ozero__class_Ozero(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__foldl) ).
fof(f37641,plain,
spl635_955,
inference(avatar_split_clause,[],[f17584,f37639]) ).
fof(f37639,plain,
( spl635_955
<=> ! [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,[spl635_955])]) ).
fof(f17584,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,[],[f10344]) ).
fof(f10344,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,[],[f5509]) ).
fof(f5509,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,[],[f995]) ).
fof(f995,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Groups_Oone__class_Oone(X5)) = hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OMin) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_arith__simps_I31_J) ).
fof(f37637,plain,
spl635_954,
inference(avatar_split_clause,[],[f17456,f37635]) ).
fof(f37635,plain,
( spl635_954
<=> ! [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,[spl635_954])]) ).
fof(f17456,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,[],[f3034]) ).
fof(f3034,axiom,
! [X8] : c_Relation_Orefl__on(X8,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X8),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__empty) ).
fof(f37633,plain,
spl635_953,
inference(avatar_split_clause,[],[f17455,f37631]) ).
fof(f37631,plain,
( spl635_953
<=> ! [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,[spl635_953])]) ).
fof(f17455,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,[],[f156]) ).
fof(f156,axiom,
! [X24] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X24),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),X24))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__square) ).
fof(f37629,plain,
spl635_952,
inference(avatar_split_clause,[],[f17453,f37627]) ).
fof(f37627,plain,
( spl635_952
<=> ! [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,[spl635_952])]) ).
fof(f17453,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,[],[f893]) ).
fof(f893,axiom,
! [X4] : 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,X4))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__zminus__int) ).
fof(f37625,plain,
spl635_951,
inference(avatar_split_clause,[],[f17450,f37623]) ).
fof(f17450,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,[],[f1055]) ).
fof(f1055,axiom,
! [X24] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X24)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__int__eq) ).
fof(f37612,plain,
( spl635_950
| ~ spl635_2
| ~ spl635_931 ),
inference(avatar_split_clause,[],[f37507,f34540,f29301,f37609]) ).
fof(f34540,plain,
( spl635_931
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| hBOOL(hAPP(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_931])]) ).
fof(f37507,plain,
( hBOOL(hAPP(v_ts,sK89))
| ~ spl635_2
| ~ spl635_931 ),
inference(resolution,[],[f34541,f29303]) ).
fof(f34541,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| hBOOL(hAPP(X0,X1)) )
| ~ spl635_931 ),
inference(avatar_component_clause,[],[f34540]) ).
fof(f37404,plain,
( spl635_949
| ~ spl635_466
| ~ spl635_912 ),
inference(avatar_split_clause,[],[f37282,f34463,f31467,f37402]) ).
fof(f37402,plain,
( spl635_949
<=> ! [X0] : sP10(c_Int_OPls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_949])]) ).
fof(f31467,plain,
( spl635_466
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OPls),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_466])]) ).
fof(f34463,plain,
( spl635_912
<=> ! [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,[spl635_912])]) ).
fof(f37282,plain,
( ! [X0] : sP10(c_Int_OPls,X0)
| ~ spl635_466
| ~ spl635_912 ),
inference(trivial_inequality_removal,[],[f37276]) ).
fof(f37276,plain,
( ! [X0] :
( c_Int_OPls != c_Int_OPls
| sP10(c_Int_OPls,X0) )
| ~ spl635_466
| ~ spl635_912 ),
inference(superposition,[],[f34464,f31468]) ).
fof(f31468,plain,
( ! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OPls),X0)
| ~ spl635_466 ),
inference(avatar_component_clause,[],[f31467]) ).
fof(f34464,plain,
( ! [X0,X1] :
( c_Int_OPls != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| sP10(X1,X0) )
| ~ spl635_912 ),
inference(avatar_component_clause,[],[f34463]) ).
fof(f37098,plain,
( spl635_948
| ~ spl635_542
| ~ spl635_880
| ~ spl635_882 ),
inference(avatar_split_clause,[],[f36962,f34335,f34326,f31810,f37095]) ).
fof(f37095,plain,
( spl635_948
<=> c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olist_ONil(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_948])]) ).
fof(f31810,plain,
( spl635_542
<=> ! [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,[spl635_542])]) ).
fof(f34326,plain,
( spl635_880
<=> 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,[spl635_880])]) ).
fof(f34335,plain,
( spl635_882
<=> ! [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,[spl635_882])]) ).
fof(f36962,plain,
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olist_ONil(tc_Nat_Onat))
| ~ spl635_542
| ~ spl635_880
| ~ spl635_882 ),
inference(forward_demodulation,[],[f36952,f34328]) ).
fof(f34328,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)))
| ~ spl635_880 ),
inference(avatar_component_clause,[],[f34326]) ).
fof(f36952,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))))
| ~ spl635_542
| ~ spl635_882 ),
inference(superposition,[],[f31811,f34336]) ).
fof(f34336,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))
| ~ spl635_882 ),
inference(avatar_component_clause,[],[f34335]) ).
fof(f31811,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)))
| ~ spl635_542 ),
inference(avatar_component_clause,[],[f31810]) ).
fof(f36936,plain,
( spl635_947
| ~ spl635_816
| ~ spl635_872 ),
inference(avatar_split_clause,[],[f36891,f34285,f34060,f36933]) ).
fof(f36933,plain,
( spl635_947
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,sK194(c_Nat__Numeral_Oneg))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_947])]) ).
fof(f34285,plain,
( spl635_872
<=> ! [X0] : hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Hilbert__Choice_OEps(X0,c_Nat__Numeral_Oneg))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_872])]) ).
fof(f36891,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,sK194(c_Nat__Numeral_Oneg)))
| ~ spl635_816
| ~ spl635_872 ),
inference(resolution,[],[f34286,f34061]) ).
fof(f34286,plain,
( ! [X0] : hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Hilbert__Choice_OEps(X0,c_Nat__Numeral_Oneg)))
| ~ spl635_872 ),
inference(avatar_component_clause,[],[f34285]) ).
fof(f36608,plain,
( spl635_946
| ~ spl635_330
| ~ spl635_728 ),
inference(avatar_split_clause,[],[f33732,f32815,f30880,f36606]) ).
fof(f36606,plain,
( spl635_946
<=> ! [X0] :
( c_Int_OPls = X0
| ~ sP11(X0,c_Int_OMin) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_946])]) ).
fof(f30880,plain,
( spl635_330
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_330])]) ).
fof(f32815,plain,
( spl635_728
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Int_OPls = X0
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_728])]) ).
fof(f33732,plain,
( ! [X0] :
( c_Int_OPls = X0
| ~ sP11(X0,c_Int_OMin) )
| ~ spl635_330
| ~ spl635_728 ),
inference(resolution,[],[f32816,f30882]) ).
fof(f30882,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))
| ~ spl635_330 ),
inference(avatar_component_clause,[],[f30880]) ).
fof(f32816,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Int_OPls = X0
| ~ sP11(X0,X1) )
| ~ spl635_728 ),
inference(avatar_component_clause,[],[f32815]) ).
fof(f36236,plain,
( spl635_945
| ~ spl635_330
| ~ spl635_712 ),
inference(avatar_split_clause,[],[f33686,f32750,f30880,f36233]) ).
fof(f36233,plain,
( spl635_945
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_945])]) ).
fof(f32750,plain,
( spl635_712
<=> ! [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,[spl635_712])]) ).
fof(f33686,plain,
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OMin)
| ~ spl635_330
| ~ spl635_712 ),
inference(resolution,[],[f32751,f30882]) ).
fof(f32751,plain,
( ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,X0) )
| ~ spl635_712 ),
inference(avatar_component_clause,[],[f32750]) ).
fof(f35766,plain,
( ~ spl635_944
| ~ spl635_462
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33346,f32548,f31449,f35763]) ).
fof(f35763,plain,
( spl635_944
<=> sP31(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,[spl635_944])]) ).
fof(f31449,plain,
( spl635_462
<=> 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,[spl635_462])]) ).
fof(f33346,plain,
( ~ sP31(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint))
| ~ spl635_462
| ~ spl635_665 ),
inference(resolution,[],[f32549,f31451]) ).
fof(f31451,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl635_462 ),
inference(avatar_component_clause,[],[f31449]) ).
fof(f35369,plain,
( spl635_943
| ~ spl635_483
| ~ spl635_807 ),
inference(avatar_split_clause,[],[f35279,f34024,f31570,f35367]) ).
fof(f35367,plain,
( spl635_943
<=> ! [X0] :
( c_Nat__Transfer_Ois__nat(c_Int_OBit0(X0))
| ~ c_Nat__Transfer_Ois__nat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_943])]) ).
fof(f31570,plain,
( spl635_483
<=> ! [X0] : c_Int_OBit0(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_483])]) ).
fof(f34024,plain,
( spl635_807
<=> ! [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,[spl635_807])]) ).
fof(f35279,plain,
( ! [X0] :
( c_Nat__Transfer_Ois__nat(c_Int_OBit0(X0))
| ~ c_Nat__Transfer_Ois__nat(X0) )
| ~ spl635_483
| ~ spl635_807 ),
inference(duplicate_literal_removal,[],[f35276]) ).
fof(f35276,plain,
( ! [X0] :
( c_Nat__Transfer_Ois__nat(c_Int_OBit0(X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X0) )
| ~ spl635_483
| ~ spl635_807 ),
inference(superposition,[],[f34025,f31571]) ).
fof(f31571,plain,
( ! [X0] : c_Int_OBit0(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0)
| ~ spl635_483 ),
inference(avatar_component_clause,[],[f31570]) ).
fof(f34025,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) )
| ~ spl635_807 ),
inference(avatar_component_clause,[],[f34024]) ).
fof(f35085,plain,
( ~ spl635_942
| ~ spl635_461
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33345,f32548,f31444,f35082]) ).
fof(f35082,plain,
( spl635_942
<=> sP31(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,[spl635_942])]) ).
fof(f31444,plain,
( spl635_461
<=> 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,[spl635_461])]) ).
fof(f33345,plain,
( ~ sP31(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Int_OPls,c_Orderings_Oord__class_Oless(tc_Int_Oint))
| ~ spl635_461
| ~ spl635_665 ),
inference(resolution,[],[f32549,f31446]) ).
fof(f31446,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl635_461 ),
inference(avatar_component_clause,[],[f31444]) ).
fof(f35044,plain,
( spl635_941
| ~ spl635_419
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33333,f32548,f31271,f35042]) ).
fof(f35042,plain,
( spl635_941
<=> ! [X0,X1] :
( ~ sP31(X0,X1,c_fimplies)
| ~ hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_941])]) ).
fof(f31271,plain,
( spl635_419
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_419])]) ).
fof(f33333,plain,
( ! [X0,X1] :
( ~ sP31(X0,X1,c_fimplies)
| ~ hBOOL(X0) )
| ~ spl635_419
| ~ spl635_665 ),
inference(resolution,[],[f32549,f31272]) ).
fof(f31272,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) )
| ~ spl635_419 ),
inference(avatar_component_clause,[],[f31271]) ).
fof(f34670,plain,
( spl635_940
| ~ spl635_372
| ~ spl635_741 ),
inference(avatar_split_clause,[],[f34573,f33755,f31052,f34667]) ).
fof(f34667,plain,
( spl635_940
<=> c_Relation_Osym(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_940])]) ).
fof(f31052,plain,
( spl635_372
<=> ! [X2,X0,X1] :
( c_Relation_Osym(X2,X0)
| ~ c_Equiv__Relations_Oequiv(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_372])]) ).
fof(f33755,plain,
( spl635_741
<=> 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,[spl635_741])]) ).
fof(f34573,plain,
( c_Relation_Osym(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel)
| ~ spl635_372
| ~ spl635_741 ),
inference(resolution,[],[f33757,f31053]) ).
fof(f31053,plain,
( ! [X2,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X2,X1,X0)
| c_Relation_Osym(X2,X0) )
| ~ spl635_372 ),
inference(avatar_component_clause,[],[f31052]) ).
fof(f33757,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)
| ~ spl635_741 ),
inference(avatar_component_clause,[],[f33755]) ).
fof(f34628,plain,
( spl635_939
| ~ spl635_373
| ~ spl635_741 ),
inference(avatar_split_clause,[],[f34572,f33755,f31056,f34625]) ).
fof(f34625,plain,
( spl635_939
<=> c_Relation_Otrans(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_939])]) ).
fof(f31056,plain,
( spl635_373
<=> ! [X2,X0,X1] :
( c_Relation_Otrans(X2,X0)
| ~ c_Equiv__Relations_Oequiv(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_373])]) ).
fof(f34572,plain,
( c_Relation_Otrans(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel)
| ~ spl635_373
| ~ spl635_741 ),
inference(resolution,[],[f33757,f31057]) ).
fof(f31057,plain,
( ! [X2,X0,X1] :
( ~ c_Equiv__Relations_Oequiv(X2,X1,X0)
| c_Relation_Otrans(X2,X0) )
| ~ spl635_373 ),
inference(avatar_component_clause,[],[f31056]) ).
fof(f34570,plain,
spl635_938,
inference(avatar_split_clause,[],[f28634,f34568]) ).
fof(f34568,plain,
( spl635_938
<=> ! [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,[spl635_938])]) ).
fof(f28634,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,[],[f21638,f17187]) ).
fof(f21638,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,[],[f8302]) ).
fof(f8302,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,[],[f17]) ).
fof(f17,axiom,
! [X17,X18,X19,X8] : hAPP(hAPP(c_Power_Opower_Opower(X8,X19,X18),X17),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(f34566,plain,
spl635_937,
inference(avatar_split_clause,[],[f28559,f34564]) ).
fof(f34564,plain,
( spl635_937
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP42(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_937])]) ).
fof(f28559,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP42(X0,X1,X2) ),
inference(forward_demodulation,[],[f21396,f17176]) ).
fof(f21396,plain,
! [X2,X0,X1] :
( sP42(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,[],[f15924]) ).
fof(f15924,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(tc_Int_Oint),sK381(X0,X1,X2)),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK381(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))
| ~ sP42(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK380,sK381])],[f15921,f15923,f15922]) ).
fof(f15922,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,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(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(f15923,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(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),sK380(X0,X1,X2))),sK381(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK381(X0,X1,X2)),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK381(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15921,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(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))
| ~ sP42(X0,X1,X2) ) ),
inference(rectify,[],[f15920]) ).
fof(f15920,plain,
! [X2,X1,X0] :
( ( sP42(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))
| ~ sP42(X2,X1,X0) ) ),
inference(flattening,[],[f15919]) ).
fof(f15919,plain,
! [X2,X1,X0] :
( ( sP42(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))
| ~ sP42(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14599]) ).
fof(f34562,plain,
spl635_936,
inference(avatar_split_clause,[],[f28554,f34560]) ).
fof(f28554,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP43(X0,X1,X2) ),
inference(forward_demodulation,[],[f21390,f17176]) ).
fof(f21390,plain,
! [X2,X0,X1] :
( sP43(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,[],[f15918]) ).
fof(f15918,plain,
! [X0,X1,X2] :
( ( sP43(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK378(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK378(X0,X1,X2))),sK379(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK379(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK379(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)))
| ~ sP43(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK378,sK379])],[f15915,f15917,f15916]) ).
fof(f15916,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,sK378(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),sK378(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(f15917,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),sK378(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),sK378(X0,X1,X2))),sK379(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK379(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK379(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15915,plain,
! [X0,X1,X2] :
( ( sP43(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)))
| ~ sP43(X0,X1,X2) ) ),
inference(rectify,[],[f15914]) ).
fof(f15914,plain,
! [X2,X1,X0] :
( ( sP43(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)))
| ~ sP43(X2,X1,X0) ) ),
inference(flattening,[],[f15913]) ).
fof(f15913,plain,
! [X2,X1,X0] :
( ( sP43(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)))
| ~ sP43(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14600]) ).
fof(f34558,plain,
( spl635_935
| ~ spl635_420
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33332,f32548,f31275,f34556]) ).
fof(f34556,plain,
( spl635_935
<=> ! [X0,X1] :
( ~ sP31(X0,X1,c_fimplies)
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_935])]) ).
fof(f31275,plain,
( spl635_420
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_420])]) ).
fof(f33332,plain,
( ! [X0,X1] :
( ~ sP31(X0,X1,c_fimplies)
| hBOOL(X1) )
| ~ spl635_420
| ~ spl635_665 ),
inference(resolution,[],[f32549,f31276]) ).
fof(f31276,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) )
| ~ spl635_420 ),
inference(avatar_component_clause,[],[f31275]) ).
fof(f34554,plain,
spl635_934,
inference(avatar_split_clause,[],[f28533,f34552]) ).
fof(f34552,plain,
( spl635_934
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP37(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_934])]) ).
fof(f28533,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP37(X0,X1,X2) ),
inference(forward_demodulation,[],[f21316,f17176]) ).
fof(f21316,plain,
! [X2,X0,X1] :
( sP37(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,[],[f15868]) ).
fof(f15868,plain,
! [X0,X1,X2] :
( ( sP37(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK370(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK369(X0,X1,X2))),sK370(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK370(X0,X1,X2)),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK370(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))
| ~ sP37(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK369,sK370])],[f15866,f15867]) ).
fof(f15867,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,sK370(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK369(X0,X1,X2))),sK370(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK370(X0,X1,X2)),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK370(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15866,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(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))
| ~ sP37(X0,X1,X2) ) ),
inference(rectify,[],[f15865]) ).
fof(f15865,plain,
! [X2,X1,X0] :
( ( sP37(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))
| ~ sP37(X2,X1,X0) ) ),
inference(flattening,[],[f15864]) ).
fof(f15864,plain,
! [X2,X1,X0] :
( ( sP37(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))
| ~ sP37(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14591]) ).
fof(f14591,plain,
! [X2,X1,X0] :
( sP37(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,[sP37])]) ).
fof(f34550,plain,
spl635_933,
inference(avatar_split_clause,[],[f28528,f34548]) ).
fof(f28528,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP38(X0,X1,X2) ),
inference(forward_demodulation,[],[f21310,f17176]) ).
fof(f21310,plain,
! [X2,X0,X1] :
( sP38(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,[],[f15863]) ).
fof(f15863,plain,
! [X0,X1,X2] :
( ( sP38(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK368(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK367(X0,X1,X2))),sK368(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK368(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK368(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)))
| ~ sP38(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK367,sK368])],[f15861,f15862]) ).
fof(f15862,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,sK368(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK367(X0,X1,X2))),sK368(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK368(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK368(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15861,plain,
! [X0,X1,X2] :
( ( sP38(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)))
| ~ sP38(X0,X1,X2) ) ),
inference(rectify,[],[f15860]) ).
fof(f15860,plain,
! [X2,X1,X0] :
( ( sP38(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)))
| ~ sP38(X2,X1,X0) ) ),
inference(flattening,[],[f15859]) ).
fof(f15859,plain,
! [X2,X1,X0] :
( ( sP38(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)))
| ~ sP38(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14592]) ).
fof(f14592,plain,
! [X2,X1,X0] :
( sP38(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,[sP38])]) ).
fof(f34546,plain,
spl635_932,
inference(avatar_split_clause,[],[f28499,f34544]) ).
fof(f34544,plain,
( spl635_932
<=> ! [X2,X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| sP35(X1,X0)
| ~ sP36(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_932])]) ).
fof(f28499,plain,
! [X2,X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| sP35(X1,X0)
| ~ sP36(X0,X1,X2) ),
inference(forward_demodulation,[],[f21266,f17187]) ).
fof(f21266,plain,
! [X2,X0,X1] :
( sP35(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP36(X0,X1,X2) ),
inference(cnf_transformation,[],[f15829]) ).
fof(f34542,plain,
spl635_931,
inference(avatar_split_clause,[],[f28394,f34540]) ).
fof(f28394,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| hBOOL(hAPP(X0,X1)) ),
inference(forward_demodulation,[],[f20983,f17832]) ).
fof(f20983,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_Set_OCollect(X2),X0))) ),
inference(cnf_transformation,[],[f12464]) ).
fof(f12464,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_Set_OCollect(X2),X0))) ),
inference(ennf_transformation,[],[f8021]) ).
fof(f8021,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_Set_OCollect(X2),X0)))
=> hBOOL(hAPP(X0,X1)) ),
inference(rectify,[],[f3385]) ).
fof(f3385,axiom,
! [X29,X17,X8] :
( hBOOL(hAPP(hAPP(c_member(X8),X17),hAPP(c_Set_OCollect(X8),X29)))
=> hBOOL(hAPP(X29,X17)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectE) ).
fof(f34538,plain,
spl635_930,
inference(avatar_split_clause,[],[f28362,f34536]) ).
fof(f34536,plain,
( spl635_930
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP30(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_930])]) ).
fof(f28362,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP30(X2,X0,X1) ),
inference(forward_demodulation,[],[f20923,f17176]) ).
fof(f20923,plain,
! [X2,X0,X1] :
( sP30(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,[],[f14579]) ).
fof(f14579,plain,
! [X0,X1,X2] :
( sP30(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,[],[f12410,f14578,f14577]) ).
fof(f14577,plain,
! [X1,X0,X2] :
( sP29(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,[sP29])]) ).
fof(f14578,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)))
<=> sP29(X1,X0,X2) )
| ~ sP30(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP30])]) ).
fof(f12410,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,[],[f12409]) ).
fof(f12409,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,[],[f7979]) ).
fof(f7979,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,[],[f1030]) ).
fof(f1030,axiom,
! [X15,X29,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))
=> ( hBOOL(hAPP(hAPP(X29,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15),X48)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,X48)))
<=> ! [X85,X36] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X85)),X36) = X15
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X48))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36)) )
=> hBOOL(hAPP(hAPP(X29,X85),X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__pos__lemma) ).
fof(f34534,plain,
spl635_929,
inference(avatar_split_clause,[],[f28299,f34532]) ).
fof(f34532,plain,
( spl635_929
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP28(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_929])]) ).
fof(f28299,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP28(X2,X0,X1) ),
inference(forward_demodulation,[],[f20881,f17176]) ).
fof(f20881,plain,
! [X2,X0,X1] :
( sP28(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,[],[f14576]) ).
fof(f14576,plain,
! [X0,X1,X2] :
( sP28(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,[],[f12380,f14575,f14574]) ).
fof(f14574,plain,
! [X1,X0,X2] :
( sP27(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,[sP27])]) ).
fof(f14575,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)))
<=> sP27(X1,X0,X2) )
| ~ sP28(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP28])]) ).
fof(f12380,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,[],[f12379]) ).
fof(f12379,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,[],[f7962]) ).
fof(f7962,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,[],[f906]) ).
fof(f906,axiom,
! [X15,X29,X48] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(X29,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X15),X48)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,X48)))
<=> ! [X85,X36] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X85)),X36) = X15
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X36),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),X36)) )
=> hBOOL(hAPP(hAPP(X29,X85),X36)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__neg__lemma) ).
fof(f34530,plain,
spl635_928,
inference(avatar_split_clause,[],[f28220,f34528]) ).
fof(f34528,plain,
( spl635_928
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_928])]) ).
fof(f28220,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(forward_demodulation,[],[f20692,f17832]) ).
fof(f20692,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(c_Set_OCollect(X0),X2)))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(cnf_transformation,[],[f12191]) ).
fof(f12191,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(c_Set_OCollect(X0),X2)))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(ennf_transformation,[],[f7827]) ).
fof(f7827,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,X1))
=> hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(c_Set_OCollect(X0),X2))) ),
inference(rectify,[],[f3369]) ).
fof(f3369,axiom,
! [X8,X17,X29] :
( hBOOL(hAPP(X29,X17))
=> hBOOL(hAPP(hAPP(c_member(X8),X17),hAPP(c_Set_OCollect(X8),X29))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_CollectI) ).
fof(f34526,plain,
spl635_927,
inference(avatar_split_clause,[],[f27970,f34523]) ).
fof(f34523,plain,
( spl635_927
<=> 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,[spl635_927])]) ).
fof(f27970,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,[],[f27969,f26072]) ).
fof(f26072,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,[],[f17408,f17187]) ).
fof(f17408,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,[],[f5346]) ).
fof(f5346,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,[],[f188]) ).
fof(f188,axiom,
! [X4] : 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)),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0) ).
fof(f27969,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,[],[f27968,f26072]) ).
fof(f27968,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,[],[f25467,f17187]) ).
fof(f25467,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,[],[f19930]) ).
fof(f19930,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,[],[f11347]) ).
fof(f11347,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,[],[f7224]) ).
fof(f7224,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,[],[f957]) ).
fof(f957,axiom,
! [X4,X24,X40] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X40
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),X4) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X4)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X40
=> 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),X40),X24)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X40),X4)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
fof(f34521,plain,
spl635_926,
inference(avatar_split_clause,[],[f27692,f34519]) ).
fof(f34519,plain,
( spl635_926
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_926])]) ).
fof(f27692,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP15(X0,X1) ),
inference(forward_demodulation,[],[f27691,f25953]) ).
fof(f27691,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP15(X0,X1) ),
inference(forward_demodulation,[],[f27690,f17187]) ).
fof(f27690,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP15(X0,X1) ),
inference(forward_demodulation,[],[f19484,f17187]) ).
fof(f19484,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
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f15251]) ).
fof(f15251,plain,
! [X0,X1] :
( ( sP15(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 )
| ~ sP15(X0,X1) ) ),
inference(flattening,[],[f15250]) ).
fof(f15250,plain,
! [X0,X1] :
( ( sP15(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 )
| ~ sP15(X0,X1) ) ),
inference(nnf_transformation,[],[f14555]) ).
fof(f34517,plain,
spl635_925,
inference(avatar_split_clause,[],[f27689,f34515]) ).
fof(f34515,plain,
( spl635_925
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_925])]) ).
fof(f27689,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP15(X0,X1) ),
inference(forward_demodulation,[],[f27688,f17187]) ).
fof(f27688,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP15(X0,X1) ),
inference(forward_demodulation,[],[f19485,f17187]) ).
fof(f19485,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f15251]) ).
fof(f34513,plain,
( spl635_924
| ~ spl635_417
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33331,f32548,f31263,f34511]) ).
fof(f34511,plain,
( spl635_924
<=> ! [X0,X1] :
( ~ sP31(X0,X1,c_fdisj)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_924])]) ).
fof(f31263,plain,
( spl635_417
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_417])]) ).
fof(f33331,plain,
( ! [X0,X1] :
( ~ sP31(X0,X1,c_fdisj)
| ~ hBOOL(X1) )
| ~ spl635_417
| ~ spl635_665 ),
inference(resolution,[],[f32549,f31264]) ).
fof(f31264,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) )
| ~ spl635_417 ),
inference(avatar_component_clause,[],[f31263]) ).
fof(f34509,plain,
spl635_923,
inference(avatar_split_clause,[],[f27687,f34507]) ).
fof(f34507,plain,
( spl635_923
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_923])]) ).
fof(f27687,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP15(X0,X1) ),
inference(forward_demodulation,[],[f27686,f25953]) ).
fof(f27686,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP15(X0,X1) ),
inference(forward_demodulation,[],[f27685,f17187]) ).
fof(f27685,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
| ~ sP15(X0,X1) ),
inference(forward_demodulation,[],[f27684,f25953]) ).
fof(f27684,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
| ~ sP15(X0,X1) ),
inference(forward_demodulation,[],[f19486,f17187]) ).
fof(f19486,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
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f15251]) ).
fof(f34505,plain,
spl635_922,
inference(avatar_split_clause,[],[f27683,f34503]) ).
fof(f34503,plain,
( spl635_922
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP15(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_922])]) ).
fof(f27683,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP15(X0,X1) ),
inference(forward_demodulation,[],[f27682,f17187]) ).
fof(f27682,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP15(X0,X1) ),
inference(forward_demodulation,[],[f27681,f25953]) ).
fof(f27681,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP15(X0,X1) ),
inference(forward_demodulation,[],[f19487,f17187]) ).
fof(f19487,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
| ~ sP15(X0,X1) ),
inference(cnf_transformation,[],[f15251]) ).
fof(f34501,plain,
spl635_921,
inference(avatar_split_clause,[],[f27672,f34499]) ).
fof(f34499,plain,
( spl635_921
<=> ! [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,[spl635_921])]) ).
fof(f27672,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,[],[f27671,f25953]) ).
fof(f27671,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,[],[f27670,f17187]) ).
fof(f27670,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,[],[f19476,f17187]) ).
fof(f19476,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,[],[f15248]) ).
fof(f15248,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,[],[f15247]) ).
fof(f15247,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,[],[f14553]) ).
fof(f34497,plain,
spl635_920,
inference(avatar_split_clause,[],[f27669,f34495]) ).
fof(f34495,plain,
( spl635_920
<=> ! [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,[spl635_920])]) ).
fof(f27669,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,[],[f27668,f17187]) ).
fof(f27668,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,[],[f19477,f17187]) ).
fof(f19477,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,[],[f15248]) ).
fof(f34493,plain,
spl635_919,
inference(avatar_split_clause,[],[f27667,f34491]) ).
fof(f34491,plain,
( spl635_919
<=> ! [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,[spl635_919])]) ).
fof(f27667,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,[],[f27666,f25953]) ).
fof(f27666,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,[],[f27665,f17187]) ).
fof(f27665,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,[],[f27664,f25953]) ).
fof(f27664,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,[],[f19478,f17187]) ).
fof(f19478,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,[],[f15248]) ).
fof(f34489,plain,
spl635_918,
inference(avatar_split_clause,[],[f27663,f34487]) ).
fof(f34487,plain,
( spl635_918
<=> ! [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,[spl635_918])]) ).
fof(f27663,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,[],[f27662,f17187]) ).
fof(f27662,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,[],[f27661,f25953]) ).
fof(f27661,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,[],[f19479,f17187]) ).
fof(f19479,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,[],[f15248]) ).
fof(f34485,plain,
spl635_917,
inference(avatar_split_clause,[],[f27632,f34483]) ).
fof(f34483,plain,
( spl635_917
<=> ! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| sP13(c_HOL_Obool_Obool__size(c_fTrue),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_917])]) ).
fof(f27632,plain,
! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| sP13(c_HOL_Obool_Obool__size(c_fTrue),X1) ),
inference(forward_demodulation,[],[f27631,f17176]) ).
fof(f27631,plain,
! [X1] :
( sP13(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,[],[f25436,f17187]) ).
fof(f25436,plain,
! [X1] :
( sP13(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,[],[f19449]) ).
fof(f19449,plain,
! [X0,X1] :
( sP13(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,[],[f15230]) ).
fof(f15230,plain,
! [X0,X1] :
( ( sP13(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)) )
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
| ~ sP13(X0,X1) ) ),
inference(flattening,[],[f15229]) ).
fof(f15229,plain,
! [X0,X1] :
( ( sP13(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)) )
| ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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)) )
& ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
| ~ sP13(X0,X1) ) ),
inference(nnf_transformation,[],[f14551]) ).
fof(f34481,plain,
spl635_916,
inference(avatar_split_clause,[],[f27630,f34479]) ).
fof(f34479,plain,
( spl635_916
<=> ! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Int_OPls))
| sP13(c_HOL_Obool_Obool__size(c_fTrue),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_916])]) ).
fof(f27630,plain,
! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Int_OPls))
| sP13(c_HOL_Obool_Obool__size(c_fTrue),X1) ),
inference(forward_demodulation,[],[f27629,f25969]) ).
fof(f25969,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,[],[f25968,f17176]) ).
fof(f25968,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,[],[f17235,f17187]) ).
fof(f17235,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,[],[f319]) ).
fof(f319,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',fact_transfer__int__nat__numerals_I1_J) ).
fof(f27629,plain,
! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Obool_Obool__size(c_fTrue))))
| sP13(c_HOL_Obool_Obool__size(c_fTrue),X1) ),
inference(forward_demodulation,[],[f27628,f17187]) ).
fof(f27628,plain,
! [X1] :
( sP13(c_HOL_Obool_Obool__size(c_fTrue),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(forward_demodulation,[],[f25435,f17187]) ).
fof(f25435,plain,
! [X1] :
( sP13(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(equality_resolution,[],[f19450]) ).
fof(f19450,plain,
! [X0,X1] :
( sP13(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f15230]) ).
fof(f34477,plain,
spl635_915,
inference(avatar_split_clause,[],[f27592,f34475]) ).
fof(f34475,plain,
( spl635_915
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| hBOOL(hAPP(X0,sK203(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_915])]) ).
fof(f27592,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| hBOOL(hAPP(X0,sK203(X0))) ),
inference(forward_demodulation,[],[f19367,f17832]) ).
fof(f19367,plain,
! [X0,X1] :
( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK203(X0))) ),
inference(cnf_transformation,[],[f15185]) ).
fof(f15185,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK203(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,[sK203])],[f15183,f15184]) ).
fof(f15184,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X0,sK203(X0))) ),
introduced(choice_axiom,[]) ).
fof(f15183,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,[],[f15182]) ).
fof(f15182,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,[],[f6840]) ).
fof(f6840,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,[],[f3375]) ).
fof(f3375,axiom,
! [X29,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X8),X29)
<=> ! [X2] : ~ hBOOL(hAPP(X29,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__Collect__eq) ).
fof(f34473,plain,
spl635_914,
inference(avatar_split_clause,[],[f27590,f34471]) ).
fof(f34471,plain,
( spl635_914
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| hBOOL(hAPP(X0,sK202(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_914])]) ).
fof(f27590,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| hBOOL(hAPP(X0,sK202(X0))) ),
inference(forward_demodulation,[],[f19365,f17832]) ).
fof(f19365,plain,
! [X0,X1] :
( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK202(X0))) ),
inference(cnf_transformation,[],[f15181]) ).
fof(f15181,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK202(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,[sK202])],[f15179,f15180]) ).
fof(f15180,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X0,sK202(X0))) ),
introduced(choice_axiom,[]) ).
fof(f15179,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,[],[f15178]) ).
fof(f15178,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,[],[f6839]) ).
fof(f6839,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,[],[f3376]) ).
fof(f3376,axiom,
! [X29,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X8),X29)
<=> ! [X2] : ~ hBOOL(hAPP(X29,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(f34469,plain,
( spl635_913
| ~ spl635_418
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33330,f32548,f31267,f34467]) ).
fof(f34467,plain,
( spl635_913
<=> ! [X0,X1] :
( ~ sP31(X0,X1,c_fdisj)
| ~ hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_913])]) ).
fof(f31267,plain,
( spl635_418
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_418])]) ).
fof(f33330,plain,
( ! [X0,X1] :
( ~ sP31(X0,X1,c_fdisj)
| ~ hBOOL(X0) )
| ~ spl635_418
| ~ spl635_665 ),
inference(resolution,[],[f32549,f31268]) ).
fof(f31268,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) )
| ~ spl635_418 ),
inference(avatar_component_clause,[],[f31267]) ).
fof(f34465,plain,
spl635_912,
inference(avatar_split_clause,[],[f27577,f34463]) ).
fof(f27577,plain,
! [X0,X1] :
( c_Int_OPls != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| sP10(X1,X0) ),
inference(forward_demodulation,[],[f19354,f17176]) ).
fof(f19354,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,[],[f15172]) ).
fof(f15172,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,[],[f14547]) ).
fof(f14547,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,[],[f6835,f14546]) ).
fof(f14546,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(f6835,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,[],[f873]) ).
fof(f873,axiom,
! [X48,X14] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X14),X48)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),X14))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),X48))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X14)) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X48 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
fof(f34461,plain,
spl635_911,
inference(avatar_split_clause,[],[f27576,f34459]) ).
fof(f34459,plain,
( spl635_911
<=> ! [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,[spl635_911])]) ).
fof(f27576,plain,
! [X0,X1] :
( c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| ~ sP10(X1,X0) ),
inference(forward_demodulation,[],[f19355,f17176]) ).
fof(f19355,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,[],[f15172]) ).
fof(f34457,plain,
spl635_910,
inference(avatar_split_clause,[],[f27542,f34455]) ).
fof(f34455,plain,
( spl635_910
<=> ! [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,[spl635_910])]) ).
fof(f27542,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,[],[f25391,f17176]) ).
fof(f25391,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,[],[f19253]) ).
fof(f19253,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,[],[f15103]) ).
fof(f15103,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),sK195(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,[sK195])],[f15101,f15102]) ).
fof(f15102,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),sK195(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f15101,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,[],[f15100]) ).
fof(f15100,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,[],[f6794]) ).
fof(f6794,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,[],[f964]) ).
fof(f964,axiom,
! [X72,X27] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X27,X72)
<=> ? [X93] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X72),X93) = X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
fof(f34453,plain,
spl635_909,
inference(avatar_split_clause,[],[f27523,f34451]) ).
fof(f34451,plain,
( spl635_909
<=> ! [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,[spl635_909])]) ).
fof(f27523,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,[],[f27522,f17176]) ).
fof(f27522,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,[],[f25380,f17187]) ).
fof(f25380,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,[],[f19209]) ).
fof(f19209,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,[],[f15062]) ).
fof(f15062,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,[],[f15061]) ).
fof(f15061,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,[],[f14540]) ).
fof(f14540,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(f34449,plain,
spl635_908,
inference(avatar_split_clause,[],[f27515,f34447]) ).
fof(f34447,plain,
( spl635_908
<=> ! [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,[spl635_908])]) ).
fof(f27515,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,[],[f27514,f17176]) ).
fof(f27514,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,[],[f25375,f17187]) ).
fof(f25375,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,[],[f19201]) ).
fof(f19201,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,[],[f15059]) ).
fof(f15059,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,[],[f15058]) ).
fof(f15058,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,[],[f15057]) ).
fof(f15057,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,[],[f14538]) ).
fof(f14538,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(f34445,plain,
spl635_907,
inference(avatar_split_clause,[],[f27511,f34443]) ).
fof(f34443,plain,
( spl635_907
<=> ! [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,[spl635_907])]) ).
fof(f27511,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,[],[f24603,f17832]) ).
fof(f24603,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,[],[f19159,f19665]) ).
fof(f19159,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,[],[f15013]) ).
fof(f15013,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,[],[f6765]) ).
fof(f6765,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,[],[f3560]) ).
fof(f3560,axiom,
! [X98,X8] :
( c_Wellfounded_OwfP(X8,X98)
<=> c_Wellfounded_Owf(X8,hAPP(c_Set_OCollect(tc_prod(X8,X8)),hAPP(c_Product__Type_Oprod_Oprod__case(X8,X8,tc_HOL_Obool),X98))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__def) ).
fof(f34441,plain,
spl635_906,
inference(avatar_split_clause,[],[f27510,f34439]) ).
fof(f34439,plain,
( spl635_906
<=> ! [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,[spl635_906])]) ).
fof(f27510,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,[],[f24602,f17832]) ).
fof(f24602,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,[],[f19160,f19665]) ).
fof(f19160,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,[],[f15013]) ).
fof(f34437,plain,
spl635_905,
inference(avatar_split_clause,[],[f27507,f34435]) ).
fof(f34435,plain,
( spl635_905
<=> ! [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,[spl635_905])]) ).
fof(f27507,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,[],[f24601,f17832]) ).
fof(f24601,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,[],[f19131,f19665]) ).
fof(f19131,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,[],[f14989]) ).
fof(f14989,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,[],[f6759]) ).
fof(f6759,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,[],[f4932]) ).
fof(f4932,axiom,
! [X98,X8] :
( c_Predicate_Otransp(X8,X98)
<=> c_Relation_Otrans(X8,hAPP(c_Set_OCollect(tc_prod(X8,X8)),hAPP(c_Product__Type_Oprod_Oprod__case(X8,X8,tc_HOL_Obool),X98))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transp__def) ).
fof(f34433,plain,
spl635_904,
inference(avatar_split_clause,[],[f27506,f34431]) ).
fof(f34431,plain,
( spl635_904
<=> ! [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,[spl635_904])]) ).
fof(f27506,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,[],[f24600,f17832]) ).
fof(f24600,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,[],[f19132,f19665]) ).
fof(f19132,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,[],[f14989]) ).
fof(f34429,plain,
spl635_903,
inference(avatar_split_clause,[],[f27505,f34427]) ).
fof(f34427,plain,
( spl635_903
<=> ! [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,[spl635_903])]) ).
fof(f27505,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,[],[f24599,f17832]) ).
fof(f24599,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,[],[f19129,f19665]) ).
fof(f19129,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,[],[f14988]) ).
fof(f14988,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,[],[f6758]) ).
fof(f6758,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,[],[f4968]) ).
fof(f4968,axiom,
! [X98,X8] :
( c_Predicate_Osymp(X8,X98)
<=> c_Relation_Osym(X8,hAPP(c_Set_OCollect(tc_prod(X8,X8)),hAPP(c_Product__Type_Oprod_Oprod__case(X8,X8,tc_HOL_Obool),X98))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_symp__def) ).
fof(f34425,plain,
( spl635_902
| ~ spl635_465
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33328,f32548,f31463,f34423]) ).
fof(f34423,plain,
( spl635_902
<=> ! [X0] : ~ sP31(X0,c_HOL_Obool_Obool__size(c_fTrue),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_902])]) ).
fof(f31463,plain,
( spl635_465
<=> ! [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,[spl635_465])]) ).
fof(f33328,plain,
( ! [X0] : ~ sP31(X0,c_HOL_Obool_Obool__size(c_fTrue),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat))
| ~ spl635_465
| ~ spl635_665 ),
inference(resolution,[],[f32549,f31464]) ).
fof(f31464,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0))
| ~ spl635_465 ),
inference(avatar_component_clause,[],[f31463]) ).
fof(f34421,plain,
spl635_901,
inference(avatar_split_clause,[],[f27504,f34419]) ).
fof(f34419,plain,
( spl635_901
<=> ! [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,[spl635_901])]) ).
fof(f27504,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,[],[f24598,f17832]) ).
fof(f24598,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,[],[f19130,f19665]) ).
fof(f19130,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,[],[f14988]) ).
fof(f34417,plain,
spl635_900,
inference(avatar_split_clause,[],[f27008,f34415]) ).
fof(f34415,plain,
( spl635_900
<=> ! [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,[spl635_900])]) ).
fof(f27008,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,[],[f24537,f17832]) ).
fof(f24537,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,[],[f18742,f19665]) ).
fof(f18742,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,[],[f10898]) ).
fof(f10898,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,[],[f6451]) ).
fof(f6451,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,[],[f3569]) ).
fof(f3569,axiom,
! [X98,X8] :
( c_Wellfounded_OwfP(X8,X98)
=> c_Wellfounded_Oacyclic(X8,hAPP(c_Set_OCollect(tc_prod(X8,X8)),hAPP(c_Product__Type_Oprod_Oprod__case(X8,X8,tc_HOL_Obool),X98))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__acyclicP) ).
fof(f34413,plain,
spl635_899,
inference(avatar_split_clause,[],[f26993,f34411]) ).
fof(f34411,plain,
( spl635_899
<=> ! [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,[spl635_899])]) ).
fof(f26993,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,[],[f18619,f26500]) ).
fof(f18619,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,[],[f10764]) ).
fof(f10764,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,[],[f6363]) ).
fof(f6363,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,[],[f2657]) ).
fof(f2657,axiom,
! [X30,X8] :
( class_Orderings_Olinorder(X8)
=> c_Big__Operators_Olattice_OInf__fin(X8,c_Orderings_Oord__class_Omin(X8),hAPP(hAPP(c_Set_Oinsert(X8),X30),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).
fof(f34409,plain,
spl635_898,
inference(avatar_split_clause,[],[f26992,f34407]) ).
fof(f34407,plain,
( spl635_898
<=> ! [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,[spl635_898])]) ).
fof(f26992,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,[],[f18618,f26500]) ).
fof(f18618,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,[],[f10763]) ).
fof(f10763,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,[],[f6362]) ).
fof(f6362,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,[],[f2645]) ).
fof(f2645,axiom,
! [X30,X8] :
( class_Orderings_Olinorder(X8)
=> c_Big__Operators_Olattice_OSup__fin(X8,c_Orderings_Oord__class_Omax(X8),hAPP(hAPP(c_Set_Oinsert(X8),X30),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).
fof(f34405,plain,
spl635_897,
inference(avatar_split_clause,[],[f26645,f34403]) ).
fof(f34403,plain,
( spl635_897
<=> ! [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,[spl635_897])]) ).
fof(f26645,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,[],[f18236,f17187]) ).
fof(f18236,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,[],[f10461]) ).
fof(f10461,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,[],[f6073]) ).
fof(f6073,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,[],[f4351]) ).
fof(f4351,axiom,
! [X39,X8] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X39))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nitpick_Ocard_H(X8,X39) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X39))
=> c_Nitpick_Ocard_H(X8,X39) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),c_Hilbert__Choice_OEps(tc_List_Olist(X8),hAPP(hAPP(c_COMBS(tc_List_Olist(X8),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X8)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X8),tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X8,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X8)),c_fequal),c_List_Oset(X8))),X39))),c_List_Odistinct(X8)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nitpick_Ocard_H__def) ).
fof(f34401,plain,
spl635_896,
inference(avatar_split_clause,[],[f26490,f34399]) ).
fof(f34399,plain,
( spl635_896
<=> ! [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,[spl635_896])]) ).
fof(f26490,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,[],[f17921,f17176]) ).
fof(f17921,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,[],[f5773]) ).
fof(f5773,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,[],[f968]) ).
fof(f968,axiom,
! [X34,X33] : 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,X33,X34)),X34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).
fof(f34397,plain,
spl635_895,
inference(avatar_split_clause,[],[f26486,f34395]) ).
fof(f34395,plain,
( spl635_895
<=> ! [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,[spl635_895])]) ).
fof(f26486,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,[],[f17906,f17187]) ).
fof(f17906,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,[],[f5758]) ).
fof(f5758,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,[],[f3823]) ).
fof(f3823,axiom,
! [X1,X8] : c_Fun_Oid(X8) = hAPP(hAPP(c_Nat_Ocompow(X8,X8),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_funpow_Osimps_I1_J) ).
fof(f34392,plain,
spl635_894,
inference(avatar_split_clause,[],[f26433,f34389]) ).
fof(f34389,plain,
( spl635_894
<=> 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,[spl635_894])]) ).
fof(f26433,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,[],[f25290,f17176]) ).
fof(f25290,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,[],[f17786]) ).
fof(f17786,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,[],[f14762]) ).
fof(f14762,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,[],[f1126]) ).
fof(f1126,axiom,
! [X53] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X53)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X53 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).
fof(f34387,plain,
spl635_893,
inference(avatar_split_clause,[],[f26360,f34385]) ).
fof(f34385,plain,
( spl635_893
<=> ! [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,[spl635_893])]) ).
fof(f26360,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,[],[f17698,f17176]) ).
fof(f17698,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,[],[f14706]) ).
fof(f14706,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,[],[f5609]) ).
fof(f5609,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,[],[f870]) ).
fof(f870,axiom,
! [X86] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X86))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X86),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__def) ).
fof(f34383,plain,
spl635_892,
inference(avatar_split_clause,[],[f26359,f34381]) ).
fof(f34381,plain,
( spl635_892
<=> ! [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,[spl635_892])]) ).
fof(f26359,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,[],[f17699,f17176]) ).
fof(f17699,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,[],[f14706]) ).
fof(f34379,plain,
( spl635_891
| ~ spl635_468
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33325,f32548,f31475,f34377]) ).
fof(f34377,plain,
( spl635_891
<=> ! [X0] : ~ sP31(X0,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_891])]) ).
fof(f31475,plain,
( spl635_468
<=> ! [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,[spl635_468])]) ).
fof(f33325,plain,
( ! [X0] : ~ sP31(X0,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Rings_Odvd__class_Odvd(tc_Nat_Onat))
| ~ spl635_468
| ~ spl635_665 ),
inference(resolution,[],[f32549,f31476]) ).
fof(f31476,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0))
| ~ spl635_468 ),
inference(avatar_component_clause,[],[f31475]) ).
fof(f34375,plain,
spl635_890,
inference(avatar_split_clause,[],[f26358,f34373]) ).
fof(f34373,plain,
( spl635_890
<=> ! [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,[spl635_890])]) ).
fof(f26358,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,[],[f17688,f17176]) ).
fof(f17688,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,[],[f14701]) ).
fof(f14701,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,[],[f5604]) ).
fof(f5604,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,[],[f869]) ).
fof(f869,axiom,
! [X30] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X30))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__eq__ge__0) ).
fof(f34371,plain,
spl635_889,
inference(avatar_split_clause,[],[f26357,f34369]) ).
fof(f26357,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,[],[f17689,f17176]) ).
fof(f17689,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,[],[f14701]) ).
fof(f34362,plain,
( spl635_888
| ~ spl635_328
| ~ spl635_486
| ~ spl635_887 ),
inference(avatar_split_clause,[],[f34358,f34355,f31582,f30869,f34360]) ).
fof(f34360,plain,
( spl635_888
<=> ! [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,[spl635_888])]) ).
fof(f34355,plain,
( spl635_887
<=> ! [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,[spl635_887])]) ).
fof(f34358,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) )
| ~ spl635_328
| ~ spl635_486
| ~ spl635_887 ),
inference(forward_demodulation,[],[f34356,f31991]) ).
fof(f34356,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) )
| ~ spl635_887 ),
inference(avatar_component_clause,[],[f34355]) ).
fof(f34357,plain,
spl635_887,
inference(avatar_split_clause,[],[f26230,f34355]) ).
fof(f26230,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,[],[f26229,f25942]) ).
fof(f26229,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,[],[f24299,f17174]) ).
fof(f24299,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,[],[f17579,f24179]) ).
fof(f17579,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,[],[f10339]) ).
fof(f10339,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,[],[f5504]) ).
fof(f5504,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,[],[f1205]) ).
fof(f1205,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> ~ c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__iszero__Numeral1) ).
fof(f34353,plain,
spl635_886,
inference(avatar_split_clause,[],[f26107,f34351]) ).
fof(f34351,plain,
( spl635_886
<=> ! [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,[spl635_886])]) ).
fof(f26107,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,[],[f17473,f17327]) ).
fof(f17473,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,[],[f5411]) ).
fof(f5411,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,[],[f1007]) ).
fof(f1007,axiom,
! [X33] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X33) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X33),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__minus1__right) ).
fof(f34349,plain,
spl635_885,
inference(avatar_split_clause,[],[f26103,f34347]) ).
fof(f34347,plain,
( spl635_885
<=> ! [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,[spl635_885])]) ).
fof(f26103,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,[],[f17471,f17176]) ).
fof(f17471,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,[],[f5409]) ).
fof(f5409,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,[],[f1536]) ).
fof(f1536,axiom,
! [X34] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X34) = 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',fact_posDivAlg__0) ).
fof(f34345,plain,
spl635_884,
inference(avatar_split_clause,[],[f26092,f34343]) ).
fof(f34343,plain,
( spl635_884
<=> ! [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,[spl635_884])]) ).
fof(f26092,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,[],[f17446,f17176]) ).
fof(f17446,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,[],[f5384]) ).
fof(f5384,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,[],[f454]) ).
fof(f454,axiom,
! [X31] : 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),X31)),X31),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(f34341,plain,
spl635_883,
inference(avatar_split_clause,[],[f26084,f34339]) ).
fof(f34339,plain,
( spl635_883
<=> ! [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,[spl635_883])]) ).
fof(f26084,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,[],[f17433,f17187]) ).
fof(f17433,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,[],[f1994]) ).
fof(f1994,axiom,
! [X15] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X15) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast0LessThan) ).
fof(f34337,plain,
spl635_882,
inference(avatar_split_clause,[],[f26083,f34335]) ).
fof(f26083,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,[],[f17430,f17187]) ).
fof(f17430,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,[],[f5368]) ).
fof(f5368,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,[],[f2354]) ).
fof(f2354,axiom,
! [X27] : c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X27),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastLessThan0) ).
fof(f34333,plain,
( spl635_881
| ~ spl635_330
| ~ spl635_658 ),
inference(avatar_split_clause,[],[f33172,f32520,f30880,f34331]) ).
fof(f34331,plain,
( spl635_881
<=> ! [X0] : hBOOL(hAPP(c_Nat__Numeral_Oneg,sK216(c_Nat__Numeral_Oneg,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_881])]) ).
fof(f33172,plain,
( ! [X0] : hBOOL(hAPP(c_Nat__Numeral_Oneg,sK216(c_Nat__Numeral_Oneg,X0)))
| ~ spl635_330
| ~ spl635_658 ),
inference(resolution,[],[f32521,f30882]) ).
fof(f34329,plain,
( spl635_880
| ~ spl635_879 ),
inference(avatar_split_clause,[],[f34324,f34321,f34326]) ).
fof(f34321,plain,
( spl635_879
<=> ! [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,[spl635_879])]) ).
fof(f34324,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)))
| ~ spl635_879 ),
inference(forward_demodulation,[],[f34322,f26083]) ).
fof(f34322,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)))
| ~ spl635_879 ),
inference(avatar_component_clause,[],[f34321]) ).
fof(f34323,plain,
spl635_879,
inference(avatar_split_clause,[],[f26044,f34321]) ).
fof(f26044,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,[],[f24248,f17187]) ).
fof(f24248,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,[],[f17334,f17916]) ).
fof(f17916,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,[],[f5768]) ).
fof(f5768,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,[],[f4611]) ).
fof(f4611,axiom,
! [X15,X27] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X27),X15)) = c_List_Oupt(X27,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__range) ).
fof(f17334,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f5272]) ).
fof(f5272,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f4605]) ).
fof(f4605,axiom,
! [X42] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X42,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_upt__0) ).
fof(f34314,plain,
( spl635_878
| ~ spl635_328
| ~ spl635_486
| ~ spl635_877 ),
inference(avatar_split_clause,[],[f34309,f34305,f31582,f30869,f34311]) ).
fof(f34311,plain,
( spl635_878
<=> 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,[spl635_878])]) ).
fof(f34305,plain,
( spl635_877
<=> 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,[spl635_877])]) ).
fof(f34309,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)
| ~ spl635_328
| ~ spl635_486
| ~ spl635_877 ),
inference(forward_demodulation,[],[f34307,f31991]) ).
fof(f34307,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)
| ~ spl635_877 ),
inference(avatar_component_clause,[],[f34305]) ).
fof(f34308,plain,
spl635_877,
inference(avatar_split_clause,[],[f25942,f34305]) ).
fof(f34303,plain,
spl635_876,
inference(avatar_split_clause,[],[f25775,f34301]) ).
fof(f34301,plain,
( spl635_876
<=> ! [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,[spl635_876])]) ).
fof(f25775,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,[],[f23079]) ).
fof(f23079,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,[],[f13649]) ).
fof(f13649,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,[],[f9355]) ).
fof(f9355,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,[],[f1805]) ).
fof(f1805,axiom,
! [X1,X30,X8,X25,X14] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X14
=> hAPP(c_New__DSequence_Opos__decr__bind(X25,X8,X30,X1),X14) = hAPP(c_Lazy__Sequence_Obind(X25,X8,hAPP(X30,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X14),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(X25,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X8)),X1),X14)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X14
=> hAPP(c_New__DSequence_Opos__decr__bind(X25,X8,X30,X1),X14) = c_Lazy__Sequence_Oempty(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__decr__bind__def) ).
fof(f34299,plain,
spl635_875,
inference(avatar_split_clause,[],[f25774,f34297]) ).
fof(f34297,plain,
( spl635_875
<=> ! [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,[spl635_875])]) ).
fof(f25774,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,[],[f23077]) ).
fof(f23077,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,[],[f13648]) ).
fof(f13648,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,[],[f9354]) ).
fof(f9354,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,[],[f1823]) ).
fof(f1823,axiom,
! [X1,X30,X8,X25,X14] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X14
=> hAPP(c_New__DSequence_Oneg__decr__bind(X25,X8,X30,X1),X14) = c_Lazy__Sequence_Ohb__bind(X25,X8,hAPP(X30,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X14),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X25,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X8))),X1),X14)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X14
=> hAPP(c_New__DSequence_Oneg__decr__bind(X25,X8,X30,X1),X14) = c_Lazy__Sequence_Ohit__bound(X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__decr__bind__def) ).
fof(f34295,plain,
spl635_874,
inference(avatar_split_clause,[],[f25660,f34293]) ).
fof(f34293,plain,
( spl635_874
<=> ! [X0,X1,X3] : c_List_Oremove1(X1,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_874])]) ).
fof(f25660,plain,
! [X3,X0,X1] : c_List_Oremove1(X1,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X0)) = X0,
inference(equality_resolution,[],[f21807]) ).
fof(f21807,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,[],[f12698]) ).
fof(f12698,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,[],[f8470]) ).
fof(f8470,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,[],[f4427]) ).
fof(f4427,axiom,
! [X208,X5,X12,X13] :
( ( X12 != X13
=> c_List_Oremove1(X5,X13,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X208)) = hAPP(hAPP(c_List_Olist_OCons(X5),X12),c_List_Oremove1(X5,X13,X208)) )
& ( X12 = X13
=> c_List_Oremove1(X5,X13,hAPP(hAPP(c_List_Olist_OCons(X5),X12),X208)) = X208 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1_Osimps_I2_J) ).
fof(f34291,plain,
spl635_873,
inference(avatar_split_clause,[],[f25498,f34289]) ).
fof(f34289,plain,
( spl635_873
<=> ! [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,[spl635_873])]) ).
fof(f25498,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,[],[f20156]) ).
fof(f20156,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,[],[f15419]) ).
fof(f15419,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,[],[f11513]) ).
fof(f11513,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,[],[f7395]) ).
fof(f7395,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,[],[f598]) ).
fof(f598,axiom,
! [X17,X47,X8] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X8)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X8),X47),X17) = X47
<=> c_Groups_Ozero__class_Ozero(X8) = X17 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(f34287,plain,
( spl635_872
| ~ spl635_330
| ~ spl635_640 ),
inference(avatar_split_clause,[],[f32983,f32448,f30880,f34285]) ).
fof(f32983,plain,
( ! [X0] : hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Hilbert__Choice_OEps(X0,c_Nat__Numeral_Oneg)))
| ~ spl635_330
| ~ spl635_640 ),
inference(resolution,[],[f32449,f30882]) ).
fof(f34283,plain,
spl635_871,
inference(avatar_split_clause,[],[f25484,f34281]) ).
fof(f34281,plain,
( spl635_871
<=> ! [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,[spl635_871])]) ).
fof(f25484,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,[],[f20036]) ).
fof(f20036,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,[],[f15390]) ).
fof(f15390,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,[],[f11408]) ).
fof(f11408,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,[],[f7307]) ).
fof(f7307,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,[],[f564]) ).
fof(f564,axiom,
! [X47,X17,X8] :
( class_Groups_Oab__group__add(X8)
=> ( X17 = X47
<=> c_Groups_Ozero__class_Ozero(X8) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X8),X17),X47) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(f34278,plain,
spl635_870,
inference(avatar_split_clause,[],[f25293,f34276]) ).
fof(f34276,plain,
( spl635_870
<=> ! [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,[spl635_870])]) ).
fof(f25293,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,[],[f24456]) ).
fof(f24456,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,[],[f18211,f17923]) ).
fof(f17923,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,[],[f5775]) ).
fof(f5775,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,[],[f1815]) ).
fof(f1815,axiom,
! [X4,X42] : c_Code__Numeral_Onat__of__aux(X42,X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X42)),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__aux__def) ).
fof(f18211,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,[],[f10450]) ).
fof(f10450,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,[],[f6062]) ).
fof(f6062,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,[],[f1464]) ).
fof(f1464,axiom,
! [X4,X42] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X42
=> c_Code__Numeral_Onat__of__aux(X42,X4) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X42),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X4)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X42
=> c_Code__Numeral_Onat__of__aux(X42,X4) = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__aux__code) ).
fof(f34274,plain,
spl635_869,
inference(avatar_split_clause,[],[f24372,f34272]) ).
fof(f34272,plain,
( spl635_869
<=> ! [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,[spl635_869])]) ).
fof(f24372,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,[],[f17912,f17309]) ).
fof(f17912,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,[],[f5764]) ).
fof(f5764,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,[],[f4199]) ).
fof(f4199,axiom,
! [X71,X14] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X14,X71) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X14,X71)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__upto) ).
fof(f34270,plain,
spl635_868,
inference(avatar_split_clause,[],[f24371,f34268]) ).
fof(f34268,plain,
( spl635_868
<=> ! [X0,X1] : hAPP(c_List_Omember(X1),X0) = hAPP(c_List_Omember(X1),c_List_Oremdups(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_868])]) ).
fof(f24371,plain,
! [X0,X1] : hAPP(c_List_Omember(X1),X0) = hAPP(c_List_Omember(X1),c_List_Oremdups(X1,X0)),
inference(definition_unfolding,[],[f17911,f17309,f17309]) ).
fof(f17911,plain,
! [X0,X1] : hAPP(c_List_Oset(X1),X0) = hAPP(c_List_Oset(X1),c_List_Oremdups(X1,X0)),
inference(cnf_transformation,[],[f5763]) ).
fof(f5763,plain,
! [X0,X1] : hAPP(c_List_Oset(X1),X0) = hAPP(c_List_Oset(X1),c_List_Oremdups(X1,X0)),
inference(rectify,[],[f4514]) ).
fof(f4514,axiom,
! [X210,X8] : hAPP(c_List_Oset(X8),X210) = hAPP(c_List_Oset(X8),c_List_Oremdups(X8,X210)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_set__remdups) ).
fof(f34266,plain,
spl635_867,
inference(avatar_split_clause,[],[f24354,f34264]) ).
fof(f34264,plain,
( spl635_867
<=> ! [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,[spl635_867])]) ).
fof(f24354,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,[],[f17846,f17916]) ).
fof(f17846,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X0))),
inference(cnf_transformation,[],[f5698]) ).
fof(f5698,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X0))),
inference(rectify,[],[f4612]) ).
fof(f4612,axiom,
! [X41,X42] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X42,X41))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__upt) ).
fof(f34262,plain,
spl635_866,
inference(avatar_split_clause,[],[f24245,f34260]) ).
fof(f34260,plain,
( spl635_866
<=> ! [X0] : c_Relation_Osingle__valued(X0,X0,c_Transitive__Closure_Ortrancl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_866])]) ).
fof(f24245,plain,
! [X0] : c_Relation_Osingle__valued(X0,X0,c_Transitive__Closure_Ortrancl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))),
inference(definition_unfolding,[],[f17312,f17426]) ).
fof(f17426,plain,
! [X0] : c_Relation_OId(X0) = c_Transitive__Closure_Ortrancl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f5364]) ).
fof(f5364,plain,
! [X0] : c_Relation_OId(X0) = c_Transitive__Closure_Ortrancl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f3731]) ).
fof(f3731,axiom,
! [X8] : c_Relation_OId(X8) = c_Transitive__Closure_Ortrancl(X8,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X8),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__empty) ).
fof(f17312,plain,
! [X0] : c_Relation_Osingle__valued(X0,X0,c_Relation_OId(X0)),
inference(cnf_transformation,[],[f5250]) ).
fof(f5250,plain,
! [X0] : c_Relation_Osingle__valued(X0,X0,c_Relation_OId(X0)),
inference(rectify,[],[f3792]) ).
fof(f3792,axiom,
! [X8] : c_Relation_Osingle__valued(X8,X8,c_Relation_OId(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_single__valued__Id) ).
fof(f34258,plain,
spl635_865,
inference(avatar_split_clause,[],[f23717,f34256]) ).
fof(f34256,plain,
( spl635_865
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| X0 = X3
| ~ sP83(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_865])]) ).
fof(f23717,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X0 = X3
| ~ sP83(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16828]) ).
fof(f16828,plain,
! [X0,X1,X2,X3] :
( ( sP83(X0,X1,X2,X3)
| ( ( X0 != X1
| X2 != X3 )
& ( X0 != X3
| X1 != X2 ) ) )
& ( ( X0 = X1
& X2 = X3 )
| ( X0 = X3
& X1 = X2 )
| ~ sP83(X0,X1,X2,X3) ) ),
inference(rectify,[],[f16827]) ).
fof(f16827,plain,
! [X2,X1,X3,X0] :
( ( sP83(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP83(X2,X1,X3,X0) ) ),
inference(flattening,[],[f16826]) ).
fof(f16826,plain,
! [X2,X1,X3,X0] :
( ( sP83(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP83(X2,X1,X3,X0) ) ),
inference(nnf_transformation,[],[f14672]) ).
fof(f14672,plain,
! [X2,X1,X3,X0] :
( sP83(X2,X1,X3,X0)
<=> ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP83])]) ).
fof(f34254,plain,
spl635_864,
inference(avatar_split_clause,[],[f23716,f34252]) ).
fof(f34252,plain,
( spl635_864
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| X1 = X2
| ~ sP83(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_864])]) ).
fof(f23716,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X1 = X2
| ~ sP83(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16828]) ).
fof(f34250,plain,
spl635_863,
inference(avatar_split_clause,[],[f23715,f34248]) ).
fof(f34248,plain,
( spl635_863
<=> ! [X0,X3,X2,X1] :
( X2 = X3
| X0 = X3
| ~ sP83(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_863])]) ).
fof(f23715,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X0 = X3
| ~ sP83(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16828]) ).
fof(f34246,plain,
spl635_862,
inference(avatar_split_clause,[],[f23714,f34244]) ).
fof(f34244,plain,
( spl635_862
<=> ! [X2,X0,X1,X3] :
( X2 = X3
| X1 = X2
| ~ sP83(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_862])]) ).
fof(f23714,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X1 = X2
| ~ sP83(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16828]) ).
fof(f34242,plain,
spl635_861,
inference(avatar_split_clause,[],[f22687,f34240]) ).
fof(f34240,plain,
( spl635_861
<=> ! [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,[spl635_861])]) ).
fof(f22687,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,[],[f16357]) ).
fof(f16357,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,[],[f9165]) ).
fof(f9165,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,[],[f4479]) ).
fof(f4479,axiom,
! [X209,X29,X25,X8] :
( c_List_Olist__all2(X8,X25,X29,c_List_Olist_ONil(X8),X209)
<=> c_List_Olist_ONil(X25) = X209 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__Nil) ).
fof(f34238,plain,
spl635_860,
inference(avatar_split_clause,[],[f22685,f34236]) ).
fof(f34236,plain,
( spl635_860
<=> ! [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,[spl635_860])]) ).
fof(f22685,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,[],[f16356]) ).
fof(f16356,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,[],[f9164]) ).
fof(f9164,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,[],[f4478]) ).
fof(f4478,axiom,
! [X210,X29,X25,X8] :
( c_List_Olist__all2(X8,X25,X29,X210,c_List_Olist_ONil(X25))
<=> c_List_Olist_ONil(X8) = X210 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__Nil2) ).
fof(f34234,plain,
spl635_859,
inference(avatar_split_clause,[],[f22352,f34232]) ).
fof(f34232,plain,
( spl635_859
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X1,sK433(X0,X1,X2)))
| ~ sP57(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_859])]) ).
fof(f22352,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X1,sK433(X0,X1,X2)))
| ~ sP57(X0,X1,X2) ),
inference(cnf_transformation,[],[f16212]) ).
fof(f34230,plain,
spl635_858,
inference(avatar_split_clause,[],[f21637,f34228]) ).
fof(f34228,plain,
( spl635_858
<=> ! [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,[spl635_858])]) ).
fof(f21637,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0) = c_Nat_Onat_Onat__case(X3,X2,X1,hAPP(c_Nat_OSuc,X0)),
inference(cnf_transformation,[],[f8301]) ).
fof(f8301,plain,
! [X0,X1,X2,X3] : hAPP(X1,X0) = c_Nat_Onat_Onat__case(X3,X2,X1,hAPP(c_Nat_OSuc,X0)),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X11,X20,X21,X8] : c_Nat_Onat_Onat__case(X8,X21,X20,hAPP(c_Nat_OSuc,X11)) = hAPP(X20,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
fof(f34226,plain,
spl635_857,
inference(avatar_split_clause,[],[f21636,f34224]) ).
fof(f34224,plain,
( spl635_857
<=> ! [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,[spl635_857])]) ).
fof(f21636,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,[],[f8300]) ).
fof(f8300,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,[],[f2528]) ).
fof(f2528,axiom,
! [X35,X30,X25,X8] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X8,tc_fun(X25,tc_HOL_Obool))),X30),X35)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot2E) ).
fof(f34222,plain,
spl635_856,
inference(avatar_split_clause,[],[f21625,f34220]) ).
fof(f34220,plain,
( spl635_856
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK412(X0,X1,X2)))
| ~ c_List_Olist__ex(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_856])]) ).
fof(f21625,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK412(X0,X1,X2)))
| ~ c_List_Olist__ex(X2,X0,X1) ),
inference(cnf_transformation,[],[f16101]) ).
fof(f16101,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(X0,sK412(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK412(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,[sK412])],[f16099,f16100]) ).
fof(f16100,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,sK412(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK412(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f16099,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,[],[f16098]) ).
fof(f16098,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,[],[f8289]) ).
fof(f8289,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,[],[f4903]) ).
fof(f4903,axiom,
! [X29,X210,X8] :
( ? [X2] :
( hBOOL(hAPP(X29,X2))
& hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(c_List_Oset(X8),X210))) )
<=> c_List_Olist__ex(X8,X29,X210) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bex__set__list__ex) ).
fof(f34218,plain,
spl635_855,
inference(avatar_split_clause,[],[f21617,f34216]) ).
fof(f34216,plain,
( spl635_855
<=> ! [X2,X0,X1] :
( c_List_Olist__all(X2,X0,X1)
| ~ hBOOL(hAPP(X0,sK409(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_855])]) ).
fof(f21617,plain,
! [X2,X0,X1] :
( c_List_Olist__all(X2,X0,X1)
| ~ hBOOL(hAPP(X0,sK409(X0,X1,X2))) ),
inference(cnf_transformation,[],[f16092]) ).
fof(f16092,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,sK409(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK409(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK409])],[f16090,f16091]) ).
fof(f16091,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,sK409(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK409(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f16090,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,[],[f16089]) ).
fof(f16089,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,[],[f12696]) ).
fof(f12696,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,[],[f8287]) ).
fof(f8287,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,[],[f4815]) ).
fof(f4815,axiom,
! [X29,X210,X8] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(c_List_Oset(X8),X210)))
=> hBOOL(hAPP(X29,X2)) )
<=> c_List_Olist__all(X8,X29,X210) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ball__set__list__all) ).
fof(f34214,plain,
spl635_854,
inference(avatar_split_clause,[],[f21414,f34212]) ).
fof(f34212,plain,
( spl635_854
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK384(X0,X1,X2)))
| ~ sP46(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_854])]) ).
fof(f21414,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK384(X0,X1,X2)))
| ~ sP46(X0,X1,X2) ),
inference(cnf_transformation,[],[f15936]) ).
fof(f15936,plain,
! [X0,X1,X2] :
( ( sP46(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,sK384(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,sK384(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),sK384(X0,X1,X2))),X2)) )
| ~ sP46(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK384])],[f15934,f15935]) ).
fof(f15935,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,sK384(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,sK384(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),sK384(X0,X1,X2))),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15934,plain,
! [X0,X1,X2] :
( ( sP46(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)) )
| ~ sP46(X0,X1,X2) ) ),
inference(rectify,[],[f15933]) ).
fof(f15933,plain,
! [X2,X0,X1] :
( ( sP46(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)) )
| ~ sP46(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f14605]) ).
fof(f34210,plain,
spl635_853,
inference(avatar_split_clause,[],[f21407,f34208]) ).
fof(f34208,plain,
( spl635_853
<=> ! [X2,X0,X1] :
( sP45(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK382(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_853])]) ).
fof(f21407,plain,
! [X2,X0,X1] :
( sP45(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK382(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15930]) ).
fof(f15930,plain,
! [X0,X1,X2] :
( ( sP45(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK382(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK382(X0,X1,X2))),sK383(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK383(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
| ~ sP45(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK382,sK383])],[f15928,f15929]) ).
fof(f15929,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,sK382(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK382(X0,X1,X2))),sK383(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK383(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15928,plain,
! [X0,X1,X2] :
( ( sP45(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
| ~ sP45(X0,X1,X2) ) ),
inference(rectify,[],[f15927]) ).
fof(f15927,plain,
! [X2,X1,X0] :
( ( sP45(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
| ~ sP45(X2,X1,X0) ) ),
inference(flattening,[],[f15926]) ).
fof(f15926,plain,
! [X2,X1,X0] :
( ( sP45(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
| ~ sP45(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14603]) ).
fof(f34206,plain,
spl635_852,
inference(avatar_split_clause,[],[f21400,f34204]) ).
fof(f34204,plain,
( spl635_852
<=> ! [X2,X0,X1] :
( sP42(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK380(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_852])]) ).
fof(f21400,plain,
! [X2,X0,X1] :
( sP42(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK380(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15924]) ).
fof(f34202,plain,
spl635_851,
inference(avatar_split_clause,[],[f21394,f34200]) ).
fof(f34200,plain,
( spl635_851
<=> ! [X2,X0,X1] :
( sP43(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK378(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_851])]) ).
fof(f21394,plain,
! [X2,X0,X1] :
( sP43(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK378(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15918]) ).
fof(f34198,plain,
spl635_850,
inference(avatar_split_clause,[],[f21339,f34196]) ).
fof(f34196,plain,
( spl635_850
<=> ! [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,[spl635_850])]) ).
fof(f21339,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,[],[f15880]) ).
fof(f15880,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,[],[f8193]) ).
fof(f8193,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,[],[f4812]) ).
fof(f4812,axiom,
! [X210,X29,X8] :
( c_List_Olist__all(X8,X29,hAPP(c_List_Orev(X8),X210))
<=> c_List_Olist__all(X8,X29,X210) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__rev) ).
fof(f34194,plain,
spl635_849,
inference(avatar_split_clause,[],[f21338,f34192]) ).
fof(f34192,plain,
( spl635_849
<=> ! [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,[spl635_849])]) ).
fof(f21338,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,[],[f15880]) ).
fof(f34190,plain,
spl635_848,
inference(avatar_split_clause,[],[f21337,f34188]) ).
fof(f34188,plain,
( spl635_848
<=> ! [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,[spl635_848])]) ).
fof(f21337,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,[],[f15879]) ).
fof(f15879,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,[],[f8192]) ).
fof(f8192,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,[],[f4803]) ).
fof(f4803,axiom,
! [X210,X29,X8] :
( c_List_Olist__ex(X8,X29,hAPP(c_List_Orev(X8),X210))
<=> c_List_Olist__ex(X8,X29,X210) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__rev) ).
fof(f34186,plain,
spl635_847,
inference(avatar_split_clause,[],[f21336,f34184]) ).
fof(f34184,plain,
( spl635_847
<=> ! [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,[spl635_847])]) ).
fof(f21336,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,[],[f15879]) ).
fof(f34182,plain,
spl635_846,
inference(avatar_split_clause,[],[f21329,f34180]) ).
fof(f34180,plain,
( spl635_846
<=> ! [X2,X0,X1] :
( sP40(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_846])]) ).
fof(f21329,plain,
! [X2,X0,X1] :
( sP40(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f15876]) ).
fof(f34178,plain,
spl635_845,
inference(avatar_split_clause,[],[f21327,f34176]) ).
fof(f34176,plain,
( spl635_845
<=> ! [X2,X0,X1] :
( sP40(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK372(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_845])]) ).
fof(f21327,plain,
! [X2,X0,X1] :
( sP40(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK372(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15874]) ).
fof(f15874,plain,
! [X0,X1,X2] :
( ( sP40(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK372(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK371(X0,X1,X2))),sK372(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK372(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
| ~ sP40(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK371,sK372])],[f15872,f15873]) ).
fof(f15873,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,sK372(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK371(X0,X1,X2))),sK372(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK372(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15872,plain,
! [X0,X1,X2] :
( ( sP40(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
| ~ sP40(X0,X1,X2) ) ),
inference(rectify,[],[f15871]) ).
fof(f15871,plain,
! [X2,X1,X0] :
( ( sP40(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
| ~ sP40(X2,X1,X0) ) ),
inference(flattening,[],[f15870]) ).
fof(f15870,plain,
! [X2,X1,X0] :
( ( sP40(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
| ~ sP40(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14595]) ).
fof(f34174,plain,
spl635_844,
inference(avatar_split_clause,[],[f21322,f34172]) ).
fof(f34172,plain,
( spl635_844
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_844])]) ).
fof(f21322,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f15869]) ).
fof(f15869,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
| ~ sP39(X0,X1,X2) )
& ( sP39(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))) ) ),
inference(nnf_transformation,[],[f14594]) ).
fof(f14594,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
<=> sP39(X0,X1,X2) ),
inference(definition_folding,[],[f12679,f14593,f14592,f14591]) ).
fof(f14593,plain,
! [X0,X1,X2] :
( sP39(X0,X1,X2)
<=> ( sP38(X2,X1,X0)
& sP37(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP39])]) ).
fof(f12679,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,[],[f12678]) ).
fof(f12678,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,[],[f8188]) ).
fof(f8188,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,[],[f1025]) ).
fof(f1025,axiom,
! [X48,X15,X29] :
( hBOOL(hAPP(X29,c_Divides_Odiv__class_Omod(tc_Int_Oint,X15,X48)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X85,X36] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X85)),X36) = X15
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X36),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X48),X36)) )
=> hBOOL(hAPP(X29,X36)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X48))
=> ! [X85,X36] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X48),X85)),X36) = X15
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X36),X48))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X36)) )
=> hBOOL(hAPP(X29,X36)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X48
=> hBOOL(hAPP(X29,X15)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__zmod) ).
fof(f34170,plain,
spl635_843,
inference(avatar_split_clause,[],[f21321,f34168]) ).
fof(f34168,plain,
( spl635_843
<=> ! [X2,X0,X1] :
( sP39(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_843])]) ).
fof(f21321,plain,
! [X2,X0,X1] :
( sP39(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))) ),
inference(cnf_transformation,[],[f15869]) ).
fof(f34166,plain,
spl635_842,
inference(avatar_split_clause,[],[f21320,f34164]) ).
fof(f34164,plain,
( spl635_842
<=> ! [X2,X0,X1] :
( sP37(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK370(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_842])]) ).
fof(f21320,plain,
! [X2,X0,X1] :
( sP37(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK370(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15868]) ).
fof(f34162,plain,
spl635_841,
inference(avatar_split_clause,[],[f21314,f34160]) ).
fof(f34160,plain,
( spl635_841
<=> ! [X2,X0,X1] :
( sP38(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK368(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_841])]) ).
fof(f21314,plain,
! [X2,X0,X1] :
( sP38(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK368(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15863]) ).
fof(f34158,plain,
spl635_840,
inference(avatar_split_clause,[],[f21232,f34156]) ).
fof(f34156,plain,
( spl635_840
<=> ! [X2,X0,X1] :
( c_List_Olist__all(X2,X1,X0)
| ~ hBOOL(hAPP(X1,sK352(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_840])]) ).
fof(f21232,plain,
! [X2,X0,X1] :
( c_List_Olist__all(X2,X1,X0)
| ~ hBOOL(hAPP(X1,sK352(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15794]) ).
fof(f15794,plain,
! [X0,X1,X2] :
( ( c_List_Olist__all(X2,X1,X0)
| ( ~ hBOOL(hAPP(X1,sK352(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK352(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,[sK352])],[f15792,f15793]) ).
fof(f15793,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,sK352(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK352(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15792,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,[],[f15791]) ).
fof(f15791,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,[],[f12665]) ).
fof(f12665,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,[],[f8169]) ).
fof(f8169,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,[],[f4813]) ).
fof(f4813,axiom,
! [X210,X29,X8] :
( c_List_Olist__all(X8,X29,X210)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(c_List_Oset(X8),X210)))
=> hBOOL(hAPP(X29,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff) ).
fof(f34154,plain,
spl635_839,
inference(avatar_split_clause,[],[f21229,f34152]) ).
fof(f34152,plain,
( spl635_839
<=> ! [X2,X0,X1] :
( c_List_Olist__all(X2,X1,X0)
| ~ hBOOL(hAPP(X1,sK351(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_839])]) ).
fof(f21229,plain,
! [X2,X0,X1] :
( c_List_Olist__all(X2,X1,X0)
| ~ hBOOL(hAPP(X1,sK351(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15790]) ).
fof(f15790,plain,
! [X0,X1,X2] :
( ( c_List_Olist__all(X2,X1,X0)
| ( ~ hBOOL(hAPP(X1,sK351(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK351(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,[sK351])],[f15788,f15789]) ).
fof(f15789,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,sK351(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK351(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15788,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,[],[f15787]) ).
fof(f15787,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,[],[f12664]) ).
fof(f12664,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,[],[f8168]) ).
fof(f8168,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,[],[f4817]) ).
fof(f4817,axiom,
! [X210,X29,X8] :
( c_List_Olist__all(X8,X29,X210)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(c_List_Oset(X8),X210)))
=> hBOOL(hAPP(X29,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff__raw) ).
fof(f34150,plain,
spl635_838,
inference(avatar_split_clause,[],[f21216,f34148]) ).
fof(f34148,plain,
( spl635_838
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X1,sK347(X0,X1,X2)))
| ~ c_List_Olist__ex(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_838])]) ).
fof(f21216,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X1,sK347(X0,X1,X2)))
| ~ c_List_Olist__ex(X2,X1,X0) ),
inference(cnf_transformation,[],[f15777]) ).
fof(f15777,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,sK347(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK347(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olist__ex(X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK347])],[f15775,f15776]) ).
fof(f15776,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,sK347(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK347(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15775,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,[],[f15774]) ).
fof(f15774,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,[],[f8165]) ).
fof(f8165,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,[],[f4904]) ).
fof(f4904,axiom,
! [X210,X29,X8] :
( c_List_Olist__ex(X8,X29,X210)
<=> ? [X2] :
( hBOOL(hAPP(X29,X2))
& hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(c_List_Oset(X8),X210))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__iff__raw) ).
fof(f34146,plain,
spl635_837,
inference(avatar_split_clause,[],[f21213,f34144]) ).
fof(f34144,plain,
( spl635_837
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X1,sK346(X0,X1,X2)))
| ~ c_List_Olist__ex(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_837])]) ).
fof(f21213,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X1,sK346(X0,X1,X2)))
| ~ c_List_Olist__ex(X2,X1,X0) ),
inference(cnf_transformation,[],[f15773]) ).
fof(f15773,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,sK346(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK346(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) )
| ~ c_List_Olist__ex(X2,X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK346])],[f15771,f15772]) ).
fof(f15772,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,sK346(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK346(X0,X1,X2)),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15771,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,[],[f15770]) ).
fof(f15770,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,[],[f8164]) ).
fof(f8164,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,[],[f4804]) ).
fof(f4804,axiom,
! [X210,X29,X8] :
( c_List_Olist__ex(X8,X29,X210)
<=> ? [X2] :
( hBOOL(hAPP(X29,X2))
& hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(c_List_Oset(X8),X210))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__iff) ).
fof(f34142,plain,
spl635_836,
inference(avatar_split_clause,[],[f21205,f34140]) ).
fof(f34140,plain,
( spl635_836
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK345(X0,X1,X2)))
| ~ sP33(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_836])]) ).
fof(f21205,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK345(X0,X1,X2)))
| ~ sP33(X0,X1,X2) ),
inference(cnf_transformation,[],[f15768]) ).
fof(f15768,plain,
! [X0,X1,X2] :
( ( sP33(X0,X1,X2)
| ! [X3] :
( ( sK344(X0,X1,X2,X3) != X3
& hBOOL(hAPP(X0,sK344(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X2),sK344(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] :
( sK345(X0,X1,X2) = X6
| ~ hBOOL(hAPP(X0,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),hAPP(c_List_Oset(X2),X1))) )
& hBOOL(hAPP(X0,sK345(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK345(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) )
| ~ sP33(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK344,sK345])],[f15765,f15767,f15766]) ).
fof(f15766,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))) )
=> ( sK344(X0,X1,X2,X3) != X3
& hBOOL(hAPP(X0,sK344(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X2),sK344(X0,X1,X2,X3)),hAPP(c_List_Oset(X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15767,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] :
( sK345(X0,X1,X2) = X6
| ~ hBOOL(hAPP(X0,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),hAPP(c_List_Oset(X2),X1))) )
& hBOOL(hAPP(X0,sK345(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK345(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15765,plain,
! [X0,X1,X2] :
( ( sP33(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))) )
| ~ sP33(X0,X1,X2) ) ),
inference(rectify,[],[f15764]) ).
fof(f15764,plain,
! [X1,X0,X2] :
( ( sP33(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))) )
| ~ sP33(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f14584]) ).
fof(f14584,plain,
! [X1,X0,X2] :
( sP33(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,[sP33])]) ).
fof(f34138,plain,
spl635_835,
inference(avatar_split_clause,[],[f21197,f34136]) ).
fof(f34136,plain,
( spl635_835
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK343(X0,X1,X2)))
| ~ sP32(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_835])]) ).
fof(f21197,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK343(X0,X1,X2)))
| ~ sP32(X0,X1,X2) ),
inference(cnf_transformation,[],[f15762]) ).
fof(f15762,plain,
! [X0,X1,X2] :
( ( sP32(X0,X1,X2)
| ! [X3] :
( ( sK342(X0,X1,X2,X3) != X3
& hBOOL(hAPP(X0,sK342(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X2),sK342(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] :
( sK343(X0,X1,X2) = X6
| ~ hBOOL(hAPP(X0,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),hAPP(c_List_Oset(X2),X1))) )
& hBOOL(hAPP(X0,sK343(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK343(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) )
| ~ sP32(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK342,sK343])],[f15759,f15761,f15760]) ).
fof(f15760,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))) )
=> ( sK342(X0,X1,X2,X3) != X3
& hBOOL(hAPP(X0,sK342(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X2),sK342(X0,X1,X2,X3)),hAPP(c_List_Oset(X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15761,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] :
( sK343(X0,X1,X2) = X6
| ~ hBOOL(hAPP(X0,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),hAPP(c_List_Oset(X2),X1))) )
& hBOOL(hAPP(X0,sK343(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X2),sK343(X0,X1,X2)),hAPP(c_List_Oset(X2),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15759,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,[],[f15758]) ).
fof(f15758,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,[],[f14582]) ).
fof(f14582,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(f34134,plain,
spl635_834,
inference(avatar_split_clause,[],[f21195,f34132]) ).
fof(f34132,plain,
( spl635_834
<=> ! [X2,X0,X1] :
( c_List_Oall__interval__int(X2,X1,X0)
| ~ hBOOL(hAPP(X2,sK341(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_834])]) ).
fof(f21195,plain,
! [X2,X0,X1] :
( c_List_Oall__interval__int(X2,X1,X0)
| ~ hBOOL(hAPP(X2,sK341(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15757]) ).
fof(f15757,plain,
! [X0,X1,X2] :
( ( c_List_Oall__interval__int(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,sK341(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK341(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,[sK341])],[f15755,f15756]) ).
fof(f15756,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,sK341(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK341(X0,X1,X2)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f15755,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,[],[f15754]) ).
fof(f15754,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,[],[f12657]) ).
fof(f12657,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,[],[f8161]) ).
fof(f8161,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,[],[f4898]) ).
fof(f4898,axiom,
! [X71,X14,X29] :
( c_List_Oall__interval__int(X29,X14,X71)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X14,X71)))
=> hBOOL(hAPP(X29,X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__interval__int__def) ).
fof(f34130,plain,
spl635_833,
inference(avatar_split_clause,[],[f21141,f34128]) ).
fof(f34128,plain,
( spl635_833
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
| ~ sP31(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_833])]) ).
fof(f21141,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f15705]) ).
fof(f15705,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1)) )
| ~ sP31(X0,X1,X2) ),
inference(rectify,[],[f15704]) ).
fof(f15704,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) )
| ~ sP31(X2,X1,X0) ),
inference(nnf_transformation,[],[f14580]) ).
fof(f14580,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) )
| ~ sP31(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP31])]) ).
fof(f34126,plain,
spl635_832,
inference(avatar_split_clause,[],[f20663,f34124]) ).
fof(f34124,plain,
( spl635_832
<=> ! [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,[spl635_832])]) ).
fof(f20663,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,[],[f12157]) ).
fof(f12157,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,[],[f7799]) ).
fof(f7799,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,[],[f3537]) ).
fof(f3537,axiom,
! [X15,X98,X8] :
( c_Wellfounded_Owf(X8,X98)
=> c_Wellfounded_Owf(tc_List_Olist(X8),hAPP(c_List_Olexn(X8,X98),X15)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__lexn) ).
fof(f34122,plain,
spl635_831,
inference(avatar_split_clause,[],[f20334,f34120]) ).
fof(f34120,plain,
( spl635_831
<=> ! [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,[spl635_831])]) ).
fof(f20334,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,[],[f11745]) ).
fof(f11745,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,[],[f11744]) ).
fof(f11744,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,[],[f7554]) ).
fof(f7554,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,[],[f4703]) ).
fof(f4703,axiom,
! [X29,X210,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_List_Olinorder__class_Osorted(X8,X210)
=> c_List_Olinorder__class_Osorted(X8,c_List_OtakeWhile(X8,X29,X210)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__takeWhile) ).
fof(f34118,plain,
spl635_830,
inference(avatar_split_clause,[],[f20333,f34116]) ).
fof(f34116,plain,
( spl635_830
<=> ! [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,[spl635_830])]) ).
fof(f20333,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,[],[f11743]) ).
fof(f11743,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,[],[f11742]) ).
fof(f11742,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,[],[f7553]) ).
fof(f7553,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,[],[f4638]) ).
fof(f4638,axiom,
! [X33,X208,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_List_Olinorder__class_Osorted(X5,X208)
=> c_List_Olinorder__class_Osorted(X5,c_List_Oremove1(X5,X33,X208)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__remove1) ).
fof(f34114,plain,
spl635_829,
inference(avatar_split_clause,[],[f20306,f34112]) ).
fof(f34112,plain,
( spl635_829
<=> ! [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,[spl635_829])]) ).
fof(f20306,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,[],[f11710]) ).
fof(f11710,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,[],[f7526]) ).
fof(f7526,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,[],[f4528]) ).
fof(f4528,axiom,
! [X1,X8,X25] :
( class_Orderings_Olinorder(X25)
=> c_List_Olist_ONil(X8) = c_List_Olinorder__class_Osort__key(X8,X25,X1,c_List_Olist_ONil(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sort__key__simps_I1_J) ).
fof(f34110,plain,
spl635_828,
inference(avatar_split_clause,[],[f20198,f34108]) ).
fof(f34108,plain,
( spl635_828
<=> ! [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,[spl635_828])]) ).
fof(f20198,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,[],[f11559]) ).
fof(f11559,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,[],[f7426]) ).
fof(f7426,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,[],[f2315]) ).
fof(f2315,axiom,
! [X30,X25,X8] :
( class_Orderings_Obot(X8)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X25,X8)),X30) = c_Orderings_Obot__class_Obot(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__apply) ).
fof(f34106,plain,
spl635_827,
inference(avatar_split_clause,[],[f20154,f34104]) ).
fof(f34104,plain,
( spl635_827
<=> ! [X2,X0,X1] :
( c_Orderings_Otop__class_Otop(X2) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X0)
| ~ class_Orderings_Otop(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_827])]) ).
fof(f20154,plain,
! [X2,X0,X1] :
( c_Orderings_Otop__class_Otop(X2) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X0)
| ~ class_Orderings_Otop(X2) ),
inference(cnf_transformation,[],[f11512]) ).
fof(f11512,plain,
! [X0,X1,X2] :
( c_Orderings_Otop__class_Otop(X2) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X0)
| ~ class_Orderings_Otop(X2) ),
inference(ennf_transformation,[],[f7394]) ).
fof(f7394,plain,
! [X0,X1,X2] :
( class_Orderings_Otop(X2)
=> c_Orderings_Otop__class_Otop(X2) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X0) ),
inference(rectify,[],[f3144]) ).
fof(f3144,axiom,
! [X30,X25,X8] :
( class_Orderings_Otop(X8)
=> c_Orderings_Otop__class_Otop(X8) = hAPP(c_Orderings_Otop__class_Otop(tc_fun(X25,X8)),X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__apply) ).
fof(f34102,plain,
spl635_826,
inference(avatar_split_clause,[],[f19968,f34100]) ).
fof(f34100,plain,
( spl635_826
<=> ! [X2,X0,X1] :
( c_FunDef_OTHE__default(X1,X0,X2) = X0
| hBOOL(hAPP(X2,sK218(X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_826])]) ).
fof(f19968,plain,
! [X2,X0,X1] :
( c_FunDef_OTHE__default(X1,X0,X2) = X0
| hBOOL(hAPP(X2,sK218(X2))) ),
inference(cnf_transformation,[],[f15366]) ).
fof(f15366,plain,
! [X0,X1,X2] :
( ( c_FunDef_OTHE__default(X1,X0,X2) = X0
| ( ! [X4] :
( sK218(X2) = X4
| ~ hBOOL(hAPP(X2,X4)) )
& hBOOL(hAPP(X2,sK218(X2))) ) )
& ( c_FunDef_OTHE__default(X1,X0,X2) = c_HOL_OThe(X1,X2)
| ! [X5] :
( ( sK219(X2,X5) != X5
& hBOOL(hAPP(X2,sK219(X2,X5))) )
| ~ hBOOL(hAPP(X2,X5)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK218,sK219])],[f11364,f15365,f15364]) ).
fof(f15364,plain,
! [X2] :
( ? [X3] :
( ! [X4] :
( X3 = X4
| ~ hBOOL(hAPP(X2,X4)) )
& hBOOL(hAPP(X2,X3)) )
=> ( ! [X4] :
( sK218(X2) = X4
| ~ hBOOL(hAPP(X2,X4)) )
& hBOOL(hAPP(X2,sK218(X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15365,plain,
! [X2,X5] :
( ? [X6] :
( X5 != X6
& hBOOL(hAPP(X2,X6)) )
=> ( sK219(X2,X5) != X5
& hBOOL(hAPP(X2,sK219(X2,X5))) ) ),
introduced(choice_axiom,[]) ).
fof(f11364,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,[],[f7241]) ).
fof(f7241,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,[],[f4886]) ).
fof(f4886,axiom,
! [X72,X8,X29] :
( ( ~ ? [X2] :
( ! [X45] :
( hBOOL(hAPP(X29,X45))
=> X2 = X45 )
& hBOOL(hAPP(X29,X2)) )
=> c_FunDef_OTHE__default(X8,X72,X29) = X72 )
& ( ? [X2] :
( ! [X45] :
( hBOOL(hAPP(X29,X45))
=> X2 = X45 )
& hBOOL(hAPP(X29,X2)) )
=> c_HOL_OThe(X8,X29) = c_FunDef_OTHE__default(X8,X72,X29) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_THE__default__def) ).
fof(f34098,plain,
spl635_825,
inference(avatar_split_clause,[],[f19682,f34096]) ).
fof(f34096,plain,
( spl635_825
<=> ! [X2,X0,X1] : hAPP(c_Relation_Oconverse(X2,X1),hAPP(c_Relation_Oconverse(X1,X2),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_825])]) ).
fof(f19682,plain,
! [X2,X0,X1] : hAPP(c_Relation_Oconverse(X2,X1),hAPP(c_Relation_Oconverse(X1,X2),X0)) = X0,
inference(cnf_transformation,[],[f6977]) ).
fof(f6977,plain,
! [X0,X1,X2] : hAPP(c_Relation_Oconverse(X2,X1),hAPP(c_Relation_Oconverse(X1,X2),X0)) = X0,
inference(rectify,[],[f3770]) ).
fof(f3770,axiom,
! [X98,X8,X25] : hAPP(c_Relation_Oconverse(X25,X8),hAPP(c_Relation_Oconverse(X8,X25),X98)) = X98,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_converse__converse) ).
fof(f34094,plain,
spl635_824,
inference(avatar_split_clause,[],[f19681,f34092]) ).
fof(f34092,plain,
( spl635_824
<=> ! [X2,X0,X1] : hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_824])]) ).
fof(f19681,plain,
! [X2,X0,X1] : hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X0,
inference(cnf_transformation,[],[f6976]) ).
fof(f6976,plain,
! [X0,X1,X2] : hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X0,
inference(rectify,[],[f4333]) ).
fof(f4333,axiom,
! [X208,X13,X5] : hAPP(c_List_Otl(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X208)) = X208,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl_Osimps_I2_J) ).
fof(f34090,plain,
spl635_823,
inference(avatar_split_clause,[],[f19680,f34088]) ).
fof(f34088,plain,
( spl635_823
<=> ! [X2,X0,X1] : hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_823])]) ).
fof(f19680,plain,
! [X2,X0,X1] : hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X1,
inference(cnf_transformation,[],[f6975]) ).
fof(f6975,plain,
! [X0,X1,X2] : hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X1,
inference(rectify,[],[f4312]) ).
fof(f4312,axiom,
! [X208,X13,X5] : hAPP(c_List_Ohd(X5),hAPP(hAPP(c_List_Olist_OCons(X5),X13),X208)) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_hd_Osimps) ).
fof(f34086,plain,
spl635_822,
inference(avatar_split_clause,[],[f19679,f34084]) ).
fof(f34084,plain,
( spl635_822
<=> ! [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,[spl635_822])]) ).
fof(f19679,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,[],[f6974]) ).
fof(f6974,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,[],[f4485]) ).
fof(f4485,axiom,
! [X243,X8,X5] : c_List_Olist_ONil(tc_prod(X5,X8)) = c_Enum_Oproduct(X5,X8,c_List_Olist_ONil(X5),X243),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_product_Osimps_I1_J) ).
fof(f34082,plain,
spl635_821,
inference(avatar_split_clause,[],[f19677,f34080]) ).
fof(f34080,plain,
( spl635_821
<=> ! [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,[spl635_821])]) ).
fof(f19677,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,[],[f6972]) ).
fof(f6972,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,[],[f4229]) ).
fof(f4229,axiom,
! [X12,X42,X5] : c_List_Olist_ONil(X5) = hAPP(hAPP(c_List_Olist__update(X5,c_List_Olist_ONil(X5)),X42),X12),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__update__code_I1_J) ).
fof(f34078,plain,
spl635_820,
inference(avatar_split_clause,[],[f19676,f34076]) ).
fof(f34076,plain,
( spl635_820
<=> ! [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,[spl635_820])]) ).
fof(f19676,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,[],[f6971]) ).
fof(f6971,plain,
! [X0,X1,X2] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Omap(X2,X1),X0),c_List_Olist_ONil(X2)),
inference(rectify,[],[f4121]) ).
fof(f4121,axiom,
! [X1,X8,X25] : c_List_Olist_ONil(X8) = hAPP(hAPP(c_List_Omap(X25,X8),X1),c_List_Olist_ONil(X25)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_map_Osimps_I1_J) ).
fof(f34074,plain,
spl635_819,
inference(avatar_split_clause,[],[f19674,f34072]) ).
fof(f34072,plain,
( spl635_819
<=> ! [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,[spl635_819])]) ).
fof(f19674,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,[],[f6969]) ).
fof(f6969,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,[],[f2302]) ).
fof(f2302,axiom,
! [X39,X17,X8] : hAPP(hAPP(c_Set_Oinsert(X8),X17),X39) != c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__not__empty) ).
fof(f34070,plain,
spl635_818,
inference(avatar_split_clause,[],[f19261,f34068]) ).
fof(f34068,plain,
( spl635_818
<=> ! [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,[spl635_818])]) ).
fof(f19261,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != hAPP(c_List_Orev(X1),X0) ),
inference(cnf_transformation,[],[f15111]) ).
fof(f15111,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,[],[f6798]) ).
fof(f6798,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = hAPP(c_List_Orev(X1),X0)
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f4668]) ).
fof(f4668,axiom,
! [X210,X8] :
( c_List_Olist_ONil(X8) = hAPP(c_List_Orev(X8),X210)
<=> c_List_Olist_ONil(X8) = X210 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__is__Nil__conv) ).
fof(f34066,plain,
spl635_817,
inference(avatar_split_clause,[],[f19259,f34064]) ).
fof(f34064,plain,
( spl635_817
<=> ! [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,[spl635_817])]) ).
fof(f19259,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != hAPP(c_List_Orotate1(X1),X0) ),
inference(cnf_transformation,[],[f15110]) ).
fof(f15110,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,[],[f6797]) ).
fof(f6797,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),X0)
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f4286]) ).
fof(f4286,axiom,
! [X210,X8] :
( c_List_Olist_ONil(X8) = hAPP(c_List_Orotate1(X8),X210)
<=> c_List_Olist_ONil(X8) = X210 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rotate1__is__Nil__conv) ).
fof(f34062,plain,
spl635_816,
inference(avatar_split_clause,[],[f19246,f34060]) ).
fof(f19246,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,sK194(X1)))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ),
inference(cnf_transformation,[],[f15097]) ).
fof(f15097,plain,
! [X0,X1] :
( ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ! [X2] : ~ hBOOL(hAPP(X1,X2)) )
& ( hBOOL(hAPP(X1,sK194(X1)))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK194])],[f15095,f15096]) ).
fof(f15096,plain,
! [X1] :
( ? [X3] : hBOOL(hAPP(X1,X3))
=> hBOOL(hAPP(X1,sK194(X1))) ),
introduced(choice_axiom,[]) ).
fof(f15095,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,[],[f15094]) ).
fof(f15094,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,[],[f6791]) ).
fof(f6791,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
<=> ? [X2] : hBOOL(hAPP(X1,X2)) ),
inference(rectify,[],[f3660]) ).
fof(f3660,axiom,
! [X8,X29] :
( hBOOL(hAPP(X29,c_Hilbert__Choice_OEps(X8,X29)))
<=> ? [X65] : hBOOL(hAPP(X29,X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__ex) ).
fof(f34058,plain,
spl635_815,
inference(avatar_split_clause,[],[f19162,f34056]) ).
fof(f34056,plain,
( spl635_815
<=> ! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK171(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_815])]) ).
fof(f19162,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK171(X0,X1))) ),
inference(cnf_transformation,[],[f15017]) ).
fof(f15017,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])],[f15015,f15016]) ).
fof(f15016,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(f15015,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,[],[f15014]) ).
fof(f15014,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,[],[f6766]) ).
fof(f6766,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
<=> ! [X2] : hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) ),
inference(rectify,[],[f3563]) ).
fof(f3563,axiom,
! [X98,X8] :
( c_Wellfounded_OwfP(X8,X98)
<=> ! [X65] : hBOOL(hAPP(c_Wellfounded_Oaccp(X8,X98),X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).
fof(f34054,plain,
spl635_814,
inference(avatar_split_clause,[],[f19147,f34052]) ).
fof(f34052,plain,
( spl635_814
<=> ! [X2,X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ sP4(X0)
| ~ hBOOL(hAPP(hAPP(X0,X2),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_814])]) ).
fof(f19147,plain,
! [X2,X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ sP4(X0)
| ~ hBOOL(hAPP(hAPP(X0,X2),X2)) ),
inference(cnf_transformation,[],[f15004]) ).
fof(f15004,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])],[f15002,f15003]) ).
fof(f15003,plain,
! [X0] :
( ? [X3] : hBOOL(hAPP(hAPP(X0,X3),X3))
=> hBOOL(hAPP(hAPP(X0,sK168(X0)),sK168(X0))) ),
introduced(choice_axiom,[]) ).
fof(f15002,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,[],[f15001]) ).
fof(f15001,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,[],[f15000]) ).
fof(f15000,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,[],[f14535]) ).
fof(f14535,plain,
! [X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
<=> ( sP4(X0)
& ? [X4] : hBOOL(hAPP(hAPP(X0,X4),X4)) ) ),
inference(definition_folding,[],[f6761,f14534]) ).
fof(f14534,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(f6761,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,[],[f4972]) ).
fof(f4972,axiom,
! [X122,X8] :
( c_Equiv__Relations_Opart__equivp(X8,X122)
<=> ( ! [X2,X45] :
( hBOOL(hAPP(hAPP(X122,X2),X45))
<=> ( hAPP(X122,X2) = hAPP(X122,X45)
& hBOOL(hAPP(hAPP(X122,X45),X45))
& hBOOL(hAPP(hAPP(X122,X2),X2)) ) )
& ? [X2] : hBOOL(hAPP(hAPP(X122,X2),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__def) ).
fof(f34050,plain,
spl635_813,
inference(avatar_split_clause,[],[f19145,f34048]) ).
fof(f34048,plain,
( spl635_813
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(X0,sK168(X0)),sK168(X0)))
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_813])]) ).
fof(f19145,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(X0,sK168(X0)),sK168(X0)))
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(cnf_transformation,[],[f15004]) ).
fof(f34046,plain,
spl635_812,
inference(avatar_split_clause,[],[f19133,f34044]) ).
fof(f34044,plain,
( spl635_812
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(X0,sK165(X0)),sK165(X0)))
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_812])]) ).
fof(f19133,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(X0,sK165(X0)),sK165(X0)))
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(cnf_transformation,[],[f14994]) ).
fof(f14994,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])],[f14992,f14993]) ).
fof(f14993,plain,
! [X0] :
( ? [X3] : hBOOL(hAPP(hAPP(X0,X3),X3))
=> hBOOL(hAPP(hAPP(X0,sK165(X0)),sK165(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14992,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,[],[f14991]) ).
fof(f14991,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,[],[f14990]) ).
fof(f14990,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,[],[f6760]) ).
fof(f6760,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,[],[f4969]) ).
fof(f4969,axiom,
! [X122,X8] :
( c_Equiv__Relations_Opart__equivp(X8,X122)
<=> ( c_Predicate_Otransp(X8,X122)
& c_Predicate_Osymp(X8,X122)
& ? [X2] : hBOOL(hAPP(hAPP(X122,X2),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivp__refl__symp__transp) ).
fof(f34042,plain,
spl635_811,
inference(avatar_split_clause,[],[f19113,f34040]) ).
fof(f34040,plain,
( spl635_811
<=> ! [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,[spl635_811])]) ).
fof(f19113,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,[],[f14981]) ).
fof(f14981,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])],[f11310,f14980]) ).
fof(f14980,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(f11310,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,[],[f6746]) ).
fof(f6746,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,[],[f3666]) ).
fof(f3666,axiom,
! [X122,X8] :
( ! [X164] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X164),hAPP(c_Relation_OImage(X8,X8,X122),X164)))
=> c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = X164 )
=> c_Wellfounded_Owf(X8,X122) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfI__pf) ).
fof(f34038,plain,
spl635_810,
inference(avatar_split_clause,[],[f19111,f34036]) ).
fof(f34036,plain,
( spl635_810
<=> ! [X0,X1] :
( hBOOL(hAPP(X1,X0))
| ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,sK163(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_810])]) ).
fof(f19111,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,X0))
| ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,sK163(X1)))) ),
inference(cnf_transformation,[],[f14979]) ).
fof(f14979,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])],[f11309,f14978]) ).
fof(f14978,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(f11309,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,[],[f6745]) ).
fof(f6745,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,[],[f3577]) ).
fof(f3577,axiom,
! [X30,X29] :
( ! [X45] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X45),c_Int_OInteg))
=> hBOOL(hAPP(X29,hAPP(c_Int_OAbs__Integ,X45))) )
=> hBOOL(hAPP(X29,X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Abs__Integ__induct) ).
fof(f34034,plain,
spl635_809,
inference(avatar_split_clause,[],[f18734,f34032]) ).
fof(f34032,plain,
( spl635_809
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(X0,sK143(X0)),sK143(X0)))
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_809])]) ).
fof(f18734,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(X0,sK143(X0)),sK143(X0)))
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(cnf_transformation,[],[f14899]) ).
fof(f14899,plain,
! [X0,X1] :
( ( c_Predicate_Otransp(X1,X0)
& c_Predicate_Osymp(X1,X0)
& hBOOL(hAPP(hAPP(X0,sK143(X0)),sK143(X0))) )
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK143])],[f10893,f14898]) ).
fof(f14898,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(hAPP(X0,X2),X2))
=> hBOOL(hAPP(hAPP(X0,sK143(X0)),sK143(X0))) ),
introduced(choice_axiom,[]) ).
fof(f10893,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,[],[f10892]) ).
fof(f10892,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,[],[f6447]) ).
fof(f6447,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,[],[f4975]) ).
fof(f4975,axiom,
! [X122,X8] :
( c_Equiv__Relations_Opart__equivp(X8,X122)
=> ~ ( ? [X2] : hBOOL(hAPP(hAPP(X122,X2),X2))
=> ( c_Predicate_Osymp(X8,X122)
=> ~ c_Predicate_Otransp(X8,X122) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_part__equivpE) ).
fof(f34030,plain,
spl635_808,
inference(avatar_split_clause,[],[f18725,f34028]) ).
fof(f34028,plain,
( spl635_808
<=> ! [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,[spl635_808])]) ).
fof(f18725,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,[],[f10880]) ).
fof(f10880,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,[],[f10879]) ).
fof(f10879,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,[],[f6439]) ).
fof(f6439,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,[],[f1371]) ).
fof(f1371,axiom,
! [X12,X13] :
( c_Nat__Transfer_Ois__nat(X13)
=> ( c_Nat__Transfer_Ois__nat(X12)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X13),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) ).
fof(f34026,plain,
spl635_807,
inference(avatar_split_clause,[],[f18724,f34024]) ).
fof(f18724,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,[],[f10878]) ).
fof(f10878,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,[],[f10877]) ).
fof(f10877,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,[],[f6438]) ).
fof(f6438,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,[],[f1368]) ).
fof(f1368,axiom,
! [X12,X13] :
( c_Nat__Transfer_Ois__nat(X13)
=> ( c_Nat__Transfer_Ois__nat(X12)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X13),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).
fof(f34022,plain,
spl635_806,
inference(avatar_split_clause,[],[f18723,f34020]) ).
fof(f34020,plain,
( spl635_806
<=> ! [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,[spl635_806])]) ).
fof(f18723,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,[],[f10876]) ).
fof(f10876,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,[],[f10875]) ).
fof(f10875,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,[],[f6437]) ).
fof(f6437,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,[],[f1373]) ).
fof(f1373,axiom,
! [X12,X13] :
( c_Nat__Transfer_Ois__nat(X13)
=> ( c_Nat__Transfer_Ois__nat(X12)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X13),X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I1_J) ).
fof(f34018,plain,
spl635_805,
inference(avatar_split_clause,[],[f18715,f34016]) ).
fof(f34016,plain,
( spl635_805
<=> ! [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,[spl635_805])]) ).
fof(f18715,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,[],[f10864]) ).
fof(f10864,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,[],[f10863]) ).
fof(f10863,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,[],[f6430]) ).
fof(f6430,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,[],[f2486]) ).
fof(f2486,axiom,
! [X30,X39] :
( c_Nat__Transfer_Onat__set(X39)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X30),X39))
=> c_Nat__Transfer_Ois__nat(X30) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) ).
fof(f34014,plain,
spl635_804,
inference(avatar_split_clause,[],[f18700,f34012]) ).
fof(f18700,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,[],[f14885]) ).
fof(f34010,plain,
spl635_803,
inference(avatar_split_clause,[],[f18697,f34008]) ).
fof(f34008,plain,
( spl635_803
<=> ! [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,[spl635_803])]) ).
fof(f18697,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,[],[f14881]) ).
fof(f34006,plain,
spl635_802,
inference(avatar_split_clause,[],[f18624,f34004]) ).
fof(f34004,plain,
( spl635_802
<=> ! [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,[spl635_802])]) ).
fof(f18624,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,[],[f10771]) ).
fof(f10771,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,[],[f10770]) ).
fof(f10770,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,[],[f6368]) ).
fof(f6368,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,[],[f4634]) ).
fof(f4634,axiom,
! [X208,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_List_Olinorder__class_Osorted(X5,X208)
=> c_List_Olinorder__class_Osorted(X5,hAPP(c_List_Otl(X5),X208)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__tl) ).
fof(f34002,plain,
( spl635_801
| ~ spl635_564
| ~ spl635_713 ),
inference(avatar_split_clause,[],[f33690,f32754,f31901,f34000]) ).
fof(f34000,plain,
( spl635_801
<=> ! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| ~ c_Nat__Transfer_Ois__nat(sK94(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_801])]) ).
fof(f31901,plain,
( spl635_564
<=> ! [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,[spl635_564])]) ).
fof(f32754,plain,
( spl635_713
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK94(X0)))
| c_Nat__Transfer_Onat__set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_713])]) ).
fof(f33690,plain,
( ! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| ~ c_Nat__Transfer_Ois__nat(sK94(X0)) )
| ~ spl635_564
| ~ spl635_713 ),
inference(resolution,[],[f32755,f31902]) ).
fof(f31902,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| ~ c_Nat__Transfer_Ois__nat(X0) )
| ~ spl635_564 ),
inference(avatar_component_clause,[],[f31901]) ).
fof(f32755,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK94(X0)))
| c_Nat__Transfer_Onat__set(X0) )
| ~ spl635_713 ),
inference(avatar_component_clause,[],[f32754]) ).
fof(f33998,plain,
spl635_800,
inference(avatar_split_clause,[],[f18601,f33996]) ).
fof(f33996,plain,
( spl635_800
<=> ! [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,[spl635_800])]) ).
fof(f18601,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,[],[f10745]) ).
fof(f10745,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,[],[f6345]) ).
fof(f6345,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,[],[f592]) ).
fof(f592,axiom,
! [X33,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X33) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0) ).
fof(f33994,plain,
spl635_799,
inference(avatar_split_clause,[],[f18600,f33992]) ).
fof(f33992,plain,
( spl635_799
<=> ! [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,[spl635_799])]) ).
fof(f18600,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,[],[f10744]) ).
fof(f10744,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,[],[f6344]) ).
fof(f6344,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,[],[f595]) ).
fof(f595,axiom,
! [X33,X5] :
( class_Groups_Ocomm__monoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X33),c_Groups_Ozero__class_Ozero(X5)) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(f33990,plain,
spl635_798,
inference(avatar_split_clause,[],[f18589,f33988]) ).
fof(f33988,plain,
( spl635_798
<=> ! [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,[spl635_798])]) ).
fof(f18589,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,[],[f10731]) ).
fof(f10731,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,[],[f6333]) ).
fof(f6333,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,[],[f373]) ).
fof(f373,axiom,
! [X33,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X33) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(f33986,plain,
spl635_797,
inference(avatar_split_clause,[],[f18588,f33984]) ).
fof(f33984,plain,
( spl635_797
<=> ! [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,[spl635_797])]) ).
fof(f18588,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,[],[f10730]) ).
fof(f10730,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,[],[f6332]) ).
fof(f6332,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,[],[f596]) ).
fof(f596,axiom,
! [X33,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X33) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(f33982,plain,
spl635_796,
inference(avatar_split_clause,[],[f18587,f33980]) ).
fof(f33980,plain,
( spl635_796
<=> ! [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,[spl635_796])]) ).
fof(f18587,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,[],[f10729]) ).
fof(f10729,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,[],[f6331]) ).
fof(f6331,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,[],[f372]) ).
fof(f372,axiom,
! [X33,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X33),c_Groups_Oone__class_Oone(X5)) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(f33978,plain,
spl635_795,
inference(avatar_split_clause,[],[f18586,f33976]) ).
fof(f33976,plain,
( spl635_795
<=> ! [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,[spl635_795])]) ).
fof(f18586,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,[],[f10728]) ).
fof(f10728,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,[],[f6330]) ).
fof(f6330,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,[],[f597]) ).
fof(f597,axiom,
! [X33,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X33),c_Groups_Ozero__class_Ozero(X5)) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(f33974,plain,
spl635_794,
inference(avatar_split_clause,[],[f18585,f33972]) ).
fof(f33972,plain,
( spl635_794
<=> ! [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,[spl635_794])]) ).
fof(f18585,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,[],[f10727]) ).
fof(f10727,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,[],[f6329]) ).
fof(f6329,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,[],[f851]) ).
fof(f851,axiom,
! [X33,X5] :
( class_Divides_Osemiring__div(X5)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X5),X33),c_Groups_Oone__class_Oone(X5)) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__by__1) ).
fof(f33970,plain,
spl635_793,
inference(avatar_split_clause,[],[f18584,f33968]) ).
fof(f33968,plain,
( spl635_793
<=> ! [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,[spl635_793])]) ).
fof(f18584,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,[],[f10726]) ).
fof(f10726,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,[],[f6328]) ).
fof(f6328,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,[],[f380]) ).
fof(f380,axiom,
! [X13,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X13),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(f33966,plain,
spl635_792,
inference(avatar_split_clause,[],[f18576,f33964]) ).
fof(f33964,plain,
( spl635_792
<=> ! [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,[spl635_792])]) ).
fof(f18576,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,[],[f10718]) ).
fof(f10718,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,[],[f6320]) ).
fof(f6320,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,[],[f376]) ).
fof(f376,axiom,
! [X33,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X33) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1) ).
fof(f33962,plain,
spl635_791,
inference(avatar_split_clause,[],[f18575,f33960]) ).
fof(f33960,plain,
( spl635_791
<=> ! [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,[spl635_791])]) ).
fof(f18575,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,[],[f10717]) ).
fof(f10717,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,[],[f6319]) ).
fof(f6319,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,[],[f374]) ).
fof(f374,axiom,
! [X33,X5] :
( class_Groups_Ocomm__monoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X33),c_Groups_Oone__class_Oone(X5)) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(f33958,plain,
( ~ spl635_790
| ~ spl635_332
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33349,f32548,f30890,f33955]) ).
fof(f33955,plain,
( spl635_790
<=> sP31(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_790])]) ).
fof(f30890,plain,
( spl635_332
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_332])]) ).
fof(f33349,plain,
( ~ sP31(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint))
| ~ spl635_332
| ~ spl635_665 ),
inference(resolution,[],[f32549,f30892]) ).
fof(f30892,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls))
| ~ spl635_332 ),
inference(avatar_component_clause,[],[f30890]) ).
fof(f33953,plain,
spl635_789,
inference(avatar_split_clause,[],[f18559,f33951]) ).
fof(f33951,plain,
( spl635_789
<=> ! [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,[spl635_789])]) ).
fof(f18559,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,[],[f10702]) ).
fof(f10702,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,[],[f6305]) ).
fof(f6305,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,[],[f377]) ).
fof(f377,axiom,
! [X33,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),c_Groups_Oone__class_Oone(X5)),X33) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(f33949,plain,
spl635_788,
inference(avatar_split_clause,[],[f18558,f33947]) ).
fof(f33947,plain,
( spl635_788
<=> ! [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,[spl635_788])]) ).
fof(f18558,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,[],[f10701]) ).
fof(f10701,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,[],[f6304]) ).
fof(f6304,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,[],[f375]) ).
fof(f375,axiom,
! [X33,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X5),X33),c_Groups_Oone__class_Oone(X5)) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(f33945,plain,
spl635_787,
inference(avatar_split_clause,[],[f18557,f33943]) ).
fof(f33943,plain,
( spl635_787
<=> ! [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,[spl635_787])]) ).
fof(f18557,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,[],[f10700]) ).
fof(f10700,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,[],[f6303]) ).
fof(f6303,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,[],[f381]) ).
fof(f381,axiom,
! [X33,X5] :
( class_Groups_Omonoid__mult(X5)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X5),X33),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(f33941,plain,
spl635_786,
inference(avatar_split_clause,[],[f18555,f33939]) ).
fof(f33939,plain,
( spl635_786
<=> ! [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,[spl635_786])]) ).
fof(f18555,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,[],[f10698]) ).
fof(f10698,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,[],[f6301]) ).
fof(f6301,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,[],[f591]) ).
fof(f591,axiom,
! [X33,X5] :
( class_Groups_Omonoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),c_Groups_Ozero__class_Ozero(X5)),X33) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(f33937,plain,
spl635_785,
inference(avatar_split_clause,[],[f18554,f33935]) ).
fof(f33935,plain,
( spl635_785
<=> ! [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,[spl635_785])]) ).
fof(f18554,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,[],[f10697]) ).
fof(f10697,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,[],[f6300]) ).
fof(f6300,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,[],[f594]) ).
fof(f594,axiom,
! [X33,X5] :
( class_Groups_Omonoid__add(X5)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X5),X33),c_Groups_Ozero__class_Ozero(X5)) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(f33933,plain,
spl635_784,
inference(avatar_split_clause,[],[f18526,f33931]) ).
fof(f33931,plain,
( spl635_784
<=> ! [X0,X1] :
( c_Inductive_Ocomplete__lattice__class_Olfp(X1,hAPP(c_COMBK(X1,X1),X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_784])]) ).
fof(f18526,plain,
! [X0,X1] :
( c_Inductive_Ocomplete__lattice__class_Olfp(X1,hAPP(c_COMBK(X1,X1),X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(cnf_transformation,[],[f10660]) ).
fof(f10660,plain,
! [X0,X1] :
( c_Inductive_Ocomplete__lattice__class_Olfp(X1,hAPP(c_COMBK(X1,X1),X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(ennf_transformation,[],[f6274]) ).
fof(f6274,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(X1)
=> c_Inductive_Ocomplete__lattice__class_Olfp(X1,hAPP(c_COMBK(X1,X1),X0)) = X0 ),
inference(rectify,[],[f2563]) ).
fof(f2563,axiom,
! [X126,X8] :
( class_Complete__Lattice_Ocomplete__lattice(X8)
=> c_Inductive_Ocomplete__lattice__class_Olfp(X8,hAPP(c_COMBK(X8,X8),X126)) = X126 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lfp__const) ).
fof(f33929,plain,
spl635_783,
inference(avatar_split_clause,[],[f18520,f33927]) ).
fof(f33927,plain,
( spl635_783
<=> ! [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,[spl635_783])]) ).
fof(f18520,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,[],[f10654]) ).
fof(f10654,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,[],[f6268]) ).
fof(f6268,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,[],[f830]) ).
fof(f830,axiom,
! [X13,X5] :
( class_Lattices_Oboolean__algebra(X5)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X13)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_double__compl) ).
fof(f33925,plain,
spl635_782,
inference(avatar_split_clause,[],[f18514,f33923]) ).
fof(f33923,plain,
( spl635_782
<=> ! [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,[spl635_782])]) ).
fof(f18514,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,[],[f10648]) ).
fof(f10648,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,[],[f6262]) ).
fof(f6262,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,[],[f2329]) ).
fof(f2329,axiom,
! [X13,X5] :
( class_Lattices_Obounded__lattice__bot(X5)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),c_Orderings_Obot__class_Obot(X5)),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__bot__left) ).
fof(f33921,plain,
spl635_781,
inference(avatar_split_clause,[],[f18513,f33919]) ).
fof(f33919,plain,
( spl635_781
<=> ! [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,[spl635_781])]) ).
fof(f18513,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,[],[f10647]) ).
fof(f10647,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,[],[f6261]) ).
fof(f6261,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,[],[f3126]) ).
fof(f3126,axiom,
! [X13,X5] :
( class_Lattices_Obounded__lattice__top(X5)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),c_Orderings_Otop__class_Otop(X5)),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__top__left) ).
fof(f33917,plain,
spl635_780,
inference(avatar_split_clause,[],[f18512,f33915]) ).
fof(f33915,plain,
( spl635_780
<=> ! [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,[spl635_780])]) ).
fof(f18512,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,[],[f10646]) ).
fof(f10646,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,[],[f6260]) ).
fof(f6260,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,[],[f2330]) ).
fof(f2330,axiom,
! [X13,X5] :
( class_Lattices_Obounded__lattice__bot(X5)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X13),c_Orderings_Obot__class_Obot(X5)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__bot__right) ).
fof(f33913,plain,
( ~ spl635_779
| ~ spl635_331
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33348,f32548,f30885,f33910]) ).
fof(f33910,plain,
( spl635_779
<=> sP31(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_779])]) ).
fof(f30885,plain,
( spl635_331
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_331])]) ).
fof(f33348,plain,
( ~ sP31(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless(tc_Int_Oint))
| ~ spl635_331
| ~ spl635_665 ),
inference(resolution,[],[f32549,f30887]) ).
fof(f30887,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls))
| ~ spl635_331 ),
inference(avatar_component_clause,[],[f30885]) ).
fof(f33908,plain,
spl635_778,
inference(avatar_split_clause,[],[f18511,f33906]) ).
fof(f33906,plain,
( spl635_778
<=> ! [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,[spl635_778])]) ).
fof(f18511,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,[],[f10645]) ).
fof(f10645,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,[],[f6259]) ).
fof(f6259,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,[],[f3127]) ).
fof(f3127,axiom,
! [X13,X5] :
( class_Lattices_Obounded__lattice__top(X5)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X13),c_Orderings_Otop__class_Otop(X5)) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__top__right) ).
fof(f33904,plain,
spl635_777,
inference(avatar_split_clause,[],[f18469,f33902]) ).
fof(f33902,plain,
( spl635_777
<=> ! [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,[spl635_777])]) ).
fof(f18469,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,[],[f10608]) ).
fof(f10608,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,[],[f6223]) ).
fof(f6223,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,[],[f684]) ).
fof(f684,axiom,
! [X40,X5] :
( class_Int_Onumber__ring(X5)
=> hAPP(c_Int_Onumber__class_Onumber__of(X5),X40) = hAPP(c_Int_Oring__1__class_Oof__int(X5),X40) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_number__of__eq) ).
fof(f33900,plain,
spl635_776,
inference(avatar_split_clause,[],[f18432,f33898]) ).
fof(f33898,plain,
( spl635_776
<=> ! [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,[spl635_776])]) ).
fof(f18432,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,[],[f10581]) ).
fof(f10581,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,[],[f6199]) ).
fof(f6199,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,[],[f515]) ).
fof(f515,axiom,
! [X33,X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Osgn__class_Osgn(X5,X33) = c_Groups_Osgn__class_Osgn(X5,c_Groups_Osgn__class_Osgn(X5,X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn__sgn) ).
fof(f33896,plain,
spl635_775,
inference(avatar_split_clause,[],[f18379,f33894]) ).
fof(f33894,plain,
( spl635_775
<=> ! [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,[spl635_775])]) ).
fof(f18379,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,[],[f10534]) ).
fof(f10534,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,[],[f6158]) ).
fof(f6158,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,[],[f562]) ).
fof(f562,axiom,
! [X33,X5] :
( class_Groups_Ogroup__add(X5)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X33),c_Groups_Ozero__class_Ozero(X5)) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(f33892,plain,
spl635_774,
inference(avatar_split_clause,[],[f18378,f33890]) ).
fof(f33890,plain,
( spl635_774
<=> ! [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,[spl635_774])]) ).
fof(f18378,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,[],[f10533]) ).
fof(f10533,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,[],[f6157]) ).
fof(f6157,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,[],[f516]) ).
fof(f516,axiom,
! [X33,X5] :
( class_Groups_Ogroup__add(X5)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X5),hAPP(c_Groups_Ouminus__class_Ouminus(X5),X33)) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(f33888,plain,
spl635_773,
inference(avatar_split_clause,[],[f18377,f33886]) ).
fof(f33886,plain,
( spl635_773
<=> ! [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,[spl635_773])]) ).
fof(f18377,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,[],[f10532]) ).
fof(f10532,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,[],[f6156]) ).
fof(f6156,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,[],[f563]) ).
fof(f563,axiom,
! [X33,X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X5),X33),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self) ).
fof(f33884,plain,
spl635_772,
inference(avatar_split_clause,[],[f17914,f33882]) ).
fof(f33882,plain,
( spl635_772
<=> ! [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,[spl635_772])]) ).
fof(f17914,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,[],[f5766]) ).
fof(f5766,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,[],[f2051]) ).
fof(f2051,axiom,
! [X75,X77] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X77),X75) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X77,X75),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastSucAtMost__greaterThanAtMost) ).
fof(f33880,plain,
spl635_771,
inference(avatar_split_clause,[],[f17905,f33878]) ).
fof(f33878,plain,
( spl635_771
<=> ! [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,[spl635_771])]) ).
fof(f17905,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,[],[f5757]) ).
fof(f5757,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,[],[f2763]) ).
fof(f2763,axiom,
! [X39,X8] : hAPP(c_Set_OPow(X8),X39) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pow__not__empty) ).
fof(f33876,plain,
spl635_770,
inference(avatar_split_clause,[],[f17802,f33874]) ).
fof(f17802,plain,
! [X0,X4] :
( hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK106(X0))))
| ~ hBOOL(hAPP(X0,X4)) ),
inference(cnf_transformation,[],[f14781]) ).
fof(f33872,plain,
spl635_769,
inference(avatar_split_clause,[],[f17797,f33870]) ).
fof(f33870,plain,
( spl635_769
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK101(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_769])]) ).
fof(f17797,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK101(X0)))) ),
inference(cnf_transformation,[],[f14771]) ).
fof(f33868,plain,
( spl635_768
| ~ spl635_343
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33324,f32548,f30935,f33866]) ).
fof(f33866,plain,
( spl635_768
<=> ! [X0] : ~ sP31(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_768])]) ).
fof(f30935,plain,
( spl635_343
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_343])]) ).
fof(f33324,plain,
( ! [X0] : ~ sP31(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat))
| ~ spl635_343
| ~ spl635_665 ),
inference(resolution,[],[f32549,f30936]) ).
fof(f30936,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0))
| ~ spl635_343 ),
inference(avatar_component_clause,[],[f30935]) ).
fof(f33864,plain,
spl635_767,
inference(avatar_split_clause,[],[f17619,f33862]) ).
fof(f33862,plain,
( spl635_767
<=> ! [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,[spl635_767])]) ).
fof(f17619,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,[],[f10379]) ).
fof(f10379,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,[],[f5544]) ).
fof(f5544,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,[],[f4453]) ).
fof(f4453,axiom,
! [X8] :
( class_Orderings_Olinorder(X8)
=> c_Finite__Set_Ofun__left__comm(X8,tc_List_Olist(X8),c_List_Olinorder__class_Oinsort__key(X8,X8,c_COMBI(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__insort) ).
fof(f33860,plain,
spl635_766,
inference(avatar_split_clause,[],[f17618,f33858]) ).
fof(f33858,plain,
( spl635_766
<=> ! [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,[spl635_766])]) ).
fof(f17618,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,[],[f10378]) ).
fof(f10378,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,[],[f5543]) ).
fof(f5543,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,[],[f4439]) ).
fof(f4439,axiom,
! [X8] :
( class_Orderings_Olinorder(X8)
=> c_List_Olist_ONil(X8) = c_List_Olinorder__class_Osorted__list__of__set(X8,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__list__of__set__empty) ).
fof(f33856,plain,
spl635_765,
inference(avatar_split_clause,[],[f17612,f33854]) ).
fof(f33854,plain,
( spl635_765
<=> ! [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,[spl635_765])]) ).
fof(f17612,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,[],[f10372]) ).
fof(f10372,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,[],[f5537]) ).
fof(f5537,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,[],[f395]) ).
fof(f395,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Ozero__class_Ozero(X5)),c_Groups_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(f33852,plain,
spl635_764,
inference(avatar_split_clause,[],[f17611,f33850]) ).
fof(f33850,plain,
( spl635_764
<=> ! [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,[spl635_764])]) ).
fof(f17611,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,[],[f10371]) ).
fof(f10371,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,[],[f5536]) ).
fof(f5536,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,[],[f397]) ).
fof(f397,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Ozero__class_Ozero(X5)),c_Groups_Oone__class_Oone(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(f33848,plain,
spl635_763,
inference(avatar_split_clause,[],[f17610,f33846]) ).
fof(f33846,plain,
( spl635_763
<=> ! [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,[spl635_763])]) ).
fof(f17610,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,[],[f10370]) ).
fof(f10370,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,[],[f5535]) ).
fof(f5535,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,[],[f396]) ).
fof(f396,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(f33844,plain,
spl635_762,
inference(avatar_split_clause,[],[f17609,f33842]) ).
fof(f33842,plain,
( spl635_762
<=> ! [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,[spl635_762])]) ).
fof(f17609,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,[],[f10369]) ).
fof(f10369,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,[],[f5534]) ).
fof(f5534,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,[],[f398]) ).
fof(f398,axiom,
! [X5] :
( class_Rings_Olinordered__semidom(X5)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),c_Groups_Oone__class_Oone(X5)),c_Groups_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(f33840,plain,
spl635_761,
inference(avatar_split_clause,[],[f17606,f33838]) ).
fof(f33838,plain,
( spl635_761
<=> ! [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,[spl635_761])]) ).
fof(f17606,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,[],[f10366]) ).
fof(f10366,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,[],[f5531]) ).
fof(f5531,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,[],[f2606]) ).
fof(f2606,axiom,
! [X8] :
( class_Rings_Osemiring__1(X8)
=> hBOOL(hAPP(hAPP(c_member(X8),c_Groups_Ozero__class_Ozero(X8)),c_Nat_Osemiring__1__class_ONats(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__0) ).
fof(f33836,plain,
spl635_760,
inference(avatar_split_clause,[],[f17605,f33834]) ).
fof(f33834,plain,
( spl635_760
<=> ! [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,[spl635_760])]) ).
fof(f17605,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,[],[f10365]) ).
fof(f10365,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,[],[f5530]) ).
fof(f5530,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,[],[f2609]) ).
fof(f2609,axiom,
! [X8] :
( class_Rings_Osemiring__1(X8)
=> hBOOL(hAPP(hAPP(c_member(X8),c_Groups_Oone__class_Oone(X8)),c_Nat_Osemiring__1__class_ONats(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nats__1) ).
fof(f33832,plain,
spl635_759,
inference(avatar_split_clause,[],[f17597,f33830]) ).
fof(f33830,plain,
( spl635_759
<=> ! [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,[spl635_759])]) ).
fof(f17597,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,[],[f10357]) ).
fof(f10357,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,[],[f5522]) ).
fof(f5522,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,[],[f430]) ).
fof(f430,axiom,
! [X8] :
( class_Power_Opower(X8)
=> c_Power_Opower__class_Opower(X8) = c_Power_Opower_Opower(X8,c_Groups_Oone__class_Oone(X8),c_Groups_Otimes__class_Otimes(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__power__power) ).
fof(f33828,plain,
spl635_758,
inference(avatar_split_clause,[],[f17594,f33826]) ).
fof(f33826,plain,
( spl635_758
<=> ! [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,[spl635_758])]) ).
fof(f17594,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,[],[f10354]) ).
fof(f10354,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,[],[f5519]) ).
fof(f5519,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,[],[f3179]) ).
fof(f3179,axiom,
! [X8] :
( class_Nat_Osemiring__char__0(X8)
=> c_Fun_Oinj__on(tc_Nat_Onat,X8,c_Nat_Osemiring__1__class_Oof__nat(X8),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__of__nat) ).
fof(f33822,plain,
spl635_757,
inference(avatar_split_clause,[],[f17593,f33820]) ).
fof(f33820,plain,
( spl635_757
<=> ! [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,[spl635_757])]) ).
fof(f17593,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,[],[f10353]) ).
fof(f10353,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,[],[f5518]) ).
fof(f5518,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,[],[f3945]) ).
fof(f3945,axiom,
! [X8] :
( class_Complete__Lattice_Ocomplete__lattice(X8)
=> c_Orderings_Obot__class_Obot(X8) = c_Complete__Lattice_OSup__class_OSup(X8,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__empty) ).
fof(f33818,plain,
spl635_756,
inference(avatar_split_clause,[],[f17592,f33816]) ).
fof(f33816,plain,
( spl635_756
<=> ! [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,[spl635_756])]) ).
fof(f17592,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,[],[f10352]) ).
fof(f10352,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,[],[f5517]) ).
fof(f5517,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,[],[f3903]) ).
fof(f3903,axiom,
! [X8] :
( class_Complete__Lattice_Ocomplete__lattice(X8)
=> c_Orderings_Obot__class_Obot(X8) = c_Complete__Lattice_OInf__class_OInf(X8,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__UNIV) ).
fof(f33814,plain,
spl635_755,
inference(avatar_split_clause,[],[f17591,f33812]) ).
fof(f33812,plain,
( spl635_755
<=> ! [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,[spl635_755])]) ).
fof(f17591,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,[],[f10351]) ).
fof(f10351,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,[],[f5516]) ).
fof(f5516,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,[],[f3948]) ).
fof(f3948,axiom,
! [X8] :
( class_Complete__Lattice_Ocomplete__lattice(X8)
=> c_Orderings_Otop__class_Otop(X8) = c_Complete__Lattice_OSup__class_OSup(X8,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__UNIV) ).
fof(f33810,plain,
spl635_754,
inference(avatar_split_clause,[],[f17590,f33808]) ).
fof(f33808,plain,
( spl635_754
<=> ! [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,[spl635_754])]) ).
fof(f17590,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,[],[f10350]) ).
fof(f10350,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,[],[f5515]) ).
fof(f5515,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,[],[f3902]) ).
fof(f3902,axiom,
! [X8] :
( class_Complete__Lattice_Ocomplete__lattice(X8)
=> c_Orderings_Otop__class_Otop(X8) = c_Complete__Lattice_OInf__class_OInf(X8,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__empty) ).
fof(f33806,plain,
spl635_753,
inference(avatar_split_clause,[],[f17574,f33804]) ).
fof(f33804,plain,
( spl635_753
<=> ! [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,[spl635_753])]) ).
fof(f17574,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,[],[f10334]) ).
fof(f10334,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,[],[f5499]) ).
fof(f5499,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,[],[f2592]) ).
fof(f2592,axiom,
! [X8] :
( class_Rings_Oring__1(X8)
=> hBOOL(hAPP(hAPP(c_member(X8),c_Groups_Ozero__class_Ozero(X8)),c_Int_Oring__1__class_OInts(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__0) ).
fof(f33802,plain,
spl635_752,
inference(avatar_split_clause,[],[f17573,f33800]) ).
fof(f33800,plain,
( spl635_752
<=> ! [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,[spl635_752])]) ).
fof(f17573,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,[],[f10333]) ).
fof(f10333,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,[],[f5498]) ).
fof(f5498,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,[],[f2597]) ).
fof(f2597,axiom,
! [X8] :
( class_Rings_Oring__1(X8)
=> hBOOL(hAPP(hAPP(c_member(X8),c_Groups_Oone__class_Oone(X8)),c_Int_Oring__1__class_OInts(X8))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Ints__1) ).
fof(f33798,plain,
spl635_751,
inference(avatar_split_clause,[],[f17443,f33796]) ).
fof(f33796,plain,
( spl635_751
<=> ! [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,[spl635_751])]) ).
fof(f17443,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,[],[f5381]) ).
fof(f5381,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,[],[f622]) ).
fof(f622,axiom,
! [X4] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
fof(f33794,plain,
spl635_750,
inference(avatar_split_clause,[],[f17441,f33792]) ).
fof(f33792,plain,
( spl635_750
<=> ! [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,[spl635_750])]) ).
fof(f17441,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,[],[f5379]) ).
fof(f5379,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,[],[f2076]) ).
fof(f2076,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',fact_lessThan__Suc__atMost) ).
fof(f33790,plain,
spl635_749,
inference(avatar_split_clause,[],[f17440,f33788]) ).
fof(f33788,plain,
( spl635_749
<=> ! [X0] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_749])]) ).
fof(f17440,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f5378]) ).
fof(f5378,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X0),
inference(rectify,[],[f2207]) ).
fof(f2207,axiom,
! [X48] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X48)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X48),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast__Suc__greaterThan) ).
fof(f33786,plain,
spl635_748,
inference(avatar_split_clause,[],[f17437,f33784]) ).
fof(f33784,plain,
( spl635_748
<=> ! [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,[spl635_748])]) ).
fof(f17437,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,[],[f5375]) ).
fof(f5375,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,[],[f1249]) ).
fof(f1249,axiom,
! [X40] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(X40)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X40)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Bit0) ).
fof(f33782,plain,
( spl635_747
| ~ spl635_730 ),
inference(avatar_split_clause,[],[f33746,f32823,f33780]) ).
fof(f33780,plain,
( spl635_747
<=> ! [X0] : sP12(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_747])]) ).
fof(f32823,plain,
( spl635_730
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) != hAPP(c_Int_Onat,X1)
| sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_730])]) ).
fof(f33746,plain,
( ! [X0] : sP12(X0,X0)
| ~ spl635_730 ),
inference(equality_resolution,[],[f32824]) ).
fof(f32824,plain,
( ! [X0,X1] :
( hAPP(c_Int_Onat,X0) != hAPP(c_Int_Onat,X1)
| sP12(X0,X1) )
| ~ spl635_730 ),
inference(avatar_component_clause,[],[f32823]) ).
fof(f33778,plain,
spl635_746,
inference(avatar_split_clause,[],[f17436,f33776]) ).
fof(f33776,plain,
( spl635_746
<=> ! [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,[spl635_746])]) ).
fof(f17436,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,[],[f5374]) ).
fof(f5374,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,[],[f1496]) ).
fof(f1496,axiom,
! [X15] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X15)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(f33774,plain,
spl635_745,
inference(avatar_split_clause,[],[f17434,f33772]) ).
fof(f33772,plain,
( spl635_745
<=> ! [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,[spl635_745])]) ).
fof(f17434,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,[],[f972]) ).
fof(f972,axiom,
! [X40] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X40) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X40),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Min) ).
fof(f33770,plain,
spl635_744,
inference(avatar_split_clause,[],[f17429,f33768]) ).
fof(f33768,plain,
( spl635_744
<=> ! [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,[spl635_744])]) ).
fof(f17429,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,[],[f5367]) ).
fof(f5367,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,[],[f647]) ).
fof(f647,axiom,
! [X4] : hAPP(c_Nat_OSuc,X4) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f33766,plain,
spl635_743,
inference(avatar_split_clause,[],[f17428,f33764]) ).
fof(f33764,plain,
( spl635_743
<=> ! [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,[spl635_743])]) ).
fof(f33762,plain,
spl635_742,
inference(avatar_split_clause,[],[f17427,f33760]) ).
fof(f33760,plain,
( spl635_742
<=> ! [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,[spl635_742])]) ).
fof(f17427,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,[],[f5365]) ).
fof(f5365,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,[],[f2067]) ).
fof(f2067,axiom,
! [X75] : hAPP(c_Nat_OSuc,X75) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X75)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__atMost) ).
fof(f33758,plain,
spl635_741,
inference(avatar_split_clause,[],[f17259,f33755]) ).
fof(f17259,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,[],[f3148]) ).
fof(f3148,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',fact_equiv__intrel) ).
fof(f33739,plain,
( spl635_740
| ~ spl635_342
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33323,f32548,f30931,f33737]) ).
fof(f33737,plain,
( spl635_740
<=> ! [X0] : ~ sP31(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_740])]) ).
fof(f30931,plain,
( spl635_342
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_342])]) ).
fof(f33323,plain,
( ! [X0] : ~ sP31(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint))
| ~ spl635_342
| ~ spl635_665 ),
inference(resolution,[],[f32549,f30932]) ).
fof(f30932,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0))
| ~ spl635_342 ),
inference(avatar_component_clause,[],[f30931]) ).
fof(f33713,plain,
( spl635_739
| ~ spl635_341
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33322,f32548,f30927,f33711]) ).
fof(f33711,plain,
( spl635_739
<=> ! [X0] : ~ sP31(X0,X0,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_739])]) ).
fof(f30927,plain,
( spl635_341
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_341])]) ).
fof(f33322,plain,
( ! [X0] : ~ sP31(X0,X0,c_Rings_Odvd__class_Odvd(tc_Nat_Onat))
| ~ spl635_341
| ~ spl635_665 ),
inference(resolution,[],[f32549,f30928]) ).
fof(f30928,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0))
| ~ spl635_341 ),
inference(avatar_component_clause,[],[f30927]) ).
fof(f33606,plain,
( spl635_738
| ~ spl635_301
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33321,f32548,f30722,f33604]) ).
fof(f33604,plain,
( spl635_738
<=> ! [X0] : ~ sP31(X0,X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_738])]) ).
fof(f30722,plain,
( spl635_301
<=> ! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_301])]) ).
fof(f33321,plain,
( ! [X0] : ~ sP31(X0,X0,c_fequal)
| ~ spl635_301
| ~ spl635_665 ),
inference(resolution,[],[f32549,f30723]) ).
fof(f30723,plain,
( ! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1))
| ~ spl635_301 ),
inference(avatar_component_clause,[],[f30722]) ).
fof(f33484,plain,
( ~ spl635_737
| ~ spl635_2
| ~ spl635_665 ),
inference(avatar_split_clause,[],[f33352,f32548,f29301,f33481]) ).
fof(f33481,plain,
( spl635_737
<=> sP31(v_ts,sK89,c_member(tc_Hoare__Mirabelle_Otriple(t_a))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_737])]) ).
fof(f33352,plain,
( ~ sP31(v_ts,sK89,c_member(tc_Hoare__Mirabelle_Otriple(t_a)))
| ~ spl635_2
| ~ spl635_665 ),
inference(resolution,[],[f32549,f29303]) ).
fof(f32916,plain,
( spl635_735
| ~ spl635_736
| ~ spl635_563
| ~ spl635_619 ),
inference(avatar_split_clause,[],[f32884,f32364,f31897,f32913,f32909]) ).
fof(f32909,plain,
( spl635_735
<=> c_Nat__Transfer_Ois__nat(c_Orderings_Otop__class_Otop(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_735])]) ).
fof(f32913,plain,
( spl635_736
<=> class_Orderings_Otop(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_736])]) ).
fof(f32364,plain,
( spl635_619
<=> ! [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,[spl635_619])]) ).
fof(f32884,plain,
( ~ class_Orderings_Otop(tc_Int_Oint)
| c_Nat__Transfer_Ois__nat(c_Orderings_Otop__class_Otop(tc_Int_Oint))
| ~ spl635_563
| ~ spl635_619 ),
inference(resolution,[],[f32365,f31898]) ).
fof(f32365,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) )
| ~ spl635_619 ),
inference(avatar_component_clause,[],[f32364]) ).
fof(f32883,plain,
( spl635_734
| ~ spl635_26
| ~ spl635_210
| ~ spl635_599 ),
inference(avatar_split_clause,[],[f32847,f32284,f30335,f29421,f32880]) ).
fof(f32880,plain,
( spl635_734
<=> c_Int_OPls = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_734])]) ).
fof(f29421,plain,
( spl635_26
<=> class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_26])]) ).
fof(f30335,plain,
( spl635_210
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl635_210])]) ).
fof(f32284,plain,
( spl635_599
<=> ! [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,[spl635_599])]) ).
fof(f32847,plain,
( c_Int_OPls = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Int_OPls)
| ~ spl635_26
| ~ spl635_210
| ~ spl635_599 ),
inference(forward_demodulation,[],[f32846,f30337]) ).
fof(f30337,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls
| ~ spl635_210 ),
inference(avatar_component_clause,[],[f30335]) ).
fof(f32846,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))
| ~ spl635_26
| ~ spl635_599 ),
inference(resolution,[],[f32285,f29423]) ).
fof(f29423,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint)
| ~ spl635_26 ),
inference(avatar_component_clause,[],[f29421]) ).
fof(f32285,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)) )
| ~ spl635_599 ),
inference(avatar_component_clause,[],[f32284]) ).
fof(f32842,plain,
( spl635_733
| ~ spl635_367
| ~ spl635_593 ),
inference(avatar_split_clause,[],[f32834,f32257,f31032,f32840]) ).
fof(f32840,plain,
( spl635_733
<=> ! [X0] : ~ class_Finite__Set_Ofinite(tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_733])]) ).
fof(f31032,plain,
( spl635_367
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_367])]) ).
fof(f32257,plain,
( spl635_593
<=> ! [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,[spl635_593])]) ).
fof(f32834,plain,
( ! [X0] : ~ class_Finite__Set_Ofinite(tc_List_Olist(X0))
| ~ spl635_367
| ~ spl635_593 ),
inference(resolution,[],[f32258,f31033]) ).
fof(f31033,plain,
( ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) )
| ~ spl635_367 ),
inference(avatar_component_clause,[],[f31032]) ).
fof(f32258,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))))
| ~ spl635_593 ),
inference(avatar_component_clause,[],[f32257]) ).
fof(f32833,plain,
spl635_732,
inference(avatar_split_clause,[],[f28948,f32831]) ).
fof(f32831,plain,
( spl635_732
<=> ! [X2,X1,X3] : hBOOL(hAPP(hAPP(c_List_Omember(X3),c_List_Oinsert(X3,X2,X1)),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_732])]) ).
fof(f28948,plain,
! [X2,X3,X1] : hBOOL(hAPP(hAPP(c_List_Omember(X3),c_List_Oinsert(X3,X2,X1)),X2)),
inference(forward_demodulation,[],[f25752,f27883]) ).
fof(f27883,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,[],[f24701,f24693]) ).
fof(f24693,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,[],[f19734,f17309,f17309]) ).
fof(f19734,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,[],[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),c_List_Oinsert(X2,X1,X0)),
inference(rectify,[],[f4761]) ).
fof(f4761,axiom,
! [X210,X30,X8] : hAPP(hAPP(c_Set_Oinsert(X8),X30),hAPP(c_List_Oset(X8),X210)) = hAPP(c_List_Oset(X8),c_List_Oinsert(X8,X30,X210)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oset__insert) ).
fof(f24701,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,[],[f19752,f17309,f17309]) ).
fof(f19752,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,[],[f7047]) ).
fof(f7047,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,[],[f4071]) ).
fof(f4071,axiom,
! [X210,X30,X8] : hAPP(c_List_Oset(X8),hAPP(hAPP(c_List_Olist_OCons(X8),X30),X210)) = hAPP(hAPP(c_Set_Oinsert(X8),X30),hAPP(c_List_Oset(X8),X210)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).
fof(f25752,plain,
! [X2,X3,X1] : hBOOL(hAPP(hAPP(c_List_Omember(X3),hAPP(hAPP(c_List_Olist_OCons(X3),X2),X1)),X2)),
inference(equality_resolution,[],[f22764]) ).
fof(f22764,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,[],[f16408]) ).
fof(f16408,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,[],[f16407]) ).
fof(f16407,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,[],[f9193]) ).
fof(f9193,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,[],[f4882]) ).
fof(f4882,axiom,
! [X35,X210,X30,X8] :
( hBOOL(hAPP(hAPP(c_List_Omember(X8),hAPP(hAPP(c_List_Olist_OCons(X8),X30),X210)),X35))
<=> ( hBOOL(hAPP(hAPP(c_List_Omember(X8),X210),X35))
| X30 = X35 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_member__rec_I1_J) ).
fof(f32829,plain,
spl635_731,
inference(avatar_split_clause,[],[f28110,f32827]) ).
fof(f32827,plain,
( spl635_731
<=> ! [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,[spl635_731])]) ).
fof(f28110,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,[],[f20240,f17187]) ).
fof(f20240,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,[],[f11622]) ).
fof(f11622,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,[],[f7464]) ).
fof(f7464,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,[],[f16]) ).
fof(f16,axiom,
! [X14,X16,X8] :
( class_Rings_Osemiring__1(X8)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X8,X16,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X14) = X14 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).
fof(f32825,plain,
spl635_730,
inference(avatar_split_clause,[],[f27624,f32823]) ).
fof(f27624,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) != hAPP(c_Int_Onat,X1)
| sP12(X0,X1) ),
inference(forward_demodulation,[],[f27623,f26085]) ).
fof(f27623,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,[],[f19391,f26085]) ).
fof(f19391,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,[],[f15197]) ).
fof(f15197,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,[],[f14550]) ).
fof(f14550,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,[],[f11331,f14549,f14548]) ).
fof(f14548,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(f11331,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,[],[f6846]) ).
fof(f6846,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,[],[f894]) ).
fof(f894,axiom,
! [X88,X70] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X70) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X88)
<=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X70)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X88)))
=> X70 = X88 )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X88)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X70) ) ) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X70)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X88)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__nat__number__of) ).
fof(f32821,plain,
spl635_729,
inference(avatar_split_clause,[],[f27622,f32819]) ).
fof(f32819,plain,
( spl635_729
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) = hAPP(c_Int_Onat,X1)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_729])]) ).
fof(f27622,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = hAPP(c_Int_Onat,X1)
| ~ sP12(X0,X1) ),
inference(forward_demodulation,[],[f27621,f26085]) ).
fof(f27621,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,[],[f19392,f26085]) ).
fof(f19392,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,[],[f15197]) ).
fof(f32817,plain,
spl635_728,
inference(avatar_split_clause,[],[f27620,f32815]) ).
fof(f27620,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Int_OPls = X0
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f27619,f17327]) ).
fof(f27619,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,[],[f27618,f17176]) ).
fof(f27618,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,[],[f19385,f17327]) ).
fof(f19385,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,[],[f15196]) ).
fof(f15196,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,[],[f15195]) ).
fof(f15195,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,[],[f15194]) ).
fof(f15194,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,[],[f14548]) ).
fof(f32813,plain,
spl635_727,
inference(avatar_split_clause,[],[f27617,f32811]) ).
fof(f32811,plain,
( spl635_727
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| X0 = X1
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_727])]) ).
fof(f27617,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| X0 = X1
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f19386,f17327]) ).
fof(f19386,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,[],[f15196]) ).
fof(f32809,plain,
spl635_726,
inference(avatar_split_clause,[],[f27616,f32807]) ).
fof(f32807,plain,
( spl635_726
<=> ! [X0,X1] :
( c_Int_OPls != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_726])]) ).
fof(f27616,plain,
! [X0,X1] :
( c_Int_OPls != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X0,X1) ),
inference(forward_demodulation,[],[f27615,f17176]) ).
fof(f27615,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,[],[f27614,f17327]) ).
fof(f27614,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,[],[f19388,f17327]) ).
fof(f19388,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,[],[f15196]) ).
fof(f32805,plain,
spl635_725,
inference(avatar_split_clause,[],[f27607,f32803]) ).
fof(f32803,plain,
( spl635_725
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X1,X0)
| ~ sP12(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_725])]) ).
fof(f27607,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X1,X0)
| ~ sP12(X0,X1) ),
inference(forward_demodulation,[],[f19380,f17327]) ).
fof(f19380,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,[],[f15193]) ).
fof(f32801,plain,
spl635_724,
inference(avatar_split_clause,[],[f27603,f32799]) ).
fof(f32799,plain,
( spl635_724
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP12(X0,X1)
| ~ sP11(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_724])]) ).
fof(f27603,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP12(X0,X1)
| ~ sP11(X1,X0) ),
inference(forward_demodulation,[],[f19383,f17327]) ).
fof(f19383,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,[],[f15193]) ).
fof(f32797,plain,
spl635_723,
inference(avatar_split_clause,[],[f27591,f32795]) ).
fof(f32795,plain,
( spl635_723
<=> ! [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,[spl635_723])]) ).
fof(f27591,plain,
! [X3,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0
| ~ hBOOL(hAPP(X0,X3)) ),
inference(forward_demodulation,[],[f19364,f17832]) ).
fof(f19364,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,[],[f15181]) ).
fof(f32793,plain,
spl635_722,
inference(avatar_split_clause,[],[f27567,f32791]) ).
fof(f32791,plain,
( spl635_722
<=> ! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_722])]) ).
fof(f27567,plain,
! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP9(X0,X1) ),
inference(forward_demodulation,[],[f19339,f17327]) ).
fof(f19339,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,[],[f15167]) ).
fof(f15167,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,[],[f15166]) ).
fof(f15166,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,[],[f14544]) ).
fof(f32789,plain,
spl635_721,
inference(avatar_split_clause,[],[f27566,f32787]) ).
fof(f32787,plain,
( spl635_721
<=> ! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_721])]) ).
fof(f27566,plain,
! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP9(X0,X1) ),
inference(forward_demodulation,[],[f19340,f17327]) ).
fof(f19340,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,[],[f15167]) ).
fof(f32785,plain,
( ~ spl635_158
| spl635_720
| ~ spl635_223
| ~ spl635_350 ),
inference(avatar_split_clause,[],[f31138,f30963,f30396,f32782,f30081]) ).
fof(f30081,plain,
( spl635_158
<=> class_Lattices_Osemilattice__sup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_158])]) ).
fof(f32782,plain,
( spl635_720
<=> c_Finite__Set_Ofun__left__comm__idem(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_720])]) ).
fof(f30396,plain,
( spl635_223
<=> c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_223])]) ).
fof(f30963,plain,
( spl635_350
<=> ! [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,[spl635_350])]) ).
fof(f31138,plain,
( c_Finite__Set_Ofun__left__comm__idem(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omax(tc_Nat_Onat))
| ~ class_Lattices_Osemilattice__sup(tc_Nat_Onat)
| ~ spl635_223
| ~ spl635_350 ),
inference(superposition,[],[f30964,f30398]) ).
fof(f30398,plain,
( c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)
| ~ spl635_223 ),
inference(avatar_component_clause,[],[f30396]) ).
fof(f30964,plain,
( ! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__sup__class_Osup(X0))
| ~ class_Lattices_Osemilattice__sup(X0) )
| ~ spl635_350 ),
inference(avatar_component_clause,[],[f30963]) ).
fof(f32780,plain,
spl635_719,
inference(avatar_split_clause,[],[f27565,f32778]) ).
fof(f32778,plain,
( spl635_719
<=> ! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_719])]) ).
fof(f27565,plain,
! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP9(X0,X1) ),
inference(forward_demodulation,[],[f19341,f17327]) ).
fof(f19341,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,[],[f15167]) ).
fof(f32776,plain,
spl635_718,
inference(avatar_split_clause,[],[f27564,f32774]) ).
fof(f32774,plain,
( spl635_718
<=> ! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP9(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_718])]) ).
fof(f27564,plain,
! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP9(X0,X1) ),
inference(forward_demodulation,[],[f19342,f17327]) ).
fof(f19342,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,[],[f15167]) ).
fof(f32772,plain,
spl635_717,
inference(avatar_split_clause,[],[f27004,f32770]) ).
fof(f32770,plain,
( spl635_717
<=> ! [X0,X1] :
( hAPP(c_fequal,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_717])]) ).
fof(f27004,plain,
! [X0,X1] :
( hAPP(c_fequal,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(forward_demodulation,[],[f18684,f26500]) ).
fof(f18684,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,[],[f10833]) ).
fof(f10833,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,[],[f6410]) ).
fof(f6410,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,[],[f2352]) ).
fof(f2352,axiom,
! [X17,X8] :
( class_Orderings_Oorder(X8)
=> hAPP(hAPP(c_Set_Oinsert(X8),X17),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X8,X17,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton) ).
fof(f32768,plain,
spl635_716,
inference(avatar_split_clause,[],[f26637,f32766]) ).
fof(f32766,plain,
( spl635_716
<=> ! [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,[spl635_716])]) ).
fof(f26637,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,[],[f25301,f17187]) ).
fof(f25301,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,[],[f18225]) ).
fof(f18225,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,[],[f10456]) ).
fof(f10456,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,[],[f6068]) ).
fof(f6068,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,[],[f790]) ).
fof(f790,axiom,
! [X51,X24] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X24
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X51),X24) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X51),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X51),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X24
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X51),X24) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(f32764,plain,
spl635_715,
inference(avatar_split_clause,[],[f26482,f32762]) ).
fof(f32762,plain,
( spl635_715
<=> ! [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,[spl635_715])]) ).
fof(f26482,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,[],[f17894,f17187]) ).
fof(f17894,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,[],[f5746]) ).
fof(f5746,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,[],[f4142]) ).
fof(f4142,axiom,
! [X208,X5] : c_List_Olist_ONil(X5) = hAPP(hAPP(c_List_Otake(X5),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X208),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__0) ).
fof(f32760,plain,
spl635_714,
inference(avatar_split_clause,[],[f26372,f32758]) ).
fof(f32758,plain,
( spl635_714
<=> ! [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,[spl635_714])]) ).
fof(f26372,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,[],[f26371,f17176]) ).
fof(f26371,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,[],[f17712,f17187]) ).
fof(f17712,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,[],[f14720]) ).
fof(f14720,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,[],[f5615]) ).
fof(f5615,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,[],[f300]) ).
fof(f300,axiom,
! [X15] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X15)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).
fof(f32756,plain,
spl635_713,
inference(avatar_split_clause,[],[f26351,f32754]) ).
fof(f26351,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK94(X0)))
| c_Nat__Transfer_Onat__set(X0) ),
inference(forward_demodulation,[],[f17683,f17176]) ).
fof(f17683,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)),sK94(X0))) ),
inference(cnf_transformation,[],[f14698]) ).
fof(f14698,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)),sK94(X0)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK94(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,[sK94])],[f14696,f14697]) ).
fof(f14697,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)),sK94(X0)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK94(X0)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14696,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,[],[f14695]) ).
fof(f14695,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,[],[f10441]) ).
fof(f10441,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,[],[f5601]) ).
fof(f5601,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,[],[f2074]) ).
fof(f2074,axiom,
! [X145] :
( c_Nat__Transfer_Onat__set(X145)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X145))
=> 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',fact_nat__set__def) ).
fof(f32752,plain,
spl635_712,
inference(avatar_split_clause,[],[f26250,f32750]) ).
fof(f26250,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f17639,f17187]) ).
fof(f17639,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,[],[f10398]) ).
fof(f10398,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,[],[f5563]) ).
fof(f5563,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0) ),
inference(rectify,[],[f871]) ).
fof(f871,axiom,
! [X31] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X31))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X31) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__nat) ).
fof(f32748,plain,
spl635_711,
inference(avatar_split_clause,[],[f26238,f32746]) ).
fof(f32746,plain,
( spl635_711
<=> ! [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,[spl635_711])]) ).
fof(f26238,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,[],[f17604,f17187]) ).
fof(f17604,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,[],[f10364]) ).
fof(f10364,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,[],[f5529]) ).
fof(f5529,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,[],[f250]) ).
fof(f250,axiom,
! [X5] :
( class_Rings_Osemiring__1(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__0) ).
fof(f32744,plain,
spl635_710,
inference(avatar_split_clause,[],[f26102,f32742]) ).
fof(f32742,plain,
( spl635_710
<=> ! [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,[spl635_710])]) ).
fof(f26102,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,[],[f26101,f25953]) ).
fof(f26101,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,[],[f17467,f17187]) ).
fof(f17467,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,[],[f5405]) ).
fof(f5405,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,[],[f242]) ).
fof(f242,axiom,
! [X4] : 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))),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_power__Suc__0) ).
fof(f32740,plain,
( spl635_709
| ~ spl635_325
| ~ spl635_339 ),
inference(avatar_split_clause,[],[f31130,f30919,f30854,f32737]) ).
fof(f32737,plain,
( spl635_709
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Code__Numeral_Onat__of,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_709])]) ).
fof(f30854,plain,
( spl635_325
<=> 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,[spl635_325])]) ).
fof(f30919,plain,
( spl635_339
<=> ! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_339])]) ).
fof(f31130,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Code__Numeral_Onat__of,c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| ~ spl635_325
| ~ spl635_339 ),
inference(superposition,[],[f30920,f30856]) ).
fof(f30856,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))
| ~ spl635_325 ),
inference(avatar_component_clause,[],[f30854]) ).
fof(f30920,plain,
( ! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0
| ~ spl635_339 ),
inference(avatar_component_clause,[],[f30919]) ).
fof(f32735,plain,
spl635_708,
inference(avatar_split_clause,[],[f26090,f32733]) ).
fof(f32733,plain,
( spl635_708
<=> ! [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,[spl635_708])]) ).
fof(f26090,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,[],[f17444,f17176]) ).
fof(f17444,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,[],[f5382]) ).
fof(f5382,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,[],[f325]) ).
fof(f325,axiom,
! [X31] : 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),X31))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
fof(f32731,plain,
spl635_707,
inference(avatar_split_clause,[],[f26086,f32729]) ).
fof(f32729,plain,
( spl635_707
<=> ! [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,[spl635_707])]) ).
fof(f26086,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,[],[f17438,f26085]) ).
fof(f17438,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,[],[f5376]) ).
fof(f5376,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,[],[f1812]) ).
fof(f1812,axiom,
! [X40] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X40)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X40),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__number) ).
fof(f32727,plain,
spl635_706,
inference(avatar_split_clause,[],[f26082,f32725]) ).
fof(f26082,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,[],[f17424,f17176]) ).
fof(f17424,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,[],[f5362]) ).
fof(f5362,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,[],[f284]) ).
fof(f284,axiom,
! [X40] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X40)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__less__0__conv) ).
fof(f32723,plain,
spl635_705,
inference(avatar_split_clause,[],[f26079,f32721]) ).
fof(f32721,plain,
( spl635_705
<=> ! [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,[spl635_705])]) ).
fof(f26079,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,[],[f17422,f17187]) ).
fof(f17422,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,[],[f5360]) ).
fof(f5360,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,[],[f29]) ).
fof(f29,axiom,
! [X4] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(f32719,plain,
spl635_704,
inference(avatar_split_clause,[],[f26076,f32717]) ).
fof(f32717,plain,
( spl635_704
<=> ! [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,[spl635_704])]) ).
fof(f26076,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,[],[f17417,f17187]) ).
fof(f17417,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,[],[f5355]) ).
fof(f5355,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,[],[f2075]) ).
fof(f2075,axiom,
! [X15] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X15) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast0AtMost) ).
fof(f32715,plain,
spl635_703,
inference(avatar_split_clause,[],[f26075,f32713]) ).
fof(f32713,plain,
( spl635_703
<=> ! [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,[spl635_703])]) ).
fof(f26075,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,[],[f17410,f17187]) ).
fof(f17410,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,[],[f5348]) ).
fof(f5348,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,[],[f2347]) ).
fof(f2347,axiom,
! [X8] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X8),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card_Oempty) ).
fof(f32711,plain,
spl635_702,
inference(avatar_split_clause,[],[f26072,f32709]) ).
fof(f32709,plain,
( spl635_702
<=> ! [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,[spl635_702])]) ).
fof(f32707,plain,
spl635_701,
inference(avatar_split_clause,[],[f26071,f32705]) ).
fof(f32705,plain,
( spl635_701
<=> ! [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,[spl635_701])]) ).
fof(f26071,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,[],[f17407,f17187]) ).
fof(f17407,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,[],[f5345]) ).
fof(f5345,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,[],[f617]) ).
fof(f617,axiom,
! [X4] : 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)),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(f32703,plain,
spl635_700,
inference(avatar_split_clause,[],[f26070,f32701]) ).
fof(f32701,plain,
( spl635_700
<=> ! [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,[spl635_700])]) ).
fof(f26070,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,[],[f17406,f17187]) ).
fof(f17406,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,[],[f5344]) ).
fof(f5344,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,[],[f1662]) ).
fof(f1662,axiom,
! [X4] : 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)),X4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__0L) ).
fof(f32699,plain,
spl635_699,
inference(avatar_split_clause,[],[f26069,f32697]) ).
fof(f32697,plain,
( spl635_699
<=> ! [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,[spl635_699])]) ).
fof(f26069,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,[],[f17405,f17187]) ).
fof(f17405,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,[],[f5343]) ).
fof(f5343,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,[],[f187]) ).
fof(f187,axiom,
! [X24] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__0__right) ).
fof(f32695,plain,
spl635_698,
inference(avatar_split_clause,[],[f26068,f32693]) ).
fof(f32693,plain,
( spl635_698
<=> ! [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,[spl635_698])]) ).
fof(f26068,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,[],[f17404,f17187]) ).
fof(f17404,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,[],[f5342]) ).
fof(f5342,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,[],[f1663]) ).
fof(f1663,axiom,
! [X4] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__0R) ).
fof(f32691,plain,
spl635_697,
inference(avatar_split_clause,[],[f25990,f32688]) ).
fof(f32688,plain,
( spl635_697
<=> 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,[spl635_697])]) ).
fof(f25990,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,[],[f17257,f17175]) ).
fof(f17175,plain,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
inference(cnf_transformation,[],[f1481]) ).
fof(f1481,axiom,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subtract__code__numeral__def) ).
fof(f17257,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,[],[f1354]) ).
fof(f1354,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',fact_code__numeral__zero__minus__one) ).
fof(f32686,plain,
spl635_696,
inference(avatar_split_clause,[],[f25985,f32683]) ).
fof(f32683,plain,
( spl635_696
<=> 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,[spl635_696])]) ).
fof(f25985,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,[],[f17253,f17187]) ).
fof(f17253,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f2359]) ).
fof(f2359,axiom,
c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessThan__0) ).
fof(f32681,plain,
spl635_695,
inference(avatar_split_clause,[],[f25984,f32678]) ).
fof(f32678,plain,
( spl635_695
<=> 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,[spl635_695])]) ).
fof(f25984,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,[],[f17252,f17187]) ).
fof(f17252,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,[],[f3180]) ).
fof(f3180,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',fact_atLeast__0) ).
fof(f32674,plain,
( spl635_694
| ~ spl635_328
| ~ spl635_486
| ~ spl635_693 ),
inference(avatar_split_clause,[],[f32669,f32665,f31582,f30869,f32671]) ).
fof(f32671,plain,
( spl635_694
<=> 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,[spl635_694])]) ).
fof(f32665,plain,
( spl635_693
<=> 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,[spl635_693])]) ).
fof(f32669,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))
| ~ spl635_328
| ~ spl635_486
| ~ spl635_693 ),
inference(forward_demodulation,[],[f32667,f31991]) ).
fof(f32667,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))
| ~ spl635_693 ),
inference(avatar_component_clause,[],[f32665]) ).
fof(f32668,plain,
spl635_693,
inference(avatar_split_clause,[],[f25965,f32665]) ).
fof(f25965,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,[],[f25964,f25942]) ).
fof(f25964,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,[],[f24216,f17174]) ).
fof(f24216,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,[],[f17233,f24179]) ).
fof(f17233,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,[],[f1201]) ).
fof(f1201,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',fact_Numeral1__eq1__nat) ).
fof(f32662,plain,
spl635_692,
inference(avatar_split_clause,[],[f25963,f32659]) ).
fof(f32659,plain,
( spl635_692
<=> 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,[spl635_692])]) ).
fof(f25963,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,[],[f25962,f25942]) ).
fof(f25962,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,[],[f24215,f17174]) ).
fof(f24215,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,[],[f17232,f24179]) ).
fof(f17232,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,[],[f1200]) ).
fof(f1200,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',fact_one__is__num__one) ).
fof(f32657,plain,
( spl635_691
| ~ spl635_328
| ~ spl635_486
| ~ spl635_690 ),
inference(avatar_split_clause,[],[f32652,f32648,f31582,f30869,f32654]) ).
fof(f32654,plain,
( spl635_691
<=> 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,[spl635_691])]) ).
fof(f32648,plain,
( spl635_690
<=> 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,[spl635_690])]) ).
fof(f32652,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))
| ~ spl635_328
| ~ spl635_486
| ~ spl635_690 ),
inference(forward_demodulation,[],[f32650,f31991]) ).
fof(f32650,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))
| ~ spl635_690 ),
inference(avatar_component_clause,[],[f32648]) ).
fof(f32651,plain,
spl635_690,
inference(avatar_split_clause,[],[f25961,f32648]) ).
fof(f25961,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,[],[f25960,f25942]) ).
fof(f25960,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,[],[f24214,f17174]) ).
fof(f24214,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,[],[f17229,f24179]) ).
fof(f17229,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,[],[f1348]) ).
fof(f1348,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',fact_one__code__numeral__code) ).
fof(f32646,plain,
spl635_689,
inference(avatar_split_clause,[],[f25390,f32644]) ).
fof(f32644,plain,
( spl635_689
<=> ! [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,[spl635_689])]) ).
fof(f25390,plain,
! [X3,X0] :
( hBOOL(hAPP(X0,X3))
| ~ sP8(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) ),
inference(equality_resolution,[],[f19238]) ).
fof(f19238,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,[],[f15092]) ).
fof(f15092,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,sK193(X0,X1)))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK193(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,[sK193])],[f15090,f15091]) ).
fof(f15091,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP(X0,X2))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X1 )
=> ( ~ hBOOL(hAPP(X0,sK193(X0,X1)))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK193(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f15090,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,[],[f15089]) ).
fof(f15089,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,[],[f15088]) ).
fof(f15088,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,[],[f14542]) ).
fof(f14542,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(f32642,plain,
spl635_688,
inference(avatar_split_clause,[],[f25318,f32640]) ).
fof(f32640,plain,
( spl635_688
<=> ! [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,[spl635_688])]) ).
fof(f25318,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,[],[f18356]) ).
fof(f18356,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,[],[f14799]) ).
fof(f32638,plain,
spl635_687,
inference(avatar_split_clause,[],[f24343,f32636]) ).
fof(f32636,plain,
( spl635_687
<=> ! [X0,X1] : c_Int_OBit0(X1) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_687])]) ).
fof(f24343,plain,
! [X0,X1] : c_Int_OBit0(X1) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin),
inference(definition_unfolding,[],[f17816,f24179]) ).
fof(f17816,plain,
! [X0,X1] : c_Int_OBit1(X0) != c_Int_OBit0(X1),
inference(cnf_transformation,[],[f5668]) ).
fof(f5668,plain,
! [X0,X1] : c_Int_OBit1(X0) != c_Int_OBit0(X1),
inference(rectify,[],[f1244]) ).
fof(f1244,axiom,
! [X46,X40] : c_Int_OBit1(X46) != c_Int_OBit0(X40),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).
fof(f32634,plain,
spl635_686,
inference(avatar_split_clause,[],[f24260,f32632]) ).
fof(f32632,plain,
( spl635_686
<=> ! [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,[spl635_686])]) ).
fof(f24260,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,[],[f17416,f17309]) ).
fof(f17416,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,[],[f5354]) ).
fof(f5354,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,[],[f4119]) ).
fof(f4119,axiom,
! [X8] : c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = hAPP(c_List_Oset(X8),c_List_Olist_ONil(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).
fof(f32630,plain,
spl635_685,
inference(avatar_split_clause,[],[f24242,f32628]) ).
fof(f32628,plain,
( spl635_685
<=> ! [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,[spl635_685])]) ).
fof(f24242,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,[],[f17305,f17412]) ).
fof(f17305,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X0),
inference(cnf_transformation,[],[f5243]) ).
fof(f5243,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X0),
inference(rectify,[],[f1477]) ).
fof(f1477,axiom,
! [X104] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X104),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I2_J) ).
fof(f32626,plain,
spl635_684,
inference(avatar_split_clause,[],[f24240,f32624]) ).
fof(f32624,plain,
( spl635_684
<=> ! [X0] : c_Relation_Osym(X0,c_Transitive__Closure_Ortrancl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_684])]) ).
fof(f24240,plain,
! [X0] : c_Relation_Osym(X0,c_Transitive__Closure_Ortrancl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))),
inference(definition_unfolding,[],[f17303,f17426]) ).
fof(f17303,plain,
! [X0] : c_Relation_Osym(X0,c_Relation_OId(X0)),
inference(cnf_transformation,[],[f5241]) ).
fof(f5241,plain,
! [X0] : c_Relation_Osym(X0,c_Relation_OId(X0)),
inference(rectify,[],[f4956]) ).
fof(f4956,axiom,
! [X8] : c_Relation_Osym(X8,c_Relation_OId(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__Id) ).
fof(f32622,plain,
spl635_683,
inference(avatar_split_clause,[],[f24239,f32620]) ).
fof(f32620,plain,
( spl635_683
<=> ! [X0] : c_Relation_Oantisym(X0,c_Transitive__Closure_Ortrancl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_683])]) ).
fof(f24239,plain,
! [X0] : c_Relation_Oantisym(X0,c_Transitive__Closure_Ortrancl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)))),
inference(definition_unfolding,[],[f17302,f17426]) ).
fof(f17302,plain,
! [X0] : c_Relation_Oantisym(X0,c_Relation_OId(X0)),
inference(cnf_transformation,[],[f5240]) ).
fof(f5240,plain,
! [X0] : c_Relation_Oantisym(X0,c_Relation_OId(X0)),
inference(rectify,[],[f4942]) ).
fof(f4942,axiom,
! [X8] : c_Relation_Oantisym(X8,c_Relation_OId(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__Id) ).
fof(f32618,plain,
spl635_682,
inference(avatar_split_clause,[],[f23614,f32616]) ).
fof(f32616,plain,
( spl635_682
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,X3))
| ~ sP78(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_682])]) ).
fof(f23614,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X1,X3))
| ~ sP78(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16745]) ).
fof(f16745,plain,
! [X0,X1,X2,X3,X4] :
( ( sP78(X0,X1,X2,X3,X4)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X2,X1),X6) != X0
| ~ hBOOL(hAPP(X1,X3))
| ( hBOOL(hAPP(X1,sK572(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK572(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),sK574(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),sK573(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK573(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK574(X0,X1,X2,X3,X4))) = X4 )
| ~ sP78(X0,X1,X2,X3,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK572,sK573,sK574])],[f16742,f16744,f16743]) ).
fof(f16743,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,sK572(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK572(X1,X2,X5)),hAPP(c_List_Oset(X2),X5))) ) ),
introduced(choice_axiom,[]) ).
fof(f16744,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),sK574(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),sK573(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK573(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK574(X0,X1,X2,X3,X4))) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f16742,plain,
! [X0,X1,X2,X3,X4] :
( ( sP78(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 )
| ~ sP78(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16741]) ).
fof(f16741,plain,
! [X0,X3,X4,X1,X2] :
( ( sP78(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 )
| ~ sP78(X0,X3,X4,X1,X2) ) ),
inference(nnf_transformation,[],[f14662]) ).
fof(f14662,plain,
! [X0,X3,X4,X1,X2] :
( sP78(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,[sP78])]) ).
fof(f32614,plain,
spl635_681,
inference(avatar_split_clause,[],[f23606,f32612]) ).
fof(f32612,plain,
( spl635_681
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,X3))
| ~ sP77(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_681])]) ).
fof(f23606,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X1,X3))
| ~ sP77(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16739]) ).
fof(f16739,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,sK569(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK569(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),sK571(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),sK570(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK570(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK571(X0,X1,X2,X3,X4))) = X4 )
| ~ sP77(X0,X1,X2,X3,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK569,sK570,sK571])],[f16736,f16738,f16737]) ).
fof(f16737,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,sK569(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK569(X1,X2,X5)),hAPP(c_List_Oset(X2),X5))) ) ),
introduced(choice_axiom,[]) ).
fof(f16738,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),sK571(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),sK570(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK570(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK571(X0,X1,X2,X3,X4))) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f16736,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,[],[f16735]) ).
fof(f16735,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,[],[f14660]) ).
fof(f14660,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(f32610,plain,
spl635_680,
inference(avatar_split_clause,[],[f22974,f32608]) ).
fof(f32608,plain,
( spl635_680
<=> ! [X4,X0,X3,X2,X1] : hAPP(c_Fun_Ofun__upd(X4,X3,X2,X1,X0),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_680])]) ).
fof(f22974,plain,
! [X2,X3,X0,X1,X4] : hAPP(c_Fun_Ofun__upd(X4,X3,X2,X1,X0),X1) = X0,
inference(cnf_transformation,[],[f9251]) ).
fof(f9251,plain,
! [X0,X1,X2,X3,X4] : hAPP(c_Fun_Ofun__upd(X4,X3,X2,X1,X0),X1) = X0,
inference(rectify,[],[f2673]) ).
fof(f2673,axiom,
! [X35,X30,X1,X8,X25] : hAPP(c_Fun_Ofun__upd(X25,X8,X1,X30,X35),X30) = X35,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__same) ).
fof(f32606,plain,
spl635_679,
inference(avatar_split_clause,[],[f22971,f32604]) ).
fof(f32604,plain,
( spl635_679
<=> ! [X0,X3,X2,X1] :
( sP71(X0,X1,X2,X3)
| ~ sP72(X0,X1,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_679])]) ).
fof(f22971,plain,
! [X2,X3,X0,X1] :
( sP71(X0,X1,X2,X3)
| ~ sP72(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f16558]) ).
fof(f16558,plain,
! [X0,X1,X2,X3] :
( ( sP71(X0,X1,X2,X3)
| ~ sP72(X0,X1,X3,X2) )
& ( sP72(X0,X1,X3,X2)
| ~ sP71(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f14652]) ).
fof(f14652,plain,
! [X0,X1,X2,X3] :
( sP71(X0,X1,X2,X3)
<=> sP72(X0,X1,X3,X2) ),
inference(definition_folding,[],[f9249,f14651,f14650]) ).
fof(f14651,plain,
! [X0,X1,X3,X2] :
( sP72(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,[sP72])]) ).
fof(f9249,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,[],[f2109]) ).
fof(f2109,axiom,
! [X29,X38,X39,X8] :
( ? [X2] :
( hBOOL(hAPP(X29,X2))
& hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X39),X38))) )
<=> ( ? [X2] :
( hBOOL(hAPP(X29,X2))
& hBOOL(hAPP(hAPP(c_member(X8),X2),X38)) )
| ? [X2] :
( hBOOL(hAPP(X29,X2))
& hBOOL(hAPP(hAPP(c_member(X8),X2),X39)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__Un) ).
fof(f32602,plain,
spl635_678,
inference(avatar_split_clause,[],[f22970,f32600]) ).
fof(f32600,plain,
( spl635_678
<=> ! [X0,X3,X2,X1] :
( sP72(X0,X1,X3,X2)
| ~ sP71(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_678])]) ).
fof(f22970,plain,
! [X2,X3,X0,X1] :
( sP72(X0,X1,X3,X2)
| ~ sP71(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16558]) ).
fof(f32598,plain,
spl635_677,
inference(avatar_split_clause,[],[f22672,f32596]) ).
fof(f32596,plain,
( spl635_677
<=> ! [X0,X3,X2,X1] :
( sP61(X2,X0,X3,X1)
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_677])]) ).
fof(f22672,plain,
! [X2,X3,X0,X1] :
( sP61(X2,X0,X3,X1)
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16340]) ).
fof(f16340,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
| ~ sP61(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)) )
& ( ( sP61(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,[],[f16339]) ).
fof(f16339,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
| ~ sP61(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)) )
& ( ( sP61(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,[],[f14633]) ).
fof(f14633,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
<=> ( sP61(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,[],[f13632,f14632]) ).
fof(f14632,plain,
! [X2,X0,X3,X1] :
( sP61(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,[sP61])]) ).
fof(f13632,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,[],[f9159]) ).
fof(f9159,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,[],[f3264]) ).
fof(f3264,axiom,
! [X153,X112,X122,X8] :
( c_Wellfounded_Omax__extp(X8,X122,X112,X153)
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X112))
=> ? [X142] :
( hBOOL(hAPP(hAPP(X122,X2),X142))
& hBOOL(hAPP(hAPP(c_member(X8),X142),X153)) ) )
& c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) != X153
& hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X153))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X112)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp_Oequations) ).
fof(f32594,plain,
spl635_676,
inference(avatar_split_clause,[],[f22663,f32592]) ).
fof(f32592,plain,
( spl635_676
<=> ! [X0,X3,X2,X1] :
( sP60(X2,X0,X3,X1)
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_676])]) ).
fof(f22663,plain,
! [X2,X3,X0,X1] :
( sP60(X2,X0,X3,X1)
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16333]) ).
fof(f16333,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,[],[f16332]) ).
fof(f16332,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,[],[f14631]) ).
fof(f14631,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,[],[f13631,f14630]) ).
fof(f14630,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(f13631,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,[],[f9158]) ).
fof(f9158,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,[],[f4938]) ).
fof(f4938,axiom,
! [X153,X112,X122,X8] :
( c_Wellfounded_Omax__extp(X8,X122,X112,X153)
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X112))
=> ? [X142] :
( hBOOL(hAPP(hAPP(X122,X2),X142))
& hBOOL(hAPP(hAPP(c_member(X8),X142),X153)) ) )
& c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) != X153
& hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X153))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X112)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__extp_Osimps) ).
fof(f32590,plain,
spl635_675,
inference(avatar_split_clause,[],[f22661,f32588]) ).
fof(f32588,plain,
( spl635_675
<=> ! [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,[spl635_675])]) ).
fof(f22661,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16333]) ).
fof(f32586,plain,
spl635_674,
inference(avatar_split_clause,[],[f22660,f32584]) ).
fof(f32584,plain,
( spl635_674
<=> ! [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,[spl635_674])]) ).
fof(f22660,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16333]) ).
fof(f32582,plain,
spl635_673,
inference(avatar_split_clause,[],[f21634,f32580]) ).
fof(f32580,plain,
( spl635_673
<=> ! [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,[spl635_673])]) ).
fof(f21634,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,[],[f8298]) ).
fof(f8298,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,[],[f2556]) ).
fof(f2556,axiom,
! [X153,X112,X25,X8] : c_Nitpick_Ofold__graph_H(X8,X25,X112,X153,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)),X153),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
fof(f32578,plain,
spl635_672,
inference(avatar_split_clause,[],[f21633,f32576]) ).
fof(f32576,plain,
( spl635_672
<=> ! [X2,X0,X1,X3] : c_Fun_Ofun__upd(X3,X2,X1,X0,hAPP(X1,X0)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_672])]) ).
fof(f21633,plain,
! [X2,X3,X0,X1] : c_Fun_Ofun__upd(X3,X2,X1,X0,hAPP(X1,X0)) = X1,
inference(cnf_transformation,[],[f8297]) ).
fof(f8297,plain,
! [X0,X1,X2,X3] : c_Fun_Ofun__upd(X3,X2,X1,X0,hAPP(X1,X0)) = X1,
inference(rectify,[],[f2668]) ).
fof(f2668,axiom,
! [X30,X1,X25,X8] : c_Fun_Ofun__upd(X8,X25,X1,X30,hAPP(X1,X30)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__upd__triv) ).
fof(f32574,plain,
spl635_671,
inference(avatar_split_clause,[],[f21632,f32572]) ).
fof(f32572,plain,
( spl635_671
<=> ! [X2,X0,X1,X3] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_671])]) ).
fof(f21632,plain,
! [X2,X3,X0,X1] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0,
inference(cnf_transformation,[],[f8296]) ).
fof(f8296,plain,
! [X0,X1,X2,X3] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0,
inference(rectify,[],[f4363]) ).
fof(f4363,axiom,
! [X17,X1,X25,X8] : hAPP(c_List_Ofoldl(X8,X25,X1,X17),c_List_Olist_ONil(X25)) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_foldl__Nil) ).
fof(f32570,plain,
spl635_670,
inference(avatar_split_clause,[],[f21631,f32568]) ).
fof(f32568,plain,
( spl635_670
<=> ! [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,[spl635_670])]) ).
fof(f21631,plain,
! [X2,X3,X0,X1] : hAPP(c_List_Olist_Olist__case(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X1,
inference(cnf_transformation,[],[f8295]) ).
fof(f8295,plain,
! [X0,X1,X2,X3] : hAPP(c_List_Olist_Olist__case(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X1,
inference(rectify,[],[f4195]) ).
fof(f4195,axiom,
! [X20,X21,X25,X8] : hAPP(c_List_Olist_Olist__case(X8,X25,X21,X20),c_List_Olist_ONil(X25)) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).
fof(f32566,plain,
spl635_669,
inference(avatar_split_clause,[],[f21293,f32564]) ).
fof(f32564,plain,
( spl635_669
<=> ! [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,[spl635_669])]) ).
fof(f21293,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,[],[f15846]) ).
fof(f15846,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,[],[f8183]) ).
fof(f8183,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,[],[f4896]) ).
fof(f4896,axiom,
! [X71,X14,X29] :
( c_List_Olist__all(tc_Int_Oint,X29,c_List_Oupto(X14,X71))
<=> c_List_Oall__interval__int(X29,X14,X71) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__iff__all__interval__int) ).
fof(f32562,plain,
spl635_668,
inference(avatar_split_clause,[],[f21292,f32560]) ).
fof(f32560,plain,
( spl635_668
<=> ! [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,[spl635_668])]) ).
fof(f21292,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,[],[f15846]) ).
fof(f32558,plain,
spl635_667,
inference(avatar_split_clause,[],[f21280,f32556]) ).
fof(f32556,plain,
( spl635_667
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP36(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_667])]) ).
fof(f21280,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP36(X1,X0,X2) ),
inference(cnf_transformation,[],[f15832]) ).
fof(f15832,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP36(X1,X0,X2) )
& ( sP36(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ) ),
inference(nnf_transformation,[],[f14590]) ).
fof(f14590,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
<=> sP36(X1,X0,X2) ),
inference(definition_folding,[],[f12672,f14589,f14588]) ).
fof(f14588,plain,
! [X0,X1] :
( sP35(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,[sP35])]) ).
fof(f12672,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,[],[f8178]) ).
fof(f8178,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,[],[f1671]) ).
fof(f1671,axiom,
! [X130,X15,X27] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X27,X15),X130))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X15
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X130)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X15),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X130))) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X15))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X130)),X15))
& 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),X130))) ) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X15
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X130) )
& 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),X130)),X15)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X130)) = X27 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__def) ).
fof(f32554,plain,
spl635_666,
inference(avatar_split_clause,[],[f21279,f32552]) ).
fof(f32552,plain,
( spl635_666
<=> ! [X2,X0,X1] :
( sP36(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_666])]) ).
fof(f21279,plain,
! [X2,X0,X1] :
( sP36(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ),
inference(cnf_transformation,[],[f15832]) ).
fof(f32550,plain,
spl635_665,
inference(avatar_split_clause,[],[f21142,f32548]) ).
fof(f21142,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f15705]) ).
fof(f32546,plain,
spl635_664,
inference(avatar_split_clause,[],[f20807,f32544]) ).
fof(f32544,plain,
( spl635_664
<=> ! [X0,X1] :
( sK262(X0,X1) != sK263(X0,X1)
| ~ sP26(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_664])]) ).
fof(f20807,plain,
! [X0,X1] :
( sK262(X0,X1) != sK263(X0,X1)
| ~ sP26(X0,X1) ),
inference(cnf_transformation,[],[f15585]) ).
fof(f15585,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)),sK262(X0,X1)),sK263(X0,X1))
& sK262(X0,X1) != sK263(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK263(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK262(X0,X1)),X1)) )
| ~ sP26(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK262,sK263])],[f15582,f15584,f15583]) ).
fof(f15583,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)),sK262(X0,X1)),X3)
& sK262(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)),sK262(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15584,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)),sK262(X0,X1)),X3)
& sK262(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)),sK262(X0,X1)),sK263(X0,X1))
& sK262(X0,X1) != sK263(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK263(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15582,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)) )
| ~ sP26(X0,X1) ),
inference(rectify,[],[f15581]) ).
fof(f15581,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)) )
| ~ sP26(X2,X1) ),
inference(nnf_transformation,[],[f14572]) ).
fof(f14572,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)) )
| ~ sP26(X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP26])]) ).
fof(f32542,plain,
spl635_663,
inference(avatar_split_clause,[],[f20799,f32540]) ).
fof(f20799,plain,
! [X2,X0,X1] :
( c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0) ),
inference(cnf_transformation,[],[f12293]) ).
fof(f12293,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0) ),
inference(ennf_transformation,[],[f7899]) ).
fof(f7899,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0)
=> c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X3,X4,X5] :
( c_Hoare__Mirabelle_Otriple__valid(X5,hAPP(c_Nat_OSuc,X4),X3)
=> c_Hoare__Mirabelle_Otriple__valid(X5,X4,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple__valid__Suc) ).
fof(f32538,plain,
spl635_662,
inference(avatar_split_clause,[],[f19673,f32536]) ).
fof(f32536,plain,
( spl635_662
<=> ! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_662])]) ).
fof(f19673,plain,
! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0,
inference(cnf_transformation,[],[f6968]) ).
fof(f6968,plain,
! [X0,X1,X2] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0,
inference(rectify,[],[f3584]) ).
fof(f3584,axiom,
! [X0,X8,X25] : hAPP(c_Fun_Ocomp(X25,X25,X8,c_Fun_Oid(X25)),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__o) ).
fof(f32534,plain,
spl635_661,
inference(avatar_split_clause,[],[f19672,f32532]) ).
fof(f32532,plain,
( spl635_661
<=> ! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_661])]) ).
fof(f19672,plain,
! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0,
inference(cnf_transformation,[],[f6967]) ).
fof(f6967,plain,
! [X0,X1,X2] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0,
inference(rectify,[],[f3585]) ).
fof(f3585,axiom,
! [X1,X25,X8] : hAPP(c_Fun_Ocomp(X8,X25,X8,X1),c_Fun_Oid(X8)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_o__id) ).
fof(f32530,plain,
spl635_660,
inference(avatar_split_clause,[],[f19670,f32528]) ).
fof(f32528,plain,
( spl635_660
<=> ! [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,[spl635_660])]) ).
fof(f19670,plain,
! [X2,X0,X1] : hAPP(c_New__DSequence_Opos__single(X2,X1),X0) = hAPP(c_Lazy__Sequence_Osingle(X2),X1),
inference(cnf_transformation,[],[f6965]) ).
fof(f6965,plain,
! [X0,X1,X2] : hAPP(c_New__DSequence_Opos__single(X2,X1),X0) = hAPP(c_Lazy__Sequence_Osingle(X2),X1),
inference(rectify,[],[f3655]) ).
fof(f3655,axiom,
! [X138,X13,X5] : hAPP(c_New__DSequence_Opos__single(X5,X13),X138) = hAPP(c_Lazy__Sequence_Osingle(X5),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
fof(f32526,plain,
spl635_659,
inference(avatar_split_clause,[],[f19669,f32524]) ).
fof(f32524,plain,
( spl635_659
<=> ! [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,[spl635_659])]) ).
fof(f19669,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,[],[f6964]) ).
fof(f6964,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,[],[f3156]) ).
fof(f3156,axiom,
! [X30,X1,X8] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X8,X1,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))),X30)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__fold1SetE) ).
fof(f32522,plain,
spl635_658,
inference(avatar_split_clause,[],[f19651,f32520]) ).
fof(f19651,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(X0,sK216(X0,X1)))
| ~ hBOOL(hAPP(X0,X3)) ),
inference(cnf_transformation,[],[f15363]) ).
fof(f15363,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(X0,sK216(X0,X1)))
& hBOOL(hAPP(hAPP(c_member(X1),sK216(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) )
| ! [X3] : ~ hBOOL(hAPP(X0,X3)) )
& ( hBOOL(hAPP(X0,sK217(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,[sK216,sK217])],[f15360,f15362,f15361]) ).
fof(f15361,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,sK216(X0,X1)))
& hBOOL(hAPP(hAPP(c_member(X1),sK216(X0,X1)),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ) ),
introduced(choice_axiom,[]) ).
fof(f15362,plain,
! [X0] :
( ? [X4] : hBOOL(hAPP(X0,X4))
=> hBOOL(hAPP(X0,sK217(X0))) ),
introduced(choice_axiom,[]) ).
fof(f15360,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,[],[f15359]) ).
fof(f15359,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,[],[f6946]) ).
fof(f6946,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,[],[f4908]) ).
fof(f4908,axiom,
! [X29,X8] :
( ? [X2] :
( hBOOL(hAPP(X29,X2))
& hBOOL(hAPP(hAPP(c_member(X8),X2),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))) )
<=> ? [X65] : hBOOL(hAPP(X29,X65)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bex__UNIV) ).
fof(f32518,plain,
spl635_657,
inference(avatar_split_clause,[],[f19326,f32516]) ).
fof(f32516,plain,
( spl635_657
<=> ! [X0,X1] :
( c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Otrans(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_657])]) ).
fof(f19326,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Otrans(X1,X0) ),
inference(cnf_transformation,[],[f15159]) ).
fof(f15159,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,[],[f6827]) ).
fof(f6827,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
<=> c_Relation_Otrans(X1,X0) ),
inference(rectify,[],[f4912]) ).
fof(f4912,axiom,
! [X98,X8] :
( c_Relation_Otrans(X8,hAPP(c_Relation_Oconverse(X8,X8),X98))
<=> c_Relation_Otrans(X8,X98) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__converse) ).
fof(f32514,plain,
spl635_656,
inference(avatar_split_clause,[],[f19325,f32512]) ).
fof(f32512,plain,
( spl635_656
<=> ! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| ~ c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_656])]) ).
fof(f19325,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
| ~ c_Relation_Otrans(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ),
inference(cnf_transformation,[],[f15159]) ).
fof(f32510,plain,
spl635_655,
inference(avatar_split_clause,[],[f19324,f32508]) ).
fof(f32508,plain,
( spl635_655
<=> ! [X0,X1] :
( c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Osym(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_655])]) ).
fof(f19324,plain,
! [X0,X1] :
( c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Osym(X1,X0) ),
inference(cnf_transformation,[],[f15158]) ).
fof(f15158,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,[],[f6826]) ).
fof(f6826,plain,
! [X0,X1] :
( c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
<=> c_Relation_Osym(X1,X0) ),
inference(rectify,[],[f4954]) ).
fof(f4954,axiom,
! [X98,X8] :
( c_Relation_Osym(X8,hAPP(c_Relation_Oconverse(X8,X8),X98))
<=> c_Relation_Osym(X8,X98) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__converse) ).
fof(f32506,plain,
spl635_654,
inference(avatar_split_clause,[],[f19323,f32504]) ).
fof(f32504,plain,
( spl635_654
<=> ! [X0,X1] :
( c_Relation_Osym(X1,X0)
| ~ c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_654])]) ).
fof(f19323,plain,
! [X0,X1] :
( c_Relation_Osym(X1,X0)
| ~ c_Relation_Osym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ),
inference(cnf_transformation,[],[f15158]) ).
fof(f32502,plain,
spl635_653,
inference(avatar_split_clause,[],[f19322,f32500]) ).
fof(f32500,plain,
( spl635_653
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Oantisym(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_653])]) ).
fof(f19322,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Relation_Oantisym(X1,X0) ),
inference(cnf_transformation,[],[f15157]) ).
fof(f15157,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,[],[f6825]) ).
fof(f6825,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
<=> c_Relation_Oantisym(X1,X0) ),
inference(rectify,[],[f4943]) ).
fof(f4943,axiom,
! [X98,X8] :
( c_Relation_Oantisym(X8,hAPP(c_Relation_Oconverse(X8,X8),X98))
<=> c_Relation_Oantisym(X8,X98) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__converse) ).
fof(f32498,plain,
spl635_652,
inference(avatar_split_clause,[],[f19321,f32496]) ).
fof(f32496,plain,
( spl635_652
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| ~ c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_652])]) ).
fof(f19321,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| ~ c_Relation_Oantisym(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ),
inference(cnf_transformation,[],[f15157]) ).
fof(f32494,plain,
spl635_651,
inference(avatar_split_clause,[],[f19320,f32492]) ).
fof(f32492,plain,
( spl635_651
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_651])]) ).
fof(f19320,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ),
inference(cnf_transformation,[],[f15156]) ).
fof(f15156,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,[],[f6824]) ).
fof(f6824,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
<=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f3774]) ).
fof(f3774,axiom,
! [X98,X8] :
( c_Wellfounded_Oacyclic(X8,hAPP(c_Relation_Oconverse(X8,X8),X98))
<=> c_Wellfounded_Oacyclic(X8,X98) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__converse) ).
fof(f32490,plain,
( spl635_650
| ~ spl635_367
| ~ spl635_537 ),
inference(avatar_split_clause,[],[f32155,f31789,f31032,f32488]) ).
fof(f32488,plain,
( spl635_650
<=> ! [X2,X0,X1] :
( sP25(X0,X1,X2)
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_650])]) ).
fof(f31789,plain,
( spl635_537
<=> ! [X2,X0,X1] :
( sP25(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_537])]) ).
fof(f32155,plain,
( ! [X2,X0,X1] :
( sP25(X0,X1,X2)
| ~ class_Finite__Set_Ofinite(X0) )
| ~ spl635_367
| ~ spl635_537 ),
inference(resolution,[],[f31790,f31033]) ).
fof(f31790,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| sP25(X2,X1,X0) )
| ~ spl635_537 ),
inference(avatar_component_clause,[],[f31789]) ).
fof(f32486,plain,
spl635_649,
inference(avatar_split_clause,[],[f19319,f32484]) ).
fof(f32484,plain,
( spl635_649
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_649])]) ).
fof(f19319,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ),
inference(cnf_transformation,[],[f15156]) ).
fof(f32482,plain,
spl635_648,
inference(avatar_split_clause,[],[f19274,f32480]) ).
fof(f32480,plain,
( spl635_648
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Oof__nat,X0) != hAPP(c_Code__Numeral_Oof__nat,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_648])]) ).
fof(f19274,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Oof__nat,X0) != hAPP(c_Code__Numeral_Oof__nat,X1) ),
inference(cnf_transformation,[],[f15120]) ).
fof(f15120,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,[],[f6804]) ).
fof(f6804,plain,
! [X0,X1] :
( hAPP(c_Code__Numeral_Oof__nat,X0) = hAPP(c_Code__Numeral_Oof__nat,X1)
<=> X0 = X1 ),
inference(rectify,[],[f1792]) ).
fof(f1792,axiom,
! [X27,X15] :
( hAPP(c_Code__Numeral_Oof__nat,X15) = hAPP(c_Code__Numeral_Oof__nat,X27)
<=> X15 = X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).
fof(f32478,plain,
spl635_647,
inference(avatar_split_clause,[],[f19270,f32476]) ).
fof(f32476,plain,
( spl635_647
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Onat__of,X0) != hAPP(c_Code__Numeral_Onat__of,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_647])]) ).
fof(f19270,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Onat__of,X0) != hAPP(c_Code__Numeral_Onat__of,X1) ),
inference(cnf_transformation,[],[f15118]) ).
fof(f15118,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,[],[f6802]) ).
fof(f6802,plain,
! [X0,X1] :
( hAPP(c_Code__Numeral_Onat__of,X0) = hAPP(c_Code__Numeral_Onat__of,X1)
<=> X0 = X1 ),
inference(rectify,[],[f1807]) ).
fof(f1807,axiom,
! [X35,X30] :
( hAPP(c_Code__Numeral_Onat__of,X30) = hAPP(c_Code__Numeral_Onat__of,X35)
<=> X30 = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).
fof(f32474,plain,
spl635_646,
inference(avatar_split_clause,[],[f19268,f32472]) ).
fof(f32472,plain,
( spl635_646
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Int_ORep__Integ,X0) != hAPP(c_Int_ORep__Integ,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_646])]) ).
fof(f19268,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Int_ORep__Integ,X0) != hAPP(c_Int_ORep__Integ,X1) ),
inference(cnf_transformation,[],[f15117]) ).
fof(f15117,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,[],[f6801]) ).
fof(f6801,plain,
! [X0,X1] :
( hAPP(c_Int_ORep__Integ,X0) = hAPP(c_Int_ORep__Integ,X1)
<=> X0 = X1 ),
inference(rectify,[],[f2446]) ).
fof(f2446,axiom,
! [X35,X30] :
( hAPP(c_Int_ORep__Integ,X30) = hAPP(c_Int_ORep__Integ,X35)
<=> X30 = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
fof(f32470,plain,
spl635_645,
inference(avatar_split_clause,[],[f19222,f32468]) ).
fof(f32468,plain,
( spl635_645
<=> ! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != c_List_Oremdups(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_645])]) ).
fof(f19222,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != c_List_Oremdups(X1,X0) ),
inference(cnf_transformation,[],[f15074]) ).
fof(f15074,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,[],[f6784]) ).
fof(f6784,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = c_List_Oremdups(X1,X0)
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f4520]) ).
fof(f4520,axiom,
! [X30,X8] :
( c_List_Olist_ONil(X8) = c_List_Oremdups(X8,X30)
<=> c_List_Olist_ONil(X8) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__eq__nil__iff) ).
fof(f32466,plain,
spl635_644,
inference(avatar_split_clause,[],[f19213,f32464]) ).
fof(f32464,plain,
( spl635_644
<=> ! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| c_List_Oremdups(X1,X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_644])]) ).
fof(f19213,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| c_List_Oremdups(X1,X0) != X0 ),
inference(cnf_transformation,[],[f15064]) ).
fof(f15064,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,[],[f6781]) ).
fof(f6781,plain,
! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
<=> hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(rectify,[],[f4511]) ).
fof(f4511,axiom,
! [X210,X8] :
( c_List_Oremdups(X8,X210) = X210
<=> hBOOL(hAPP(c_List_Odistinct(X8),X210)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__id__iff__distinct) ).
fof(f32462,plain,
spl635_643,
inference(avatar_split_clause,[],[f19170,f32460]) ).
fof(f32460,plain,
( spl635_643
<=> ! [X0,X1] :
( c_Relation_Osym(X1,X0)
| hAPP(c_Relation_Oconverse(X1,X1),X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_643])]) ).
fof(f19170,plain,
! [X0,X1] :
( c_Relation_Osym(X1,X0)
| hAPP(c_Relation_Oconverse(X1,X1),X0) != X0 ),
inference(cnf_transformation,[],[f15026]) ).
fof(f15026,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,[],[f6769]) ).
fof(f6769,plain,
! [X0,X1] :
( c_Relation_Osym(X1,X0)
<=> hAPP(c_Relation_Oconverse(X1,X1),X0) = X0 ),
inference(rectify,[],[f4955]) ).
fof(f4955,axiom,
! [X98,X8] :
( c_Relation_Osym(X8,X98)
<=> hAPP(c_Relation_Oconverse(X8,X8),X98) = X98 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__conv__converse__eq) ).
fof(f32458,plain,
spl635_642,
inference(avatar_split_clause,[],[f19169,f32456]) ).
fof(f32456,plain,
( spl635_642
<=> ! [X0,X1] :
( hAPP(c_Relation_Oconverse(X1,X1),X0) = X0
| ~ c_Relation_Osym(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_642])]) ).
fof(f19169,plain,
! [X0,X1] :
( hAPP(c_Relation_Oconverse(X1,X1),X0) = X0
| ~ c_Relation_Osym(X1,X0) ),
inference(cnf_transformation,[],[f15026]) ).
fof(f32454,plain,
spl635_641,
inference(avatar_split_clause,[],[f19168,f32452]) ).
fof(f32452,plain,
( spl635_641
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| sK173(X0,X1) != sK174(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_641])]) ).
fof(f19168,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,X0)
| sK173(X0,X1) != sK174(X0,X1) ),
inference(cnf_transformation,[],[f15025]) ).
fof(f15025,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])],[f15023,f15024]) ).
fof(f15024,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(f15023,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,[],[f15022]) ).
fof(f15022,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,[],[f11318]) ).
fof(f11318,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,[],[f11317]) ).
fof(f11317,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,[],[f6768]) ).
fof(f6768,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,[],[f4946]) ).
fof(f4946,axiom,
! [X98,X8] :
( c_Relation_Oantisym(X8,X98)
<=> ! [X2,X45] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X2),X45)),X98))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X45),X2)),X98))
=> X2 = X45 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__def) ).
fof(f32450,plain,
spl635_640,
inference(avatar_split_clause,[],[f19114,f32448]) ).
fof(f19114,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(cnf_transformation,[],[f11311]) ).
fof(f11311,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ! [X2] : ~ hBOOL(hAPP(X1,X2)) ),
inference(ennf_transformation,[],[f6747]) ).
fof(f6747,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(X1,X2))
=> hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ),
inference(rectify,[],[f3662]) ).
fof(f3662,axiom,
! [X8,X196] :
( ? [X2] : hBOOL(hAPP(X196,X2))
=> hBOOL(hAPP(X196,c_Hilbert__Choice_OEps(X8,X196))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__some) ).
fof(f32446,plain,
( spl635_639
| ~ spl635_367
| ~ spl635_536 ),
inference(avatar_split_clause,[],[f32141,f31785,f31032,f32444]) ).
fof(f32444,plain,
( spl635_639
<=> ! [X2,X0,X1] :
( sP23(X0,X1,X2)
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_639])]) ).
fof(f31785,plain,
( spl635_536
<=> ! [X2,X0,X1] :
( sP23(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_536])]) ).
fof(f32141,plain,
( ! [X2,X0,X1] :
( sP23(X0,X1,X2)
| ~ class_Finite__Set_Ofinite(X0) )
| ~ spl635_367
| ~ spl635_536 ),
inference(resolution,[],[f31786,f31033]) ).
fof(f31786,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| sP23(X2,X1,X0) )
| ~ spl635_536 ),
inference(avatar_component_clause,[],[f31785]) ).
fof(f32442,plain,
spl635_638,
inference(avatar_split_clause,[],[f18810,f32440]) ).
fof(f32440,plain,
( spl635_638
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_638])]) ).
fof(f18810,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ),
inference(cnf_transformation,[],[f10963]) ).
fof(f10963,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ),
inference(ennf_transformation,[],[f6506]) ).
fof(f6506,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Nat_OSuc,X1)
=> X0 = X1 ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X12,X13] :
( hAPP(c_Nat_OSuc,X13) = hAPP(c_Nat_OSuc,X12)
=> X12 = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
fof(f32438,plain,
spl635_637,
inference(avatar_split_clause,[],[f18799,f32436]) ).
fof(f32436,plain,
( spl635_637
<=> ! [X0,X1] :
( sK147(X0,X1) != sK148(X0,X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_637])]) ).
fof(f18799,plain,
! [X0,X1] :
( sK147(X0,X1) != sK148(X0,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f14912]) ).
fof(f14912,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),sK147(X0,X1))),hAPP(c_List_Oset(X0),sK148(X0,X1)))
& sK147(X0,X1) != sK148(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),sK148(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1)))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),sK147(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK147,sK148])],[f14909,f14911,f14910]) ).
fof(f14910,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),sK147(X0,X1))),hAPP(c_List_Oset(X0),X3))
& sK147(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)),sK147(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f14911,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),sK147(X0,X1))),hAPP(c_List_Oset(X0),X3))
& sK147(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),sK147(X0,X1))),hAPP(c_List_Oset(X0),sK148(X0,X1)))
& sK147(X0,X1) != sK148(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),sK148(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f14909,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,[],[f14908]) ).
fof(f14908,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,[],[f14530]) ).
fof(f14530,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(f32434,plain,
spl635_636,
inference(avatar_split_clause,[],[f18786,f32432]) ).
fof(f32432,plain,
( spl635_636
<=> ! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_636])]) ).
fof(f18786,plain,
! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(cnf_transformation,[],[f10944]) ).
fof(f10944,plain,
! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(ennf_transformation,[],[f6490]) ).
fof(f6490,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
=> c_List_Oremdups(X1,X0) = X0 ),
inference(rectify,[],[f4512]) ).
fof(f4512,axiom,
! [X208,X5] :
( hBOOL(hAPP(c_List_Odistinct(X5),X208))
=> c_List_Oremdups(X5,X208) = X208 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remdups__id) ).
fof(f32430,plain,
spl635_635,
inference(avatar_split_clause,[],[f18760,f32428]) ).
fof(f32428,plain,
( spl635_635
<=> ! [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,[spl635_635])]) ).
fof(f18760,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,[],[f10918]) ).
fof(f10918,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,[],[f6469]) ).
fof(f6469,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,[],[f3500]) ).
fof(f3500,axiom,
! [X98,X8] :
( c_Wellfounded_Owf(X8,X98)
=> c_Wellfounded_Owf(tc_fun(X8,tc_HOL_Obool),c_Wellfounded_Omax__ext(X8,X98)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ext__wf) ).
fof(f32426,plain,
spl635_634,
inference(avatar_split_clause,[],[f18759,f32424]) ).
fof(f32424,plain,
( spl635_634
<=> ! [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,[spl635_634])]) ).
fof(f18759,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,[],[f10917]) ).
fof(f10917,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,[],[f6468]) ).
fof(f6468,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,[],[f3496]) ).
fof(f3496,axiom,
! [X98,X8] :
( c_Wellfounded_Owf(X8,X98)
=> c_Wellfounded_Owf(tc_fun(X8,tc_HOL_Obool),c_Wellfounded_Omin__ext(X8,X98)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__ext__wf) ).
fof(f32422,plain,
spl635_633,
inference(avatar_split_clause,[],[f18670,f32420]) ).
fof(f32420,plain,
( spl635_633
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_633])]) ).
fof(f18670,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10814]) ).
fof(f10814,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6396]) ).
fof(f6396,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0 ),
inference(rectify,[],[f2127]) ).
fof(f2127,axiom,
! [X13,X5] :
( class_Lattices_Olattice(X5)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X13),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Oidem) ).
fof(f32418,plain,
spl635_632,
inference(avatar_split_clause,[],[f18669,f32416]) ).
fof(f32416,plain,
( spl635_632
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_632])]) ).
fof(f18669,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10813]) ).
fof(f10813,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6395]) ).
fof(f6395,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0 ),
inference(rectify,[],[f2845]) ).
fof(f2845,axiom,
! [X13,X5] :
( class_Lattices_Olattice(X5)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X13),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Oidem) ).
fof(f32414,plain,
spl635_631,
inference(avatar_split_clause,[],[f18664,f32412]) ).
fof(f32412,plain,
( spl635_631
<=> ! [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,[spl635_631])]) ).
fof(f18664,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(cnf_transformation,[],[f10808]) ).
fof(f10808,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(ennf_transformation,[],[f6390]) ).
fof(f6390,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0 ),
inference(rectify,[],[f2861]) ).
fof(f2861,axiom,
! [X33,X5] :
( class_Lattices_Osemilattice__inf(X5)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X5),X33),X33) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf_Oidem) ).
fof(f32410,plain,
spl635_630,
inference(avatar_split_clause,[],[f18662,f32408]) ).
fof(f32408,plain,
( spl635_630
<=> ! [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,[spl635_630])]) ).
fof(f18662,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(cnf_transformation,[],[f10806]) ).
fof(f10806,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(ennf_transformation,[],[f6388]) ).
fof(f6388,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0 ),
inference(rectify,[],[f2111]) ).
fof(f2111,axiom,
! [X33,X5] :
( class_Lattices_Osemilattice__sup(X5)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X5),X33),X33) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup_Oidem) ).
fof(f32406,plain,
spl635_629,
inference(avatar_split_clause,[],[f18623,f32404]) ).
fof(f32404,plain,
( spl635_629
<=> ! [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,[spl635_629])]) ).
fof(f18623,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,[],[f10769]) ).
fof(f10769,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,[],[f10768]) ).
fof(f10768,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,[],[f6367]) ).
fof(f6367,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,[],[f4644]) ).
fof(f4644,axiom,
! [X46,X5] :
( class_Orderings_Olinorder(X5)
=> ( c_List_Olinorder__class_Osorted(X5,X46)
=> c_List_Olinorder__class_Osorted(X5,c_List_Oremdups(X5,X46)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__remdups) ).
fof(f32402,plain,
( spl635_628
| ~ spl635_385
| ~ spl635_530 ),
inference(avatar_split_clause,[],[f32113,f31761,f31111,f32400]) ).
fof(f32400,plain,
( spl635_628
<=> ! [X0,X1] : ~ sP8(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_628])]) ).
fof(f31111,plain,
( spl635_385
<=> ! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_385])]) ).
fof(f32113,plain,
( ! [X0,X1] : ~ sP8(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1)
| ~ spl635_385
| ~ spl635_530 ),
inference(resolution,[],[f31762,f31112]) ).
fof(f31112,plain,
( ! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0))
| ~ spl635_385 ),
inference(avatar_component_clause,[],[f31111]) ).
fof(f32398,plain,
spl635_627,
inference(avatar_split_clause,[],[f18609,f32396]) ).
fof(f32396,plain,
( spl635_627
<=> ! [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,[spl635_627])]) ).
fof(f18609,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,[],[f10754]) ).
fof(f10754,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,[],[f6353]) ).
fof(f6353,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,[],[f4632]) ).
fof(f4632,axiom,
! [X210,X8] :
( class_Orderings_Olinorder(X8)
=> c_List_Olinorder__class_Osorted(X8,c_List_Olinorder__class_Osort__key(X8,X8,c_COMBI(X8),X210)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__sort) ).
fof(f32394,plain,
spl635_626,
inference(avatar_split_clause,[],[f18607,f32392]) ).
fof(f32392,plain,
( spl635_626
<=> ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_626])]) ).
fof(f18607,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10752]) ).
fof(f10752,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6351]) ).
fof(f6351,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0 ),
inference(rectify,[],[f1634]) ).
fof(f1634,axiom,
! [X33,X5] :
( class_Orderings_Olinorder(X5)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X5),X33),X33) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Oinf_Oidem) ).
fof(f32390,plain,
spl635_625,
inference(avatar_split_clause,[],[f18605,f32388]) ).
fof(f32388,plain,
( spl635_625
<=> ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_625])]) ).
fof(f18605,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10750]) ).
fof(f10750,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6349]) ).
fof(f6349,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0 ),
inference(rectify,[],[f1744]) ).
fof(f1744,axiom,
! [X13,X5] :
( class_Orderings_Olinorder(X5)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X5),X13),X13) = X13 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Oidem) ).
fof(f32386,plain,
spl635_624,
inference(avatar_split_clause,[],[f18583,f32384]) ).
fof(f32384,plain,
( spl635_624
<=> ! [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,[spl635_624])]) ).
fof(f18583,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,[],[f10725]) ).
fof(f10725,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,[],[f6327]) ).
fof(f6327,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,[],[f1849]) ).
fof(f1849,axiom,
! [X33,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),c_Groups_Oone__class_Oone(X5)),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__dvd) ).
fof(f32382,plain,
spl635_623,
inference(avatar_split_clause,[],[f18582,f32380]) ).
fof(f32380,plain,
( spl635_623
<=> ! [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,[spl635_623])]) ).
fof(f18582,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,[],[f10724]) ).
fof(f10724,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,[],[f6326]) ).
fof(f6326,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,[],[f1843]) ).
fof(f1843,axiom,
! [X33,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X33),c_Groups_Ozero__class_Ozero(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__0__right) ).
fof(f32378,plain,
spl635_622,
inference(avatar_split_clause,[],[f18581,f32376]) ).
fof(f32376,plain,
( spl635_622
<=> ! [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,[spl635_622])]) ).
fof(f18581,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,[],[f10723]) ).
fof(f10723,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,[],[f6325]) ).
fof(f6325,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,[],[f910]) ).
fof(f910,axiom,
! [X33,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(X5,c_Groups_Ozero__class_Ozero(X5),X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__0) ).
fof(f32374,plain,
spl635_621,
inference(avatar_split_clause,[],[f18580,f32372]) ).
fof(f32372,plain,
( spl635_621
<=> ! [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,[spl635_621])]) ).
fof(f18580,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,[],[f10722]) ).
fof(f10722,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,[],[f6324]) ).
fof(f6324,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,[],[f953]) ).
fof(f953,axiom,
! [X33,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(X5,X33,c_Groups_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__1) ).
fof(f32370,plain,
spl635_620,
inference(avatar_split_clause,[],[f18551,f32368]) ).
fof(f32368,plain,
( spl635_620
<=> ! [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,[spl635_620])]) ).
fof(f18551,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,[],[f10693]) ).
fof(f10693,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,[],[f6297]) ).
fof(f6297,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,[],[f2322]) ).
fof(f2322,axiom,
! [X13,X5] :
( class_Orderings_Obot(X5)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),c_Orderings_Obot__class_Obot(X5)),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__least) ).
fof(f32366,plain,
spl635_619,
inference(avatar_split_clause,[],[f18510,f32364]) ).
fof(f18510,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,[],[f10644]) ).
fof(f10644,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,[],[f6258]) ).
fof(f6258,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,[],[f3145]) ).
fof(f3145,axiom,
! [X13,X5] :
( class_Orderings_Otop(X5)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X13),c_Orderings_Otop__class_Otop(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top__greatest) ).
fof(f32362,plain,
spl635_618,
inference(avatar_split_clause,[],[f18321,f32360]) ).
fof(f32360,plain,
( spl635_618
<=> ! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_618])]) ).
fof(f18321,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ),
inference(cnf_transformation,[],[f6114]) ).
fof(f6114,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ),
inference(rectify,[],[f5223]) ).
fof(f5223,axiom,
! [X129,X29] :
( hBOOL(X129)
| ~ hBOOL(X29)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X29),X129)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__3) ).
fof(f32358,plain,
( spl635_617
| ~ spl635_361
| ~ spl635_529 ),
inference(avatar_split_clause,[],[f32082,f31757,f31007,f32356]) ).
fof(f32356,plain,
( spl635_617
<=> ! [X0,X1] : sP8(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_617])]) ).
fof(f31007,plain,
( spl635_361
<=> ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_361])]) ).
fof(f32082,plain,
( ! [X0,X1] : sP8(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),X1)
| ~ spl635_361
| ~ spl635_529 ),
inference(resolution,[],[f31758,f31008]) ).
fof(f31008,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0))
| ~ spl635_361 ),
inference(avatar_component_clause,[],[f31007]) ).
fof(f32354,plain,
spl635_616,
inference(avatar_split_clause,[],[f18320,f32352]) ).
fof(f32352,plain,
( spl635_616
<=> ! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_616])]) ).
fof(f18320,plain,
! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ),
inference(cnf_transformation,[],[f6113]) ).
fof(f6113,plain,
! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ),
inference(rectify,[],[f5220]) ).
fof(f5220,axiom,
! [X129,X29] :
( hBOOL(X129)
| hBOOL(X29)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X29),X129)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__3) ).
fof(f32350,plain,
spl635_615,
inference(avatar_split_clause,[],[f18314,f32348]) ).
fof(f32348,plain,
( spl635_615
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_615])]) ).
fof(f18314,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6107]) ).
fof(f6107,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(rectify,[],[f5215]) ).
fof(f5215,axiom,
! [X129,X29] :
( hBOOL(hAPP(hAPP(c_fconj,X29),X129))
| ~ hBOOL(X129)
| ~ hBOOL(X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).
fof(f32346,plain,
spl635_614,
inference(avatar_split_clause,[],[f17904,f32344]) ).
fof(f32344,plain,
( spl635_614
<=> ! [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,[spl635_614])]) ).
fof(f17904,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,[],[f5756]) ).
fof(f5756,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,[],[f1054]) ).
fof(f1054,axiom,
! [X4,X24] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,X4)),X24)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).
fof(f32342,plain,
spl635_613,
inference(avatar_split_clause,[],[f17902,f32340]) ).
fof(f32340,plain,
( spl635_613
<=> ! [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,[spl635_613])]) ).
fof(f17902,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5754]) ).
fof(f5754,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f3218]) ).
fof(f3218,axiom,
! [X30,X8] : hBOOL(hAPP(hAPP(c_member(X8),X30),c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
fof(f32338,plain,
spl635_612,
inference(avatar_split_clause,[],[f17900,f32336]) ).
fof(f32336,plain,
( spl635_612
<=> ! [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,[spl635_612])]) ).
fof(f17900,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(cnf_transformation,[],[f5752]) ).
fof(f5752,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(rectify,[],[f2104]) ).
fof(f2104,axiom,
! [X39,X8] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X39),X39) = X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Un__absorb) ).
fof(f32334,plain,
spl635_611,
inference(avatar_split_clause,[],[f17899,f32332]) ).
fof(f32332,plain,
( spl635_611
<=> ! [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,[spl635_611])]) ).
fof(f17899,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(cnf_transformation,[],[f5751]) ).
fof(f5751,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(rectify,[],[f2866]) ).
fof(f2866,axiom,
! [X39,X8] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X39),X39) = X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int__absorb) ).
fof(f32330,plain,
spl635_610,
inference(avatar_split_clause,[],[f17898,f32328]) ).
fof(f32328,plain,
( spl635_610
<=> ! [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,[spl635_610])]) ).
fof(f17898,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,[],[f5750]) ).
fof(f5750,plain,
! [X0,X1] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X0)) = X0,
inference(rectify,[],[f3930]) ).
fof(f3930,axiom,
! [X39,X8] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X8,tc_HOL_Obool),hAPP(c_Set_OPow(X8),X39)) = X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Union__Pow__eq) ).
fof(f32326,plain,
spl635_609,
inference(avatar_split_clause,[],[f17897,f32324]) ).
fof(f32324,plain,
( spl635_609
<=> ! [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,[spl635_609])]) ).
fof(f17897,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5749]) ).
fof(f5749,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f4140]) ).
fof(f4140,axiom,
! [X4,X5] : c_List_Olist_ONil(X5) = hAPP(hAPP(c_List_Otake(X5),X4),c_List_Olist_ONil(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_take__Nil) ).
fof(f32322,plain,
spl635_608,
inference(avatar_split_clause,[],[f17896,f32320]) ).
fof(f32320,plain,
( spl635_608
<=> ! [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,[spl635_608])]) ).
fof(f17896,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Odrop(X1),X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5748]) ).
fof(f5748,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Odrop(X1),X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f4285]) ).
fof(f4285,axiom,
! [X4,X5] : c_List_Olist_ONil(X5) = hAPP(hAPP(c_List_Odrop(X5),X4),c_List_Olist_ONil(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__Nil) ).
fof(f32318,plain,
spl635_607,
inference(avatar_split_clause,[],[f17892,f32316]) ).
fof(f32316,plain,
( spl635_607
<=> ! [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,[spl635_607])]) ).
fof(f17892,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5744]) ).
fof(f5744,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f2428]) ).
fof(f2428,axiom,
! [X23,X8] : ~ hBOOL(hAPP(hAPP(c_member(X8),X23),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_empty__iff) ).
fof(f32314,plain,
( spl635_606
| ~ spl635_367
| ~ spl635_529 ),
inference(avatar_split_clause,[],[f32081,f31757,f31032,f32312]) ).
fof(f32312,plain,
( spl635_606
<=> ! [X0,X1] :
( sP8(c_Finite__Set_Ofinite(X0),X1)
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_606])]) ).
fof(f32081,plain,
( ! [X0,X1] :
( sP8(c_Finite__Set_Ofinite(X0),X1)
| ~ class_Finite__Set_Ofinite(X0) )
| ~ spl635_367
| ~ spl635_529 ),
inference(resolution,[],[f31758,f31033]) ).
fof(f32310,plain,
spl635_605,
inference(avatar_split_clause,[],[f17682,f32308]) ).
fof(f32308,plain,
( spl635_605
<=> ! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK94(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_605])]) ).
fof(f17682,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK94(X0)),X0)) ),
inference(cnf_transformation,[],[f14698]) ).
fof(f32306,plain,
spl635_604,
inference(avatar_split_clause,[],[f17603,f32304]) ).
fof(f32304,plain,
( spl635_604
<=> ! [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,[spl635_604])]) ).
fof(f17603,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,[],[f10363]) ).
fof(f10363,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,[],[f5528]) ).
fof(f5528,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,[],[f364]) ).
fof(f364,axiom,
! [X5] :
( class_Rings_Osemiring__1(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X5),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__nat__1) ).
fof(f32302,plain,
spl635_603,
inference(avatar_split_clause,[],[f17599,f32300]) ).
fof(f32300,plain,
( spl635_603
<=> ! [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,[spl635_603])]) ).
fof(f17599,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,[],[f10359]) ).
fof(f10359,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,[],[f5524]) ).
fof(f5524,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,[],[f4175]) ).
fof(f4175,axiom,
! [X5] :
( class_Groups_Omonoid__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(c_List_Omonoid__add__class_Olistsum(X5),c_List_Olist_ONil(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsum__simps_I1_J) ).
fof(f32298,plain,
spl635_602,
inference(avatar_split_clause,[],[f17589,f32296]) ).
fof(f32296,plain,
( spl635_602
<=> ! [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,[spl635_602])]) ).
fof(f17589,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,[],[f10349]) ).
fof(f10349,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,[],[f5514]) ).
fof(f5514,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,[],[f3183]) ).
fof(f3183,axiom,
! [X5] :
( class_Lattices_Oboolean__algebra(X5)
=> c_Orderings_Obot__class_Obot(X5) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Orderings_Otop__class_Otop(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__top__eq) ).
fof(f32294,plain,
spl635_601,
inference(avatar_split_clause,[],[f17588,f32292]) ).
fof(f32292,plain,
( spl635_601
<=> ! [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,[spl635_601])]) ).
fof(f17588,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,[],[f10348]) ).
fof(f10348,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,[],[f5513]) ).
fof(f5513,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,[],[f3184]) ).
fof(f3184,axiom,
! [X5] :
( class_Lattices_Oboolean__algebra(X5)
=> c_Orderings_Otop__class_Otop(X5) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Orderings_Obot__class_Obot(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_compl__bot__eq) ).
fof(f32290,plain,
spl635_600,
inference(avatar_split_clause,[],[f17576,f32288]) ).
fof(f32288,plain,
( spl635_600
<=> ! [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,[spl635_600])]) ).
fof(f17576,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,[],[f10336]) ).
fof(f10336,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,[],[f5501]) ).
fof(f5501,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,[],[f1048]) ).
fof(f1048,axiom,
! [X5] :
( class_Rings_Olinordered__idom(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(c_Groups_Oabs__class_Oabs(X5),c_Groups_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__one) ).
fof(f32286,plain,
spl635_599,
inference(avatar_split_clause,[],[f17575,f32284]) ).
fof(f17575,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,[],[f10335]) ).
fof(f10335,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,[],[f5500]) ).
fof(f5500,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,[],[f1042]) ).
fof(f1042,axiom,
! [X5] :
( class_Groups_Oordered__ab__group__add__abs(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Groups_Oabs__class_Oabs(X5),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_abs__zero) ).
fof(f32282,plain,
spl635_598,
inference(avatar_split_clause,[],[f17571,f32280]) ).
fof(f32280,plain,
( spl635_598
<=> ! [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,[spl635_598])]) ).
fof(f17571,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,[],[f10331]) ).
fof(f10331,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,[],[f5496]) ).
fof(f5496,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,[],[f367]) ).
fof(f367,axiom,
! [X5] :
( class_Rings_Oring__1(X5)
=> c_Groups_Oone__class_Oone(X5) = hAPP(c_Int_Oring__1__class_Oof__int(X5),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__1) ).
fof(f32278,plain,
spl635_597,
inference(avatar_split_clause,[],[f17570,f32276]) ).
fof(f32276,plain,
( spl635_597
<=> ! [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,[spl635_597])]) ).
fof(f17570,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,[],[f10330]) ).
fof(f10330,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,[],[f5495]) ).
fof(f5495,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,[],[f571]) ).
fof(f571,axiom,
! [X5] :
( class_Groups_Ogroup__add(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Groups_Ouminus__class_Ouminus(X5),c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__zero) ).
fof(f32274,plain,
spl635_596,
inference(avatar_split_clause,[],[f17419,f32272]) ).
fof(f32272,plain,
( spl635_596
<=> ! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_596])]) ).
fof(f17419,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)),
inference(cnf_transformation,[],[f5357]) ).
fof(f5357,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)),
inference(rectify,[],[f4079]) ).
fof(f4079,axiom,
! [X8] : hAPP(c_List_Omap(X8,X8),c_COMBI(X8)) = c_Fun_Oid(tc_List_Olist(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omap_Oidentity) ).
fof(f32267,plain,
spl635_595,
inference(avatar_split_clause,[],[f17418,f32265]) ).
fof(f32265,plain,
( spl635_595
<=> ! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_595])]) ).
fof(f17418,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)),
inference(cnf_transformation,[],[f5356]) ).
fof(f5356,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)),
inference(rectify,[],[f4078]) ).
fof(f4078,axiom,
! [X8] : hAPP(c_List_Omap(X8,X8),c_Fun_Oid(X8)) = c_Fun_Oid(tc_List_Olist(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_List_Omap_Oid) ).
fof(f32263,plain,
spl635_594,
inference(avatar_split_clause,[],[f17415,f32261]) ).
fof(f32261,plain,
( spl635_594
<=> ! [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,[spl635_594])]) ).
fof(f17415,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,[],[f5353]) ).
fof(f5353,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,[],[f4786]) ).
fof(f4786,axiom,
! [X49] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,X49) = c_Lazy__Sequence_Osmall__lazy_H(X49,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X49)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_small__lazy__int__def) ).
fof(f32259,plain,
spl635_593,
inference(avatar_split_clause,[],[f17401,f32257]) ).
fof(f17401,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,[],[f5339]) ).
fof(f5339,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,[],[f4049]) ).
fof(f4049,axiom,
! [X8] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X8)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X8),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_infinite__UNIV__listI) ).
fof(f32255,plain,
spl635_592,
inference(avatar_split_clause,[],[f17256,f32252]) ).
fof(f32252,plain,
( spl635_592
<=> 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,[spl635_592])]) ).
fof(f17256,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,[],[f3226]) ).
fof(f3226,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',fact_type__definition__Integ) ).
fof(f32250,plain,
spl635_591,
inference(avatar_split_clause,[],[f17251,f32247]) ).
fof(f32247,plain,
( spl635_591
<=> 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,[spl635_591])]) ).
fof(f17251,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,[],[f3623]) ).
fof(f3623,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',fact_number__of__code__numeral__def) ).
fof(f32245,plain,
spl635_590,
inference(avatar_split_clause,[],[f17250,f32242]) ).
fof(f32242,plain,
( spl635_590
<=> 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,[spl635_590])]) ).
fof(f17250,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,[],[f3146]) ).
fof(f3146,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',fact_card__UNIV__unit) ).
fof(f32240,plain,
spl635_589,
inference(avatar_split_clause,[],[f17248,f32237]) ).
fof(f32237,plain,
( spl635_589
<=> 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,[spl635_589])]) ).
fof(f17248,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,[],[f3624]) ).
fof(f3624,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',fact_int__of__def) ).
fof(f32214,plain,
( ~ spl635_588
| spl635_321
| ~ spl635_564 ),
inference(avatar_split_clause,[],[f32202,f31901,f30834,f32211]) ).
fof(f32211,plain,
( spl635_588
<=> c_Nat__Transfer_Ois__nat(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_588])]) ).
fof(f30834,plain,
( spl635_321
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_321])]) ).
fof(f32202,plain,
( ~ c_Nat__Transfer_Ois__nat(c_Int_OMin)
| spl635_321
| ~ spl635_564 ),
inference(resolution,[],[f31902,f30836]) ).
fof(f30836,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| spl635_321 ),
inference(avatar_component_clause,[],[f30834]) ).
fof(f32064,plain,
( ~ spl635_131
| ~ spl635_264
| spl635_587 ),
inference(avatar_split_clause,[],[f32056,f32020,f30574,f29946]) ).
fof(f29946,plain,
( spl635_131
<=> class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_131])]) ).
fof(f30574,plain,
( spl635_264
<=> ! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_264])]) ).
fof(f32020,plain,
( spl635_587
<=> c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_587])]) ).
fof(f32056,plain,
( ~ class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral)
| ~ spl635_264
| spl635_587 ),
inference(resolution,[],[f32021,f30575]) ).
fof(f30575,plain,
( ! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) )
| ~ spl635_264 ),
inference(avatar_component_clause,[],[f30574]) ).
fof(f32021,plain,
( ~ c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| spl635_587 ),
inference(avatar_component_clause,[],[f32020]) ).
fof(f32023,plain,
( ~ spl635_586
| spl635_587
| ~ spl635_327
| ~ spl635_407 ),
inference(avatar_split_clause,[],[f31519,f31222,f30864,f32020,f32016]) ).
fof(f32016,plain,
( spl635_586
<=> class_Int_Onumber__ring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_586])]) ).
fof(f30864,plain,
( spl635_327
<=> 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,[spl635_327])]) ).
fof(f31222,plain,
( spl635_407
<=> ! [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,[spl635_407])]) ).
fof(f31519,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)
| ~ spl635_327
| ~ spl635_407 ),
inference(superposition,[],[f31223,f30866]) ).
fof(f30866,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)
| ~ spl635_327 ),
inference(avatar_component_clause,[],[f30864]) ).
fof(f31223,plain,
( ! [X0] :
( c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) )
| ~ spl635_407 ),
inference(avatar_component_clause,[],[f31222]) ).
fof(f31995,plain,
( spl635_585
| ~ spl635_241
| ~ spl635_396 ),
inference(avatar_split_clause,[],[f31510,f31178,f30473,f31993]) ).
fof(f31993,plain,
( spl635_585
<=> ! [X0] : sP6(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_585])]) ).
fof(f30473,plain,
( spl635_241
<=> ! [X0] : sP6(hAPP(c_Int_Onat,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_241])]) ).
fof(f31178,plain,
( spl635_396
<=> ! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_396])]) ).
fof(f31510,plain,
( ! [X0] : sP6(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ spl635_241
| ~ spl635_396 ),
inference(superposition,[],[f30474,f31179]) ).
fof(f31179,plain,
( ! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0
| ~ spl635_396 ),
inference(avatar_component_clause,[],[f31178]) ).
fof(f30474,plain,
( ! [X0] : sP6(hAPP(c_Int_Onat,X0),X0)
| ~ spl635_241 ),
inference(avatar_component_clause,[],[f30473]) ).
fof(f31985,plain,
spl635_584,
inference(avatar_split_clause,[],[f28986,f31983]) ).
fof(f31983,plain,
( spl635_584
<=> ! [X2,X1,X3] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(c_fequal,X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_584])]) ).
fof(f28986,plain,
! [X2,X3,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(c_fequal,X1)),X1)),
inference(forward_demodulation,[],[f25762,f26500]) ).
fof(f25762,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,[],[f22830]) ).
fof(f22830,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,[],[f16454]) ).
fof(f31981,plain,
spl635_583,
inference(avatar_split_clause,[],[f27971,f31979]) ).
fof(f31979,plain,
( spl635_583
<=> ! [X0,X1] : c_List_Olast(X1,c_List_Oinsert(X1,X0,c_List_Olist_ONil(X1))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_583])]) ).
fof(f27971,plain,
! [X0,X1] : c_List_Olast(X1,c_List_Oinsert(X1,X0,c_List_Olist_ONil(X1))) = X0,
inference(forward_demodulation,[],[f25468,f17957]) ).
fof(f25468,plain,
! [X0,X1] : c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1))) = X0,
inference(equality_resolution,[],[f19932]) ).
fof(f19932,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,[],[f11348]) ).
fof(f11348,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,[],[f7225]) ).
fof(f7225,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,[],[f4395]) ).
fof(f4395,axiom,
! [X13,X5,X208] :
( ( c_List_Olist_ONil(X5) != X208
=> c_List_Olast(X5,X208) = c_List_Olast(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X13),X208)) )
& ( c_List_Olist_ONil(X5) = X208
=> c_List_Olast(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X13),X208)) = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_last_Osimps) ).
fof(f31977,plain,
spl635_582,
inference(avatar_split_clause,[],[f27869,f31975]) ).
fof(f31975,plain,
( spl635_582
<=> ! [X2,X0,X1] : hAPP(c_Finite__Set_Ofold1(X2,X1),hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_582])]) ).
fof(f27869,plain,
! [X2,X0,X1] : hAPP(c_Finite__Set_Ofold1(X2,X1),hAPP(c_fequal,X0)) = X0,
inference(forward_demodulation,[],[f19709,f26500]) ).
fof(f19709,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,[],[f7004]) ).
fof(f7004,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,[],[f3289]) ).
fof(f3289,axiom,
! [X17,X1,X8] : hAPP(c_Finite__Set_Ofold1(X8,X1),hAPP(hAPP(c_Set_Oinsert(X8),X17),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))) = X17,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold1__singleton) ).
fof(f31973,plain,
( spl635_581
| ~ spl635_242
| ~ spl635_396 ),
inference(avatar_split_clause,[],[f31509,f31178,f30477,f31971]) ).
fof(f31971,plain,
( spl635_581
<=> ! [X0] : sP7(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_581])]) ).
fof(f30477,plain,
( spl635_242
<=> ! [X1] : sP7(hAPP(c_Int_Onat,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_242])]) ).
fof(f31509,plain,
( ! [X0] : sP7(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ spl635_242
| ~ spl635_396 ),
inference(superposition,[],[f30478,f31179]) ).
fof(f30478,plain,
( ! [X1] : sP7(hAPP(c_Int_Onat,X1),X1)
| ~ spl635_242 ),
inference(avatar_component_clause,[],[f30477]) ).
fof(f31969,plain,
spl635_580,
inference(avatar_split_clause,[],[f27860,f31967]) ).
fof(f31967,plain,
( spl635_580
<=> ! [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,[spl635_580])]) ).
fof(f27860,plain,
! [X2,X0,X1] : hAPP(c_Nat_Onat_Onat__rec(X2,X1,X0),c_HOL_Obool_Obool__size(c_fTrue)) = X1,
inference(forward_demodulation,[],[f19667,f17187]) ).
fof(f19667,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,[],[f6962]) ).
fof(f6962,plain,
! [X0,X1,X2] : hAPP(c_Nat_Onat_Onat__rec(X2,X1,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rectify,[],[f18]) ).
fof(f18,axiom,
! [X20,X21,X8] : hAPP(c_Nat_Onat_Onat__rec(X8,X21,X20),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__rec__0) ).
fof(f31965,plain,
spl635_579,
inference(avatar_split_clause,[],[f27746,f31962]) ).
fof(f31962,plain,
( spl635_579
<=> 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,[spl635_579])]) ).
fof(f27746,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,[],[f27745,f26637]) ).
fof(f27745,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,[],[f25457,f17187]) ).
fof(f25457,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,[],[f19548]) ).
fof(f19548,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,[],[f15284]) ).
fof(f15284,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,[],[f15283]) ).
fof(f15283,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,[],[f6907]) ).
fof(f6907,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,[],[f246]) ).
fof(f246,axiom,
! [X15,X30] :
( 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),X30),X15)))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X15
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X30)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(f31960,plain,
spl635_578,
inference(avatar_split_clause,[],[f27001,f31958]) ).
fof(f31958,plain,
( spl635_578
<=> ! [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,[spl635_578])]) ).
fof(f27001,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(forward_demodulation,[],[f18672,f26500]) ).
fof(f18672,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,[],[f10816]) ).
fof(f10816,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,[],[f6398]) ).
fof(f6398,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,[],[f2591]) ).
fof(f2591,axiom,
! [X30,X8] :
( class_Lattices_Olattice(X8)
=> c_Big__Operators_Olattice__class_OSup__fin(X8,hAPP(hAPP(c_Set_Oinsert(X8),X30),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__fin_Osingleton) ).
fof(f31956,plain,
spl635_577,
inference(avatar_split_clause,[],[f27000,f31954]) ).
fof(f31954,plain,
( spl635_577
<=> ! [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,[spl635_577])]) ).
fof(f27000,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(forward_demodulation,[],[f18671,f26500]) ).
fof(f18671,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,[],[f10815]) ).
fof(f10815,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,[],[f6397]) ).
fof(f6397,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,[],[f3033]) ).
fof(f3033,axiom,
! [X30,X8] :
( class_Lattices_Olattice(X8)
=> c_Big__Operators_Olattice__class_OInf__fin(X8,hAPP(hAPP(c_Set_Oinsert(X8),X30),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__fin_Osingleton) ).
fof(f31952,plain,
spl635_576,
inference(avatar_split_clause,[],[f26991,f31950]) ).
fof(f31950,plain,
( spl635_576
<=> ! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_576])]) ).
fof(f26991,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(forward_demodulation,[],[f18612,f26500]) ).
fof(f18612,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,[],[f10757]) ).
fof(f10757,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,[],[f6356]) ).
fof(f6356,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,[],[f2628]) ).
fof(f2628,axiom,
! [X30,X8] :
( class_Orderings_Olinorder(X8)
=> c_Big__Operators_Olinorder__class_OMin(X8,hAPP(hAPP(c_Set_Oinsert(X8),X30),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Min_Osingleton) ).
fof(f31948,plain,
spl635_575,
inference(avatar_split_clause,[],[f26990,f31946]) ).
fof(f31946,plain,
( spl635_575
<=> ! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_575])]) ).
fof(f26990,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(forward_demodulation,[],[f18611,f26500]) ).
fof(f18611,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,[],[f10756]) ).
fof(f10756,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,[],[f6355]) ).
fof(f6355,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,[],[f2590]) ).
fof(f2590,axiom,
! [X30,X8] :
( class_Orderings_Olinorder(X8)
=> c_Big__Operators_Olinorder__class_OMax(X8,hAPP(hAPP(c_Set_Oinsert(X8),X30),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))) = X30 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Max_Osingleton) ).
fof(f31944,plain,
spl635_574,
inference(avatar_split_clause,[],[f26989,f31942]) ).
fof(f31942,plain,
( spl635_574
<=> ! [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,[spl635_574])]) ).
fof(f26989,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,[],[f18610,f17957]) ).
fof(f18610,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,[],[f10755]) ).
fof(f10755,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,[],[f6354]) ).
fof(f6354,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,[],[f4630]) ).
fof(f4630,axiom,
! [X13,X5] :
( class_Orderings_Olinorder(X5)
=> c_List_Olinorder__class_Osorted(X5,hAPP(hAPP(c_List_Olist_OCons(X5),X13),c_List_Olist_ONil(X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__single) ).
fof(f31940,plain,
spl635_573,
inference(avatar_split_clause,[],[f26961,f31938]) ).
fof(f31938,plain,
( spl635_573
<=> ! [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,[spl635_573])]) ).
fof(f26961,plain,
! [X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(forward_demodulation,[],[f18528,f26500]) ).
fof(f18528,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,[],[f10662]) ).
fof(f10662,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,[],[f6276]) ).
fof(f6276,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,[],[f3946]) ).
fof(f3946,axiom,
! [X17,X8] :
( class_Complete__Lattice_Ocomplete__lattice(X8)
=> c_Complete__Lattice_OSup__class_OSup(X8,hAPP(hAPP(c_Set_Oinsert(X8),X17),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))) = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Sup__singleton) ).
fof(f31936,plain,
spl635_572,
inference(avatar_split_clause,[],[f26960,f31934]) ).
fof(f31934,plain,
( spl635_572
<=> ! [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,[spl635_572])]) ).
fof(f26960,plain,
! [X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(forward_demodulation,[],[f18527,f26500]) ).
fof(f18527,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,[],[f10661]) ).
fof(f10661,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,[],[f6275]) ).
fof(f6275,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,[],[f3901]) ).
fof(f3901,axiom,
! [X17,X8] :
( class_Complete__Lattice_Ocomplete__lattice(X8)
=> c_Complete__Lattice_OInf__class_OInf(X8,hAPP(hAPP(c_Set_Oinsert(X8),X17),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))) = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Inf__singleton) ).
fof(f31932,plain,
spl635_571,
inference(avatar_split_clause,[],[f26853,f31930]) ).
fof(f31930,plain,
( spl635_571
<=> ! [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,[spl635_571])]) ).
fof(f26853,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,[],[f25316,f17176]) ).
fof(f25316,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,[],[f18349]) ).
fof(f18349,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,[],[f14797]) ).
fof(f31928,plain,
( spl635_570
| ~ spl635_222
| ~ spl635_270 ),
inference(avatar_split_clause,[],[f30790,f30598,f30391,f31926]) ).
fof(f31926,plain,
( spl635_570
<=> ! [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,[spl635_570])]) ).
fof(f30391,plain,
( spl635_222
<=> c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_222])]) ).
fof(f30598,plain,
( spl635_270
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_270])]) ).
fof(f30790,plain,
( ! [X0] : c_Fun_Oinj__on(tc_Int_Oint,tc_Int_Oint,c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)
| ~ spl635_222
| ~ spl635_270 ),
inference(superposition,[],[f30599,f30393]) ).
fof(f30393,plain,
( c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint)
| ~ spl635_222 ),
inference(avatar_component_clause,[],[f30391]) ).
fof(f30599,plain,
( ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0)
| ~ spl635_270 ),
inference(avatar_component_clause,[],[f30598]) ).
fof(f31924,plain,
spl635_569,
inference(avatar_split_clause,[],[f26481,f31922]) ).
fof(f31922,plain,
( spl635_569
<=> ! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_569])]) ).
fof(f26481,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f17877,f17187]) ).
fof(f17877,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f5729]) ).
fof(f5729,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f4281]) ).
fof(f4281,axiom,
! [X208,X5] : hAPP(hAPP(c_List_Odrop(X5),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X208) = X208,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_drop__0) ).
fof(f31920,plain,
spl635_568,
inference(avatar_split_clause,[],[f26480,f31918]) ).
fof(f31918,plain,
( spl635_568
<=> ! [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,[spl635_568])]) ).
fof(f26480,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,[],[f17870,f17187]) ).
fof(f17870,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,[],[f5722]) ).
fof(f5722,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,[],[f4891]) ).
fof(f4891,axiom,
! [X133,X8] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(X8,X133),c_Lazy__Sequence_Olazy__sequence_OEmpty(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osize_I1_J) ).
fof(f31916,plain,
spl635_567,
inference(avatar_split_clause,[],[f26395,f31914]) ).
fof(f31914,plain,
( spl635_567
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_567])]) ).
fof(f26395,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f26394,f17327]) ).
fof(f26394,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,[],[f17723,f17327]) ).
fof(f17723,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,[],[f14728]) ).
fof(f14728,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,[],[f5620]) ).
fof(f5620,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,[],[f1269]) ).
fof(f1269,axiom,
! [X52] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X52))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X52))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__number__of__Bit0) ).
fof(f31912,plain,
spl635_566,
inference(avatar_split_clause,[],[f26393,f31910]) ).
fof(f31910,plain,
( spl635_566
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_566])]) ).
fof(f26393,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0))) ),
inference(forward_demodulation,[],[f26392,f17327]) ).
fof(f26392,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,[],[f17724,f17327]) ).
fof(f17724,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,[],[f14728]) ).
fof(f31908,plain,
~ spl635_565,
inference(avatar_split_clause,[],[f26362,f31905]) ).
fof(f31905,plain,
( spl635_565
<=> 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,[spl635_565])]) ).
fof(f26362,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,[],[f26361,f25943]) ).
fof(f26361,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,[],[f25283,f17187]) ).
fof(f25283,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,[],[f17709]) ).
fof(f17709,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,[],[f14718]) ).
fof(f31903,plain,
spl635_564,
inference(avatar_split_clause,[],[f26354,f31901]) ).
fof(f26354,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,[],[f17684,f17176]) ).
fof(f17684,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,[],[f14699]) ).
fof(f14699,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,[],[f5602]) ).
fof(f5602,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,[],[f1422]) ).
fof(f1422,axiom,
! [X30] :
( c_Nat__Transfer_Ois__nat(X30)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_is__nat__def) ).
fof(f31899,plain,
spl635_563,
inference(avatar_split_clause,[],[f26353,f31897]) ).
fof(f26353,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,[],[f17685,f17176]) ).
fof(f17685,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,[],[f14699]) ).
fof(f31895,plain,
spl635_562,
inference(avatar_split_clause,[],[f26228,f31893]) ).
fof(f31893,plain,
( spl635_562
<=> ! [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,[spl635_562])]) ).
fof(f26228,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,[],[f17572,f17176]) ).
fof(f17572,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,[],[f10332]) ).
fof(f10332,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,[],[f5497]) ).
fof(f5497,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,[],[f341]) ).
fof(f341,axiom,
! [X5] :
( class_Rings_Oring__1(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Int_Oring__1__class_Oof__int(X5),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__0) ).
fof(f31891,plain,
spl635_561,
inference(avatar_split_clause,[],[f26089,f31889]) ).
fof(f31889,plain,
( spl635_561
<=> ! [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,[spl635_561])]) ).
fof(f26089,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,[],[f26088,f25953]) ).
fof(f26088,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,[],[f17442,f17187]) ).
fof(f17442,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,[],[f5380]) ).
fof(f5380,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,[],[f955]) ).
fof(f955,axiom,
! [X24] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X24),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X24,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__1) ).
fof(f31887,plain,
spl635_560,
inference(avatar_split_clause,[],[f26064,f31885]) ).
fof(f31885,plain,
( spl635_560
<=> ! [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,[spl635_560])]) ).
fof(f26064,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f17397,f17187]) ).
fof(f17397,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,[],[f5335]) ).
fof(f5335,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f640]) ).
fof(f640,axiom,
! [X4] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(f31883,plain,
spl635_559,
inference(avatar_split_clause,[],[f26062,f31881]) ).
fof(f31881,plain,
( spl635_559
<=> ! [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,[spl635_559])]) ).
fof(f26062,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f17395,f17187]) ).
fof(f17395,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,[],[f5333]) ).
fof(f5333,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f1709]) ).
fof(f1709,axiom,
! [X4] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__0L) ).
fof(f31879,plain,
spl635_558,
inference(avatar_split_clause,[],[f26061,f31877]) ).
fof(f31877,plain,
( spl635_558
<=> ! [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,[spl635_558])]) ).
fof(f26061,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17392,f17187]) ).
fof(f17392,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,[],[f5330]) ).
fof(f5330,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f639]) ).
fof(f639,axiom,
! [X24] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X24,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(f31875,plain,
spl635_557,
inference(avatar_split_clause,[],[f26059,f31873]) ).
fof(f31873,plain,
( spl635_557
<=> ! [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,[spl635_557])]) ).
fof(f26059,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17390,f17187]) ).
fof(f17390,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,[],[f5328]) ).
fof(f5328,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f616]) ).
fof(f616,axiom,
! [X24] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X24,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(f31871,plain,
spl635_556,
inference(avatar_split_clause,[],[f26058,f31869]) ).
fof(f31869,plain,
( spl635_556
<=> ! [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,[spl635_556])]) ).
fof(f26058,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17389,f17187]) ).
fof(f17389,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,[],[f5327]) ).
fof(f5327,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f1708]) ).
fof(f1708,axiom,
! [X4] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__0R) ).
fof(f31867,plain,
spl635_555,
inference(avatar_split_clause,[],[f26056,f31865]) ).
fof(f31865,plain,
( spl635_555
<=> ! [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,[spl635_555])]) ).
fof(f26056,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0),
inference(forward_demodulation,[],[f17378,f17187]) ).
fof(f17378,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,[],[f5316]) ).
fof(f5316,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0),
inference(rectify,[],[f615]) ).
fof(f615,axiom,
! [X24] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X24),X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(f31863,plain,
spl635_554,
inference(avatar_split_clause,[],[f26055,f31861]) ).
fof(f31861,plain,
( spl635_554
<=> ! [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,[spl635_554])]) ).
fof(f26055,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,[],[f17377,f17187]) ).
fof(f17377,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,[],[f5315]) ).
fof(f5315,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,[],[f4131]) ).
fof(f4131,axiom,
! [X5] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X5)),c_List_Olist_ONil(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osize_I3_J) ).
fof(f31859,plain,
spl635_553,
inference(avatar_split_clause,[],[f26054,f31857]) ).
fof(f31857,plain,
( spl635_553
<=> ! [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,[spl635_553])]) ).
fof(f26054,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,[],[f17376,f17187]) ).
fof(f17376,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,[],[f5314]) ).
fof(f5314,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,[],[f4890]) ).
fof(f4890,axiom,
! [X5] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(X5)),c_Lazy__Sequence_Olazy__sequence_OEmpty(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osize_I3_J) ).
fof(f31854,plain,
spl635_552,
inference(avatar_split_clause,[],[f25955,f31851]) ).
fof(f31851,plain,
( spl635_552
<=> 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,[spl635_552])]) ).
fof(f25955,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,[],[f25954,f25942]) ).
fof(f25954,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,[],[f24211,f17174]) ).
fof(f24211,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,[],[f17218,f24179]) ).
fof(f17218,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,[],[f1352]) ).
fof(f1352,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',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J) ).
fof(f31849,plain,
spl635_551,
inference(avatar_split_clause,[],[f25740,f31847]) ).
fof(f31847,plain,
( spl635_551
<=> ! [X2,X1,X3] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_551])]) ).
fof(f25740,plain,
! [X2,X3,X1] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X2)),
inference(equality_resolution,[],[f22693]) ).
fof(f22693,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
| X0 != X2 ),
inference(cnf_transformation,[],[f16361]) ).
fof(f31845,plain,
spl635_550,
inference(avatar_split_clause,[],[f25625,f31843]) ).
fof(f31843,plain,
( spl635_550
<=> ! [X2,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_550])]) ).
fof(f25625,plain,
! [X2,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X1)),
inference(equality_resolution,[],[f21439]) ).
fof(f21439,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,[],[f15953]) ).
fof(f15953,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,[],[f15952]) ).
fof(f15952,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,[],[f8217]) ).
fof(f8217,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,[],[f304]) ).
fof(f304,axiom,
! [X38,X39,X8] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8,tc_HOL_Obool)),X39),X38))
<=> ( X38 != X39
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X39),X38)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_psubset__eq) ).
fof(f31841,plain,
( ~ spl635_133
| spl635_549
| ~ spl635_225
| ~ spl635_264 ),
inference(avatar_split_clause,[],[f30788,f30574,f30406,f31838,f29956]) ).
fof(f29956,plain,
( spl635_133
<=> class_Rings_Osemiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_133])]) ).
fof(f31838,plain,
( spl635_549
<=> c_Int_Oiszero(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_549])]) ).
fof(f30406,plain,
( spl635_225
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_225])]) ).
fof(f30788,plain,
( c_Int_Oiszero(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue))
| ~ class_Rings_Osemiring__1(tc_Nat_Onat)
| ~ spl635_225
| ~ spl635_264 ),
inference(superposition,[],[f30575,f30408]) ).
fof(f30408,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue)
| ~ spl635_225 ),
inference(avatar_component_clause,[],[f30406]) ).
fof(f31836,plain,
spl635_548,
inference(avatar_split_clause,[],[f25624,f31834]) ).
fof(f31834,plain,
( spl635_548
<=> ! [X2,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_548])]) ).
fof(f25624,plain,
! [X2,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X1))),
inference(equality_resolution,[],[f21437]) ).
fof(f21437,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
| X0 != X1 ),
inference(cnf_transformation,[],[f15951]) ).
fof(f15951,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,[],[f8216]) ).
fof(f8216,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
<=> X0 = X1 ),
inference(rectify,[],[f2451]) ).
fof(f2451,axiom,
! [X35,X30,X8] :
( hBOOL(hAPP(hAPP(c_member(X8),X30),hAPP(c_fequal,X35)))
<=> X30 = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(f31832,plain,
spl635_547,
inference(avatar_split_clause,[],[f25529,f31830]) ).
fof(f31830,plain,
( spl635_547
<=> ! [X2,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_547])]) ).
fof(f25529,plain,
! [X2,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f20620]) ).
fof(f20620,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,[],[f15526]) ).
fof(f15526,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,[],[f15525]) ).
fof(f15525,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,[],[f12122]) ).
fof(f12122,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,[],[f7771]) ).
fof(f7771,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,[],[f100]) ).
fof(f100,axiom,
! [X35,X30,X8] :
( class_Orderings_Oorder(X8)
=> ( X30 = X35
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X35),X30))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X30),X35)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(f31828,plain,
spl635_546,
inference(avatar_split_clause,[],[f25525,f31826]) ).
fof(f31826,plain,
( spl635_546
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_546])]) ).
fof(f25525,plain,
! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f20604]) ).
fof(f20604,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f12095]) ).
fof(f12095,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f12094]) ).
fof(f12094,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f7757]) ).
fof(f7757,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
=> X0 != X1 ) ),
inference(rectify,[],[f77]) ).
fof(f77,axiom,
! [X12,X13,X5] :
( class_Orderings_Oorder(X5)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X13),X12))
=> X12 != X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__imp__not__eq2) ).
fof(f31824,plain,
spl635_545,
inference(avatar_split_clause,[],[f25516,f31822]) ).
fof(f31822,plain,
( spl635_545
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_545])]) ).
fof(f25516,plain,
! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(equality_resolution,[],[f20461]) ).
fof(f20461,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f15475]) ).
fof(f15475,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,[],[f15474]) ).
fof(f15474,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,[],[f11948]) ).
fof(f11948,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,[],[f7656]) ).
fof(f7656,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,[],[f107]) ).
fof(f107,axiom,
! [X35,X30,X8] :
( class_Orderings_Olinorder(X8)
=> ( X30 != X35
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X35),X30))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X30),X35)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(f31820,plain,
spl635_544,
inference(avatar_split_clause,[],[f25328,f31818]) ).
fof(f31818,plain,
( spl635_544
<=> ! [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,[spl635_544])]) ).
fof(f25328,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,[],[f18448]) ).
fof(f18448,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,[],[f14821]) ).
fof(f31816,plain,
spl635_543,
inference(avatar_split_clause,[],[f24351,f31814]) ).
fof(f31814,plain,
( spl635_543
<=> ! [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,[spl635_543])]) ).
fof(f24351,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,[],[f17833,f17354]) ).
fof(f17354,plain,
! [X0] : c_Wellfounded_Omeasure(X0) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0),c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f5292]) ).
fof(f5292,plain,
! [X0] : c_Wellfounded_Omeasure(X0) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0),c_Wellfounded_Oless__than),
inference(rectify,[],[f2738]) ).
fof(f2738,axiom,
! [X8] : c_Wellfounded_Omeasure(X8) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X8),c_Wellfounded_Oless__than),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_measure__def) ).
fof(f17833,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X0)),
inference(cnf_transformation,[],[f5685]) ).
fof(f5685,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X0)),
inference(rectify,[],[f3490]) ).
fof(f3490,axiom,
! [X1,X8] : c_Wellfounded_Owf(X8,hAPP(c_Wellfounded_Omeasure(X8),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__measure) ).
fof(f31812,plain,
spl635_542,
inference(avatar_split_clause,[],[f24345,f31810]) ).
fof(f24345,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,[],[f17821,f17916]) ).
fof(f17821,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X0)),
inference(cnf_transformation,[],[f5673]) ).
fof(f5673,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X0)),
inference(rectify,[],[f4631]) ).
fof(f4631,axiom,
! [X41,X42] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X42,X41)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__upt) ).
fof(f31808,plain,
spl635_541,
inference(avatar_split_clause,[],[f24235,f31806]) ).
fof(f31806,plain,
( spl635_541
<=> ! [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,[spl635_541])]) ).
fof(f24235,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,[],[f17298,f24179]) ).
fof(f17298,plain,
! [X0] : c_Int_OPls != c_Int_OBit1(X0),
inference(cnf_transformation,[],[f5236]) ).
fof(f5236,plain,
! [X0] : c_Int_OPls != c_Int_OBit1(X0),
inference(rectify,[],[f1171]) ).
fof(f1171,axiom,
! [X46] : c_Int_OPls != c_Int_OBit1(X46),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I39_J) ).
fof(f31804,plain,
spl635_540,
inference(avatar_split_clause,[],[f24204,f31801]) ).
fof(f31801,plain,
( spl635_540
<=> 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,[spl635_540])]) ).
fof(f24204,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,[],[f17172,f24179]) ).
fof(f17172,plain,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
inference(cnf_transformation,[],[f1173]) ).
fof(f1173,axiom,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit1__Min) ).
fof(f31799,plain,
spl635_539,
inference(avatar_split_clause,[],[f21627,f31797]) ).
fof(f31797,plain,
( spl635_539
<=> ! [X2,X0,X1,X3] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_539])]) ).
fof(f21627,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1,
inference(cnf_transformation,[],[f8291]) ).
fof(f8291,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1,
inference(rectify,[],[f5205]) ).
fof(f5205,axiom,
! [X266,X265,X8,X5] : hAPP(hAPP(c_COMBK(X5,X8),X265),X266) = X265,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(f31795,plain,
spl635_538,
inference(avatar_split_clause,[],[f21181,f31793]) ).
fof(f31793,plain,
( spl635_538
<=> ! [X2,X0,X1] :
( X1 = X2
| ~ c_List_Olist__all2(X0,X0,c_fequal,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_538])]) ).
fof(f21181,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ c_List_Olist__all2(X0,X0,c_fequal,X2,X1) ),
inference(cnf_transformation,[],[f15741]) ).
fof(f15741,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,[],[f8154]) ).
fof(f8154,plain,
! [X0,X1,X2] :
( X1 = X2
<=> c_List_Olist__all2(X0,X0,c_fequal,X2,X1) ),
inference(rectify,[],[f4481]) ).
fof(f4481,axiom,
! [X8,X209,X210] :
( X209 = X210
<=> c_List_Olist__all2(X8,X8,c_fequal,X210,X209) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all2__eq) ).
fof(f31791,plain,
spl635_537,
inference(avatar_split_clause,[],[f20790,f31789]) ).
fof(f20790,plain,
! [X2,X0,X1] :
( sP25(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(cnf_transformation,[],[f14571]) ).
fof(f14571,plain,
! [X0,X1,X2] :
( sP25(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(definition_folding,[],[f12287,f14570,f14569]) ).
fof(f14570,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)
<=> sP24(X0,X1,X2) )
| ~ sP25(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP25])]) ).
fof(f12287,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,[],[f12286]) ).
fof(f12286,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,[],[f7893]) ).
fof(f7893,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,[],[f2265]) ).
fof(f2265,axiom,
! [X1,X39,X8] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X39))
=> ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,tc_Nat_Onat),X1),X39)
<=> ? [X2] :
( ! [X142] :
( hBOOL(hAPP(hAPP(c_member(X8),X142),X39))
=> ( X2 != X142
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X1,X142) ) )
& hAPP(X1,X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(X8),X2),X39)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__eq__Suc0__iff) ).
fof(f31787,plain,
spl635_536,
inference(avatar_split_clause,[],[f20778,f31785]) ).
fof(f20778,plain,
! [X2,X0,X1] :
( sP23(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(cnf_transformation,[],[f14568]) ).
fof(f14568,plain,
! [X0,X1,X2] :
( sP23(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(definition_folding,[],[f12284,f14567,f14566]) ).
fof(f14567,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)
<=> sP22(X0,X1,X2) )
| ~ sP23(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).
fof(f12284,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,[],[f12283]) ).
fof(f12283,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,[],[f7891]) ).
fof(f7891,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,[],[f2266]) ).
fof(f2266,axiom,
! [X1,X39,X8] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X39))
=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X8,tc_Nat_Onat),X1),X39)
<=> ? [X2] :
( ! [X142] :
( hBOOL(hAPP(hAPP(c_member(X8),X142),X39))
=> ( X2 != X142
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X1,X142) ) )
& hAPP(X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(X8),X2),X39)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_setsum__eq__1__iff) ).
fof(f31783,plain,
spl635_535,
inference(avatar_split_clause,[],[f20653,f31781]) ).
fof(f31781,plain,
( spl635_535
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_535])]) ).
fof(f20653,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(cnf_transformation,[],[f12142]) ).
fof(f12142,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(ennf_transformation,[],[f7789]) ).
fof(f7789,plain,
! [X0,X1,X2] :
( c_Equiv__Relations_Oequivp(X2,X1)
=> hBOOL(hAPP(hAPP(X1,X0),X0)) ),
inference(rectify,[],[f3222]) ).
fof(f3222,axiom,
! [X30,X122,X8] :
( c_Equiv__Relations_Oequivp(X8,X122)
=> hBOOL(hAPP(hAPP(X122,X30),X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__reflp) ).
fof(f31779,plain,
spl635_534,
inference(avatar_split_clause,[],[f20652,f31777]) ).
fof(f31777,plain,
( spl635_534
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_534])]) ).
fof(f20652,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ),
inference(cnf_transformation,[],[f12141]) ).
fof(f12141,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ),
inference(ennf_transformation,[],[f7788]) ).
fof(f7788,plain,
! [X0,X1,X2] :
( c_Predicate_Oreflp(X2,X1)
=> hBOOL(hAPP(hAPP(X1,X0),X0)) ),
inference(rectify,[],[f3452]) ).
fof(f3452,axiom,
! [X30,X98,X8] :
( c_Predicate_Oreflp(X8,X98)
=> hBOOL(hAPP(hAPP(X98,X30),X30)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflpE) ).
fof(f31775,plain,
spl635_533,
inference(avatar_split_clause,[],[f19668,f31773]) ).
fof(f31773,plain,
( spl635_533
<=> ! [X2,X0,X1] : c_Predicate_Oconversep(X2,X1,c_Predicate_Oconversep(X1,X2,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_533])]) ).
fof(f19668,plain,
! [X2,X0,X1] : c_Predicate_Oconversep(X2,X1,c_Predicate_Oconversep(X1,X2,X0)) = X0,
inference(cnf_transformation,[],[f6963]) ).
fof(f6963,plain,
! [X0,X1,X2] : c_Predicate_Oconversep(X2,X1,c_Predicate_Oconversep(X1,X2,X0)) = X0,
inference(rectify,[],[f4850]) ).
fof(f4850,axiom,
! [X98,X8,X25] : c_Predicate_Oconversep(X25,X8,c_Predicate_Oconversep(X8,X25,X98)) = X98,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__conversep) ).
fof(f31771,plain,
spl635_532,
inference(avatar_split_clause,[],[f19666,f31769]) ).
fof(f31769,plain,
( spl635_532
<=> ! [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,[spl635_532])]) ).
fof(f19666,plain,
! [X2,X0,X1] : hAPP(c_New__DSequence_Oneg__single(X2,X1),X0) = c_Lazy__Sequence_Ohb__single(X2,X1),
inference(cnf_transformation,[],[f6961]) ).
fof(f6961,plain,
! [X0,X1,X2] : hAPP(c_New__DSequence_Oneg__single(X2,X1),X0) = c_Lazy__Sequence_Ohb__single(X2,X1),
inference(rectify,[],[f3653]) ).
fof(f3653,axiom,
! [X138,X13,X5] : hAPP(c_New__DSequence_Oneg__single(X5,X13),X138) = c_Lazy__Sequence_Ohb__single(X5,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
fof(f31767,plain,
spl635_531,
inference(avatar_split_clause,[],[f19662,f31765]) ).
fof(f31765,plain,
( spl635_531
<=> ! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_531])]) ).
fof(f19662,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[],[f6957]) ).
fof(f6957,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2),
inference(rectify,[],[f4134]) ).
fof(f4134,axiom,
! [X217,X87,X5] : c_List_Olist_ONil(X5) != hAPP(hAPP(c_List_Olist_OCons(X5),X87),X217),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
fof(f31763,plain,
spl635_530,
inference(avatar_split_clause,[],[f19245,f31761]) ).
fof(f19245,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP8(X1,X0) ),
inference(cnf_transformation,[],[f15093]) ).
fof(f15093,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,[],[f14543]) ).
fof(f14543,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
<=> sP8(X1,X0) ),
inference(definition_folding,[],[f11329,f14542]) ).
fof(f11329,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,[],[f6790]) ).
fof(f6790,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,[],[f437]) ).
fof(f437,axiom,
! [X14,X29] :
( hBOOL(hAPP(X29,hAPP(c_Int_Onat,X14)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X14),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(X29,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X9] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X9) = X14
=> hBOOL(hAPP(X29,X9)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__nat) ).
fof(f31759,plain,
spl635_529,
inference(avatar_split_clause,[],[f19244,f31757]) ).
fof(f19244,plain,
! [X0,X1] :
( sP8(X1,X0)
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ),
inference(cnf_transformation,[],[f15093]) ).
fof(f31755,plain,
spl635_528,
inference(avatar_split_clause,[],[f19161,f31753]) ).
fof(f31753,plain,
( spl635_528
<=> ! [X0,X1,X3] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_528])]) ).
fof(f19161,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ),
inference(cnf_transformation,[],[f15017]) ).
fof(f31751,plain,
spl635_527,
inference(avatar_split_clause,[],[f18758,f31749]) ).
fof(f31749,plain,
( spl635_527
<=> ! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_527])]) ).
fof(f18758,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10916]) ).
fof(f10916,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6467]) ).
fof(f6467,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0)) ),
inference(rectify,[],[f3567]) ).
fof(f3567,axiom,
! [X122,X8] :
( c_Wellfounded_Owf(X8,X122)
=> c_Wellfounded_OwfP(X8,c_FunDef_Oin__rel(X8,X8,X122)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__in__rel) ).
fof(f31747,plain,
spl635_526,
inference(avatar_split_clause,[],[f18750,f31745]) ).
fof(f31745,plain,
( spl635_526
<=> ! [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,[spl635_526])]) ).
fof(f18750,plain,
! [X0,X1] :
( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olistrel(X1,X0))
| ~ c_Relation_Otrans(X1,X0) ),
inference(cnf_transformation,[],[f10907]) ).
fof(f10907,plain,
! [X0,X1] :
( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olistrel(X1,X0))
| ~ c_Relation_Otrans(X1,X0) ),
inference(ennf_transformation,[],[f6459]) ).
fof(f6459,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
=> c_Relation_Otrans(tc_List_Olist(X1),c_List_Olistrel(X1,X0)) ),
inference(rectify,[],[f4910]) ).
fof(f4910,axiom,
! [X98,X8] :
( c_Relation_Otrans(X8,X98)
=> c_Relation_Otrans(tc_List_Olist(X8),c_List_Olistrel(X8,X98)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__trans) ).
fof(f31743,plain,
spl635_525,
inference(avatar_split_clause,[],[f18749,f31741]) ).
fof(f31741,plain,
( spl635_525
<=> ! [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,[spl635_525])]) ).
fof(f18749,plain,
! [X0,X1] :
( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olexord(X1,X0))
| ~ c_Relation_Otrans(X1,X0) ),
inference(cnf_transformation,[],[f10906]) ).
fof(f10906,plain,
! [X0,X1] :
( c_Relation_Otrans(tc_List_Olist(X1),c_List_Olexord(X1,X0))
| ~ c_Relation_Otrans(X1,X0) ),
inference(ennf_transformation,[],[f6458]) ).
fof(f6458,plain,
! [X0,X1] :
( c_Relation_Otrans(X1,X0)
=> c_Relation_Otrans(tc_List_Olist(X1),c_List_Olexord(X1,X0)) ),
inference(rectify,[],[f4913]) ).
fof(f4913,axiom,
! [X98,X8] :
( c_Relation_Otrans(X8,X98)
=> c_Relation_Otrans(tc_List_Olist(X8),c_List_Olexord(X8,X98)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lexord__transI) ).
fof(f31739,plain,
spl635_524,
inference(avatar_split_clause,[],[f18746,f31737]) ).
fof(f31737,plain,
( spl635_524
<=> ! [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,[spl635_524])]) ).
fof(f18746,plain,
! [X0,X1] :
( c_Relation_Osym(tc_List_Olist(X1),c_List_Olistrel(X1,X0))
| ~ c_Relation_Osym(X1,X0) ),
inference(cnf_transformation,[],[f10902]) ).
fof(f10902,plain,
! [X0,X1] :
( c_Relation_Osym(tc_List_Olist(X1),c_List_Olistrel(X1,X0))
| ~ c_Relation_Osym(X1,X0) ),
inference(ennf_transformation,[],[f6455]) ).
fof(f6455,plain,
! [X0,X1] :
( c_Relation_Osym(X1,X0)
=> c_Relation_Osym(tc_List_Olist(X1),c_List_Olistrel(X1,X0)) ),
inference(rectify,[],[f4953]) ).
fof(f4953,axiom,
! [X98,X8] :
( c_Relation_Osym(X8,X98)
=> c_Relation_Osym(tc_List_Olist(X8),c_List_Olistrel(X8,X98)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrel__sym) ).
fof(f31735,plain,
spl635_523,
inference(avatar_split_clause,[],[f18722,f31733]) ).
fof(f31733,plain,
( spl635_523
<=> ! [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,[spl635_523])]) ).
fof(f18722,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,[],[f10874]) ).
fof(f10874,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,[],[f10873]) ).
fof(f10873,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,[],[f6436]) ).
fof(f6436,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,[],[f1372]) ).
fof(f1372,axiom,
! [X12,X13] :
( c_Nat__Transfer_Ois__nat(X13)
=> ( c_Nat__Transfer_Ois__nat(X12)
=> c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X13,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).
fof(f31731,plain,
spl635_522,
inference(avatar_split_clause,[],[f18718,f31729]) ).
fof(f31729,plain,
( spl635_522
<=> ! [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,[spl635_522])]) ).
fof(f18718,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,[],[f10868]) ).
fof(f10868,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,[],[f6433]) ).
fof(f6433,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,[],[f1374]) ).
fof(f1374,axiom,
! [X4,X13] :
( c_Nat__Transfer_Ois__nat(X13)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X13),X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).
fof(f31727,plain,
spl635_521,
inference(avatar_split_clause,[],[f18681,f31725]) ).
fof(f31725,plain,
( spl635_521
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_521])]) ).
fof(f18681,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10830]) ).
fof(f10830,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6407]) ).
fof(f6407,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0)) ),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X13,X5] :
( class_Orderings_Opreorder(X5)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X5),X13),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__refl) ).
fof(f31723,plain,
spl635_520,
inference(avatar_split_clause,[],[f18680,f31721]) ).
fof(f31721,plain,
( spl635_520
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_520])]) ).
fof(f18680,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10829]) ).
fof(f10829,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6406]) ).
fof(f6406,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0)) ),
inference(rectify,[],[f110]) ).
fof(f110,axiom,
! [X13,X5] :
( class_Orderings_Opreorder(X5)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X5),X13),X13)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(f31719,plain,
spl635_519,
inference(avatar_split_clause,[],[f18648,f31717]) ).
fof(f31717,plain,
( spl635_519
<=> ! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_519])]) ).
fof(f18648,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f14854]) ).
fof(f14854,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,[],[f14528]) ).
fof(f14528,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(f31715,plain,
spl635_518,
inference(avatar_split_clause,[],[f18647,f31713]) ).
fof(f31713,plain,
( spl635_518
<=> ! [X0,X1] :
( sP0(X1,X0)
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_518])]) ).
fof(f18647,plain,
! [X0,X1] :
( sP0(X1,X0)
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f14854]) ).
fof(f31711,plain,
spl635_517,
inference(avatar_split_clause,[],[f18579,f31709]) ).
fof(f31709,plain,
( spl635_517
<=> ! [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,[spl635_517])]) ).
fof(f18579,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f10721]) ).
fof(f10721,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f6323]) ).
fof(f6323,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0)) ),
inference(rectify,[],[f1884]) ).
fof(f1884,axiom,
! [X33,X5] :
( class_Rings_Ocomm__semiring__1(X5)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X5),X33),X33)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__refl) ).
fof(f31707,plain,
spl635_516,
inference(avatar_split_clause,[],[f18578,f31705]) ).
fof(f31705,plain,
( spl635_516
<=> ! [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,[spl635_516])]) ).
fof(f18578,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,[],[f10720]) ).
fof(f10720,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,[],[f6322]) ).
fof(f6322,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f911]) ).
fof(f911,axiom,
! [X33,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Divides_Odiv__class_Omod(X5,X33,c_Groups_Ozero__class_Ozero(X5)) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__by__0) ).
fof(f31703,plain,
spl635_515,
inference(avatar_split_clause,[],[f18577,f31701]) ).
fof(f31701,plain,
( spl635_515
<=> ! [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,[spl635_515])]) ).
fof(f18577,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,[],[f10719]) ).
fof(f10719,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,[],[f6321]) ).
fof(f6321,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0) ),
inference(rectify,[],[f912]) ).
fof(f912,axiom,
! [X33,X5] :
( class_Divides_Osemiring__div(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Divides_Odiv__class_Omod(X5,X33,X33) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__self) ).
fof(f31699,plain,
spl635_514,
inference(avatar_split_clause,[],[f18567,f31697]) ).
fof(f31697,plain,
( spl635_514
<=> ! [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,[spl635_514])]) ).
fof(f18567,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Int_Oiszero(X1,X0)
| ~ class_Rings_Osemiring__1(X1) ),
inference(cnf_transformation,[],[f14840]) ).
fof(f14840,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,[],[f10711]) ).
fof(f10711,plain,
! [X0,X1] :
( ( c_Int_Oiszero(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Rings_Osemiring__1(X1) ),
inference(ennf_transformation,[],[f6313]) ).
fof(f6313,plain,
! [X0,X1] :
( class_Rings_Osemiring__1(X1)
=> ( c_Int_Oiszero(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f856]) ).
fof(f856,axiom,
! [X53,X8] :
( class_Rings_Osemiring__1(X8)
=> ( c_Int_Oiszero(X8,X53)
<=> c_Groups_Ozero__class_Ozero(X8) = X53 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__def) ).
fof(f31695,plain,
spl635_513,
inference(avatar_split_clause,[],[f18322,f31693]) ).
fof(f31693,plain,
( spl635_513
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_513])]) ).
fof(f18322,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ),
inference(cnf_transformation,[],[f6115]) ).
fof(f6115,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ),
inference(rectify,[],[f5209]) ).
fof(f5209,axiom,
! [X35,X30] :
( X30 = X35
| ~ hBOOL(hAPP(hAPP(c_fequal,X30),X35)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(f31691,plain,
spl635_512,
inference(avatar_split_clause,[],[f17891,f31689]) ).
fof(f31689,plain,
( spl635_512
<=> ! [X0,X1] : c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_512])]) ).
fof(f17891,plain,
! [X0,X1] : c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X0)),
inference(cnf_transformation,[],[f5743]) ).
fof(f5743,plain,
! [X0,X1] : c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X0)),
inference(rectify,[],[f3728]) ).
fof(f3728,axiom,
! [X98,X8] : c_Relation_Orefl__on(X8,c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X8,X98)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__rtrancl) ).
fof(f31687,plain,
spl635_511,
inference(avatar_split_clause,[],[f17890,f31685]) ).
fof(f31685,plain,
( spl635_511
<=> ! [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,[spl635_511])]) ).
fof(f17890,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X0)),
inference(cnf_transformation,[],[f5742]) ).
fof(f5742,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X0)),
inference(rectify,[],[f303]) ).
fof(f303,axiom,
! [X39,X8] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X39),X39)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(f31683,plain,
spl635_510,
inference(avatar_split_clause,[],[f17889,f31681]) ).
fof(f31681,plain,
( spl635_510
<=> ! [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,[spl635_510])]) ).
fof(f17889,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,[],[f5741]) ).
fof(f5741,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,[],[f2226]) ).
fof(f2226,axiom,
! [X75,X77] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X77),X75))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
fof(f31679,plain,
spl635_509,
inference(avatar_split_clause,[],[f17888,f31677]) ).
fof(f31677,plain,
( spl635_509
<=> ! [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,[spl635_509])]) ).
fof(f17888,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,[],[f5740]) ).
fof(f5740,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,[],[f2231]) ).
fof(f2231,axiom,
! [X75,X77] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X77),X75))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan__int) ).
fof(f31675,plain,
( ~ spl635_28
| ~ spl635_508
| ~ spl635_259
| ~ spl635_406 ),
inference(avatar_split_clause,[],[f31518,f31218,f30554,f31672,f29431]) ).
fof(f29431,plain,
( spl635_28
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_28])]) ).
fof(f31672,plain,
( spl635_508
<=> c_Int_Oiszero(tc_Int_Oint,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_508])]) ).
fof(f30554,plain,
( spl635_259
<=> ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_259])]) ).
fof(f31218,plain,
( spl635_406
<=> ! [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,[spl635_406])]) ).
fof(f31518,plain,
( ~ c_Int_Oiszero(tc_Int_Oint,c_Int_OMin)
| ~ class_Int_Onumber__ring(tc_Int_Oint)
| ~ spl635_259
| ~ spl635_406 ),
inference(superposition,[],[f31219,f30555]) ).
fof(f30555,plain,
( ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0
| ~ spl635_259 ),
inference(avatar_component_clause,[],[f30554]) ).
fof(f31219,plain,
( ! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) )
| ~ spl635_406 ),
inference(avatar_component_clause,[],[f31218]) ).
fof(f31670,plain,
spl635_507,
inference(avatar_split_clause,[],[f17887,f31668]) ).
fof(f31668,plain,
( spl635_507
<=> ! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_507])]) ).
fof(f17887,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(cnf_transformation,[],[f5739]) ).
fof(f5739,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(rectify,[],[f2187]) ).
fof(f2187,axiom,
! [X148,X8] : hAPP(c_Set_Oimage(X8,X8,c_COMBI(X8)),X148) = X148,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__ident) ).
fof(f31666,plain,
spl635_506,
inference(avatar_split_clause,[],[f17886,f31664]) ).
fof(f31664,plain,
( spl635_506
<=> ! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_506])]) ).
fof(f17886,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(cnf_transformation,[],[f5738]) ).
fof(f5738,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(rectify,[],[f3455]) ).
fof(f3455,axiom,
! [X148,X8] : hAPP(c_Set_Oimage(X8,X8,c_Fun_Oid(X8)),X148) = X148,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__id) ).
fof(f31662,plain,
spl635_505,
inference(avatar_split_clause,[],[f17884,f31660]) ).
fof(f31660,plain,
( spl635_505
<=> ! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_505])]) ).
fof(f17884,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(cnf_transformation,[],[f5736]) ).
fof(f5736,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(rectify,[],[f3232]) ).
fof(f3232,axiom,
! [X148,X8] : hAPP(c_Set_Ovimage(X8,X8,c_COMBI(X8)),X148) = X148,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__ident) ).
fof(f31658,plain,
spl635_504,
inference(avatar_split_clause,[],[f17883,f31656]) ).
fof(f31656,plain,
( spl635_504
<=> ! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_504])]) ).
fof(f17883,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(cnf_transformation,[],[f5735]) ).
fof(f5735,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(rectify,[],[f3447]) ).
fof(f3447,axiom,
! [X39,X8] : hAPP(c_Set_Ovimage(X8,X8,c_Fun_Oid(X8)),X39) = X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__id) ).
fof(f31654,plain,
spl635_503,
inference(avatar_split_clause,[],[f17880,f31652]) ).
fof(f31652,plain,
( spl635_503
<=> ! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_503])]) ).
fof(f17880,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0,
inference(cnf_transformation,[],[f5732]) ).
fof(f5732,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0,
inference(rectify,[],[f4239]) ).
fof(f4239,axiom,
! [X207,X5] : hAPP(hAPP(c_List_Oappend(X5),c_List_Olist_ONil(X5)),X207) = X207,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil) ).
fof(f31650,plain,
spl635_502,
inference(avatar_split_clause,[],[f17879,f31648]) ).
fof(f31648,plain,
( spl635_502
<=> ! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_502])]) ).
fof(f17879,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0,
inference(cnf_transformation,[],[f5731]) ).
fof(f5731,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0,
inference(rectify,[],[f4237]) ).
fof(f4237,axiom,
! [X208,X5] : hAPP(hAPP(c_List_Oappend(X5),X208),c_List_Olist_ONil(X5)) = X208,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_append__Nil2) ).
fof(f31646,plain,
spl635_501,
inference(avatar_split_clause,[],[f17878,f31644]) ).
fof(f31644,plain,
( spl635_501
<=> ! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_501])]) ).
fof(f17878,plain,
! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0,
inference(cnf_transformation,[],[f5730]) ).
fof(f5730,plain,
! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0,
inference(rectify,[],[f4681]) ).
fof(f4681,axiom,
! [X208,X5] : hAPP(c_List_Orev(X5),hAPP(c_List_Orev(X5),X208)) = X208,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(f31642,plain,
spl635_500,
inference(avatar_split_clause,[],[f17876,f31640]) ).
fof(f31640,plain,
( spl635_500
<=> ! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_500])]) ).
fof(f17876,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(cnf_transformation,[],[f5728]) ).
fof(f5728,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(rectify,[],[f3729]) ).
fof(f3729,axiom,
! [X98,X8] : c_Transitive__Closure_Ortrancl(X8,X98) = c_Transitive__Closure_Ortrancl(X8,c_Transitive__Closure_Ortrancl(X8,X98)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
fof(f31638,plain,
spl635_499,
inference(avatar_split_clause,[],[f17873,f31636]) ).
fof(f31636,plain,
( spl635_499
<=> ! [X0,X1] : c_List_Oremdups(X1,X0) = c_List_Oremdups(X1,c_List_Oremdups(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_499])]) ).
fof(f17873,plain,
! [X0,X1] : c_List_Oremdups(X1,X0) = c_List_Oremdups(X1,c_List_Oremdups(X1,X0)),
inference(cnf_transformation,[],[f5725]) ).
fof(f5725,plain,
! [X0,X1] : c_List_Oremdups(X1,X0) = c_List_Oremdups(X1,c_List_Oremdups(X1,X0)),
inference(rectify,[],[f4516]) ).
fof(f4516,axiom,
! [X208,X5] : c_List_Oremdups(X5,X208) = c_List_Oremdups(X5,c_List_Oremdups(X5,X208)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups__remdups) ).
fof(f31634,plain,
spl635_498,
inference(avatar_split_clause,[],[f17872,f31632]) ).
fof(f31632,plain,
( spl635_498
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_498])]) ).
fof(f17872,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5724]) ).
fof(f5724,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f4563]) ).
fof(f4563,axiom,
! [X29,X8] : c_List_Olist_ONil(X8) = hAPP(c_List_Ofilter(X8,X29),c_List_Olist_ONil(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_filter_Osimps_I1_J) ).
fof(f31629,plain,
spl635_497,
inference(avatar_split_clause,[],[f17679,f31627]) ).
fof(f31627,plain,
( spl635_497
<=> ! [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,[spl635_497])]) ).
fof(f17679,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,[],[f10439]) ).
fof(f10439,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,[],[f10438]) ).
fof(f10438,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,[],[f5599]) ).
fof(f5599,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,[],[f2867]) ).
fof(f2867,axiom,
! [X8] :
( ( class_Orderings_Olinorder(X8)
& class_Lattices_Osemilattice__inf(X8) )
=> c_Orderings_Oord__class_Omin(X8) = c_Lattices_Osemilattice__inf__class_Oinf(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inf__min) ).
fof(f31625,plain,
spl635_496,
inference(avatar_split_clause,[],[f17678,f31623]) ).
fof(f31623,plain,
( spl635_496
<=> ! [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,[spl635_496])]) ).
fof(f17678,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,[],[f10437]) ).
fof(f10437,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,[],[f10436]) ).
fof(f10436,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,[],[f5598]) ).
fof(f5598,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,[],[f2103]) ).
fof(f2103,axiom,
! [X8] :
( ( class_Orderings_Olinorder(X8)
& class_Lattices_Osemilattice__sup(X8) )
=> c_Orderings_Oord__class_Omax(X8) = c_Lattices_Osemilattice__sup__class_Osup(X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sup__max) ).
fof(f31621,plain,
spl635_495,
inference(avatar_split_clause,[],[f17626,f31619]) ).
fof(f31619,plain,
( spl635_495
<=> ! [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,[spl635_495])]) ).
fof(f17626,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,[],[f10386]) ).
fof(f10386,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,[],[f5551]) ).
fof(f5551,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,[],[f1675]) ).
fof(f1675,axiom,
! [X8] :
( class_Orderings_Oord(X8)
=> c_Orderings_Oord__class_Omin(X8) = c_Orderings_Oord_Omin(X8,c_Orderings_Oord__class_Oless__eq(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__ord__min) ).
fof(f31617,plain,
spl635_494,
inference(avatar_split_clause,[],[f17625,f31615]) ).
fof(f31615,plain,
( spl635_494
<=> ! [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,[spl635_494])]) ).
fof(f17625,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,[],[f10385]) ).
fof(f10385,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,[],[f5550]) ).
fof(f5550,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,[],[f1733]) ).
fof(f1733,axiom,
! [X8] :
( class_Orderings_Oord(X8)
=> c_Orderings_Oord__class_Omax(X8) = c_Orderings_Oord_Omax(X8,c_Orderings_Oord__class_Oless__eq(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_max__ord__max) ).
fof(f31613,plain,
spl635_493,
inference(avatar_split_clause,[],[f17580,f31611]) ).
fof(f31611,plain,
( spl635_493
<=> ! [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,[spl635_493])]) ).
fof(f17580,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,[],[f10340]) ).
fof(f10340,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,[],[f5505]) ).
fof(f5505,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,[],[f1095]) ).
fof(f1095,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> c_Groups_Ozero__class_Ozero(X5) = hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OPls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semiring__norm_I112_J) ).
fof(f31609,plain,
spl635_492,
inference(avatar_split_clause,[],[f17568,f31607]) ).
fof(f31607,plain,
( spl635_492
<=> ! [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,[spl635_492])]) ).
fof(f17568,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,[],[f10328]) ).
fof(f10328,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,[],[f5493]) ).
fof(f5493,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,[],[f692]) ).
fof(f692,axiom,
! [X5] :
( class_Groups_Osgn__if(X5)
=> c_Groups_Ozero__class_Ozero(X5) = c_Groups_Osgn__class_Osgn(X5,c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sgn0) ).
fof(f31605,plain,
spl635_491,
inference(avatar_split_clause,[],[f17400,f31603]) ).
fof(f31603,plain,
( spl635_491
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_491])]) ).
fof(f17400,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))),
inference(cnf_transformation,[],[f5338]) ).
fof(f5338,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X4] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),hAPP(c_Nat_OSuc,X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lessI) ).
fof(f31601,plain,
spl635_490,
inference(avatar_split_clause,[],[f17399,f31599]) ).
fof(f31599,plain,
( spl635_490
<=> ! [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,[spl635_490])]) ).
fof(f17399,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,[],[f5337]) ).
fof(f5337,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f382]) ).
fof(f382,axiom,
! [X4] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X4) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(f31597,plain,
spl635_489,
inference(avatar_split_clause,[],[f17398,f31595]) ).
fof(f31595,plain,
( spl635_489
<=> ! [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,[spl635_489])]) ).
fof(f17398,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,[],[f5336]) ).
fof(f5336,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
inference(rectify,[],[f387]) ).
fof(f387,axiom,
! [X31] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X31) = X31,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(f31593,plain,
spl635_488,
inference(avatar_split_clause,[],[f17394,f31591]) ).
fof(f31591,plain,
( spl635_488
<=> ! [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,[spl635_488])]) ).
fof(f17394,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,[],[f5332]) ).
fof(f5332,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(rectify,[],[f384]) ).
fof(f384,axiom,
! [X4] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X4),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(f31588,plain,
spl635_487,
inference(avatar_split_clause,[],[f17393,f31586]) ).
fof(f31586,plain,
( spl635_487
<=> ! [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,[spl635_487])]) ).
fof(f17393,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,[],[f5331]) ).
fof(f5331,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
inference(rectify,[],[f386]) ).
fof(f386,axiom,
! [X31] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X31),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X31,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(f31584,plain,
spl635_486,
inference(avatar_split_clause,[],[f17388,f31582]) ).
fof(f17388,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,[],[f5326]) ).
fof(f5326,plain,
! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = X0,
inference(rectify,[],[f481]) ).
fof(f481,axiom,
! [X31] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X31)) = X31,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(f31580,plain,
spl635_485,
inference(avatar_split_clause,[],[f17387,f31578]) ).
fof(f31578,plain,
( spl635_485
<=> ! [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,[spl635_485])]) ).
fof(f17387,plain,
! [X0] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)) = X0,
inference(cnf_transformation,[],[f5325]) ).
fof(f5325,plain,
! [X0] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)) = X0,
inference(rectify,[],[f2069]) ).
fof(f2069,axiom,
! [X75] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X75)) = X75,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_card__lessThan) ).
fof(f31576,plain,
spl635_484,
inference(avatar_split_clause,[],[f17384,f31574]) ).
fof(f31574,plain,
( spl635_484
<=> ! [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,[spl635_484])]) ).
fof(f17384,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,[],[f4562]) ).
fof(f4562,axiom,
! [X5] : c_List_Olist_ONil(tc_List_Olist(X5)) = c_List_Otranspose(X5,c_List_Olist_ONil(tc_List_Olist(X5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_transpose_Osimps_I1_J) ).
fof(f31572,plain,
spl635_483,
inference(avatar_split_clause,[],[f17383,f31570]) ).
fof(f17383,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,[],[f1246]) ).
fof(f1246,axiom,
! [X40] : c_Int_OBit0(X40) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X40),X40),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f31567,plain,
spl635_482,
inference(avatar_split_clause,[],[f17375,f31565]) ).
fof(f31565,plain,
( spl635_482
<=> ! [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,[spl635_482])]) ).
fof(f17375,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X0)),
inference(cnf_transformation,[],[f5313]) ).
fof(f5313,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X0)),
inference(rectify,[],[f134]) ).
fof(f134,axiom,
! [X4] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X4)),X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(f31563,plain,
spl635_481,
inference(avatar_split_clause,[],[f17374,f31561]) ).
fof(f31561,plain,
( spl635_481
<=> ! [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,[spl635_481])]) ).
fof(f17374,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,[],[f5312]) ).
fof(f5312,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,[],[f3129]) ).
fof(f3129,axiom,
! [X8] : c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) != c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).
fof(f31559,plain,
spl635_480,
inference(avatar_split_clause,[],[f17247,f31556]) ).
fof(f31556,plain,
( spl635_480
<=> 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,[spl635_480])]) ).
fof(f17247,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,[],[f3228]) ).
fof(f3228,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',fact_type__definition__code__numeral) ).
fof(f31554,plain,
spl635_479,
inference(avatar_split_clause,[],[f17246,f31551]) ).
fof(f31551,plain,
( spl635_479
<=> 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,[spl635_479])]) ).
fof(f17246,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,[],[f3153]) ).
fof(f3153,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',fact_inj__int) ).
fof(f31543,plain,
( spl635_478
| spl635_221
| ~ spl635_386 ),
inference(avatar_split_clause,[],[f31148,f31115,f30386,f31540]) ).
fof(f31540,plain,
( spl635_478
<=> sP11(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_478])]) ).
fof(f30386,plain,
( spl635_221
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_221])]) ).
fof(f31148,plain,
( sP11(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| spl635_221
| ~ spl635_386 ),
inference(resolution,[],[f31116,f30388]) ).
fof(f30388,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| spl635_221 ),
inference(avatar_component_clause,[],[f30386]) ).
fof(f31538,plain,
( ~ spl635_477
| ~ spl635_307
| ~ spl635_383 ),
inference(avatar_split_clause,[],[f31143,f31101,f30750,f31535]) ).
fof(f31535,plain,
( spl635_477
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_477])]) ).
fof(f30750,plain,
( spl635_307
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_307])]) ).
fof(f31101,plain,
( spl635_383
<=> 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,[spl635_383])]) ).
fof(f31143,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_HOL_Obool_Obool__size(c_fTrue)
| ~ spl635_307
| ~ spl635_383 ),
inference(superposition,[],[f30751,f31103]) ).
fof(f31103,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))
| ~ spl635_383 ),
inference(avatar_component_clause,[],[f31101]) ).
fof(f30751,plain,
( ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0)
| ~ spl635_307 ),
inference(avatar_component_clause,[],[f30750]) ).
fof(f31526,plain,
( ~ spl635_476
| ~ spl635_367
| spl635_391 ),
inference(avatar_split_clause,[],[f31504,f31156,f31032,f31523]) ).
fof(f31523,plain,
( spl635_476
<=> class_Finite__Set_Ofinite(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_476])]) ).
fof(f31156,plain,
( spl635_391
<=> 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,[spl635_391])]) ).
fof(f31504,plain,
( ~ class_Finite__Set_Ofinite(tc_Nat_Onat)
| ~ spl635_367
| spl635_391 ),
inference(resolution,[],[f31158,f31033]) ).
fof(f31158,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| spl635_391 ),
inference(avatar_component_clause,[],[f31156]) ).
fof(f31515,plain,
( ~ spl635_475
| ~ spl635_367
| spl635_390 ),
inference(avatar_split_clause,[],[f31503,f31151,f31032,f31512]) ).
fof(f31512,plain,
( spl635_475
<=> class_Finite__Set_Ofinite(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_475])]) ).
fof(f31151,plain,
( spl635_390
<=> 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,[spl635_390])]) ).
fof(f31503,plain,
( ~ class_Finite__Set_Ofinite(tc_Int_Oint)
| ~ spl635_367
| spl635_390 ),
inference(resolution,[],[f31153,f31033]) ).
fof(f31153,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool))))
| spl635_390 ),
inference(avatar_component_clause,[],[f31151]) ).
fof(f31502,plain,
( spl635_474
| ~ spl635_241
| ~ spl635_326 ),
inference(avatar_split_clause,[],[f31124,f30859,f30473,f31499]) ).
fof(f31499,plain,
( spl635_474
<=> sP6(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_474])]) ).
fof(f30859,plain,
( spl635_326
<=> 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,[spl635_326])]) ).
fof(f31124,plain,
( sP6(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl635_241
| ~ spl635_326 ),
inference(superposition,[],[f30474,f30861]) ).
fof(f30861,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl635_326 ),
inference(avatar_component_clause,[],[f30859]) ).
fof(f31497,plain,
spl635_473,
inference(avatar_split_clause,[],[f28551,f31495]) ).
fof(f31495,plain,
( spl635_473
<=> ! [X2,X1] :
( ~ sP44(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,c_Int_OPls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_473])]) ).
fof(f28551,plain,
! [X2,X1] :
( ~ sP44(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,c_Int_OPls)) ),
inference(forward_demodulation,[],[f28550,f17176]) ).
fof(f28550,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,c_Int_OPls))
| ~ sP44(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(forward_demodulation,[],[f25615,f17176]) ).
fof(f25615,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP44(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(equality_resolution,[],[f21384]) ).
fof(f21384,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ sP44(X0,X1,X2) ),
inference(cnf_transformation,[],[f15912]) ).
fof(f15912,plain,
! [X0,X1,X2] :
( ( sP44(X0,X1,X2)
| ~ sP43(X2,X1,X0)
| ~ sP42(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP43(X2,X1,X0)
& sP42(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP44(X0,X1,X2) ) ),
inference(flattening,[],[f15911]) ).
fof(f15911,plain,
! [X0,X1,X2] :
( ( sP44(X0,X1,X2)
| ~ sP43(X2,X1,X0)
| ~ sP42(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP43(X2,X1,X0)
& sP42(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP44(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14601]) ).
fof(f31493,plain,
spl635_472,
inference(avatar_split_clause,[],[f28525,f31491]) ).
fof(f31491,plain,
( spl635_472
<=> ! [X2,X1] :
( ~ sP39(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_472])]) ).
fof(f28525,plain,
! [X2,X1] :
( ~ sP39(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,X1)) ),
inference(forward_demodulation,[],[f25591,f17176]) ).
fof(f25591,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,X1))
| ~ sP39(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(equality_resolution,[],[f21304]) ).
fof(f21304,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f15858]) ).
fof(f15858,plain,
! [X0,X1,X2] :
( ( sP39(X0,X1,X2)
| ~ sP38(X2,X1,X0)
| ~ sP37(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP38(X2,X1,X0)
& sP37(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP39(X0,X1,X2) ) ),
inference(flattening,[],[f15857]) ).
fof(f15857,plain,
! [X0,X1,X2] :
( ( sP39(X0,X1,X2)
| ~ sP38(X2,X1,X0)
| ~ sP37(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP38(X2,X1,X0)
& sP37(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP39(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14593]) ).
fof(f31489,plain,
spl635_471,
inference(avatar_split_clause,[],[f27859,f31487]) ).
fof(f31487,plain,
( spl635_471
<=> ! [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,[spl635_471])]) ).
fof(f27859,plain,
! [X2,X0,X1] : c_Nat_Onat_Onat__case(X2,X1,X0,c_HOL_Obool_Obool__size(c_fTrue)) = X1,
inference(forward_demodulation,[],[f19660,f17187]) ).
fof(f19660,plain,
! [X2,X0,X1] : c_Nat_Onat_Onat__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(cnf_transformation,[],[f6955]) ).
fof(f6955,plain,
! [X0,X1,X2] : c_Nat_Onat_Onat__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X20,X21,X8] : c_Nat_Onat_Onat__case(X8,X21,X20,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__case__0) ).
fof(f31485,plain,
spl635_470,
inference(avatar_split_clause,[],[f26165,f31483]) ).
fof(f31483,plain,
( spl635_470
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_470])]) ).
fof(f26165,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Int_OPls),
inference(forward_demodulation,[],[f17539,f17176]) ).
fof(f17539,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,[],[f5477]) ).
fof(f5477,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,[],[f969]) ).
fof(f969,axiom,
! [X33] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X33,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X33
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X33),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).
fof(f31481,plain,
spl635_469,
inference(avatar_split_clause,[],[f26085,f31479]) ).
fof(f31479,plain,
( spl635_469
<=> ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_469])]) ).
fof(f31477,plain,
spl635_468,
inference(avatar_split_clause,[],[f26081,f31475]) ).
fof(f26081,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,[],[f26080,f25953]) ).
fof(f26080,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,[],[f17423,f17187]) ).
fof(f17423,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,[],[f5361]) ).
fof(f5361,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,[],[f1844]) ).
fof(f1844,axiom,
! [X40] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X40)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd__1__left) ).
fof(f31473,plain,
spl635_467,
inference(avatar_split_clause,[],[f26074,f31471]) ).
fof(f31471,plain,
( spl635_467
<=> ! [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,[spl635_467])]) ).
fof(f26074,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,[],[f26073,f25953]) ).
fof(f26073,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,[],[f17409,f17187]) ).
fof(f17409,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,[],[f5347]) ).
fof(f5347,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,[],[f1085]) ).
fof(f1085,axiom,
! [X24] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X24,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__1) ).
fof(f31469,plain,
spl635_466,
inference(avatar_split_clause,[],[f26065,f31467]) ).
fof(f26065,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OPls),X0),
inference(forward_demodulation,[],[f17402,f17176]) ).
fof(f17402,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,[],[f5340]) ).
fof(f5340,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,[],[f846]) ).
fof(f846,axiom,
! [X34] : 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)),X34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zdiv__zero) ).
fof(f31465,plain,
spl635_465,
inference(avatar_split_clause,[],[f26052,f31463]) ).
fof(f26052,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,[],[f17367,f17187]) ).
fof(f17367,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,[],[f5305]) ).
fof(f5305,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,[],[f34]) ).
fof(f34,axiom,
! [X4] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(f31461,plain,
spl635_464,
inference(avatar_split_clause,[],[f26046,f31459]) ).
fof(f31459,plain,
( spl635_464
<=> ! [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,[spl635_464])]) ).
fof(f26046,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f17349,f17187]) ).
fof(f17349,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,[],[f5287]) ).
fof(f5287,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X4] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(f31457,plain,
( spl635_463
| ~ spl635_242
| ~ spl635_326 ),
inference(avatar_split_clause,[],[f31123,f30859,f30477,f31454]) ).
fof(f31454,plain,
( spl635_463
<=> sP7(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_463])]) ).
fof(f31123,plain,
( sP7(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl635_242
| ~ spl635_326 ),
inference(superposition,[],[f30478,f30861]) ).
fof(f31452,plain,
spl635_462,
inference(avatar_split_clause,[],[f25980,f31449]) ).
fof(f25980,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,[],[f17244,f17176]) ).
fof(f17244,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,[],[f406]) ).
fof(f406,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',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(f31447,plain,
spl635_461,
inference(avatar_split_clause,[],[f25979,f31444]) ).
fof(f25979,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,[],[f17243,f17176]) ).
fof(f17243,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,[],[f407]) ).
fof(f407,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',fact_int__0__less__1) ).
fof(f31442,plain,
spl635_460,
inference(avatar_split_clause,[],[f25973,f31439]) ).
fof(f31439,plain,
( spl635_460
<=> 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,[spl635_460])]) ).
fof(f25973,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,[],[f17238,f17187]) ).
fof(f17238,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,[],[f1466]) ).
fof(f1466,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',fact_code__numeral_Osize_I3_J) ).
fof(f31437,plain,
spl635_459,
inference(avatar_split_clause,[],[f25735,f31435]) ).
fof(f31435,plain,
( spl635_459
<=> ! [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,[spl635_459])]) ).
fof(f25735,plain,
! [X2,X3,X1] : c_List_Olist__all2(X3,X2,X1,c_List_Olist_ONil(X3),c_List_Olist_ONil(X2)),
inference(equality_resolution,[],[f22686]) ).
fof(f22686,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,[],[f16356]) ).
fof(f31433,plain,
spl635_458,
inference(avatar_split_clause,[],[f25733,f31431]) ).
fof(f31431,plain,
( spl635_458
<=> ! [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,[spl635_458])]) ).
fof(f25733,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,[],[f22662]) ).
fof(f22662,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,[],[f16333]) ).
fof(f31429,plain,
spl635_457,
inference(avatar_split_clause,[],[f25394,f31427]) ).
fof(f31427,plain,
( spl635_457
<=> ! [X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_457])]) ).
fof(f25394,plain,
! [X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)),
inference(equality_resolution,[],[f19260]) ).
fof(f19260,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),X0)
| c_List_Olist_ONil(X1) != X0 ),
inference(cnf_transformation,[],[f15110]) ).
fof(f31425,plain,
spl635_456,
inference(avatar_split_clause,[],[f24359,f31423]) ).
fof(f31423,plain,
( spl635_456
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Omember(X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_456])]) ).
fof(f24359,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Omember(X1),X0))),
inference(definition_unfolding,[],[f17867,f17309]) ).
fof(f17867,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X0))),
inference(cnf_transformation,[],[f5719]) ).
fof(f5719,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X0))),
inference(rectify,[],[f4066]) ).
fof(f4066,axiom,
! [X210,X8] : hBOOL(hAPP(c_Finite__Set_Ofinite(X8),hAPP(c_List_Oset(X8),X210))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__set) ).
fof(f31421,plain,
spl635_455,
inference(avatar_split_clause,[],[f24205,f31418]) ).
fof(f31418,plain,
( spl635_455
<=> 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,[spl635_455])]) ).
fof(f24205,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin),
inference(definition_unfolding,[],[f17173,f17386]) ).
fof(f17173,plain,
c_Int_OPls = c_Int_Osucc(c_Int_OMin),
inference(cnf_transformation,[],[f1114]) ).
fof(f1114,axiom,
c_Int_OPls = c_Int_Osucc(c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_succ__Min) ).
fof(f31416,plain,
spl635_454,
inference(avatar_split_clause,[],[f23297,f31414]) ).
fof(f31414,plain,
( spl635_454
<=> ! [X2,X4,X0,X3,X1] :
( sP74(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_454])]) ).
fof(f23297,plain,
! [X2,X3,X0,X1,X4] :
( sP74(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ),
inference(cnf_transformation,[],[f14655]) ).
fof(f14655,plain,
! [X0,X1,X2,X3,X4] :
( sP74(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ),
inference(definition_folding,[],[f13900,f14654,f14653]) ).
fof(f14654,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)))
<=> sP73(X0,X1,X4,X2,X3) )
| ~ sP74(X3,X2,X4,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP74])]) ).
fof(f13900,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,[],[f9520]) ).
fof(f9520,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,[],[f2006]) ).
fof(f2006,axiom,
! [X72,X23,X47,X17,X8] :
( class_Orderings_Oorder(X8)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X17,X47)),c_SetInterval_Oord__class_OatLeastAtMost(X8,X23,X72)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X23),X72))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X47),X72))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X23),X17)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X47),X72))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X23),X17)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X17),X47)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeastatMost__psubset__iff) ).
fof(f31412,plain,
spl635_453,
inference(avatar_split_clause,[],[f21386,f31410]) ).
fof(f31410,plain,
( spl635_453
<=> ! [X2,X0,X1] :
( sP43(X2,X1,X0)
| ~ sP44(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_453])]) ).
fof(f21386,plain,
! [X2,X0,X1] :
( sP43(X2,X1,X0)
| ~ sP44(X0,X1,X2) ),
inference(cnf_transformation,[],[f15912]) ).
fof(f31408,plain,
( spl635_452
| ~ spl635_227
| ~ spl635_295 ),
inference(avatar_split_clause,[],[f30809,f30698,f30416,f31405]) ).
fof(f31405,plain,
( spl635_452
<=> sP5(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_452])]) ).
fof(f30416,plain,
( spl635_227
<=> c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_227])]) ).
fof(f30698,plain,
( spl635_295
<=> ! [X0,X1] :
( sP5(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_295])]) ).
fof(f30809,plain,
( sP5(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl635_227
| ~ spl635_295 ),
inference(resolution,[],[f30699,f30418]) ).
fof(f30418,plain,
( c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl635_227 ),
inference(avatar_component_clause,[],[f30416]) ).
fof(f30699,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,X0)
| sP5(X1,X0) )
| ~ spl635_295 ),
inference(avatar_component_clause,[],[f30698]) ).
fof(f31403,plain,
spl635_451,
inference(avatar_split_clause,[],[f21385,f31401]) ).
fof(f31401,plain,
( spl635_451
<=> ! [X2,X0,X1] :
( sP42(X2,X1,X0)
| ~ sP44(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_451])]) ).
fof(f21385,plain,
! [X2,X0,X1] :
( sP42(X2,X1,X0)
| ~ sP44(X0,X1,X2) ),
inference(cnf_transformation,[],[f15912]) ).
fof(f31399,plain,
spl635_450,
inference(avatar_split_clause,[],[f21306,f31397]) ).
fof(f31397,plain,
( spl635_450
<=> ! [X2,X0,X1] :
( sP38(X2,X1,X0)
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_450])]) ).
fof(f21306,plain,
! [X2,X0,X1] :
( sP38(X2,X1,X0)
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f15858]) ).
fof(f31395,plain,
spl635_449,
inference(avatar_split_clause,[],[f21305,f31393]) ).
fof(f31393,plain,
( spl635_449
<=> ! [X2,X0,X1] :
( sP37(X2,X1,X0)
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_449])]) ).
fof(f21305,plain,
! [X2,X0,X1] :
( sP37(X2,X1,X0)
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f15858]) ).
fof(f31391,plain,
spl635_448,
inference(avatar_split_clause,[],[f21255,f31389]) ).
fof(f31389,plain,
( spl635_448
<=> ! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP34(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_448])]) ).
fof(f21255,plain,
! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP34(X0,X2,X1) ),
inference(cnf_transformation,[],[f15817]) ).
fof(f15817,plain,
! [X0,X1,X2] :
( ( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP34(X0,X2,X1) )
& ( sP34(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14587]) ).
fof(f14587,plain,
! [X0,X1,X2] :
( c_Relation_Orefl__on(X2,X1,X0)
<=> sP34(X0,X2,X1) ),
inference(definition_folding,[],[f12669,f14586]) ).
fof(f14586,plain,
! [X0,X2,X1] :
( sP34(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,[sP34])]) ).
fof(f12669,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,[],[f8174]) ).
fof(f8174,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,[],[f3029]) ).
fof(f3029,axiom,
! [X98,X39,X8] :
( c_Relation_Orefl__on(X8,X39,X98)
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X39))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X2),X2)),X98)) )
& ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),X2),X98))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X8,X8,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X8,tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X8),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X8)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X8),c_fconj),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X39)))),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X39))),X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_refl__on__def_H) ).
fof(f31387,plain,
spl635_447,
inference(avatar_split_clause,[],[f21254,f31385]) ).
fof(f31385,plain,
( spl635_447
<=> ! [X2,X0,X1] :
( sP34(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_447])]) ).
fof(f21254,plain,
! [X2,X0,X1] :
( sP34(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f15817]) ).
fof(f31383,plain,
spl635_446,
inference(avatar_split_clause,[],[f21211,f31381]) ).
fof(f31381,plain,
( spl635_446
<=> ! [X2,X0,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| ~ sP33(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_446])]) ).
fof(f21211,plain,
! [X2,X0,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| ~ sP33(X1,X0,X2) ),
inference(cnf_transformation,[],[f15769]) ).
fof(f15769,plain,
! [X0,X1,X2] :
( ( c_List_Olist__ex1(X2,X1,X0)
| ~ sP33(X1,X0,X2) )
& ( sP33(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14585]) ).
fof(f14585,plain,
! [X0,X1,X2] :
( c_List_Olist__ex1(X2,X1,X0)
<=> sP33(X1,X0,X2) ),
inference(definition_folding,[],[f12661,f14584]) ).
fof(f12661,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,[],[f12660]) ).
fof(f12660,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,[],[f8163]) ).
fof(f8163,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,[],[f4824]) ).
fof(f4824,axiom,
! [X210,X29,X8] :
( c_List_Olist__ex1(X8,X29,X210)
<=> ? [X2] :
( ! [X45] :
( ( hBOOL(hAPP(X29,X45))
& hBOOL(hAPP(hAPP(c_member(X8),X45),hAPP(c_List_Oset(X8),X210))) )
=> X2 = X45 )
& hBOOL(hAPP(X29,X2))
& hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(c_List_Oset(X8),X210))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__iff) ).
fof(f31379,plain,
spl635_445,
inference(avatar_split_clause,[],[f21210,f31377]) ).
fof(f31377,plain,
( spl635_445
<=> ! [X2,X0,X1] :
( sP33(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_445])]) ).
fof(f21210,plain,
! [X2,X0,X1] :
( sP33(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ),
inference(cnf_transformation,[],[f15769]) ).
fof(f31375,plain,
spl635_444,
inference(avatar_split_clause,[],[f21203,f31373]) ).
fof(f31373,plain,
( spl635_444
<=> ! [X2,X0,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| ~ sP32(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_444])]) ).
fof(f21203,plain,
! [X2,X0,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| ~ sP32(X1,X0,X2) ),
inference(cnf_transformation,[],[f15763]) ).
fof(f15763,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,[],[f14583]) ).
fof(f14583,plain,
! [X0,X1,X2] :
( c_List_Olist__ex1(X2,X1,X0)
<=> sP32(X1,X0,X2) ),
inference(definition_folding,[],[f12659,f14582]) ).
fof(f12659,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,[],[f12658]) ).
fof(f12658,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,[],[f8162]) ).
fof(f8162,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,[],[f4884]) ).
fof(f4884,axiom,
! [X210,X29,X8] :
( c_List_Olist__ex1(X8,X29,X210)
<=> ? [X2] :
( ! [X45] :
( ( hBOOL(hAPP(X29,X45))
& hBOOL(hAPP(hAPP(c_member(X8),X45),hAPP(c_List_Oset(X8),X210))) )
=> X2 = X45 )
& hBOOL(hAPP(X29,X2))
& hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(c_List_Oset(X8),X210))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__iff__raw) ).
fof(f31371,plain,
spl635_443,
inference(avatar_split_clause,[],[f21202,f31369]) ).
fof(f31369,plain,
( spl635_443
<=> ! [X2,X0,X1] :
( sP32(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_443])]) ).
fof(f21202,plain,
! [X2,X0,X1] :
( sP32(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ),
inference(cnf_transformation,[],[f15763]) ).
fof(f31367,plain,
spl635_442,
inference(avatar_split_clause,[],[f20697,f31365]) ).
fof(f31365,plain,
( spl635_442
<=> ! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ c_Equiv__Relations_Oequiv(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_442])]) ).
fof(f20697,plain,
! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ c_Equiv__Relations_Oequiv(X2,X1,X0) ),
inference(cnf_transformation,[],[f12197]) ).
fof(f12197,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,[],[f12196]) ).
fof(f12196,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,[],[f7832]) ).
fof(f7832,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,[],[f4965]) ).
fof(f4965,axiom,
! [X98,X39,X8] :
( c_Equiv__Relations_Oequiv(X8,X39,X98)
=> ~ ( c_Relation_Orefl__on(X8,X39,X98)
=> ( c_Relation_Osym(X8,X98)
=> ~ c_Relation_Otrans(X8,X98) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivE) ).
fof(f31363,plain,
( spl635_441
| ~ spl635_227
| ~ spl635_294 ),
inference(avatar_split_clause,[],[f30806,f30694,f30416,f31360]) ).
fof(f31360,plain,
( spl635_441
<=> c_Wellfounded_Oacyclic(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_441])]) ).
fof(f30694,plain,
( spl635_294
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_294])]) ).
fof(f30806,plain,
( c_Wellfounded_Oacyclic(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl635_227
| ~ spl635_294 ),
inference(resolution,[],[f30695,f30418]) ).
fof(f30695,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,X0)
| c_Wellfounded_Oacyclic(X1,X0) )
| ~ spl635_294 ),
inference(avatar_component_clause,[],[f30694]) ).
fof(f31358,plain,
spl635_440,
inference(avatar_split_clause,[],[f19661,f31356]) ).
fof(f31356,plain,
( spl635_440
<=> ! [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,[spl635_440])]) ).
fof(f19661,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,[],[f6956]) ).
fof(f6956,plain,
! [X0,X1,X2] : c_Fun_Oinj__on(X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(rectify,[],[f3053]) ).
fof(f3053,axiom,
! [X1,X25,X8] : c_Fun_Oinj__on(X8,X25,X1,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__empty) ).
fof(f31354,plain,
spl635_439,
inference(avatar_split_clause,[],[f19659,f31352]) ).
fof(f31352,plain,
( spl635_439
<=> ! [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,[spl635_439])]) ).
fof(f19659,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,[],[f6954]) ).
fof(f6954,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,[],[f1523]) ).
fof(f1523,axiom,
! [X20,X21,X8] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X8,X21,X20,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Orecs_I1_J) ).
fof(f31350,plain,
spl635_438,
inference(avatar_split_clause,[],[f19658,f31348]) ).
fof(f31348,plain,
( spl635_438
<=> ! [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,[spl635_438])]) ).
fof(f19658,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,[],[f6953]) ).
fof(f6953,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,[],[f1467]) ).
fof(f1467,axiom,
! [X20,X21,X8] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X8,X21,X20,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X21,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I4_J) ).
fof(f31346,plain,
spl635_437,
inference(avatar_split_clause,[],[f19656,f31344]) ).
fof(f31344,plain,
( spl635_437
<=> ! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_437])]) ).
fof(f19656,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != X0,
inference(cnf_transformation,[],[f6951]) ).
fof(f6951,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != X0,
inference(rectify,[],[f3998]) ).
fof(f3998,axiom,
! [X208,X13,X5] : hAPP(hAPP(c_List_Olist_OCons(X5),X13),X208) != X208,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__Cons__self2) ).
fof(f31342,plain,
spl635_436,
inference(avatar_split_clause,[],[f19212,f31340]) ).
fof(f31340,plain,
( spl635_436
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_436])]) ).
fof(f19212,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f15063]) ).
fof(f15063,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onat,X1) = X0
| ~ sP7(X0,X1) )
& ( sP7(X0,X1)
| hAPP(c_Int_Onat,X1) != X0 ) ),
inference(nnf_transformation,[],[f14541]) ).
fof(f14541,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
<=> sP7(X0,X1) ),
inference(definition_folding,[],[f11324,f14540]) ).
fof(f11324,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,[],[f6780]) ).
fof(f6780,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,[],[f435]) ).
fof(f435,axiom,
! [X27,X52] :
( hAPP(c_Int_Onat,X52) = X27
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X52))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X27 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X52))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27) = X52 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__iff) ).
fof(f31338,plain,
spl635_435,
inference(avatar_split_clause,[],[f19204,f31336]) ).
fof(f31336,plain,
( spl635_435
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| ~ sP6(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_435])]) ).
fof(f19204,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| ~ sP6(X1,X0) ),
inference(cnf_transformation,[],[f15060]) ).
fof(f15060,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onat,X0) = X1
| ~ sP6(X1,X0) )
& ( sP6(X1,X0)
| hAPP(c_Int_Onat,X0) != X1 ) ),
inference(nnf_transformation,[],[f14539]) ).
fof(f14539,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
<=> sP6(X1,X0) ),
inference(definition_folding,[],[f11323,f14538]) ).
fof(f11323,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,[],[f6779]) ).
fof(f6779,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,[],[f434]) ).
fof(f434,axiom,
! [X52,X27] :
( hAPP(c_Int_Onat,X52) = X27
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X52))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X27 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X52))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X27) = X52 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__eq__iff2) ).
fof(f31334,plain,
spl635_434,
inference(avatar_split_clause,[],[f19193,f31332]) ).
fof(f31332,plain,
( spl635_434
<=> ! [X0,X1] :
( X0 = X1
| c_Int_OBit0(X0) != c_Int_OBit0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_434])]) ).
fof(f19193,plain,
! [X0,X1] :
( X0 = X1
| c_Int_OBit0(X0) != c_Int_OBit0(X1) ),
inference(cnf_transformation,[],[f15055]) ).
fof(f15055,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,[],[f6777]) ).
fof(f6777,plain,
! [X0,X1] :
( c_Int_OBit0(X0) = c_Int_OBit0(X1)
<=> X0 = X1 ),
inference(rectify,[],[f1235]) ).
fof(f1235,axiom,
! [X77,X48] :
( c_Int_OBit0(X48) = c_Int_OBit0(X77)
<=> X48 = X77 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I48_J) ).
fof(f31330,plain,
spl635_433,
inference(avatar_split_clause,[],[f19086,f31328]) ).
fof(f31328,plain,
( spl635_433
<=> ! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_433])]) ).
fof(f19086,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f11283]) ).
fof(f11283,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(flattening,[],[f11282]) ).
fof(f11282,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6729]) ).
fof(f6729,plain,
! [X0,X1] :
( ( class_Enum_Oenum(X0)
& class_Enum_Oenum(X1) )
=> class_Enum_Oenum(tc_fun(X1,X0)) ),
inference(rectify,[],[f5002]) ).
fof(f5002,axiom,
! [X264,X263] :
( ( class_Enum_Oenum(X264)
& class_Enum_Oenum(X263) )
=> class_Enum_Oenum(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Enum_Oenum) ).
fof(f31326,plain,
spl635_432,
inference(avatar_split_clause,[],[f19085,f31324]) ).
fof(f31324,plain,
( spl635_432
<=> ! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_432])]) ).
fof(f19085,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f11281]) ).
fof(f11281,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(flattening,[],[f11280]) ).
fof(f11280,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6728]) ).
fof(f6728,plain,
! [X0,X1] :
( ( class_Enum_Oenum(X0)
& class_Enum_Oenum(X1) )
=> class_Enum_Oenum(tc_prod(X1,X0)) ),
inference(rectify,[],[f5153]) ).
fof(f5153,axiom,
! [X264,X263] :
( ( class_Enum_Oenum(X264)
& class_Enum_Oenum(X263) )
=> class_Enum_Oenum(tc_prod(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Enum_Oenum) ).
fof(f31322,plain,
spl635_431,
inference(avatar_split_clause,[],[f19084,f31320]) ).
fof(f31320,plain,
( spl635_431
<=> ! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_431])]) ).
fof(f19084,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f11279]) ).
fof(f11279,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(flattening,[],[f11278]) ).
fof(f11278,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6727]) ).
fof(f6727,plain,
! [X0,X1] :
( ( class_Enum_Oenum(X0)
& class_Enum_Oenum(X1) )
=> class_Enum_Oenum(tc_sum(X1,X0)) ),
inference(rectify,[],[f5145]) ).
fof(f5145,axiom,
! [X264,X263] :
( ( class_Enum_Oenum(X264)
& class_Enum_Oenum(X263) )
=> class_Enum_Oenum(tc_sum(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Enum_Oenum) ).
fof(f31318,plain,
spl635_430,
inference(avatar_split_clause,[],[f19083,f31316]) ).
fof(f31316,plain,
( spl635_430
<=> ! [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,[spl635_430])]) ).
fof(f19083,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11277]) ).
fof(f11277,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11276]) ).
fof(f11276,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6726]) ).
fof(f6726,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,
! [X264,X263] :
( ( class_Finite__Set_Ofinite(X264)
& class_Finite__Set_Ofinite(X263) )
=> class_Finite__Set_Ofinite(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
fof(f31314,plain,
spl635_429,
inference(avatar_split_clause,[],[f19082,f31312]) ).
fof(f31312,plain,
( spl635_429
<=> ! [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,[spl635_429])]) ).
fof(f19082,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11275]) ).
fof(f11275,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11274]) ).
fof(f11274,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6725]) ).
fof(f6725,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,
! [X264,X263] :
( ( class_Finite__Set_Ofinite(X264)
& class_Finite__Set_Ofinite(X263) )
=> class_Finite__Set_Ofinite(tc_prod(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
fof(f31310,plain,
spl635_428,
inference(avatar_split_clause,[],[f19081,f31308]) ).
fof(f31308,plain,
( spl635_428
<=> ! [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,[spl635_428])]) ).
fof(f19081,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11273]) ).
fof(f11273,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11272]) ).
fof(f11272,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6724]) ).
fof(f6724,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,
! [X264,X263] :
( ( class_Finite__Set_Ofinite(X264)
& class_Finite__Set_Ofinite(X263) )
=> class_Finite__Set_Ofinite(tc_sum(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
fof(f31306,plain,
spl635_427,
inference(avatar_split_clause,[],[f19080,f31304]) ).
fof(f31304,plain,
( spl635_427
<=> ! [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,[spl635_427])]) ).
fof(f19080,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,[],[f11271]) ).
fof(f11271,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,[],[f11270]) ).
fof(f11270,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,[],[f6723]) ).
fof(f6723,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,
! [X264,X263] :
( ( class_Lazy__Sequence_Osmall__lazy(X264)
& class_Lazy__Sequence_Osmall__lazy(X263) )
=> class_Lazy__Sequence_Osmall__lazy(tc_prod(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Lazy__Sequence_Osmall__lazy) ).
fof(f31302,plain,
spl635_426,
inference(avatar_split_clause,[],[f18745,f31300]) ).
fof(f31300,plain,
( spl635_426
<=> ! [X0,X1] :
( c_Relation_Osym(X1,c_Transitive__Closure_Ortrancl(X1,X0))
| ~ c_Relation_Osym(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_426])]) ).
fof(f18745,plain,
! [X0,X1] :
( c_Relation_Osym(X1,c_Transitive__Closure_Ortrancl(X1,X0))
| ~ c_Relation_Osym(X1,X0) ),
inference(cnf_transformation,[],[f10901]) ).
fof(f10901,plain,
! [X0,X1] :
( c_Relation_Osym(X1,c_Transitive__Closure_Ortrancl(X1,X0))
| ~ c_Relation_Osym(X1,X0) ),
inference(ennf_transformation,[],[f6454]) ).
fof(f6454,plain,
! [X0,X1] :
( c_Relation_Osym(X1,X0)
=> c_Relation_Osym(X1,c_Transitive__Closure_Ortrancl(X1,X0)) ),
inference(rectify,[],[f4960]) ).
fof(f4960,axiom,
! [X98,X8] :
( c_Relation_Osym(X8,X98)
=> c_Relation_Osym(X8,c_Transitive__Closure_Ortrancl(X8,X98)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sym__rtrancl) ).
fof(f31298,plain,
spl635_425,
inference(avatar_split_clause,[],[f18743,f31296]) ).
fof(f31296,plain,
( spl635_425
<=> ! [X0,X1] :
( c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_425])]) ).
fof(f18743,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ),
inference(cnf_transformation,[],[f10899]) ).
fof(f10899,plain,
! [X0,X1] :
( c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ),
inference(ennf_transformation,[],[f6452]) ).
fof(f6452,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
=> c_Relation_Oantisym(X1,c_Transitive__Closure_Ortrancl(X1,X0)) ),
inference(rectify,[],[f4948]) ).
fof(f4948,axiom,
! [X98,X8] :
( c_Wellfounded_Oacyclic(X8,X98)
=> c_Relation_Oantisym(X8,c_Transitive__Closure_Ortrancl(X8,X98)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).
fof(f31294,plain,
spl635_424,
inference(avatar_split_clause,[],[f18721,f31292]) ).
fof(f31292,plain,
( spl635_424
<=> ! [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,[spl635_424])]) ).
fof(f18721,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,[],[f10872]) ).
fof(f10872,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,[],[f10871]) ).
fof(f10871,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,[],[f6435]) ).
fof(f6435,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,[],[f1404]) ).
fof(f1404,axiom,
! [X12,X13] :
( c_Nat__Transfer_Ois__nat(X13)
=> ( c_Nat__Transfer_Ois__nat(X12)
=> c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X13,X12)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) ).
fof(f31290,plain,
spl635_423,
inference(avatar_split_clause,[],[f18387,f31288]) ).
fof(f31288,plain,
( spl635_423
<=> ! [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,[spl635_423])]) ).
fof(f18387,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,[],[f10540]) ).
fof(f10540,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,[],[f6164]) ).
fof(f6164,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,[],[f3054]) ).
fof(f3054,axiom,
! [X39,X8] :
( class_Groups_Oordered__ab__group__add(X8)
=> c_Fun_Oinj__on(X8,X8,c_Groups_Ouminus__class_Ouminus(X8),X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__uminus) ).
fof(f31286,plain,
spl635_422,
inference(avatar_split_clause,[],[f18324,f31284]) ).
fof(f31284,plain,
( spl635_422
<=> ! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_422])]) ).
fof(f18324,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(cnf_transformation,[],[f6117]) ).
fof(f6117,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(rectify,[],[f5216]) ).
fof(f5216,axiom,
! [X129,X29] :
( hBOOL(X29)
| ~ hBOOL(hAPP(hAPP(c_fconj,X29),X129)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).
fof(f31282,plain,
spl635_421,
inference(avatar_split_clause,[],[f18323,f31280]) ).
fof(f31280,plain,
( spl635_421
<=> ! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_421])]) ).
fof(f18323,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(cnf_transformation,[],[f6116]) ).
fof(f6116,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(rectify,[],[f5217]) ).
fof(f5217,axiom,
! [X129,X29] :
( hBOOL(X129)
| ~ hBOOL(hAPP(hAPP(c_fconj,X29),X129)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).
fof(f31277,plain,
spl635_420,
inference(avatar_split_clause,[],[f18318,f31275]) ).
fof(f18318,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ),
inference(cnf_transformation,[],[f6111]) ).
fof(f6111,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ),
inference(rectify,[],[f5221]) ).
fof(f5221,axiom,
! [X129,X29] :
( hBOOL(hAPP(hAPP(c_fimplies,X29),X129))
| hBOOL(X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__1) ).
fof(f31273,plain,
spl635_419,
inference(avatar_split_clause,[],[f18317,f31271]) ).
fof(f18317,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6110]) ).
fof(f6110,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5222]) ).
fof(f5222,axiom,
! [X29,X129] :
( hBOOL(hAPP(hAPP(c_fimplies,X29),X129))
| ~ hBOOL(X129) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__2) ).
fof(f31269,plain,
spl635_418,
inference(avatar_split_clause,[],[f18316,f31267]) ).
fof(f18316,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6109]) ).
fof(f6109,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5219]) ).
fof(f5219,axiom,
! [X29,X129] :
( hBOOL(hAPP(hAPP(c_fdisj,X29),X129))
| ~ hBOOL(X129) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__2) ).
fof(f31265,plain,
spl635_417,
inference(avatar_split_clause,[],[f18315,f31263]) ).
fof(f18315,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6108]) ).
fof(f6108,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5218]) ).
fof(f5218,axiom,
! [X129,X29] :
( hBOOL(hAPP(hAPP(c_fdisj,X29),X129))
| ~ hBOOL(X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__1) ).
fof(f31261,plain,
spl635_416,
inference(avatar_split_clause,[],[f17869,f31259]) ).
fof(f31259,plain,
( spl635_416
<=> ! [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,[spl635_416])]) ).
fof(f17869,plain,
! [X0,X1] : c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X0),
inference(cnf_transformation,[],[f5721]) ).
fof(f5721,plain,
! [X0,X1] : c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X0),
inference(rectify,[],[f4664]) ).
fof(f4664,axiom,
! [X39,X8] : c_Fun_Oinj__on(tc_List_Olist(X8),tc_List_Olist(X8),c_List_Orev(X8),X39),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__rev) ).
fof(f31257,plain,
spl635_415,
inference(avatar_split_clause,[],[f17866,f31255]) ).
fof(f31255,plain,
( spl635_415
<=> ! [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,[spl635_415])]) ).
fof(f17866,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,[],[f5718]) ).
fof(f5718,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f2228]) ).
fof(f2228,axiom,
! [X75,X77] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X77,X75))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).
fof(f31253,plain,
spl635_414,
inference(avatar_split_clause,[],[f17865,f31251]) ).
fof(f31251,plain,
( spl635_414
<=> ! [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,[spl635_414])]) ).
fof(f17865,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,[],[f5717]) ).
fof(f5717,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f2232]) ).
fof(f2232,axiom,
! [X75,X77] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X77,X75))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost) ).
fof(f31249,plain,
spl635_413,
inference(avatar_split_clause,[],[f17864,f31247]) ).
fof(f31247,plain,
( spl635_413
<=> ! [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,[spl635_413])]) ).
fof(f17864,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,[],[f5716]) ).
fof(f5716,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f2235]) ).
fof(f2235,axiom,
! [X75,X77] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X77,X75))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan) ).
fof(f31245,plain,
spl635_412,
inference(avatar_split_clause,[],[f17863,f31243]) ).
fof(f31243,plain,
( spl635_412
<=> ! [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,[spl635_412])]) ).
fof(f17863,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,[],[f5715]) ).
fof(f5715,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f2227]) ).
fof(f2227,axiom,
! [X75,X77] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X77,X75))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastAtMost__int) ).
fof(f31241,plain,
spl635_411,
inference(avatar_split_clause,[],[f17862,f31239]) ).
fof(f31239,plain,
( spl635_411
<=> ! [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,[spl635_411])]) ).
fof(f17862,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,[],[f5714]) ).
fof(f5714,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f2233]) ).
fof(f2233,axiom,
! [X75,X77] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X77,X75))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost__int) ).
fof(f31236,plain,
spl635_410,
inference(avatar_split_clause,[],[f17861,f31234]) ).
fof(f31234,plain,
( spl635_410
<=> ! [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,[spl635_410])]) ).
fof(f17861,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,[],[f5713]) ).
fof(f5713,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f2234]) ).
fof(f2234,axiom,
! [X75,X77] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X77,X75))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan__int) ).
fof(f31232,plain,
spl635_409,
inference(avatar_split_clause,[],[f17860,f31230]) ).
fof(f31230,plain,
( spl635_409
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_409])]) ).
fof(f17860,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5712]) ).
fof(f5712,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4712]) ).
fof(f4712,axiom,
! [X29,X8] : c_List_Olist_ONil(X8) = c_List_OtakeWhile(X8,X29,c_List_Olist_ONil(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).
fof(f31228,plain,
spl635_408,
inference(avatar_split_clause,[],[f17859,f31226]) ).
fof(f31226,plain,
( spl635_408
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_408])]) ).
fof(f17859,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5711]) ).
fof(f5711,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4428]) ).
fof(f4428,axiom,
! [X13,X5] : c_List_Olist_ONil(X5) = c_List_Oremove1(X5,X13,c_List_Olist_ONil(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remove1_Osimps_I1_J) ).
fof(f31224,plain,
spl635_407,
inference(avatar_split_clause,[],[f17578,f31222]) ).
fof(f17578,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,[],[f10338]) ).
fof(f10338,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,[],[f5503]) ).
fof(f5503,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls)) ),
inference(rectify,[],[f1113]) ).
fof(f1113,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OPls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__Numeral0) ).
fof(f31220,plain,
spl635_406,
inference(avatar_split_clause,[],[f17577,f31218]) ).
fof(f17577,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,[],[f10337]) ).
fof(f10337,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,[],[f5502]) ).
fof(f5502,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin)) ),
inference(rectify,[],[f974]) ).
fof(f974,axiom,
! [X5] :
( class_Int_Onumber__ring(X5)
=> ~ c_Int_Oiszero(X5,hAPP(c_Int_Onumber__class_Onumber__of(X5),c_Int_OMin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nonzero__number__of__Min) ).
fof(f31216,plain,
spl635_405,
inference(avatar_split_clause,[],[f17372,f31214]) ).
fof(f31214,plain,
( spl635_405
<=> ! [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,[spl635_405])]) ).
fof(f17372,plain,
! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f5310]) ).
fof(f5310,plain,
! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f3487]) ).
fof(f3487,axiom,
! [X8] : c_Wellfounded_Owf(X8,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X8),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__empty) ).
fof(f31212,plain,
spl635_404,
inference(avatar_split_clause,[],[f17371,f31210]) ).
fof(f31210,plain,
( spl635_404
<=> ! [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,[spl635_404])]) ).
fof(f17371,plain,
! [X0] : c_Relation_Oantisym(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f5309]) ).
fof(f5309,plain,
! [X0] : c_Relation_Oantisym(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f4944]) ).
fof(f4944,axiom,
! [X8] : c_Relation_Oantisym(X8,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X8),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_antisym__empty) ).
fof(f31208,plain,
spl635_403,
inference(avatar_split_clause,[],[f17369,f31206]) ).
fof(f31206,plain,
( spl635_403
<=> ! [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,[spl635_403])]) ).
fof(f17369,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5307]) ).
fof(f5307,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(rectify,[],[f2300]) ).
fof(f2300,axiom,
! [X8] : hBOOL(hAPP(c_Finite__Set_Ofinite(X8),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).
fof(f31204,plain,
spl635_402,
inference(avatar_split_clause,[],[f17366,f31202]) ).
fof(f31202,plain,
( spl635_402
<=> ! [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,[spl635_402])]) ).
fof(f17366,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0))),
inference(cnf_transformation,[],[f5304]) ).
fof(f5304,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0))),
inference(rectify,[],[f2229]) ).
fof(f2229,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',fact_finite__lessThan) ).
fof(f31200,plain,
spl635_401,
inference(avatar_split_clause,[],[f17365,f31198]) ).
fof(f31198,plain,
( spl635_401
<=> ! [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,[spl635_401])]) ).
fof(f17365,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(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_OatMost(tc_Nat_Onat),X0))),
inference(rectify,[],[f2230]) ).
fof(f2230,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',fact_finite__atMost) ).
fof(f31196,plain,
spl635_400,
inference(avatar_split_clause,[],[f17364,f31194]) ).
fof(f31194,plain,
( spl635_400
<=> ! [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,[spl635_400])]) ).
fof(f17364,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,[],[f5302]) ).
fof(f5302,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,[],[f2078]) ).
fof(f2078,axiom,
! [X58] : 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)),X58)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) ).
fof(f31192,plain,
spl635_399,
inference(avatar_split_clause,[],[f17363,f31190]) ).
fof(f31190,plain,
( spl635_399
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_399])]) ).
fof(f17363,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(cnf_transformation,[],[f5301]) ).
fof(f5301,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(rectify,[],[f1061]) ).
fof(f1061,axiom,
! [X40] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X40),c_Int_OPls) = X40,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(f31188,plain,
spl635_398,
inference(avatar_split_clause,[],[f17362,f31186]) ).
fof(f31186,plain,
( spl635_398
<=> ! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_398])]) ).
fof(f31184,plain,
spl635_397,
inference(avatar_split_clause,[],[f17361,f31182]) ).
fof(f31182,plain,
( spl635_397
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_397])]) ).
fof(f17361,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0,
inference(cnf_transformation,[],[f5299]) ).
fof(f5299,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0,
inference(rectify,[],[f1062]) ).
fof(f1062,axiom,
! [X40] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X40) = X40,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(f31180,plain,
spl635_396,
inference(avatar_split_clause,[],[f17360,f31178]) ).
fof(f17360,plain,
! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0,
inference(cnf_transformation,[],[f5298]) ).
fof(f5298,plain,
! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0,
inference(rectify,[],[f371]) ).
fof(f371,axiom,
! [X4] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4)) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__int) ).
fof(f31176,plain,
spl635_395,
inference(avatar_split_clause,[],[f17357,f31174]) ).
fof(f31174,plain,
( spl635_395
<=> ! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_395])]) ).
fof(f17357,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5295]) ).
fof(f5295,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)),
inference(rectify,[],[f4666]) ).
fof(f4666,axiom,
! [X5] : c_List_Olist_ONil(X5) = hAPP(c_List_Orev(X5),c_List_Olist_ONil(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev_Osimps_I1_J) ).
fof(f31172,plain,
spl635_394,
inference(avatar_split_clause,[],[f17356,f31170]) ).
fof(f31170,plain,
( spl635_394
<=> ! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_394])]) ).
fof(f17356,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5294]) ).
fof(f5294,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)),
inference(rectify,[],[f4330]) ).
fof(f4330,axiom,
! [X5] : c_List_Olist_ONil(X5) = hAPP(c_List_Otl(X5),c_List_Olist_ONil(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tl_Osimps_I1_J) ).
fof(f31168,plain,
spl635_393,
inference(avatar_split_clause,[],[f17352,f31166]) ).
fof(f31166,plain,
( spl635_393
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_393])]) ).
fof(f17352,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0),
inference(cnf_transformation,[],[f5290]) ).
fof(f5290,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0),
inference(rectify,[],[f1063]) ).
fof(f1063,axiom,
! [X59] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X59),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__Pls) ).
fof(f31164,plain,
spl635_392,
inference(avatar_split_clause,[],[f17230,f31161]) ).
fof(f31161,plain,
( spl635_392
<=> 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,[spl635_392])]) ).
fof(f17230,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,[],[f366]) ).
fof(f366,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',fact_transfer__int__nat__numerals_I2_J) ).
fof(f31159,plain,
~ spl635_391,
inference(avatar_split_clause,[],[f17226,f31156]) ).
fof(f17226,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,[],[f3140]) ).
fof(f3140,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',fact_infinite__UNIV__nat) ).
fof(f31154,plain,
~ spl635_390,
inference(avatar_split_clause,[],[f17225,f31151]) ).
fof(f17225,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,[],[f3141]) ).
fof(f3141,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',fact_infinite__UNIV__int) ).
fof(f31135,plain,
( spl635_389
| ~ spl635_315 ),
inference(avatar_split_clause,[],[f30821,f30783,f31132]) ).
fof(f31132,plain,
( spl635_389
<=> sP11(c_Int_OPls,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_389])]) ).
fof(f30783,plain,
( spl635_315
<=> ! [X1] :
( c_Int_OPls != X1
| sP11(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_315])]) ).
fof(f30821,plain,
( sP11(c_Int_OPls,c_Int_OPls)
| ~ spl635_315 ),
inference(equality_resolution,[],[f30784]) ).
fof(f30784,plain,
( ! [X1] :
( c_Int_OPls != X1
| sP11(X1,X1) )
| ~ spl635_315 ),
inference(avatar_component_clause,[],[f30783]) ).
fof(f31129,plain,
( spl635_388
| ~ spl635_198
| ~ spl635_295 ),
inference(avatar_split_clause,[],[f30808,f30698,f30282,f31126]) ).
fof(f31126,plain,
( spl635_388
<=> sP5(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_388])]) ).
fof(f30282,plain,
( spl635_198
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_198])]) ).
fof(f30808,plain,
( sP5(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl635_198
| ~ spl635_295 ),
inference(resolution,[],[f30699,f30284]) ).
fof(f30284,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl635_198 ),
inference(avatar_component_clause,[],[f30282]) ).
fof(f31122,plain,
( spl635_387
| ~ spl635_197
| ~ spl635_295 ),
inference(avatar_split_clause,[],[f30807,f30698,f30277,f31119]) ).
fof(f31119,plain,
( spl635_387
<=> sP5(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_387])]) ).
fof(f30277,plain,
( spl635_197
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_197])]) ).
fof(f30807,plain,
( sP5(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl635_197
| ~ spl635_295 ),
inference(resolution,[],[f30699,f30279]) ).
fof(f30279,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl635_197 ),
inference(avatar_component_clause,[],[f30277]) ).
fof(f31117,plain,
spl635_386,
inference(avatar_split_clause,[],[f27613,f31115]) ).
fof(f27613,plain,
! [X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X1,X1) ),
inference(forward_demodulation,[],[f25426,f17327]) ).
fof(f25426,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,[],[f19389]) ).
fof(f19389,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,[],[f15196]) ).
fof(f31113,plain,
spl635_385,
inference(avatar_split_clause,[],[f26473,f31111]) ).
fof(f26473,plain,
! [X0,X1] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0)),
inference(forward_demodulation,[],[f17854,f24260]) ).
fof(f17854,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X1),c_List_Olist_ONil(X1)),X0)),
inference(cnf_transformation,[],[f5706]) ).
fof(f5706,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X1),c_List_Olist_ONil(X1)),X0)),
inference(rectify,[],[f4880]) ).
fof(f4880,axiom,
! [X12,X5] : ~ hBOOL(hAPP(hAPP(c_List_Omember(X5),c_List_Olist_ONil(X5)),X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_member__rec_I2_J) ).
fof(f31109,plain,
spl635_384,
inference(avatar_split_clause,[],[f25969,f31106]) ).
fof(f31106,plain,
( spl635_384
<=> 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,[spl635_384])]) ).
fof(f31104,plain,
spl635_383,
inference(avatar_split_clause,[],[f25953,f31101]) ).
fof(f31099,plain,
spl635_382,
inference(avatar_split_clause,[],[f25951,f31096]) ).
fof(f31096,plain,
( spl635_382
<=> 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,[spl635_382])]) ).
fof(f25951,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17214,f17187]) ).
fof(f17214,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,[],[f1105]) ).
fof(f1105,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',fact_semiring__norm_I113_J) ).
fof(f31094,plain,
spl635_381,
inference(avatar_split_clause,[],[f25950,f31091]) ).
fof(f31091,plain,
( spl635_381
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_381])]) ).
fof(f25950,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
inference(forward_demodulation,[],[f17213,f17187]) ).
fof(f17213,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
inference(cnf_transformation,[],[f4000]) ).
fof(f4000,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',fact_bool_Osize_I4_J) ).
fof(f31089,plain,
spl635_380,
inference(avatar_split_clause,[],[f25949,f31086]) ).
fof(f31086,plain,
( spl635_380
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_380])]) ).
fof(f25949,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
inference(forward_demodulation,[],[f17212,f17187]) ).
fof(f17212,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
inference(cnf_transformation,[],[f4001]) ).
fof(f4001,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',fact_bool_Osize_I3_J) ).
fof(f31084,plain,
spl635_379,
inference(avatar_split_clause,[],[f25943,f31081]) ).
fof(f31081,plain,
( spl635_379
<=> 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,[spl635_379])]) ).
fof(f31079,plain,
spl635_378,
inference(avatar_split_clause,[],[f25403,f31077]) ).
fof(f31077,plain,
( spl635_378
<=> ! [X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_378])]) ).
fof(f25403,plain,
! [X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)),
inference(equality_resolution,[],[f19295]) ).
fof(f19295,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f15131]) ).
fof(f15131,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,[],[f15130]) ).
fof(f15130,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,[],[f6813]) ).
fof(f6813,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,[],[f282]) ).
fof(f282,axiom,
! [X52,X53] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X53),X52))
<=> ( X52 != X53
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X53),X52)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zless__le) ).
fof(f31075,plain,
( spl635_377
| ~ spl635_198
| ~ spl635_294 ),
inference(avatar_split_clause,[],[f30805,f30694,f30282,f31072]) ).
fof(f31072,plain,
( spl635_377
<=> c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_377])]) ).
fof(f30805,plain,
( c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl635_198
| ~ spl635_294 ),
inference(resolution,[],[f30695,f30284]) ).
fof(f31070,plain,
spl635_376,
inference(avatar_split_clause,[],[f24312,f31068]) ).
fof(f31068,plain,
( spl635_376
<=> ! [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,[spl635_376])]) ).
fof(f24312,plain,
! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Omember(tc_Int_Oint),X0)) ),
inference(definition_unfolding,[],[f17680,f17309]) ).
fof(f17680,plain,
! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ),
inference(cnf_transformation,[],[f10440]) ).
fof(f10440,plain,
! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ),
inference(ennf_transformation,[],[f10132]) ).
fof(f10132,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,[],[f5600]) ).
fof(f5600,plain,
! [X0] :
( c_List_Onat__list(X0)
<=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ),
inference(rectify,[],[f4271]) ).
fof(f4271,axiom,
! [X77] :
( c_List_Onat__list(X77)
<=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X77)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__list__def) ).
fof(f31066,plain,
spl635_375,
inference(avatar_split_clause,[],[f21904,f31064]) ).
fof(f31064,plain,
( spl635_375
<=> ! [X0,X3,X2,X1] :
( sP54(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_375])]) ).
fof(f21904,plain,
! [X2,X3,X0,X1] :
( sP54(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f14620]) ).
fof(f14620,plain,
! [X0,X1,X2,X3] :
( sP54(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f12753,f14619,f14618]) ).
fof(f14618,plain,
! [X1,X0,X3,X2] :
( sP53(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,[sP53])]) ).
fof(f14619,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)))
<=> sP53(X1,X0,X3,X2) )
| ~ sP54(X2,X3,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP54])]) ).
fof(f12753,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,[],[f8559]) ).
fof(f8559,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,[],[f210]) ).
fof(f210,axiom,
! [X47,X17,X23,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X17)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X23),X47)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X47),X17))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X23),c_Groups_Ozero__class_Ozero(X8))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X17),X47))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X23)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(f31062,plain,
spl635_374,
inference(avatar_split_clause,[],[f21895,f31060]) ).
fof(f31060,plain,
( spl635_374
<=> ! [X0,X3,X2,X1] :
( sP52(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_374])]) ).
fof(f21895,plain,
! [X2,X3,X0,X1] :
( sP52(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f14617]) ).
fof(f14617,plain,
! [X0,X1,X2,X3] :
( sP52(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f12752,f14616,f14615]) ).
fof(f14615,plain,
! [X2,X0,X3,X1] :
( sP51(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,[sP51])]) ).
fof(f14616,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)))
<=> sP51(X2,X0,X3,X1) )
| ~ sP52(X1,X3,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP52])]) ).
fof(f12752,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,[],[f8558]) ).
fof(f8558,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,[],[f209]) ).
fof(f209,axiom,
! [X47,X23,X17,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X17),X23)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X47),X23)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X47),X17))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X23),c_Groups_Ozero__class_Ozero(X8))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),X17),X47))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X8),c_Groups_Ozero__class_Ozero(X8)),X23)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(f31058,plain,
spl635_373,
inference(avatar_split_clause,[],[f20699,f31056]) ).
fof(f20699,plain,
! [X2,X0,X1] :
( c_Relation_Otrans(X2,X0)
| ~ c_Equiv__Relations_Oequiv(X2,X1,X0) ),
inference(cnf_transformation,[],[f12197]) ).
fof(f31054,plain,
spl635_372,
inference(avatar_split_clause,[],[f20698,f31052]) ).
fof(f20698,plain,
! [X2,X0,X1] :
( c_Relation_Osym(X2,X0)
| ~ c_Equiv__Relations_Oequiv(X2,X1,X0) ),
inference(cnf_transformation,[],[f12197]) ).
fof(f31050,plain,
spl635_371,
inference(avatar_split_clause,[],[f20476,f31048]) ).
fof(f31048,plain,
( spl635_371
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X1)
| ~ sP20(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_371])]) ).
fof(f20476,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X1)
| ~ sP20(X0,X1,X2) ),
inference(cnf_transformation,[],[f15489]) ).
fof(f15489,plain,
! [X0,X1,X2] :
( ( sP20(X0,X1,X2)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK237(X0,X1,X2)),sK238(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK238(X0,X1,X2)),hAPP(c_List_Oset(X0),X1)))
& hBOOL(hAPP(hAPP(c_member(X0),sK237(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) )
| ~ sP20(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK237,sK238])],[f15486,f15488,f15487]) ).
fof(f15487,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),sK237(X0,X1,X2)),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X1))) )
& hBOOL(hAPP(hAPP(c_member(X0),sK237(X0,X1,X2)),hAPP(c_List_Oset(X0),X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15488,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK237(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),sK237(X0,X1,X2)),sK238(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK238(X0,X1,X2)),hAPP(c_List_Oset(X0),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15486,plain,
! [X0,X1,X2] :
( ( sP20(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) )
| ~ sP20(X0,X1,X2) ) ),
inference(rectify,[],[f15485]) ).
fof(f15485,plain,
! [X2,X0,X1] :
( ( sP20(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) )
| ~ sP20(X2,X0,X1) ) ),
inference(flattening,[],[f15484]) ).
fof(f15484,plain,
! [X2,X0,X1] :
( ( sP20(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) )
| ~ sP20(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f14563]) ).
fof(f14563,plain,
! [X2,X0,X1] :
( sP20(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,[sP20])]) ).
fof(f31046,plain,
spl635_370,
inference(avatar_split_clause,[],[f20475,f31044]) ).
fof(f31044,plain,
( spl635_370
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X2)
| ~ sP20(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_370])]) ).
fof(f20475,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X2)
| ~ sP20(X0,X1,X2) ),
inference(cnf_transformation,[],[f15489]) ).
fof(f31042,plain,
spl635_369,
inference(avatar_split_clause,[],[f19654,f31040]) ).
fof(f31040,plain,
( spl635_369
<=> ! [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,[spl635_369])]) ).
fof(f19654,plain,
! [X2,X0,X1] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X2) != c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X1,X0),
inference(cnf_transformation,[],[f6949]) ).
fof(f6949,plain,
! [X0,X1,X2] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X2) != c_Lazy__Sequence_Olazy__sequence_OInsert(X2,X1,X0),
inference(rectify,[],[f4894]) ).
fof(f4894,axiom,
! [X261,X87,X5] : c_Lazy__Sequence_Olazy__sequence_OEmpty(X5) != c_Lazy__Sequence_Olazy__sequence_OInsert(X5,X87,X261),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_lazy__sequence_Osimps_I3_J) ).
fof(f31038,plain,
spl635_368,
inference(avatar_split_clause,[],[f18717,f31036]) ).
fof(f31036,plain,
( spl635_368
<=> ! [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,[spl635_368])]) ).
fof(f18717,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,[],[f10867]) ).
fof(f10867,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,[],[f6432]) ).
fof(f6432,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,[],[f2080]) ).
fof(f2080,axiom,
! [X35,X30] :
( c_Nat__Transfer_Ois__nat(X30)
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X30,X35)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__function__closures) ).
fof(f31034,plain,
spl635_367,
inference(avatar_split_clause,[],[f18695,f31032]) ).
fof(f18695,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f10843]) ).
fof(f10843,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6417]) ).
fof(f6417,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(X1)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(rectify,[],[f2276]) ).
fof(f2276,axiom,
! [X39,X8] :
( class_Finite__Set_Ofinite(X8)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X39)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite) ).
fof(f31030,plain,
( spl635_366
| ~ spl635_197
| ~ spl635_294 ),
inference(avatar_split_clause,[],[f30804,f30694,f30277,f31027]) ).
fof(f31027,plain,
( spl635_366
<=> c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_366])]) ).
fof(f30804,plain,
( c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl635_197
| ~ spl635_294 ),
inference(resolution,[],[f30695,f30279]) ).
fof(f31025,plain,
spl635_365,
inference(avatar_split_clause,[],[f17852,f31023]) ).
fof(f31023,plain,
( spl635_365
<=> ! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_365])]) ).
fof(f17852,plain,
! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5704]) ).
fof(f5704,plain,
! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(rectify,[],[f4128]) ).
fof(f4128,axiom,
! [X98,X8] : c_List_Olistrelp(X8,X98,c_List_Olist_ONil(X8),c_List_Olist_ONil(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listrelp_Oequations_I1_J) ).
fof(f31021,plain,
spl635_364,
inference(avatar_split_clause,[],[f17851,f31019]) ).
fof(f31019,plain,
( spl635_364
<=> ! [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,[spl635_364])]) ).
fof(f17851,plain,
! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(cnf_transformation,[],[f5703]) ).
fof(f5703,plain,
! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(rectify,[],[f3796]) ).
fof(f3796,axiom,
! [X98,X8] : c_Relation_Ototal__on(X8,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)),X98),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_total__on__empty) ).
fof(f31017,plain,
spl635_363,
inference(avatar_split_clause,[],[f17849,f31015]) ).
fof(f31015,plain,
( spl635_363
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Olistsp(X1,X0),c_List_Olist_ONil(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_363])]) ).
fof(f17849,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Olistsp(X1,X0),c_List_Olist_ONil(X1))),
inference(cnf_transformation,[],[f5701]) ).
fof(f5701,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Olistsp(X1,X0),c_List_Olist_ONil(X1))),
inference(rectify,[],[f4445]) ).
fof(f4445,axiom,
! [X39,X8] : hBOOL(hAPP(c_List_Olistsp(X8,X39),c_List_Olist_ONil(X8))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_listsp_ONil) ).
fof(f31013,plain,
spl635_362,
inference(avatar_split_clause,[],[f17848,f31011]) ).
fof(f31011,plain,
( spl635_362
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_362])]) ).
fof(f17848,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X0))),
inference(cnf_transformation,[],[f5700]) ).
fof(f5700,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X0))),
inference(rectify,[],[f4509]) ).
fof(f4509,axiom,
! [X208,X5] : hBOOL(hAPP(c_List_Odistinct(X5),c_List_Oremdups(X5,X208))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__remdups) ).
fof(f31009,plain,
spl635_361,
inference(avatar_split_clause,[],[f17847,f31007]) ).
fof(f17847,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)),
inference(cnf_transformation,[],[f5699]) ).
fof(f5699,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)),
inference(rectify,[],[f3216]) ).
fof(f3216,axiom,
! [X30,X8] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X8,tc_HOL_Obool)),X30)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_top1I) ).
fof(f31005,plain,
spl635_360,
inference(avatar_split_clause,[],[f17845,f31003]) ).
fof(f31003,plain,
( spl635_360
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_360])]) ).
fof(f17845,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))),
inference(cnf_transformation,[],[f5697]) ).
fof(f5697,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))),
inference(rectify,[],[f4332]) ).
fof(f4332,axiom,
! [X41,X42] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X42,X41))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct__upto) ).
fof(f31001,plain,
spl635_359,
inference(avatar_split_clause,[],[f17844,f30999]) ).
fof(f30999,plain,
( spl635_359
<=> ! [X0,X1] : c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_359])]) ).
fof(f17844,plain,
! [X0,X1] : c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),X0) = X0,
inference(cnf_transformation,[],[f5696]) ).
fof(f5696,plain,
! [X0,X1] : c_Lazy__Sequence_Oappend(X1,c_Lazy__Sequence_Olazy__sequence_OEmpty(X1),X0) = X0,
inference(rectify,[],[f4895]) ).
fof(f4895,axiom,
! [X255,X5] : c_Lazy__Sequence_Oappend(X5,c_Lazy__Sequence_Olazy__sequence_OEmpty(X5),X255) = X255,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact__02) ).
fof(f30997,plain,
spl635_358,
inference(avatar_split_clause,[],[f17843,f30995]) ).
fof(f30995,plain,
( spl635_358
<=> ! [X0,X1] : c_List_Osplice(X1,c_List_Olist_ONil(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_358])]) ).
fof(f17843,plain,
! [X0,X1] : c_List_Osplice(X1,c_List_Olist_ONil(X1),X0) = X0,
inference(cnf_transformation,[],[f5695]) ).
fof(f5695,plain,
! [X0,X1] : c_List_Osplice(X1,c_List_Olist_ONil(X1),X0) = X0,
inference(rectify,[],[f4823]) ).
fof(f4823,axiom,
! [X207,X5] : c_List_Osplice(X5,c_List_Olist_ONil(X5),X207) = X207,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice_Osimps_I1_J) ).
fof(f30993,plain,
spl635_357,
inference(avatar_split_clause,[],[f17842,f30991]) ).
fof(f30991,plain,
( spl635_357
<=> ! [X0,X1] : c_List_Osplice(X1,X0,c_List_Olist_ONil(X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_357])]) ).
fof(f17842,plain,
! [X0,X1] : c_List_Osplice(X1,X0,c_List_Olist_ONil(X1)) = X0,
inference(cnf_transformation,[],[f5694]) ).
fof(f5694,plain,
! [X0,X1] : c_List_Osplice(X1,X0,c_List_Olist_ONil(X1)) = X0,
inference(rectify,[],[f4821]) ).
fof(f4821,axiom,
! [X208,X5] : c_List_Osplice(X5,X208,c_List_Olist_ONil(X5)) = X208,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_splice__Nil2) ).
fof(f30989,plain,
spl635_356,
inference(avatar_split_clause,[],[f17841,f30987]) ).
fof(f30987,plain,
( spl635_356
<=> ! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_356])]) ).
fof(f17841,plain,
! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0,
inference(cnf_transformation,[],[f5693]) ).
fof(f5693,plain,
! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0,
inference(rectify,[],[f1788]) ).
fof(f1788,axiom,
! [X30,X8] : c_HOL_OThe(X8,hAPP(c_fequal,X30)) = X30,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_the__sym__eq__trivial) ).
fof(f30985,plain,
( spl635_355
| ~ spl635_203
| ~ spl635_293 ),
inference(avatar_split_clause,[],[f30803,f30690,f30303,f30983]) ).
fof(f30983,plain,
( spl635_355
<=> ! [X0] : c_Predicate_Otransp(X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_355])]) ).
fof(f30303,plain,
( spl635_203
<=> ! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_203])]) ).
fof(f30690,plain,
( spl635_293
<=> ! [X0,X1] :
( c_Predicate_Otransp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_293])]) ).
fof(f30803,plain,
( ! [X0] : c_Predicate_Otransp(X0,c_fequal)
| ~ spl635_203
| ~ spl635_293 ),
inference(resolution,[],[f30691,f30304]) ).
fof(f30304,plain,
( ! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal)
| ~ spl635_203 ),
inference(avatar_component_clause,[],[f30303]) ).
fof(f30691,plain,
( ! [X0,X1] :
( ~ c_Equiv__Relations_Oequivp(X1,X0)
| c_Predicate_Otransp(X1,X0) )
| ~ spl635_293 ),
inference(avatar_component_clause,[],[f30690]) ).
fof(f30981,plain,
spl635_354,
inference(avatar_split_clause,[],[f17840,f30979]) ).
fof(f30979,plain,
( spl635_354
<=> ! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_354])]) ).
fof(f17840,plain,
! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0,
inference(cnf_transformation,[],[f5692]) ).
fof(f5692,plain,
! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0,
inference(rectify,[],[f3658]) ).
fof(f3658,axiom,
! [X30,X8] : c_Hilbert__Choice_OEps(X8,hAPP(c_fequal,X30)) = X30,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).
fof(f30977,plain,
spl635_353,
inference(avatar_split_clause,[],[f17839,f30975]) ).
fof(f30975,plain,
( spl635_353
<=> ! [X0,X1] : hAPP(c_New__DSequence_Opos__empty(X1),X0) = c_Lazy__Sequence_Oempty(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_353])]) ).
fof(f17839,plain,
! [X0,X1] : hAPP(c_New__DSequence_Opos__empty(X1),X0) = c_Lazy__Sequence_Oempty(X1),
inference(cnf_transformation,[],[f5691]) ).
fof(f5691,plain,
! [X0,X1] : hAPP(c_New__DSequence_Opos__empty(X1),X0) = c_Lazy__Sequence_Oempty(X1),
inference(rectify,[],[f1821]) ).
fof(f1821,axiom,
! [X138,X5] : hAPP(c_New__DSequence_Opos__empty(X5),X138) = c_Lazy__Sequence_Oempty(X5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
fof(f30973,plain,
spl635_352,
inference(avatar_split_clause,[],[f17694,f30971]) ).
fof(f30971,plain,
( spl635_352
<=> ! [X0] :
( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_352])]) ).
fof(f17694,plain,
! [X0] :
( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) ),
inference(cnf_transformation,[],[f14704]) ).
fof(f14704,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,[],[f5607]) ).
fof(f5607,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
<=> c_Int_OPls = X0 ),
inference(rectify,[],[f1240]) ).
fof(f1240,axiom,
! [X48] :
( c_Int_OPls = c_Int_OBit0(X48)
<=> c_Int_OPls = X48 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).
fof(f30969,plain,
spl635_351,
inference(avatar_split_clause,[],[f17624,f30967]) ).
fof(f30967,plain,
( spl635_351
<=> ! [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,[spl635_351])]) ).
fof(f17624,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,[],[f10384]) ).
fof(f10384,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,[],[f5549]) ).
fof(f5549,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,[],[f3359]) ).
fof(f3359,axiom,
! [X8] :
( class_Lattices_Osemilattice__inf(X8)
=> c_Finite__Set_Ofun__left__comm__idem(X8,X8,c_Lattices_Osemilattice__inf__class_Oinf(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem__inf) ).
fof(f30965,plain,
spl635_350,
inference(avatar_split_clause,[],[f17623,f30963]) ).
fof(f17623,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,[],[f10383]) ).
fof(f10383,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,[],[f5548]) ).
fof(f5548,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,[],[f3358]) ).
fof(f3358,axiom,
! [X8] :
( class_Lattices_Osemilattice__sup(X8)
=> c_Finite__Set_Ofun__left__comm__idem(X8,X8,c_Lattices_Osemilattice__sup__class_Osup(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem__sup) ).
fof(f30961,plain,
spl635_349,
inference(avatar_split_clause,[],[f17617,f30959]) ).
fof(f30959,plain,
( spl635_349
<=> ! [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,[spl635_349])]) ).
fof(f17617,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10377]) ).
fof(f10377,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(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_Omin(X0)) ),
inference(rectify,[],[f3364]) ).
fof(f3364,axiom,
! [X8] :
( class_Orderings_Olinorder(X8)
=> c_Finite__Set_Ofun__left__comm__idem(X8,X8,c_Orderings_Oord__class_Omin(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofun__left__comm__idem__inf) ).
fof(f30957,plain,
spl635_348,
inference(avatar_split_clause,[],[f17616,f30955]) ).
fof(f30955,plain,
( spl635_348
<=> ! [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,[spl635_348])]) ).
fof(f17616,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10376]) ).
fof(f10376,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5541]) ).
fof(f5541,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0)) ),
inference(rectify,[],[f3365]) ).
fof(f3365,axiom,
! [X8] :
( class_Orderings_Olinorder(X8)
=> c_Finite__Set_Ofun__left__comm__idem(X8,X8,c_Orderings_Oord__class_Omax(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_min__max_Ofun__left__comm__idem__sup) ).
fof(f30953,plain,
spl635_347,
inference(avatar_split_clause,[],[f17598,f30951]) ).
fof(f30951,plain,
( spl635_347
<=> ! [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,[spl635_347])]) ).
fof(f17598,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,[],[f10358]) ).
fof(f10358,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,[],[f5523]) ).
fof(f5523,plain,
! [X0] :
( class_Groups_Oab__semigroup__mult(X0)
=> c_Finite__Set_Ofun__left__comm(X0,X0,c_Groups_Otimes__class_Otimes(X0)) ),
inference(rectify,[],[f3877]) ).
fof(f3877,axiom,
! [X8] :
( class_Groups_Oab__semigroup__mult(X8)
=> c_Finite__Set_Ofun__left__comm(X8,X8,c_Groups_Otimes__class_Otimes(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm) ).
fof(f30949,plain,
spl635_346,
inference(avatar_split_clause,[],[f17595,f30947]) ).
fof(f30947,plain,
( spl635_346
<=> ! [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,[spl635_346])]) ).
fof(f17595,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(cnf_transformation,[],[f10355]) ).
fof(f10355,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(ennf_transformation,[],[f5520]) ).
fof(f5520,plain,
! [X0] :
( class_Rings_Ozero__neq__one(X0)
=> c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) ),
inference(rectify,[],[f370]) ).
fof(f370,axiom,
! [X5] :
( class_Rings_Ozero__neq__one(X5)
=> c_Groups_Ozero__class_Ozero(X5) != c_Groups_Oone__class_Oone(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(f30945,plain,
spl635_345,
inference(avatar_split_clause,[],[f17348,f30943]) ).
fof(f30943,plain,
( spl635_345
<=> ! [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,[spl635_345])]) ).
fof(f17348,plain,
! [X0] : c_Finite__Set_Ofun__left__comm__idem(X0,tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0)),
inference(cnf_transformation,[],[f5286]) ).
fof(f5286,plain,
! [X0] : c_Finite__Set_Ofun__left__comm__idem(X0,tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0)),
inference(rectify,[],[f3363]) ).
fof(f3363,axiom,
! [X8] : c_Finite__Set_Ofun__left__comm__idem(X8,tc_fun(X8,tc_HOL_Obool),c_Set_Oinsert(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fun__left__comm__idem__insert) ).
fof(f30941,plain,
( spl635_344
| ~ spl635_203
| ~ spl635_292 ),
inference(avatar_split_clause,[],[f30802,f30686,f30303,f30939]) ).
fof(f30939,plain,
( spl635_344
<=> ! [X0] : c_Predicate_Osymp(X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_344])]) ).
fof(f30686,plain,
( spl635_292
<=> ! [X0,X1] :
( c_Predicate_Osymp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_292])]) ).
fof(f30802,plain,
( ! [X0] : c_Predicate_Osymp(X0,c_fequal)
| ~ spl635_203
| ~ spl635_292 ),
inference(resolution,[],[f30687,f30304]) ).
fof(f30687,plain,
( ! [X0,X1] :
( ~ c_Equiv__Relations_Oequivp(X1,X0)
| c_Predicate_Osymp(X1,X0) )
| ~ spl635_292 ),
inference(avatar_component_clause,[],[f30686]) ).
fof(f30937,plain,
spl635_343,
inference(avatar_split_clause,[],[f17347,f30935]) ).
fof(f17347,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f5285]) ).
fof(f5285,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f155]) ).
fof(f155,axiom,
! [X4] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X4),X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
fof(f30933,plain,
spl635_342,
inference(avatar_split_clause,[],[f17346,f30931]) ).
fof(f17346,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)),
inference(cnf_transformation,[],[f5284]) ).
fof(f5284,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)),
inference(rectify,[],[f333]) ).
fof(f333,axiom,
! [X59] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X59),X59)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(f30929,plain,
spl635_341,
inference(avatar_split_clause,[],[f17345,f30927]) ).
fof(f17345,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f5283]) ).
fof(f5283,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f1842]) ).
fof(f1842,axiom,
! [X13] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X13),X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
fof(f30925,plain,
spl635_340,
inference(avatar_split_clause,[],[f17343,f30923]) ).
fof(f30923,plain,
( spl635_340
<=> ! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_340])]) ).
fof(f17343,plain,
! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0,
inference(cnf_transformation,[],[f5281]) ).
fof(f5281,plain,
! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0,
inference(rectify,[],[f1810]) ).
fof(f1810,axiom,
! [X13] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X13)) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__inverse) ).
fof(f30921,plain,
spl635_339,
inference(avatar_split_clause,[],[f17342,f30919]) ).
fof(f17342,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0,
inference(cnf_transformation,[],[f5280]) ).
fof(f5280,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0,
inference(rectify,[],[f1808]) ).
fof(f1808,axiom,
! [X4] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X4)) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__of__of__nat) ).
fof(f30917,plain,
spl635_338,
inference(avatar_split_clause,[],[f17341,f30915]) ).
fof(f30915,plain,
( spl635_338
<=> ! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_338])]) ).
fof(f17341,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0,
inference(cnf_transformation,[],[f5279]) ).
fof(f5279,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0,
inference(rectify,[],[f2792]) ).
fof(f2792,axiom,
! [X30] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X30)) = X30,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inverse) ).
fof(f30913,plain,
spl635_337,
inference(avatar_split_clause,[],[f17337,f30911]) ).
fof(f30911,plain,
( spl635_337
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(X0,c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_337])]) ).
fof(f17337,plain,
! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(X0,c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5275]) ).
fof(f5275,plain,
! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(X0,c_List_Olist_ONil(X0)),
inference(rectify,[],[f4518]) ).
fof(f4518,axiom,
! [X5] : c_List_Olist_ONil(X5) = c_List_Oremdups(X5,c_List_Olist_ONil(X5)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_remdups_Osimps_I1_J) ).
fof(f30909,plain,
spl635_336,
inference(avatar_split_clause,[],[f17335,f30907]) ).
fof(f30907,plain,
( spl635_336
<=> ! [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,[spl635_336])]) ).
fof(f17335,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,[],[f5273]) ).
fof(f5273,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,[],[f1825]) ).
fof(f1825,axiom,
! [X40] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Quickcheck_Obeyond(X40,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_beyond__zero) ).
fof(f30905,plain,
spl635_335,
inference(avatar_split_clause,[],[f17332,f30903]) ).
fof(f30903,plain,
( spl635_335
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_335])]) ).
fof(f17332,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f5270]) ).
fof(f5270,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X4] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(f30901,plain,
spl635_334,
inference(avatar_split_clause,[],[f17331,f30899]) ).
fof(f30899,plain,
( spl635_334
<=> ! [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,[spl635_334])]) ).
fof(f17331,plain,
! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(cnf_transformation,[],[f5269]) ).
fof(f5269,plain,
! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(rectify,[],[f853]) ).
fof(f853,axiom,
! [X4] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__int) ).
fof(f30897,plain,
( spl635_333
| ~ spl635_203
| ~ spl635_291 ),
inference(avatar_split_clause,[],[f30801,f30682,f30303,f30895]) ).
fof(f30895,plain,
( spl635_333
<=> ! [X0] : c_Predicate_Oreflp(X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_333])]) ).
fof(f30682,plain,
( spl635_291
<=> ! [X0,X1] :
( c_Predicate_Oreflp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_291])]) ).
fof(f30801,plain,
( ! [X0] : c_Predicate_Oreflp(X0,c_fequal)
| ~ spl635_203
| ~ spl635_291 ),
inference(resolution,[],[f30683,f30304]) ).
fof(f30683,plain,
( ! [X0,X1] :
( ~ c_Equiv__Relations_Oequivp(X1,X0)
| c_Predicate_Oreflp(X1,X0) )
| ~ spl635_291 ),
inference(avatar_component_clause,[],[f30682]) ).
fof(f30893,plain,
spl635_332,
inference(avatar_split_clause,[],[f17223,f30890]) ).
fof(f17223,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f1107]) ).
fof(f1107,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',fact_rel__simps_I23_J) ).
fof(f30888,plain,
spl635_331,
inference(avatar_split_clause,[],[f17221,f30885]) ).
fof(f17221,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f1110]) ).
fof(f1110,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',fact_rel__simps_I6_J) ).
fof(f30883,plain,
( spl635_330
| ~ spl635_259
| ~ spl635_329 ),
inference(avatar_split_clause,[],[f30878,f30874,f30554,f30880]) ).
fof(f30874,plain,
( spl635_329
<=> 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,[spl635_329])]) ).
fof(f30878,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))
| ~ spl635_259
| ~ spl635_329 ),
inference(forward_demodulation,[],[f30876,f30555]) ).
fof(f30876,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)))
| ~ spl635_329 ),
inference(avatar_component_clause,[],[f30874]) ).
fof(f30877,plain,
spl635_329,
inference(avatar_split_clause,[],[f17220,f30874]) ).
fof(f17220,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
inference(cnf_transformation,[],[f973]) ).
fof(f973,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',fact_neg__number__of__Min) ).
fof(f30872,plain,
spl635_328,
inference(avatar_split_clause,[],[f17217,f30869]) ).
fof(f17217,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin,
inference(cnf_transformation,[],[f971]) ).
fof(f971,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Int_OMin__def) ).
fof(f30867,plain,
spl635_327,
inference(avatar_split_clause,[],[f17208,f30864]) ).
fof(f17208,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,[],[f1442]) ).
fof(f1442,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',fact_zero__code__numeral__code) ).
fof(f30862,plain,
spl635_326,
inference(avatar_split_clause,[],[f17206,f30859]) ).
fof(f17206,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f362]) ).
fof(f362,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',fact_transfer__nat__int__numerals_I2_J) ).
fof(f30857,plain,
spl635_325,
inference(avatar_split_clause,[],[f17205,f30854]) ).
fof(f17205,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,[],[f1796]) ).
fof(f1796,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',fact_one__code__numeral__def) ).
fof(f30852,plain,
spl635_324,
inference(avatar_split_clause,[],[f17203,f30849]) ).
fof(f30849,plain,
( spl635_324
<=> 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,[spl635_324])]) ).
fof(f17203,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,[],[f2733]) ).
fof(f2733,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',fact_pair__less__def) ).
fof(f30847,plain,
spl635_323,
inference(avatar_split_clause,[],[f17202,f30844]) ).
fof(f30844,plain,
( spl635_323
<=> 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,[spl635_323])]) ).
fof(f17202,plain,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f2726]) ).
fof(f2726,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',fact_max__strict__def) ).
fof(f30842,plain,
spl635_322,
inference(avatar_split_clause,[],[f17201,f30839]) ).
fof(f30839,plain,
( spl635_322
<=> 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,[spl635_322])]) ).
fof(f17201,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f2728]) ).
fof(f2728,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',fact_min__strict__def) ).
fof(f30837,plain,
~ spl635_321,
inference(avatar_split_clause,[],[f17200,f30834]) ).
fof(f17200,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f1108]) ).
fof(f1108,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',fact_rel__simps_I20_J) ).
fof(f30832,plain,
~ spl635_320,
inference(avatar_split_clause,[],[f17198,f30829]) ).
fof(f30829,plain,
( spl635_320
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_320])]) ).
fof(f17198,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f1109]) ).
fof(f1109,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',fact_rel__simps_I3_J) ).
fof(f30826,plain,
~ spl635_319,
inference(avatar_split_clause,[],[f17196,f30823]) ).
fof(f30823,plain,
( spl635_319
<=> 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,[spl635_319])]) ).
fof(f17196,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(cnf_transformation,[],[f1112]) ).
fof(f1112,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',fact_not__neg__number__of__Pls) ).
fof(f30820,plain,
( spl635_318
| ~ spl635_240
| ~ spl635_317 ),
inference(avatar_split_clause,[],[f30812,f30798,f30469,f30817]) ).
fof(f30817,plain,
( spl635_318
<=> sP4(c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_318])]) ).
fof(f30469,plain,
( spl635_240
<=> ! [X0,X1] :
( sP4(X0)
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_240])]) ).
fof(f30798,plain,
( spl635_317
<=> ! [X0] : c_Equiv__Relations_Opart__equivp(X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_317])]) ).
fof(f30812,plain,
( sP4(c_fequal)
| ~ spl635_240
| ~ spl635_317 ),
inference(resolution,[],[f30799,f30470]) ).
fof(f30470,plain,
( ! [X0,X1] :
( ~ c_Equiv__Relations_Opart__equivp(X1,X0)
| sP4(X0) )
| ~ spl635_240 ),
inference(avatar_component_clause,[],[f30469]) ).
fof(f30799,plain,
( ! [X0] : c_Equiv__Relations_Opart__equivp(X0,c_fequal)
| ~ spl635_317 ),
inference(avatar_component_clause,[],[f30798]) ).
fof(f30800,plain,
( spl635_317
| ~ spl635_203
| ~ spl635_290 ),
inference(avatar_split_clause,[],[f30796,f30678,f30303,f30798]) ).
fof(f30678,plain,
( spl635_290
<=> ! [X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_290])]) ).
fof(f30796,plain,
( ! [X0] : c_Equiv__Relations_Opart__equivp(X0,c_fequal)
| ~ spl635_203
| ~ spl635_290 ),
inference(resolution,[],[f30679,f30304]) ).
fof(f30679,plain,
( ! [X0,X1] :
( ~ c_Equiv__Relations_Oequivp(X1,X0)
| c_Equiv__Relations_Opart__equivp(X1,X0) )
| ~ spl635_290 ),
inference(avatar_component_clause,[],[f30678]) ).
fof(f30795,plain,
( ~ spl635_132
| spl635_316
| ~ spl635_210
| ~ spl635_264 ),
inference(avatar_split_clause,[],[f30787,f30574,f30335,f30792,f29951]) ).
fof(f29951,plain,
( spl635_132
<=> class_Rings_Osemiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_132])]) ).
fof(f30792,plain,
( spl635_316
<=> c_Int_Oiszero(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_316])]) ).
fof(f30787,plain,
( c_Int_Oiszero(tc_Int_Oint,c_Int_OPls)
| ~ class_Rings_Osemiring__1(tc_Int_Oint)
| ~ spl635_210
| ~ spl635_264 ),
inference(superposition,[],[f30575,f30337]) ).
fof(f30785,plain,
spl635_315,
inference(avatar_split_clause,[],[f27612,f30783]) ).
fof(f27612,plain,
! [X1] :
( c_Int_OPls != X1
| sP11(X1,X1) ),
inference(forward_demodulation,[],[f27611,f17176]) ).
fof(f27611,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
| sP11(X1,X1) ),
inference(forward_demodulation,[],[f25425,f17327]) ).
fof(f25425,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,[],[f19390]) ).
fof(f19390,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,[],[f15196]) ).
fof(f30781,plain,
spl635_314,
inference(avatar_split_clause,[],[f26633,f30779]) ).
fof(f30779,plain,
( spl635_314
<=> ! [X0] : c_Nitpick_Onat__gcd(X0,c_HOL_Obool_Obool__size(c_fTrue)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_314])]) ).
fof(f26633,plain,
! [X0] : c_Nitpick_Onat__gcd(X0,c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f25299,f17187]) ).
fof(f25299,plain,
! [X0] : c_Nitpick_Onat__gcd(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(equality_resolution,[],[f18221]) ).
fof(f18221,plain,
! [X0,X1] :
( c_Nitpick_Onat__gcd(X0,X1) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f10454]) ).
fof(f10454,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,[],[f6066]) ).
fof(f6066,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,[],[f1751]) ).
fof(f1751,axiom,
! [X13,X12] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X12
=> c_Nitpick_Onat__gcd(X13,X12) = c_Nitpick_Onat__gcd(X12,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X13,X12)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X12
=> c_Nitpick_Onat__gcd(X13,X12) = X13 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__gcd_Osimps) ).
fof(f30777,plain,
spl635_313,
inference(avatar_split_clause,[],[f26176,f30774]) ).
fof(f30774,plain,
( spl635_313
<=> 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,[spl635_313])]) ).
fof(f26176,plain,
c_Int_OPls = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(forward_demodulation,[],[f25276,f17176]) ).
fof(f25276,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,[],[f17541]) ).
fof(f17541,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,[],[f10316]) ).
fof(f10316,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,[],[f5478]) ).
fof(f5478,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,[],[f1347]) ).
fof(f1347,axiom,
! [X40] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X40
=> ( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X40,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,X40) = 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),X40),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,X40,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,X40) = 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),X40),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) = X40
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X40) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__of__code) ).
fof(f30772,plain,
spl635_312,
inference(avatar_split_clause,[],[f26164,f30770]) ).
fof(f30770,plain,
( spl635_312
<=> ! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_312])]) ).
fof(f26164,plain,
! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(forward_demodulation,[],[f17540,f17176]) ).
fof(f17540,plain,
! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f5477]) ).
fof(f30768,plain,
spl635_311,
inference(avatar_split_clause,[],[f26067,f30766]) ).
fof(f30766,plain,
( spl635_311
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_311])]) ).
fof(f26067,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin),
inference(forward_demodulation,[],[f26066,f17176]) ).
fof(f26066,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,[],[f17403,f17327]) ).
fof(f17403,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,[],[f5341]) ).
fof(f5341,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,[],[f909]) ).
fof(f909,axiom,
! [X33] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X33,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__minus1__right) ).
fof(f30764,plain,
spl635_310,
inference(avatar_split_clause,[],[f26057,f30762]) ).
fof(f30762,plain,
( spl635_310
<=> ! [X0] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_310])]) ).
fof(f26057,plain,
! [X0] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) = X0,
inference(forward_demodulation,[],[f17385,f17327]) ).
fof(f17385,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,[],[f705]) ).
fof(f705,axiom,
! [X59] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X59) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X59),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__number__of__def) ).
fof(f30760,plain,
spl635_309,
inference(avatar_split_clause,[],[f26049,f30758]) ).
fof(f30758,plain,
( spl635_309
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OPls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_309])]) ).
fof(f26049,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OPls,X0),
inference(forward_demodulation,[],[f17353,f17176]) ).
fof(f17353,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,[],[f5291]) ).
fof(f5291,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,[],[f938]) ).
fof(f938,axiom,
! [X34] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X34),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__zero) ).
fof(f30756,plain,
spl635_308,
inference(avatar_split_clause,[],[f26045,f30754]) ).
fof(f30754,plain,
( spl635_308
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_308])]) ).
fof(f26045,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(forward_demodulation,[],[f17336,f17176]) ).
fof(f17336,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f5274]) ).
fof(f5274,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(rectify,[],[f937]) ).
fof(f937,axiom,
! [X33] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X33,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zmod__self) ).
fof(f30752,plain,
spl635_307,
inference(avatar_split_clause,[],[f26038,f30750]) ).
fof(f26038,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0),
inference(forward_demodulation,[],[f17314,f17187]) ).
fof(f17314,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X0),
inference(cnf_transformation,[],[f5252]) ).
fof(f5252,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X0),
inference(rectify,[],[f142]) ).
fof(f142,axiom,
! [X43] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X43),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Osimps_I2_J) ).
fof(f30748,plain,
~ spl635_306,
inference(avatar_split_clause,[],[f25976,f30745]) ).
fof(f30745,plain,
( spl635_306
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl635_306])]) ).
fof(f25976,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != c_Int_OPls,
inference(forward_demodulation,[],[f17241,f25944]) ).
fof(f25944,plain,
c_Int_OPls = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(forward_demodulation,[],[f17209,f17176]) ).
fof(f17209,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,[],[f1106]) ).
fof(f1106,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',fact_zero__is__num__zero) ).
fof(f17241,plain,
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_OPls),
inference(cnf_transformation,[],[f1111]) ).
fof(f1111,axiom,
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_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__number__of__Pls__Min) ).
fof(f30743,plain,
spl635_305,
inference(avatar_split_clause,[],[f25946,f30740]) ).
fof(f30740,plain,
( spl635_305
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_305])]) ).
fof(f25946,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OPls),
inference(forward_demodulation,[],[f25945,f17187]) ).
fof(f25945,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(forward_demodulation,[],[f17210,f17176]) ).
fof(f17210,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f389]) ).
fof(f389,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',fact_nat__0) ).
fof(f30738,plain,
spl635_304,
inference(avatar_split_clause,[],[f25941,f30735]) ).
fof(f30735,plain,
( spl635_304
<=> 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,[spl635_304])]) ).
fof(f25941,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Nat_Onat_Onat__size(c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17195,f17187]) ).
fof(f17195,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,[],[f1499]) ).
fof(f1499,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',fact_nat_Osize_I1_J) ).
fof(f30733,plain,
spl635_303,
inference(avatar_split_clause,[],[f25940,f30730]) ).
fof(f30730,plain,
( spl635_303
<=> 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,[spl635_303])]) ).
fof(f25940,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,[],[f17194,f17187]) ).
fof(f17194,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,[],[f1465]) ).
fof(f1465,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',fact_code__numeral_Osize_I1_J) ).
fof(f30728,plain,
spl635_302,
inference(avatar_split_clause,[],[f25573,f30726]) ).
fof(f30726,plain,
( spl635_302
<=> ! [X2,X0] : c_List_Olist__all2(X0,X0,c_fequal,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_302])]) ).
fof(f25573,plain,
! [X2,X0] : c_List_Olist__all2(X0,X0,c_fequal,X2,X2),
inference(equality_resolution,[],[f21180]) ).
fof(f21180,plain,
! [X2,X0,X1] :
( c_List_Olist__all2(X0,X0,c_fequal,X2,X1)
| X1 != X2 ),
inference(cnf_transformation,[],[f15741]) ).
fof(f30724,plain,
spl635_301,
inference(avatar_split_clause,[],[f25308,f30722]) ).
fof(f25308,plain,
! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_resolution,[],[f18319]) ).
fof(f18319,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f6112]) ).
fof(f6112,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
| X0 != X1 ),
inference(rectify,[],[f5210]) ).
fof(f5210,axiom,
! [X35,X30] :
( hBOOL(hAPP(hAPP(c_fequal,X30),X35))
| X30 != X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(f30720,plain,
spl635_300,
inference(avatar_split_clause,[],[f25292,f30718]) ).
fof(f30718,plain,
( spl635_300
<=> ! [X1] : c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_300])]) ).
fof(f25292,plain,
! [X1] : c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X1),
inference(equality_resolution,[],[f18209]) ).
fof(f18209,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f10449]) ).
fof(f30716,plain,
spl635_299,
inference(avatar_split_clause,[],[f20481,f30714]) ).
fof(f30714,plain,
( spl635_299
<=> ! [X2,X0,X1] :
( sP21(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_299])]) ).
fof(f20481,plain,
! [X2,X0,X1] :
( sP21(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f14565]) ).
fof(f14565,plain,
! [X0,X1,X2] :
( sP21(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(definition_folding,[],[f11954,f14564,f14563]) ).
fof(f14564,plain,
! [X1,X0,X2] :
( ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Oappend(X2),X1),X0))
<=> sP20(X2,X0,X1) )
| ~ sP21(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
fof(f11954,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,[],[f7662]) ).
fof(f7662,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,[],[f4654]) ).
fof(f4654,axiom,
! [X209,X210,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_List_Olinorder__class_Osorted(X8,hAPP(hAPP(c_List_Oappend(X8),X210),X209))
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(c_List_Oset(X8),X210)))
=> ! [X142] :
( hBOOL(hAPP(hAPP(c_member(X8),X142),hAPP(c_List_Oset(X8),X209)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X2),X142)) ) )
& c_List_Olinorder__class_Osorted(X8,X209)
& c_List_Olinorder__class_Osorted(X8,X210) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__append) ).
fof(f30712,plain,
spl635_298,
inference(avatar_split_clause,[],[f20021,f30710]) ).
fof(f30710,plain,
( spl635_298
<=> ! [X2,X0,X1] :
( sP19(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_298])]) ).
fof(f20021,plain,
! [X2,X0,X1] :
( sP19(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f14562]) ).
fof(f14562,plain,
! [X0,X1,X2] :
( sP19(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f11399,f14561,f14560]) ).
fof(f14560,plain,
! [X0,X2,X1] :
( sP18(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,[sP18])]) ).
fof(f14561,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)))
<=> sP18(X0,X2,X1) )
| ~ sP19(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f11399,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,[],[f7298]) ).
fof(f7298,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,[],[f193]) ).
fof(f193,axiom,
! [X47,X17,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X17),X47)),c_Groups_Ozero__class_Ozero(X8)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X47))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X17),c_Groups_Ozero__class_Ozero(X8))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X47),c_Groups_Ozero__class_Ozero(X8)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X17)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(f30708,plain,
spl635_297,
inference(avatar_split_clause,[],[f20012,f30706]) ).
fof(f30706,plain,
( spl635_297
<=> ! [X2,X0,X1] :
( sP17(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_297])]) ).
fof(f20012,plain,
! [X2,X0,X1] :
( sP17(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f14559]) ).
fof(f14559,plain,
! [X0,X1,X2] :
( sP17(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f11398,f14558,f14557]) ).
fof(f14557,plain,
! [X2,X0,X1] :
( sP16(X2,X0,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f14558,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)))
<=> sP16(X2,X0,X1) )
| ~ sP17(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f11398,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,[],[f7297]) ).
fof(f7297,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,[],[f192]) ).
fof(f192,axiom,
! [X47,X17,X8] :
( class_Rings_Olinordered__ring__strict(X8)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X8),X17),X47)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X47),c_Groups_Ozero__class_Ozero(X8)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X17),c_Groups_Ozero__class_Ozero(X8))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X47))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),c_Groups_Ozero__class_Ozero(X8)),X17)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(f30704,plain,
spl635_296,
inference(avatar_split_clause,[],[f19190,f30702]) ).
fof(f30702,plain,
( spl635_296
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ sP5(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_296])]) ).
fof(f19190,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ sP5(X1,X0) ),
inference(cnf_transformation,[],[f15053]) ).
fof(f15053,plain,
! [X0,X1] :
( ( c_Wellfounded_Owf(X1,X0)
| ~ sP5(X1,X0) )
& ( sP5(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
inference(nnf_transformation,[],[f14537]) ).
fof(f14537,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> sP5(X1,X0) ),
inference(definition_folding,[],[f11322,f14536]) ).
fof(f14536,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(f11322,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,[],[f6775]) ).
fof(f6775,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,[],[f3968]) ).
fof(f3968,axiom,
! [X98,X8] :
( c_Wellfounded_Owf(X8,X98)
<=> ! [X203] :
( ? [X2] : hBOOL(hAPP(hAPP(c_member(X8),X2),X203))
=> ? [X2] :
( ! [X45] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X45),X2)),X98))
=> ~ hBOOL(hAPP(hAPP(c_member(X8),X45),X203)) )
& hBOOL(hAPP(hAPP(c_member(X8),X2),X203)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
fof(f30700,plain,
spl635_295,
inference(avatar_split_clause,[],[f19189,f30698]) ).
fof(f19189,plain,
! [X0,X1] :
( sP5(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f15053]) ).
fof(f30696,plain,
spl635_294,
inference(avatar_split_clause,[],[f18754,f30694]) ).
fof(f18754,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10912]) ).
fof(f10912,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6463]) ).
fof(f6463,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f3573]) ).
fof(f3573,axiom,
! [X98,X8] :
( c_Wellfounded_Owf(X8,X98)
=> c_Wellfounded_Oacyclic(X8,X98) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__acyclic) ).
fof(f30692,plain,
spl635_293,
inference(avatar_split_clause,[],[f18741,f30690]) ).
fof(f18741,plain,
! [X0,X1] :
( c_Predicate_Otransp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ),
inference(cnf_transformation,[],[f10897]) ).
fof(f10897,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,[],[f10896]) ).
fof(f10896,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,[],[f6450]) ).
fof(f6450,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,[],[f4937]) ).
fof(f4937,axiom,
! [X122,X8] :
( c_Equiv__Relations_Oequivp(X8,X122)
=> ~ ( c_Predicate_Oreflp(X8,X122)
=> ( c_Predicate_Osymp(X8,X122)
=> ~ c_Predicate_Otransp(X8,X122) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivpE) ).
fof(f30688,plain,
spl635_292,
inference(avatar_split_clause,[],[f18740,f30686]) ).
fof(f18740,plain,
! [X0,X1] :
( c_Predicate_Osymp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ),
inference(cnf_transformation,[],[f10897]) ).
fof(f30684,plain,
spl635_291,
inference(avatar_split_clause,[],[f18739,f30682]) ).
fof(f18739,plain,
! [X0,X1] :
( c_Predicate_Oreflp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ),
inference(cnf_transformation,[],[f10897]) ).
fof(f30680,plain,
spl635_290,
inference(avatar_split_clause,[],[f18738,f30678]) ).
fof(f18738,plain,
! [X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ),
inference(cnf_transformation,[],[f10895]) ).
fof(f10895,plain,
! [X0,X1] :
( c_Equiv__Relations_Opart__equivp(X1,X0)
| ~ c_Equiv__Relations_Oequivp(X1,X0) ),
inference(ennf_transformation,[],[f6449]) ).
fof(f6449,plain,
! [X0,X1] :
( c_Equiv__Relations_Oequivp(X1,X0)
=> c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(rectify,[],[f4971]) ).
fof(f4971,axiom,
! [X122,X8] :
( c_Equiv__Relations_Oequivp(X8,X122)
=> c_Equiv__Relations_Opart__equivp(X8,X122) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__implies__part__equivp) ).
fof(f30676,plain,
spl635_289,
inference(avatar_split_clause,[],[f18736,f30674]) ).
fof(f30674,plain,
( spl635_289
<=> ! [X0,X1] :
( c_Predicate_Otransp(X1,X0)
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_289])]) ).
fof(f18736,plain,
! [X0,X1] :
( c_Predicate_Otransp(X1,X0)
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(cnf_transformation,[],[f14899]) ).
fof(f30672,plain,
spl635_288,
inference(avatar_split_clause,[],[f18735,f30670]) ).
fof(f30670,plain,
( spl635_288
<=> ! [X0,X1] :
( c_Predicate_Osymp(X1,X0)
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_288])]) ).
fof(f18735,plain,
! [X0,X1] :
( c_Predicate_Osymp(X1,X0)
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(cnf_transformation,[],[f14899]) ).
fof(f30668,plain,
spl635_287,
inference(avatar_split_clause,[],[f18683,f30666]) ).
fof(f30666,plain,
( spl635_287
<=> ! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_287])]) ).
fof(f18683,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f10832]) ).
fof(f10832,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f6409]) ).
fof(f6409,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> class_Orderings_Oorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f4996]) ).
fof(f4996,axiom,
! [X263,X264] :
( class_Orderings_Oorder(X264)
=> class_Orderings_Oorder(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(f30664,plain,
spl635_286,
inference(avatar_split_clause,[],[f18682,f30662]) ).
fof(f30662,plain,
( spl635_286
<=> ! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_286])]) ).
fof(f18682,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(cnf_transformation,[],[f10831]) ).
fof(f10831,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(ennf_transformation,[],[f6408]) ).
fof(f6408,plain,
! [X0,X1] :
( class_Orderings_Oord(X1)
=> class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(rectify,[],[f4998]) ).
fof(f4998,axiom,
! [X263,X264] :
( class_Orderings_Oord(X264)
=> class_Orderings_Oord(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(f30660,plain,
spl635_285,
inference(avatar_split_clause,[],[f18679,f30658]) ).
fof(f30658,plain,
( spl635_285
<=> ! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_285])]) ).
fof(f18679,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10828]) ).
fof(f10828,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6405]) ).
fof(f6405,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> class_Orderings_Opreorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f4993]) ).
fof(f4993,axiom,
! [X263,X264] :
( class_Orderings_Opreorder(X264)
=> class_Orderings_Opreorder(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(f30656,plain,
spl635_284,
inference(avatar_split_clause,[],[f18678,f30654]) ).
fof(f30654,plain,
( spl635_284
<=> ! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_284])]) ).
fof(f18678,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(cnf_transformation,[],[f10827]) ).
fof(f10827,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(ennf_transformation,[],[f6404]) ).
fof(f6404,plain,
! [X0,X1] :
( class_Groups_Ominus(X1)
=> class_Groups_Ominus(tc_fun(X0,X1)) ),
inference(rectify,[],[f5001]) ).
fof(f5001,axiom,
! [X263,X264] :
( class_Groups_Ominus(X264)
=> class_Groups_Ominus(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(f30652,plain,
spl635_283,
inference(avatar_split_clause,[],[f18668,f30650]) ).
fof(f30650,plain,
( spl635_283
<=> ! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_283])]) ).
fof(f18668,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10812]) ).
fof(f10812,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6394]) ).
fof(f6394,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Olattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4995]) ).
fof(f4995,axiom,
! [X263,X264] :
( class_Lattices_Olattice(X264)
=> class_Lattices_Olattice(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
fof(f30648,plain,
spl635_282,
inference(avatar_split_clause,[],[f18667,f30646]) ).
fof(f30646,plain,
( spl635_282
<=> ! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_282])]) ).
fof(f18667,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10811]) ).
fof(f10811,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6393]) ).
fof(f6393,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__inf(tc_fun(X0,X1)) ),
inference(rectify,[],[f4990]) ).
fof(f4990,axiom,
! [X263,X264] :
( class_Lattices_Olattice(X264)
=> class_Lattices_Osemilattice__inf(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
fof(f30644,plain,
spl635_281,
inference(avatar_split_clause,[],[f18666,f30642]) ).
fof(f30642,plain,
( spl635_281
<=> ! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_281])]) ).
fof(f18666,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10810]) ).
fof(f10810,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6392]) ).
fof(f6392,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__sup(tc_fun(X0,X1)) ),
inference(rectify,[],[f4989]) ).
fof(f4989,axiom,
! [X263,X264] :
( class_Lattices_Olattice(X264)
=> class_Lattices_Osemilattice__sup(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).
fof(f30640,plain,
spl635_280,
inference(avatar_split_clause,[],[f18661,f30638]) ).
fof(f30638,plain,
( spl635_280
<=> ! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_280])]) ).
fof(f18661,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(cnf_transformation,[],[f10805]) ).
fof(f10805,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(ennf_transformation,[],[f6387]) ).
fof(f6387,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(X1)
=> class_Lattices_Odistrib__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4991]) ).
fof(f4991,axiom,
! [X263,X264] :
( class_Lattices_Odistrib__lattice(X264)
=> class_Lattices_Odistrib__lattice(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).
fof(f30636,plain,
spl635_279,
inference(avatar_split_clause,[],[f18550,f30634]) ).
fof(f30634,plain,
( spl635_279
<=> ! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_279])]) ).
fof(f18550,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(cnf_transformation,[],[f10692]) ).
fof(f10692,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(ennf_transformation,[],[f6296]) ).
fof(f6296,plain,
! [X0,X1] :
( class_Orderings_Obot(X1)
=> class_Orderings_Obot(tc_fun(X0,X1)) ),
inference(rectify,[],[f4999]) ).
fof(f4999,axiom,
! [X263,X264] :
( class_Orderings_Obot(X264)
=> class_Orderings_Obot(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
fof(f30632,plain,
spl635_278,
inference(avatar_split_clause,[],[f18547,f30630]) ).
fof(f30630,plain,
( spl635_278
<=> ! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_278])]) ).
fof(f18547,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(cnf_transformation,[],[f10689]) ).
fof(f10689,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(ennf_transformation,[],[f6293]) ).
fof(f6293,plain,
! [X0,X1] :
( class_Groups_Ouminus(X1)
=> class_Groups_Ouminus(tc_fun(X0,X1)) ),
inference(rectify,[],[f5000]) ).
fof(f5000,axiom,
! [X263,X264] :
( class_Groups_Ouminus(X264)
=> class_Groups_Ouminus(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(f30628,plain,
spl635_277,
inference(avatar_split_clause,[],[f18525,f30626]) ).
fof(f30626,plain,
( spl635_277
<=> ! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_277])]) ).
fof(f18525,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(cnf_transformation,[],[f10659]) ).
fof(f10659,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(ennf_transformation,[],[f6273]) ).
fof(f6273,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(X1)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4986]) ).
fof(f4986,axiom,
! [X263,X264] :
( class_Complete__Lattice_Ocomplete__lattice(X264)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f30624,plain,
spl635_276,
inference(avatar_split_clause,[],[f18519,f30622]) ).
fof(f30622,plain,
( spl635_276
<=> ! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_276])]) ).
fof(f18519,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f10653]) ).
fof(f10653,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f6267]) ).
fof(f6267,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
inference(rectify,[],[f4992]) ).
fof(f4992,axiom,
! [X263,X264] :
( class_Lattices_Oboolean__algebra(X264)
=> class_Lattices_Oboolean__algebra(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(f30620,plain,
spl635_275,
inference(avatar_split_clause,[],[f18509,f30618]) ).
fof(f30618,plain,
( spl635_275
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_275])]) ).
fof(f18509,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10643]) ).
fof(f10643,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6257]) ).
fof(f6257,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1)) ),
inference(rectify,[],[f4988]) ).
fof(f4988,axiom,
! [X263,X264] :
( class_Lattices_Obounded__lattice(X264)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).
fof(f30616,plain,
spl635_274,
inference(avatar_split_clause,[],[f18508,f30614]) ).
fof(f30614,plain,
( spl635_274
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_274])]) ).
fof(f18508,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10642]) ).
fof(f10642,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6256]) ).
fof(f6256,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice__top(tc_fun(X0,X1)) ),
inference(rectify,[],[f4987]) ).
fof(f4987,axiom,
! [X263,X264] :
( class_Lattices_Obounded__lattice(X264)
=> class_Lattices_Obounded__lattice__top(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).
fof(f30612,plain,
spl635_273,
inference(avatar_split_clause,[],[f18507,f30610]) ).
fof(f30610,plain,
( spl635_273
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_273])]) ).
fof(f18507,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10641]) ).
fof(f10641,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6255]) ).
fof(f6255,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4985]) ).
fof(f4985,axiom,
! [X263,X264] :
( class_Lattices_Obounded__lattice(X264)
=> class_Lattices_Obounded__lattice(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
fof(f30608,plain,
spl635_272,
inference(avatar_split_clause,[],[f18506,f30606]) ).
fof(f30606,plain,
( spl635_272
<=> ! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_272])]) ).
fof(f18506,plain,
! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ),
inference(cnf_transformation,[],[f10640]) ).
fof(f10640,plain,
! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ),
inference(ennf_transformation,[],[f6254]) ).
fof(f6254,plain,
! [X0,X1] :
( class_Orderings_Otop(X1)
=> class_Orderings_Otop(tc_fun(X0,X1)) ),
inference(rectify,[],[f4997]) ).
fof(f4997,axiom,
! [X263,X264] :
( class_Orderings_Otop(X264)
=> class_Orderings_Otop(tc_fun(X263,X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
fof(f30604,plain,
spl635_271,
inference(avatar_split_clause,[],[f17837,f30602]) ).
fof(f30602,plain,
( spl635_271
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_271])]) ).
fof(f17837,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0),
inference(cnf_transformation,[],[f5689]) ).
fof(f5689,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0),
inference(rectify,[],[f3062]) ).
fof(f3062,axiom,
! [X39,X8] : c_Fun_Oinj__on(X8,X8,c_COMBI(X8),X39),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id2) ).
fof(f30600,plain,
spl635_270,
inference(avatar_split_clause,[],[f17836,f30598]) ).
fof(f17836,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0),
inference(cnf_transformation,[],[f5688]) ).
fof(f5688,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0),
inference(rectify,[],[f3445]) ).
fof(f3445,axiom,
! [X39,X8] : c_Fun_Oinj__on(X8,X8,c_Fun_Oid(X8),X39),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__on__id) ).
fof(f30596,plain,
spl635_269,
inference(avatar_split_clause,[],[f17832,f30594]) ).
fof(f30594,plain,
( spl635_269
<=> ! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_269])]) ).
fof(f30592,plain,
spl635_268,
inference(avatar_split_clause,[],[f17831,f30590]) ).
fof(f30590,plain,
( spl635_268
<=> ! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_268])]) ).
fof(f17831,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f5683]) ).
fof(f5683,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(rectify,[],[f5204]) ).
fof(f5204,axiom,
! [X265,X5] : hAPP(c_COMBI(X5),X265) = X265,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(f30588,plain,
spl635_267,
inference(avatar_split_clause,[],[f17829,f30586]) ).
fof(f30586,plain,
( spl635_267
<=> ! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_267])]) ).
fof(f17829,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0,
inference(cnf_transformation,[],[f5681]) ).
fof(f5681,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0,
inference(rectify,[],[f3449]) ).
fof(f3449,axiom,
! [X13,X5] : hAPP(c_Fun_Oid(X5),X13) = X13,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_id__apply) ).
fof(f30584,plain,
spl635_266,
inference(avatar_split_clause,[],[f17807,f30582]) ).
fof(f30582,plain,
( spl635_266
<=> ! [X0] : hAPP(c_Int_OAbs__Integ,sK109(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_266])]) ).
fof(f17807,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,sK109(X0)) = X0,
inference(cnf_transformation,[],[f14788]) ).
fof(f30580,plain,
spl635_265,
inference(avatar_split_clause,[],[f17614,f30578]) ).
fof(f30578,plain,
( spl635_265
<=> ! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_265])]) ).
fof(f17614,plain,
! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10374]) ).
fof(f10374,plain,
! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5539]) ).
fof(f5539,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0)) ),
inference(rectify,[],[f4629]) ).
fof(f4629,axiom,
! [X5] :
( class_Orderings_Olinorder(X5)
=> c_List_Olinorder__class_Osorted(X5,c_List_Olist_ONil(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_ONil) ).
fof(f30576,plain,
spl635_264,
inference(avatar_split_clause,[],[f17602,f30574]) ).
fof(f17602,plain,
! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10362]) ).
fof(f10362,plain,
! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(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_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f855]) ).
fof(f855,axiom,
! [X5] :
( class_Rings_Osemiring__1(X5)
=> c_Int_Oiszero(X5,c_Groups_Ozero__class_Ozero(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_iszero__0) ).
fof(f30572,plain,
spl635_263,
inference(avatar_split_clause,[],[f17601,f30570]) ).
fof(f30570,plain,
( spl635_263
<=> ! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_263])]) ).
fof(f17601,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10361]) ).
fof(f10361,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5526]) ).
fof(f5526,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f858]) ).
fof(f858,axiom,
! [X5] :
( class_Rings_Osemiring__1(X5)
=> ~ c_Int_Oiszero(X5,c_Groups_Oone__class_Oone(X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__iszero__1) ).
fof(f30568,plain,
spl635_262,
inference(avatar_split_clause,[],[f17566,f30566]) ).
fof(f30566,plain,
( spl635_262
<=> ! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_262])]) ).
fof(f17566,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ),
inference(cnf_transformation,[],[f5490]) ).
fof(f5490,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ),
inference(rectify,[],[f5213]) ).
fof(f5213,axiom,
! [X29] :
( ~ hBOOL(X29)
| ~ hBOOL(hAPP(c_fNot,X29)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(f30564,plain,
spl635_261,
inference(avatar_split_clause,[],[f17565,f30562]) ).
fof(f30562,plain,
( spl635_261
<=> ! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_261])]) ).
fof(f17565,plain,
! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f5489]) ).
fof(f5489,plain,
! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f5214]) ).
fof(f5214,axiom,
! [X29] :
( hBOOL(hAPP(c_fNot,X29))
| hBOOL(X29) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
fof(f30560,plain,
spl635_260,
inference(avatar_split_clause,[],[f17328,f30558]) ).
fof(f30558,plain,
( spl635_260
<=> ! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_260])]) ).
fof(f17328,plain,
! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))),
inference(cnf_transformation,[],[f5266]) ).
fof(f5266,plain,
! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))),
inference(rectify,[],[f4331]) ).
fof(f4331,axiom,
! [X5] : hBOOL(hAPP(c_List_Odistinct(X5),c_List_Olist_ONil(X5))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
fof(f30556,plain,
spl635_259,
inference(avatar_split_clause,[],[f17327,f30554]) ).
fof(f30552,plain,
spl635_258,
inference(avatar_split_clause,[],[f17326,f30550]) ).
fof(f30550,plain,
( spl635_258
<=> ! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_258])]) ).
fof(f17326,plain,
! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f5264]) ).
fof(f5264,plain,
! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0,
inference(rectify,[],[f1633]) ).
fof(f1633,axiom,
! [X4] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X4) = X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__size) ).
fof(f30548,plain,
spl635_257,
inference(avatar_split_clause,[],[f17320,f30546]) ).
fof(f30546,plain,
( spl635_257
<=> ! [X0] : c_fequal = c_Predicate_Oconversep(X0,X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_257])]) ).
fof(f17320,plain,
! [X0] : c_fequal = c_Predicate_Oconversep(X0,X0,c_fequal),
inference(cnf_transformation,[],[f5258]) ).
fof(f5258,plain,
! [X0] : c_fequal = c_Predicate_Oconversep(X0,X0,c_fequal),
inference(rectify,[],[f4851]) ).
fof(f4851,axiom,
! [X8] : c_fequal = c_Predicate_Oconversep(X8,X8,c_fequal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_conversep__eq) ).
fof(f30544,plain,
spl635_256,
inference(avatar_split_clause,[],[f17192,f30541]) ).
fof(f30541,plain,
( spl635_256
<=> c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_256])]) ).
fof(f17192,plain,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
inference(cnf_transformation,[],[f1065]) ).
fof(f1065,axiom,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_minus__Pls) ).
fof(f30539,plain,
spl635_255,
inference(avatar_split_clause,[],[f28563,f30537]) ).
fof(f30537,plain,
( spl635_255
<=> ! [X0,X1] : sP45(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_255])]) ).
fof(f28563,plain,
! [X0,X1] : sP45(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25618,f17187]) ).
fof(f25618,plain,
! [X0,X1] : sP45(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f21404]) ).
fof(f21404,plain,
! [X2,X0,X1] :
( sP45(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f15930]) ).
fof(f30535,plain,
spl635_254,
inference(avatar_split_clause,[],[f28537,f30533]) ).
fof(f30533,plain,
( spl635_254
<=> ! [X0,X1] : sP40(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_254])]) ).
fof(f28537,plain,
! [X0,X1] : sP40(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25594,f17187]) ).
fof(f25594,plain,
! [X0,X1] : sP40(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f21324]) ).
fof(f21324,plain,
! [X2,X0,X1] :
( sP40(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f15874]) ).
fof(f30531,plain,
spl635_253,
inference(avatar_split_clause,[],[f27680,f30528]) ).
fof(f30528,plain,
( spl635_253
<=> sP15(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_253])]) ).
fof(f27680,plain,
sP15(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f27679,f25953]) ).
fof(f27679,plain,
sP15(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f25448,f17187]) ).
fof(f25448,plain,
sP15(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f25447]) ).
fof(f25447,plain,
! [X1] :
( sP15(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,[],[f19488]) ).
fof(f19488,plain,
! [X0,X1] :
( sP15(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,[],[f15251]) ).
fof(f30526,plain,
spl635_252,
inference(avatar_split_clause,[],[f27678,f30523]) ).
fof(f30523,plain,
( spl635_252
<=> sP15(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_252])]) ).
fof(f27678,plain,
sP15(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f27677,f25953]) ).
fof(f27677,plain,
sP15(hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25446,f17187]) ).
fof(f25446,plain,
sP15(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f25445]) ).
fof(f25445,plain,
! [X1] :
( sP15(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,[],[f19489]) ).
fof(f19489,plain,
! [X0,X1] :
( sP15(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,[],[f15251]) ).
fof(f30521,plain,
spl635_251,
inference(avatar_split_clause,[],[f27660,f30518]) ).
fof(f30518,plain,
( spl635_251
<=> sP14(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_251])]) ).
fof(f27660,plain,
sP14(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f27659,f25953]) ).
fof(f27659,plain,
sP14(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f25444,f17187]) ).
fof(f25444,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,[],[f25443]) ).
fof(f25443,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,[],[f19480]) ).
fof(f19480,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,[],[f15248]) ).
fof(f30516,plain,
spl635_250,
inference(avatar_split_clause,[],[f27658,f30513]) ).
fof(f30513,plain,
( spl635_250
<=> sP14(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_250])]) ).
fof(f27658,plain,
sP14(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f27657,f25953]) ).
fof(f27657,plain,
sP14(hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25442,f17187]) ).
fof(f25442,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,[],[f25441]) ).
fof(f25441,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,[],[f19481]) ).
fof(f19481,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,[],[f15248]) ).
fof(f30511,plain,
spl635_249,
inference(avatar_split_clause,[],[f26182,f30508]) ).
fof(f30508,plain,
( spl635_249
<=> c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_249])]) ).
fof(f26182,plain,
c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls),
inference(forward_demodulation,[],[f25277,f17176]) ).
fof(f25277,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,[],[f17544]) ).
fof(f17544,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,[],[f10317]) ).
fof(f10317,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,[],[f5479]) ).
fof(f5479,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,[],[f625]) ).
fof(f625,axiom,
! [X42] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X42
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X42))
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X42) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X42))
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X42) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X42
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X42) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_zsgn__def) ).
fof(f30506,plain,
spl635_248,
inference(avatar_split_clause,[],[f25939,f30503]) ).
fof(f30503,plain,
( spl635_248
<=> c_HOL_Obool_Obool__size(c_fTrue) = c_Orderings_Obot__class_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_248])]) ).
fof(f25939,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
inference(forward_demodulation,[],[f17189,f17187]) ).
fof(f17189,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f2399]) ).
fof(f2399,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bot__nat__def) ).
fof(f30501,plain,
spl635_247,
inference(avatar_split_clause,[],[f25938,f30498]) ).
fof(f30498,plain,
( spl635_247
<=> c_HOL_Obool_Obool__size(c_fFalse) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_247])]) ).
fof(f25938,plain,
c_HOL_Obool_Obool__size(c_fFalse) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17188,f17187]) ).
fof(f17188,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
inference(cnf_transformation,[],[f1765]) ).
fof(f1765,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_bool_Osize_I2_J) ).
fof(f30496,plain,
spl635_246,
inference(avatar_split_clause,[],[f25868,f30494]) ).
fof(f30494,plain,
( spl635_246
<=> ! [X2,X3] : sP83(X3,X2,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_246])]) ).
fof(f25868,plain,
! [X2,X3] : sP83(X3,X2,X2,X3),
inference(equality_resolution,[],[f25867]) ).
fof(f25867,plain,
! [X2,X3,X1] :
( sP83(X3,X1,X2,X3)
| X1 != X2 ),
inference(equality_resolution,[],[f23718]) ).
fof(f23718,plain,
! [X2,X3,X0,X1] :
( sP83(X0,X1,X2,X3)
| X0 != X3
| X1 != X2 ),
inference(cnf_transformation,[],[f16828]) ).
fof(f30492,plain,
spl635_245,
inference(avatar_split_clause,[],[f25866,f30490]) ).
fof(f30490,plain,
( spl635_245
<=> ! [X1,X3] : sP83(X1,X1,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_245])]) ).
fof(f25866,plain,
! [X3,X1] : sP83(X1,X1,X3,X3),
inference(equality_resolution,[],[f25865]) ).
fof(f25865,plain,
! [X2,X3,X1] :
( sP83(X1,X1,X2,X3)
| X2 != X3 ),
inference(equality_resolution,[],[f23719]) ).
fof(f23719,plain,
! [X2,X3,X0,X1] :
( sP83(X0,X1,X2,X3)
| X0 != X1
| X2 != X3 ),
inference(cnf_transformation,[],[f16828]) ).
fof(f30488,plain,
spl635_244,
inference(avatar_split_clause,[],[f25634,f30486]) ).
fof(f30486,plain,
( spl635_244
<=> ! [X0,X1] : sP49(X0,X1,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_244])]) ).
fof(f25634,plain,
! [X0,X1] : sP49(X0,X1,c_List_Olist_ONil(X1)),
inference(equality_resolution,[],[f21482]) ).
fof(f21482,plain,
! [X2,X0,X1] :
( sP49(X0,X1,X2)
| c_List_Olist_ONil(X1) != X2 ),
inference(cnf_transformation,[],[f15992]) ).
fof(f15992,plain,
! [X0,X1,X2] :
( ( sP49(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)),sK396(X0,X1,X2)),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),sK395(X0,X1,X2)),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),sK395(X0,X1,X2)),sK396(X0,X1,X2)) = X2 )
| c_List_Olist_ONil(X1) = X2
| ~ sP49(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK395,sK396])],[f15990,f15991]) ).
fof(f15991,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)),sK396(X0,X1,X2)),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),sK395(X0,X1,X2)),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),sK395(X0,X1,X2)),sK396(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f15990,plain,
! [X0,X1,X2] :
( ( sP49(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
| ~ sP49(X0,X1,X2) ) ),
inference(rectify,[],[f15989]) ).
fof(f15989,plain,
! [X0,X2,X1] :
( ( sP49(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
| ~ sP49(X0,X2,X1) ) ),
inference(flattening,[],[f15988]) ).
fof(f15988,plain,
! [X0,X2,X1] :
( ( sP49(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
| ~ sP49(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f14611]) ).
fof(f14611,plain,
! [X0,X2,X1] :
( sP49(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,[sP49])]) ).
fof(f30484,plain,
spl635_243,
inference(avatar_split_clause,[],[f25414,f30481]) ).
fof(f30481,plain,
( spl635_243
<=> sP9(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_243])]) ).
fof(f25414,plain,
sP9(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(equality_resolution,[],[f25413]) ).
fof(f25413,plain,
! [X1] :
( sP9(c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ),
inference(equality_resolution,[],[f19343]) ).
fof(f19343,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,[],[f15167]) ).
fof(f30479,plain,
spl635_242,
inference(avatar_split_clause,[],[f25382,f30477]) ).
fof(f25382,plain,
! [X1] : sP7(hAPP(c_Int_Onat,X1),X1),
inference(equality_resolution,[],[f19211]) ).
fof(f19211,plain,
! [X0,X1] :
( sP7(X0,X1)
| hAPP(c_Int_Onat,X1) != X0 ),
inference(cnf_transformation,[],[f15063]) ).
fof(f30475,plain,
spl635_241,
inference(avatar_split_clause,[],[f25377,f30473]) ).
fof(f25377,plain,
! [X0] : sP6(hAPP(c_Int_Onat,X0),X0),
inference(equality_resolution,[],[f19203]) ).
fof(f19203,plain,
! [X0,X1] :
( sP6(X1,X0)
| hAPP(c_Int_Onat,X0) != X1 ),
inference(cnf_transformation,[],[f15060]) ).
fof(f30471,plain,
spl635_240,
inference(avatar_split_clause,[],[f19146,f30469]) ).
fof(f19146,plain,
! [X0,X1] :
( sP4(X0)
| ~ c_Equiv__Relations_Opart__equivp(X1,X0) ),
inference(cnf_transformation,[],[f15004]) ).
fof(f30467,plain,
spl635_239,
inference(avatar_split_clause,[],[f18655,f30465]) ).
fof(f30465,plain,
( spl635_239
<=> ! [X0,X1] :
( sP1(X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_239])]) ).
fof(f18655,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f14529]) ).
fof(f14529,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(definition_folding,[],[f10802,f14528,f14527]) ).
fof(f10802,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,[],[f6384]) ).
fof(f6384,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,[],[f4744]) ).
fof(f4744,axiom,
! [X17,X8] :
( class_Orderings_Olinorder(X8)
=> ( c_List_Olinorder__class_Osorted(X8,X17)
<=> ( ? [X215,X2] :
( c_List_Olinorder__class_Osorted(X8,X215)
& ! [X142] :
( hBOOL(hAPP(hAPP(c_member(X8),X142),hAPP(c_List_Oset(X8),X215)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X8),X2),X142)) )
& hAPP(hAPP(c_List_Olist_OCons(X8),X2),X215) = X17 )
| c_List_Olist_ONil(X8) = X17 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted_Osimps) ).
fof(f30463,plain,
spl635_238,
inference(avatar_split_clause,[],[f17828,f30461]) ).
fof(f30461,plain,
( spl635_238
<=> ! [X0,X1] : c_List_Olist__all(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_238])]) ).
fof(f17828,plain,
! [X0,X1] : c_List_Olist__all(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5680]) ).
fof(f5680,plain,
! [X0,X1] : c_List_Olist__all(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4811]) ).
fof(f4811,axiom,
! [X29,X8] : c_List_Olist__all(X8,X29,c_List_Olist_ONil(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__all__simps_I2_J) ).
fof(f30459,plain,
spl635_237,
inference(avatar_split_clause,[],[f17826,f30457]) ).
fof(f30457,plain,
( spl635_237
<=> ! [X0,X1] : c_Relation_Otrans(X1,c_Transitive__Closure_Ortrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_237])]) ).
fof(f17826,plain,
! [X0,X1] : c_Relation_Otrans(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(cnf_transformation,[],[f5678]) ).
fof(f5678,plain,
! [X0,X1] : c_Relation_Otrans(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(rectify,[],[f4919]) ).
fof(f4919,axiom,
! [X98,X8] : c_Relation_Otrans(X8,c_Transitive__Closure_Ortrancl(X8,X98)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__rtrancl) ).
fof(f30455,plain,
spl635_236,
inference(avatar_split_clause,[],[f17820,f30453]) ).
fof(f30453,plain,
( spl635_236
<=> ! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_236])]) ).
fof(f17820,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)),
inference(cnf_transformation,[],[f5672]) ).
fof(f5672,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)),
inference(rectify,[],[f4635]) ).
fof(f4635,axiom,
! [X41,X42] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X42,X41)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sorted__upto) ).
fof(f30451,plain,
spl635_235,
inference(avatar_split_clause,[],[f17819,f30449]) ).
fof(f30449,plain,
( spl635_235
<=> ! [X0,X1] : ~ c_List_Olist__ex(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_235])]) ).
fof(f17819,plain,
! [X0,X1] : ~ c_List_Olist__ex(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5671]) ).
fof(f5671,plain,
! [X0,X1] : ~ c_List_Olist__ex(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4802]) ).
fof(f4802,axiom,
! [X29,X8] : ~ c_List_Olist__ex(X8,X29,c_List_Olist_ONil(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex__simps_I2_J) ).
fof(f30447,plain,
spl635_234,
inference(avatar_split_clause,[],[f17818,f30445]) ).
fof(f30445,plain,
( spl635_234
<=> ! [X0,X1] : ~ c_List_Olist__ex1(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_234])]) ).
fof(f17818,plain,
! [X0,X1] : ~ c_List_Olist__ex1(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5670]) ).
fof(f5670,plain,
! [X0,X1] : ~ c_List_Olist__ex1(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4822]) ).
fof(f4822,axiom,
! [X29,X8] : ~ c_List_Olist__ex1(X8,X29,c_List_Olist_ONil(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_list__ex1__simps_I1_J) ).
fof(f30443,plain,
spl635_233,
inference(avatar_split_clause,[],[f17629,f30441]) ).
fof(f30441,plain,
( spl635_233
<=> ! [X0] :
( class_Enum_Oenum(tc_Option_Ooption(X0))
| ~ class_Enum_Oenum(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_233])]) ).
fof(f17629,plain,
! [X0] :
( class_Enum_Oenum(tc_Option_Ooption(X0))
| ~ class_Enum_Oenum(X0) ),
inference(cnf_transformation,[],[f10389]) ).
fof(f10389,plain,
! [X0] :
( class_Enum_Oenum(tc_Option_Ooption(X0))
| ~ class_Enum_Oenum(X0) ),
inference(ennf_transformation,[],[f5554]) ).
fof(f5554,plain,
! [X0] :
( class_Enum_Oenum(X0)
=> class_Enum_Oenum(tc_Option_Ooption(X0)) ),
inference(rectify,[],[f5148]) ).
fof(f5148,axiom,
! [X264] :
( class_Enum_Oenum(X264)
=> class_Enum_Oenum(tc_Option_Ooption(X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Enum_Oenum) ).
fof(f30439,plain,
spl635_232,
inference(avatar_split_clause,[],[f17627,f30437]) ).
fof(f30437,plain,
( spl635_232
<=> ! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_232])]) ).
fof(f17627,plain,
! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(cnf_transformation,[],[f10387]) ).
fof(f10387,plain,
! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(ennf_transformation,[],[f5552]) ).
fof(f5552,plain,
! [X0] :
( class_Finite__Set_Ofinite(X0)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X0)) ),
inference(rectify,[],[f5147]) ).
fof(f5147,axiom,
! [X264] :
( class_Finite__Set_Ofinite(X264)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(f30435,plain,
spl635_231,
inference(avatar_split_clause,[],[f17622,f30433]) ).
fof(f30433,plain,
( spl635_231
<=> ! [X0] :
( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X0))
| ~ class_Lazy__Sequence_Osmall__lazy(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_231])]) ).
fof(f17622,plain,
! [X0] :
( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X0))
| ~ class_Lazy__Sequence_Osmall__lazy(X0) ),
inference(cnf_transformation,[],[f10382]) ).
fof(f10382,plain,
! [X0] :
( class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X0))
| ~ class_Lazy__Sequence_Osmall__lazy(X0) ),
inference(ennf_transformation,[],[f5547]) ).
fof(f5547,plain,
! [X0] :
( class_Lazy__Sequence_Osmall__lazy(X0)
=> class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X0)) ),
inference(rectify,[],[f5142]) ).
fof(f5142,axiom,
! [X264] :
( class_Lazy__Sequence_Osmall__lazy(X264)
=> class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(X264)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List__Olist__Lazy__Sequence_Osmall__lazy) ).
fof(f30431,plain,
spl635_230,
inference(avatar_split_clause,[],[f17313,f30429]) ).
fof(f30429,plain,
( spl635_230
<=> ! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_230])]) ).
fof(f17313,plain,
! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0),
inference(cnf_transformation,[],[f5251]) ).
fof(f5251,plain,
! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0),
inference(rectify,[],[f3085]) ).
fof(f3085,axiom,
! [X149] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X149),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_inj__Suc) ).
fof(f30427,plain,
spl635_229,
inference(avatar_split_clause,[],[f17311,f30425]) ).
fof(f30425,plain,
( spl635_229
<=> ! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_229])]) ).
fof(f17311,plain,
! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f5249]) ).
fof(f5249,plain,
! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(rectify,[],[f1369]) ).
fof(f1369,axiom,
! [X31] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X31)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).
fof(f30423,plain,
spl635_228,
inference(avatar_split_clause,[],[f17307,f30421]) ).
fof(f30421,plain,
( spl635_228
<=> ! [X0] : hAPP(c_Nat_OSuc,X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl635_228])]) ).
fof(f17307,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(cnf_transformation,[],[f5245]) ).
fof(f5245,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X4] : hAPP(c_Nat_OSuc,X4) != X4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(f30419,plain,
spl635_227,
inference(avatar_split_clause,[],[f17191,f30416]) ).
fof(f17191,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f3499]) ).
fof(f3499,axiom,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pair__less) ).
fof(f30414,plain,
spl635_226,
inference(avatar_split_clause,[],[f17190,f30411]) ).
fof(f30411,plain,
( spl635_226
<=> c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_226])]) ).
fof(f17190,plain,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
inference(cnf_transformation,[],[f2320]) ).
fof(f2320,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',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J) ).
fof(f30409,plain,
spl635_225,
inference(avatar_split_clause,[],[f17187,f30406]) ).
fof(f30404,plain,
spl635_224,
inference(avatar_split_clause,[],[f17185,f30401]) ).
fof(f30401,plain,
( spl635_224
<=> c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_224])]) ).
fof(f17185,plain,
c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),
inference(cnf_transformation,[],[f3017]) ).
fof(f3017,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',fact_inf__nat__def) ).
fof(f30399,plain,
spl635_223,
inference(avatar_split_clause,[],[f17184,f30396]) ).
fof(f17184,plain,
c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),
inference(cnf_transformation,[],[f2196]) ).
fof(f2196,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',fact_sup__nat__def) ).
fof(f30394,plain,
spl635_222,
inference(avatar_split_clause,[],[f17183,f30391]) ).
fof(f17183,plain,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
inference(cnf_transformation,[],[f3446]) ).
fof(f3446,axiom,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_of__int__eq__id) ).
fof(f30389,plain,
~ spl635_221,
inference(avatar_split_clause,[],[f17179,f30386]) ).
fof(f17179,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f854]) ).
fof(f854,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__1) ).
fof(f30383,plain,
spl635_220,
inference(avatar_split_clause,[],[f27521,f30380]) ).
fof(f30380,plain,
( spl635_220
<=> sP7(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_220])]) ).
fof(f27521,plain,
sP7(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls),
inference(forward_demodulation,[],[f27520,f25969]) ).
fof(f27520,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,[],[f25379,f17187]) ).
fof(f25379,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,[],[f25378]) ).
fof(f25378,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,[],[f19210]) ).
fof(f19210,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,[],[f15062]) ).
fof(f30378,plain,
spl635_219,
inference(avatar_split_clause,[],[f27513,f30375]) ).
fof(f30375,plain,
( spl635_219
<=> sP6(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_219])]) ).
fof(f27513,plain,
sP6(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls),
inference(forward_demodulation,[],[f27512,f25969]) ).
fof(f27512,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,[],[f25374,f17187]) ).
fof(f25374,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,[],[f25373]) ).
fof(f25373,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,[],[f19202]) ).
fof(f19202,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,[],[f15059]) ).
fof(f30373,plain,
~ spl635_218,
inference(avatar_split_clause,[],[f25937,f30370]) ).
fof(f30370,plain,
( spl635_218
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_218])]) ).
fof(f25937,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)),
inference(forward_demodulation,[],[f17180,f17176]) ).
fof(f17180,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(cnf_transformation,[],[f852]) ).
fof(f852,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__neg__0) ).
fof(f30368,plain,
~ spl635_217,
inference(avatar_split_clause,[],[f25936,f30365]) ).
fof(f30365,plain,
( spl635_217
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl635_217])]) ).
fof(f25936,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Int_OPls,
inference(forward_demodulation,[],[f17178,f17176]) ).
fof(f17178,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f379]) ).
fof(f379,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(f30363,plain,
spl635_216,
inference(avatar_split_clause,[],[f25338,f30361]) ).
fof(f30361,plain,
( spl635_216
<=> ! [X0] : sP0(X0,c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_216])]) ).
fof(f25338,plain,
! [X0] : sP0(X0,c_List_Olist_ONil(X0)),
inference(equality_resolution,[],[f18652]) ).
fof(f18652,plain,
! [X0,X1] :
( sP0(X0,X1)
| c_List_Olist_ONil(X0) != X1 ),
inference(cnf_transformation,[],[f14860]) ).
fof(f30359,plain,
spl635_215,
inference(avatar_split_clause,[],[f17815,f30357]) ).
fof(f30357,plain,
( spl635_215
<=> ! [X0,X1] : class_Nat_Osize(tc_prod(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_215])]) ).
fof(f17815,plain,
! [X0,X1] : class_Nat_Osize(tc_prod(X1,X0)),
inference(cnf_transformation,[],[f5667]) ).
fof(f5667,plain,
! [X0,X1] : class_Nat_Osize(tc_prod(X1,X0)),
inference(rectify,[],[f5154]) ).
fof(f5154,axiom,
! [X264,X263] : class_Nat_Osize(tc_prod(X263,X264)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_prod__Nat_Osize) ).
fof(f30355,plain,
spl635_214,
inference(avatar_split_clause,[],[f17814,f30353]) ).
fof(f30353,plain,
( spl635_214
<=> ! [X0,X1] : class_Nat_Osize(tc_sum(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_214])]) ).
fof(f17814,plain,
! [X0,X1] : class_Nat_Osize(tc_sum(X1,X0)),
inference(cnf_transformation,[],[f5666]) ).
fof(f5666,plain,
! [X0,X1] : class_Nat_Osize(tc_sum(X1,X0)),
inference(rectify,[],[f5146]) ).
fof(f5146,axiom,
! [X264,X263] : class_Nat_Osize(tc_sum(X263,X264)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum__Nat_Osize) ).
fof(f30351,plain,
spl635_213,
inference(avatar_split_clause,[],[f17813,f30349]) ).
fof(f30349,plain,
( spl635_213
<=> ! [X0,X1] : class_Nat_Osize(tc_Nitpick_Opair__box(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_213])]) ).
fof(f17813,plain,
! [X0,X1] : class_Nat_Osize(tc_Nitpick_Opair__box(X1,X0)),
inference(cnf_transformation,[],[f5665]) ).
fof(f5665,plain,
! [X0,X1] : class_Nat_Osize(tc_Nitpick_Opair__box(X1,X0)),
inference(rectify,[],[f5150]) ).
fof(f5150,axiom,
! [X264,X263] : class_Nat_Osize(tc_Nitpick_Opair__box(X263,X264)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nitpick__Opair____box__Nat_Osize) ).
fof(f30347,plain,
spl635_212,
inference(avatar_split_clause,[],[f17296,f30345]) ).
fof(f30345,plain,
( spl635_212
<=> ! [X0] : c_Int_OMin != c_Int_OBit0(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_212])]) ).
fof(f17296,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,[],[f1250]) ).
fof(f1250,axiom,
! [X40] : c_Int_OMin != c_Int_OBit0(X40),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I45_J) ).
fof(f30343,plain,
spl635_211,
inference(avatar_split_clause,[],[f17177,f30340]) ).
fof(f30340,plain,
( spl635_211
<=> c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_211])]) ).
fof(f17177,plain,
c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
inference(cnf_transformation,[],[f13]) ).
fof(f13,axiom,
c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mono__Suc) ).
fof(f30338,plain,
spl635_210,
inference(avatar_split_clause,[],[f17176,f30335]) ).
fof(f30333,plain,
spl635_209,
inference(avatar_split_clause,[],[f17175,f30330]) ).
fof(f30330,plain,
( spl635_209
<=> c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral ),
introduced(avatar_definition,[new_symbols(naming,[spl635_209])]) ).
fof(f30328,plain,
spl635_208,
inference(avatar_split_clause,[],[f17174,f30325]) ).
fof(f30325,plain,
( spl635_208
<=> c_Int_OPls = c_Int_OBit0(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_208])]) ).
fof(f30323,plain,
spl635_207,
inference(avatar_split_clause,[],[f17170,f30320]) ).
fof(f30320,plain,
( spl635_207
<=> c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_207])]) ).
fof(f17170,plain,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f1793]) ).
fof(f1793,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',fact_Code__Numeral_Oof__nat__code) ).
fof(f30318,plain,
spl635_206,
inference(avatar_split_clause,[],[f27570,f30316]) ).
fof(f30316,plain,
( spl635_206
<=> ! [X0] : sP10(X0,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_206])]) ).
fof(f27570,plain,
! [X0] : sP10(X0,c_Int_OPls),
inference(forward_demodulation,[],[f25415,f17176]) ).
fof(f25415,plain,
! [X0] : sP10(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(equality_resolution,[],[f19351]) ).
fof(f19351,plain,
! [X0,X1] :
( sP10(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ),
inference(cnf_transformation,[],[f15171]) ).
fof(f15171,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,[],[f15170]) ).
fof(f15170,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,[],[f15169]) ).
fof(f15169,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,[],[f14546]) ).
fof(f30314,plain,
spl635_205,
inference(avatar_split_clause,[],[f27563,f30311]) ).
fof(f30311,plain,
( spl635_205
<=> sP9(c_Int_OMin,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_205])]) ).
fof(f27563,plain,
sP9(c_Int_OMin,c_Int_OMin),
inference(forward_demodulation,[],[f25412,f17327]) ).
fof(f25412,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,[],[f25411]) ).
fof(f25411,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,[],[f19344]) ).
fof(f19344,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,[],[f15167]) ).
fof(f30309,plain,
spl635_204,
inference(avatar_split_clause,[],[f17810,f30307]) ).
fof(f30307,plain,
( spl635_204
<=> ! [X0,X1] : c_FunDef_Ois__measure(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_204])]) ).
fof(f17810,plain,
! [X0,X1] : c_FunDef_Ois__measure(X1,X0),
inference(cnf_transformation,[],[f5662]) ).
fof(f5662,plain,
! [X0,X1] : c_FunDef_Ois__measure(X1,X0),
inference(rectify,[],[f3988]) ).
fof(f3988,axiom,
! [X17,X8] : c_FunDef_Ois__measure(X8,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_is__measure_Oequations) ).
fof(f30305,plain,
spl635_203,
inference(avatar_split_clause,[],[f17295,f30303]) ).
fof(f17295,plain,
! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal),
inference(cnf_transformation,[],[f5233]) ).
fof(f5233,plain,
! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal),
inference(rectify,[],[f3220]) ).
fof(f3220,axiom,
! [X8] : c_Equiv__Relations_Oequivp(X8,c_fequal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_identity__equivp) ).
fof(f30301,plain,
spl635_202,
inference(avatar_split_clause,[],[f17294,f30299]) ).
fof(f30299,plain,
( spl635_202
<=> ! [X0] : class_Nat_Osize(tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_202])]) ).
fof(f17294,plain,
! [X0] : class_Nat_Osize(tc_List_Olist(X0)),
inference(cnf_transformation,[],[f5232]) ).
fof(f5232,plain,
! [X0] : class_Nat_Osize(tc_List_Olist(X0)),
inference(rectify,[],[f5143]) ).
fof(f5143,axiom,
! [X264] : class_Nat_Osize(tc_List_Olist(X264)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_List__Olist__Nat_Osize) ).
fof(f30297,plain,
spl635_201,
inference(avatar_split_clause,[],[f17293,f30295]) ).
fof(f30295,plain,
( spl635_201
<=> ! [X0] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_201])]) ).
fof(f17293,plain,
! [X0] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)),
inference(cnf_transformation,[],[f5231]) ).
fof(f5231,plain,
! [X0] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)),
inference(rectify,[],[f5203]) ).
fof(f5203,axiom,
! [X264] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X264)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Lazy____Sequence__Olazy____sequence__Nat_Osize) ).
fof(f30293,plain,
spl635_200,
inference(avatar_split_clause,[],[f17292,f30291]) ).
fof(f30291,plain,
( spl635_200
<=> ! [X0] : class_Nat_Osize(tc_Option_Ooption(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_200])]) ).
fof(f17292,plain,
! [X0] : class_Nat_Osize(tc_Option_Ooption(X0)),
inference(cnf_transformation,[],[f5230]) ).
fof(f5230,plain,
! [X0] : class_Nat_Osize(tc_Option_Ooption(X0)),
inference(rectify,[],[f5149]) ).
fof(f5149,axiom,
! [X264] : class_Nat_Osize(tc_Option_Ooption(X264)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Option__Ooption__Nat_Osize) ).
fof(f30289,plain,
spl635_199,
inference(avatar_split_clause,[],[f17291,f30287]) ).
fof(f30287,plain,
( spl635_199
<=> ! [X0] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_199])]) ).
fof(f17291,plain,
! [X0] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X0)),
inference(cnf_transformation,[],[f5229]) ).
fof(f5229,plain,
! [X0] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X0)),
inference(rectify,[],[f5160]) ).
fof(f5160,axiom,
! [X264] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X264)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Hoare____Mirabelle__Otriple__Nat_Osize) ).
fof(f30285,plain,
spl635_198,
inference(avatar_split_clause,[],[f17169,f30282]) ).
fof(f17169,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f3485]) ).
fof(f3485,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__less__than) ).
fof(f30280,plain,
spl635_197,
inference(avatar_split_clause,[],[f17168,f30277]) ).
fof(f17168,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f3540]) ).
fof(f3540,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
fof(f30275,plain,
spl635_196,
inference(avatar_split_clause,[],[f17167,f30272]) ).
fof(f30272,plain,
( spl635_196
<=> c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_196])]) ).
fof(f17167,plain,
c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f4901]) ).
fof(f4901,axiom,
c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__than) ).
fof(f30270,plain,
( spl635_195
| ~ spl635_194 ),
inference(avatar_split_clause,[],[f30265,f30261,f30267]) ).
fof(f30267,plain,
( spl635_195
<=> c_Nat__Transfer_Ois__nat(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_195])]) ).
fof(f30261,plain,
( spl635_194
<=> c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_194])]) ).
fof(f30265,plain,
( c_Nat__Transfer_Ois__nat(c_Int_OPls)
| ~ spl635_194 ),
inference(forward_demodulation,[],[f30263,f17176]) ).
fof(f30263,plain,
( c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl635_194 ),
inference(avatar_component_clause,[],[f30261]) ).
fof(f30264,plain,
spl635_194,
inference(avatar_split_clause,[],[f17166,f30261]) ).
fof(f17166,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f1367]) ).
fof(f1367,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).
fof(f30259,plain,
spl635_193,
inference(avatar_split_clause,[],[f17165,f30256]) ).
fof(f30256,plain,
( spl635_193
<=> c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_193])]) ).
fof(f17165,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f1370]) ).
fof(f1370,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).
fof(f30254,plain,
~ spl635_192,
inference(avatar_split_clause,[],[f17163,f30251]) ).
fof(f30251,plain,
( spl635_192
<=> c_Int_OMin = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl635_192])]) ).
fof(f17163,plain,
c_Int_OMin != c_Int_OPls,
inference(cnf_transformation,[],[f1067]) ).
fof(f1067,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rel__simps_I40_J) ).
fof(f30249,plain,
spl635_191,
inference(avatar_split_clause,[],[f17162,f30246]) ).
fof(f30246,plain,
( spl635_191
<=> hBOOL(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_191])]) ).
fof(f17162,plain,
hBOOL(c_fTrue),
inference(cnf_transformation,[],[f5212]) ).
fof(f5212,axiom,
hBOOL(c_fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).
fof(f30244,plain,
spl635_190,
inference(avatar_split_clause,[],[f17161,f30241]) ).
fof(f30241,plain,
( spl635_190
<=> class_Nat_Osize(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_190])]) ).
fof(f17161,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',arity_HOL__Obool__Nat_Osize) ).
fof(f30239,plain,
spl635_189,
inference(avatar_split_clause,[],[f17160,f30236]) ).
fof(f30236,plain,
( spl635_189
<=> class_Nat_Osize(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_189])]) ).
fof(f17160,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',arity_Nat__Onat__Nat_Osize) ).
fof(f30234,plain,
spl635_188,
inference(avatar_split_clause,[],[f17159,f30231]) ).
fof(f30231,plain,
( spl635_188
<=> class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_188])]) ).
fof(f17159,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',arity_Code____Numeral__Ocode____numeral__Nat_Osize) ).
fof(f30229,plain,
spl635_187,
inference(avatar_split_clause,[],[f17158,f30226]) ).
fof(f30226,plain,
( spl635_187
<=> class_Nat_Osize(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_187])]) ).
fof(f17158,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',arity_Product____Type__Ounit__Nat_Osize) ).
fof(f30224,plain,
spl635_186,
inference(avatar_split_clause,[],[f17157,f30221]) ).
fof(f30221,plain,
( spl635_186
<=> class_Nat_Osize(tc_Code__Evaluation_Oterm) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_186])]) ).
fof(f17157,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',arity_Code____Evaluation__Oterm__Nat_Osize) ).
fof(f30219,plain,
spl635_185,
inference(avatar_split_clause,[],[f17156,f30216]) ).
fof(f17156,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',arity_HOL__Obool__Enum_Oenum) ).
fof(f30214,plain,
spl635_184,
inference(avatar_split_clause,[],[f17155,f30211]) ).
fof(f17155,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',arity_Product____Type__Ounit__Enum_Oenum) ).
fof(f30209,plain,
spl635_183,
inference(avatar_split_clause,[],[f17154,f30206]) ).
fof(f30206,plain,
( spl635_183
<=> class_Finite__Set_Ofinite(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_183])]) ).
fof(f17154,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',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(f30204,plain,
spl635_182,
inference(avatar_split_clause,[],[f17153,f30201]) ).
fof(f30201,plain,
( spl635_182
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_182])]) ).
fof(f17153,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',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(f30199,plain,
spl635_181,
inference(avatar_split_clause,[],[f17152,f30196]) ).
fof(f30196,plain,
( spl635_181
<=> class_Orderings_Oorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_181])]) ).
fof(f17152,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',arity_HOL__Obool__Orderings_Oorder) ).
fof(f30194,plain,
spl635_180,
inference(avatar_split_clause,[],[f17151,f30191]) ).
fof(f30191,plain,
( spl635_180
<=> class_Orderings_Oorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_180])]) ).
fof(f17151,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',arity_Nat__Onat__Orderings_Oorder) ).
fof(f30189,plain,
spl635_179,
inference(avatar_split_clause,[],[f17150,f30186]) ).
fof(f30186,plain,
( spl635_179
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_179])]) ).
fof(f17150,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',arity_Int__Oint__Orderings_Oorder) ).
fof(f30184,plain,
spl635_178,
inference(avatar_split_clause,[],[f17149,f30181]) ).
fof(f30181,plain,
( spl635_178
<=> class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_178])]) ).
fof(f17149,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',arity_Code____Numeral__Ocode____numeral__Orderings_Oorder) ).
fof(f30179,plain,
spl635_177,
inference(avatar_split_clause,[],[f17148,f30176]) ).
fof(f30176,plain,
( spl635_177
<=> class_Orderings_Oord(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_177])]) ).
fof(f17148,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',arity_HOL__Obool__Orderings_Oord) ).
fof(f30174,plain,
spl635_176,
inference(avatar_split_clause,[],[f17147,f30171]) ).
fof(f30171,plain,
( spl635_176
<=> class_Orderings_Oord(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_176])]) ).
fof(f17147,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',arity_Nat__Onat__Orderings_Oord) ).
fof(f30169,plain,
spl635_175,
inference(avatar_split_clause,[],[f17146,f30166]) ).
fof(f30166,plain,
( spl635_175
<=> class_Orderings_Oord(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_175])]) ).
fof(f17146,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',arity_Int__Oint__Orderings_Oord) ).
fof(f30164,plain,
spl635_174,
inference(avatar_split_clause,[],[f17145,f30161]) ).
fof(f30161,plain,
( spl635_174
<=> class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_174])]) ).
fof(f17145,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',arity_Code____Numeral__Ocode____numeral__Orderings_Oord) ).
fof(f30159,plain,
spl635_173,
inference(avatar_split_clause,[],[f17144,f30156]) ).
fof(f30156,plain,
( spl635_173
<=> class_Orderings_Opreorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_173])]) ).
fof(f17144,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',arity_HOL__Obool__Orderings_Opreorder) ).
fof(f30154,plain,
spl635_172,
inference(avatar_split_clause,[],[f17143,f30151]) ).
fof(f30151,plain,
( spl635_172
<=> class_Orderings_Opreorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_172])]) ).
fof(f17143,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',arity_Nat__Onat__Orderings_Opreorder) ).
fof(f30149,plain,
spl635_171,
inference(avatar_split_clause,[],[f17142,f30146]) ).
fof(f30146,plain,
( spl635_171
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_171])]) ).
fof(f17142,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',arity_Int__Oint__Orderings_Opreorder) ).
fof(f30144,plain,
spl635_170,
inference(avatar_split_clause,[],[f17141,f30141]) ).
fof(f30141,plain,
( spl635_170
<=> class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_170])]) ).
fof(f17141,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',arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder) ).
fof(f30139,plain,
spl635_169,
inference(avatar_split_clause,[],[f17140,f30136]) ).
fof(f30136,plain,
( spl635_169
<=> class_Groups_Ominus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_169])]) ).
fof(f17140,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',arity_HOL__Obool__Groups_Ominus) ).
fof(f30134,plain,
spl635_168,
inference(avatar_split_clause,[],[f17139,f30131]) ).
fof(f30131,plain,
( spl635_168
<=> class_Groups_Ominus(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_168])]) ).
fof(f17139,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',arity_Nat__Onat__Groups_Ominus) ).
fof(f30129,plain,
spl635_167,
inference(avatar_split_clause,[],[f17138,f30126]) ).
fof(f30126,plain,
( spl635_167
<=> class_Groups_Ominus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_167])]) ).
fof(f17138,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',arity_Int__Oint__Groups_Ominus) ).
fof(f30124,plain,
spl635_166,
inference(avatar_split_clause,[],[f17137,f30121]) ).
fof(f30121,plain,
( spl635_166
<=> class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_166])]) ).
fof(f17137,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',arity_Code____Numeral__Ocode____numeral__Groups_Ominus) ).
fof(f30119,plain,
spl635_165,
inference(avatar_split_clause,[],[f17136,f30116]) ).
fof(f30116,plain,
( spl635_165
<=> class_Lattices_Olattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_165])]) ).
fof(f17136,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',arity_HOL__Obool__Lattices_Olattice) ).
fof(f30114,plain,
spl635_164,
inference(avatar_split_clause,[],[f17135,f30111]) ).
fof(f30111,plain,
( spl635_164
<=> class_Lattices_Olattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_164])]) ).
fof(f17135,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',arity_Nat__Onat__Lattices_Olattice) ).
fof(f30109,plain,
spl635_163,
inference(avatar_split_clause,[],[f17134,f30106]) ).
fof(f30106,plain,
( spl635_163
<=> class_Lattices_Olattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_163])]) ).
fof(f17134,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',arity_Int__Oint__Lattices_Olattice) ).
fof(f30104,plain,
spl635_162,
inference(avatar_split_clause,[],[f17133,f30101]) ).
fof(f30101,plain,
( spl635_162
<=> class_Lattices_Osemilattice__inf(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_162])]) ).
fof(f17133,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',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
fof(f30099,plain,
spl635_161,
inference(avatar_split_clause,[],[f17132,f30096]) ).
fof(f30096,plain,
( spl635_161
<=> class_Lattices_Osemilattice__inf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_161])]) ).
fof(f17132,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',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
fof(f30094,plain,
spl635_160,
inference(avatar_split_clause,[],[f17131,f30091]) ).
fof(f30091,plain,
( spl635_160
<=> class_Lattices_Osemilattice__inf(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_160])]) ).
fof(f17131,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',arity_Int__Oint__Lattices_Osemilattice__inf) ).
fof(f30089,plain,
spl635_159,
inference(avatar_split_clause,[],[f17130,f30086]) ).
fof(f30086,plain,
( spl635_159
<=> class_Lattices_Osemilattice__sup(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_159])]) ).
fof(f17130,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',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
fof(f30084,plain,
spl635_158,
inference(avatar_split_clause,[],[f17129,f30081]) ).
fof(f17129,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',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
fof(f30079,plain,
spl635_157,
inference(avatar_split_clause,[],[f17128,f30076]) ).
fof(f30076,plain,
( spl635_157
<=> class_Lattices_Osemilattice__sup(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_157])]) ).
fof(f17128,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',arity_Int__Oint__Lattices_Osemilattice__sup) ).
fof(f30074,plain,
spl635_156,
inference(avatar_split_clause,[],[f17127,f30071]) ).
fof(f30071,plain,
( spl635_156
<=> class_Lattices_Odistrib__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_156])]) ).
fof(f17127,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',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
fof(f30069,plain,
spl635_155,
inference(avatar_split_clause,[],[f17126,f30066]) ).
fof(f30066,plain,
( spl635_155
<=> class_Lattices_Odistrib__lattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_155])]) ).
fof(f17126,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',arity_Nat__Onat__Lattices_Odistrib__lattice) ).
fof(f30064,plain,
spl635_154,
inference(avatar_split_clause,[],[f17125,f30061]) ).
fof(f30061,plain,
( spl635_154
<=> class_Lattices_Odistrib__lattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_154])]) ).
fof(f17125,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',arity_Int__Oint__Lattices_Odistrib__lattice) ).
fof(f30059,plain,
spl635_153,
inference(avatar_split_clause,[],[f17124,f30056]) ).
fof(f30056,plain,
( spl635_153
<=> class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_153])]) ).
fof(f17124,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',arity_Int__Oint__Lazy__Sequence_Osmall__lazy) ).
fof(f30054,plain,
spl635_152,
inference(avatar_split_clause,[],[f17123,f30051]) ).
fof(f30051,plain,
( spl635_152
<=> class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_152])]) ).
fof(f17123,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',arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy) ).
fof(f30049,plain,
spl635_151,
inference(avatar_split_clause,[],[f17122,f30046]) ).
fof(f30046,plain,
( spl635_151
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_151])]) ).
fof(f17122,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',arity_Nat__Onat__Orderings_Olinorder) ).
fof(f30044,plain,
spl635_150,
inference(avatar_split_clause,[],[f17121,f30041]) ).
fof(f30041,plain,
( spl635_150
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_150])]) ).
fof(f17121,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',arity_Int__Oint__Orderings_Olinorder) ).
fof(f30039,plain,
spl635_149,
inference(avatar_split_clause,[],[f17120,f30036]) ).
fof(f30036,plain,
( spl635_149
<=> class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_149])]) ).
fof(f17120,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',arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) ).
fof(f30034,plain,
spl635_148,
inference(avatar_split_clause,[],[f17119,f30031]) ).
fof(f30031,plain,
( spl635_148
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_148])]) ).
fof(f17119,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',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(f30029,plain,
spl635_147,
inference(avatar_split_clause,[],[f17118,f30026]) ).
fof(f30026,plain,
( spl635_147
<=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_147])]) ).
fof(f17118,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',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(f30024,plain,
spl635_146,
inference(avatar_split_clause,[],[f17117,f30021]) ).
fof(f30021,plain,
( spl635_146
<=> class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_146])]) ).
fof(f17117,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',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) ).
fof(f30019,plain,
spl635_145,
inference(avatar_split_clause,[],[f17116,f30016]) ).
fof(f30016,plain,
( spl635_145
<=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_145])]) ).
fof(f17116,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',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(f30014,plain,
spl635_144,
inference(avatar_split_clause,[],[f17115,f30011]) ).
fof(f30011,plain,
( spl635_144
<=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_144])]) ).
fof(f17115,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',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(f30009,plain,
spl635_143,
inference(avatar_split_clause,[],[f17114,f30006]) ).
fof(f30006,plain,
( spl635_143
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_143])]) ).
fof(f17114,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',arity_Int__Oint__Divides_Osemiring__div) ).
fof(f30004,plain,
spl635_142,
inference(avatar_split_clause,[],[f17113,f30001]) ).
fof(f30001,plain,
( spl635_142
<=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_142])]) ).
fof(f17113,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',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(f29999,plain,
spl635_141,
inference(avatar_split_clause,[],[f17112,f29996]) ).
fof(f29996,plain,
( spl635_141
<=> class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_141])]) ).
fof(f17112,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',arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) ).
fof(f29994,plain,
spl635_140,
inference(avatar_split_clause,[],[f17111,f29991]) ).
fof(f29991,plain,
( spl635_140
<=> class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_140])]) ).
fof(f17111,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',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).
fof(f29989,plain,
spl635_139,
inference(avatar_split_clause,[],[f17110,f29986]) ).
fof(f29986,plain,
( spl635_139
<=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_139])]) ).
fof(f17110,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',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(f29984,plain,
spl635_138,
inference(avatar_split_clause,[],[f17109,f29981]) ).
fof(f29981,plain,
( spl635_138
<=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_138])]) ).
fof(f17109,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',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(f29979,plain,
spl635_137,
inference(avatar_split_clause,[],[f17108,f29976]) ).
fof(f29976,plain,
( spl635_137
<=> class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_137])]) ).
fof(f17108,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',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult) ).
fof(f29974,plain,
spl635_136,
inference(avatar_split_clause,[],[f17107,f29971]) ).
fof(f29971,plain,
( spl635_136
<=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_136])]) ).
fof(f17107,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',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(f29969,plain,
spl635_135,
inference(avatar_split_clause,[],[f17106,f29966]) ).
fof(f29966,plain,
( spl635_135
<=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_135])]) ).
fof(f17106,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',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(f29964,plain,
spl635_134,
inference(avatar_split_clause,[],[f17105,f29961]) ).
fof(f29961,plain,
( spl635_134
<=> class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_134])]) ).
fof(f17105,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',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) ).
fof(f29959,plain,
spl635_133,
inference(avatar_split_clause,[],[f17104,f29956]) ).
fof(f17104,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',arity_Nat__Onat__Rings_Osemiring__1) ).
fof(f29954,plain,
spl635_132,
inference(avatar_split_clause,[],[f17103,f29951]) ).
fof(f17103,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',arity_Int__Oint__Rings_Osemiring__1) ).
fof(f29949,plain,
spl635_131,
inference(avatar_split_clause,[],[f17102,f29946]) ).
fof(f17102,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',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).
fof(f29944,plain,
spl635_130,
inference(avatar_split_clause,[],[f17101,f29941]) ).
fof(f29941,plain,
( spl635_130
<=> class_Int_Onumber(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_130])]) ).
fof(f17101,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',arity_Nat__Onat__Int_Onumber) ).
fof(f29939,plain,
spl635_129,
inference(avatar_split_clause,[],[f17100,f29936]) ).
fof(f29936,plain,
( spl635_129
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_129])]) ).
fof(f17100,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',arity_Int__Oint__Int_Onumber) ).
fof(f29934,plain,
spl635_128,
inference(avatar_split_clause,[],[f17099,f29931]) ).
fof(f29931,plain,
( spl635_128
<=> class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_128])]) ).
fof(f17099,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',arity_Code____Numeral__Ocode____numeral__Int_Onumber) ).
fof(f29929,plain,
spl635_127,
inference(avatar_split_clause,[],[f17098,f29926]) ).
fof(f29926,plain,
( spl635_127
<=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_127])]) ).
fof(f17098,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',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(f29924,plain,
spl635_126,
inference(avatar_split_clause,[],[f17097,f29921]) ).
fof(f29921,plain,
( spl635_126
<=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_126])]) ).
fof(f17097,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',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(f29919,plain,
spl635_125,
inference(avatar_split_clause,[],[f17096,f29916]) ).
fof(f29916,plain,
( spl635_125
<=> class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_125])]) ).
fof(f17096,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',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) ).
fof(f29914,plain,
spl635_124,
inference(avatar_split_clause,[],[f17095,f29911]) ).
fof(f29911,plain,
( spl635_124
<=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_124])]) ).
fof(f17095,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',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(f29909,plain,
spl635_123,
inference(avatar_split_clause,[],[f17094,f29906]) ).
fof(f29906,plain,
( spl635_123
<=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_123])]) ).
fof(f17094,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',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(f29904,plain,
spl635_122,
inference(avatar_split_clause,[],[f17093,f29901]) ).
fof(f29901,plain,
( spl635_122
<=> class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_122])]) ).
fof(f17093,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',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add) ).
fof(f29899,plain,
spl635_121,
inference(avatar_split_clause,[],[f17092,f29896]) ).
fof(f29896,plain,
( spl635_121
<=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_121])]) ).
fof(f17092,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',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(f29894,plain,
spl635_120,
inference(avatar_split_clause,[],[f17091,f29891]) ).
fof(f29891,plain,
( spl635_120
<=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_120])]) ).
fof(f17091,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',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(f29889,plain,
spl635_119,
inference(avatar_split_clause,[],[f17090,f29886]) ).
fof(f29886,plain,
( spl635_119
<=> class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_119])]) ).
fof(f17090,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',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) ).
fof(f29884,plain,
spl635_118,
inference(avatar_split_clause,[],[f17089,f29881]) ).
fof(f29881,plain,
( spl635_118
<=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_118])]) ).
fof(f17089,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',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(f29879,plain,
spl635_117,
inference(avatar_split_clause,[],[f17088,f29876]) ).
fof(f29876,plain,
( spl635_117
<=> class_Groups_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_117])]) ).
fof(f17088,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',arity_Int__Oint__Groups_Omonoid__add) ).
fof(f29874,plain,
spl635_116,
inference(avatar_split_clause,[],[f17087,f29871]) ).
fof(f29871,plain,
( spl635_116
<=> class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_116])]) ).
fof(f17087,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',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) ).
fof(f29869,plain,
spl635_115,
inference(avatar_split_clause,[],[f17086,f29866]) ).
fof(f29866,plain,
( spl635_115
<=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_115])]) ).
fof(f17086,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',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(f29864,plain,
spl635_114,
inference(avatar_split_clause,[],[f17085,f29861]) ).
fof(f29861,plain,
( spl635_114
<=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_114])]) ).
fof(f17085,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',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(f29859,plain,
spl635_113,
inference(avatar_split_clause,[],[f17084,f29856]) ).
fof(f29856,plain,
( spl635_113
<=> class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_113])]) ).
fof(f17084,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',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) ).
fof(f29854,plain,
spl635_112,
inference(avatar_split_clause,[],[f17083,f29851]) ).
fof(f29851,plain,
( spl635_112
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_112])]) ).
fof(f17083,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',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f29849,plain,
spl635_111,
inference(avatar_split_clause,[],[f17082,f29846]) ).
fof(f29846,plain,
( spl635_111
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_111])]) ).
fof(f17082,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',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f29844,plain,
spl635_110,
inference(avatar_split_clause,[],[f17081,f29841]) ).
fof(f29841,plain,
( spl635_110
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_110])]) ).
fof(f17081,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',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f29839,plain,
spl635_109,
inference(avatar_split_clause,[],[f17080,f29836]) ).
fof(f29836,plain,
( spl635_109
<=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_109])]) ).
fof(f17080,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',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(f29834,plain,
spl635_108,
inference(avatar_split_clause,[],[f17079,f29831]) ).
fof(f29831,plain,
( spl635_108
<=> class_Rings_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_108])]) ).
fof(f17079,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',arity_Int__Oint__Rings_Osemiring__0) ).
fof(f29829,plain,
spl635_107,
inference(avatar_split_clause,[],[f17078,f29826]) ).
fof(f29826,plain,
( spl635_107
<=> class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_107])]) ).
fof(f17078,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',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).
fof(f29824,plain,
spl635_106,
inference(avatar_split_clause,[],[f17077,f29821]) ).
fof(f29821,plain,
( spl635_106
<=> class_Power_Opower(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_106])]) ).
fof(f17077,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',arity_Nat__Onat__Power_Opower) ).
fof(f29819,plain,
spl635_105,
inference(avatar_split_clause,[],[f17076,f29816]) ).
fof(f29816,plain,
( spl635_105
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_105])]) ).
fof(f17076,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',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f29814,plain,
spl635_104,
inference(avatar_split_clause,[],[f17075,f29811]) ).
fof(f29811,plain,
( spl635_104
<=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_104])]) ).
fof(f17075,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',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(f29809,plain,
spl635_103,
inference(avatar_split_clause,[],[f17074,f29806]) ).
fof(f29806,plain,
( spl635_103
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_103])]) ).
fof(f17074,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',arity_Int__Oint__Power_Opower) ).
fof(f29804,plain,
spl635_102,
inference(avatar_split_clause,[],[f17073,f29801]) ).
fof(f29801,plain,
( spl635_102
<=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_102])]) ).
fof(f17073,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',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(f29799,plain,
spl635_101,
inference(avatar_split_clause,[],[f17072,f29796]) ).
fof(f29796,plain,
( spl635_101
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_101])]) ).
fof(f17072,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',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f29794,plain,
spl635_100,
inference(avatar_split_clause,[],[f17071,f29791]) ).
fof(f29791,plain,
( spl635_100
<=> class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_100])]) ).
fof(f17071,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',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) ).
fof(f29789,plain,
spl635_99,
inference(avatar_split_clause,[],[f17070,f29786]) ).
fof(f29786,plain,
( spl635_99
<=> class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_99])]) ).
fof(f17070,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',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).
fof(f29784,plain,
spl635_98,
inference(avatar_split_clause,[],[f17069,f29781]) ).
fof(f29781,plain,
( spl635_98
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_98])]) ).
fof(f17069,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',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f29779,plain,
spl635_97,
inference(avatar_split_clause,[],[f17068,f29776]) ).
fof(f29776,plain,
( spl635_97
<=> class_Rings_Odvd(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_97])]) ).
fof(f17068,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',arity_Nat__Onat__Rings_Odvd) ).
fof(f29774,plain,
spl635_96,
inference(avatar_split_clause,[],[f17067,f29771]) ).
fof(f29771,plain,
( spl635_96
<=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_96])]) ).
fof(f17067,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',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(f29769,plain,
spl635_95,
inference(avatar_split_clause,[],[f17066,f29766]) ).
fof(f29766,plain,
( spl635_95
<=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_95])]) ).
fof(f17066,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',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(f29764,plain,
spl635_94,
inference(avatar_split_clause,[],[f17065,f29761]) ).
fof(f29761,plain,
( spl635_94
<=> class_Rings_Odvd(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_94])]) ).
fof(f17065,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',arity_Int__Oint__Rings_Odvd) ).
fof(f29759,plain,
spl635_93,
inference(avatar_split_clause,[],[f17064,f29756]) ).
fof(f29756,plain,
( spl635_93
<=> class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_93])]) ).
fof(f17064,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',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) ).
fof(f29754,plain,
spl635_92,
inference(avatar_split_clause,[],[f17063,f29751]) ).
fof(f29751,plain,
( spl635_92
<=> class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_92])]) ).
fof(f17063,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',arity_Code____Numeral__Ocode____numeral__Rings_Odvd) ).
fof(f29749,plain,
spl635_91,
inference(avatar_split_clause,[],[f17062,f29746]) ).
fof(f29746,plain,
( spl635_91
<=> class_Orderings_Obot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_91])]) ).
fof(f17062,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',arity_HOL__Obool__Orderings_Obot) ).
fof(f29744,plain,
spl635_90,
inference(avatar_split_clause,[],[f17061,f29741]) ).
fof(f29741,plain,
( spl635_90
<=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_90])]) ).
fof(f17061,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',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(f29739,plain,
spl635_89,
inference(avatar_split_clause,[],[f17060,f29736]) ).
fof(f29736,plain,
( spl635_89
<=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_89])]) ).
fof(f17060,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',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(f29734,plain,
spl635_88,
inference(avatar_split_clause,[],[f17059,f29731]) ).
fof(f29731,plain,
( spl635_88
<=> class_Orderings_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_88])]) ).
fof(f17059,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',arity_Nat__Onat__Orderings_Obot) ).
fof(f29729,plain,
spl635_87,
inference(avatar_split_clause,[],[f17058,f29726]) ).
fof(f29726,plain,
( spl635_87
<=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_87])]) ).
fof(f17058,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',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(f29724,plain,
spl635_86,
inference(avatar_split_clause,[],[f17057,f29721]) ).
fof(f29721,plain,
( spl635_86
<=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_86])]) ).
fof(f17057,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',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(f29719,plain,
spl635_85,
inference(avatar_split_clause,[],[f17056,f29716]) ).
fof(f29716,plain,
( spl635_85
<=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_85])]) ).
fof(f17056,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',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(f29714,plain,
spl635_84,
inference(avatar_split_clause,[],[f17055,f29711]) ).
fof(f29711,plain,
( spl635_84
<=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_84])]) ).
fof(f17055,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',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(f29709,plain,
spl635_83,
inference(avatar_split_clause,[],[f17054,f29706]) ).
fof(f29706,plain,
( spl635_83
<=> class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_83])]) ).
fof(f17054,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',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) ).
fof(f29704,plain,
spl635_82,
inference(avatar_split_clause,[],[f17053,f29701]) ).
fof(f29701,plain,
( spl635_82
<=> class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_82])]) ).
fof(f17053,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',arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) ).
fof(f29699,plain,
spl635_81,
inference(avatar_split_clause,[],[f17052,f29696]) ).
fof(f29696,plain,
( spl635_81
<=> class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_81])]) ).
fof(f17052,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',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) ).
fof(f29694,plain,
spl635_80,
inference(avatar_split_clause,[],[f17051,f29691]) ).
fof(f29691,plain,
( spl635_80
<=> class_Groups_Ouminus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_80])]) ).
fof(f17051,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',arity_HOL__Obool__Groups_Ouminus) ).
fof(f29689,plain,
spl635_79,
inference(avatar_split_clause,[],[f17050,f29686]) ).
fof(f29686,plain,
( spl635_79
<=> class_Rings_Omult__zero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_79])]) ).
fof(f17050,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',arity_Nat__Onat__Rings_Omult__zero) ).
fof(f29684,plain,
spl635_78,
inference(avatar_split_clause,[],[f17049,f29681]) ).
fof(f29681,plain,
( spl635_78
<=> class_Rings_Osemiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_78])]) ).
fof(f17049,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',arity_Nat__Onat__Rings_Osemiring) ).
fof(f29679,plain,
spl635_77,
inference(avatar_split_clause,[],[f17048,f29676]) ).
fof(f29676,plain,
( spl635_77
<=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_77])]) ).
fof(f17048,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',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(f29674,plain,
spl635_76,
inference(avatar_split_clause,[],[f17047,f29671]) ).
fof(f29671,plain,
( spl635_76
<=> class_Rings_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_76])]) ).
fof(f17047,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',arity_Int__Oint__Rings_Osemiring) ).
fof(f29669,plain,
spl635_75,
inference(avatar_split_clause,[],[f17046,f29666]) ).
fof(f29666,plain,
( spl635_75
<=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_75])]) ).
fof(f17046,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',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(f29664,plain,
spl635_74,
inference(avatar_split_clause,[],[f17045,f29661]) ).
fof(f29661,plain,
( spl635_74
<=> class_Rings_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_74])]) ).
fof(f17045,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',arity_Int__Oint__Rings_Omult__zero) ).
fof(f29659,plain,
spl635_73,
inference(avatar_split_clause,[],[f17044,f29656]) ).
fof(f29656,plain,
( spl635_73
<=> class_Groups_Ouminus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_73])]) ).
fof(f17044,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',arity_Int__Oint__Groups_Ouminus) ).
fof(f29654,plain,
spl635_72,
inference(avatar_split_clause,[],[f17043,f29651]) ).
fof(f29651,plain,
( spl635_72
<=> class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_72])]) ).
fof(f17043,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',arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one) ).
fof(f29649,plain,
spl635_71,
inference(avatar_split_clause,[],[f17042,f29646]) ).
fof(f29646,plain,
( spl635_71
<=> class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_71])]) ).
fof(f17042,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',arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero) ).
fof(f29644,plain,
spl635_70,
inference(avatar_split_clause,[],[f17041,f29641]) ).
fof(f29641,plain,
( spl635_70
<=> class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_70])]) ).
fof(f17041,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',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring) ).
fof(f29639,plain,
spl635_69,
inference(avatar_split_clause,[],[f17040,f29636]) ).
fof(f29636,plain,
( spl635_69
<=> class_Nat_Osemiring__char__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_69])]) ).
fof(f17040,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',arity_Nat__Onat__Nat_Osemiring__char__0) ).
fof(f29634,plain,
spl635_68,
inference(avatar_split_clause,[],[f17039,f29631]) ).
fof(f29631,plain,
( spl635_68
<=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_68])]) ).
fof(f17039,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',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(f29629,plain,
spl635_67,
inference(avatar_split_clause,[],[f17038,f29626]) ).
fof(f29626,plain,
( spl635_67
<=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_67])]) ).
fof(f17038,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',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(f29624,plain,
spl635_66,
inference(avatar_split_clause,[],[f17037,f29621]) ).
fof(f29621,plain,
( spl635_66
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_66])]) ).
fof(f17037,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',arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add) ).
fof(f29619,plain,
spl635_65,
inference(avatar_split_clause,[],[f17036,f29616]) ).
fof(f29616,plain,
( spl635_65
<=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_65])]) ).
fof(f17036,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',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(f29614,plain,
spl635_64,
inference(avatar_split_clause,[],[f17035,f29611]) ).
fof(f29611,plain,
( spl635_64
<=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_64])]) ).
fof(f17035,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',arity_Int__Oint__Nat_Osemiring__char__0) ).
fof(f29609,plain,
spl635_63,
inference(avatar_split_clause,[],[f17034,f29606]) ).
fof(f29606,plain,
( spl635_63
<=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_63])]) ).
fof(f17034,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',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(f29604,plain,
spl635_62,
inference(avatar_split_clause,[],[f17033,f29601]) ).
fof(f29601,plain,
( spl635_62
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_62])]) ).
fof(f17033,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',arity_Int__Oint__Groups_Olinordered__ab__semigroup__add) ).
fof(f29599,plain,
spl635_61,
inference(avatar_split_clause,[],[f17032,f29596]) ).
fof(f29596,plain,
( spl635_61
<=> class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_61])]) ).
fof(f17032,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',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) ).
fof(f29594,plain,
spl635_60,
inference(avatar_split_clause,[],[f17031,f29591]) ).
fof(f29591,plain,
( spl635_60
<=> class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_60])]) ).
fof(f17031,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',arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0) ).
fof(f29589,plain,
spl635_59,
inference(avatar_split_clause,[],[f17030,f29586]) ).
fof(f29586,plain,
( spl635_59
<=> class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_59])]) ).
fof(f17030,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',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) ).
fof(f29584,plain,
spl635_58,
inference(avatar_split_clause,[],[f17029,f29581]) ).
fof(f29581,plain,
( spl635_58
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_58])]) ).
fof(f17029,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',arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) ).
fof(f29579,plain,
spl635_57,
inference(avatar_split_clause,[],[f17028,f29576]) ).
fof(f29576,plain,
( spl635_57
<=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_57])]) ).
fof(f17028,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',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(f29574,plain,
spl635_56,
inference(avatar_split_clause,[],[f17027,f29571]) ).
fof(f29571,plain,
( spl635_56
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_56])]) ).
fof(f17027,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',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(f29569,plain,
spl635_55,
inference(avatar_split_clause,[],[f17026,f29566]) ).
fof(f29566,plain,
( spl635_55
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_55])]) ).
fof(f17026,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',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(f29564,plain,
spl635_54,
inference(avatar_split_clause,[],[f17025,f29561]) ).
fof(f29561,plain,
( spl635_54
<=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_54])]) ).
fof(f17025,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',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(f29559,plain,
spl635_53,
inference(avatar_split_clause,[],[f17024,f29556]) ).
fof(f29556,plain,
( spl635_53
<=> class_Groups_Osemigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_53])]) ).
fof(f17024,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',arity_Nat__Onat__Groups_Osemigroup__add) ).
fof(f29554,plain,
spl635_52,
inference(avatar_split_clause,[],[f17023,f29551]) ).
fof(f29551,plain,
( spl635_52
<=> class_Groups_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_52])]) ).
fof(f17023,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',arity_Nat__Onat__Groups_Oone) ).
fof(f29549,plain,
spl635_51,
inference(avatar_split_clause,[],[f17022,f29546]) ).
fof(f29546,plain,
( spl635_51
<=> class_Groups_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_51])]) ).
fof(f17022,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',arity_Nat__Onat__Groups_Ozero) ).
fof(f29544,plain,
spl635_50,
inference(avatar_split_clause,[],[f17021,f29541]) ).
fof(f29541,plain,
( spl635_50
<=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_50])]) ).
fof(f17021,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',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(f29539,plain,
spl635_49,
inference(avatar_split_clause,[],[f17020,f29536]) ).
fof(f29536,plain,
( spl635_49
<=> class_Groups_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_49])]) ).
fof(f17020,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',arity_Int__Oint__Groups_Oone) ).
fof(f29534,plain,
spl635_48,
inference(avatar_split_clause,[],[f17019,f29531]) ).
fof(f29531,plain,
( spl635_48
<=> class_Groups_Osemigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_48])]) ).
fof(f17019,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',arity_Int__Oint__Groups_Osemigroup__add) ).
fof(f29529,plain,
spl635_47,
inference(avatar_split_clause,[],[f17018,f29526]) ).
fof(f29526,plain,
( spl635_47
<=> class_Groups_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_47])]) ).
fof(f17018,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',arity_Int__Oint__Groups_Ozero) ).
fof(f29524,plain,
spl635_46,
inference(avatar_split_clause,[],[f17017,f29521]) ).
fof(f29521,plain,
( spl635_46
<=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_46])]) ).
fof(f17017,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',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(f29519,plain,
spl635_45,
inference(avatar_split_clause,[],[f17016,f29516]) ).
fof(f29516,plain,
( spl635_45
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_45])]) ).
fof(f17016,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',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(f29514,plain,
spl635_44,
inference(avatar_split_clause,[],[f17015,f29511]) ).
fof(f29511,plain,
( spl635_44
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_44])]) ).
fof(f17015,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',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(f29509,plain,
spl635_43,
inference(avatar_split_clause,[],[f17014,f29506]) ).
fof(f29506,plain,
( spl635_43
<=> class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_43])]) ).
fof(f17014,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',arity_Code____Numeral__Ocode____numeral__Groups_Oone) ).
fof(f29504,plain,
spl635_42,
inference(avatar_split_clause,[],[f17013,f29501]) ).
fof(f29501,plain,
( spl635_42
<=> class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_42])]) ).
fof(f17013,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',arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add) ).
fof(f29499,plain,
spl635_41,
inference(avatar_split_clause,[],[f17012,f29496]) ).
fof(f29496,plain,
( spl635_41
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_41])]) ).
fof(f17012,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',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) ).
fof(f29494,plain,
spl635_40,
inference(avatar_split_clause,[],[f17011,f29491]) ).
fof(f29491,plain,
( spl635_40
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_40])]) ).
fof(f17011,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',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict) ).
fof(f29489,plain,
spl635_39,
inference(avatar_split_clause,[],[f17010,f29486]) ).
fof(f29486,plain,
( spl635_39
<=> class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_39])]) ).
fof(f17010,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',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring) ).
fof(f29484,plain,
spl635_38,
inference(avatar_split_clause,[],[f17009,f29481]) ).
fof(f29481,plain,
( spl635_38
<=> class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_38])]) ).
fof(f17009,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',arity_Code____Numeral__Ocode____numeral__Groups_Ozero) ).
fof(f29479,plain,
spl635_37,
inference(avatar_split_clause,[],[f17008,f29476]) ).
fof(f29476,plain,
( spl635_37
<=> class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_37])]) ).
fof(f17008,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',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) ).
fof(f29474,plain,
spl635_36,
inference(avatar_split_clause,[],[f17007,f29471]) ).
fof(f29471,plain,
( spl635_36
<=> class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_36])]) ).
fof(f17007,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',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
fof(f29469,plain,
spl635_35,
inference(avatar_split_clause,[],[f17006,f29466]) ).
fof(f29466,plain,
( spl635_35
<=> class_Lattices_Oboolean__algebra(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_35])]) ).
fof(f17006,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',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(f29464,plain,
spl635_34,
inference(avatar_split_clause,[],[f17005,f29461]) ).
fof(f29461,plain,
( spl635_34
<=> class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_34])]) ).
fof(f17005,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',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(f29459,plain,
spl635_33,
inference(avatar_split_clause,[],[f17004,f29456]) ).
fof(f29456,plain,
( spl635_33
<=> class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_33])]) ).
fof(f17004,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',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
fof(f29454,plain,
spl635_32,
inference(avatar_split_clause,[],[f17003,f29451]) ).
fof(f29451,plain,
( spl635_32
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_32])]) ).
fof(f17003,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',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f29449,plain,
spl635_31,
inference(avatar_split_clause,[],[f17002,f29446]) ).
fof(f29446,plain,
( spl635_31
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_31])]) ).
fof(f17002,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',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f29444,plain,
spl635_30,
inference(avatar_split_clause,[],[f17001,f29441]) ).
fof(f29441,plain,
( spl635_30
<=> class_Lattices_Obounded__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_30])]) ).
fof(f17001,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',arity_HOL__Obool__Lattices_Obounded__lattice) ).
fof(f29439,plain,
spl635_29,
inference(avatar_split_clause,[],[f17000,f29436]) ).
fof(f29436,plain,
( spl635_29
<=> class_Orderings_Otop(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_29])]) ).
fof(f17000,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',arity_HOL__Obool__Orderings_Otop) ).
fof(f29434,plain,
spl635_28,
inference(avatar_split_clause,[],[f16999,f29431]) ).
fof(f16999,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',arity_Int__Oint__Int_Onumber__ring) ).
fof(f29429,plain,
spl635_27,
inference(avatar_split_clause,[],[f16998,f29426]) ).
fof(f29426,plain,
( spl635_27
<=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_27])]) ).
fof(f16998,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',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(f29424,plain,
spl635_26,
inference(avatar_split_clause,[],[f16997,f29421]) ).
fof(f16997,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',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(f29419,plain,
spl635_25,
inference(avatar_split_clause,[],[f16996,f29416]) ).
fof(f29416,plain,
( spl635_25
<=> class_Rings_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_25])]) ).
fof(f16996,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',arity_Int__Oint__Rings_Oring__1) ).
fof(f29414,plain,
spl635_24,
inference(avatar_split_clause,[],[f16995,f29411]) ).
fof(f29411,plain,
( spl635_24
<=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_24])]) ).
fof(f16995,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',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(f29409,plain,
spl635_23,
inference(avatar_split_clause,[],[f16994,f29406]) ).
fof(f29406,plain,
( spl635_23
<=> class_Groups_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_23])]) ).
fof(f16994,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',arity_Int__Oint__Groups_Ogroup__add) ).
fof(f29404,plain,
spl635_22,
inference(avatar_split_clause,[],[f16993,f29401]) ).
fof(f29401,plain,
( spl635_22
<=> class_Groups_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_22])]) ).
fof(f16993,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',arity_Int__Oint__Groups_Oab__group__add) ).
fof(f29399,plain,
spl635_21,
inference(avatar_split_clause,[],[f16992,f29396]) ).
fof(f29396,plain,
( spl635_21
<=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_21])]) ).
fof(f16992,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',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(f29394,plain,
spl635_20,
inference(avatar_split_clause,[],[f16991,f29391]) ).
fof(f29391,plain,
( spl635_20
<=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_20])]) ).
fof(f16991,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',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(f29389,plain,
spl635_19,
inference(avatar_split_clause,[],[f16990,f29386]) ).
fof(f29386,plain,
( spl635_19
<=> class_Rings_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_19])]) ).
fof(f16990,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',arity_Int__Oint__Rings_Oring) ).
fof(f29384,plain,
spl635_18,
inference(avatar_split_clause,[],[f16989,f29381]) ).
fof(f29381,plain,
( spl635_18
<=> class_Divides_Oring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_18])]) ).
fof(f16989,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',arity_Int__Oint__Divides_Oring__div) ).
fof(f29379,plain,
spl635_17,
inference(avatar_split_clause,[],[f16988,f29376]) ).
fof(f29376,plain,
( spl635_17
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_17])]) ).
fof(f16988,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',arity_Int__Oint__Int_Oring__char__0) ).
fof(f29374,plain,
spl635_16,
inference(avatar_split_clause,[],[f16987,f29371]) ).
fof(f29371,plain,
( spl635_16
<=> class_Rings_Oordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_16])]) ).
fof(f16987,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',arity_Int__Oint__Rings_Oordered__ring) ).
fof(f29369,plain,
spl635_15,
inference(avatar_split_clause,[],[f16986,f29366]) ).
fof(f29366,plain,
( spl635_15
<=> class_Orderings_Owellorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_15])]) ).
fof(f16986,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',arity_Nat__Onat__Orderings_Owellorder) ).
fof(f29364,plain,
spl635_14,
inference(avatar_split_clause,[],[f16985,f29361]) ).
fof(f29361,plain,
( spl635_14
<=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_14])]) ).
fof(f16985,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',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(f29359,plain,
spl635_13,
inference(avatar_split_clause,[],[f16984,f29356]) ).
fof(f29356,plain,
( spl635_13
<=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_13])]) ).
fof(f16984,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',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(f29354,plain,
spl635_12,
inference(avatar_split_clause,[],[f16983,f29351]) ).
fof(f29351,plain,
( spl635_12
<=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_12])]) ).
fof(f16983,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',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(f29349,plain,
spl635_11,
inference(avatar_split_clause,[],[f16982,f29346]) ).
fof(f29346,plain,
( spl635_11
<=> class_Rings_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_11])]) ).
fof(f16982,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',arity_Int__Oint__Rings_Oidom) ).
fof(f29344,plain,
spl635_10,
inference(avatar_split_clause,[],[f16981,f29341]) ).
fof(f29341,plain,
( spl635_10
<=> class_Rings_Ocomm__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_10])]) ).
fof(f16981,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',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(f29339,plain,
spl635_9,
inference(avatar_split_clause,[],[f16980,f29336]) ).
fof(f29336,plain,
( spl635_9
<=> class_Groups_Osgn__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_9])]) ).
fof(f16980,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',arity_Int__Oint__Groups_Osgn__if) ).
fof(f29334,plain,
spl635_8,
inference(avatar_split_clause,[],[f16979,f29331]) ).
fof(f29331,plain,
( spl635_8
<=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_8])]) ).
fof(f16979,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',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(f29329,plain,
spl635_7,
inference(avatar_split_clause,[],[f16978,f29326]) ).
fof(f29326,plain,
( spl635_7
<=> class_Groups_Oabs__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_7])]) ).
fof(f16978,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',arity_Int__Oint__Groups_Oabs__if) ).
fof(f29324,plain,
spl635_6,
inference(avatar_split_clause,[],[f16977,f29321]) ).
fof(f29321,plain,
( spl635_6
<=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_6])]) ).
fof(f16977,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',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(f29319,plain,
spl635_5,
inference(avatar_split_clause,[],[f16976,f29316]) ).
fof(f29316,plain,
( spl635_5
<=> class_Rings_Oordered__ring__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_5])]) ).
fof(f16976,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',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(f29314,plain,
spl635_4,
inference(avatar_split_clause,[],[f16975,f29311]) ).
fof(f29311,plain,
( spl635_4
<=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_4])]) ).
fof(f16975,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',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(f29309,plain,
~ spl635_3,
inference(avatar_split_clause,[],[f16974,f29306]) ).
fof(f29306,plain,
( spl635_3
<=> hBOOL(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl635_3])]) ).
fof(f16974,plain,
~ hBOOL(c_fFalse),
inference(cnf_transformation,[],[f5211]) ).
fof(f5211,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).
fof(f29304,plain,
spl635_2,
inference(avatar_split_clause,[],[f16971,f29301]) ).
fof(f16971,plain,
hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK89),v_ts)),
inference(cnf_transformation,[],[f14685]) ).
fof(f14685,plain,
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK89)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK89),v_ts)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK89])],[f10314,f14684]) ).
fof(f14684,plain,
( ? [X0] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X0)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts)) )
=> ( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK89)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),sK89),v_ts)) ) ),
introduced(choice_axiom,[]) ).
fof(f10314,plain,
? [X0] :
( ~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X0)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts)) ),
inference(ennf_transformation,[],[f5227]) ).
fof(f5227,plain,
~ ! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X0),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X0) ),
inference(rectify,[],[f5226]) ).
fof(f5226,negated_conjecture,
~ ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X2) ),
inference(negated_conjecture,[],[f5225]) ).
fof(f5225,conjecture,
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),X2),v_ts))
=> c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
fof(f29299,plain,
~ spl635_1,
inference(avatar_split_clause,[],[f16972,f29296]) ).
fof(f16972,plain,
~ c_Hoare__Mirabelle_Otriple__valid(t_a,v_n,sK89),
inference(cnf_transformation,[],[f14685]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW298+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n010.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Apr 30 02:52:50 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (17639)Running in auto input_syntax mode. Trying TPTP
% 0.58/0.76 % (17685)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.58/0.76 % (17681)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.58/0.77 % (17682)WARNING: value z3 for option sas not known
% 0.58/0.77 % (17680)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.58/0.77 % (17683)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.58/0.77 % (17684)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.58/0.77 % (17682)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.58/0.77 % (17686)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 12.08/2.42 % (17684)First to succeed.
% 12.44/2.54 % (17684)Refutation found. Thanks to Tanya!
% 12.44/2.54 % SZS status Theorem for theBenchmark
% 12.44/2.54 % SZS output start Proof for theBenchmark
% See solution above
% 13.13/2.61 % (17684)------------------------------
% 13.13/2.61 % (17684)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 13.13/2.61 % (17684)Termination reason: Refutation
% 13.13/2.61
% 13.13/2.61 % (17684)Memory used [KB]: 29301
% 13.13/2.61 % (17684)Time elapsed: 1.764 s
% 13.13/2.61 % (17684)Instructions burned: 3300 (million)
% 13.13/2.61 % (17684)------------------------------
% 13.13/2.61 % (17684)------------------------------
% 13.13/2.61 % (17639)Success in time 2.226 s
%------------------------------------------------------------------------------