TSTP Solution File: SWW344+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW344+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 : n006.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 : Sun May 5 11:37:14 EDT 2024
% Result : Theorem 9.25s 2.09s
% Output : Refutation 9.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1772
% Syntax : Number of formulae : 4967 (2294 unt; 0 def)
% Number of atoms : 10103 (2772 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 7944 (2808 ~;2517 |; 889 &)
% (1153 <=>; 577 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 1087 (1085 usr; 918 prp; 0-6 aty)
% Number of functors : 257 ( 257 usr; 44 con; 0-5 aty)
% Number of variables : 6807 (6610 !; 197 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33067,plain,
$false,
inference(avatar_sat_refutation,[],[f28102,f28107,f28112,f28117,f28122,f28127,f28132,f28137,f28142,f28147,f28152,f28157,f28162,f28167,f28172,f28177,f28182,f28187,f28192,f28197,f28202,f28207,f28212,f28217,f28222,f28227,f28232,f28237,f28242,f28247,f28252,f28257,f28262,f28267,f28272,f28277,f28282,f28287,f28292,f28297,f28302,f28307,f28312,f28317,f28322,f28327,f28332,f28337,f28342,f28347,f28352,f28357,f28362,f28367,f28372,f28377,f28382,f28387,f28392,f28397,f28402,f28407,f28412,f28417,f28422,f28427,f28432,f28437,f28442,f28447,f28452,f28457,f28462,f28467,f28472,f28477,f28482,f28487,f28492,f28497,f28502,f28507,f28512,f28517,f28522,f28527,f28532,f28537,f28542,f28547,f28552,f28557,f28562,f28567,f28572,f28577,f28582,f28587,f28592,f28597,f28602,f28607,f28612,f28617,f28622,f28627,f28632,f28637,f28642,f28647,f28652,f28657,f28662,f28667,f28672,f28677,f28682,f28687,f28692,f28697,f28702,f28707,f28712,f28717,f28722,f28727,f28732,f28737,f28742,f28747,f28752,f28757,f28762,f28767,f28772,f28777,f28782,f28787,f28792,f28797,f28802,f28807,f28812,f28817,f28822,f28827,f28832,f28837,f28842,f28847,f28852,f28857,f28862,f28867,f28872,f28877,f28882,f28887,f28892,f28897,f28902,f28907,f28912,f28917,f28922,f28927,f28932,f28937,f28942,f28947,f28952,f28957,f28962,f28967,f28972,f28977,f28982,f28987,f28992,f28997,f29002,f29007,f29012,f29017,f29022,f29027,f29032,f29038,f29043,f29048,f29052,f29057,f29061,f29066,f29071,f29076,f29081,f29086,f29090,f29094,f29099,f29104,f29109,f29114,f29120,f29125,f29130,f29135,f29140,f29145,f29150,f29155,f29161,f29165,f29169,f29173,f29177,f29181,f29185,f29189,f29193,f29197,f29201,f29205,f29209,f29214,f29218,f29222,f29226,f29231,f29236,f29241,f29246,f29251,f29256,f29261,f29266,f29270,f29274,f29279,f29284,f29289,f29293,f29297,f29301,f29305,f29309,f29313,f29317,f29321,f29325,f29329,f29333,f29337,f29341,f29345,f29349,f29353,f29357,f29361,f29365,f29369,f29373,f29377,f29381,f29385,f29389,f29393,f29397,f29401,f29405,f29409,f29413,f29417,f29421,f29425,f29429,f29433,f29437,f29441,f29445,f29449,f29453,f29457,f29461,f29466,f29471,f29476,f29481,f29485,f29489,f29493,f29497,f29501,f29505,f29510,f29514,f29518,f29527,f29536,f29544,f29553,f29559,f29564,f29569,f29574,f29579,f29584,f29589,f29594,f29599,f29604,f29609,f29614,f29620,f29625,f29631,f29636,f29641,f29646,f29650,f29654,f29658,f29662,f29666,f29670,f29674,f29678,f29682,f29686,f29690,f29694,f29698,f29702,f29706,f29710,f29714,f29718,f29723,f29727,f29731,f29735,f29739,f29743,f29747,f29751,f29755,f29759,f29763,f29768,f29772,f29776,f29780,f29784,f29788,f29792,f29796,f29800,f29804,f29809,f29813,f29817,f29821,f29825,f29830,f29835,f29840,f29845,f29850,f29855,f29860,f29864,f29868,f29872,f29877,f29884,f29895,f29901,f29915,f29920,f29925,f29930,f29935,f29940,f29944,f29948,f29952,f29956,f29960,f29964,f29968,f29972,f29976,f29980,f29984,f29988,f29992,f29996,f30001,f30005,f30009,f30013,f30017,f30021,f30025,f30029,f30033,f30037,f30041,f30046,f30050,f30054,f30058,f30062,f30066,f30070,f30074,f30078,f30082,f30086,f30090,f30094,f30098,f30102,f30106,f30110,f30114,f30118,f30122,f30126,f30130,f30134,f30138,f30142,f30146,f30150,f30154,f30158,f30162,f30166,f30171,f30175,f30179,f30183,f30187,f30191,f30195,f30199,f30203,f30207,f30211,f30215,f30219,f30224,f30228,f30232,f30237,f30242,f30247,f30251,f30255,f30259,f30263,f30267,f30271,f30275,f30279,f30283,f30287,f30291,f30295,f30299,f30314,f30325,f30339,f30345,f30367,f30372,f30377,f30381,f30385,f30390,f30394,f30398,f30402,f30406,f30410,f30414,f30418,f30422,f30426,f30430,f30435,f30439,f30443,f30447,f30451,f30455,f30459,f30463,f30467,f30471,f30475,f30479,f30483,f30487,f30491,f30495,f30499,f30503,f30507,f30511,f30515,f30519,f30523,f30527,f30531,f30535,f30539,f30548,f30552,f30556,f30560,f30564,f30568,f30572,f30576,f30580,f30584,f30588,f30592,f30596,f30600,f30604,f30608,f30612,f30616,f30620,f30624,f30628,f30633,f30637,f30641,f30646,f30652,f30657,f30661,f30665,f30669,f30673,f30674,f30678,f30682,f30686,f30690,f30694,f30698,f30702,f30706,f30710,f30714,f30718,f30722,f30726,f30730,f30734,f30738,f30742,f30746,f30751,f30755,f30762,f30766,f30770,f30774,f30778,f30782,f30786,f30790,f30794,f30798,f30806,f30810,f30814,f30818,f30828,f30839,f30851,f30887,f31005,f31010,f31015,f31022,f31035,f31052,f31077,f31097,f31102,f31107,f31112,f31116,f31120,f31124,f31128,f31132,f31136,f31140,f31144,f31148,f31152,f31156,f31161,f31165,f31169,f31173,f31177,f31181,f31185,f31189,f31193,f31197,f31201,f31205,f31209,f31213,f31217,f31221,f31225,f31229,f31233,f31237,f31241,f31245,f31249,f31253,f31257,f31261,f31265,f31269,f31273,f31277,f31281,f31285,f31289,f31293,f31297,f31302,f31306,f31310,f31314,f31318,f31322,f31326,f31330,f31334,f31338,f31342,f31346,f31350,f31354,f31358,f31362,f31366,f31370,f31374,f31378,f31382,f31391,f31395,f31399,f31403,f31407,f31411,f31415,f31419,f31423,f31427,f31431,f31435,f31439,f31443,f31447,f31451,f31455,f31459,f31463,f31467,f31471,f31476,f31481,f31487,f31491,f31495,f31499,f31503,f31507,f31511,f31515,f31520,f31524,f31528,f31532,f31536,f31540,f31544,f31548,f31552,f31556,f31560,f31564,f31568,f31572,f31576,f31580,f31584,f31588,f31592,f31596,f31600,f31604,f31609,f31613,f31617,f31621,f31625,f31629,f31633,f31637,f31641,f31645,f31650,f31654,f31664,f31674,f31705,f31743,f32147,f32173,f32181,f32212,f32263,f32290,f32318,f32330,f32334,f32341,f32345,f32351,f32355,f32359,f32363,f32367,f32371,f32375,f32379,f32383,f32387,f32392,f32396,f32400,f32404,f32408,f32412,f32416,f32420,f32424,f32428,f32432,f32437,f32441,f32445,f32449,f32453,f32457,f32461,f32465,f32469,f32473,f32477,f32481,f32485,f32489,f32493,f32497,f32501,f32505,f32509,f32513,f32517,f32521,f32525,f32529,f32533,f32537,f32541,f32545,f32549,f32553,f32557,f32561,f32565,f32569,f32573,f32577,f32581,f32585,f32589,f32593,f32597,f32601,f32605,f32609,f32613,f32617,f32621,f32625,f32629,f32633,f32637,f32641,f32645,f32649,f32653,f32657,f32661,f32665,f32669,f32673,f32677,f32681,f32685,f32689,f32693,f32697,f32701,f32705,f32709,f32713,f32717,f32721,f32725,f32729,f32733,f32737,f32741,f32745,f32749,f32753,f32757,f32761,f32765,f32769,f32773,f32777,f32781,f32785,f32790,f32794,f32798,f32802,f32806,f32810,f32814,f32818,f32824,f32828,f32832,f32836,f32840,f32844,f32848,f32852,f32856,f32860,f32864,f32868,f32873,f32878,f32882,f32886,f32890,f32894,f32898,f32902,f32906,f32910,f32914,f32918,f32922,f32926,f32930,f32935,f32939,f32943,f32947,f32951,f32955,f32959,f32963,f32967,f32971,f32976,f32980,f32984,f32989,f32993,f32997,f33001,f33005,f33009,f33013,f33017,f33022,f33026,f33030,f33066]) ).
fof(f33066,plain,
( spl573_1
| ~ spl573_863
| ~ spl573_904 ),
inference(avatar_split_clause,[],[f33018,f32973,f32804,f28099]) ).
fof(f28099,plain,
( spl573_1
<=> v_R(v_Z,v_s_H) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_1])]) ).
fof(f32804,plain,
( spl573_863
<=> ! [X0] :
( v_R(X0,v_s_H)
| ~ v_Q(X0,v_s1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_863])]) ).
fof(f32973,plain,
( spl573_904
<=> v_Q(v_Z,v_s1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_904])]) ).
fof(f33018,plain,
( v_R(v_Z,v_s_H)
| ~ spl573_863
| ~ spl573_904 ),
inference(resolution,[],[f32975,f32805]) ).
fof(f32805,plain,
( ! [X0] :
( ~ v_Q(X0,v_s1)
| v_R(X0,v_s_H) )
| ~ spl573_863 ),
inference(avatar_component_clause,[],[f32804]) ).
fof(f32975,plain,
( v_Q(v_Z,v_s1)
| ~ spl573_904 ),
inference(avatar_component_clause,[],[f32973]) ).
fof(f33030,plain,
spl573_917,
inference(avatar_split_clause,[],[f27460,f33028]) ).
fof(f33028,plain,
( spl573_917
<=> ! [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,[spl573_917])]) ).
fof(f27460,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,[],[f21089,f16841]) ).
fof(f16841,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
inference(cnf_transformation,[],[f226]) ).
fof(f226,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I1_J) ).
fof(f21089,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,[],[f8193]) ).
fof(f8193,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,[],[f1283]) ).
fof(f1283,axiom,
! [X76,X164,X165,X7] : hAPP(hAPP(c_Power_Opower_Opower(X7,X165,X164),X76),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X165,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(f33026,plain,
spl573_916,
inference(avatar_split_clause,[],[f27381,f33024]) ).
fof(f33024,plain,
( spl573_916
<=> ! [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,[spl573_916])]) ).
fof(f27381,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,[],[f20843,f16829]) ).
fof(f16829,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
inference(cnf_transformation,[],[f1333]) ).
fof(f1333,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(f20843,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,[],[f15617]) ).
fof(f15617,plain,
! [X0,X1,X2] :
( ( sP37(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK335(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK335(X0,X1,X2))),sK336(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK336(X0,X1,X2)),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK336(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))
| ~ sP37(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK335,sK336])],[f15614,f15616,f15615]) ).
fof(f15615,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,sK335(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),sK335(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(f15616,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),sK335(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),sK335(X0,X1,X2))),sK336(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK336(X0,X1,X2)),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK336(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15614,plain,
! [X0,X1,X2] :
( ( sP37(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))
| ~ sP37(X0,X1,X2) ) ),
inference(rectify,[],[f15613]) ).
fof(f15613,plain,
! [X2,X1,X0] :
( ( sP37(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))
| ~ sP37(X2,X1,X0) ) ),
inference(flattening,[],[f15612]) ).
fof(f15612,plain,
! [X2,X1,X0] :
( ( sP37(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))
| ~ sP37(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14409]) ).
fof(f14409,plain,
! [X2,X1,X0] :
( sP37(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,[sP37])]) ).
fof(f33022,plain,
spl573_915,
inference(avatar_split_clause,[],[f27376,f33020]) ).
fof(f33020,plain,
( spl573_915
<=> ! [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,[spl573_915])]) ).
fof(f27376,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,[],[f20837,f16829]) ).
fof(f20837,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,[],[f15611]) ).
fof(f15611,plain,
! [X0,X1,X2] :
( ( sP38(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK333(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK333(X0,X1,X2))),sK334(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK334(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK334(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)))
| ~ sP38(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK333,sK334])],[f15608,f15610,f15609]) ).
fof(f15609,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,sK333(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),sK333(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(f15610,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),sK333(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),sK333(X0,X1,X2))),sK334(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK334(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK334(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15608,plain,
! [X0,X1,X2] :
( ( sP38(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)))
| ~ sP38(X0,X1,X2) ) ),
inference(rectify,[],[f15607]) ).
fof(f15607,plain,
! [X2,X1,X0] :
( ( sP38(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)))
| ~ sP38(X2,X1,X0) ) ),
inference(flattening,[],[f15606]) ).
fof(f15606,plain,
! [X2,X1,X0] :
( ( sP38(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)))
| ~ sP38(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14410]) ).
fof(f14410,plain,
! [X2,X1,X0] :
( sP38(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,[sP38])]) ).
fof(f33017,plain,
spl573_914,
inference(avatar_split_clause,[],[f27355,f33015]) ).
fof(f33015,plain,
( spl573_914
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP32(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_914])]) ).
fof(f27355,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP32(X0,X1,X2) ),
inference(forward_demodulation,[],[f20760,f16829]) ).
fof(f20760,plain,
! [X2,X0,X1] :
( sP32(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,[],[f15559]) ).
fof(f15559,plain,
! [X0,X1,X2] :
( ( sP32(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK326(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK325(X0,X1,X2))),sK326(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK326(X0,X1,X2)),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK326(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))
| ~ sP32(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK325,sK326])],[f15557,f15558]) ).
fof(f15558,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,sK326(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK325(X0,X1,X2))),sK326(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK326(X0,X1,X2)),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK326(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15557,plain,
! [X0,X1,X2] :
( ( sP32(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))
| ~ sP32(X0,X1,X2) ) ),
inference(rectify,[],[f15556]) ).
fof(f15556,plain,
! [X2,X1,X0] :
( ( sP32(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))
| ~ sP32(X2,X1,X0) ) ),
inference(flattening,[],[f15555]) ).
fof(f15555,plain,
! [X2,X1,X0] :
( ( sP32(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))
| ~ sP32(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14401]) ).
fof(f14401,plain,
! [X2,X1,X0] :
( sP32(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,[sP32])]) ).
fof(f33013,plain,
spl573_913,
inference(avatar_split_clause,[],[f27350,f33011]) ).
fof(f33011,plain,
( spl573_913
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP33(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_913])]) ).
fof(f27350,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP33(X0,X1,X2) ),
inference(forward_demodulation,[],[f20754,f16829]) ).
fof(f20754,plain,
! [X2,X0,X1] :
( sP33(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,[],[f15554]) ).
fof(f15554,plain,
! [X0,X1,X2] :
( ( sP33(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK324(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK323(X0,X1,X2))),sK324(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK324(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK324(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)))
| ~ sP33(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK323,sK324])],[f15552,f15553]) ).
fof(f15553,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,sK324(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X2),sK323(X0,X1,X2))),sK324(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK324(X0,X1,X2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),sK324(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15552,plain,
! [X0,X1,X2] :
( ( sP33(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)))
| ~ sP33(X0,X1,X2) ) ),
inference(rectify,[],[f15551]) ).
fof(f15551,plain,
! [X2,X1,X0] :
( ( sP33(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)))
| ~ sP33(X2,X1,X0) ) ),
inference(flattening,[],[f15550]) ).
fof(f15550,plain,
! [X2,X1,X0] :
( ( sP33(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)))
| ~ sP33(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14402]) ).
fof(f14402,plain,
! [X2,X1,X0] :
( sP33(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,[sP33])]) ).
fof(f33009,plain,
spl573_912,
inference(avatar_split_clause,[],[f27331,f33007]) ).
fof(f33007,plain,
( spl573_912
<=> ! [X2,X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| sP30(X1,X0)
| ~ sP31(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_912])]) ).
fof(f27331,plain,
! [X2,X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| sP30(X1,X0)
| ~ sP31(X0,X1,X2) ),
inference(forward_demodulation,[],[f20724,f16841]) ).
fof(f20724,plain,
! [X2,X0,X1] :
( sP30(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP31(X0,X1,X2) ),
inference(cnf_transformation,[],[f15532]) ).
fof(f15532,plain,
! [X0,X1,X2] :
( ( sP31(X0,X1,X2)
| ( ~ sP30(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 )
& ( ( ( sP30(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 )
| ~ sP31(X0,X1,X2) ) ),
inference(rectify,[],[f15531]) ).
fof(f15531,plain,
! [X1,X0,X2] :
( ( sP31(X1,X0,X2)
| ( ~ sP30(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 )
& ( ( ( sP30(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 )
| ~ sP31(X1,X0,X2) ) ),
inference(flattening,[],[f15530]) ).
fof(f15530,plain,
! [X1,X0,X2] :
( ( sP31(X1,X0,X2)
| ( ~ sP30(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 )
& ( ( ( sP30(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 )
| ~ sP31(X1,X0,X2) ) ),
inference(nnf_transformation,[],[f14399]) ).
fof(f14399,plain,
! [X1,X0,X2] :
( sP31(X1,X0,X2)
<=> ( ( sP30(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,[sP31])]) ).
fof(f33005,plain,
spl573_911,
inference(avatar_split_clause,[],[f27237,f33003]) ).
fof(f33003,plain,
( spl573_911
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| hBOOL(hAPP(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_911])]) ).
fof(f27237,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| hBOOL(hAPP(X0,X1)) ),
inference(forward_demodulation,[],[f20486,f17482]) ).
fof(f17482,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(cnf_transformation,[],[f5663]) ).
fof(f5663,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(rectify,[],[f3629]) ).
fof(f3629,axiom,
! [X5,X7] : hAPP(c_Set_OCollect(X7),X5) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(f20486,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_Set_OCollect(X2),X0))) ),
inference(cnf_transformation,[],[f12329]) ).
fof(f12329,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_Set_OCollect(X2),X0))) ),
inference(ennf_transformation,[],[f7921]) ).
fof(f7921,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_Set_OCollect(X2),X0)))
=> hBOOL(hAPP(X0,X1)) ),
inference(rectify,[],[f3642]) ).
fof(f3642,axiom,
! [X5,X76,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X76),hAPP(c_Set_OCollect(X7),X5)))
=> hBOOL(hAPP(X5,X76)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectE) ).
fof(f33001,plain,
spl573_910,
inference(avatar_split_clause,[],[f27204,f32999]) ).
fof(f32999,plain,
( spl573_910
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP26(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_910])]) ).
fof(f27204,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),X2))
| sP26(X2,X0,X1) ),
inference(forward_demodulation,[],[f20427,f16829]) ).
fof(f20427,plain,
! [X2,X0,X1] :
( sP26(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,[],[f14391]) ).
fof(f14391,plain,
! [X0,X1,X2] :
( sP26(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,[],[f12275,f14390,f14389]) ).
fof(f14389,plain,
! [X1,X0,X2] :
( sP25(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,[sP25])]) ).
fof(f14390,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)))
<=> sP25(X1,X0,X2) )
| ~ sP26(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP26])]) ).
fof(f12275,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,[],[f12274]) ).
fof(f12274,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,[],[f7880]) ).
fof(f7880,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,[],[f888]) ).
fof(f888,axiom,
! [X6,X5,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
=> ( hBOOL(hAPP(hAPP(X5,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X94)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6,X94)))
<=> ! [X144,X118] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X144)),X118) = X6
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X118),X94))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X118)) )
=> hBOOL(hAPP(hAPP(X5,X144),X118)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__pos__lemma) ).
fof(f32997,plain,
spl573_909,
inference(avatar_split_clause,[],[f27141,f32995]) ).
fof(f32995,plain,
( spl573_909
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP24(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_909])]) ).
fof(f27141,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X2),c_Int_OPls))
| sP24(X2,X0,X1) ),
inference(forward_demodulation,[],[f20385,f16829]) ).
fof(f20385,plain,
! [X2,X0,X1] :
( sP24(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,[],[f14388]) ).
fof(f14388,plain,
! [X0,X1,X2] :
( sP24(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,[],[f12245,f14387,f14386]) ).
fof(f14386,plain,
! [X1,X0,X2] :
( sP23(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,[sP23])]) ).
fof(f14387,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)))
<=> sP23(X1,X0,X2) )
| ~ sP24(X2,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).
fof(f12245,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,[],[f12244]) ).
fof(f12244,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,[],[f7863]) ).
fof(f7863,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,[],[f889]) ).
fof(f889,axiom,
! [X6,X5,X94] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( hBOOL(hAPP(hAPP(X5,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X6),X94)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X6,X94)))
<=> ! [X144,X118] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X144)),X118) = X6
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X118),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X118)) )
=> hBOOL(hAPP(hAPP(X5,X144),X118)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__neg__lemma) ).
fof(f32993,plain,
spl573_908,
inference(avatar_split_clause,[],[f27066,f32991]) ).
fof(f32991,plain,
( spl573_908
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
| ~ hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_908])]) ).
fof(f27066,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(forward_demodulation,[],[f20207,f17482]) ).
fof(f20207,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(c_Set_OCollect(X0),X2)))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(cnf_transformation,[],[f12068]) ).
fof(f12068,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(c_Set_OCollect(X0),X2)))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(ennf_transformation,[],[f7735]) ).
fof(f7735,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,X1))
=> hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(c_Set_OCollect(X0),X2))) ),
inference(rectify,[],[f3613]) ).
fof(f3613,axiom,
! [X7,X76,X5] :
( hBOOL(hAPP(X5,X76))
=> hBOOL(hAPP(hAPP(c_member(X7),X76),hAPP(c_Set_OCollect(X7),X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_CollectI) ).
fof(f32989,plain,
spl573_907,
inference(avatar_split_clause,[],[f26889,f32986]) ).
fof(f32986,plain,
( spl573_907
<=> 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,[spl573_907])]) ).
fof(f26889,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,[],[f26888,f25278]) ).
fof(f25278,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,[],[f17061,f16841]) ).
fof(f17061,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,[],[f5329]) ).
fof(f5329,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,[],[f630]) ).
fof(f630,axiom,
! [X12] : 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)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0) ).
fof(f26888,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,[],[f26887,f25278]) ).
fof(f26887,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,[],[f24715,f16841]) ).
fof(f24715,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,[],[f19471]) ).
fof(f19471,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,[],[f11259]) ).
fof(f11259,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,[],[f7153]) ).
fof(f7153,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,[],[f918]) ).
fof(f918,axiom,
! [X12,X85,X96] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X96
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X85),X12) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X85)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X12)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X96
=> 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),X96),X85)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X96),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
fof(f32984,plain,
spl573_906,
inference(avatar_split_clause,[],[f26622,f32982]) ).
fof(f32982,plain,
( spl573_906
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_906])]) ).
fof(f26622,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f26621,f25195]) ).
fof(f25195,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f16873,f16841]) ).
fof(f16873,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f726]) ).
fof(f726,axiom,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(f26621,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f26620,f16841]) ).
fof(f26620,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f19022,f16841]) ).
fof(f19022,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
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f15004]) ).
fof(f15004,plain,
! [X0,X1] :
( ( sP11(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 )
| ~ sP11(X0,X1) ) ),
inference(flattening,[],[f15003]) ).
fof(f15003,plain,
! [X0,X1] :
( ( sP11(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 )
| ~ sP11(X0,X1) ) ),
inference(nnf_transformation,[],[f14367]) ).
fof(f14367,plain,
! [X0,X1] :
( sP11(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,[sP11])]) ).
fof(f32980,plain,
spl573_905,
inference(avatar_split_clause,[],[f26619,f32978]) ).
fof(f32978,plain,
( spl573_905
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_905])]) ).
fof(f26619,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f26618,f16841]) ).
fof(f26618,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f19023,f16841]) ).
fof(f19023,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f15004]) ).
fof(f32976,plain,
( spl573_904
| ~ spl573_184
| ~ spl573_873 ),
inference(avatar_split_clause,[],[f32931,f32846,f29014,f32973]) ).
fof(f29014,plain,
( spl573_184
<=> v_P(v_Z,v_s) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_184])]) ).
fof(f32846,plain,
( spl573_873
<=> ! [X0] :
( v_Q(X0,v_s1)
| ~ v_P(X0,v_s) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_873])]) ).
fof(f32931,plain,
( v_Q(v_Z,v_s1)
| ~ spl573_184
| ~ spl573_873 ),
inference(resolution,[],[f32847,f29016]) ).
fof(f29016,plain,
( v_P(v_Z,v_s)
| ~ spl573_184 ),
inference(avatar_component_clause,[],[f29014]) ).
fof(f32847,plain,
( ! [X0] :
( ~ v_P(X0,v_s)
| v_Q(X0,v_s1) )
| ~ spl573_873 ),
inference(avatar_component_clause,[],[f32846]) ).
fof(f32971,plain,
spl573_903,
inference(avatar_split_clause,[],[f26617,f32969]) ).
fof(f32969,plain,
( spl573_903
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_903])]) ).
fof(f26617,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f26616,f25195]) ).
fof(f26616,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f26615,f16841]) ).
fof(f26615,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
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f26614,f25195]) ).
fof(f26614,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
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f19024,f16841]) ).
fof(f19024,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
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f15004]) ).
fof(f32967,plain,
spl573_902,
inference(avatar_split_clause,[],[f26613,f32965]) ).
fof(f32965,plain,
( spl573_902
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_902])]) ).
fof(f26613,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f26612,f16841]) ).
fof(f26612,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f26611,f25195]) ).
fof(f26611,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f19025,f16841]) ).
fof(f19025,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
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f15004]) ).
fof(f32963,plain,
spl573_901,
inference(avatar_split_clause,[],[f26602,f32961]) ).
fof(f32961,plain,
( spl573_901
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_901])]) ).
fof(f26602,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f26601,f25195]) ).
fof(f26601,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X1
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f26600,f16841]) ).
fof(f26600,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f19014,f16841]) ).
fof(f19014,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
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f15001]) ).
fof(f15001,plain,
! [X0,X1] :
( ( sP10(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 )
| ~ sP10(X0,X1) ) ),
inference(flattening,[],[f15000]) ).
fof(f15000,plain,
! [X0,X1] :
( ( sP10(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 )
| ~ sP10(X0,X1) ) ),
inference(nnf_transformation,[],[f14365]) ).
fof(f14365,plain,
! [X0,X1] :
( sP10(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,[sP10])]) ).
fof(f32959,plain,
spl573_900,
inference(avatar_split_clause,[],[f26599,f32957]) ).
fof(f32957,plain,
( spl573_900
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_900])]) ).
fof(f26599,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_HOL_Obool_Obool__size(c_fTrue) = X1
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f26598,f16841]) ).
fof(f26598,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f19015,f16841]) ).
fof(f19015,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f15001]) ).
fof(f32955,plain,
spl573_899,
inference(avatar_split_clause,[],[f26597,f32953]) ).
fof(f32953,plain,
( spl573_899
<=> ! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_899])]) ).
fof(f26597,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f26596,f25195]) ).
fof(f26596,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f26595,f16841]) ).
fof(f26595,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
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f26594,f25195]) ).
fof(f26594,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
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f19016,f16841]) ).
fof(f19016,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
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f15001]) ).
fof(f32951,plain,
spl573_898,
inference(avatar_split_clause,[],[f26593,f32949]) ).
fof(f32949,plain,
( spl573_898
<=> ! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_898])]) ).
fof(f26593,plain,
! [X0,X1] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f26592,f16841]) ).
fof(f26592,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f26591,f25195]) ).
fof(f26591,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f19017,f16841]) ).
fof(f19017,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
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f15001]) ).
fof(f32947,plain,
spl573_897,
inference(avatar_split_clause,[],[f26562,f32945]) ).
fof(f32945,plain,
( spl573_897
<=> ! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| sP9(c_HOL_Obool_Obool__size(c_fTrue),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_897])]) ).
fof(f26562,plain,
! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| sP9(c_HOL_Obool_Obool__size(c_fTrue),X1) ),
inference(forward_demodulation,[],[f26561,f16829]) ).
fof(f26561,plain,
! [X1] :
( sP9(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,[],[f24684,f16841]) ).
fof(f24684,plain,
! [X1] :
( sP9(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,[],[f18987]) ).
fof(f18987,plain,
! [X0,X1] :
( sP9(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,[],[f14983]) ).
fof(f14983,plain,
! [X0,X1] :
( ( sP9(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)) ) )
| ~ sP9(X0,X1) ) ),
inference(flattening,[],[f14982]) ).
fof(f14982,plain,
! [X0,X1] :
( ( sP9(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)) ) )
| ~ sP9(X0,X1) ) ),
inference(nnf_transformation,[],[f14363]) ).
fof(f14363,plain,
! [X0,X1] :
( sP9(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,[sP9])]) ).
fof(f32943,plain,
spl573_896,
inference(avatar_split_clause,[],[f26560,f32941]) ).
fof(f32941,plain,
( spl573_896
<=> ! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Int_OPls))
| sP9(c_HOL_Obool_Obool__size(c_fTrue),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_896])]) ).
fof(f26560,plain,
! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),X1),c_Int_OPls))
| sP9(c_HOL_Obool_Obool__size(c_fTrue),X1) ),
inference(forward_demodulation,[],[f26559,f25199]) ).
fof(f25199,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,[],[f25198,f16829]) ).
fof(f25198,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,[],[f16892,f16841]) ).
fof(f16892,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,[],[f368]) ).
fof(f368,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/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I1_J) ).
fof(f26559,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))))
| sP9(c_HOL_Obool_Obool__size(c_fTrue),X1) ),
inference(forward_demodulation,[],[f26558,f16841]) ).
fof(f26558,plain,
! [X1] :
( sP9(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,[],[f24683,f16841]) ).
fof(f24683,plain,
! [X1] :
( sP9(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,[],[f18988]) ).
fof(f18988,plain,
! [X0,X1] :
( sP9(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,[],[f14983]) ).
fof(f32939,plain,
spl573_895,
inference(avatar_split_clause,[],[f26522,f32937]) ).
fof(f32937,plain,
( spl573_895
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| hBOOL(hAPP(X0,sK178(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_895])]) ).
fof(f26522,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| hBOOL(hAPP(X0,sK178(X0))) ),
inference(forward_demodulation,[],[f18911,f17482]) ).
fof(f18911,plain,
! [X0,X1] :
( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK178(X0))) ),
inference(cnf_transformation,[],[f14942]) ).
fof(f14942,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK178(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,[sK178])],[f14940,f14941]) ).
fof(f14941,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X0,sK178(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14940,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,[],[f14939]) ).
fof(f14939,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,[],[f6763]) ).
fof(f6763,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,[],[f3634]) ).
fof(f3634,axiom,
! [X5,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7),X5)
<=> ! [X2] : ~ hBOOL(hAPP(X5,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__empty__eq) ).
fof(f32935,plain,
spl573_894,
inference(avatar_split_clause,[],[f26520,f32933]) ).
fof(f32933,plain,
( spl573_894
<=> ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| hBOOL(hAPP(X0,sK177(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_894])]) ).
fof(f26520,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| hBOOL(hAPP(X0,sK177(X0))) ),
inference(forward_demodulation,[],[f18909,f17482]) ).
fof(f18909,plain,
! [X0,X1] :
( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK177(X0))) ),
inference(cnf_transformation,[],[f14938]) ).
fof(f14938,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK177(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,[sK177])],[f14936,f14937]) ).
fof(f14937,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X0,sK177(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14936,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,[],[f14935]) ).
fof(f14935,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,[],[f6762]) ).
fof(f6762,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,[],[f3635]) ).
fof(f3635,axiom,
! [X5,X7] :
( c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X7),X5)
<=> ! [X2] : ~ hBOOL(hAPP(X5,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__Collect__eq) ).
fof(f32930,plain,
spl573_893,
inference(avatar_split_clause,[],[f26507,f32928]) ).
fof(f32928,plain,
( spl573_893
<=> ! [X0,X1] :
( c_Int_OPls != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| sP6(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_893])]) ).
fof(f26507,plain,
! [X0,X1] :
( c_Int_OPls != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| sP6(X1,X0) ),
inference(forward_demodulation,[],[f18898,f16829]) ).
fof(f18898,plain,
! [X0,X1] :
( sP6(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,[],[f14929]) ).
fof(f14929,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| ~ sP6(X1,X0) )
& ( sP6(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,[],[f14359]) ).
fof(f14359,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
<=> sP6(X1,X0) ),
inference(definition_folding,[],[f6758,f14358]) ).
fof(f14358,plain,
! [X1,X0] :
( sP6(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,[sP6])]) ).
fof(f6758,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,[],[f946]) ).
fof(f946,axiom,
! [X94,X71] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X71),X94)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X71))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),X94))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X71)) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X94 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__eq__0__iff) ).
fof(f32926,plain,
spl573_892,
inference(avatar_split_clause,[],[f26506,f32924]) ).
fof(f32924,plain,
( spl573_892
<=> ! [X0,X1] :
( c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| ~ sP6(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_892])]) ).
fof(f26506,plain,
! [X0,X1] :
( c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| ~ sP6(X1,X0) ),
inference(forward_demodulation,[],[f18899,f16829]) ).
fof(f18899,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)
| ~ sP6(X1,X0) ),
inference(cnf_transformation,[],[f14929]) ).
fof(f32922,plain,
spl573_891,
inference(avatar_split_clause,[],[f26472,f32920]) ).
fof(f32920,plain,
( spl573_891
<=> ! [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,[spl573_891])]) ).
fof(f26472,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,[],[f24637,f16829]) ).
fof(f24637,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,[],[f18793]) ).
fof(f18793,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,[],[f14857]) ).
fof(f14857,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),sK170(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,[sK170])],[f14855,f14856]) ).
fof(f14856,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),sK170(X0,X1)) = X1 ),
introduced(choice_axiom,[]) ).
fof(f14855,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,[],[f14854]) ).
fof(f14854,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,[],[f6716]) ).
fof(f6716,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,[],[f869]) ).
fof(f869,axiom,
! [X133,X95] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X95,X133)
<=> ? [X147] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X133),X147) = X95 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__eq__0__iff) ).
fof(f32918,plain,
spl573_890,
inference(avatar_split_clause,[],[f26453,f32916]) ).
fof(f32916,plain,
( spl573_890
<=> ! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| sP3(c_HOL_Obool_Obool__size(c_fTrue),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_890])]) ).
fof(f26453,plain,
! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| sP3(c_HOL_Obool_Obool__size(c_fTrue),X1) ),
inference(forward_demodulation,[],[f26452,f16829]) ).
fof(f26452,plain,
! [X1] :
( sP3(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,[],[f24628,f16841]) ).
fof(f24628,plain,
! [X1] :
( sP3(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,[],[f18750]) ).
fof(f18750,plain,
! [X0,X1] :
( sP3(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,[],[f14816]) ).
fof(f14816,plain,
! [X0,X1] :
( ( sP3(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)) ) )
| ~ sP3(X0,X1) ) ),
inference(rectify,[],[f14815]) ).
fof(f14815,plain,
! [X1,X0] :
( ( sP3(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)) ) )
| ~ sP3(X1,X0) ) ),
inference(flattening,[],[f14814]) ).
fof(f14814,plain,
! [X1,X0] :
( ( sP3(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)) ) )
| ~ sP3(X1,X0) ) ),
inference(nnf_transformation,[],[f14352]) ).
fof(f14352,plain,
! [X1,X0] :
( sP3(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,[sP3])]) ).
fof(f32914,plain,
spl573_889,
inference(avatar_split_clause,[],[f26445,f32912]) ).
fof(f32912,plain,
( spl573_889
<=> ! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| sP2(c_HOL_Obool_Obool__size(c_fTrue),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_889])]) ).
fof(f26445,plain,
! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X1))
| sP2(c_HOL_Obool_Obool__size(c_fTrue),X1) ),
inference(forward_demodulation,[],[f26444,f16829]) ).
fof(f26444,plain,
! [X1] :
( sP2(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,[],[f24623,f16841]) ).
fof(f24623,plain,
! [X1] :
( sP2(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,[],[f18742]) ).
fof(f18742,plain,
! [X0,X1] :
( sP2(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,[],[f14812]) ).
fof(f14812,plain,
! [X0,X1] :
( ( sP2(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)) ) )
| ~ sP2(X0,X1) ) ),
inference(flattening,[],[f14811]) ).
fof(f14811,plain,
! [X0,X1] :
( ( sP2(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)) ) )
| ~ sP2(X0,X1) ) ),
inference(nnf_transformation,[],[f14350]) ).
fof(f14350,plain,
! [X0,X1] :
( sP2(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,[sP2])]) ).
fof(f32910,plain,
spl573_888,
inference(avatar_split_clause,[],[f26441,f32908]) ).
fof(f32908,plain,
( spl573_888
<=> ! [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,[spl573_888])]) ).
fof(f26441,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,[],[f24049,f17482]) ).
fof(f24049,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,[],[f18713,f19206]) ).
fof(f19206,plain,
! [X2,X0,X1] : c_Product__Type_Oprod_Oprod__case(X2,X1,X0) = c_Product__Type_Ointernal__split(X2,X1,X0),
inference(cnf_transformation,[],[f6888]) ).
fof(f6888,plain,
! [X0,X1,X2] : c_Product__Type_Oprod_Oprod__case(X2,X1,X0) = c_Product__Type_Ointernal__split(X2,X1,X0),
inference(rectify,[],[f2007]) ).
fof(f2007,axiom,
! [X107,X58,X7] : c_Product__Type_Oprod_Oprod__case(X7,X58,X107) = c_Product__Type_Ointernal__split(X7,X58,X107),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__def) ).
fof(f18713,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,[],[f14781]) ).
fof(f14781,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,[],[f6692]) ).
fof(f6692,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,[],[f3803]) ).
fof(f3803,axiom,
! [X169,X7] :
( c_Wellfounded_OwfP(X7,X169)
<=> c_Wellfounded_Owf(X7,hAPP(c_Set_OCollect(tc_prod(X7,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),X169))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__def) ).
fof(f32906,plain,
spl573_887,
inference(avatar_split_clause,[],[f26440,f32904]) ).
fof(f32904,plain,
( spl573_887
<=> ! [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,[spl573_887])]) ).
fof(f26440,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,[],[f24048,f17482]) ).
fof(f24048,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,[],[f18714,f19206]) ).
fof(f18714,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,[],[f14781]) ).
fof(f32902,plain,
spl573_886,
inference(avatar_split_clause,[],[f26048,f32900]) ).
fof(f32900,plain,
( spl573_886
<=> ! [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,[spl573_886])]) ).
fof(f26048,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,[],[f24009,f17482]) ).
fof(f24009,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,[],[f18333,f19206]) ).
fof(f18333,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,[],[f10836]) ).
fof(f10836,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,[],[f6395]) ).
fof(f6395,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,[],[f3828]) ).
fof(f3828,axiom,
! [X169,X7] :
( c_Wellfounded_OwfP(X7,X169)
=> c_Wellfounded_Oacyclic(X7,hAPP(c_Set_OCollect(tc_prod(X7,X7)),hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),X169))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__acyclicP) ).
fof(f32898,plain,
spl573_885,
inference(avatar_split_clause,[],[f26034,f32896]) ).
fof(f32896,plain,
( spl573_885
<=> ! [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,[spl573_885])]) ).
fof(f26034,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,[],[f18248,f25661]) ).
fof(f25661,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,[],[f17672,f17482]) ).
fof(f17672,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,[],[f5853]) ).
fof(f5853,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,[],[f3648]) ).
fof(f3648,axiom,
! [X76,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X76),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X7),hAPP(c_fequal,X76)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__conv2) ).
fof(f18248,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,[],[f10724]) ).
fof(f10724,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,[],[f6323]) ).
fof(f6323,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,[],[f2876]) ).
fof(f2876,axiom,
! [X99,X7] :
( class_Orderings_Olinorder(X7)
=> c_Big__Operators_Olattice_OInf__fin(X7,c_Orderings_Oord__class_Omin(X7),hAPP(hAPP(c_Set_Oinsert(X7),X99),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X99 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).
fof(f32894,plain,
spl573_884,
inference(avatar_split_clause,[],[f26033,f32892]) ).
fof(f32892,plain,
( spl573_884
<=> ! [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,[spl573_884])]) ).
fof(f26033,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,[],[f18247,f25661]) ).
fof(f18247,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,[],[f10723]) ).
fof(f10723,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,[],[f6322]) ).
fof(f6322,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,[],[f2877]) ).
fof(f2877,axiom,
! [X99,X7] :
( class_Orderings_Olinorder(X7)
=> c_Big__Operators_Olattice_OSup__fin(X7,c_Orderings_Oord__class_Omax(X7),hAPP(hAPP(c_Set_Oinsert(X7),X99),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X99 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).
fof(f32890,plain,
spl573_883,
inference(avatar_split_clause,[],[f25785,f32888]) ).
fof(f32888,plain,
( spl573_883
<=> ! [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,[spl573_883])]) ).
fof(f25785,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,[],[f17876,f16841]) ).
fof(f17876,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,[],[f10437]) ).
fof(f10437,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,[],[f6043]) ).
fof(f6043,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,[],[f4383]) ).
fof(f4383,axiom,
! [X148,X7] :
( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X148))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nitpick_Ocard_H(X7,X148) )
& ( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X148))
=> c_Nitpick_Ocard_H(X7,X148) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X7)),c_Hilbert__Choice_OEps(tc_List_Olist(X7),hAPP(hAPP(c_COMBS(tc_List_Olist(X7),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(X7)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(X7),tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(X7,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(X7)),c_fequal),c_List_Oset(X7))),X148))),c_List_Odistinct(X7)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Ocard_H__def) ).
fof(f32886,plain,
spl573_882,
inference(avatar_split_clause,[],[f25648,f32884]) ).
fof(f32884,plain,
( spl573_882
<=> ! [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,[spl573_882])]) ).
fof(f25648,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,[],[f17568,f16829]) ).
fof(f17568,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,[],[f5749]) ).
fof(f5749,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,[],[f929]) ).
fof(f929,axiom,
! [X100,X88] : 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,X88,X100)),X100),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zdiv__trivial) ).
fof(f32882,plain,
spl573_881,
inference(avatar_split_clause,[],[f25646,f32880]) ).
fof(f32880,plain,
( spl573_881
<=> ! [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,[spl573_881])]) ).
fof(f25646,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,[],[f17555,f16841]) ).
fof(f17555,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,[],[f5736]) ).
fof(f5736,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,[],[f4003]) ).
fof(f4003,axiom,
! [X1,X7] : c_Fun_Oid(X7) = hAPP(hAPP(c_Nat_Ocompow(X7,X7),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funpow_Osimps_I1_J) ).
fof(f32878,plain,
spl573_880,
inference(avatar_split_clause,[],[f25645,f32876]) ).
fof(f32876,plain,
( spl573_880
<=> ! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),hAPP(c_Option_Ooption_OSome(X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_880])]) ).
fof(f25645,plain,
! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(forward_demodulation,[],[f17554,f16841]) ).
fof(f17554,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(cnf_transformation,[],[f5735]) ).
fof(f5735,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X1)),hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(rectify,[],[f333]) ).
fof(f333,axiom,
! [X88,X13] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X13)),hAPP(c_Option_Ooption_OSome(X13),X88)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osize_I4_J) ).
fof(f32873,plain,
spl573_879,
inference(avatar_split_clause,[],[f25600,f32870]) ).
fof(f32870,plain,
( spl573_879
<=> 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,[spl573_879])]) ).
fof(f25600,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,[],[f24541,f16829]) ).
fof(f24541,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,[],[f17442]) ).
fof(f17442,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,[],[f14585]) ).
fof(f14585,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,[],[f5636]) ).
fof(f5636,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,[],[f1197]) ).
fof(f1197,axiom,
! [X121] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X121)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X121 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).
fof(f32868,plain,
spl573_878,
inference(avatar_split_clause,[],[f25527,f32866]) ).
fof(f32866,plain,
( spl573_878
<=> ! [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,[spl573_878])]) ).
fof(f25527,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,[],[f17352,f16829]) ).
fof(f17352,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,[],[f14525]) ).
fof(f14525,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,[],[f5593]) ).
fof(f5593,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,[],[f1280]) ).
fof(f1280,axiom,
! [X163] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X163))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X163),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__def) ).
fof(f32864,plain,
spl573_877,
inference(avatar_split_clause,[],[f25526,f32862]) ).
fof(f32862,plain,
( spl573_877
<=> ! [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,[spl573_877])]) ).
fof(f25526,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,[],[f17353,f16829]) ).
fof(f17353,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,[],[f14525]) ).
fof(f32860,plain,
spl573_876,
inference(avatar_split_clause,[],[f25525,f32858]) ).
fof(f32858,plain,
( spl573_876
<=> ! [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,[spl573_876])]) ).
fof(f25525,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,[],[f17342,f16829]) ).
fof(f17342,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,[],[f14520]) ).
fof(f14520,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,[],[f5588]) ).
fof(f5588,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,[],[f1279]) ).
fof(f1279,axiom,
! [X99] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X99))
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X99)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__eq__ge__0) ).
fof(f32856,plain,
spl573_875,
inference(avatar_split_clause,[],[f25524,f32854]) ).
fof(f32854,plain,
( spl573_875
<=> ! [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,[spl573_875])]) ).
fof(f25524,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,[],[f17343,f16829]) ).
fof(f17343,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,[],[f14520]) ).
fof(f32852,plain,
spl573_874,
inference(avatar_split_clause,[],[f25376,f32850]) ).
fof(f32850,plain,
( spl573_874
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OBit1(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_874])]) ).
fof(f25376,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OBit1(X0)) ),
inference(forward_demodulation,[],[f25375,f16979]) ).
fof(f16979,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(cnf_transformation,[],[f5247]) ).
fof(f5247,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(rectify,[],[f1211]) ).
fof(f1211,axiom,
! [X96] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X96) = X96,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(f25375,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OBit1(X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f25374,f16841]) ).
fof(f25374,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OBit1(X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f17201,f25292]) ).
fof(f25292,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X0),
inference(forward_demodulation,[],[f17088,f16979]) ).
fof(f17088,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,[],[f5356]) ).
fof(f5356,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,[],[f1224]) ).
fof(f1224,axiom,
! [X136] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X136) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X136)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__def) ).
fof(f17201,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f10295]) ).
fof(f10295,plain,
! [X0] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X0)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ),
inference(ennf_transformation,[],[f5464]) ).
fof(f5464,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_OBit1(X0)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X0)) ) ),
inference(rectify,[],[f1725]) ).
fof(f1725,axiom,
! [X122] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X122)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X122)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat)))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(X122)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Bit1) ).
fof(f32848,plain,
( spl573_873
| ~ spl573_205
| ~ spl573_747 ),
inference(avatar_split_clause,[],[f32336,f32332,f29117,f32846]) ).
fof(f29117,plain,
( spl573_205
<=> c_Natural_Oevaln(v_c,v_s,v_n,v_s1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_205])]) ).
fof(f32332,plain,
( spl573_747
<=> ! [X2,X0,X1] :
( v_Q(X0,X2)
| ~ c_Natural_Oevaln(v_c,X1,v_n,X2)
| ~ v_P(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_747])]) ).
fof(f32336,plain,
( ! [X0] :
( v_Q(X0,v_s1)
| ~ v_P(X0,v_s) )
| ~ spl573_205
| ~ spl573_747 ),
inference(resolution,[],[f32333,f29119]) ).
fof(f29119,plain,
( c_Natural_Oevaln(v_c,v_s,v_n,v_s1)
| ~ spl573_205 ),
inference(avatar_component_clause,[],[f29117]) ).
fof(f32333,plain,
( ! [X2,X0,X1] :
( ~ c_Natural_Oevaln(v_c,X1,v_n,X2)
| v_Q(X0,X2)
| ~ v_P(X0,X1) )
| ~ spl573_747 ),
inference(avatar_component_clause,[],[f32332]) ).
fof(f32844,plain,
spl573_872,
inference(avatar_split_clause,[],[f25314,f32842]) ).
fof(f32842,plain,
( spl573_872
<=> ! [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,[spl573_872])]) ).
fof(f25314,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,[],[f17127,f16979]) ).
fof(f17127,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,[],[f5395]) ).
fof(f5395,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,[],[f1320]) ).
fof(f1320,axiom,
! [X88] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X88) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X88),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__minus1__right) ).
fof(f32840,plain,
spl573_871,
inference(avatar_split_clause,[],[f25310,f32838]) ).
fof(f32838,plain,
( spl573_871
<=> ! [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,[spl573_871])]) ).
fof(f25310,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,[],[f17125,f16829]) ).
fof(f17125,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,[],[f5393]) ).
fof(f5393,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,[],[f1746]) ).
fof(f1746,axiom,
! [X100] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X100) = 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/sandbox/benchmark/theBenchmark.p',fact_posDivAlg__0) ).
fof(f32836,plain,
spl573_870,
inference(avatar_split_clause,[],[f25299,f32834]) ).
fof(f32834,plain,
( spl573_870
<=> ! [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,[spl573_870])]) ).
fof(f25299,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,[],[f17099,f16829]) ).
fof(f17099,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,[],[f5367]) ).
fof(f5367,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,[],[f526]) ).
fof(f526,axiom,
! [X97] : 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),X97)),X97),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(f32832,plain,
spl573_869,
inference(avatar_split_clause,[],[f25291,f32830]) ).
fof(f32830,plain,
( spl573_869
<=> ! [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,[spl573_869])]) ).
fof(f25291,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,[],[f17086,f16841]) ).
fof(f17086,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,[],[f5354]) ).
fof(f5354,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,[],[f2212]) ).
fof(f2212,axiom,
! [X6] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X6) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast0LessThan) ).
fof(f32828,plain,
spl573_868,
inference(avatar_split_clause,[],[f25290,f32826]) ).
fof(f32826,plain,
( spl573_868
<=> ! [X0] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_HOL_Obool_Obool__size(c_fTrue)) = c_Option_Oset(tc_Nat_Onat,c_Option_Ooption_ONone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_868])]) ).
fof(f25290,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),c_HOL_Obool_Obool__size(c_fTrue)) = c_Option_Oset(tc_Nat_Onat,c_Option_Ooption_ONone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f25289,f17037]) ).
fof(f17037,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Option_Oset(X0,c_Option_Ooption_ONone(X0)),
inference(cnf_transformation,[],[f5305]) ).
fof(f5305,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Option_Oset(X0,c_Option_Ooption_ONone(X0)),
inference(rectify,[],[f2651]) ).
fof(f2651,axiom,
! [X7] : c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = c_Option_Oset(X7,c_Option_Ooption_ONone(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Oset_Osimps_I1_J) ).
fof(f25289,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,[],[f17083,f16841]) ).
fof(f17083,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,[],[f5351]) ).
fof(f5351,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,[],[f2505]) ).
fof(f2505,axiom,
! [X95] : c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan0) ).
fof(f32824,plain,
( spl573_867
| ~ spl573_866 ),
inference(avatar_split_clause,[],[f32819,f32816,f32821]) ).
fof(f32821,plain,
( spl573_867
<=> c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Option_Oset(tc_Nat_Onat,c_Option_Ooption_ONone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_867])]) ).
fof(f32816,plain,
( spl573_866
<=> ! [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,[spl573_866])]) ).
fof(f32819,plain,
( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Option_Oset(tc_Nat_Onat,c_Option_Ooption_ONone(tc_Nat_Onat)))
| ~ spl573_866 ),
inference(forward_demodulation,[],[f32817,f25290]) ).
fof(f32817,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)))
| ~ spl573_866 ),
inference(avatar_component_clause,[],[f32816]) ).
fof(f32818,plain,
spl573_866,
inference(avatar_split_clause,[],[f25248,f32816]) ).
fof(f25248,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,[],[f23774,f16841]) ).
fof(f23774,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,[],[f16985,f17563]) ).
fof(f17563,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,[],[f5744]) ).
fof(f5744,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,[],[f4874]) ).
fof(f4874,axiom,
! [X6,X95] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X95),X6)) = c_List_Oupt(X95,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__range) ).
fof(f16985,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f5253]) ).
fof(f5253,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f4876]) ).
fof(f4876,axiom,
! [X116] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__0) ).
fof(f32814,plain,
spl573_865,
inference(avatar_split_clause,[],[f25016,f32812]) ).
fof(f32812,plain,
( spl573_865
<=> ! [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,[spl573_865])]) ).
fof(f25016,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,[],[f22510]) ).
fof(f22510,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,[],[f13449]) ).
fof(f13449,plain,
! [X0,X1,X2,X3,X4] :
( ( hAPP(c_New__DSequence_Opos__decr__bind(X3,X2,X1,X0),X4) = 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,[],[f9262]) ).
fof(f9262,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) = 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,[],[f2009]) ).
fof(f2009,axiom,
! [X1,X99,X7,X58,X71] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X71
=> hAPP(c_New__DSequence_Opos__decr__bind(X58,X7,X99,X1),X71) = c_Lazy__Sequence_Obind(X58,X7,hAPP(X99,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X71),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X58,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(X7)),X1),X71)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X71
=> hAPP(c_New__DSequence_Opos__decr__bind(X58,X7,X99,X1),X71) = c_Lazy__Sequence_Oempty(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__decr__bind__def) ).
fof(f32810,plain,
spl573_864,
inference(avatar_split_clause,[],[f25015,f32808]) ).
fof(f32808,plain,
( spl573_864
<=> ! [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,[spl573_864])]) ).
fof(f25015,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,[],[f22508]) ).
fof(f22508,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,[],[f13448]) ).
fof(f13448,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,[],[f9261]) ).
fof(f9261,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,[],[f2010]) ).
fof(f2010,axiom,
! [X1,X99,X7,X58,X71] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X71
=> hAPP(c_New__DSequence_Oneg__decr__bind(X58,X7,X99,X1),X71) = c_Lazy__Sequence_Ohb__bind(X58,X7,hAPP(X99,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X71),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(X58,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(X7))),X1),X71)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X71
=> hAPP(c_New__DSequence_Oneg__decr__bind(X58,X7,X99,X1),X71) = c_Lazy__Sequence_Ohit__bound(X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__decr__bind__def) ).
fof(f32806,plain,
( spl573_863
| ~ spl573_206
| ~ spl573_746 ),
inference(avatar_split_clause,[],[f32335,f32328,f29122,f32804]) ).
fof(f29122,plain,
( spl573_206
<=> c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_206])]) ).
fof(f32328,plain,
( spl573_746
<=> ! [X2,X0,X1] :
( v_R(X0,X2)
| ~ c_Natural_Oevaln(v_d,X1,v_n,X2)
| ~ v_Q(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_746])]) ).
fof(f32335,plain,
( ! [X0] :
( v_R(X0,v_s_H)
| ~ v_Q(X0,v_s1) )
| ~ spl573_206
| ~ spl573_746 ),
inference(resolution,[],[f32329,f29124]) ).
fof(f29124,plain,
( c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H)
| ~ spl573_206 ),
inference(avatar_component_clause,[],[f29122]) ).
fof(f32329,plain,
( ! [X2,X0,X1] :
( ~ c_Natural_Oevaln(v_d,X1,v_n,X2)
| v_R(X0,X2)
| ~ v_Q(X0,X1) )
| ~ spl573_746 ),
inference(avatar_component_clause,[],[f32328]) ).
fof(f32802,plain,
spl573_862,
inference(avatar_split_clause,[],[f24901,f32800]) ).
fof(f32800,plain,
( spl573_862
<=> ! [X0,X1,X3] : c_List_Oremove1(X1,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_862])]) ).
fof(f24901,plain,
! [X3,X0,X1] : c_List_Oremove1(X1,X3,hAPP(hAPP(c_List_Olist_OCons(X1),X3),X0)) = X0,
inference(equality_resolution,[],[f21258]) ).
fof(f21258,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,[],[f12541]) ).
fof(f12541,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,[],[f8361]) ).
fof(f8361,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,[],[f4403]) ).
fof(f4403,axiom,
! [X290,X13,X60,X61] :
( ( X60 != X61
=> c_List_Oremove1(X13,X61,hAPP(hAPP(c_List_Olist_OCons(X13),X60),X290)) = hAPP(hAPP(c_List_Olist_OCons(X13),X60),c_List_Oremove1(X13,X61,X290)) )
& ( X60 = X61
=> c_List_Oremove1(X13,X61,hAPP(hAPP(c_List_Olist_OCons(X13),X60),X290)) = X290 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1_Osimps_I2_J) ).
fof(f32798,plain,
spl573_861,
inference(avatar_split_clause,[],[f24746,f32796]) ).
fof(f32796,plain,
( spl573_861
<=> ! [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,[spl573_861])]) ).
fof(f24746,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,[],[f19688]) ).
fof(f19688,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,[],[f15165]) ).
fof(f15165,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,[],[f11417]) ).
fof(f11417,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,[],[f7319]) ).
fof(f7319,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,[],[f205]) ).
fof(f205,axiom,
! [X76,X27,X7] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(X7)
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(X7),X27),X76) = X27
<=> c_Groups_Ozero__class_Ozero(X7) = X76 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__iff) ).
fof(f32794,plain,
spl573_860,
inference(avatar_split_clause,[],[f24732,f32792]) ).
fof(f32792,plain,
( spl573_860
<=> ! [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,[spl573_860])]) ).
fof(f24732,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,[],[f19568]) ).
fof(f19568,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,[],[f15136]) ).
fof(f15136,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,[],[f11312]) ).
fof(f11312,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,[],[f7231]) ).
fof(f7231,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,[],[f999]) ).
fof(f999,axiom,
! [X27,X76,X7] :
( class_Groups_Oab__group__add(X7)
=> ( X27 = X76
<=> c_Groups_Ozero__class_Ozero(X7) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X7),X76),X27) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__iff__diff__eq__0) ).
fof(f32790,plain,
spl573_859,
inference(avatar_split_clause,[],[f24716,f32788]) ).
fof(f32788,plain,
( spl573_859
<=> ! [X0,X1] : c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_859])]) ).
fof(f24716,plain,
! [X0,X1] : c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1))) = X0,
inference(equality_resolution,[],[f19473]) ).
fof(f19473,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,[],[f11260]) ).
fof(f11260,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,[],[f7154]) ).
fof(f7154,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,[],[f4769]) ).
fof(f4769,axiom,
! [X61,X13,X290] :
( ( c_List_Olist_ONil(X13) != X290
=> c_List_Olast(X13,X290) = c_List_Olast(X13,hAPP(hAPP(c_List_Olist_OCons(X13),X61),X290)) )
& ( c_List_Olist_ONil(X13) = X290
=> c_List_Olast(X13,hAPP(hAPP(c_List_Olist_OCons(X13),X61),X290)) = X61 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_last_Osimps) ).
fof(f32785,plain,
spl573_858,
inference(avatar_split_clause,[],[f24544,f32783]) ).
fof(f32783,plain,
( spl573_858
<=> ! [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,[spl573_858])]) ).
fof(f24544,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,[],[f23951]) ).
fof(f23951,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,[],[f17853,f17570]) ).
fof(f17570,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,[],[f5751]) ).
fof(f5751,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,[],[f1980]) ).
fof(f1980,axiom,
! [X12,X116] : c_Code__Numeral_Onat__of__aux(X116,X12) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,X116)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__aux__def) ).
fof(f17853,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,[],[f10427]) ).
fof(f10427,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,[],[f6033]) ).
fof(f6033,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,[],[f1672]) ).
fof(f1672,axiom,
! [X12,X116] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X116
=> c_Code__Numeral_Onat__of__aux(X116,X12) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),X116),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,X12)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X116
=> c_Code__Numeral_Onat__of__aux(X116,X12) = X12 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__aux__code) ).
fof(f32781,plain,
spl573_857,
inference(avatar_split_clause,[],[f23867,f32779]) ).
fof(f32779,plain,
( spl573_857
<=> ! [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,[spl573_857])]) ).
fof(f23867,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,[],[f17497,f17563]) ).
fof(f17497,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X0))),
inference(cnf_transformation,[],[f5678]) ).
fof(f5678,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X1,X0))),
inference(rectify,[],[f4870]) ).
fof(f4870,axiom,
! [X115,X116] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(X116,X115))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__upt) ).
fof(f32777,plain,
spl573_856,
inference(avatar_split_clause,[],[f23772,f32775]) ).
fof(f32775,plain,
( spl573_856
<=> ! [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,[spl573_856])]) ).
fof(f23772,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,[],[f16966,f17079]) ).
fof(f17079,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,[],[f5347]) ).
fof(f5347,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,[],[f3922]) ).
fof(f3922,axiom,
! [X7] : c_Relation_OId(X7) = c_Transitive__Closure_Ortrancl(X7,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__empty) ).
fof(f16966,plain,
! [X0] : c_Relation_Osingle__valued(X0,X0,c_Relation_OId(X0)),
inference(cnf_transformation,[],[f5234]) ).
fof(f5234,plain,
! [X0] : c_Relation_Osingle__valued(X0,X0,c_Relation_OId(X0)),
inference(rectify,[],[f4016]) ).
fof(f4016,axiom,
! [X7] : c_Relation_Osingle__valued(X7,X7,c_Relation_OId(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id) ).
fof(f32773,plain,
spl573_855,
inference(avatar_split_clause,[],[f23156,f32771]) ).
fof(f32771,plain,
( spl573_855
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| X0 = X3
| ~ sP77(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_855])]) ).
fof(f23156,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X0 = X3
| ~ sP77(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16463]) ).
fof(f16463,plain,
! [X0,X1,X2,X3] :
( ( sP77(X0,X1,X2,X3)
| ( ( X0 != X1
| X2 != X3 )
& ( X0 != X3
| X1 != X2 ) ) )
& ( ( X0 = X1
& X2 = X3 )
| ( X0 = X3
& X1 = X2 )
| ~ sP77(X0,X1,X2,X3) ) ),
inference(rectify,[],[f16462]) ).
fof(f16462,plain,
! [X2,X1,X3,X0] :
( ( sP77(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP77(X2,X1,X3,X0) ) ),
inference(flattening,[],[f16461]) ).
fof(f16461,plain,
! [X2,X1,X3,X0] :
( ( sP77(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP77(X2,X1,X3,X0) ) ),
inference(nnf_transformation,[],[f14481]) ).
fof(f14481,plain,
! [X2,X1,X3,X0] :
( sP77(X2,X1,X3,X0)
<=> ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP77])]) ).
fof(f32769,plain,
spl573_854,
inference(avatar_split_clause,[],[f23155,f32767]) ).
fof(f32767,plain,
( spl573_854
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| X1 = X2
| ~ sP77(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_854])]) ).
fof(f23155,plain,
! [X2,X3,X0,X1] :
( X0 = X1
| X1 = X2
| ~ sP77(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16463]) ).
fof(f32765,plain,
spl573_853,
inference(avatar_split_clause,[],[f23154,f32763]) ).
fof(f32763,plain,
( spl573_853
<=> ! [X0,X3,X2,X1] :
( X2 = X3
| X0 = X3
| ~ sP77(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_853])]) ).
fof(f23154,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X0 = X3
| ~ sP77(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16463]) ).
fof(f32761,plain,
spl573_852,
inference(avatar_split_clause,[],[f23153,f32759]) ).
fof(f32759,plain,
( spl573_852
<=> ! [X2,X0,X1,X3] :
( X2 = X3
| X1 = X2
| ~ sP77(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_852])]) ).
fof(f23153,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| X1 = X2
| ~ sP77(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16463]) ).
fof(f32757,plain,
spl573_851,
inference(avatar_split_clause,[],[f21766,f32755]) ).
fof(f32755,plain,
( spl573_851
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X1,sK373(X0,X1,X2)))
| ~ sP50(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_851])]) ).
fof(f21766,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X1,sK373(X0,X1,X2)))
| ~ sP50(X0,X1,X2) ),
inference(cnf_transformation,[],[f15866]) ).
fof(f15866,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Set_Oinsert(X0),sK372(X0,X1,X2)),sK373(X0,X1,X2))))
& hBOOL(hAPP(X1,sK373(X0,X1,X2)))
& ~ hBOOL(hAPP(hAPP(c_member(X0),sK372(X0,X1,X2)),sK373(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK372(X0,X1,X2)),X2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X0),sK373(X0,X1,X2))) )
| ~ sP50(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK372,sK373])],[f15864,f15865]) ).
fof(f15865,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),sK372(X0,X1,X2)),sK373(X0,X1,X2))))
& hBOOL(hAPP(X1,sK373(X0,X1,X2)))
& ~ hBOOL(hAPP(hAPP(c_member(X0),sK372(X0,X1,X2)),sK373(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK372(X0,X1,X2)),X2))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X0),sK373(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15864,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)) )
| ~ sP50(X0,X1,X2) ),
inference(rectify,[],[f15863]) ).
fof(f15863,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)) )
| ~ sP50(X3,X0,X1) ),
inference(nnf_transformation,[],[f14431]) ).
fof(f14431,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)) )
| ~ sP50(X3,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP50])]) ).
fof(f32753,plain,
spl573_850,
inference(avatar_split_clause,[],[f21725,f32751]) ).
fof(f32751,plain,
( spl573_850
<=> ! [X0,X3,X2,X1] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X1),X2,X0,X2)
| hBOOL(hAPP(X3,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_850])]) ).
fof(f21725,plain,
! [X2,X3,X0,X1] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X1),X2,X0,X2)
| hBOOL(hAPP(X3,X2)) ),
inference(cnf_transformation,[],[f13072]) ).
fof(f13072,plain,
! [X0,X1,X2,X3] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X1),X2,X0,X2)
| hBOOL(hAPP(X3,X2)) ),
inference(ennf_transformation,[],[f8760]) ).
fof(f8760,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(X3,X2))
=> c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X1),X2,X0,X2) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X6,X4,X26,X27] :
( ~ hBOOL(hAPP(X27,X26))
=> c_Natural_Oevaln(c_Com_Ocom_OWhile(X27,X4),X26,X6,X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OWhileFalse) ).
fof(f32749,plain,
spl573_849,
inference(avatar_split_clause,[],[f21090,f32747]) ).
fof(f32747,plain,
( spl573_849
<=> ! [X0,X3,X2,X1] : c_Fun_Ooverride__on(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_849])]) ).
fof(f21090,plain,
! [X2,X3,X0,X1] : c_Fun_Ooverride__on(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) = X1,
inference(cnf_transformation,[],[f8194]) ).
fof(f8194,plain,
! [X0,X1,X2,X3] : c_Fun_Ooverride__on(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) = X1,
inference(rectify,[],[f3676]) ).
fof(f3676,axiom,
! [X0,X1,X58,X7] : c_Fun_Ooverride__on(X7,X58,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_override__on__emptyset) ).
fof(f32745,plain,
spl573_848,
inference(avatar_split_clause,[],[f21088,f32743]) ).
fof(f32743,plain,
( spl573_848
<=> ! [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,[spl573_848])]) ).
fof(f21088,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0) = c_Nat_Onat_Onat__case(X3,X2,X1,hAPP(c_Nat_OSuc,X0)),
inference(cnf_transformation,[],[f8192]) ).
fof(f8192,plain,
! [X0,X1,X2,X3] : hAPP(X1,X0) = c_Nat_Onat_Onat__case(X3,X2,X1,hAPP(c_Nat_OSuc,X0)),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X63,X70,X57,X7] : c_Nat_Onat_Onat__case(X7,X57,X70,hAPP(c_Nat_OSuc,X63)) = hAPP(X70,X63),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
fof(f32741,plain,
spl573_847,
inference(avatar_split_clause,[],[f21087,f32739]) ).
fof(f32739,plain,
( spl573_847
<=> ! [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,[spl573_847])]) ).
fof(f21087,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,[],[f8191]) ).
fof(f8191,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,[],[f2761]) ).
fof(f2761,axiom,
! [X124,X99,X58,X7] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X7,tc_fun(X58,tc_HOL_Obool))),X99),X124)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot2E) ).
fof(f32737,plain,
spl573_846,
inference(avatar_split_clause,[],[f21083,f32735]) ).
fof(f32735,plain,
( spl573_846
<=> ! [X0,X3,X2,X1] : hAPP(c_Sum__Type_OInr(X3,X2),X1) != hAPP(c_Sum__Type_OInl(X2,X3),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_846])]) ).
fof(f21083,plain,
! [X2,X3,X0,X1] : hAPP(c_Sum__Type_OInr(X3,X2),X1) != hAPP(c_Sum__Type_OInl(X2,X3),X0),
inference(cnf_transformation,[],[f8187]) ).
fof(f8187,plain,
! [X0,X1,X2,X3] : hAPP(c_Sum__Type_OInr(X3,X2),X1) != hAPP(c_Sum__Type_OInl(X2,X3),X0),
inference(rectify,[],[f249]) ).
fof(f249,axiom,
! [X109,X110,X111,X112] : hAPP(c_Sum__Type_OInr(X112,X111),X110) != hAPP(c_Sum__Type_OInl(X111,X112),X109),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I4_J) ).
fof(f32733,plain,
spl573_845,
inference(avatar_split_clause,[],[f20861,f32731]) ).
fof(f32731,plain,
( spl573_845
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK339(X0,X1,X2)))
| ~ sP41(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_845])]) ).
fof(f20861,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X0,sK339(X0,X1,X2)))
| ~ sP41(X0,X1,X2) ),
inference(cnf_transformation,[],[f15629]) ).
fof(f15629,plain,
! [X0,X1,X2] :
( ( sP41(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,sK339(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,sK339(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),sK339(X0,X1,X2))),X2)) )
| ~ sP41(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK339])],[f15627,f15628]) ).
fof(f15628,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,sK339(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,sK339(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),sK339(X0,X1,X2))),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15627,plain,
! [X0,X1,X2] :
( ( sP41(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)) )
| ~ sP41(X0,X1,X2) ) ),
inference(rectify,[],[f15626]) ).
fof(f15626,plain,
! [X2,X0,X1] :
( ( sP41(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)) )
| ~ sP41(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f14415]) ).
fof(f14415,plain,
! [X2,X0,X1] :
( sP41(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,[sP41])]) ).
fof(f32729,plain,
spl573_844,
inference(avatar_split_clause,[],[f20854,f32727]) ).
fof(f32727,plain,
( spl573_844
<=> ! [X2,X0,X1] :
( sP40(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK337(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_844])]) ).
fof(f20854,plain,
! [X2,X0,X1] :
( sP40(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK337(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15623]) ).
fof(f15623,plain,
! [X0,X1,X2] :
( ( sP40(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK337(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK337(X0,X1,X2))),sK338(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK338(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
| ~ sP40(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK337,sK338])],[f15621,f15622]) ).
fof(f15622,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,sK337(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK337(X0,X1,X2))),sK338(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK338(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15621,plain,
! [X0,X1,X2] :
( ( sP40(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
| ~ sP40(X0,X1,X2) ) ),
inference(rectify,[],[f15620]) ).
fof(f15620,plain,
! [X2,X1,X0] :
( ( sP40(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
| ~ sP40(X2,X1,X0) ) ),
inference(flattening,[],[f15619]) ).
fof(f15619,plain,
! [X2,X1,X0] :
( ( sP40(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
| ~ sP40(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14413]) ).
fof(f14413,plain,
! [X2,X1,X0] :
( sP40(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,[sP40])]) ).
fof(f32725,plain,
spl573_843,
inference(avatar_split_clause,[],[f20847,f32723]) ).
fof(f32723,plain,
( spl573_843
<=> ! [X2,X0,X1] :
( sP37(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK335(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_843])]) ).
fof(f20847,plain,
! [X2,X0,X1] :
( sP37(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK335(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15617]) ).
fof(f32721,plain,
spl573_842,
inference(avatar_split_clause,[],[f20841,f32719]) ).
fof(f32719,plain,
( spl573_842
<=> ! [X2,X0,X1] :
( sP38(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK333(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_842])]) ).
fof(f20841,plain,
! [X2,X0,X1] :
( sP38(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK333(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15611]) ).
fof(f32717,plain,
spl573_841,
inference(avatar_split_clause,[],[f20773,f32715]) ).
fof(f32715,plain,
( spl573_841
<=> ! [X2,X0,X1] :
( sP35(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_841])]) ).
fof(f20773,plain,
! [X2,X0,X1] :
( sP35(X2,X1,X0)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0))) ),
inference(cnf_transformation,[],[f15567]) ).
fof(f15567,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
| ~ sP35(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP35(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,[],[f15566]) ).
fof(f15566,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
| ~ sP35(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) )
& ( ( sP35(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,[],[f14406]) ).
fof(f14406,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)))
<=> ( sP35(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ) ),
inference(definition_folding,[],[f12524,f14405]) ).
fof(f14405,plain,
! [X2,X1,X0] :
( sP35(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,[sP35])]) ).
fof(f12524,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,[],[f12523]) ).
fof(f12523,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,[],[f8067]) ).
fof(f8067,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,[],[f978]) ).
fof(f978,axiom,
! [X94,X6,X5] :
( hBOOL(hAPP(X5,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X6,X94)))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X94
=> ! [X144,X118] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X118),X94))
=> ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X94),X144)),X118) = X6
=> hBOOL(hAPP(X5,X118)) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X94
=> hBOOL(hAPP(X5,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__mod) ).
fof(f32713,plain,
spl573_840,
inference(avatar_split_clause,[],[f20771,f32711]) ).
fof(f32711,plain,
( spl573_840
<=> ! [X2,X0,X1] :
( sP35(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK328(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_840])]) ).
fof(f20771,plain,
! [X2,X0,X1] :
( sP35(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK328(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15565]) ).
fof(f15565,plain,
! [X0,X1,X2] :
( ( sP35(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK328(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK327(X0,X1,X2))),sK328(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK328(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
| ~ sP35(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK327,sK328])],[f15563,f15564]) ).
fof(f15564,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,sK328(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK327(X0,X1,X2))),sK328(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK328(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15563,plain,
! [X0,X1,X2] :
( ( sP35(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
| ~ sP35(X0,X1,X2) ) ),
inference(rectify,[],[f15562]) ).
fof(f15562,plain,
! [X2,X1,X0] :
( ( sP35(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
| ~ sP35(X2,X1,X0) ) ),
inference(flattening,[],[f15561]) ).
fof(f15561,plain,
! [X2,X1,X0] :
( ( sP35(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
| ~ sP35(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14405]) ).
fof(f32709,plain,
spl573_839,
inference(avatar_split_clause,[],[f20766,f32707]) ).
fof(f32707,plain,
( spl573_839
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
| ~ sP34(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_839])]) ).
fof(f20766,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
| ~ sP34(X0,X1,X2) ),
inference(cnf_transformation,[],[f15560]) ).
fof(f15560,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
| ~ sP34(X0,X1,X2) )
& ( sP34(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))) ) ),
inference(nnf_transformation,[],[f14404]) ).
fof(f14404,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)))
<=> sP34(X0,X1,X2) ),
inference(definition_folding,[],[f12522,f14403,f14402,f14401]) ).
fof(f14403,plain,
! [X0,X1,X2] :
( sP34(X0,X1,X2)
<=> ( sP33(X2,X1,X0)
& sP32(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP34])]) ).
fof(f12522,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,[],[f12521]) ).
fof(f12521,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,[],[f8066]) ).
fof(f8066,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,[],[f885]) ).
fof(f885,axiom,
! [X94,X6,X5] :
( hBOOL(hAPP(X5,c_Divides_Odiv__class_Omod(tc_Int_Oint,X6,X94)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ! [X144,X118] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X144)),X118) = X6
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X118),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X94),X118)) )
=> hBOOL(hAPP(X5,X118)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X94))
=> ! [X144,X118] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X94),X144)),X118) = X6
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X118),X94))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X118)) )
=> hBOOL(hAPP(X5,X118)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X94
=> hBOOL(hAPP(X5,X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__zmod) ).
fof(f32705,plain,
spl573_838,
inference(avatar_split_clause,[],[f20765,f32703]) ).
fof(f32703,plain,
( spl573_838
<=> ! [X2,X0,X1] :
( sP34(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_838])]) ).
fof(f20765,plain,
! [X2,X0,X1] :
( sP34(X0,X1,X2)
| ~ hBOOL(hAPP(X2,c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))) ),
inference(cnf_transformation,[],[f15560]) ).
fof(f32701,plain,
spl573_837,
inference(avatar_split_clause,[],[f20764,f32699]) ).
fof(f32699,plain,
( spl573_837
<=> ! [X2,X0,X1] :
( sP32(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK326(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_837])]) ).
fof(f20764,plain,
! [X2,X0,X1] :
( sP32(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK326(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15559]) ).
fof(f32697,plain,
spl573_836,
inference(avatar_split_clause,[],[f20758,f32695]) ).
fof(f32695,plain,
( spl573_836
<=> ! [X2,X0,X1] :
( sP33(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK324(X0,X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_836])]) ).
fof(f20758,plain,
! [X2,X0,X1] :
( sP33(X0,X1,X2)
| ~ hBOOL(hAPP(X0,sK324(X0,X1,X2))) ),
inference(cnf_transformation,[],[f15554]) ).
fof(f32693,plain,
spl573_835,
inference(avatar_split_clause,[],[f20635,f32691]) ).
fof(f32691,plain,
( spl573_835
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
| ~ sP27(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_835])]) ).
fof(f20635,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1))
| ~ sP27(X0,X1,X2) ),
inference(cnf_transformation,[],[f15443]) ).
fof(f15443,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1)) )
| ~ sP27(X0,X1,X2) ),
inference(rectify,[],[f15442]) ).
fof(f15442,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) )
| ~ sP27(X2,X1,X0) ),
inference(nnf_transformation,[],[f14392]) ).
fof(f14392,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) )
| ~ sP27(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP27])]) ).
fof(f32689,plain,
spl573_834,
inference(avatar_split_clause,[],[f20370,f32687]) ).
fof(f32687,plain,
( spl573_834
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X0))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_834])]) ).
fof(f20370,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X0))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X1,X0))) ),
inference(cnf_transformation,[],[f12235]) ).
fof(f12235,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Com_OWT,X0))
& hBOOL(hAPP(c_Com_OWT,X1)) )
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X1,X0))) ),
inference(ennf_transformation,[],[f7855]) ).
fof(f7855,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X1,X0)))
=> ~ ( hBOOL(hAPP(c_Com_OWT,X1))
=> ~ hBOOL(hAPP(c_Com_OWT,X0)) ) ),
inference(rectify,[],[f59]) ).
fof(f59,axiom,
! [X29,X25,X27] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X27,X25,X29)))
=> ~ ( hBOOL(hAPP(c_Com_OWT,X25))
=> ~ hBOOL(hAPP(c_Com_OWT,X29)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I5_J) ).
fof(f32685,plain,
spl573_833,
inference(avatar_split_clause,[],[f20369,f32683]) ).
fof(f32683,plain,
( spl573_833
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_833])]) ).
fof(f20369,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(X2,X1,X0))) ),
inference(cnf_transformation,[],[f12235]) ).
fof(f32681,plain,
spl573_832,
inference(avatar_split_clause,[],[f20367,f32679]) ).
fof(f32679,plain,
( spl573_832
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X0))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X2,X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_832])]) ).
fof(f20367,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X0))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X2,X1,X0))) ),
inference(cnf_transformation,[],[f12233]) ).
fof(f12233,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Com_OWT,X0))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X2,X1,X0))) ),
inference(ennf_transformation,[],[f7853]) ).
fof(f7853,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X2,X1,X0)))
=> hBOOL(hAPP(c_Com_OWT,X0)) ),
inference(rectify,[],[f61]) ).
fof(f61,axiom,
! [X4,X76,X77] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X77,X76,X4)))
=> hBOOL(hAPP(c_Com_OWT,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I3_J) ).
fof(f32677,plain,
spl573_831,
inference(avatar_split_clause,[],[f20204,f32675]) ).
fof(f32675,plain,
( spl573_831
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X1,X0,X2)))
| ~ hBOOL(hAPP(c_Com_OWT,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_831])]) ).
fof(f20204,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X1,X0,X2)))
| ~ hBOOL(hAPP(c_Com_OWT,X2)) ),
inference(cnf_transformation,[],[f12064]) ).
fof(f12064,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X1,X0,X2)))
| ~ hBOOL(hAPP(c_Com_OWT,X2)) ),
inference(ennf_transformation,[],[f7732]) ).
fof(f7732,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Com_OWT,X2))
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X1,X0,X2))) ),
inference(rectify,[],[f69]) ).
fof(f69,axiom,
! [X76,X77,X4] :
( hBOOL(hAPP(c_Com_OWT,X4))
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(X77,X76,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OLocal) ).
fof(f32673,plain,
spl573_830,
inference(avatar_split_clause,[],[f20179,f32671]) ).
fof(f32671,plain,
( spl573_830
<=> ! [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,[spl573_830])]) ).
fof(f20179,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,[],[f12034]) ).
fof(f12034,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,[],[f7708]) ).
fof(f7708,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,[],[f3783]) ).
fof(f3783,axiom,
! [X6,X169,X7] :
( c_Wellfounded_Owf(X7,X169)
=> c_Wellfounded_Owf(tc_List_Olist(X7),hAPP(c_List_Olexn(X7,X169),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lexn) ).
fof(f32669,plain,
spl573_829,
inference(avatar_split_clause,[],[f19857,f32667]) ).
fof(f32667,plain,
( spl573_829
<=> ! [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,[spl573_829])]) ).
fof(f19857,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,[],[f11632]) ).
fof(f11632,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,[],[f11631]) ).
fof(f11631,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,[],[f7469]) ).
fof(f7469,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,[],[f4871]) ).
fof(f4871,axiom,
! [X88,X290,X13] :
( class_Orderings_Olinorder(X13)
=> ( c_List_Olinorder__class_Osorted(X13,X290)
=> c_List_Olinorder__class_Osorted(X13,c_List_Oremove1(X13,X88,X290)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__remove1) ).
fof(f32665,plain,
spl573_828,
inference(avatar_split_clause,[],[f19856,f32663]) ).
fof(f32663,plain,
( spl573_828
<=> ! [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,[spl573_828])]) ).
fof(f19856,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,[],[f11630]) ).
fof(f11630,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,[],[f11629]) ).
fof(f11629,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,[],[f7468]) ).
fof(f7468,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,[],[f4973]) ).
fof(f4973,axiom,
! [X5,X283,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,X283)
=> c_List_Olinorder__class_Osorted(X7,c_List_OtakeWhile(X7,X5,X283)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__takeWhile) ).
fof(f32661,plain,
spl573_827,
inference(avatar_split_clause,[],[f19723,f32659]) ).
fof(f32659,plain,
( spl573_827
<=> ! [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,[spl573_827])]) ).
fof(f19723,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,[],[f11449]) ).
fof(f11449,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,[],[f7343]) ).
fof(f7343,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,[],[f2475]) ).
fof(f2475,axiom,
! [X99,X58,X7] :
( class_Orderings_Obot(X7)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X58,X7)),X99) = c_Orderings_Obot__class_Obot(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__fun__def) ).
fof(f32657,plain,
spl573_826,
inference(avatar_split_clause,[],[f19686,f32655]) ).
fof(f32655,plain,
( spl573_826
<=> ! [X2,X0,X1] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X0) = c_Orderings_Otop__class_Otop(X2)
| ~ class_Orderings_Otop(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_826])]) ).
fof(f19686,plain,
! [X2,X0,X1] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X0) = c_Orderings_Otop__class_Otop(X2)
| ~ class_Orderings_Otop(X2) ),
inference(cnf_transformation,[],[f11416]) ).
fof(f11416,plain,
! [X0,X1,X2] :
( hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X0) = c_Orderings_Otop__class_Otop(X2)
| ~ class_Orderings_Otop(X2) ),
inference(ennf_transformation,[],[f7318]) ).
fof(f7318,plain,
! [X0,X1,X2] :
( class_Orderings_Otop(X2)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,X2)),X0) = c_Orderings_Otop__class_Otop(X2) ),
inference(rectify,[],[f2420]) ).
fof(f2420,axiom,
! [X99,X58,X7] :
( class_Orderings_Otop(X7)
=> hAPP(c_Orderings_Otop__class_Otop(tc_fun(X58,X7)),X99) = c_Orderings_Otop__class_Otop(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__apply) ).
fof(f32653,plain,
spl573_825,
inference(avatar_split_clause,[],[f19226,f32651]) ).
fof(f32651,plain,
( spl573_825
<=> ! [X2,X0,X1] : hAPP(c_Relation_Oconverse(X2,X1),hAPP(c_Relation_Oconverse(X1,X2),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_825])]) ).
fof(f19226,plain,
! [X2,X0,X1] : hAPP(c_Relation_Oconverse(X2,X1),hAPP(c_Relation_Oconverse(X1,X2),X0)) = X0,
inference(cnf_transformation,[],[f6908]) ).
fof(f6908,plain,
! [X0,X1,X2] : hAPP(c_Relation_Oconverse(X2,X1),hAPP(c_Relation_Oconverse(X1,X2),X0)) = X0,
inference(rectify,[],[f3961]) ).
fof(f3961,axiom,
! [X169,X7,X58] : hAPP(c_Relation_Oconverse(X58,X7),hAPP(c_Relation_Oconverse(X7,X58),X169)) = X169,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__converse) ).
fof(f32649,plain,
spl573_824,
inference(avatar_split_clause,[],[f19225,f32647]) ).
fof(f32647,plain,
( spl573_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,[spl573_824])]) ).
fof(f19225,plain,
! [X2,X0,X1] : hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X0,
inference(cnf_transformation,[],[f6907]) ).
fof(f6907,plain,
! [X0,X1,X2] : hAPP(c_List_Otl(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X0,
inference(rectify,[],[f4693]) ).
fof(f4693,axiom,
! [X290,X61,X13] : hAPP(c_List_Otl(X13),hAPP(hAPP(c_List_Olist_OCons(X13),X61),X290)) = X290,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl_Osimps_I2_J) ).
fof(f32645,plain,
spl573_823,
inference(avatar_split_clause,[],[f19224,f32643]) ).
fof(f32643,plain,
( spl573_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,[spl573_823])]) ).
fof(f19224,plain,
! [X2,X0,X1] : hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X1,
inference(cnf_transformation,[],[f6906]) ).
fof(f6906,plain,
! [X0,X1,X2] : hAPP(c_List_Ohd(X2),hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0)) = X1,
inference(rectify,[],[f4680]) ).
fof(f4680,axiom,
! [X290,X61,X13] : hAPP(c_List_Ohd(X13),hAPP(hAPP(c_List_Olist_OCons(X13),X61),X290)) = X61,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hd_Osimps) ).
fof(f32641,plain,
spl573_822,
inference(avatar_split_clause,[],[f19222,f32639]) ).
fof(f32639,plain,
( spl573_822
<=> ! [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,[spl573_822])]) ).
fof(f19222,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,[],[f6904]) ).
fof(f6904,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,[],[f4515]) ).
fof(f4515,axiom,
! [X60,X116,X13] : c_List_Olist_ONil(X13) = hAPP(hAPP(c_List_Olist__update(X13,c_List_Olist_ONil(X13)),X116),X60),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__update__code_I1_J) ).
fof(f32637,plain,
spl573_821,
inference(avatar_split_clause,[],[f19221,f32635]) ).
fof(f32635,plain,
( spl573_821
<=> ! [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,[spl573_821])]) ).
fof(f19221,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,[],[f6903]) ).
fof(f6903,plain,
! [X0,X1,X2] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Omap(X2,X1),X0),c_List_Olist_ONil(X2)),
inference(rectify,[],[f4446]) ).
fof(f4446,axiom,
! [X1,X7,X58] : c_List_Olist_ONil(X7) = hAPP(hAPP(c_List_Omap(X58,X7),X1),c_List_Olist_ONil(X58)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map_Osimps_I1_J) ).
fof(f32633,plain,
spl573_820,
inference(avatar_split_clause,[],[f19220,f32631]) ).
fof(f32631,plain,
( spl573_820
<=> ! [X2,X0,X1] : c_Option_Ooption_ONone(X1) = hAPP(hAPP(c_Option_Omap(X2,X1),X0),c_Option_Ooption_ONone(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_820])]) ).
fof(f19220,plain,
! [X2,X0,X1] : c_Option_Ooption_ONone(X1) = hAPP(hAPP(c_Option_Omap(X2,X1),X0),c_Option_Ooption_ONone(X2)),
inference(cnf_transformation,[],[f6902]) ).
fof(f6902,plain,
! [X0,X1,X2] : c_Option_Ooption_ONone(X1) = hAPP(hAPP(c_Option_Omap(X2,X1),X0),c_Option_Ooption_ONone(X2)),
inference(rectify,[],[f4300]) ).
fof(f4300,axiom,
! [X1,X7,X58] : c_Option_Ooption_ONone(X7) = hAPP(hAPP(c_Option_Omap(X58,X7),X1),c_Option_Ooption_ONone(X58)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option__map__None) ).
fof(f32629,plain,
spl573_819,
inference(avatar_split_clause,[],[f19218,f32627]) ).
fof(f32627,plain,
( spl573_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,[spl573_819])]) ).
fof(f19218,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,[],[f6900]) ).
fof(f6900,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,[],[f2459]) ).
fof(f2459,axiom,
! [X148,X76,X7] : c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(X7),X76),X148),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__not__empty) ).
fof(f32625,plain,
spl573_818,
inference(avatar_split_clause,[],[f18801,f32623]) ).
fof(f32623,plain,
( spl573_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,[spl573_818])]) ).
fof(f18801,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != hAPP(c_List_Orev(X1),X0) ),
inference(cnf_transformation,[],[f14865]) ).
fof(f14865,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,[],[f6720]) ).
fof(f6720,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = hAPP(c_List_Orev(X1),X0)
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f4919]) ).
fof(f4919,axiom,
! [X283,X7] :
( c_List_Olist_ONil(X7) = hAPP(c_List_Orev(X7),X283)
<=> c_List_Olist_ONil(X7) = X283 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nil__is__rev__conv) ).
fof(f32621,plain,
spl573_817,
inference(avatar_split_clause,[],[f18799,f32619]) ).
fof(f32619,plain,
( spl573_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,[spl573_817])]) ).
fof(f18799,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != hAPP(c_List_Orotate1(X1),X0) ),
inference(cnf_transformation,[],[f14864]) ).
fof(f14864,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,[],[f6719]) ).
fof(f6719,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),X0)
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f4658]) ).
fof(f4658,axiom,
! [X283,X7] :
( c_List_Olist_ONil(X7) = hAPP(c_List_Orotate1(X7),X283)
<=> c_List_Olist_ONil(X7) = X283 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__is__Nil__conv) ).
fof(f32617,plain,
spl573_816,
inference(avatar_split_clause,[],[f18786,f32615]) ).
fof(f32615,plain,
( spl573_816
<=> ! [X0,X1] :
( hBOOL(hAPP(X1,sK169(X1)))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_816])]) ).
fof(f18786,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,sK169(X1)))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ),
inference(cnf_transformation,[],[f14851]) ).
fof(f14851,plain,
! [X0,X1] :
( ( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ! [X2] : ~ hBOOL(hAPP(X1,X2)) )
& ( hBOOL(hAPP(X1,sK169(X1)))
| ~ hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK169])],[f14849,f14850]) ).
fof(f14850,plain,
! [X1] :
( ? [X3] : hBOOL(hAPP(X1,X3))
=> hBOOL(hAPP(X1,sK169(X1))) ),
introduced(choice_axiom,[]) ).
fof(f14849,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,[],[f14848]) ).
fof(f14848,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,[],[f6713]) ).
fof(f6713,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
<=> ? [X2] : hBOOL(hAPP(X1,X2)) ),
inference(rectify,[],[f3852]) ).
fof(f3852,axiom,
! [X7,X5] :
( hBOOL(hAPP(X5,c_Hilbert__Choice_OEps(X7,X5)))
<=> ? [X138] : hBOOL(hAPP(X5,X138)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__eq__ex) ).
fof(f32613,plain,
spl573_815,
inference(avatar_split_clause,[],[f18716,f32611]) ).
fof(f32611,plain,
( spl573_815
<=> ! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK153(X0,X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_815])]) ).
fof(f18716,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK153(X0,X1))) ),
inference(cnf_transformation,[],[f14785]) ).
fof(f14785,plain,
! [X0,X1] :
( ( c_Wellfounded_OwfP(X1,X0)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK153(X0,X1))) )
& ( ! [X3] : hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK153])],[f14783,f14784]) ).
fof(f14784,plain,
! [X0,X1] :
( ? [X2] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2))
=> ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK153(X0,X1))) ),
introduced(choice_axiom,[]) ).
fof(f14783,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,[],[f14782]) ).
fof(f14782,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,[],[f6693]) ).
fof(f6693,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
<=> ! [X2] : hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) ),
inference(rectify,[],[f3807]) ).
fof(f3807,axiom,
! [X169,X7] :
( c_Wellfounded_OwfP(X7,X169)
<=> ! [X138] : hBOOL(hAPP(c_Wellfounded_Oaccp(X7,X169),X138)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).
fof(f32609,plain,
spl573_814,
inference(avatar_split_clause,[],[f18688,f32607]) ).
fof(f32607,plain,
( spl573_814
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != sK149(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_814])]) ).
fof(f18688,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != sK149(X0,X1) ),
inference(cnf_transformation,[],[f14764]) ).
fof(f14764,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != sK149(X0,X1)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),sK149(X0,X1)),hAPP(c_Relation_OImage(X1,X1,X0),sK149(X0,X1)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK149])],[f11230,f14763]) ).
fof(f14763,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)) != sK149(X0,X1)
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),sK149(X0,X1)),hAPP(c_Relation_OImage(X1,X1,X0),sK149(X0,X1)))) ) ),
introduced(choice_axiom,[]) ).
fof(f11230,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,[],[f6677]) ).
fof(f6677,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,[],[f3859]) ).
fof(f3859,axiom,
! [X189,X7] :
( ! [X227] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X227),hAPP(c_Relation_OImage(X7,X7,X189),X227)))
=> c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = X227 )
=> c_Wellfounded_Owf(X7,X189) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfI__pf) ).
fof(f32605,plain,
spl573_813,
inference(avatar_split_clause,[],[f18686,f32603]) ).
fof(f32603,plain,
( spl573_813
<=> ! [X0,X1] :
( hBOOL(hAPP(X1,X0))
| ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,sK148(X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_813])]) ).
fof(f18686,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,X0))
| ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,sK148(X1)))) ),
inference(cnf_transformation,[],[f14762]) ).
fof(f14762,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,X0))
| ( ~ hBOOL(hAPP(X1,hAPP(c_Int_OAbs__Integ,sK148(X1))))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK148(X1)),c_Int_OInteg)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK148])],[f11229,f14761]) ).
fof(f14761,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,sK148(X1))))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK148(X1)),c_Int_OInteg)) ) ),
introduced(choice_axiom,[]) ).
fof(f11229,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,[],[f6676]) ).
fof(f6676,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,[],[f3842]) ).
fof(f3842,axiom,
! [X99,X5] :
( ! [X113] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X113),c_Int_OInteg))
=> hBOOL(hAPP(X5,hAPP(c_Int_OAbs__Integ,X113))) )
=> hBOOL(hAPP(X5,X99)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Abs__Integ__induct) ).
fof(f32601,plain,
spl573_812,
inference(avatar_split_clause,[],[f18633,f32599]) ).
fof(f32599,plain,
( spl573_812
<=> ! [X0,X1] :
( ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(X0)))
| ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_812])]) ).
fof(f18633,plain,
! [X0,X1] :
( ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(X0)))
| ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(cnf_transformation,[],[f11168]) ).
fof(f11168,plain,
! [X0,X1] :
( ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(X0)))
| ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(flattening,[],[f11167]) ).
fof(f11167,plain,
! [X0,X1] :
( ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(X0)))
| ~ class_Int_Oring__char__0(X1)
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f6643]) ).
fof(f6643,plain,
! [X0,X1] :
( ( class_Int_Oring__char__0(X1)
& class_Int_Onumber__ring(X1) )
=> ~ c_Int_Oiszero(X1,hAPP(c_Int_Onumber__class_Onumber__of(X1),c_Int_OBit1(X0))) ),
inference(rectify,[],[f1404]) ).
fof(f1404,axiom,
! [X128,X13] :
( ( class_Int_Oring__char__0(X13)
& class_Int_Onumber__ring(X13) )
=> ~ c_Int_Oiszero(X13,hAPP(c_Int_Onumber__class_Onumber__of(X13),c_Int_OBit1(X128))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__number__of__Bit1) ).
fof(f32597,plain,
spl573_811,
inference(avatar_split_clause,[],[f18325,f32595]) ).
fof(f32595,plain,
( spl573_811
<=> ! [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,[spl573_811])]) ).
fof(f18325,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,[],[f10826]) ).
fof(f10826,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,[],[f10825]) ).
fof(f10825,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,[],[f6388]) ).
fof(f6388,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,[],[f1579]) ).
fof(f1579,axiom,
! [X60,X61] :
( c_Nat__Transfer_Ois__nat(X61)
=> ( c_Nat__Transfer_Ois__nat(X60)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X61),X60)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) ).
fof(f32593,plain,
spl573_810,
inference(avatar_split_clause,[],[f18324,f32591]) ).
fof(f32591,plain,
( spl573_810
<=> ! [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,[spl573_810])]) ).
fof(f18324,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,[],[f10824]) ).
fof(f10824,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,[],[f10823]) ).
fof(f10823,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,[],[f6387]) ).
fof(f6387,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,[],[f1576]) ).
fof(f1576,axiom,
! [X60,X61] :
( c_Nat__Transfer_Ois__nat(X61)
=> ( c_Nat__Transfer_Ois__nat(X60)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),X60)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) ).
fof(f32589,plain,
spl573_809,
inference(avatar_split_clause,[],[f18323,f32587]) ).
fof(f32587,plain,
( spl573_809
<=> ! [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,[spl573_809])]) ).
fof(f18323,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,[],[f10822]) ).
fof(f10822,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,[],[f10821]) ).
fof(f10821,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,[],[f6386]) ).
fof(f6386,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,[],[f1581]) ).
fof(f1581,axiom,
! [X60,X61] :
( c_Nat__Transfer_Ois__nat(X61)
=> ( c_Nat__Transfer_Ois__nat(X60)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X61),X60)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I1_J) ).
fof(f32585,plain,
spl573_808,
inference(avatar_split_clause,[],[f18315,f32583]) ).
fof(f32583,plain,
( spl573_808
<=> ! [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,[spl573_808])]) ).
fof(f18315,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,[],[f10810]) ).
fof(f10810,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,[],[f10809]) ).
fof(f10809,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,[],[f6379]) ).
fof(f6379,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,[],[f2708]) ).
fof(f2708,axiom,
! [X99,X148] :
( c_Nat__Transfer_Onat__set(X148)
=> ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X99),X148))
=> c_Nat__Transfer_Ois__nat(X99) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) ).
fof(f32581,plain,
spl573_807,
inference(avatar_split_clause,[],[f18251,f32579]) ).
fof(f32579,plain,
( spl573_807
<=> ! [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,[spl573_807])]) ).
fof(f18251,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,[],[f10728]) ).
fof(f10728,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,[],[f10727]) ).
fof(f10727,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,[],[f6326]) ).
fof(f6326,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,[],[f4878]) ).
fof(f4878,axiom,
! [X290,X13] :
( class_Orderings_Olinorder(X13)
=> ( c_List_Olinorder__class_Osorted(X13,X290)
=> c_List_Olinorder__class_Osorted(X13,hAPP(c_List_Otl(X13),X290)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__tl) ).
fof(f32577,plain,
spl573_806,
inference(avatar_split_clause,[],[f18240,f32575]) ).
fof(f32575,plain,
( spl573_806
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_806])]) ).
fof(f18240,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,[],[f10716]) ).
fof(f10716,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,[],[f6315]) ).
fof(f6315,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,[],[f4843]) ).
fof(f4843,axiom,
! [X61,X13] :
( class_Orderings_Olinorder(X13)
=> c_List_Olinorder__class_Osorted(X13,hAPP(hAPP(c_List_Olist_OCons(X13),X61),c_List_Olist_ONil(X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__single) ).
fof(f32573,plain,
spl573_805,
inference(avatar_split_clause,[],[f18232,f32571]) ).
fof(f32571,plain,
( spl573_805
<=> ! [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,[spl573_805])]) ).
fof(f18232,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,[],[f10707]) ).
fof(f10707,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,[],[f6307]) ).
fof(f6307,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,[],[f200]) ).
fof(f200,axiom,
! [X88,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),c_Groups_Ozero__class_Ozero(X13)),X88) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0) ).
fof(f32569,plain,
spl573_804,
inference(avatar_split_clause,[],[f18231,f32567]) ).
fof(f32567,plain,
( spl573_804
<=> ! [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,[spl573_804])]) ).
fof(f18231,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,[],[f10706]) ).
fof(f10706,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,[],[f6306]) ).
fof(f6306,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,[],[f204]) ).
fof(f204,axiom,
! [X88,X13] :
( class_Groups_Ocomm__monoid__add(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X88),c_Groups_Ozero__class_Ozero(X13)) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add_Ocomm__neutral) ).
fof(f32565,plain,
spl573_803,
inference(avatar_split_clause,[],[f18220,f32563]) ).
fof(f32563,plain,
( spl573_803
<=> ! [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,[spl573_803])]) ).
fof(f18220,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,[],[f10693]) ).
fof(f10693,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,[],[f6295]) ).
fof(f6295,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,[],[f443]) ).
fof(f443,axiom,
! [X88,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),c_Groups_Oone__class_Oone(X13)),X88) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).
fof(f32561,plain,
( spl573_802
| ~ spl573_569
| ~ spl573_709 ),
inference(avatar_split_clause,[],[f32259,f31554,f30744,f32559]) ).
fof(f32559,plain,
( spl573_802
<=> ! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| ~ c_Nat__Transfer_Ois__nat(sK93(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_802])]) ).
fof(f30744,plain,
( spl573_569
<=> ! [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,[spl573_569])]) ).
fof(f31554,plain,
( spl573_709
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK93(X0)))
| c_Nat__Transfer_Onat__set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_709])]) ).
fof(f32259,plain,
( ! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| ~ c_Nat__Transfer_Ois__nat(sK93(X0)) )
| ~ spl573_569
| ~ spl573_709 ),
inference(resolution,[],[f31555,f30745]) ).
fof(f30745,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| ~ c_Nat__Transfer_Ois__nat(X0) )
| ~ spl573_569 ),
inference(avatar_component_clause,[],[f30744]) ).
fof(f31555,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK93(X0)))
| c_Nat__Transfer_Onat__set(X0) )
| ~ spl573_709 ),
inference(avatar_component_clause,[],[f31554]) ).
fof(f32557,plain,
spl573_801,
inference(avatar_split_clause,[],[f18219,f32555]) ).
fof(f32555,plain,
( spl573_801
<=> ! [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,[spl573_801])]) ).
fof(f18219,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,[],[f10692]) ).
fof(f10692,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,[],[f6294]) ).
fof(f6294,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,[],[f199]) ).
fof(f199,axiom,
! [X88,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),c_Groups_Ozero__class_Ozero(X13)),X88) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(f32553,plain,
spl573_800,
inference(avatar_split_clause,[],[f18218,f32551]) ).
fof(f32551,plain,
( spl573_800
<=> ! [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,[spl573_800])]) ).
fof(f18218,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,[],[f10691]) ).
fof(f10691,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,[],[f6293]) ).
fof(f6293,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,[],[f438]) ).
fof(f438,axiom,
! [X88,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X88),c_Groups_Oone__class_Oone(X13)) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) ).
fof(f32549,plain,
spl573_799,
inference(avatar_split_clause,[],[f18217,f32547]) ).
fof(f32547,plain,
( spl573_799
<=> ! [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,[spl573_799])]) ).
fof(f18217,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,[],[f10690]) ).
fof(f10690,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,[],[f6292]) ).
fof(f6292,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,[],[f203]) ).
fof(f203,axiom,
! [X88,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X88),c_Groups_Ozero__class_Ozero(X13)) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(f32545,plain,
spl573_798,
inference(avatar_split_clause,[],[f18216,f32543]) ).
fof(f32543,plain,
( spl573_798
<=> ! [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,[spl573_798])]) ).
fof(f18216,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,[],[f10689]) ).
fof(f10689,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,[],[f6291]) ).
fof(f6291,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,[],[f913]) ).
fof(f913,axiom,
! [X88,X13] :
( class_Divides_Osemiring__div(X13)
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(X13),X88),c_Groups_Oone__class_Oone(X13)) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__by__1) ).
fof(f32541,plain,
spl573_797,
inference(avatar_split_clause,[],[f18215,f32539]) ).
fof(f32539,plain,
( spl573_797
<=> ! [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,[spl573_797])]) ).
fof(f18215,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,[],[f10688]) ).
fof(f10688,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,[],[f6290]) ).
fof(f6290,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,[],[f1141]) ).
fof(f1141,axiom,
! [X61,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X13),X61),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X61 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) ).
fof(f32537,plain,
spl573_796,
inference(avatar_split_clause,[],[f18207,f32535]) ).
fof(f32535,plain,
( spl573_796
<=> ! [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,[spl573_796])]) ).
fof(f18207,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,[],[f10680]) ).
fof(f10680,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,[],[f6282]) ).
fof(f6282,plain,
! [X0,X1] :
( class_Groups_Ocomm__monoid__mult(X1)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X1),c_Groups_Oone__class_Oone(X1)),X0) = X0 ),
inference(rectify,[],[f442]) ).
fof(f442,axiom,
! [X88,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),c_Groups_Oone__class_Oone(X13)),X88) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1) ).
fof(f32533,plain,
spl573_795,
inference(avatar_split_clause,[],[f18206,f32531]) ).
fof(f32531,plain,
( spl573_795
<=> ! [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,[spl573_795])]) ).
fof(f18206,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,[],[f10679]) ).
fof(f10679,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,[],[f6281]) ).
fof(f6281,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,[],[f437]) ).
fof(f437,axiom,
! [X88,X13] :
( class_Groups_Ocomm__monoid__mult(X13)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X88),c_Groups_Oone__class_Oone(X13)) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult_Ocomm__neutral) ).
fof(f32529,plain,
spl573_794,
inference(avatar_split_clause,[],[f18190,f32527]) ).
fof(f32527,plain,
( spl573_794
<=> ! [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,[spl573_794])]) ).
fof(f18190,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,[],[f10664]) ).
fof(f10664,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,[],[f6267]) ).
fof(f6267,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,[],[f444]) ).
fof(f444,axiom,
! [X88,X13] :
( class_Groups_Omonoid__mult(X13)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),c_Groups_Oone__class_Oone(X13)),X88) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__left) ).
fof(f32525,plain,
spl573_793,
inference(avatar_split_clause,[],[f18189,f32523]) ).
fof(f32523,plain,
( spl573_793
<=> ! [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,[spl573_793])]) ).
fof(f18189,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,[],[f10663]) ).
fof(f10663,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,[],[f6266]) ).
fof(f6266,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,[],[f439]) ).
fof(f439,axiom,
! [X88,X13] :
( class_Groups_Omonoid__mult(X13)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(X13),X88),c_Groups_Oone__class_Oone(X13)) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__1__right) ).
fof(f32521,plain,
spl573_792,
inference(avatar_split_clause,[],[f18188,f32519]) ).
fof(f32519,plain,
( spl573_792
<=> ! [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,[spl573_792])]) ).
fof(f18188,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,[],[f10662]) ).
fof(f10662,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,[],[f6265]) ).
fof(f6265,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,[],[f1241]) ).
fof(f1241,axiom,
! [X88,X13] :
( class_Groups_Omonoid__mult(X13)
=> hAPP(hAPP(c_Power_Opower__class_Opower(X13),X88),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__one__right) ).
fof(f32517,plain,
spl573_791,
inference(avatar_split_clause,[],[f18185,f32515]) ).
fof(f32515,plain,
( spl573_791
<=> ! [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,[spl573_791])]) ).
fof(f18185,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,[],[f10658]) ).
fof(f10658,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,[],[f6262]) ).
fof(f6262,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,[],[f198]) ).
fof(f198,axiom,
! [X88,X13] :
( class_Groups_Omonoid__add(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),c_Groups_Ozero__class_Ozero(X13)),X88) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__left) ).
fof(f32513,plain,
spl573_790,
inference(avatar_split_clause,[],[f18184,f32511]) ).
fof(f32511,plain,
( spl573_790
<=> ! [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,[spl573_790])]) ).
fof(f18184,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,[],[f10657]) ).
fof(f10657,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,[],[f6261]) ).
fof(f6261,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,[],[f202]) ).
fof(f202,axiom,
! [X88,X13] :
( class_Groups_Omonoid__add(X13)
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(X13),X88),c_Groups_Ozero__class_Ozero(X13)) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__0__right) ).
fof(f32509,plain,
spl573_789,
inference(avatar_split_clause,[],[f18158,f32507]) ).
fof(f32507,plain,
( spl573_789
<=> ! [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,[spl573_789])]) ).
fof(f18158,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,[],[f10629]) ).
fof(f10629,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,[],[f6237]) ).
fof(f6237,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,[],[f883]) ).
fof(f883,axiom,
! [X61,X13] :
( class_Lattices_Oboolean__algebra(X13)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X13),hAPP(c_Groups_Ouminus__class_Ouminus(X13),X61)) = X61 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__compl) ).
fof(f32505,plain,
spl573_788,
inference(avatar_split_clause,[],[f18152,f32503]) ).
fof(f32503,plain,
( spl573_788
<=> ! [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,[spl573_788])]) ).
fof(f18152,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,[],[f10623]) ).
fof(f10623,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,[],[f6231]) ).
fof(f6231,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,[],[f2482]) ).
fof(f2482,axiom,
! [X61,X13] :
( class_Lattices_Obounded__lattice__bot(X13)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13),c_Orderings_Obot__class_Obot(X13)),X61) = X61 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__left) ).
fof(f32501,plain,
spl573_787,
inference(avatar_split_clause,[],[f18151,f32499]) ).
fof(f32499,plain,
( spl573_787
<=> ! [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,[spl573_787])]) ).
fof(f18151,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,[],[f10622]) ).
fof(f10622,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,[],[f6230]) ).
fof(f6230,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,[],[f3121]) ).
fof(f3121,axiom,
! [X61,X13] :
( class_Lattices_Obounded__lattice__top(X13)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13),c_Orderings_Otop__class_Otop(X13)),X61) = X61 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__top__left) ).
fof(f32497,plain,
spl573_786,
inference(avatar_split_clause,[],[f18150,f32495]) ).
fof(f32495,plain,
( spl573_786
<=> ! [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,[spl573_786])]) ).
fof(f18150,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,[],[f10621]) ).
fof(f10621,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,[],[f6229]) ).
fof(f6229,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,[],[f2483]) ).
fof(f2483,axiom,
! [X61,X13] :
( class_Lattices_Obounded__lattice__bot(X13)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13),X61),c_Orderings_Obot__class_Obot(X13)) = X61 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__right) ).
fof(f32493,plain,
spl573_785,
inference(avatar_split_clause,[],[f18149,f32491]) ).
fof(f32491,plain,
( spl573_785
<=> ! [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,[spl573_785])]) ).
fof(f18149,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,[],[f10620]) ).
fof(f10620,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,[],[f6228]) ).
fof(f6228,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,[],[f3120]) ).
fof(f3120,axiom,
! [X61,X13] :
( class_Lattices_Obounded__lattice__top(X13)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13),X61),c_Orderings_Otop__class_Otop(X13)) = X61 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__top__right) ).
fof(f32489,plain,
spl573_784,
inference(avatar_split_clause,[],[f18107,f32487]) ).
fof(f32487,plain,
( spl573_784
<=> ! [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,[spl573_784])]) ).
fof(f18107,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,[],[f10583]) ).
fof(f10583,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,[],[f6192]) ).
fof(f6192,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,[],[f1144]) ).
fof(f1144,axiom,
! [X96,X13] :
( class_Int_Onumber__ring(X13)
=> hAPP(c_Int_Oring__1__class_Oof__int(X13),X96) = hAPP(c_Int_Onumber__class_Onumber__of(X13),X96) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__eq) ).
fof(f32485,plain,
spl573_783,
inference(avatar_split_clause,[],[f18070,f32483]) ).
fof(f32483,plain,
( spl573_783
<=> ! [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,[spl573_783])]) ).
fof(f18070,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,[],[f10556]) ).
fof(f10556,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,[],[f6168]) ).
fof(f6168,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,[],[f577]) ).
fof(f577,axiom,
! [X88,X13] :
( class_Rings_Olinordered__idom(X13)
=> c_Groups_Osgn__class_Osgn(X13,X88) = c_Groups_Osgn__class_Osgn(X13,c_Groups_Osgn__class_Osgn(X13,X88)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__sgn) ).
fof(f32481,plain,
spl573_782,
inference(avatar_split_clause,[],[f18017,f32479]) ).
fof(f32479,plain,
( spl573_782
<=> ! [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,[spl573_782])]) ).
fof(f18017,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,[],[f10509]) ).
fof(f10509,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,[],[f6127]) ).
fof(f6127,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,[],[f1001]) ).
fof(f1001,axiom,
! [X88,X13] :
( class_Groups_Ogroup__add(X13)
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13),X88),c_Groups_Ozero__class_Ozero(X13)) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__right) ).
fof(f32477,plain,
spl573_781,
inference(avatar_split_clause,[],[f18016,f32475]) ).
fof(f32475,plain,
( spl573_781
<=> ! [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,[spl573_781])]) ).
fof(f18016,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,[],[f10508]) ).
fof(f10508,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,[],[f6126]) ).
fof(f6126,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,[],[f448]) ).
fof(f448,axiom,
! [X88,X13] :
( class_Groups_Ogroup__add(X13)
=> hAPP(c_Groups_Ouminus__class_Ouminus(X13),hAPP(c_Groups_Ouminus__class_Ouminus(X13),X88)) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__minus) ).
fof(f32473,plain,
spl573_780,
inference(avatar_split_clause,[],[f18015,f32471]) ).
fof(f32471,plain,
( spl573_780
<=> ! [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,[spl573_780])]) ).
fof(f18015,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,[],[f10507]) ).
fof(f10507,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,[],[f6125]) ).
fof(f6125,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,[],[f1000]) ).
fof(f1000,axiom,
! [X88,X13] :
( class_Groups_Ogroup__add(X13)
=> c_Groups_Ozero__class_Ozero(X13) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(X13),X88),X88) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self) ).
fof(f32469,plain,
spl573_779,
inference(avatar_split_clause,[],[f17562,f32467]) ).
fof(f32467,plain,
( spl573_779
<=> ! [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,[spl573_779])]) ).
fof(f17562,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,[],[f5743]) ).
fof(f5743,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,[],[f2245]) ).
fof(f2245,axiom,
! [X157,X154] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,X154),X157) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X154,X157),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastSucAtMost__greaterThanAtMost) ).
fof(f32465,plain,
spl573_778,
inference(avatar_split_clause,[],[f17560,f32463]) ).
fof(f32463,plain,
( spl573_778
<=> ! [X0,X1] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_778])]) ).
fof(f17560,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,[],[f5741]) ).
fof(f5741,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,[],[f4325]) ).
fof(f4325,axiom,
! [X155,X71] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X71,X155) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(X71,X155)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__upto) ).
fof(f32461,plain,
spl573_777,
inference(avatar_split_clause,[],[f17553,f32459]) ).
fof(f32459,plain,
( spl573_777
<=> ! [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,[spl573_777])]) ).
fof(f17553,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,[],[f5734]) ).
fof(f5734,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,[],[f3014]) ).
fof(f3014,axiom,
! [X148,X7] : hAPP(c_Set_OPow(X7),X148) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pow__not__empty) ).
fof(f32457,plain,
spl573_776,
inference(avatar_split_clause,[],[f17458,f32455]) ).
fof(f32455,plain,
( spl573_776
<=> ! [X4,X0] :
( hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK106(X0))))
| ~ hBOOL(hAPP(X0,X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_776])]) ).
fof(f17458,plain,
! [X0,X4] :
( hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK106(X0))))
| ~ hBOOL(hAPP(X0,X4)) ),
inference(cnf_transformation,[],[f14604]) ).
fof(f14604,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])],[f14601,f14603,f14602]) ).
fof(f14602,plain,
! [X0] :
( ? [X1] : hBOOL(hAPP(X0,X1))
=> hBOOL(hAPP(X0,sK105(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14603,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(f14601,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,[],[f14600]) ).
fof(f14600,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,[],[f5643]) ).
fof(f5643,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,[],[f742]) ).
fof(f742,axiom,
! [X5] :
( ? [X138] : hBOOL(hAPP(X5,X138))
<=> ? [X2] :
( hBOOL(hAPP(X5,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/sandbox/benchmark/theBenchmark.p',fact_ex__nat) ).
fof(f32453,plain,
spl573_775,
inference(avatar_split_clause,[],[f17453,f32451]) ).
fof(f32451,plain,
( spl573_775
<=> ! [X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK101(X0)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_775])]) ).
fof(f17453,plain,
! [X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(X0,hAPP(c_Int_Onat,sK101(X0)))) ),
inference(cnf_transformation,[],[f14594]) ).
fof(f14594,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])],[f14591,f14593,f14592]) ).
fof(f14592,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(f14593,plain,
! [X0] :
( ? [X4] : ~ hBOOL(hAPP(X0,X4))
=> ~ hBOOL(hAPP(X0,sK102(X0))) ),
introduced(choice_axiom,[]) ).
fof(f14591,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,[],[f14590]) ).
fof(f14590,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,[],[f10422]) ).
fof(f10422,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,[],[f5641]) ).
fof(f5641,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,[],[f743]) ).
fof(f743,axiom,
! [X5] :
( ! [X138] : hBOOL(hAPP(X5,X138))
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
=> hBOOL(hAPP(X5,hAPP(c_Int_Onat,X2))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__nat) ).
fof(f32449,plain,
spl573_774,
inference(avatar_split_clause,[],[f17273,f32447]) ).
fof(f32447,plain,
( spl573_774
<=> ! [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,[spl573_774])]) ).
fof(f17273,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,[],[f10356]) ).
fof(f10356,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,[],[f5528]) ).
fof(f5528,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,[],[f4360]) ).
fof(f4360,axiom,
! [X7] :
( class_Orderings_Olinorder(X7)
=> c_Finite__Set_Ofun__left__comm(X7,tc_List_Olist(X7),c_List_Olinorder__class_Oinsort__key(X7,X7,c_COMBI(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__insort) ).
fof(f32445,plain,
spl573_773,
inference(avatar_split_clause,[],[f17272,f32443]) ).
fof(f32443,plain,
( spl573_773
<=> ! [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,[spl573_773])]) ).
fof(f17272,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,[],[f10355]) ).
fof(f10355,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,[],[f5527]) ).
fof(f5527,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,[],[f4459]) ).
fof(f4459,axiom,
! [X7] :
( class_Orderings_Olinorder(X7)
=> c_List_Olist_ONil(X7) = c_List_Olinorder__class_Osorted__list__of__set(X7,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__empty) ).
fof(f32441,plain,
spl573_772,
inference(avatar_split_clause,[],[f17266,f32439]) ).
fof(f32439,plain,
( spl573_772
<=> ! [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,[spl573_772])]) ).
fof(f17266,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,[],[f10349]) ).
fof(f10349,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,[],[f5521]) ).
fof(f5521,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,[],[f709]) ).
fof(f709,axiom,
! [X13] :
( class_Rings_Olinordered__semidom(X13)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),c_Groups_Ozero__class_Ozero(X13)),c_Groups_Oone__class_Oone(X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__one) ).
fof(f32437,plain,
( ~ spl573_771
| ~ spl573_320
| ~ spl573_663 ),
inference(avatar_split_clause,[],[f32006,f31364,f29643,f32434]) ).
fof(f32434,plain,
( spl573_771
<=> sP27(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_771])]) ).
fof(f29643,plain,
( spl573_320
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_320])]) ).
fof(f31364,plain,
( spl573_663
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP27(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_663])]) ).
fof(f32006,plain,
( ~ sP27(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint))
| ~ spl573_320
| ~ spl573_663 ),
inference(resolution,[],[f31365,f29645]) ).
fof(f29645,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls))
| ~ spl573_320 ),
inference(avatar_component_clause,[],[f29643]) ).
fof(f31365,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP27(X0,X1,X2) )
| ~ spl573_663 ),
inference(avatar_component_clause,[],[f31364]) ).
fof(f32432,plain,
spl573_770,
inference(avatar_split_clause,[],[f17265,f32430]) ).
fof(f32430,plain,
( spl573_770
<=> ! [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,[spl573_770])]) ).
fof(f17265,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,[],[f10348]) ).
fof(f10348,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,[],[f5520]) ).
fof(f5520,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,[],[f522]) ).
fof(f522,axiom,
! [X13] :
( class_Rings_Olinordered__semidom(X13)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Ozero__class_Ozero(X13)),c_Groups_Oone__class_Oone(X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__one) ).
fof(f32428,plain,
spl573_769,
inference(avatar_split_clause,[],[f17264,f32426]) ).
fof(f32426,plain,
( spl573_769
<=> ! [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,[spl573_769])]) ).
fof(f17264,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,[],[f10347]) ).
fof(f10347,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,[],[f5519]) ).
fof(f5519,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,[],[f710]) ).
fof(f710,axiom,
! [X13] :
( class_Rings_Olinordered__semidom(X13)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),c_Groups_Oone__class_Oone(X13)),c_Groups_Ozero__class_Ozero(X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__le__zero) ).
fof(f32424,plain,
spl573_768,
inference(avatar_split_clause,[],[f17263,f32422]) ).
fof(f32422,plain,
( spl573_768
<=> ! [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,[spl573_768])]) ).
fof(f17263,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,[],[f10346]) ).
fof(f10346,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,[],[f5518]) ).
fof(f5518,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,[],[f521]) ).
fof(f521,axiom,
! [X13] :
( class_Rings_Olinordered__semidom(X13)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),c_Groups_Oone__class_Oone(X13)),c_Groups_Ozero__class_Ozero(X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__one__less__zero) ).
fof(f32420,plain,
spl573_767,
inference(avatar_split_clause,[],[f17260,f32418]) ).
fof(f32418,plain,
( spl573_767
<=> ! [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,[spl573_767])]) ).
fof(f17260,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,[],[f10343]) ).
fof(f10343,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,[],[f5515]) ).
fof(f5515,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,[],[f2800]) ).
fof(f2800,axiom,
! [X7] :
( class_Rings_Osemiring__1(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),c_Groups_Ozero__class_Ozero(X7)),c_Nat_Osemiring__1__class_ONats(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__0) ).
fof(f32416,plain,
spl573_766,
inference(avatar_split_clause,[],[f17259,f32414]) ).
fof(f32414,plain,
( spl573_766
<=> ! [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,[spl573_766])]) ).
fof(f17259,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,[],[f10342]) ).
fof(f10342,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,[],[f5514]) ).
fof(f5514,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,[],[f2803]) ).
fof(f2803,axiom,
! [X7] :
( class_Rings_Osemiring__1(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),c_Groups_Oone__class_Oone(X7)),c_Nat_Osemiring__1__class_ONats(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nats__1) ).
fof(f32412,plain,
spl573_765,
inference(avatar_split_clause,[],[f17251,f32410]) ).
fof(f32410,plain,
( spl573_765
<=> ! [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,[spl573_765])]) ).
fof(f17251,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,[],[f10334]) ).
fof(f10334,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,[],[f5506]) ).
fof(f5506,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,[],[f1272]) ).
fof(f1272,axiom,
! [X7] :
( class_Power_Opower(X7)
=> c_Power_Opower__class_Opower(X7) = c_Power_Opower_Opower(X7,c_Groups_Oone__class_Oone(X7),c_Groups_Otimes__class_Otimes(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__power__power) ).
fof(f32408,plain,
spl573_764,
inference(avatar_split_clause,[],[f17248,f32406]) ).
fof(f32406,plain,
( spl573_764
<=> ! [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,[spl573_764])]) ).
fof(f17248,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,[],[f10331]) ).
fof(f10331,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,[],[f5503]) ).
fof(f5503,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,[],[f3411]) ).
fof(f3411,axiom,
! [X7] :
( class_Nat_Osemiring__char__0(X7)
=> c_Fun_Oinj__on(tc_Nat_Onat,X7,c_Nat_Osemiring__1__class_Oof__nat(X7),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__of__nat) ).
fof(f32404,plain,
spl573_763,
inference(avatar_split_clause,[],[f17247,f32402]) ).
fof(f32402,plain,
( spl573_763
<=> ! [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,[spl573_763])]) ).
fof(f17247,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,[],[f10330]) ).
fof(f10330,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,[],[f5502]) ).
fof(f5502,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,[],[f4189]) ).
fof(f4189,axiom,
! [X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Orderings_Obot__class_Obot(X7) = c_Complete__Lattice_OSup__class_OSup(X7,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__empty) ).
fof(f32400,plain,
spl573_762,
inference(avatar_split_clause,[],[f17246,f32398]) ).
fof(f32398,plain,
( spl573_762
<=> ! [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,[spl573_762])]) ).
fof(f17246,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,[],[f10329]) ).
fof(f10329,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,[],[f5501]) ).
fof(f5501,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,[],[f4196]) ).
fof(f4196,axiom,
! [X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Orderings_Obot__class_Obot(X7) = c_Complete__Lattice_OInf__class_OInf(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__UNIV) ).
fof(f32396,plain,
spl573_761,
inference(avatar_split_clause,[],[f17245,f32394]) ).
fof(f32394,plain,
( spl573_761
<=> ! [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,[spl573_761])]) ).
fof(f17245,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,[],[f10328]) ).
fof(f10328,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,[],[f5500]) ).
fof(f5500,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,[],[f4194]) ).
fof(f4194,axiom,
! [X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Orderings_Otop__class_Otop(X7) = c_Complete__Lattice_OSup__class_OSup(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__UNIV) ).
fof(f32392,plain,
( ~ spl573_760
| ~ spl573_319
| ~ spl573_663 ),
inference(avatar_split_clause,[],[f32005,f31364,f29638,f32389]) ).
fof(f32389,plain,
( spl573_760
<=> sP27(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_760])]) ).
fof(f29638,plain,
( spl573_319
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_319])]) ).
fof(f32005,plain,
( ~ sP27(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless(tc_Int_Oint))
| ~ spl573_319
| ~ spl573_663 ),
inference(resolution,[],[f31365,f29640]) ).
fof(f29640,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls))
| ~ spl573_319 ),
inference(avatar_component_clause,[],[f29638]) ).
fof(f32387,plain,
spl573_759,
inference(avatar_split_clause,[],[f17244,f32385]) ).
fof(f32385,plain,
( spl573_759
<=> ! [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,[spl573_759])]) ).
fof(f17244,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,[],[f10327]) ).
fof(f10327,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,[],[f5499]) ).
fof(f5499,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,[],[f4195]) ).
fof(f4195,axiom,
! [X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Orderings_Otop__class_Otop(X7) = c_Complete__Lattice_OInf__class_OInf(X7,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__empty) ).
fof(f32383,plain,
spl573_758,
inference(avatar_split_clause,[],[f17228,f32381]) ).
fof(f32381,plain,
( spl573_758
<=> ! [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,[spl573_758])]) ).
fof(f17228,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,[],[f10311]) ).
fof(f10311,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,[],[f5483]) ).
fof(f5483,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,[],[f2812]) ).
fof(f2812,axiom,
! [X7] :
( class_Rings_Oring__1(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),c_Groups_Ozero__class_Ozero(X7)),c_Int_Oring__1__class_OInts(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__0) ).
fof(f32379,plain,
spl573_757,
inference(avatar_split_clause,[],[f17227,f32377]) ).
fof(f32377,plain,
( spl573_757
<=> ! [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,[spl573_757])]) ).
fof(f17227,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,[],[f10310]) ).
fof(f10310,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,[],[f5482]) ).
fof(f5482,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,[],[f2817]) ).
fof(f2817,axiom,
! [X7] :
( class_Rings_Oring__1(X7)
=> hBOOL(hAPP(hAPP(c_member(X7),c_Groups_Oone__class_Oone(X7)),c_Int_Oring__1__class_OInts(X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Ints__1) ).
fof(f32375,plain,
spl573_756,
inference(avatar_split_clause,[],[f17096,f32373]) ).
fof(f32373,plain,
( spl573_756
<=> ! [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,[spl573_756])]) ).
fof(f17096,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,[],[f5364]) ).
fof(f5364,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,[],[f1076]) ).
fof(f1076,axiom,
! [X12] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__Suc__1) ).
fof(f32371,plain,
spl573_755,
inference(avatar_split_clause,[],[f17094,f32369]) ).
fof(f32369,plain,
( spl573_755
<=> ! [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,[spl573_755])]) ).
fof(f17094,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,[],[f5362]) ).
fof(f5362,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,[],[f2377]) ).
fof(f2377,axiom,
! [X94] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessThan__Suc__atMost) ).
fof(f32367,plain,
spl573_754,
inference(avatar_split_clause,[],[f17093,f32365]) ).
fof(f32365,plain,
( spl573_754
<=> ! [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,[spl573_754])]) ).
fof(f17093,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,[],[f5361]) ).
fof(f5361,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,[],[f2372]) ).
fof(f2372,axiom,
! [X94] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,X94)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__Suc__greaterThan) ).
fof(f32363,plain,
spl573_753,
inference(avatar_split_clause,[],[f17089,f32361]) ).
fof(f32361,plain,
( spl573_753
<=> ! [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,[spl573_753])]) ).
fof(f17089,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,[],[f5357]) ).
fof(f5357,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,[],[f1702]) ).
fof(f1702,axiom,
! [X6] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__eq__Suc__le__raw) ).
fof(f32359,plain,
spl573_752,
inference(avatar_split_clause,[],[f17087,f32357]) ).
fof(f32357,plain,
( spl573_752
<=> ! [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,[spl573_752])]) ).
fof(f17087,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,[],[f5355]) ).
fof(f5355,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,[],[f1309]) ).
fof(f1309,axiom,
! [X96] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X96) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Min) ).
fof(f32355,plain,
spl573_751,
inference(avatar_split_clause,[],[f17082,f32353]) ).
fof(f32353,plain,
( spl573_751
<=> ! [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,[spl573_751])]) ).
fof(f17082,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,[],[f5350]) ).
fof(f5350,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,[],[f734]) ).
fof(f734,axiom,
! [X12] : hAPP(c_Nat_OSuc,X12) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f32351,plain,
spl573_750,
inference(avatar_split_clause,[],[f17081,f32349]) ).
fof(f32349,plain,
( spl573_750
<=> ! [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,[spl573_750])]) ).
fof(f17081,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,[],[f5349]) ).
fof(f5349,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,[],[f735]) ).
fof(f735,axiom,
! [X12] : hAPP(c_Nat_OSuc,X12) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X12),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(f32345,plain,
spl573_749,
inference(avatar_split_clause,[],[f17080,f32343]) ).
fof(f32343,plain,
( spl573_749
<=> ! [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,[spl573_749])]) ).
fof(f17080,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,[],[f5348]) ).
fof(f5348,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,[],[f2369]) ).
fof(f2369,axiom,
! [X157] : hAPP(c_Nat_OSuc,X157) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X157)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atMost) ).
fof(f32341,plain,
spl573_748,
inference(avatar_split_clause,[],[f16916,f32338]) ).
fof(f32338,plain,
( spl573_748
<=> 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,[spl573_748])]) ).
fof(f16916,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,[],[f3102]) ).
fof(f3102,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/sandbox/benchmark/theBenchmark.p',fact_equiv__intrel) ).
fof(f32334,plain,
spl573_747,
inference(avatar_split_clause,[],[f16634,f32332]) ).
fof(f16634,plain,
! [X2,X0,X1] :
( v_Q(X0,X2)
| ~ c_Natural_Oevaln(v_c,X1,v_n,X2)
| ~ v_P(X0,X1) ),
inference(cnf_transformation,[],[f10291]) ).
fof(f10291,plain,
! [X0,X1] :
( ! [X2] :
( v_Q(X0,X2)
| ~ c_Natural_Oevaln(v_c,X1,v_n,X2) )
| ~ v_P(X0,X1) ),
inference(ennf_transformation,[],[f5216]) ).
fof(f5216,plain,
! [X0,X1] :
( v_P(X0,X1)
=> ! [X2] :
( c_Natural_Oevaln(v_c,X1,v_n,X2)
=> v_Q(X0,X2) ) ),
inference(rectify,[],[f5206]) ).
fof(f5206,axiom,
! [X8,X9] :
( v_P(X8,X9)
=> ! [X10] :
( c_Natural_Oevaln(v_c,X9,v_n,X10)
=> v_Q(X8,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(f32330,plain,
spl573_746,
inference(avatar_split_clause,[],[f16633,f32328]) ).
fof(f16633,plain,
! [X2,X0,X1] :
( v_R(X0,X2)
| ~ c_Natural_Oevaln(v_d,X1,v_n,X2)
| ~ v_Q(X0,X1) ),
inference(cnf_transformation,[],[f10290]) ).
fof(f10290,plain,
! [X0,X1] :
( ! [X2] :
( v_R(X0,X2)
| ~ c_Natural_Oevaln(v_d,X1,v_n,X2) )
| ~ v_Q(X0,X1) ),
inference(ennf_transformation,[],[f5215]) ).
fof(f5215,plain,
! [X0,X1] :
( v_Q(X0,X1)
=> ! [X2] :
( c_Natural_Oevaln(v_d,X1,v_n,X2)
=> v_R(X0,X2) ) ),
inference(rectify,[],[f5207]) ).
fof(f5207,axiom,
! [X8,X9] :
( v_Q(X8,X9)
=> ! [X10] :
( c_Natural_Oevaln(v_d,X9,v_n,X10)
=> v_R(X8,X10) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(f32318,plain,
( spl573_745
| ~ spl573_728 ),
inference(avatar_split_clause,[],[f32312,f31631,f32316]) ).
fof(f32316,plain,
( spl573_745
<=> ! [X0] : sP8(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_745])]) ).
fof(f31631,plain,
( spl573_728
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) != hAPP(c_Int_Onat,X1)
| sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_728])]) ).
fof(f32312,plain,
( ! [X0] : sP8(X0,X0)
| ~ spl573_728 ),
inference(equality_resolution,[],[f31632]) ).
fof(f31632,plain,
( ! [X0,X1] :
( hAPP(c_Int_Onat,X0) != hAPP(c_Int_Onat,X1)
| sP8(X0,X1) )
| ~ spl573_728 ),
inference(avatar_component_clause,[],[f31631]) ).
fof(f32290,plain,
( spl573_744
| ~ spl573_328
| ~ spl573_663 ),
inference(avatar_split_clause,[],[f31981,f31364,f29676,f32288]) ).
fof(f32288,plain,
( spl573_744
<=> ! [X0] : ~ sP27(X0,X0,c_Rings_Odvd__class_Odvd(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_744])]) ).
fof(f29676,plain,
( spl573_328
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_328])]) ).
fof(f31981,plain,
( ! [X0] : ~ sP27(X0,X0,c_Rings_Odvd__class_Odvd(tc_Nat_Onat))
| ~ spl573_328
| ~ spl573_663 ),
inference(resolution,[],[f31365,f29677]) ).
fof(f29677,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0))
| ~ spl573_328 ),
inference(avatar_component_clause,[],[f29676]) ).
fof(f32263,plain,
( spl573_743
| ~ spl573_330
| ~ spl573_663 ),
inference(avatar_split_clause,[],[f31979,f31364,f29684,f32261]) ).
fof(f32261,plain,
( spl573_743
<=> ! [X0] : ~ sP27(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_743])]) ).
fof(f29684,plain,
( spl573_330
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_330])]) ).
fof(f31979,plain,
( ! [X0] : ~ sP27(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat))
| ~ spl573_330
| ~ spl573_663 ),
inference(resolution,[],[f31365,f29685]) ).
fof(f29685,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0))
| ~ spl573_330 ),
inference(avatar_component_clause,[],[f29684]) ).
fof(f32212,plain,
( spl573_742
| ~ spl573_329
| ~ spl573_663 ),
inference(avatar_split_clause,[],[f31978,f31364,f29680,f32210]) ).
fof(f32210,plain,
( spl573_742
<=> ! [X0] : ~ sP27(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_742])]) ).
fof(f29680,plain,
( spl573_329
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_329])]) ).
fof(f31978,plain,
( ! [X0] : ~ sP27(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint))
| ~ spl573_329
| ~ spl573_663 ),
inference(resolution,[],[f31365,f29681]) ).
fof(f29681,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0))
| ~ spl573_329 ),
inference(avatar_component_clause,[],[f29680]) ).
fof(f32181,plain,
( spl573_741
| ~ spl573_483
| ~ spl573_691 ),
inference(avatar_split_clause,[],[f31482,f31478,f30392,f32178]) ).
fof(f32178,plain,
( spl573_741
<=> hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) = c_Option_Oset(tc_Nat_Onat,c_Option_Ooption_ONone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_741])]) ).
fof(f30392,plain,
( spl573_483
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Option_Oset(X0,c_Option_Ooption_ONone(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_483])]) ).
fof(f31478,plain,
( spl573_691
<=> 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,[spl573_691])]) ).
fof(f31482,plain,
( hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) = c_Option_Oset(tc_Nat_Onat,c_Option_Ooption_ONone(tc_Nat_Onat))
| ~ spl573_483
| ~ spl573_691 ),
inference(forward_demodulation,[],[f31480,f30393]) ).
fof(f30393,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Option_Oset(X0,c_Option_Ooption_ONone(X0))
| ~ spl573_483 ),
inference(avatar_component_clause,[],[f30392]) ).
fof(f31480,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))
| ~ spl573_691 ),
inference(avatar_component_clause,[],[f31478]) ).
fof(f32173,plain,
( spl573_740
| ~ spl573_327
| ~ spl573_663 ),
inference(avatar_split_clause,[],[f31977,f31364,f29672,f32171]) ).
fof(f32171,plain,
( spl573_740
<=> ! [X0] : ~ sP27(X0,X0,c_Natural_Oevalc(c_Com_Ocom_OSKIP)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_740])]) ).
fof(f29672,plain,
( spl573_327
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_327])]) ).
fof(f31977,plain,
( ! [X0] : ~ sP27(X0,X0,c_Natural_Oevalc(c_Com_Ocom_OSKIP))
| ~ spl573_327
| ~ spl573_663 ),
inference(resolution,[],[f31365,f29673]) ).
fof(f29673,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X0),X0))
| ~ spl573_327 ),
inference(avatar_component_clause,[],[f29672]) ).
fof(f32147,plain,
( spl573_739
| ~ spl573_285
| ~ spl573_663 ),
inference(avatar_split_clause,[],[f31980,f31364,f29459,f32145]) ).
fof(f32145,plain,
( spl573_739
<=> ! [X0] : ~ sP27(X0,X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_739])]) ).
fof(f29459,plain,
( spl573_285
<=> ! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_285])]) ).
fof(f31980,plain,
( ! [X0] : ~ sP27(X0,X0,c_fequal)
| ~ spl573_285
| ~ spl573_663 ),
inference(resolution,[],[f31365,f29460]) ).
fof(f29460,plain,
( ! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1))
| ~ spl573_285 ),
inference(avatar_component_clause,[],[f29459]) ).
fof(f31743,plain,
( spl573_737
| ~ spl573_738
| ~ spl573_568
| ~ spl573_628 ),
inference(avatar_split_clause,[],[f31712,f31223,f30740,f31740,f31736]) ).
fof(f31736,plain,
( spl573_737
<=> c_Nat__Transfer_Ois__nat(c_Orderings_Otop__class_Otop(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_737])]) ).
fof(f31740,plain,
( spl573_738
<=> class_Orderings_Otop(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_738])]) ).
fof(f30740,plain,
( spl573_568
<=> ! [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,[spl573_568])]) ).
fof(f31223,plain,
( spl573_628
<=> ! [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,[spl573_628])]) ).
fof(f31712,plain,
( ~ class_Orderings_Otop(tc_Int_Oint)
| c_Nat__Transfer_Ois__nat(c_Orderings_Otop__class_Otop(tc_Int_Oint))
| ~ spl573_568
| ~ spl573_628 ),
inference(resolution,[],[f31224,f30741]) ).
fof(f30741,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| c_Nat__Transfer_Ois__nat(X0) )
| ~ spl573_568 ),
inference(avatar_component_clause,[],[f30740]) ).
fof(f31224,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) )
| ~ spl573_628 ),
inference(avatar_component_clause,[],[f31223]) ).
fof(f31705,plain,
( spl573_736
| ~ spl573_25
| ~ spl573_197
| ~ spl573_609 ),
inference(avatar_split_clause,[],[f31669,f31146,f29078,f28219,f31702]) ).
fof(f31702,plain,
( spl573_736
<=> c_Int_OPls = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_736])]) ).
fof(f28219,plain,
( spl573_25
<=> class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_25])]) ).
fof(f29078,plain,
( spl573_197
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl573_197])]) ).
fof(f31146,plain,
( spl573_609
<=> ! [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,[spl573_609])]) ).
fof(f31669,plain,
( c_Int_OPls = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),c_Int_OPls)
| ~ spl573_25
| ~ spl573_197
| ~ spl573_609 ),
inference(forward_demodulation,[],[f31668,f29080]) ).
fof(f29080,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls
| ~ spl573_197 ),
inference(avatar_component_clause,[],[f29078]) ).
fof(f31668,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))
| ~ spl573_25
| ~ spl573_609 ),
inference(resolution,[],[f31147,f28221]) ).
fof(f28221,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint)
| ~ spl573_25 ),
inference(avatar_component_clause,[],[f28219]) ).
fof(f31147,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)) )
| ~ spl573_609 ),
inference(avatar_component_clause,[],[f31146]) ).
fof(f31674,plain,
( spl573_735
| ~ spl573_475
| ~ spl573_611 ),
inference(avatar_split_clause,[],[f31157,f31154,f30336,f31672]) ).
fof(f31672,plain,
( spl573_735
<=> ! [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,[spl573_735])]) ).
fof(f30336,plain,
( spl573_475
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_OBit1(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_475])]) ).
fof(f31154,plain,
( spl573_611
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_611])]) ).
fof(f31157,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) )
| ~ spl573_475
| ~ spl573_611 ),
inference(forward_demodulation,[],[f31155,f30338]) ).
fof(f30338,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_OBit1(c_Int_OPls)
| ~ spl573_475 ),
inference(avatar_component_clause,[],[f30336]) ).
fof(f31155,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) )
| ~ spl573_611 ),
inference(avatar_component_clause,[],[f31154]) ).
fof(f31664,plain,
( spl573_734
| ~ spl573_350
| ~ spl573_601 ),
inference(avatar_split_clause,[],[f31655,f31114,f29766,f31662]) ).
fof(f31662,plain,
( spl573_734
<=> ! [X0] : ~ class_Finite__Set_Ofinite(tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_734])]) ).
fof(f29766,plain,
( spl573_350
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_350])]) ).
fof(f31114,plain,
( spl573_601
<=> ! [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,[spl573_601])]) ).
fof(f31655,plain,
( ! [X0] : ~ class_Finite__Set_Ofinite(tc_List_Olist(X0))
| ~ spl573_350
| ~ spl573_601 ),
inference(resolution,[],[f31115,f29767]) ).
fof(f29767,plain,
( ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) )
| ~ spl573_350 ),
inference(avatar_component_clause,[],[f29766]) ).
fof(f31115,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))))
| ~ spl573_601 ),
inference(avatar_component_clause,[],[f31114]) ).
fof(f31654,plain,
spl573_733,
inference(avatar_split_clause,[],[f26987,f31652]) ).
fof(f31652,plain,
( spl573_733
<=> ! [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,[spl573_733])]) ).
fof(f26987,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,[],[f19765,f16841]) ).
fof(f19765,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,[],[f11512]) ).
fof(f11512,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,[],[f7381]) ).
fof(f7381,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,[],[f98]) ).
fof(f98,axiom,
! [X71,X72,X7] :
( class_Rings_Osemiring__1(X7)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X7,X72,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X71) = X71 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I1_J) ).
fof(f31650,plain,
( spl573_732
| ~ spl573_313
| ~ spl573_485 ),
inference(avatar_split_clause,[],[f30829,f30400,f29606,f31647]) ).
fof(f31647,plain,
( spl573_732
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_732])]) ).
fof(f29606,plain,
( spl573_313
<=> 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,[spl573_313])]) ).
fof(f30400,plain,
( spl573_485
<=> ! [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,[spl573_485])]) ).
fof(f30829,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)
| ~ spl573_313
| ~ spl573_485 ),
inference(superposition,[],[f30401,f29608]) ).
fof(f29608,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin
| ~ spl573_313 ),
inference(avatar_component_clause,[],[f29606]) ).
fof(f30401,plain,
( ! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = X0
| ~ spl573_485 ),
inference(avatar_component_clause,[],[f30400]) ).
fof(f31645,plain,
spl573_731,
inference(avatar_split_clause,[],[f26832,f31643]) ).
fof(f31643,plain,
( spl573_731
<=> ! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_731])]) ).
fof(f26832,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)),
inference(forward_demodulation,[],[f26831,f25684]) ).
fof(f25684,plain,
! [X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f25683,f25195]) ).
fof(f25683,plain,
! [X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f17753,f16841]) ).
fof(f17753,plain,
! [X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f5934]) ).
fof(f5934,plain,
! [X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rectify,[],[f173]) ).
fof(f173,axiom,
! [X89,X90] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X90,X89)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X90)),c_Com_Ocom_Ocom__size(X89))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I4_J) ).
fof(f26831,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f26830,f25195]) ).
fof(f26830,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f19327,f16841]) ).
fof(f19327,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)),
inference(cnf_transformation,[],[f7009]) ).
fof(f7009,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)),
inference(rectify,[],[f175]) ).
fof(f175,axiom,
! [X54,X55,X56] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X56,X55,X54)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X55)),c_Com_Ocom_Ocom__size(X54))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I5_J) ).
fof(f31641,plain,
spl573_730,
inference(avatar_split_clause,[],[f26816,f31639]) ).
fof(f31639,plain,
( spl573_730
<=> ! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)) = hAPP(c_Nat_OSuc,c_Com_Ocom_Ocom__size(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_730])]) ).
fof(f26816,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)) = hAPP(c_Nat_OSuc,c_Com_Ocom_Ocom__size(X0)),
inference(forward_demodulation,[],[f26815,f17081]) ).
fof(f26815,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X0)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f26814,f25195]) ).
fof(f26814,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X0)),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f19258,f16841]) ).
fof(f19258,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X0)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)),
inference(cnf_transformation,[],[f6940]) ).
fof(f6940,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X0)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)),
inference(rectify,[],[f172]) ).
fof(f172,axiom,
! [X38,X56,X73] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X73,X56,X38)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X38)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I3_J) ).
fof(f31637,plain,
spl573_729,
inference(avatar_split_clause,[],[f26805,f31635]) ).
fof(f31635,plain,
( spl573_729
<=> ! [X2,X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X2,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_729])]) ).
fof(f26805,plain,
! [X2,X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X2,X1,X0)),
inference(forward_demodulation,[],[f19213,f16841]) ).
fof(f19213,plain,
! [X2,X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X2,X1,X0)),
inference(cnf_transformation,[],[f6895]) ).
fof(f6895,plain,
! [X0,X1,X2] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X2,X1,X0)),
inference(rectify,[],[f167]) ).
fof(f167,axiom,
! [X56,X74,X75] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(X75,X74,X56)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I16_J) ).
fof(f31633,plain,
spl573_728,
inference(avatar_split_clause,[],[f26554,f31631]) ).
fof(f26554,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) != hAPP(c_Int_Onat,X1)
| sP8(X0,X1) ),
inference(forward_demodulation,[],[f26553,f25292]) ).
fof(f26553,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) != hAPP(c_Int_Onat,X1)
| sP8(X0,X1) ),
inference(forward_demodulation,[],[f18935,f25292]) ).
fof(f18935,plain,
! [X0,X1] :
( sP8(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,[],[f14954]) ).
fof(f14954,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)
| ~ sP8(X0,X1) )
& ( sP8(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,[],[f14362]) ).
fof(f14362,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)
<=> sP8(X0,X1) ),
inference(definition_folding,[],[f11246,f14361,f14360]) ).
fof(f14360,plain,
! [X1,X0] :
( sP7(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,[sP7])]) ).
fof(f14361,plain,
! [X0,X1] :
( sP8(X0,X1)
<=> ( ( sP7(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,[sP8])]) ).
fof(f11246,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,[],[f6769]) ).
fof(f6769,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,[],[f1287]) ).
fof(f1287,axiom,
! [X166,X160] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X160) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X166)
<=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X160)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)))
=> X160 = X166 )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X160) ) ) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X160)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X166)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__nat__number__of) ).
fof(f31629,plain,
spl573_727,
inference(avatar_split_clause,[],[f26552,f31627]) ).
fof(f31627,plain,
( spl573_727
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) = hAPP(c_Int_Onat,X1)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_727])]) ).
fof(f26552,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = hAPP(c_Int_Onat,X1)
| ~ sP8(X0,X1) ),
inference(forward_demodulation,[],[f26551,f25292]) ).
fof(f26551,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X1)
| ~ sP8(X0,X1) ),
inference(forward_demodulation,[],[f18936,f25292]) ).
fof(f18936,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)
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f14954]) ).
fof(f31625,plain,
spl573_726,
inference(avatar_split_clause,[],[f26550,f31623]) ).
fof(f31623,plain,
( spl573_726
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Int_OPls = X0
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_726])]) ).
fof(f26550,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Int_OPls = X0
| ~ sP7(X0,X1) ),
inference(forward_demodulation,[],[f26549,f16979]) ).
fof(f26549,plain,
! [X0,X1] :
( c_Int_OPls = X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP7(X0,X1) ),
inference(forward_demodulation,[],[f26548,f16829]) ).
fof(f26548,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)))
| ~ sP7(X0,X1) ),
inference(forward_demodulation,[],[f18929,f16979]) ).
fof(f18929,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)))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f14953]) ).
fof(f14953,plain,
! [X0,X1] :
( ( sP7(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))) ) )
| ~ sP7(X0,X1) ) ),
inference(rectify,[],[f14952]) ).
fof(f14952,plain,
! [X1,X0] :
( ( sP7(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))) ) )
| ~ sP7(X1,X0) ) ),
inference(flattening,[],[f14951]) ).
fof(f14951,plain,
! [X1,X0] :
( ( sP7(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))) ) )
| ~ sP7(X1,X0) ) ),
inference(nnf_transformation,[],[f14360]) ).
fof(f31621,plain,
spl573_725,
inference(avatar_split_clause,[],[f26547,f31619]) ).
fof(f31619,plain,
( spl573_725
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| X0 = X1
| ~ sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_725])]) ).
fof(f26547,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| X0 = X1
| ~ sP7(X0,X1) ),
inference(forward_demodulation,[],[f18930,f16979]) ).
fof(f18930,plain,
! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f14953]) ).
fof(f31617,plain,
spl573_724,
inference(avatar_split_clause,[],[f26546,f31615]) ).
fof(f31615,plain,
( spl573_724
<=> ! [X0,X1] :
( c_Int_OPls != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP7(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_724])]) ).
fof(f26546,plain,
! [X0,X1] :
( c_Int_OPls != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP7(X0,X1) ),
inference(forward_demodulation,[],[f26545,f16829]) ).
fof(f26545,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP7(X0,X1) ),
inference(forward_demodulation,[],[f26544,f16979]) ).
fof(f26544,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP7(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ),
inference(forward_demodulation,[],[f18932,f16979]) ).
fof(f18932,plain,
! [X0,X1] :
( sP7(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,[],[f14953]) ).
fof(f31613,plain,
spl573_723,
inference(avatar_split_clause,[],[f26537,f31611]) ).
fof(f31611,plain,
( spl573_723
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP7(X1,X0)
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_723])]) ).
fof(f26537,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP7(X1,X0)
| ~ sP8(X0,X1) ),
inference(forward_demodulation,[],[f18924,f16979]) ).
fof(f18924,plain,
! [X0,X1] :
( sP7(X1,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f14950]) ).
fof(f14950,plain,
! [X0,X1] :
( ( sP8(X0,X1)
| ( ~ sP7(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))) ) )
& ( ( ( sP7(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))) ) )
| ~ sP8(X0,X1) ) ),
inference(flattening,[],[f14949]) ).
fof(f14949,plain,
! [X0,X1] :
( ( sP8(X0,X1)
| ( ~ sP7(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))) ) )
& ( ( ( sP7(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))) ) )
| ~ sP8(X0,X1) ) ),
inference(nnf_transformation,[],[f14361]) ).
fof(f31609,plain,
spl573_722,
inference(avatar_split_clause,[],[f26533,f31607]) ).
fof(f31607,plain,
( spl573_722
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP8(X0,X1)
| ~ sP7(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_722])]) ).
fof(f26533,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP8(X0,X1)
| ~ sP7(X1,X0) ),
inference(forward_demodulation,[],[f18927,f16979]) ).
fof(f18927,plain,
! [X0,X1] :
( sP8(X0,X1)
| ~ sP7(X1,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(cnf_transformation,[],[f14950]) ).
fof(f31604,plain,
spl573_721,
inference(avatar_split_clause,[],[f26521,f31602]) ).
fof(f31602,plain,
( spl573_721
<=> ! [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,[spl573_721])]) ).
fof(f26521,plain,
! [X3,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0
| ~ hBOOL(hAPP(X0,X3)) ),
inference(forward_demodulation,[],[f18908,f17482]) ).
fof(f18908,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,[],[f14938]) ).
fof(f31600,plain,
spl573_720,
inference(avatar_split_clause,[],[f26497,f31598]) ).
fof(f31598,plain,
( spl573_720
<=> ! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_720])]) ).
fof(f26497,plain,
! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f18877,f16979]) ).
fof(f18877,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
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f14920]) ).
fof(f14920,plain,
! [X0,X1] :
( ( sP5(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 )
| ~ sP5(X0,X1) ) ),
inference(flattening,[],[f14919]) ).
fof(f14919,plain,
! [X0,X1] :
( ( sP5(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 )
| ~ sP5(X0,X1) ) ),
inference(nnf_transformation,[],[f14356]) ).
fof(f14356,plain,
! [X0,X1] :
( sP5(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,[sP5])]) ).
fof(f31596,plain,
spl573_719,
inference(avatar_split_clause,[],[f26496,f31594]) ).
fof(f31594,plain,
( spl573_719
<=> ! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_719])]) ).
fof(f26496,plain,
! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f18878,f16979]) ).
fof(f18878,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
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f14920]) ).
fof(f31592,plain,
spl573_718,
inference(avatar_split_clause,[],[f26495,f31590]) ).
fof(f31590,plain,
( spl573_718
<=> ! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_718])]) ).
fof(f26495,plain,
! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f18879,f16979]) ).
fof(f18879,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
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f14920]) ).
fof(f31588,plain,
spl573_717,
inference(avatar_split_clause,[],[f26494,f31586]) ).
fof(f31586,plain,
( spl573_717
<=> ! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP5(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_717])]) ).
fof(f26494,plain,
! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP5(X0,X1) ),
inference(forward_demodulation,[],[f18880,f16979]) ).
fof(f18880,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
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f14920]) ).
fof(f31584,plain,
spl573_716,
inference(avatar_split_clause,[],[f26047,f31582]) ).
fof(f31582,plain,
( spl573_716
<=> ! [X1] : hAPP(c_fequal,X1) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_716])]) ).
fof(f26047,plain,
! [X1] : hAPP(c_fequal,X1) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X1),
inference(forward_demodulation,[],[f24588,f25661]) ).
fof(f24588,plain,
! [X1] : hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X1),
inference(equality_resolution,[],[f18332]) ).
fof(f18332,plain,
! [X0,X1] :
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X0) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| X0 != X1 ),
inference(cnf_transformation,[],[f10835]) ).
fof(f10835,plain,
! [X0,X1] :
( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X0) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| X0 != X1 ),
inference(ennf_transformation,[],[f6394]) ).
fof(f6394,plain,
! [X0,X1] :
( X0 = X1
=> c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X1,X0) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X1),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
inference(rectify,[],[f2531]) ).
fof(f2531,axiom,
! [X27,X76] :
( X27 = X76
=> c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X76,X27) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),X76),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_OatLeastAtMost__singleton_H) ).
fof(f31580,plain,
spl573_715,
inference(avatar_split_clause,[],[f26043,f31578]) ).
fof(f31578,plain,
( spl573_715
<=> ! [X0,X1] :
( hAPP(c_fequal,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_715])]) ).
fof(f26043,plain,
! [X0,X1] :
( hAPP(c_fequal,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(forward_demodulation,[],[f18294,f25661]) ).
fof(f18294,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,[],[f10784]) ).
fof(f10784,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,[],[f6364]) ).
fof(f6364,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,[],[f2501]) ).
fof(f2501,axiom,
! [X76,X7] :
( class_Orderings_Oorder(X7)
=> hAPP(hAPP(c_Set_Oinsert(X7),X76),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X7,X76,X76) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastAtMost__singleton) ).
fof(f31576,plain,
spl573_714,
inference(avatar_split_clause,[],[f25779,f31574]) ).
fof(f31574,plain,
( spl573_714
<=> ! [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,[spl573_714])]) ).
fof(f25779,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,[],[f24552,f16841]) ).
fof(f24552,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,[],[f17867]) ).
fof(f17867,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,[],[f10433]) ).
fof(f10433,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,[],[f6039]) ).
fof(f6039,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,[],[f1229]) ).
fof(f1229,axiom,
! [X159,X85] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X85
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X159),X85) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X159),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X159),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X85),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X85
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X159),X85) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(f31572,plain,
spl573_713,
inference(avatar_split_clause,[],[f25662,f31570]) ).
fof(f31570,plain,
( spl573_713
<=> ! [X0,X1] : hAPP(c_fequal,X0) = c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_713])]) ).
fof(f25662,plain,
! [X0,X1] : hAPP(c_fequal,X0) = c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(forward_demodulation,[],[f17673,f25661]) ).
fof(f17673,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(cnf_transformation,[],[f5854]) ).
fof(f5854,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(rectify,[],[f2566]) ).
fof(f2566,axiom,
! [X99,X7] : hAPP(hAPP(c_Set_Oinsert(X7),X99),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))) = c_Option_Oset(X7,hAPP(c_Option_Ooption_OSome(X7),X99)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Oset_Osimps_I2_J) ).
fof(f31568,plain,
spl573_712,
inference(avatar_split_clause,[],[f25640,f31566]) ).
fof(f31566,plain,
( spl573_712
<=> ! [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,[spl573_712])]) ).
fof(f25640,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,[],[f17542,f16841]) ).
fof(f17542,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,[],[f5723]) ).
fof(f5723,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,[],[f4584]) ).
fof(f4584,axiom,
! [X290,X13] : c_List_Olist_ONil(X13) = hAPP(hAPP(c_List_Otake(X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X290),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__0) ).
fof(f31564,plain,
( spl573_711
| ~ spl573_347
| ~ spl573_483 ),
inference(avatar_split_clause,[],[f30823,f30392,f29753,f31562]) ).
fof(f31562,plain,
( spl573_711
<=> ! [X0,X1] : c_Relation_Ototal__on(X0,c_Option_Oset(X0,c_Option_Ooption_ONone(X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_711])]) ).
fof(f29753,plain,
( spl573_347
<=> ! [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,[spl573_347])]) ).
fof(f30823,plain,
( ! [X0,X1] : c_Relation_Ototal__on(X0,c_Option_Oset(X0,c_Option_Ooption_ONone(X0)),X1)
| ~ spl573_347
| ~ spl573_483 ),
inference(superposition,[],[f29754,f30393]) ).
fof(f29754,plain,
( ! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0)
| ~ spl573_347 ),
inference(avatar_component_clause,[],[f29753]) ).
fof(f31560,plain,
spl573_710,
inference(avatar_split_clause,[],[f25552,f31558]) ).
fof(f31558,plain,
( spl573_710
<=> ! [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,[spl573_710])]) ).
fof(f25552,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,[],[f25551,f16829]) ).
fof(f25551,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,[],[f17375,f16841]) ).
fof(f17375,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,[],[f14549]) ).
fof(f14549,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,[],[f5603]) ).
fof(f5603,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,[],[f348]) ).
fof(f348,axiom,
! [X6] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X6) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).
fof(f31556,plain,
spl573_709,
inference(avatar_split_clause,[],[f25518,f31554]) ).
fof(f25518,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK93(X0)))
| c_Nat__Transfer_Onat__set(X0) ),
inference(forward_demodulation,[],[f17337,f16829]) ).
fof(f17337,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK93(X0))) ),
inference(cnf_transformation,[],[f14517]) ).
fof(f14517,plain,
! [X0] :
( ( c_Nat__Transfer_Onat__set(X0)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK93(X0)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK93(X0)),X0)) ) )
& ( ! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X0)) )
| ~ c_Nat__Transfer_Onat__set(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK93])],[f14515,f14516]) ).
fof(f14516,plain,
! [X0] :
( ? [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X0)) )
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK93(X0)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK93(X0)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14515,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,[],[f14514]) ).
fof(f14514,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,[],[f10418]) ).
fof(f10418,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,[],[f5585]) ).
fof(f5585,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,[],[f2342]) ).
fof(f2342,axiom,
! [X206] :
( c_Nat__Transfer_Onat__set(X206)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X206))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__set__def) ).
fof(f31552,plain,
spl573_708,
inference(avatar_split_clause,[],[f25427,f31550]) ).
fof(f31550,plain,
( spl573_708
<=> ! [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,[spl573_708])]) ).
fof(f25427,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f17291,f16841]) ).
fof(f17291,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,[],[f10373]) ).
fof(f10373,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,[],[f5545]) ).
fof(f5545,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0) ),
inference(rectify,[],[f1281]) ).
fof(f1281,axiom,
! [X97] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X97))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__nat) ).
fof(f31548,plain,
spl573_707,
inference(avatar_split_clause,[],[f25426,f31546]) ).
fof(f31546,plain,
( spl573_707
<=> ! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| hAPP(c_Nat_OSuc,sK87(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_707])]) ).
fof(f25426,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| hAPP(c_Nat_OSuc,sK87(X0)) = X0 ),
inference(forward_demodulation,[],[f17289,f16841]) ).
fof(f17289,plain,
! [X0] :
( hAPP(c_Nat_OSuc,sK87(X0)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(cnf_transformation,[],[f14503]) ).
fof(f14503,plain,
! [X0] :
( hAPP(c_Nat_OSuc,sK87(X0)) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK87])],[f10371,f14502]) ).
fof(f14502,plain,
! [X0] :
( ? [X1] : hAPP(c_Nat_OSuc,X1) = X0
=> hAPP(c_Nat_OSuc,sK87(X0)) = X0 ),
introduced(choice_axiom,[]) ).
fof(f10371,plain,
! [X0] :
( ? [X1] : hAPP(c_Nat_OSuc,X1) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(ennf_transformation,[],[f5543]) ).
fof(f5543,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> ? [X1] : hAPP(c_Nat_OSuc,X1) = X0 ),
inference(rectify,[],[f265]) ).
fof(f265,axiom,
! [X12] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X12
=> ? [X114] : hAPP(c_Nat_OSuc,X114) = X12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not0__implies__Suc) ).
fof(f31544,plain,
spl573_706,
inference(avatar_split_clause,[],[f25418,f31542]) ).
fof(f31542,plain,
( spl573_706
<=> ! [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,[spl573_706])]) ).
fof(f25418,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,[],[f17258,f16841]) ).
fof(f17258,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,[],[f10341]) ).
fof(f10341,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,[],[f5513]) ).
fof(f5513,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,[],[f356]) ).
fof(f356,axiom,
! [X13] :
( class_Rings_Osemiring__1(X13)
=> c_Groups_Ozero__class_Ozero(X13) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__0) ).
fof(f31540,plain,
spl573_705,
inference(avatar_split_clause,[],[f25309,f31538]) ).
fof(f31538,plain,
( spl573_705
<=> ! [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,[spl573_705])]) ).
fof(f25309,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,[],[f25308,f25195]) ).
fof(f25308,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,[],[f17121,f16841]) ).
fof(f17121,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,[],[f5389]) ).
fof(f5389,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,[],[f1217]) ).
fof(f1217,axiom,
! [X12] : 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))),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__Suc__0) ).
fof(f31536,plain,
spl573_704,
inference(avatar_split_clause,[],[f25297,f31534]) ).
fof(f31534,plain,
( spl573_704
<=> ! [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,[spl573_704])]) ).
fof(f25297,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,[],[f17097,f16829]) ).
fof(f17097,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,[],[f5365]) ).
fof(f5365,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,[],[f738]) ).
fof(f738,axiom,
! [X97] : 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),X97))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) ).
fof(f31532,plain,
spl573_703,
inference(avatar_split_clause,[],[f25293,f31530]) ).
fof(f31530,plain,
( spl573_703
<=> ! [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,[spl573_703])]) ).
fof(f25293,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,[],[f17091,f25292]) ).
fof(f17091,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,[],[f5359]) ).
fof(f5359,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,[],[f1977]) ).
fof(f1977,axiom,
! [X96] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X96)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__number) ).
fof(f31528,plain,
spl573_702,
inference(avatar_split_clause,[],[f25288,f31526]) ).
fof(f31526,plain,
( spl573_702
<=> ! [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,[spl573_702])]) ).
fof(f25288,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,[],[f17078,f16829]) ).
fof(f17078,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,[],[f5346]) ).
fof(f5346,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,[],[f371]) ).
fof(f371,axiom,
! [X96] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X96)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__less__0__conv) ).
fof(f31524,plain,
spl573_701,
inference(avatar_split_clause,[],[f25285,f31522]) ).
fof(f31522,plain,
( spl573_701
<=> ! [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,[spl573_701])]) ).
fof(f25285,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,[],[f17076,f16841]) ).
fof(f17076,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,[],[f5344]) ).
fof(f5344,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,[],[f264]) ).
fof(f264,axiom,
! [X12] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__less__Suc) ).
fof(f31520,plain,
( spl573_700
| ~ spl573_325
| ~ spl573_365 ),
inference(avatar_split_clause,[],[f29903,f29827,f29664,f31517]) ).
fof(f31517,plain,
( spl573_700
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Code__Numeral_Onat__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_700])]) ).
fof(f29664,plain,
( spl573_325
<=> ! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_325])]) ).
fof(f29827,plain,
( spl573_365
<=> 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,[spl573_365])]) ).
fof(f29903,plain,
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Code__Numeral_Onat__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| ~ spl573_325
| ~ spl573_365 ),
inference(superposition,[],[f29665,f29829]) ).
fof(f29829,plain,
( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_HOL_Obool_Obool__size(c_fTrue))
| ~ spl573_365 ),
inference(avatar_component_clause,[],[f29827]) ).
fof(f29665,plain,
( ! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0
| ~ spl573_325 ),
inference(avatar_component_clause,[],[f29664]) ).
fof(f31515,plain,
spl573_699,
inference(avatar_split_clause,[],[f25282,f31513]) ).
fof(f31513,plain,
( spl573_699
<=> ! [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,[spl573_699])]) ).
fof(f25282,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,[],[f17070,f16841]) ).
fof(f17070,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,[],[f5338]) ).
fof(f5338,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,[],[f2375]) ).
fof(f2375,axiom,
! [X6] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X6) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast0AtMost) ).
fof(f31511,plain,
spl573_698,
inference(avatar_split_clause,[],[f25281,f31509]) ).
fof(f31509,plain,
( spl573_698
<=> ! [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,[spl573_698])]) ).
fof(f25281,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,[],[f17063,f16841]) ).
fof(f17063,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,[],[f5331]) ).
fof(f5331,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,[],[f2543]) ).
fof(f2543,axiom,
! [X7] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X7),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oempty) ).
fof(f31507,plain,
spl573_697,
inference(avatar_split_clause,[],[f25278,f31505]) ).
fof(f31505,plain,
( spl573_697
<=> ! [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,[spl573_697])]) ).
fof(f31503,plain,
spl573_696,
inference(avatar_split_clause,[],[f25277,f31501]) ).
fof(f31501,plain,
( spl573_696
<=> ! [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,[spl573_696])]) ).
fof(f25277,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,[],[f17060,f16841]) ).
fof(f17060,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,[],[f5328]) ).
fof(f5328,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,[],[f1010]) ).
fof(f1010,axiom,
! [X12] : 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)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(f31499,plain,
spl573_695,
inference(avatar_split_clause,[],[f25276,f31497]) ).
fof(f31497,plain,
( spl573_695
<=> ! [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,[spl573_695])]) ).
fof(f25276,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,[],[f17059,f16841]) ).
fof(f17059,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,[],[f5327]) ).
fof(f5327,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,[],[f1829]) ).
fof(f1829,axiom,
! [X12] : 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)),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__0L) ).
fof(f31495,plain,
spl573_694,
inference(avatar_split_clause,[],[f25275,f31493]) ).
fof(f31493,plain,
( spl573_694
<=> ! [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,[spl573_694])]) ).
fof(f25275,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,[],[f17058,f16841]) ).
fof(f17058,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,[],[f5326]) ).
fof(f5326,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,[],[f631]) ).
fof(f631,axiom,
! [X85] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X85),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__0__right) ).
fof(f31491,plain,
spl573_693,
inference(avatar_split_clause,[],[f25274,f31489]) ).
fof(f31489,plain,
( spl573_693
<=> ! [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,[spl573_693])]) ).
fof(f25274,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,[],[f17057,f16841]) ).
fof(f17057,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,[],[f5325]) ).
fof(f5325,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,[],[f1830]) ).
fof(f1830,axiom,
! [X12] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__0R) ).
fof(f31487,plain,
spl573_692,
inference(avatar_split_clause,[],[f25218,f31484]) ).
fof(f31484,plain,
( spl573_692
<=> 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,[spl573_692])]) ).
fof(f25218,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,[],[f16914,f16828]) ).
fof(f16828,plain,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
inference(cnf_transformation,[],[f1683]) ).
fof(f1683,axiom,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subtract__code__numeral__def) ).
fof(f16914,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,[],[f1562]) ).
fof(f1562,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral__zero__minus__one) ).
fof(f31481,plain,
spl573_691,
inference(avatar_split_clause,[],[f25215,f31478]) ).
fof(f25215,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,[],[f16911,f16841]) ).
fof(f16911,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,[],[f2510]) ).
fof(f2510,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/sandbox/benchmark/theBenchmark.p',fact_lessThan__0) ).
fof(f31476,plain,
spl573_690,
inference(avatar_split_clause,[],[f25214,f31473]) ).
fof(f31473,plain,
( spl573_690
<=> 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,[spl573_690])]) ).
fof(f25214,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,[],[f16910,f16841]) ).
fof(f16910,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,[],[f2447]) ).
fof(f2447,axiom,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeast__0) ).
fof(f31471,plain,
spl573_689,
inference(avatar_split_clause,[],[f25145,f31469]) ).
fof(f31469,plain,
( spl573_689
<=> ! [X4,X0,X5,X3,X1] :
( X0 = X5
| ~ sP85(X0,X1,X4,X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_689])]) ).
fof(f25145,plain,
! [X3,X0,X1,X4,X5] :
( X0 = X5
| ~ sP85(X0,X1,X4,X3,X4,X5) ),
inference(equality_resolution,[],[f23654]) ).
fof(f23654,plain,
! [X2,X3,X0,X1,X4,X5] :
( X2 != X4
| X0 = X5
| ~ sP85(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f16611]) ).
fof(f16611,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( sP85(X0,X1,X2,X3,X4,X5)
| ( ( hAPP(X3,X2) != hAPP(c_Option_Ooption_OSome(X1),X0)
| X2 = X4 )
& ( X0 != X5
| X2 != X4 ) ) )
& ( ( hAPP(X3,X2) = hAPP(c_Option_Ooption_OSome(X1),X0)
& X2 != X4 )
| ( X0 = X5
& X2 = X4 )
| ~ sP85(X0,X1,X2,X3,X4,X5) ) ),
inference(rectify,[],[f16610]) ).
fof(f16610,plain,
! [X0,X5,X1,X4,X3,X2] :
( ( sP85(X0,X5,X1,X4,X3,X2)
| ( ( hAPP(X4,X1) != hAPP(c_Option_Ooption_OSome(X5),X0)
| X1 = X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( hAPP(X4,X1) = hAPP(c_Option_Ooption_OSome(X5),X0)
& X1 != X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP85(X0,X5,X1,X4,X3,X2) ) ),
inference(flattening,[],[f16609]) ).
fof(f16609,plain,
! [X0,X5,X1,X4,X3,X2] :
( ( sP85(X0,X5,X1,X4,X3,X2)
| ( ( hAPP(X4,X1) != hAPP(c_Option_Ooption_OSome(X5),X0)
| X1 = X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( hAPP(X4,X1) = hAPP(c_Option_Ooption_OSome(X5),X0)
& X1 != X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP85(X0,X5,X1,X4,X3,X2) ) ),
inference(nnf_transformation,[],[f14497]) ).
fof(f14497,plain,
! [X0,X5,X1,X4,X3,X2] :
( sP85(X0,X5,X1,X4,X3,X2)
<=> ( ( hAPP(X4,X1) = hAPP(c_Option_Ooption_OSome(X5),X0)
& X1 != X3 )
| ( X0 = X2
& X1 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP85])]) ).
fof(f31467,plain,
spl573_688,
inference(avatar_split_clause,[],[f24636,f31465]) ).
fof(f31465,plain,
( spl573_688
<=> ! [X0,X3] :
( hBOOL(hAPP(X0,X3))
| ~ sP4(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_688])]) ).
fof(f24636,plain,
! [X3,X0] :
( hBOOL(hAPP(X0,X3))
| ~ sP4(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) ),
inference(equality_resolution,[],[f18773]) ).
fof(f18773,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(X0,X3))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3) != X1
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f14843]) ).
fof(f14843,plain,
! [X0,X1] :
( ( sP4(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,sK168(X0,X1)))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK168(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 ) )
| ~ sP4(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK168])],[f14841,f14842]) ).
fof(f14842,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP(X0,X2))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X1 )
=> ( ~ hBOOL(hAPP(X0,sK168(X0,X1)))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK168(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f14841,plain,
! [X0,X1] :
( ( sP4(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 ) )
| ~ sP4(X0,X1) ) ),
inference(rectify,[],[f14840]) ).
fof(f14840,plain,
! [X1,X0] :
( ( sP4(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 ) )
| ~ sP4(X1,X0) ) ),
inference(flattening,[],[f14839]) ).
fof(f14839,plain,
! [X1,X0] :
( ( sP4(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 ) )
| ~ sP4(X1,X0) ) ),
inference(nnf_transformation,[],[f14354]) ).
fof(f14354,plain,
! [X1,X0] :
( sP4(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,[sP4])]) ).
fof(f31463,plain,
spl573_687,
inference(avatar_split_clause,[],[f24568,f31461]) ).
fof(f31461,plain,
( spl573_687
<=> ! [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,[spl573_687])]) ).
fof(f24568,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,[],[f17994]) ).
fof(f17994,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,[],[f14622]) ).
fof(f14622,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,[],[f10496]) ).
fof(f10496,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,[],[f6114]) ).
fof(f6114,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,[],[f459]) ).
fof(f459,axiom,
! [X76,X7] :
( class_Groups_Olinordered__ab__group__add(X7)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X7),X76) = X76
<=> c_Groups_Ozero__class_Ozero(X7) = X76 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equal__neg__zero) ).
fof(f31459,plain,
spl573_686,
inference(avatar_split_clause,[],[f23861,f31457]) ).
fof(f31457,plain,
( spl573_686
<=> ! [X0,X1] : c_Int_OBit1(X0) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_686])]) ).
fof(f23861,plain,
! [X0,X1] : c_Int_OBit1(X0) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X1)),
inference(definition_unfolding,[],[f17472,f23734]) ).
fof(f23734,plain,
! [X0] : c_Int_OBit0(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X0)),
inference(definition_unfolding,[],[f16974,f17033]) ).
fof(f17033,plain,
! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X0),
inference(cnf_transformation,[],[f5301]) ).
fof(f5301,plain,
! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X0),
inference(rectify,[],[f1364]) ).
fof(f1364,axiom,
! [X96] : c_Int_Opred(X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min) ).
fof(f16974,plain,
! [X0] : c_Int_OBit0(X0) = c_Int_Opred(c_Int_OBit1(X0)),
inference(cnf_transformation,[],[f5242]) ).
fof(f5242,plain,
! [X0] : c_Int_OBit0(X0) = c_Int_Opred(c_Int_OBit1(X0)),
inference(rectify,[],[f1478]) ).
fof(f1478,axiom,
! [X96] : c_Int_OBit0(X96) = c_Int_Opred(c_Int_OBit1(X96)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__Bit1) ).
fof(f17472,plain,
! [X0,X1] : c_Int_OBit1(X0) != c_Int_OBit0(X1),
inference(cnf_transformation,[],[f5653]) ).
fof(f5653,plain,
! [X0,X1] : c_Int_OBit1(X0) != c_Int_OBit0(X1),
inference(rectify,[],[f1452]) ).
fof(f1452,axiom,
! [X117,X96] : c_Int_OBit1(X117) != c_Int_OBit0(X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I49_J) ).
fof(f31455,plain,
spl573_685,
inference(avatar_split_clause,[],[f23769,f31453]) ).
fof(f31453,plain,
( spl573_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,[spl573_685])]) ).
fof(f23769,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,[],[f16960,f17065]) ).
fof(f17065,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,[],[f5333]) ).
fof(f5333,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,[],[f1984]) ).
fof(f1984,axiom,
! [X96] : c_Code__Numeral_OSuc__code__numeral(X96) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X96))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__code__numeral__def) ).
fof(f16960,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X0),
inference(cnf_transformation,[],[f5228]) ).
fof(f5228,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X0),
inference(rectify,[],[f1686]) ).
fof(f1686,axiom,
! [X175] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X175),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I3_J) ).
fof(f31451,plain,
spl573_684,
inference(avatar_split_clause,[],[f23011,f31449]) ).
fof(f31449,plain,
( spl573_684
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,X4))
| ~ sP70(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_684])]) ).
fof(f23011,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,X4))
| ~ sP70(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16351]) ).
fof(f16351,plain,
! [X0,X1,X2,X3,X4] :
( ( sP70(X0,X1,X2,X3,X4)
| ! [X5] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X5,X1,X0)
| ~ c_Natural_Oevaln(X2,X4,X1,X5) )
| ~ hBOOL(hAPP(X3,X4)) )
& ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),sK506(X0,X1,X2,X3,X4),X1,X0)
& c_Natural_Oevaln(X2,X4,X1,sK506(X0,X1,X2,X3,X4))
& hBOOL(hAPP(X3,X4)) )
| ~ sP70(X0,X1,X2,X3,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK506])],[f16349,f16350]) ).
fof(f16350,plain,
! [X0,X1,X2,X3,X4] :
( ? [X6] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X6,X1,X0)
& c_Natural_Oevaln(X2,X4,X1,X6) )
=> ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),sK506(X0,X1,X2,X3,X4),X1,X0)
& c_Natural_Oevaln(X2,X4,X1,sK506(X0,X1,X2,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f16349,plain,
! [X0,X1,X2,X3,X4] :
( ( sP70(X0,X1,X2,X3,X4)
| ! [X5] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X5,X1,X0)
| ~ c_Natural_Oevaln(X2,X4,X1,X5) )
| ~ hBOOL(hAPP(X3,X4)) )
& ( ( ? [X6] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X6,X1,X0)
& c_Natural_Oevaln(X2,X4,X1,X6) )
& hBOOL(hAPP(X3,X4)) )
| ~ sP70(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16348]) ).
fof(f16348,plain,
! [X0,X1,X3,X4,X2] :
( ( sP70(X0,X1,X3,X4,X2)
| ! [X5] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
| ~ c_Natural_Oevaln(X3,X2,X1,X5) )
| ~ hBOOL(hAPP(X4,X2)) )
& ( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) )
| ~ sP70(X0,X1,X3,X4,X2) ) ),
inference(flattening,[],[f16347]) ).
fof(f16347,plain,
! [X0,X1,X3,X4,X2] :
( ( sP70(X0,X1,X3,X4,X2)
| ! [X5] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
| ~ c_Natural_Oevaln(X3,X2,X1,X5) )
| ~ hBOOL(hAPP(X4,X2)) )
& ( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) )
| ~ sP70(X0,X1,X3,X4,X2) ) ),
inference(nnf_transformation,[],[f14467]) ).
fof(f14467,plain,
! [X0,X1,X3,X4,X2] :
( sP70(X0,X1,X3,X4,X2)
<=> ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP70])]) ).
fof(f31447,plain,
spl573_683,
inference(avatar_split_clause,[],[f22814,f31445]) ).
fof(f31445,plain,
( spl573_683
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,X4))
| ~ sP67(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_683])]) ).
fof(f22814,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,X4))
| ~ sP67(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16261]) ).
fof(f16261,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),sK467(X0,X1,X2,X3,X4),X1,X0)
& c_Natural_Oevaln(X2,X4,X1,sK467(X0,X1,X2,X3,X4))
& hBOOL(hAPP(X3,X4)) )
| ~ sP67(X0,X1,X2,X3,X4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK467])],[f16259,f16260]) ).
fof(f16260,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X5,X1,X0)
& c_Natural_Oevaln(X2,X4,X1,X5) )
=> ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),sK467(X0,X1,X2,X3,X4),X1,X0)
& c_Natural_Oevaln(X2,X4,X1,sK467(X0,X1,X2,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f16259,plain,
! [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X5,X1,X0)
& c_Natural_Oevaln(X2,X4,X1,X5) )
& hBOOL(hAPP(X3,X4)) )
| ~ sP67(X0,X1,X2,X3,X4) ),
inference(rectify,[],[f16258]) ).
fof(f16258,plain,
! [X0,X1,X3,X4,X2] :
( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) )
| ~ sP67(X0,X1,X3,X4,X2) ),
inference(nnf_transformation,[],[f14461]) ).
fof(f14461,plain,
! [X0,X1,X3,X4,X2] :
( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) )
| ~ sP67(X0,X1,X3,X4,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP67])]) ).
fof(f31443,plain,
spl573_682,
inference(avatar_split_clause,[],[f22361,f31441]) ).
fof(f31441,plain,
( spl573_682
<=> ! [X0,X3,X2,X1] :
( sP63(X0,X1,X2,X3)
| ~ sP64(X0,X1,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_682])]) ).
fof(f22361,plain,
! [X2,X3,X0,X1] :
( sP63(X0,X1,X2,X3)
| ~ sP64(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f16192]) ).
fof(f16192,plain,
! [X0,X1,X2,X3] :
( ( sP63(X0,X1,X2,X3)
| ~ sP64(X0,X1,X3,X2) )
& ( sP64(X0,X1,X3,X2)
| ~ sP63(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f14457]) ).
fof(f14457,plain,
! [X0,X1,X2,X3] :
( sP63(X0,X1,X2,X3)
<=> sP64(X0,X1,X3,X2) ),
inference(definition_folding,[],[f9115,f14456,f14455]) ).
fof(f14455,plain,
! [X0,X1,X2,X3] :
( sP63(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,[sP63])]) ).
fof(f14456,plain,
! [X0,X1,X3,X2] :
( sP64(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,[sP64])]) ).
fof(f9115,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,[],[f2322]) ).
fof(f2322,axiom,
! [X5,X152,X148,X7] :
( ? [X2] :
( hBOOL(hAPP(X5,X2))
& hBOOL(hAPP(hAPP(c_member(X7),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X148),X152))) )
<=> ( ? [X2] :
( hBOOL(hAPP(X5,X2))
& hBOOL(hAPP(hAPP(c_member(X7),X2),X152)) )
| ? [X2] :
( hBOOL(hAPP(X5,X2))
& hBOOL(hAPP(hAPP(c_member(X7),X2),X148)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__Un) ).
fof(f31439,plain,
spl573_681,
inference(avatar_split_clause,[],[f22360,f31437]) ).
fof(f31437,plain,
( spl573_681
<=> ! [X0,X3,X2,X1] :
( sP64(X0,X1,X3,X2)
| ~ sP63(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_681])]) ).
fof(f22360,plain,
! [X2,X3,X0,X1] :
( sP64(X0,X1,X3,X2)
| ~ sP63(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16192]) ).
fof(f31435,plain,
spl573_680,
inference(avatar_split_clause,[],[f22085,f31433]) ).
fof(f31433,plain,
( spl573_680
<=> ! [X2,X0,X1,X3] :
( X0 = X2
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_680])]) ).
fof(f22085,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ),
inference(cnf_transformation,[],[f15988]) ).
fof(f15988,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OWhile(X1,X0) = c_Com_Ocom_OWhile(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ) ),
inference(flattening,[],[f15987]) ).
fof(f15987,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OWhile(X1,X0) = c_Com_Ocom_OWhile(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ) ),
inference(nnf_transformation,[],[f9030]) ).
fof(f9030,plain,
! [X0,X1,X2,X3] :
( c_Com_Ocom_OWhile(X1,X0) = c_Com_Ocom_OWhile(X3,X2)
<=> ( X0 = X2
& X1 = X3 ) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X35,X53,X38,X56] :
( c_Com_Ocom_OWhile(X53,X35) = c_Com_Ocom_OWhile(X56,X38)
<=> ( X35 = X38
& X53 = X56 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I5_J) ).
fof(f31431,plain,
spl573_679,
inference(avatar_split_clause,[],[f22084,f31429]) ).
fof(f31429,plain,
( spl573_679
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_679])]) ).
fof(f22084,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ),
inference(cnf_transformation,[],[f15988]) ).
fof(f31427,plain,
spl573_678,
inference(avatar_split_clause,[],[f22082,f31425]) ).
fof(f31425,plain,
( spl573_678
<=> ! [X2,X0,X1,X3] :
( X0 = X2
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_678])]) ).
fof(f22082,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ),
inference(cnf_transformation,[],[f15986]) ).
fof(f15986,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OSemi(X1,X0) = c_Com_Ocom_OSemi(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ) ),
inference(flattening,[],[f15985]) ).
fof(f15985,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OSemi(X1,X0) = c_Com_Ocom_OSemi(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ) ),
inference(nnf_transformation,[],[f9029]) ).
fof(f9029,plain,
! [X0,X1,X2,X3] :
( c_Com_Ocom_OSemi(X1,X0) = c_Com_Ocom_OSemi(X3,X2)
<=> ( X0 = X2
& X1 = X3 ) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X51,X52,X54,X55] :
( c_Com_Ocom_OSemi(X55,X54) = c_Com_Ocom_OSemi(X52,X51)
<=> ( X51 = X54
& X52 = X55 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I3_J) ).
fof(f31423,plain,
spl573_677,
inference(avatar_split_clause,[],[f22081,f31421]) ).
fof(f31421,plain,
( spl573_677
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_677])]) ).
fof(f22081,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ),
inference(cnf_transformation,[],[f15986]) ).
fof(f31419,plain,
spl573_676,
inference(avatar_split_clause,[],[f22079,f31417]) ).
fof(f31417,plain,
( spl573_676
<=> ! [X2,X0,X1,X3] :
( X0 = X2
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_676])]) ).
fof(f22079,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ),
inference(cnf_transformation,[],[f15984]) ).
fof(f15984,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OAss(X1,X0) = c_Com_Ocom_OAss(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ) ),
inference(flattening,[],[f15983]) ).
fof(f15983,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OAss(X1,X0) = c_Com_Ocom_OAss(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ) ),
inference(nnf_transformation,[],[f9028]) ).
fof(f9028,plain,
! [X0,X1,X2,X3] :
( c_Com_Ocom_OAss(X1,X0) = c_Com_Ocom_OAss(X3,X2)
<=> ( X0 = X2
& X1 = X3 ) ),
inference(rectify,[],[f111]) ).
fof(f111,axiom,
! [X53,X79,X56,X75] :
( c_Com_Ocom_OAss(X75,X56) = c_Com_Ocom_OAss(X79,X53)
<=> ( X53 = X56
& X75 = X79 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I1_J) ).
fof(f31415,plain,
spl573_675,
inference(avatar_split_clause,[],[f22078,f31413]) ).
fof(f31413,plain,
( spl573_675
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_675])]) ).
fof(f22078,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ),
inference(cnf_transformation,[],[f15984]) ).
fof(f31411,plain,
spl573_674,
inference(avatar_split_clause,[],[f22069,f31409]) ).
fof(f31409,plain,
( spl573_674
<=> ! [X0,X3,X2,X1] :
( sP53(X2,X0,X3,X1)
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_674])]) ).
fof(f22069,plain,
! [X2,X3,X0,X1] :
( sP53(X2,X0,X3,X1)
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f15975]) ).
fof(f15975,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
| ~ sP53(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)) )
& ( ( sP53(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,[],[f15974]) ).
fof(f15974,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
| ~ sP53(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)) )
& ( ( sP53(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,[],[f14438]) ).
fof(f14438,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
<=> ( sP53(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,[],[f13433,f14437]) ).
fof(f14437,plain,
! [X2,X0,X3,X1] :
( sP53(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,[sP53])]) ).
fof(f13433,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,[],[f9025]) ).
fof(f9025,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,[],[f3509]) ).
fof(f3509,axiom,
! [X44,X46,X189,X7] :
( c_Wellfounded_Omax__extp(X7,X189,X46,X44)
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X7),X2),X46))
=> ? [X202] :
( hBOOL(hAPP(hAPP(X189,X2),X202))
& hBOOL(hAPP(hAPP(c_member(X7),X202),X44)) ) )
& c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) != X44
& hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X44))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X46)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__extp_Oequations) ).
fof(f31407,plain,
spl573_673,
inference(avatar_split_clause,[],[f22067,f31405]) ).
fof(f31405,plain,
( spl573_673
<=> ! [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,[spl573_673])]) ).
fof(f22067,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f15975]) ).
fof(f31403,plain,
spl573_672,
inference(avatar_split_clause,[],[f22066,f31401]) ).
fof(f31401,plain,
( spl573_672
<=> ! [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,[spl573_672])]) ).
fof(f22066,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f15975]) ).
fof(f31399,plain,
spl573_671,
inference(avatar_split_clause,[],[f21081,f31397]) ).
fof(f31397,plain,
( spl573_671
<=> ! [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,[spl573_671])]) ).
fof(f21081,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,[],[f8185]) ).
fof(f8185,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,[],[f2711]) ).
fof(f2711,axiom,
! [X44,X46,X58,X7] : c_Nitpick_Ofold__graph_H(X7,X58,X46,X44,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),X44),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold__graph_H_Oequations_I1_J) ).
fof(f31395,plain,
spl573_670,
inference(avatar_split_clause,[],[f21080,f31393]) ).
fof(f31393,plain,
( spl573_670
<=> ! [X2,X0,X1,X3] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_670])]) ).
fof(f21080,plain,
! [X2,X3,X0,X1] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0,
inference(cnf_transformation,[],[f8184]) ).
fof(f8184,plain,
! [X0,X1,X2,X3] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0,
inference(rectify,[],[f4717]) ).
fof(f4717,axiom,
! [X76,X1,X58,X7] : hAPP(c_List_Ofoldl(X7,X58,X1,X76),c_List_Olist_ONil(X58)) = X76,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_foldl__Nil) ).
fof(f31391,plain,
( ~ spl573_668
| ~ spl573_669
| ~ spl573_311
| ~ spl573_466
| ~ spl573_587 ),
inference(avatar_split_clause,[],[f31092,f30837,f30273,f29596,f31388,f31384]) ).
fof(f31384,plain,
( spl573_668
<=> class_Int_Onumber__ring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_668])]) ).
fof(f31388,plain,
( spl573_669
<=> c_Int_Oiszero(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_669])]) ).
fof(f29596,plain,
( spl573_311
<=> 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,[spl573_311])]) ).
fof(f30273,plain,
( spl573_466
<=> ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_466])]) ).
fof(f30837,plain,
( spl573_587
<=> ! [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,[spl573_587])]) ).
fof(f31092,plain,
( ~ c_Int_Oiszero(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Int_Onumber__ring(tc_Nat_Onat)
| ~ spl573_311
| ~ spl573_466
| ~ spl573_587 ),
inference(forward_demodulation,[],[f31091,f29598]) ).
fof(f29598,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl573_311 ),
inference(avatar_component_clause,[],[f29596]) ).
fof(f31091,plain,
( ~ c_Int_Oiszero(tc_Nat_Onat,hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ class_Int_Onumber__ring(tc_Nat_Onat)
| ~ spl573_466
| ~ spl573_587 ),
inference(superposition,[],[f30838,f30274]) ).
fof(f30274,plain,
( ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X0)
| ~ spl573_466 ),
inference(avatar_component_clause,[],[f30273]) ).
fof(f30838,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) )
| ~ spl573_587 ),
inference(avatar_component_clause,[],[f30837]) ).
fof(f31382,plain,
spl573_667,
inference(avatar_split_clause,[],[f21079,f31380]) ).
fof(f31380,plain,
( spl573_667
<=> ! [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,[spl573_667])]) ).
fof(f21079,plain,
! [X2,X3,X0,X1] : hAPP(c_List_Olist_Olist__case(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X1,
inference(cnf_transformation,[],[f8183]) ).
fof(f8183,plain,
! [X0,X1,X2,X3] : hAPP(c_List_Olist_Olist__case(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X1,
inference(rectify,[],[f4487]) ).
fof(f4487,axiom,
! [X70,X57,X58,X7] : hAPP(c_List_Olist_Olist__case(X7,X58,X57,X70),c_List_Olist_ONil(X58)) = X57,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I4_J) ).
fof(f31378,plain,
spl573_666,
inference(avatar_split_clause,[],[f21078,f31376]) ).
fof(f31376,plain,
( spl573_666
<=> ! [X2,X0,X1,X3] : hAPP(c_Option_Ooption_Ooption__case(X3,X2,X1,X0),c_Option_Ooption_ONone(X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_666])]) ).
fof(f21078,plain,
! [X2,X3,X0,X1] : hAPP(c_Option_Ooption_Ooption__case(X3,X2,X1,X0),c_Option_Ooption_ONone(X2)) = X1,
inference(cnf_transformation,[],[f8182]) ).
fof(f8182,plain,
! [X0,X1,X2,X3] : hAPP(c_Option_Ooption_Ooption__case(X3,X2,X1,X0),c_Option_Ooption_ONone(X2)) = X1,
inference(rectify,[],[f341]) ).
fof(f341,axiom,
! [X70,X57,X58,X7] : hAPP(c_Option_Ooption_Ooption__case(X7,X58,X57,X70),c_Option_Ooption_ONone(X58)) = X57,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I4_J) ).
fof(f31374,plain,
spl573_665,
inference(avatar_split_clause,[],[f20738,f31372]) ).
fof(f31372,plain,
( spl573_665
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP31(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_665])]) ).
fof(f20738,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP31(X1,X0,X2) ),
inference(cnf_transformation,[],[f15535]) ).
fof(f15535,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP31(X1,X0,X2) )
& ( sP31(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ) ),
inference(nnf_transformation,[],[f14400]) ).
fof(f14400,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
<=> sP31(X1,X0,X2) ),
inference(definition_folding,[],[f12517,f14399,f14398]) ).
fof(f14398,plain,
! [X0,X1] :
( sP30(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,[sP30])]) ).
fof(f12517,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,[],[f8062]) ).
fof(f8062,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,[],[f1909]) ).
fof(f1909,axiom,
! [X192,X6,X95] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X95,X6),X192))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X6
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X192)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X192))) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X6))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X192)),X6))
& 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),X192))) ) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X6
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X192) )
& 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),X192)),X6)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X192)) = X95 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__nat__rel__def) ).
fof(f31370,plain,
spl573_664,
inference(avatar_split_clause,[],[f20737,f31368]) ).
fof(f31368,plain,
( spl573_664
<=> ! [X2,X0,X1] :
( sP31(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_664])]) ).
fof(f20737,plain,
! [X2,X0,X1] :
( sP31(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ),
inference(cnf_transformation,[],[f15535]) ).
fof(f31366,plain,
spl573_663,
inference(avatar_split_clause,[],[f20636,f31364]) ).
fof(f20636,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP27(X0,X1,X2) ),
inference(cnf_transformation,[],[f15443]) ).
fof(f31362,plain,
spl573_662,
inference(avatar_split_clause,[],[f20306,f31360]) ).
fof(f31360,plain,
( spl573_662
<=> ! [X0,X1] :
( sK230(X0,X1) != sK231(X0,X1)
| ~ sP22(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_662])]) ).
fof(f20306,plain,
! [X0,X1] :
( sK230(X0,X1) != sK231(X0,X1)
| ~ sP22(X0,X1) ),
inference(cnf_transformation,[],[f15325]) ).
fof(f15325,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)),sK230(X0,X1)),sK231(X0,X1))
& sK230(X0,X1) != sK231(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK231(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK230(X0,X1)),X1)) )
| ~ sP22(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK230,sK231])],[f15322,f15324,f15323]) ).
fof(f15323,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)),sK230(X0,X1)),X3)
& sK230(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)),sK230(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15324,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)),sK230(X0,X1)),X3)
& sK230(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)),sK230(X0,X1)),sK231(X0,X1))
& sK230(X0,X1) != sK231(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK231(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15322,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)) )
| ~ sP22(X0,X1) ),
inference(rectify,[],[f15321]) ).
fof(f15321,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)) )
| ~ sP22(X2,X1) ),
inference(nnf_transformation,[],[f14384]) ).
fof(f14384,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)) )
| ~ sP22(X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
fof(f31358,plain,
spl573_661,
inference(avatar_split_clause,[],[f20299,f31356]) ).
fof(f31356,plain,
( spl573_661
<=> ! [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,[spl573_661])]) ).
fof(f20299,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,[],[f12155]) ).
fof(f12155,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,[],[f7797]) ).
fof(f7797,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,[],[f3]) ).
fof(f3,axiom,
! [X11,X12,X13] :
( c_Hoare__Mirabelle_Otriple__valid(X13,hAPP(c_Nat_OSuc,X12),X11)
=> c_Hoare__Mirabelle_Otriple__valid(X13,X12,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple__valid__Suc) ).
fof(f31354,plain,
spl573_660,
inference(avatar_split_clause,[],[f19217,f31352]) ).
fof(f31352,plain,
( spl573_660
<=> ! [X2,X0,X1] : c_Sum__Type_OProjr(X2,X1,hAPP(c_Sum__Type_OInr(X1,X2),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_660])]) ).
fof(f19217,plain,
! [X2,X0,X1] : c_Sum__Type_OProjr(X2,X1,hAPP(c_Sum__Type_OInr(X1,X2),X0)) = X0,
inference(cnf_transformation,[],[f6899]) ).
fof(f6899,plain,
! [X0,X1,X2] : c_Sum__Type_OProjr(X2,X1,hAPP(c_Sum__Type_OInr(X1,X2),X0)) = X0,
inference(rectify,[],[f257]) ).
fof(f257,axiom,
! [X61,X7,X13] : c_Sum__Type_OProjr(X13,X7,hAPP(c_Sum__Type_OInr(X7,X13),X61)) = X61,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Projr_Osimps) ).
fof(f31350,plain,
spl573_659,
inference(avatar_split_clause,[],[f19216,f31348]) ).
fof(f31348,plain,
( spl573_659
<=> ! [X2,X0,X1] : c_Sum__Type_OProjl(X2,X1,hAPP(c_Sum__Type_OInl(X2,X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_659])]) ).
fof(f19216,plain,
! [X2,X0,X1] : c_Sum__Type_OProjl(X2,X1,hAPP(c_Sum__Type_OInl(X2,X1),X0)) = X0,
inference(cnf_transformation,[],[f6898]) ).
fof(f6898,plain,
! [X0,X1,X2] : c_Sum__Type_OProjl(X2,X1,hAPP(c_Sum__Type_OInl(X2,X1),X0)) = X0,
inference(rectify,[],[f256]) ).
fof(f256,axiom,
! [X61,X7,X13] : c_Sum__Type_OProjl(X13,X7,hAPP(c_Sum__Type_OInl(X13,X7),X61)) = X61,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Projl_Osimps) ).
fof(f31346,plain,
spl573_658,
inference(avatar_split_clause,[],[f19215,f31344]) ).
fof(f31344,plain,
( spl573_658
<=> ! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_658])]) ).
fof(f19215,plain,
! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0,
inference(cnf_transformation,[],[f6897]) ).
fof(f6897,plain,
! [X0,X1,X2] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0,
inference(rectify,[],[f3715]) ).
fof(f3715,axiom,
! [X0,X7,X58] : hAPP(c_Fun_Ocomp(X58,X58,X7,c_Fun_Oid(X58)),X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__o) ).
fof(f31342,plain,
spl573_657,
inference(avatar_split_clause,[],[f19214,f31340]) ).
fof(f31340,plain,
( spl573_657
<=> ! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_657])]) ).
fof(f19214,plain,
! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0,
inference(cnf_transformation,[],[f6896]) ).
fof(f6896,plain,
! [X0,X1,X2] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0,
inference(rectify,[],[f3716]) ).
fof(f3716,axiom,
! [X1,X58,X7] : hAPP(c_Fun_Ocomp(X7,X58,X7,X1),c_Fun_Oid(X7)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_o__id) ).
fof(f31338,plain,
spl573_656,
inference(avatar_split_clause,[],[f19212,f31336]) ).
fof(f31336,plain,
( spl573_656
<=> ! [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,[spl573_656])]) ).
fof(f19212,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,[],[f6894]) ).
fof(f6894,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,[],[f3504]) ).
fof(f3504,axiom,
! [X99,X1,X7] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,X1,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),X99)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__fold1SetE) ).
fof(f31334,plain,
spl573_655,
inference(avatar_split_clause,[],[f18862,f31332]) ).
fof(f31332,plain,
( spl573_655
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_655])]) ).
fof(f18862,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ),
inference(cnf_transformation,[],[f14911]) ).
fof(f14911,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,[],[f6747]) ).
fof(f6747,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
<=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f3967]) ).
fof(f3967,axiom,
! [X169,X7] :
( c_Wellfounded_Oacyclic(X7,hAPP(c_Relation_Oconverse(X7,X7),X169))
<=> c_Wellfounded_Oacyclic(X7,X169) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__converse) ).
fof(f31330,plain,
spl573_654,
inference(avatar_split_clause,[],[f18861,f31328]) ).
fof(f31328,plain,
( spl573_654
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_654])]) ).
fof(f18861,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ),
inference(cnf_transformation,[],[f14911]) ).
fof(f31326,plain,
spl573_653,
inference(avatar_split_clause,[],[f18813,f31324]) ).
fof(f31324,plain,
( spl573_653
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Com_Ocom_OBODY,X0) != hAPP(c_Com_Ocom_OBODY,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_653])]) ).
fof(f18813,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Com_Ocom_OBODY,X0) != hAPP(c_Com_Ocom_OBODY,X1) ),
inference(cnf_transformation,[],[f14871]) ).
fof(f14871,plain,
! [X0,X1] :
( ( hAPP(c_Com_Ocom_OBODY,X0) = hAPP(c_Com_Ocom_OBODY,X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Com_Ocom_OBODY,X0) != hAPP(c_Com_Ocom_OBODY,X1) ) ),
inference(nnf_transformation,[],[f6726]) ).
fof(f6726,plain,
! [X0,X1] :
( hAPP(c_Com_Ocom_OBODY,X0) = hAPP(c_Com_Ocom_OBODY,X1)
<=> X0 = X1 ),
inference(rectify,[],[f112]) ).
fof(f112,axiom,
! [X78,X74] :
( hAPP(c_Com_Ocom_OBODY,X74) = hAPP(c_Com_Ocom_OBODY,X78)
<=> X74 = X78 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I6_J) ).
fof(f31322,plain,
spl573_652,
inference(avatar_split_clause,[],[f18811,f31320]) ).
fof(f31320,plain,
( spl573_652
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Oof__nat,X0) != hAPP(c_Code__Numeral_Oof__nat,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_652])]) ).
fof(f18811,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Oof__nat,X0) != hAPP(c_Code__Numeral_Oof__nat,X1) ),
inference(cnf_transformation,[],[f14870]) ).
fof(f14870,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,[],[f6725]) ).
fof(f6725,plain,
! [X0,X1] :
( hAPP(c_Code__Numeral_Oof__nat,X0) = hAPP(c_Code__Numeral_Oof__nat,X1)
<=> X0 = X1 ),
inference(rectify,[],[f1696]) ).
fof(f1696,axiom,
! [X95,X6] :
( hAPP(c_Code__Numeral_Oof__nat,X6) = hAPP(c_Code__Numeral_Oof__nat,X95)
<=> X6 = X95 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__inject) ).
fof(f31318,plain,
spl573_651,
inference(avatar_split_clause,[],[f18807,f31316]) ).
fof(f31316,plain,
( spl573_651
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Onat__of,X0) != hAPP(c_Code__Numeral_Onat__of,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_651])]) ).
fof(f18807,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Onat__of,X0) != hAPP(c_Code__Numeral_Onat__of,X1) ),
inference(cnf_transformation,[],[f14868]) ).
fof(f14868,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,[],[f6723]) ).
fof(f6723,plain,
! [X0,X1] :
( hAPP(c_Code__Numeral_Onat__of,X0) = hAPP(c_Code__Numeral_Onat__of,X1)
<=> X0 = X1 ),
inference(rectify,[],[f1972]) ).
fof(f1972,axiom,
! [X124,X99] :
( hAPP(c_Code__Numeral_Onat__of,X99) = hAPP(c_Code__Numeral_Onat__of,X124)
<=> X99 = X124 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Onat__of__inject) ).
fof(f31314,plain,
spl573_650,
inference(avatar_split_clause,[],[f18805,f31312]) ).
fof(f31312,plain,
( spl573_650
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Int_ORep__Integ,X0) != hAPP(c_Int_ORep__Integ,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_650])]) ).
fof(f18805,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Int_ORep__Integ,X0) != hAPP(c_Int_ORep__Integ,X1) ),
inference(cnf_transformation,[],[f14867]) ).
fof(f14867,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,[],[f6722]) ).
fof(f6722,plain,
! [X0,X1] :
( hAPP(c_Int_ORep__Integ,X0) = hAPP(c_Int_ORep__Integ,X1)
<=> X0 = X1 ),
inference(rectify,[],[f2616]) ).
fof(f2616,axiom,
! [X124,X99] :
( hAPP(c_Int_ORep__Integ,X99) = hAPP(c_Int_ORep__Integ,X124)
<=> X99 = X124 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
fof(f31310,plain,
spl573_649,
inference(avatar_split_clause,[],[f18689,f31308]) ).
fof(f31308,plain,
( spl573_649
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ~ hBOOL(hAPP(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_649])]) ).
fof(f18689,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(cnf_transformation,[],[f11231]) ).
fof(f11231,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ! [X2] : ~ hBOOL(hAPP(X1,X2)) ),
inference(ennf_transformation,[],[f6678]) ).
fof(f6678,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(X1,X2))
=> hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ),
inference(rectify,[],[f3854]) ).
fof(f3854,axiom,
! [X7,X258] :
( ? [X2] : hBOOL(hAPP(X258,X2))
=> hBOOL(hAPP(X258,c_Hilbert__Choice_OEps(X7,X258))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__some) ).
fof(f31306,plain,
spl573_648,
inference(avatar_split_clause,[],[f18391,f31304]) ).
fof(f31304,plain,
( spl573_648
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_648])]) ).
fof(f18391,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X0)) ),
inference(cnf_transformation,[],[f10892]) ).
fof(f10892,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X0)) ),
inference(ennf_transformation,[],[f6442]) ).
fof(f6442,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X0))
=> X0 = X1 ),
inference(rectify,[],[f103]) ).
fof(f103,axiom,
! [X11,X14] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X14),X11))
=> X11 = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I1_J) ).
fof(f31302,plain,
( ~ spl573_27
| ~ spl573_647
| ~ spl573_244
| ~ spl573_587 ),
inference(avatar_split_clause,[],[f31090,f30837,f29295,f31299,f28229]) ).
fof(f28229,plain,
( spl573_27
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_27])]) ).
fof(f31299,plain,
( spl573_647
<=> c_Int_Oiszero(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_647])]) ).
fof(f29295,plain,
( spl573_244
<=> ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_244])]) ).
fof(f31090,plain,
( ~ c_Int_Oiszero(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Int_Onumber__ring(tc_Int_Oint)
| ~ spl573_244
| ~ spl573_587 ),
inference(superposition,[],[f30838,f29296]) ).
fof(f29296,plain,
( ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0
| ~ spl573_244 ),
inference(avatar_component_clause,[],[f29295]) ).
fof(f31297,plain,
spl573_646,
inference(avatar_split_clause,[],[f18387,f31295]) ).
fof(f31295,plain,
( spl573_646
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_646])]) ).
fof(f18387,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ),
inference(cnf_transformation,[],[f10888]) ).
fof(f10888,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ),
inference(ennf_transformation,[],[f6439]) ).
fof(f6439,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Nat_OSuc,X1)
=> X0 = X1 ),
inference(rectify,[],[f40]) ).
fof(f40,axiom,
! [X60,X61] :
( hAPP(c_Nat_OSuc,X61) = hAPP(c_Nat_OSuc,X60)
=> X60 = X61 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
fof(f31293,plain,
spl573_645,
inference(avatar_split_clause,[],[f18380,f31291]) ).
fof(f31291,plain,
( spl573_645
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X0))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_645])]) ).
fof(f18380,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X0))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X1,X0))) ),
inference(cnf_transformation,[],[f10881]) ).
fof(f10881,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X0))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X1,X0))) ),
inference(ennf_transformation,[],[f6433]) ).
fof(f6433,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X1,X0)))
=> hBOOL(hAPP(c_Com_OWT,X0)) ),
inference(rectify,[],[f60]) ).
fof(f60,axiom,
! [X4,X27] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X27,X4)))
=> hBOOL(hAPP(c_Com_OWT,X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I6_J) ).
fof(f31289,plain,
spl573_644,
inference(avatar_split_clause,[],[f18379,f31287]) ).
fof(f31287,plain,
( spl573_644
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X0))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_644])]) ).
fof(f18379,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X0))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X0))) ),
inference(cnf_transformation,[],[f10880]) ).
fof(f10880,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_Com_OWT,X0))
& hBOOL(hAPP(c_Com_OWT,X1)) )
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X0))) ),
inference(ennf_transformation,[],[f6432]) ).
fof(f6432,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X0)))
=> ~ ( hBOOL(hAPP(c_Com_OWT,X1))
=> ~ hBOOL(hAPP(c_Com_OWT,X0)) ) ),
inference(rectify,[],[f56]) ).
fof(f56,axiom,
! [X59,X19] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X19,X59)))
=> ~ ( hBOOL(hAPP(c_Com_OWT,X19))
=> ~ hBOOL(hAPP(c_Com_OWT,X59)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I4_J) ).
fof(f31285,plain,
spl573_643,
inference(avatar_split_clause,[],[f18378,f31283]) ).
fof(f31283,plain,
( spl573_643
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_643])]) ).
fof(f18378,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X1))
| ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(X1,X0))) ),
inference(cnf_transformation,[],[f10880]) ).
fof(f31281,plain,
spl573_642,
inference(avatar_split_clause,[],[f18361,f31279]) ).
fof(f31279,plain,
( spl573_642
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X0,X1)))
| ~ hBOOL(hAPP(c_Com_OWT,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_642])]) ).
fof(f18361,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X0,X1)))
| ~ hBOOL(hAPP(c_Com_OWT,X1)) ),
inference(cnf_transformation,[],[f10864]) ).
fof(f10864,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X0,X1)))
| ~ hBOOL(hAPP(c_Com_OWT,X1)) ),
inference(ennf_transformation,[],[f6420]) ).
fof(f6420,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Com_OWT,X1))
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X0,X1))) ),
inference(rectify,[],[f70]) ).
fof(f70,axiom,
! [X27,X4] :
( hBOOL(hAPP(c_Com_OWT,X4))
=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(X27,X4))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_While) ).
fof(f31277,plain,
spl573_641,
inference(avatar_split_clause,[],[f18340,f31275]) ).
fof(f31275,plain,
( spl573_641
<=> ! [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,[spl573_641])]) ).
fof(f18340,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,[],[f10843]) ).
fof(f10843,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,[],[f6402]) ).
fof(f6402,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,[],[f3764]) ).
fof(f3764,axiom,
! [X169,X7] :
( c_Wellfounded_Owf(X7,X169)
=> c_Wellfounded_Owf(tc_fun(X7,tc_HOL_Obool),c_Wellfounded_Omax__ext(X7,X169)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ext__wf) ).
fof(f31273,plain,
spl573_640,
inference(avatar_split_clause,[],[f18339,f31271]) ).
fof(f31271,plain,
( spl573_640
<=> ! [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,[spl573_640])]) ).
fof(f18339,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,[],[f10842]) ).
fof(f10842,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,[],[f6401]) ).
fof(f6401,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,[],[f3759]) ).
fof(f3759,axiom,
! [X169,X7] :
( c_Wellfounded_Owf(X7,X169)
=> c_Wellfounded_Owf(tc_fun(X7,tc_HOL_Obool),c_Wellfounded_Omin__ext(X7,X169)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ext__wf) ).
fof(f31269,plain,
spl573_639,
inference(avatar_split_clause,[],[f18280,f31267]) ).
fof(f31267,plain,
( spl573_639
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_639])]) ).
fof(f18280,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10765]) ).
fof(f10765,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6350]) ).
fof(f6350,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0 ),
inference(rectify,[],[f2301]) ).
fof(f2301,axiom,
! [X61,X13] :
( class_Lattices_Olattice(X13)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13),X61),X61) = X61 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Oidem) ).
fof(f31265,plain,
spl573_638,
inference(avatar_split_clause,[],[f18279,f31263]) ).
fof(f31263,plain,
( spl573_638
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_638])]) ).
fof(f18279,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10764]) ).
fof(f10764,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6349]) ).
fof(f6349,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0 ),
inference(rectify,[],[f3175]) ).
fof(f3175,axiom,
! [X61,X13] :
( class_Lattices_Olattice(X13)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13),X61),X61) = X61 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Oidem) ).
fof(f31261,plain,
spl573_637,
inference(avatar_split_clause,[],[f18274,f31259]) ).
fof(f31259,plain,
( spl573_637
<=> ! [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,[spl573_637])]) ).
fof(f18274,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(cnf_transformation,[],[f10759]) ).
fof(f10759,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(ennf_transformation,[],[f6344]) ).
fof(f6344,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0 ),
inference(rectify,[],[f3159]) ).
fof(f3159,axiom,
! [X61,X13] :
( class_Lattices_Osemilattice__inf(X13)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X13),X61),X61) = X61 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__idem) ).
fof(f31257,plain,
spl573_636,
inference(avatar_split_clause,[],[f18272,f31255]) ).
fof(f31255,plain,
( spl573_636
<=> ! [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,[spl573_636])]) ).
fof(f18272,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(cnf_transformation,[],[f10757]) ).
fof(f10757,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(ennf_transformation,[],[f6342]) ).
fof(f6342,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0 ),
inference(rectify,[],[f2320]) ).
fof(f2320,axiom,
! [X88,X13] :
( class_Lattices_Osemilattice__sup(X13)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X13),X88),X88) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oidem) ).
fof(f31253,plain,
spl573_635,
inference(avatar_split_clause,[],[f18238,f31251]) ).
fof(f31251,plain,
( spl573_635
<=> ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_635])]) ).
fof(f18238,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10714]) ).
fof(f10714,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6313]) ).
fof(f6313,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0 ),
inference(rectify,[],[f1981]) ).
fof(f1981,axiom,
! [X61,X13] :
( class_Orderings_Olinorder(X13)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X13),X61),X61) = X61 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Oidem) ).
fof(f31249,plain,
spl573_634,
inference(avatar_split_clause,[],[f18236,f31247]) ).
fof(f31247,plain,
( spl573_634
<=> ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_634])]) ).
fof(f18236,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10712]) ).
fof(f10712,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6311]) ).
fof(f6311,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0 ),
inference(rectify,[],[f1982]) ).
fof(f1982,axiom,
! [X61,X13] :
( class_Orderings_Olinorder(X13)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X13),X61),X61) = X61 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Oidem) ).
fof(f31245,plain,
spl573_633,
inference(avatar_split_clause,[],[f18214,f31243]) ).
fof(f31243,plain,
( spl573_633
<=> ! [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,[spl573_633])]) ).
fof(f18214,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,[],[f10687]) ).
fof(f10687,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,[],[f6289]) ).
fof(f6289,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,[],[f2065]) ).
fof(f2065,axiom,
! [X88,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X13),c_Groups_Oone__class_Oone(X13)),X88)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__dvd) ).
fof(f31241,plain,
spl573_632,
inference(avatar_split_clause,[],[f18213,f31239]) ).
fof(f31239,plain,
( spl573_632
<=> ! [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,[spl573_632])]) ).
fof(f18213,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,[],[f10686]) ).
fof(f10686,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,[],[f6288]) ).
fof(f6288,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,[],[f2055]) ).
fof(f2055,axiom,
! [X88,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X13),X88),c_Groups_Ozero__class_Ozero(X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__0__right) ).
fof(f31237,plain,
spl573_631,
inference(avatar_split_clause,[],[f18212,f31235]) ).
fof(f31235,plain,
( spl573_631
<=> ! [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,[spl573_631])]) ).
fof(f18212,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,[],[f10685]) ).
fof(f10685,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,[],[f6287]) ).
fof(f6287,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,[],[f833]) ).
fof(f833,axiom,
! [X88,X13] :
( class_Divides_Osemiring__div(X13)
=> c_Groups_Ozero__class_Ozero(X13) = c_Divides_Odiv__class_Omod(X13,c_Groups_Ozero__class_Ozero(X13),X88) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__0) ).
fof(f31233,plain,
spl573_630,
inference(avatar_split_clause,[],[f18211,f31231]) ).
fof(f31231,plain,
( spl573_630
<=> ! [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,[spl573_630])]) ).
fof(f18211,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,[],[f10684]) ).
fof(f10684,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,[],[f6286]) ).
fof(f6286,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,[],[f864]) ).
fof(f864,axiom,
! [X88,X13] :
( class_Divides_Osemiring__div(X13)
=> c_Groups_Ozero__class_Ozero(X13) = c_Divides_Odiv__class_Omod(X13,X88,c_Groups_Oone__class_Oone(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__1) ).
fof(f31229,plain,
spl573_629,
inference(avatar_split_clause,[],[f18182,f31227]) ).
fof(f31227,plain,
( spl573_629
<=> ! [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,[spl573_629])]) ).
fof(f18182,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,[],[f10655]) ).
fof(f10655,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,[],[f6259]) ).
fof(f6259,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,[],[f2476]) ).
fof(f2476,axiom,
! [X61,X13] :
( class_Orderings_Obot(X13)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),c_Orderings_Obot__class_Obot(X13)),X61)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__least) ).
fof(f31225,plain,
spl573_628,
inference(avatar_split_clause,[],[f18148,f31223]) ).
fof(f18148,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,[],[f10619]) ).
fof(f10619,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,[],[f6227]) ).
fof(f6227,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,[],[f2434]) ).
fof(f2434,axiom,
! [X61,X13] :
( class_Orderings_Otop(X13)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),X61),c_Orderings_Otop__class_Otop(X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top__greatest) ).
fof(f31221,plain,
spl573_627,
inference(avatar_split_clause,[],[f17959,f31219]) ).
fof(f31219,plain,
( spl573_627
<=> ! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_627])]) ).
fof(f17959,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ),
inference(cnf_transformation,[],[f6083]) ).
fof(f6083,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ),
inference(rectify,[],[f5204]) ).
fof(f5204,axiom,
! [X3,X5] :
( hBOOL(X3)
| ~ hBOOL(X5)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X5),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__3) ).
fof(f31217,plain,
spl573_626,
inference(avatar_split_clause,[],[f17958,f31215]) ).
fof(f31215,plain,
( spl573_626
<=> ! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_626])]) ).
fof(f17958,plain,
! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ),
inference(cnf_transformation,[],[f6082]) ).
fof(f6082,plain,
! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ),
inference(rectify,[],[f5201]) ).
fof(f5201,axiom,
! [X3,X5] :
( hBOOL(X3)
| hBOOL(X5)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X5),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__3) ).
fof(f31213,plain,
spl573_625,
inference(avatar_split_clause,[],[f17952,f31211]) ).
fof(f31211,plain,
( spl573_625
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_625])]) ).
fof(f17952,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6076]) ).
fof(f6076,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(rectify,[],[f5196]) ).
fof(f5196,axiom,
! [X3,X5] :
( hBOOL(hAPP(hAPP(c_fconj,X5),X3))
| ~ hBOOL(X3)
| ~ hBOOL(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__1) ).
fof(f31209,plain,
spl573_624,
inference(avatar_split_clause,[],[f17552,f31207]) ).
fof(f31207,plain,
( spl573_624
<=> ! [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,[spl573_624])]) ).
fof(f17552,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,[],[f5733]) ).
fof(f5733,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,[],[f906]) ).
fof(f906,axiom,
! [X12,X85] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X85,X12)),X85)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).
fof(f31205,plain,
spl573_623,
inference(avatar_split_clause,[],[f17550,f31203]) ).
fof(f31203,plain,
( spl573_623
<=> ! [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,[spl573_623])]) ).
fof(f17550,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5731]) ).
fof(f5731,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f2855]) ).
fof(f2855,axiom,
! [X99,X7] : hBOOL(hAPP(hAPP(c_member(X7),X99),c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iso__tuple__UNIV__I) ).
fof(f31201,plain,
spl573_622,
inference(avatar_split_clause,[],[f17548,f31199]) ).
fof(f31199,plain,
( spl573_622
<=> ! [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,[spl573_622])]) ).
fof(f17548,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(cnf_transformation,[],[f5729]) ).
fof(f5729,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(rectify,[],[f2327]) ).
fof(f2327,axiom,
! [X148,X7] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X7,tc_HOL_Obool)),X148),X148) = X148,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb) ).
fof(f31197,plain,
spl573_621,
inference(avatar_split_clause,[],[f17547,f31195]) ).
fof(f31195,plain,
( spl573_621
<=> ! [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,[spl573_621])]) ).
fof(f17547,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(cnf_transformation,[],[f5728]) ).
fof(f5728,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(rectify,[],[f3153]) ).
fof(f3153,axiom,
! [X148,X7] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X7,tc_HOL_Obool)),X148),X148) = X148,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb) ).
fof(f31193,plain,
spl573_620,
inference(avatar_split_clause,[],[f17546,f31191]) ).
fof(f31191,plain,
( spl573_620
<=> ! [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,[spl573_620])]) ).
fof(f17546,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,[],[f5727]) ).
fof(f5727,plain,
! [X0,X1] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X0)) = X0,
inference(rectify,[],[f4164]) ).
fof(f4164,axiom,
! [X148,X7] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X7,tc_HOL_Obool),hAPP(c_Set_OPow(X7),X148)) = X148,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Union__Pow__eq) ).
fof(f31189,plain,
spl573_619,
inference(avatar_split_clause,[],[f17545,f31187]) ).
fof(f31187,plain,
( spl573_619
<=> ! [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,[spl573_619])]) ).
fof(f17545,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5726]) ).
fof(f5726,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f4586]) ).
fof(f4586,axiom,
! [X12,X13] : c_List_Olist_ONil(X13) = hAPP(hAPP(c_List_Otake(X13),X12),c_List_Olist_ONil(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_take__Nil) ).
fof(f31185,plain,
spl573_618,
inference(avatar_split_clause,[],[f17544,f31183]) ).
fof(f31183,plain,
( spl573_618
<=> ! [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,[spl573_618])]) ).
fof(f17544,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Odrop(X1),X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5725]) ).
fof(f5725,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Odrop(X1),X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f4659]) ).
fof(f4659,axiom,
! [X12,X13] : c_List_Olist_ONil(X13) = hAPP(hAPP(c_List_Odrop(X13),X12),c_List_Olist_ONil(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__Nil) ).
fof(f31181,plain,
spl573_617,
inference(avatar_split_clause,[],[f17540,f31179]) ).
fof(f31179,plain,
( spl573_617
<=> ! [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,[spl573_617])]) ).
fof(f17540,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5721]) ).
fof(f5721,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f2570]) ).
fof(f2570,axiom,
! [X76,X7] : ~ hBOOL(hAPP(hAPP(c_member(X7),X76),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
fof(f31177,plain,
spl573_616,
inference(avatar_split_clause,[],[f17336,f31175]) ).
fof(f31175,plain,
( spl573_616
<=> ! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK93(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_616])]) ).
fof(f17336,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK93(X0)),X0)) ),
inference(cnf_transformation,[],[f14517]) ).
fof(f31173,plain,
spl573_615,
inference(avatar_split_clause,[],[f17257,f31171]) ).
fof(f31171,plain,
( spl573_615
<=> ! [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,[spl573_615])]) ).
fof(f17257,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,[],[f10340]) ).
fof(f10340,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,[],[f5512]) ).
fof(f5512,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,[],[f452]) ).
fof(f452,axiom,
! [X13] :
( class_Rings_Osemiring__1(X13)
=> c_Groups_Oone__class_Oone(X13) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X13),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__1) ).
fof(f31169,plain,
spl573_614,
inference(avatar_split_clause,[],[f17253,f31167]) ).
fof(f31167,plain,
( spl573_614
<=> ! [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,[spl573_614])]) ).
fof(f17253,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,[],[f10336]) ).
fof(f10336,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,[],[f5508]) ).
fof(f5508,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,[],[f4444]) ).
fof(f4444,axiom,
! [X13] :
( class_Groups_Omonoid__add(X13)
=> c_Groups_Ozero__class_Ozero(X13) = hAPP(c_List_Omonoid__add__class_Olistsum(X13),c_List_Olist_ONil(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listsum__simps_I1_J) ).
fof(f31165,plain,
spl573_613,
inference(avatar_split_clause,[],[f17243,f31163]) ).
fof(f31163,plain,
( spl573_613
<=> ! [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,[spl573_613])]) ).
fof(f17243,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,[],[f10326]) ).
fof(f10326,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,[],[f5498]) ).
fof(f5498,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,[],[f2522]) ).
fof(f2522,axiom,
! [X13] :
( class_Lattices_Oboolean__algebra(X13)
=> c_Orderings_Obot__class_Obot(X13) = hAPP(c_Groups_Ouminus__class_Ouminus(X13),c_Orderings_Otop__class_Otop(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__top__eq) ).
fof(f31161,plain,
spl573_612,
inference(avatar_split_clause,[],[f17242,f31159]) ).
fof(f31159,plain,
( spl573_612
<=> ! [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,[spl573_612])]) ).
fof(f17242,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,[],[f10325]) ).
fof(f10325,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,[],[f5497]) ).
fof(f5497,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,[],[f2523]) ).
fof(f2523,axiom,
! [X13] :
( class_Lattices_Oboolean__algebra(X13)
=> c_Orderings_Otop__class_Otop(X13) = hAPP(c_Groups_Ouminus__class_Ouminus(X13),c_Orderings_Obot__class_Obot(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compl__bot__eq) ).
fof(f31156,plain,
spl573_611,
inference(avatar_split_clause,[],[f17236,f31154]) ).
fof(f17236,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,[],[f10319]) ).
fof(f10319,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,[],[f5491]) ).
fof(f5491,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,[],[f1409]) ).
fof(f1409,axiom,
! [X13] :
( class_Int_Onumber__ring(X13)
=> c_Groups_Oone__class_Oone(X13) = hAPP(c_Int_Onumber__class_Onumber__of(X13),c_Int_OBit1(c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I110_J) ).
fof(f31152,plain,
spl573_610,
inference(avatar_split_clause,[],[f17230,f31150]) ).
fof(f31150,plain,
( spl573_610
<=> ! [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,[spl573_610])]) ).
fof(f17230,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,[],[f10313]) ).
fof(f10313,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,[],[f5485]) ).
fof(f5485,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,[],[f1134]) ).
fof(f1134,axiom,
! [X13] :
( class_Rings_Olinordered__idom(X13)
=> c_Groups_Oone__class_Oone(X13) = hAPP(c_Groups_Oabs__class_Oabs(X13),c_Groups_Oone__class_Oone(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__one) ).
fof(f31148,plain,
spl573_609,
inference(avatar_split_clause,[],[f17229,f31146]) ).
fof(f17229,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,[],[f10312]) ).
fof(f10312,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,[],[f5484]) ).
fof(f5484,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,[],[f1128]) ).
fof(f1128,axiom,
! [X13] :
( class_Groups_Oordered__ab__group__add__abs(X13)
=> c_Groups_Ozero__class_Ozero(X13) = hAPP(c_Groups_Oabs__class_Oabs(X13),c_Groups_Ozero__class_Ozero(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_abs__zero) ).
fof(f31144,plain,
spl573_608,
inference(avatar_split_clause,[],[f17225,f31142]) ).
fof(f31142,plain,
( spl573_608
<=> ! [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,[spl573_608])]) ).
fof(f17225,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,[],[f10308]) ).
fof(f10308,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,[],[f5480]) ).
fof(f5480,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,[],[f450]) ).
fof(f450,axiom,
! [X13] :
( class_Rings_Oring__1(X13)
=> c_Groups_Oone__class_Oone(X13) = hAPP(c_Int_Oring__1__class_Oof__int(X13),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__1) ).
fof(f31140,plain,
spl573_607,
inference(avatar_split_clause,[],[f17224,f31138]) ).
fof(f31138,plain,
( spl573_607
<=> ! [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,[spl573_607])]) ).
fof(f17224,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,[],[f10307]) ).
fof(f10307,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,[],[f5479]) ).
fof(f5479,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,[],[f457]) ).
fof(f457,axiom,
! [X13] :
( class_Groups_Ogroup__add(X13)
=> c_Groups_Ozero__class_Ozero(X13) = hAPP(c_Groups_Ouminus__class_Ouminus(X13),c_Groups_Ozero__class_Ozero(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__zero) ).
fof(f31136,plain,
spl573_606,
inference(avatar_split_clause,[],[f17073,f31134]) ).
fof(f31134,plain,
( spl573_606
<=> ! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_606])]) ).
fof(f17073,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)),
inference(cnf_transformation,[],[f5341]) ).
fof(f5341,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)),
inference(rectify,[],[f4275]) ).
fof(f4275,axiom,
! [X7] : hAPP(c_List_Omap(X7,X7),c_COMBI(X7)) = c_Fun_Oid(tc_List_Olist(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Oidentity) ).
fof(f31132,plain,
spl573_605,
inference(avatar_split_clause,[],[f17072,f31130]) ).
fof(f31130,plain,
( spl573_605
<=> ! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_605])]) ).
fof(f17072,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)),
inference(cnf_transformation,[],[f5340]) ).
fof(f5340,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)),
inference(rectify,[],[f4274]) ).
fof(f4274,axiom,
! [X7] : hAPP(c_List_Omap(X7,X7),c_Fun_Oid(X7)) = c_Fun_Oid(tc_List_Olist(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Omap_Oid) ).
fof(f31128,plain,
spl573_604,
inference(avatar_split_clause,[],[f17071,f31126]) ).
fof(f31126,plain,
( spl573_604
<=> ! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_Fun_Oid(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_604])]) ).
fof(f17071,plain,
! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_Fun_Oid(X0)),
inference(cnf_transformation,[],[f5339]) ).
fof(f5339,plain,
! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_Fun_Oid(X0)),
inference(rectify,[],[f4293]) ).
fof(f4293,axiom,
! [X7] : hAPP(c_Option_Omap(X7,X7),c_Fun_Oid(X7)) = c_Fun_Oid(tc_Option_Ooption(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Omap_Oid) ).
fof(f31124,plain,
spl573_603,
inference(avatar_split_clause,[],[f17069,f31122]) ).
fof(f31122,plain,
( spl573_603
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_List_Oset(X0),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_603])]) ).
fof(f17069,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,[],[f5337]) ).
fof(f5337,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,[],[f4460]) ).
fof(f4460,axiom,
! [X7] : c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)) = hAPP(c_List_Oset(X7),c_List_Olist_ONil(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).
fof(f31120,plain,
spl573_602,
inference(avatar_split_clause,[],[f17068,f31118]) ).
fof(f31118,plain,
( spl573_602
<=> ! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_COMBI(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_602])]) ).
fof(f17068,plain,
! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_COMBI(X0)),
inference(cnf_transformation,[],[f5336]) ).
fof(f5336,plain,
! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_COMBI(X0)),
inference(rectify,[],[f4294]) ).
fof(f4294,axiom,
! [X7] : c_Fun_Oid(tc_Option_Ooption(X7)) = hAPP(c_Option_Omap(X7,X7),c_COMBI(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Option_Omap_Oidentity) ).
fof(f31116,plain,
spl573_601,
inference(avatar_split_clause,[],[f17054,f31114]) ).
fof(f17054,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,[],[f5322]) ).
fof(f5322,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,[],[f4295]) ).
fof(f4295,axiom,
! [X7] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X7)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X7),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__listI) ).
fof(f31112,plain,
spl573_600,
inference(avatar_split_clause,[],[f16913,f31109]) ).
fof(f31109,plain,
( spl573_600
<=> 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,[spl573_600])]) ).
fof(f16913,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,[],[f3345]) ).
fof(f3345,axiom,
c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition__Integ) ).
fof(f31107,plain,
spl573_599,
inference(avatar_split_clause,[],[f16909,f31104]) ).
fof(f31104,plain,
( spl573_599
<=> 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,[spl573_599])]) ).
fof(f16909,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,[],[f3064]) ).
fof(f3064,axiom,
c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__code__numeral__def) ).
fof(f31102,plain,
spl573_598,
inference(avatar_split_clause,[],[f16908,f31099]) ).
fof(f31099,plain,
( spl573_598
<=> 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,[spl573_598])]) ).
fof(f16908,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,[],[f2552]) ).
fof(f2552,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__UNIV__unit) ).
fof(f31097,plain,
spl573_597,
inference(avatar_split_clause,[],[f16906,f31094]) ).
fof(f31094,plain,
( spl573_597
<=> 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,[spl573_597])]) ).
fof(f16906,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,[],[f3065]) ).
fof(f3065,axiom,
c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__of__def) ).
fof(f31077,plain,
( ~ spl573_596
| spl573_304
| ~ spl573_569 ),
inference(avatar_split_clause,[],[f31054,f30744,f29561,f31074]) ).
fof(f31074,plain,
( spl573_596
<=> c_Nat__Transfer_Ois__nat(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_596])]) ).
fof(f29561,plain,
( spl573_304
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_304])]) ).
fof(f31054,plain,
( ~ c_Nat__Transfer_Ois__nat(c_Int_OMin)
| spl573_304
| ~ spl573_569 ),
inference(resolution,[],[f30745,f29563]) ).
fof(f29563,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| spl573_304 ),
inference(avatar_component_clause,[],[f29561]) ).
fof(f31052,plain,
( spl573_595
| ~ spl573_350
| ~ spl573_537 ),
inference(avatar_split_clause,[],[f30986,f30610,f29766,f31050]) ).
fof(f31050,plain,
( spl573_595
<=> ! [X2,X0,X1] :
( sP21(X0,X1,X2)
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_595])]) ).
fof(f30610,plain,
( spl573_537
<=> ! [X2,X0,X1] :
( sP21(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_537])]) ).
fof(f30986,plain,
( ! [X2,X0,X1] :
( sP21(X0,X1,X2)
| ~ class_Finite__Set_Ofinite(X0) )
| ~ spl573_350
| ~ spl573_537 ),
inference(resolution,[],[f30611,f29767]) ).
fof(f30611,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| sP21(X2,X1,X0) )
| ~ spl573_537 ),
inference(avatar_component_clause,[],[f30610]) ).
fof(f31035,plain,
( spl573_594
| ~ spl573_350
| ~ spl573_536 ),
inference(avatar_split_clause,[],[f30972,f30606,f29766,f31033]) ).
fof(f31033,plain,
( spl573_594
<=> ! [X2,X0,X1] :
( sP19(X0,X1,X2)
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_594])]) ).
fof(f30606,plain,
( spl573_536
<=> ! [X2,X0,X1] :
( sP19(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_536])]) ).
fof(f30972,plain,
( ! [X2,X0,X1] :
( sP19(X0,X1,X2)
| ~ class_Finite__Set_Ofinite(X0) )
| ~ spl573_350
| ~ spl573_536 ),
inference(resolution,[],[f30607,f29767]) ).
fof(f30607,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| sP19(X2,X1,X0) )
| ~ spl573_536 ),
inference(avatar_component_clause,[],[f30606]) ).
fof(f31022,plain,
( spl573_593
| ~ spl573_350
| ~ spl573_527 ),
inference(avatar_split_clause,[],[f30916,f30570,f29766,f31020]) ).
fof(f31020,plain,
( spl573_593
<=> ! [X0,X1] :
( sP4(c_Finite__Set_Ofinite(X0),X1)
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_593])]) ).
fof(f30570,plain,
( spl573_527
<=> ! [X0,X1] :
( sP4(X1,X0)
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_527])]) ).
fof(f30916,plain,
( ! [X0,X1] :
( sP4(c_Finite__Set_Ofinite(X0),X1)
| ~ class_Finite__Set_Ofinite(X0) )
| ~ spl573_350
| ~ spl573_527 ),
inference(resolution,[],[f30571,f29767]) ).
fof(f30571,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| sP4(X1,X0) )
| ~ spl573_527 ),
inference(avatar_component_clause,[],[f30570]) ).
fof(f31015,plain,
( spl573_592
| ~ spl573_475
| ~ spl573_546 ),
inference(avatar_split_clause,[],[f30653,f30649,f30336,f31012]) ).
fof(f31012,plain,
( spl573_592
<=> 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,[spl573_592])]) ).
fof(f30649,plain,
( spl573_546
<=> c_Int_OBit1(c_Int_OPls) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_546])]) ).
fof(f30653,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)
| ~ spl573_475
| ~ spl573_546 ),
inference(forward_demodulation,[],[f30651,f30338]) ).
fof(f30651,plain,
( c_Int_OBit1(c_Int_OPls) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)
| ~ spl573_546 ),
inference(avatar_component_clause,[],[f30649]) ).
fof(f31010,plain,
( spl573_591
| ~ spl573_475
| ~ spl573_545 ),
inference(avatar_split_clause,[],[f30647,f30643,f30336,f31007]) ).
fof(f31007,plain,
( spl573_591
<=> c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_591])]) ).
fof(f30643,plain,
( spl573_545
<=> c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_545])]) ).
fof(f30647,plain,
( c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl573_475
| ~ spl573_545 ),
inference(forward_demodulation,[],[f30645,f30338]) ).
fof(f30645,plain,
( c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(c_Int_OPls))
| ~ spl573_545 ),
inference(avatar_component_clause,[],[f30643]) ).
fof(f31005,plain,
( spl573_590
| ~ spl573_346
| ~ spl573_527 ),
inference(avatar_split_clause,[],[f30915,f30570,f29749,f31003]) ).
fof(f31003,plain,
( spl573_590
<=> ! [X0,X1] : sP4(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_590])]) ).
fof(f29749,plain,
( spl573_346
<=> ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_346])]) ).
fof(f30915,plain,
( ! [X0,X1] : sP4(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),X1)
| ~ spl573_346
| ~ spl573_527 ),
inference(resolution,[],[f30571,f29750]) ).
fof(f29750,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0))
| ~ spl573_346 ),
inference(avatar_component_clause,[],[f29749]) ).
fof(f30887,plain,
( ~ spl573_160
| spl573_589
| ~ spl573_210
| ~ spl573_337 ),
inference(avatar_split_clause,[],[f29889,f29712,f29142,f30884,f28894]) ).
fof(f28894,plain,
( spl573_160
<=> class_Lattices_Osemilattice__inf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_160])]) ).
fof(f30884,plain,
( spl573_589
<=> c_Finite__Set_Ofun__left__comm__idem(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_589])]) ).
fof(f29142,plain,
( spl573_210
<=> c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_210])]) ).
fof(f29712,plain,
( spl573_337
<=> ! [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,[spl573_337])]) ).
fof(f29889,plain,
( c_Finite__Set_Ofun__left__comm__idem(tc_Nat_Onat,tc_Nat_Onat,c_Orderings_Oord__class_Omin(tc_Nat_Onat))
| ~ class_Lattices_Osemilattice__inf(tc_Nat_Onat)
| ~ spl573_210
| ~ spl573_337 ),
inference(superposition,[],[f29713,f29144]) ).
fof(f29144,plain,
( c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat)
| ~ spl573_210 ),
inference(avatar_component_clause,[],[f29142]) ).
fof(f29713,plain,
( ! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__inf__class_Oinf(X0))
| ~ class_Lattices_Osemilattice__inf(X0) )
| ~ spl573_337 ),
inference(avatar_component_clause,[],[f29712]) ).
fof(f30851,plain,
( ~ spl573_157
| spl573_588
| ~ spl573_209
| ~ spl573_336 ),
inference(avatar_split_clause,[],[f29888,f29708,f29137,f30848,f28879]) ).
fof(f28879,plain,
( spl573_157
<=> class_Lattices_Osemilattice__sup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_157])]) ).
fof(f30848,plain,
( spl573_588
<=> 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,[spl573_588])]) ).
fof(f29137,plain,
( spl573_209
<=> c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_209])]) ).
fof(f29708,plain,
( spl573_336
<=> ! [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,[spl573_336])]) ).
fof(f29888,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)
| ~ spl573_209
| ~ spl573_336 ),
inference(superposition,[],[f29709,f29139]) ).
fof(f29139,plain,
( c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)
| ~ spl573_209 ),
inference(avatar_component_clause,[],[f29137]) ).
fof(f29709,plain,
( ! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__sup__class_Osup(X0))
| ~ class_Lattices_Osemilattice__sup(X0) )
| ~ spl573_336 ),
inference(avatar_component_clause,[],[f29708]) ).
fof(f30839,plain,
( spl573_587
| ~ spl573_475
| ~ spl573_492 ),
inference(avatar_split_clause,[],[f30431,f30428,f30336,f30837]) ).
fof(f30428,plain,
( spl573_492
<=> ! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_492])]) ).
fof(f30431,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) )
| ~ spl573_475
| ~ spl573_492 ),
inference(forward_demodulation,[],[f30429,f30338]) ).
fof(f30429,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) )
| ~ spl573_492 ),
inference(avatar_component_clause,[],[f30428]) ).
fof(f30828,plain,
( spl573_586
| ~ spl573_310
| ~ spl573_325 ),
inference(avatar_split_clause,[],[f29885,f29664,f29591,f30825]) ).
fof(f30825,plain,
( spl573_586
<=> 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,[spl573_586])]) ).
fof(f29591,plain,
( spl573_310
<=> 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,[spl573_310])]) ).
fof(f29885,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))
| ~ spl573_310
| ~ spl573_325 ),
inference(superposition,[],[f29665,f29593]) ).
fof(f29593,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))
| ~ spl573_310 ),
inference(avatar_component_clause,[],[f29591]) ).
fof(f30818,plain,
spl573_585,
inference(avatar_split_clause,[],[f27760,f30816]) ).
fof(f30816,plain,
( spl573_585
<=> ! [X2,X1,X3] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(c_fequal,X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_585])]) ).
fof(f27760,plain,
! [X2,X3,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(c_fequal,X1)),X1)),
inference(forward_demodulation,[],[f25005,f25661]) ).
fof(f25005,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,[],[f22231]) ).
fof(f22231,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,[],[f16100]) ).
fof(f16100,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,[],[f9079]) ).
fof(f9079,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,[],[f3506]) ).
fof(f3506,axiom,
! [X27,X76,X1,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X7,X1,hAPP(hAPP(c_Set_Oinsert(X7),X76),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),X27))
<=> X27 = X76 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1Set__sing) ).
fof(f30814,plain,
spl573_584,
inference(avatar_split_clause,[],[f26813,f30812]) ).
fof(f30812,plain,
( spl573_584
<=> ! [X2,X0,X1] : hAPP(c_Finite__Set_Ofold1(X2,X1),hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_584])]) ).
fof(f26813,plain,
! [X2,X0,X1] : hAPP(c_Finite__Set_Ofold1(X2,X1),hAPP(c_fequal,X0)) = X0,
inference(forward_demodulation,[],[f19257,f25661]) ).
fof(f19257,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,[],[f6939]) ).
fof(f6939,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,[],[f3535]) ).
fof(f3535,axiom,
! [X76,X1,X7] : hAPP(c_Finite__Set_Ofold1(X7,X1),hAPP(hAPP(c_Set_Oinsert(X7),X76),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X76,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fold1__singleton) ).
fof(f30810,plain,
spl573_583,
inference(avatar_split_clause,[],[f26804,f30808]) ).
fof(f30808,plain,
( spl573_583
<=> ! [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,[spl573_583])]) ).
fof(f26804,plain,
! [X2,X0,X1] : hAPP(c_Nat_Onat_Onat__rec(X2,X1,X0),c_HOL_Obool_Obool__size(c_fTrue)) = X1,
inference(forward_demodulation,[],[f19209,f16841]) ).
fof(f19209,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,[],[f6891]) ).
fof(f6891,plain,
! [X0,X1,X2] : hAPP(c_Nat_Onat_Onat__rec(X2,X1,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rectify,[],[f102]) ).
fof(f102,axiom,
! [X70,X57,X7] : hAPP(c_Nat_Onat_Onat__rec(X7,X57,X70),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X57,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__0) ).
fof(f30806,plain,
spl573_582,
inference(avatar_split_clause,[],[f26680,f30803]) ).
fof(f30803,plain,
( spl573_582
<=> 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,[spl573_582])]) ).
fof(f26680,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,[],[f26679,f25779]) ).
fof(f26679,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,[],[f24705,f16841]) ).
fof(f24705,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,[],[f19084]) ).
fof(f19084,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,[],[f15036]) ).
fof(f15036,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,[],[f15035]) ).
fof(f15035,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,[],[f6827]) ).
fof(f6827,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,[],[f1220]) ).
fof(f1220,axiom,
! [X6,X99] :
( 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),X99),X6)))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X6
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X99)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(f30798,plain,
spl573_581,
inference(avatar_split_clause,[],[f26040,f30796]) ).
fof(f30796,plain,
( spl573_581
<=> ! [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,[spl573_581])]) ).
fof(f26040,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(forward_demodulation,[],[f18282,f25661]) ).
fof(f18282,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,[],[f10767]) ).
fof(f10767,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,[],[f6352]) ).
fof(f6352,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,[],[f3318]) ).
fof(f3318,axiom,
! [X99,X7] :
( class_Lattices_Olattice(X7)
=> c_Big__Operators_Olattice__class_OInf__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X99),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X99 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__fin_Osingleton) ).
fof(f30794,plain,
spl573_580,
inference(avatar_split_clause,[],[f26039,f30792]) ).
fof(f30792,plain,
( spl573_580
<=> ! [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,[spl573_580])]) ).
fof(f26039,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(forward_demodulation,[],[f18281,f25661]) ).
fof(f18281,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,[],[f10766]) ).
fof(f10766,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,[],[f6351]) ).
fof(f6351,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,[],[f2811]) ).
fof(f2811,axiom,
! [X99,X7] :
( class_Lattices_Olattice(X7)
=> c_Big__Operators_Olattice__class_OSup__fin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X99),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X99 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__fin_Osingleton) ).
fof(f30790,plain,
spl573_579,
inference(avatar_split_clause,[],[f26032,f30788]) ).
fof(f30788,plain,
( spl573_579
<=> ! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_579])]) ).
fof(f26032,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(forward_demodulation,[],[f18242,f25661]) ).
fof(f18242,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,[],[f10718]) ).
fof(f10718,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,[],[f6317]) ).
fof(f6317,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,[],[f2842]) ).
fof(f2842,axiom,
! [X99,X7] :
( class_Orderings_Olinorder(X7)
=> c_Big__Operators_Olinorder__class_OMin(X7,hAPP(hAPP(c_Set_Oinsert(X7),X99),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X99 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Min_Osingleton) ).
fof(f30786,plain,
spl573_578,
inference(avatar_split_clause,[],[f26031,f30784]) ).
fof(f30784,plain,
( spl573_578
<=> ! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_578])]) ).
fof(f26031,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(forward_demodulation,[],[f18241,f25661]) ).
fof(f18241,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,[],[f10717]) ).
fof(f10717,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,[],[f6316]) ).
fof(f6316,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,[],[f2810]) ).
fof(f2810,axiom,
! [X99,X7] :
( class_Orderings_Olinorder(X7)
=> c_Big__Operators_Olinorder__class_OMax(X7,hAPP(hAPP(c_Set_Oinsert(X7),X99),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X99 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Max_Osingleton) ).
fof(f30782,plain,
spl573_577,
inference(avatar_split_clause,[],[f26016,f30780]) ).
fof(f30780,plain,
( spl573_577
<=> ! [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,[spl573_577])]) ).
fof(f26016,plain,
! [X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(forward_demodulation,[],[f18165,f25661]) ).
fof(f18165,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,[],[f10636]) ).
fof(f10636,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,[],[f6244]) ).
fof(f6244,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,[],[f4190]) ).
fof(f4190,axiom,
! [X76,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OSup__class_OSup(X7,hAPP(hAPP(c_Set_Oinsert(X7),X76),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X76 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sup__singleton) ).
fof(f30778,plain,
spl573_576,
inference(avatar_split_clause,[],[f26015,f30776]) ).
fof(f30776,plain,
( spl573_576
<=> ! [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,[spl573_576])]) ).
fof(f26015,plain,
! [X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(forward_demodulation,[],[f18164,f25661]) ).
fof(f18164,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,[],[f10635]) ).
fof(f10635,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,[],[f6243]) ).
fof(f6243,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,[],[f4193]) ).
fof(f4193,axiom,
! [X76,X7] :
( class_Complete__Lattice_Ocomplete__lattice(X7)
=> c_Complete__Lattice_OInf__class_OInf(X7,hAPP(hAPP(c_Set_Oinsert(X7),X76),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))) = X76 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inf__singleton) ).
fof(f30774,plain,
spl573_575,
inference(avatar_split_clause,[],[f25957,f30772]) ).
fof(f30772,plain,
( spl573_575
<=> ! [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,[spl573_575])]) ).
fof(f25957,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,[],[f24566,f16829]) ).
fof(f24566,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,[],[f17987]) ).
fof(f17987,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,[],[f14620]) ).
fof(f14620,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,[],[f10489]) ).
fof(f10489,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,[],[f6109]) ).
fof(f6109,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,[],[f535]) ).
fof(f535,axiom,
! [X121,X7] :
( class_Int_Oring__char__0(X7)
=> ( c_Groups_Ozero__class_Ozero(X7) = hAPP(c_Int_Oring__1__class_Oof__int(X7),X121)
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X121 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__eq__0__iff) ).
fof(f30770,plain,
spl573_574,
inference(avatar_split_clause,[],[f25639,f30768]) ).
fof(f30768,plain,
( spl573_574
<=> ! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_574])]) ).
fof(f25639,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f17524,f16841]) ).
fof(f17524,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f5705]) ).
fof(f5705,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f4655]) ).
fof(f4655,axiom,
! [X290,X13] : hAPP(hAPP(c_List_Odrop(X13),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X290) = X290,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_drop__0) ).
fof(f30766,plain,
spl573_573,
inference(avatar_split_clause,[],[f25638,f30764]) ).
fof(f30764,plain,
( spl573_573
<=> ! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_573])]) ).
fof(f25638,plain,
! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X1,X0)),
inference(forward_demodulation,[],[f17519,f16841]) ).
fof(f17519,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X1,X0)),
inference(cnf_transformation,[],[f5700]) ).
fof(f5700,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X1,X0)),
inference(rectify,[],[f168]) ).
fof(f168,axiom,
! [X56,X75] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X75,X56)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I10_J) ).
fof(f30762,plain,
spl573_572,
inference(avatar_split_clause,[],[f25566,f30760]) ).
fof(f30760,plain,
( spl573_572
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit1(X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_572])]) ).
fof(f25566,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit1(X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f25565,f16979]) ).
fof(f25565,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X0)))) ),
inference(forward_demodulation,[],[f17381,f16979]) ).
fof(f17381,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X0)))) ),
inference(cnf_transformation,[],[f14552]) ).
fof(f14552,plain,
! [X0] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X0))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X0)))) ) ),
inference(nnf_transformation,[],[f5606]) ).
fof(f5606,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X0))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(rectify,[],[f1402]) ).
fof(f1402,axiom,
! [X122] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X122))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X122))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__Bit1) ).
fof(f30755,plain,
spl573_571,
inference(avatar_split_clause,[],[f25564,f30753]) ).
fof(f30753,plain,
( spl573_571
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit1(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_571])]) ).
fof(f25564,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit1(X0))) ),
inference(forward_demodulation,[],[f25563,f16979]) ).
fof(f25563,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit1(X0)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f17382,f16979]) ).
fof(f17382,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(X0))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f14552]) ).
fof(f30751,plain,
~ spl573_570,
inference(avatar_split_clause,[],[f25529,f30748]) ).
fof(f30748,plain,
( spl573_570
<=> 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,[spl573_570])]) ).
fof(f25529,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,[],[f25528,f25184]) ).
fof(f25184,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,[],[f16863,f16841]) ).
fof(f16863,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,[],[f1716]) ).
fof(f1716,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__code__numeral__def) ).
fof(f25528,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,[],[f24534,f16841]) ).
fof(f24534,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,[],[f17363]) ).
fof(f17363,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,[],[f14537]) ).
fof(f14537,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,[],[f5597]) ).
fof(f5597,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,[],[f1693]) ).
fof(f1693,axiom,
! [X71] :
( hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X71
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X71)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral__not__eq__zero) ).
fof(f30746,plain,
spl573_569,
inference(avatar_split_clause,[],[f25521,f30744]) ).
fof(f25521,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,[],[f17338,f16829]) ).
fof(f17338,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,[],[f14518]) ).
fof(f14518,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,[],[f5586]) ).
fof(f5586,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,[],[f1630]) ).
fof(f1630,axiom,
! [X99] :
( c_Nat__Transfer_Ois__nat(X99)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X99)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_is__nat__def) ).
fof(f30742,plain,
spl573_568,
inference(avatar_split_clause,[],[f25520,f30740]) ).
fof(f25520,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,[],[f17339,f16829]) ).
fof(f17339,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,[],[f14518]) ).
fof(f30738,plain,
spl573_567,
inference(avatar_split_clause,[],[f25416,f30736]) ).
fof(f30736,plain,
( spl573_567
<=> ! [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,[spl573_567])]) ).
fof(f25416,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,[],[f17226,f16829]) ).
fof(f17226,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,[],[f10309]) ).
fof(f10309,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,[],[f5481]) ).
fof(f5481,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,[],[f533]) ).
fof(f533,axiom,
! [X13] :
( class_Rings_Oring__1(X13)
=> c_Groups_Ozero__class_Ozero(X13) = hAPP(c_Int_Oring__1__class_Oof__int(X13),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__0) ).
fof(f30734,plain,
spl573_566,
inference(avatar_split_clause,[],[f25296,f30732]) ).
fof(f30732,plain,
( spl573_566
<=> ! [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,[spl573_566])]) ).
fof(f25296,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,[],[f25295,f25195]) ).
fof(f25295,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,[],[f17095,f16841]) ).
fof(f17095,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,[],[f5363]) ).
fof(f5363,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,[],[f916]) ).
fof(f916,axiom,
! [X85] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X85),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X85,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__1) ).
fof(f30730,plain,
spl573_565,
inference(avatar_split_clause,[],[f25270,f30728]) ).
fof(f30728,plain,
( spl573_565
<=> ! [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,[spl573_565])]) ).
fof(f25270,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f17050,f16841]) ).
fof(f17050,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,[],[f5318]) ).
fof(f5318,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f190]) ).
fof(f190,axiom,
! [X12] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(f30726,plain,
spl573_564,
inference(avatar_split_clause,[],[f25268,f30724]) ).
fof(f30724,plain,
( spl573_564
<=> ! [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,[spl573_564])]) ).
fof(f25268,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f17048,f16841]) ).
fof(f17048,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,[],[f5316]) ).
fof(f5316,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f1926]) ).
fof(f1926,axiom,
! [X12] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__0L) ).
fof(f30722,plain,
spl573_563,
inference(avatar_split_clause,[],[f25267,f30720]) ).
fof(f30720,plain,
( spl573_563
<=> ! [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,[spl573_563])]) ).
fof(f25267,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17045,f16841]) ).
fof(f17045,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,[],[f5313]) ).
fof(f5313,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f189]) ).
fof(f189,axiom,
! [X85] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X85),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X85,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
fof(f30718,plain,
spl573_562,
inference(avatar_split_clause,[],[f25265,f30716]) ).
fof(f30716,plain,
( spl573_562
<=> ! [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,[spl573_562])]) ).
fof(f25265,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17043,f16841]) ).
fof(f17043,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,[],[f5311]) ).
fof(f5311,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f1011]) ).
fof(f1011,axiom,
! [X85] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X85),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X85,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__nat_Odiff__0) ).
fof(f30714,plain,
spl573_561,
inference(avatar_split_clause,[],[f25264,f30712]) ).
fof(f30712,plain,
( spl573_561
<=> ! [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,[spl573_561])]) ).
fof(f25264,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17042,f16841]) ).
fof(f17042,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,[],[f5310]) ).
fof(f5310,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f1927]) ).
fof(f1927,axiom,
! [X12] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__0R) ).
fof(f30710,plain,
spl573_560,
inference(avatar_split_clause,[],[f25262,f30708]) ).
fof(f30708,plain,
( spl573_560
<=> ! [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,[spl573_560])]) ).
fof(f25262,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0),
inference(forward_demodulation,[],[f17031,f16841]) ).
fof(f17031,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,[],[f5299]) ).
fof(f5299,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0),
inference(rectify,[],[f1012]) ).
fof(f1012,axiom,
! [X85] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X85),X85),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(f30706,plain,
spl573_559,
inference(avatar_split_clause,[],[f25261,f30704]) ).
fof(f30704,plain,
( spl573_559
<=> ! [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,[spl573_559])]) ).
fof(f25261,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,[],[f17030,f16841]) ).
fof(f17030,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,[],[f5298]) ).
fof(f5298,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,[],[f4458]) ).
fof(f4458,axiom,
! [X13] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X13)),c_List_Olist_ONil(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I3_J) ).
fof(f30702,plain,
spl573_558,
inference(avatar_split_clause,[],[f25260,f30700]) ).
fof(f30700,plain,
( spl573_558
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X0)),c_Option_Ooption_ONone(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_558])]) ).
fof(f25260,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X0)),c_Option_Ooption_ONone(X0)),
inference(forward_demodulation,[],[f17029,f16841]) ).
fof(f17029,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X0)),c_Option_Ooption_ONone(X0)),
inference(cnf_transformation,[],[f5297]) ).
fof(f5297,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X0)),c_Option_Ooption_ONone(X0)),
inference(rectify,[],[f336]) ).
fof(f336,axiom,
! [X13] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X13)),c_Option_Ooption_ONone(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osize_I3_J) ).
fof(f30698,plain,
spl573_557,
inference(avatar_split_clause,[],[f25259,f30696]) ).
fof(f30696,plain,
( spl573_557
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_557])]) ).
fof(f25259,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X0)),
inference(forward_demodulation,[],[f17028,f16841]) ).
fof(f17028,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X0)),
inference(cnf_transformation,[],[f5296]) ).
fof(f5296,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X0)),
inference(rectify,[],[f169]) ).
fof(f169,axiom,
! [X93] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,X93)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I15_J) ).
fof(f30694,plain,
spl573_556,
inference(avatar_split_clause,[],[f24982,f30692]) ).
fof(f30692,plain,
( spl573_556
<=> ! [X2,X1,X3] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_556])]) ).
fof(f24982,plain,
! [X2,X3,X1] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X2)),
inference(equality_resolution,[],[f22112]) ).
fof(f22112,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
| X0 != X2 ),
inference(cnf_transformation,[],[f16017]) ).
fof(f16017,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,[],[f16016]) ).
fof(f16016,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,[],[f9038]) ).
fof(f9038,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
<=> ( hBOOL(hAPP(X1,X0))
| X0 = X2 ) ),
inference(rectify,[],[f2421]) ).
fof(f2421,axiom,
! [X99,X148,X124,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X7),X124),X148),X99))
<=> ( hBOOL(hAPP(X148,X99))
| X99 = X124 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(f30690,plain,
spl573_555,
inference(avatar_split_clause,[],[f24869,f30688]) ).
fof(f30688,plain,
( spl573_555
<=> ! [X2,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_555])]) ).
fof(f24869,plain,
! [X2,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X1)),
inference(equality_resolution,[],[f20888]) ).
fof(f20888,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,[],[f15647]) ).
fof(f15647,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,[],[f15646]) ).
fof(f15646,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,[],[f8097]) ).
fof(f8097,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,[],[f1891]) ).
fof(f1891,axiom,
! [X152,X148,X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),X148),X152))
<=> ( X148 != X152
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X148),X152)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_psubset__eq) ).
fof(f30686,plain,
spl573_554,
inference(avatar_split_clause,[],[f24868,f30684]) ).
fof(f30684,plain,
( spl573_554
<=> ! [X2,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_554])]) ).
fof(f24868,plain,
! [X2,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X1))),
inference(equality_resolution,[],[f20884]) ).
fof(f20884,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
| X0 != X1 ),
inference(cnf_transformation,[],[f15644]) ).
fof(f15644,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,[],[f8095]) ).
fof(f8095,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
<=> X0 = X1 ),
inference(rectify,[],[f2610]) ).
fof(f2610,axiom,
! [X124,X99,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),X99),hAPP(c_fequal,X124)))
<=> X99 = X124 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(f30682,plain,
spl573_553,
inference(avatar_split_clause,[],[f24775,f30680]) ).
fof(f30680,plain,
( spl573_553
<=> ! [X2,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_553])]) ).
fof(f24775,plain,
! [X2,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f20141]) ).
fof(f20141,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,[],[f15270]) ).
fof(f15270,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,[],[f15269]) ).
fof(f15269,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,[],[f12007]) ).
fof(f12007,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,[],[f7685]) ).
fof(f7685,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,[],[f580]) ).
fof(f580,axiom,
! [X124,X99,X7] :
( class_Orderings_Oorder(X7)
=> ( X99 = X124
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X124),X99))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X99),X124)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__eq__iff) ).
fof(f30678,plain,
spl573_552,
inference(avatar_split_clause,[],[f24771,f30676]) ).
fof(f30676,plain,
( spl573_552
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_552])]) ).
fof(f24771,plain,
! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f20125]) ).
fof(f20125,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f11980]) ).
fof(f11980,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f11979]) ).
fof(f11979,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f7671]) ).
fof(f7671,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
=> X0 != X1 ) ),
inference(rectify,[],[f395]) ).
fof(f395,axiom,
! [X60,X61,X13] :
( class_Orderings_Oorder(X13)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X61),X60))
=> X60 != X61 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__imp__neq) ).
fof(f30674,plain,
( ~ spl573_132
| ~ spl573_249
| spl573_521 ),
inference(avatar_split_clause,[],[f30629,f30545,f29315,f28754]) ).
fof(f28754,plain,
( spl573_132
<=> class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_132])]) ).
fof(f29315,plain,
( spl573_249
<=> ! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_249])]) ).
fof(f30545,plain,
( spl573_521
<=> c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_521])]) ).
fof(f30629,plain,
( ~ class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral)
| ~ spl573_249
| spl573_521 ),
inference(resolution,[],[f30546,f29316]) ).
fof(f29316,plain,
( ! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) )
| ~ spl573_249 ),
inference(avatar_component_clause,[],[f29315]) ).
fof(f30546,plain,
( ~ c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| spl573_521 ),
inference(avatar_component_clause,[],[f30545]) ).
fof(f30673,plain,
spl573_551,
inference(avatar_split_clause,[],[f24762,f30671]) ).
fof(f30671,plain,
( spl573_551
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_551])]) ).
fof(f24762,plain,
! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(equality_resolution,[],[f19982]) ).
fof(f19982,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f15219]) ).
fof(f15219,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,[],[f15218]) ).
fof(f15218,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,[],[f11833]) ).
fof(f11833,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,[],[f7570]) ).
fof(f7570,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,[],[f370]) ).
fof(f370,axiom,
! [X124,X99,X7] :
( class_Orderings_Olinorder(X7)
=> ( X99 != X124
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X124),X99))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X99),X124)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__neq__iff) ).
fof(f30669,plain,
spl573_550,
inference(avatar_split_clause,[],[f24578,f30667]) ).
fof(f30667,plain,
( spl573_550
<=> ! [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,[spl573_550])]) ).
fof(f24578,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,[],[f18086]) ).
fof(f18086,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,[],[f14644]) ).
fof(f14644,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,[],[f10572]) ).
fof(f10572,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,[],[f6181]) ).
fof(f6181,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,[],[f679]) ).
fof(f679,axiom,
! [X76,X7] :
( class_Rings_Olinordered__idom(X7)
=> ( c_Groups_Ozero__class_Ozero(X7) = c_Groups_Osgn__class_Osgn(X7,X76)
<=> c_Groups_Ozero__class_Ozero(X7) = X76 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn__0__0) ).
fof(f30665,plain,
spl573_549,
inference(avatar_split_clause,[],[f23864,f30663]) ).
fof(f30663,plain,
( spl573_549
<=> ! [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,[spl573_549])]) ).
fof(f23864,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,[],[f17485,f17007]) ).
fof(f17007,plain,
! [X0] : c_Wellfounded_Omeasure(X0) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0),c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f5275]) ).
fof(f5275,plain,
! [X0] : c_Wellfounded_Omeasure(X0) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0),c_Wellfounded_Oless__than),
inference(rectify,[],[f2989]) ).
fof(f2989,axiom,
! [X7] : c_Wellfounded_Omeasure(X7) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X7),c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measure__def) ).
fof(f17485,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X0)),
inference(cnf_transformation,[],[f5666]) ).
fof(f5666,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X0)),
inference(rectify,[],[f3748]) ).
fof(f3748,axiom,
! [X1,X7] : c_Wellfounded_Owf(X7,hAPP(c_Wellfounded_Omeasure(X7),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__measure) ).
fof(f30661,plain,
spl573_548,
inference(avatar_split_clause,[],[f23863,f30659]) ).
fof(f30659,plain,
( spl573_548
<=> ! [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,[spl573_548])]) ).
fof(f23863,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,[],[f17475,f17563]) ).
fof(f17475,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X0)),
inference(cnf_transformation,[],[f5656]) ).
fof(f5656,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X0)),
inference(rectify,[],[f4872]) ).
fof(f4872,axiom,
! [X115,X116] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X116,X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__upt) ).
fof(f30657,plain,
spl573_547,
inference(avatar_split_clause,[],[f23765,f30655]) ).
fof(f30655,plain,
( spl573_547
<=> ! [X0] : c_Int_OMin != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_547])]) ).
fof(f23765,plain,
! [X0] : c_Int_OMin != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(X0)),
inference(definition_unfolding,[],[f16951,f23734]) ).
fof(f16951,plain,
! [X0] : c_Int_OMin != c_Int_OBit0(X0),
inference(cnf_transformation,[],[f5219]) ).
fof(f5219,plain,
! [X0] : c_Int_OMin != c_Int_OBit0(X0),
inference(rectify,[],[f1459]) ).
fof(f1459,axiom,
! [X117] : c_Int_OMin != c_Int_OBit0(X117),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I42_J) ).
fof(f30652,plain,
spl573_546,
inference(avatar_split_clause,[],[f23747,f30649]) ).
fof(f23747,plain,
c_Int_OBit1(c_Int_OPls) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin),
inference(definition_unfolding,[],[f16840,f17039]) ).
fof(f17039,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(cnf_transformation,[],[f5307]) ).
fof(f5307,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(rectify,[],[f1300]) ).
fof(f1300,axiom,
! [X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X96),c_Int_OMin) = c_Int_Osucc(X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I2_J) ).
fof(f16840,plain,
c_Int_OBit1(c_Int_OPls) = c_Int_Osucc(c_Int_OPls),
inference(cnf_transformation,[],[f1405]) ).
fof(f1405,axiom,
c_Int_OBit1(c_Int_OPls) = c_Int_Osucc(c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Pls) ).
fof(f30646,plain,
spl573_545,
inference(avatar_split_clause,[],[f23744,f30643]) ).
fof(f23744,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(c_Int_OPls)),
inference(definition_unfolding,[],[f16827,f23734]) ).
fof(f16827,plain,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
inference(cnf_transformation,[],[f1450]) ).
fof(f1450,axiom,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__Pls) ).
fof(f30641,plain,
spl573_544,
inference(avatar_split_clause,[],[f23170,f30639]) ).
fof(f30639,plain,
( spl573_544
<=> ! [X2,X4,X0,X5,X3,X1] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OCond(X5,X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_544])]) ).
fof(f23170,plain,
! [X2,X3,X0,X1,X4,X5] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OCond(X5,X4,X3),
inference(cnf_transformation,[],[f9686]) ).
fof(f9686,plain,
! [X0,X1,X2,X3,X4,X5] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OCond(X5,X4,X3),
inference(rectify,[],[f83]) ).
fof(f83,axiom,
! [X38,X56,X73,X51,X52,X53] : c_Com_Ocom_OCond(X53,X52,X51) != c_Com_Ocom_OLocal(X73,X56,X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I37_J) ).
fof(f30637,plain,
spl573_543,
inference(avatar_split_clause,[],[f23168,f30635]) ).
fof(f30635,plain,
( spl573_543
<=> ! [X2,X4,X0,X5,X3,X1] : c_Com_Ocom_OCall(X2,X1,X0) != c_Com_Ocom_OCond(X5,X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_543])]) ).
fof(f23168,plain,
! [X2,X3,X0,X1,X4,X5] : c_Com_Ocom_OCall(X2,X1,X0) != c_Com_Ocom_OCond(X5,X4,X3),
inference(cnf_transformation,[],[f9684]) ).
fof(f9684,plain,
! [X0,X1,X2,X3,X4,X5] : c_Com_Ocom_OCall(X2,X1,X0) != c_Com_Ocom_OCond(X5,X4,X3),
inference(rectify,[],[f84]) ).
fof(f84,axiom,
! [X53,X78,X79,X54,X55,X56] : c_Com_Ocom_OCond(X56,X55,X54) != c_Com_Ocom_OCall(X79,X78,X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I56_J) ).
fof(f30633,plain,
spl573_542,
inference(avatar_split_clause,[],[f23166,f30631]) ).
fof(f30631,plain,
( spl573_542
<=> ! [X2,X4,X0,X5,X3,X1] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OCall(X5,X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_542])]) ).
fof(f23166,plain,
! [X2,X3,X0,X1,X4,X5] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OCall(X5,X4,X3),
inference(cnf_transformation,[],[f9682]) ).
fof(f9682,plain,
! [X0,X1,X2,X3,X4,X5] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OCall(X5,X4,X3),
inference(rectify,[],[f62]) ).
fof(f62,axiom,
! [X38,X56,X73,X53,X78,X79] : c_Com_Ocom_OLocal(X73,X56,X38) != c_Com_Ocom_OCall(X79,X78,X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I43_J) ).
fof(f30628,plain,
spl573_541,
inference(avatar_split_clause,[],[f22103,f30626]) ).
fof(f30626,plain,
( spl573_541
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP(X2,X3))
| ~ sP54(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_541])]) ).
fof(f22103,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X2,X3))
| ~ sP54(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16013]) ).
fof(f16013,plain,
! [X0,X1,X2,X3] :
( ( sP54(X0,X1,X2,X3)
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X4),X0))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X4)) )
| ~ hBOOL(hAPP(X2,X3)) )
& ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),sK431(X0,X1,X2,X3)),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),sK431(X0,X1,X2,X3)))
& hBOOL(hAPP(X2,X3)) )
| ~ sP54(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK431])],[f16011,f16012]) ).
fof(f16012,plain,
! [X0,X1,X2,X3] :
( ? [X5] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X5),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X5)) )
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),sK431(X0,X1,X2,X3)),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),sK431(X0,X1,X2,X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f16011,plain,
! [X0,X1,X2,X3] :
( ( sP54(X0,X1,X2,X3)
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X4),X0))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X4)) )
| ~ hBOOL(hAPP(X2,X3)) )
& ( ( ? [X5] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X5),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X5)) )
& hBOOL(hAPP(X2,X3)) )
| ~ sP54(X0,X1,X2,X3) ) ),
inference(rectify,[],[f16010]) ).
fof(f16010,plain,
! [X0,X2,X3,X1] :
( ( sP54(X0,X2,X3,X1)
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
| ~ hBOOL(hAPP(X3,X1)) )
& ( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) )
| ~ sP54(X0,X2,X3,X1) ) ),
inference(flattening,[],[f16009]) ).
fof(f16009,plain,
! [X0,X2,X3,X1] :
( ( sP54(X0,X2,X3,X1)
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
| ~ hBOOL(hAPP(X3,X1)) )
& ( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) )
| ~ sP54(X0,X2,X3,X1) ) ),
inference(nnf_transformation,[],[f14439]) ).
fof(f14439,plain,
! [X0,X2,X3,X1] :
( sP54(X0,X2,X3,X1)
<=> ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP54])]) ).
fof(f30624,plain,
spl573_540,
inference(avatar_split_clause,[],[f21883,f30622]) ).
fof(f30622,plain,
( spl573_540
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP(X2,X3))
| ~ sP51(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_540])]) ).
fof(f21883,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X2,X3))
| ~ sP51(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f15915]) ).
fof(f15915,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),sK394(X0,X1,X2,X3)),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),sK394(X0,X1,X2,X3)))
& hBOOL(hAPP(X2,X3)) )
| ~ sP51(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK394])],[f15913,f15914]) ).
fof(f15914,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X4)) )
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),sK394(X0,X1,X2,X3)),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),sK394(X0,X1,X2,X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f15913,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X4)) )
& hBOOL(hAPP(X2,X3)) )
| ~ sP51(X0,X1,X2,X3) ),
inference(rectify,[],[f15912]) ).
fof(f15912,plain,
! [X0,X2,X3,X1] :
( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) )
| ~ sP51(X0,X2,X3,X1) ),
inference(nnf_transformation,[],[f14433]) ).
fof(f14433,plain,
! [X0,X2,X3,X1] :
( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) )
| ~ sP51(X0,X2,X3,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP51])]) ).
fof(f30620,plain,
spl573_539,
inference(avatar_split_clause,[],[f21073,f30618]) ).
fof(f30618,plain,
( spl573_539
<=> ! [X2,X0,X1,X3] : c_Option_Ooption_Ooption__rec(X3,X2,X1,X0,c_Option_Ooption_ONone(X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_539])]) ).
fof(f21073,plain,
! [X2,X3,X0,X1] : c_Option_Ooption_Ooption__rec(X3,X2,X1,X0,c_Option_Ooption_ONone(X2)) = X1,
inference(cnf_transformation,[],[f8177]) ).
fof(f8177,plain,
! [X0,X1,X2,X3] : c_Option_Ooption_Ooption__rec(X3,X2,X1,X0,c_Option_Ooption_ONone(X2)) = X1,
inference(rectify,[],[f342]) ).
fof(f342,axiom,
! [X70,X57,X58,X7] : c_Option_Ooption_Ooption__rec(X7,X58,X57,X70,c_Option_Ooption_ONone(X58)) = X57,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Orecs_I1_J) ).
fof(f30616,plain,
spl573_538,
inference(avatar_split_clause,[],[f21072,f30614]) ).
fof(f30614,plain,
( spl573_538
<=> ! [X2,X0,X1,X3] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_538])]) ).
fof(f21072,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1,
inference(cnf_transformation,[],[f8176]) ).
fof(f8176,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1,
inference(rectify,[],[f5186]) ).
fof(f5186,axiom,
! [X328,X104,X7,X13] : hAPP(hAPP(c_COMBK(X13,X7),X104),X328) = X104,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(f30612,plain,
spl573_537,
inference(avatar_split_clause,[],[f20289,f30610]) ).
fof(f20289,plain,
! [X2,X0,X1] :
( sP21(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(cnf_transformation,[],[f14383]) ).
fof(f14383,plain,
! [X0,X1,X2] :
( sP21(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(definition_folding,[],[f12148,f14382,f14381]) ).
fof(f14381,plain,
! [X0,X1,X2] :
( sP20(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,[sP20])]) ).
fof(f14382,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)
<=> sP20(X0,X1,X2) )
| ~ sP21(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
fof(f12148,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,[],[f12147]) ).
fof(f12147,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,[],[f7790]) ).
fof(f7790,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,[],[f2723]) ).
fof(f2723,axiom,
! [X1,X148,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X148))
=> ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X1),X148)
<=> ? [X2] :
( ! [X202] :
( hBOOL(hAPP(hAPP(c_member(X7),X202),X148))
=> ( X2 != X202
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X1,X202) ) )
& hAPP(X1,X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(X7),X2),X148)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__Suc0__iff) ).
fof(f30608,plain,
spl573_536,
inference(avatar_split_clause,[],[f20277,f30606]) ).
fof(f20277,plain,
! [X2,X0,X1] :
( sP19(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(cnf_transformation,[],[f14380]) ).
fof(f14380,plain,
! [X0,X1,X2] :
( sP19(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(definition_folding,[],[f12145,f14379,f14378]) ).
fof(f14378,plain,
! [X0,X1,X2] :
( sP18(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,[sP18])]) ).
fof(f14379,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)
<=> sP18(X0,X1,X2) )
| ~ sP19(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f12145,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,[],[f12144]) ).
fof(f12144,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,[],[f7788]) ).
fof(f7788,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,[],[f2725]) ).
fof(f2725,axiom,
! [X1,X148,X7] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X148))
=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X7,tc_Nat_Onat),X1),X148)
<=> ? [X2] :
( ! [X202] :
( hBOOL(hAPP(hAPP(c_member(X7),X202),X148))
=> ( X2 != X202
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X1,X202) ) )
& hAPP(X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(X7),X2),X148)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_setsum__eq__1__iff) ).
fof(f30604,plain,
spl573_535,
inference(avatar_split_clause,[],[f20174,f30602]) ).
fof(f30602,plain,
( spl573_535
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_535])]) ).
fof(f20174,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(cnf_transformation,[],[f12027]) ).
fof(f12027,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(ennf_transformation,[],[f7703]) ).
fof(f7703,plain,
! [X0,X1,X2] :
( c_Equiv__Relations_Oequivp(X2,X1)
=> hBOOL(hAPP(hAPP(X1,X0),X0)) ),
inference(rectify,[],[f3366]) ).
fof(f3366,axiom,
! [X99,X189,X7] :
( c_Equiv__Relations_Oequivp(X7,X189)
=> hBOOL(hAPP(hAPP(X189,X99),X99)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equivp__reflp) ).
fof(f30600,plain,
spl573_534,
inference(avatar_split_clause,[],[f20173,f30598]) ).
fof(f30598,plain,
( spl573_534
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_534])]) ).
fof(f20173,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ),
inference(cnf_transformation,[],[f12026]) ).
fof(f12026,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ),
inference(ennf_transformation,[],[f7702]) ).
fof(f7702,plain,
! [X0,X1,X2] :
( c_Predicate_Oreflp(X2,X1)
=> hBOOL(hAPP(hAPP(X1,X0),X0)) ),
inference(rectify,[],[f3688]) ).
fof(f3688,axiom,
! [X99,X169,X7] :
( c_Predicate_Oreflp(X7,X169)
=> hBOOL(hAPP(hAPP(X169,X99),X99)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflpE) ).
fof(f30596,plain,
spl573_533,
inference(avatar_split_clause,[],[f19211,f30594]) ).
fof(f30594,plain,
( spl573_533
<=> ! [X2,X0,X1] : c_Fun_Oinj__on(X2,tc_sum(X2,X1),c_Sum__Type_OInl(X2,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_533])]) ).
fof(f19211,plain,
! [X2,X0,X1] : c_Fun_Oinj__on(X2,tc_sum(X2,X1),c_Sum__Type_OInl(X2,X1),X0),
inference(cnf_transformation,[],[f6893]) ).
fof(f6893,plain,
! [X0,X1,X2] : c_Fun_Oinj__on(X2,tc_sum(X2,X1),c_Sum__Type_OInl(X2,X1),X0),
inference(rectify,[],[f3409]) ).
fof(f3409,axiom,
! [X148,X58,X7] : c_Fun_Oinj__on(X7,tc_sum(X7,X58),c_Sum__Type_OInl(X7,X58),X148),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Inl) ).
fof(f30592,plain,
spl573_532,
inference(avatar_split_clause,[],[f19210,f30590]) ).
fof(f30590,plain,
( spl573_532
<=> ! [X2,X0,X1] : c_Fun_Oinj__on(X2,tc_sum(X1,X2),c_Sum__Type_OInr(X2,X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_532])]) ).
fof(f19210,plain,
! [X2,X0,X1] : c_Fun_Oinj__on(X2,tc_sum(X1,X2),c_Sum__Type_OInr(X2,X1),X0),
inference(cnf_transformation,[],[f6892]) ).
fof(f6892,plain,
! [X0,X1,X2] : c_Fun_Oinj__on(X2,tc_sum(X1,X2),c_Sum__Type_OInr(X2,X1),X0),
inference(rectify,[],[f3406]) ).
fof(f3406,axiom,
! [X148,X58,X7] : c_Fun_Oinj__on(X7,tc_sum(X58,X7),c_Sum__Type_OInr(X7,X58),X148),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Inr) ).
fof(f30588,plain,
spl573_531,
inference(avatar_split_clause,[],[f19208,f30586]) ).
fof(f30586,plain,
( spl573_531
<=> ! [X2,X0,X1] : hAPP(c_New__DSequence_Opos__single(X2,X1),X0) = c_Lazy__Sequence_Osingle(X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_531])]) ).
fof(f19208,plain,
! [X2,X0,X1] : hAPP(c_New__DSequence_Opos__single(X2,X1),X0) = c_Lazy__Sequence_Osingle(X2,X1),
inference(cnf_transformation,[],[f6890]) ).
fof(f6890,plain,
! [X0,X1,X2] : hAPP(c_New__DSequence_Opos__single(X2,X1),X0) = c_Lazy__Sequence_Osingle(X2,X1),
inference(rectify,[],[f3838]) ).
fof(f3838,axiom,
! [X200,X61,X13] : hAPP(c_New__DSequence_Opos__single(X13,X61),X200) = c_Lazy__Sequence_Osingle(X13,X61),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
fof(f30584,plain,
spl573_530,
inference(avatar_split_clause,[],[f19207,f30582]) ).
fof(f30582,plain,
( spl573_530
<=> ! [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,[spl573_530])]) ).
fof(f19207,plain,
! [X2,X0,X1] : hAPP(c_New__DSequence_Oneg__single(X2,X1),X0) = c_Lazy__Sequence_Ohb__single(X2,X1),
inference(cnf_transformation,[],[f6889]) ).
fof(f6889,plain,
! [X0,X1,X2] : hAPP(c_New__DSequence_Oneg__single(X2,X1),X0) = c_Lazy__Sequence_Ohb__single(X2,X1),
inference(rectify,[],[f3836]) ).
fof(f3836,axiom,
! [X200,X61,X13] : hAPP(c_New__DSequence_Oneg__single(X13,X61),X200) = c_Lazy__Sequence_Ohb__single(X13,X61),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
fof(f30580,plain,
spl573_529,
inference(avatar_split_clause,[],[f19203,f30578]) ).
fof(f30578,plain,
( spl573_529
<=> ! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_529])]) ).
fof(f19203,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[],[f6885]) ).
fof(f6885,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2),
inference(rectify,[],[f4464]) ).
fof(f4464,axiom,
! [X299,X120,X13] : c_List_Olist_ONil(X13) != hAPP(hAPP(c_List_Olist_OCons(X13),X120),X299),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osimps_I2_J) ).
fof(f30576,plain,
spl573_528,
inference(avatar_split_clause,[],[f18780,f30574]) ).
fof(f30574,plain,
( spl573_528
<=> ! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP4(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_528])]) ).
fof(f18780,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP4(X1,X0) ),
inference(cnf_transformation,[],[f14844]) ).
fof(f14844,plain,
! [X0,X1] :
( ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP4(X1,X0) )
& ( sP4(X1,X0)
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ) ),
inference(nnf_transformation,[],[f14355]) ).
fof(f14355,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
<=> sP4(X1,X0) ),
inference(definition_folding,[],[f11244,f14354]) ).
fof(f11244,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,[],[f6710]) ).
fof(f6710,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,[],[f405]) ).
fof(f405,axiom,
! [X71,X5] :
( hBOOL(hAPP(X5,hAPP(c_Int_Onat,X71)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X71),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X17] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X17) = X71
=> hBOOL(hAPP(X5,X17)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__nat) ).
fof(f30572,plain,
spl573_527,
inference(avatar_split_clause,[],[f18779,f30570]) ).
fof(f18779,plain,
! [X0,X1] :
( sP4(X1,X0)
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ),
inference(cnf_transformation,[],[f14844]) ).
fof(f30568,plain,
spl573_526,
inference(avatar_split_clause,[],[f18715,f30566]) ).
fof(f30566,plain,
( spl573_526
<=> ! [X0,X1,X3] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_526])]) ).
fof(f18715,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ),
inference(cnf_transformation,[],[f14785]) ).
fof(f30564,plain,
spl573_525,
inference(avatar_split_clause,[],[f18338,f30562]) ).
fof(f30562,plain,
( spl573_525
<=> ! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_525])]) ).
fof(f18338,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10841]) ).
fof(f10841,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6400]) ).
fof(f6400,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0)) ),
inference(rectify,[],[f3821]) ).
fof(f3821,axiom,
! [X189,X7] :
( c_Wellfounded_Owf(X7,X189)
=> c_Wellfounded_OwfP(X7,c_FunDef_Oin__rel(X7,X7,X189)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__in__rel) ).
fof(f30560,plain,
spl573_524,
inference(avatar_split_clause,[],[f18322,f30558]) ).
fof(f30558,plain,
( spl573_524
<=> ! [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,[spl573_524])]) ).
fof(f18322,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,[],[f10820]) ).
fof(f10820,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,[],[f10819]) ).
fof(f10819,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,[],[f6385]) ).
fof(f6385,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,[],[f1580]) ).
fof(f1580,axiom,
! [X60,X61] :
( c_Nat__Transfer_Ois__nat(X61)
=> ( c_Nat__Transfer_Ois__nat(X60)
=> c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X61,X60)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Divides_Otransfer__int__nat__function__closures_I2_J) ).
fof(f30556,plain,
spl573_523,
inference(avatar_split_clause,[],[f18318,f30554]) ).
fof(f30554,plain,
( spl573_523
<=> ! [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,[spl573_523])]) ).
fof(f18318,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,[],[f10814]) ).
fof(f10814,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,[],[f6382]) ).
fof(f6382,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,[],[f1582]) ).
fof(f1582,axiom,
! [X12,X61] :
( c_Nat__Transfer_Ois__nat(X61)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X61),X12)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) ).
fof(f30552,plain,
spl573_522,
inference(avatar_split_clause,[],[f18291,f30550]) ).
fof(f30550,plain,
( spl573_522
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_522])]) ).
fof(f18291,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10781]) ).
fof(f10781,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6361]) ).
fof(f6361,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0)) ),
inference(rectify,[],[f557]) ).
fof(f557,axiom,
! [X61,X13] :
( class_Orderings_Opreorder(X13)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X13),X61),X61)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__refl) ).
fof(f30548,plain,
( ~ spl573_520
| spl573_521
| ~ spl573_312
| ~ spl573_398 ),
inference(avatar_split_clause,[],[f30318,f29994,f29601,f30545,f30541]) ).
fof(f30541,plain,
( spl573_520
<=> class_Int_Onumber__ring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_520])]) ).
fof(f29601,plain,
( spl573_312
<=> 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,[spl573_312])]) ).
fof(f29994,plain,
( spl573_398
<=> ! [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,[spl573_398])]) ).
fof(f30318,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)
| ~ spl573_312
| ~ spl573_398 ),
inference(superposition,[],[f29995,f29603]) ).
fof(f29603,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)
| ~ spl573_312 ),
inference(avatar_component_clause,[],[f29601]) ).
fof(f29995,plain,
( ! [X0] :
( c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) )
| ~ spl573_398 ),
inference(avatar_component_clause,[],[f29994]) ).
fof(f30539,plain,
spl573_519,
inference(avatar_split_clause,[],[f18290,f30537]) ).
fof(f30537,plain,
( spl573_519
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_519])]) ).
fof(f18290,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10780]) ).
fof(f10780,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6360]) ).
fof(f6360,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0)) ),
inference(rectify,[],[f369]) ).
fof(f369,axiom,
! [X61,X13] :
( class_Orderings_Opreorder(X13)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X13),X61),X61)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_order__less__irrefl) ).
fof(f30535,plain,
spl573_518,
inference(avatar_split_clause,[],[f18210,f30533]) ).
fof(f30533,plain,
( spl573_518
<=> ! [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,[spl573_518])]) ).
fof(f18210,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(cnf_transformation,[],[f10683]) ).
fof(f10683,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0))
| ~ class_Rings_Ocomm__semiring__1(X1) ),
inference(ennf_transformation,[],[f6285]) ).
fof(f6285,plain,
! [X0,X1] :
( class_Rings_Ocomm__semiring__1(X1)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X1),X0),X0)) ),
inference(rectify,[],[f2095]) ).
fof(f2095,axiom,
! [X88,X13] :
( class_Rings_Ocomm__semiring__1(X13)
=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(X13),X88),X88)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__refl) ).
fof(f30531,plain,
spl573_517,
inference(avatar_split_clause,[],[f18209,f30529]) ).
fof(f30529,plain,
( spl573_517
<=> ! [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,[spl573_517])]) ).
fof(f18209,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,[],[f10682]) ).
fof(f10682,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,[],[f6284]) ).
fof(f6284,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f834]) ).
fof(f834,axiom,
! [X88,X13] :
( class_Divides_Osemiring__div(X13)
=> c_Divides_Odiv__class_Omod(X13,X88,c_Groups_Ozero__class_Ozero(X13)) = X88 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__by__0) ).
fof(f30527,plain,
spl573_516,
inference(avatar_split_clause,[],[f18208,f30525]) ).
fof(f30525,plain,
( spl573_516
<=> ! [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,[spl573_516])]) ).
fof(f18208,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,[],[f10681]) ).
fof(f10681,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,[],[f6283]) ).
fof(f6283,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0) ),
inference(rectify,[],[f835]) ).
fof(f835,axiom,
! [X88,X13] :
( class_Divides_Osemiring__div(X13)
=> c_Groups_Ozero__class_Ozero(X13) = c_Divides_Odiv__class_Omod(X13,X88,X88) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__self) ).
fof(f30523,plain,
spl573_515,
inference(avatar_split_clause,[],[f18198,f30521]) ).
fof(f30521,plain,
( spl573_515
<=> ! [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,[spl573_515])]) ).
fof(f18198,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Int_Oiszero(X1,X0)
| ~ class_Rings_Osemiring__1(X1) ),
inference(cnf_transformation,[],[f14663]) ).
fof(f14663,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,[],[f10673]) ).
fof(f10673,plain,
! [X0,X1] :
( ( c_Int_Oiszero(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Rings_Osemiring__1(X1) ),
inference(ennf_transformation,[],[f6275]) ).
fof(f6275,plain,
! [X0,X1] :
( class_Rings_Osemiring__1(X1)
=> ( c_Int_Oiszero(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f1304]) ).
fof(f1304,axiom,
! [X121,X7] :
( class_Rings_Osemiring__1(X7)
=> ( c_Int_Oiszero(X7,X121)
<=> c_Groups_Ozero__class_Ozero(X7) = X121 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__def) ).
fof(f30519,plain,
spl573_514,
inference(avatar_split_clause,[],[f17960,f30517]) ).
fof(f30517,plain,
( spl573_514
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_514])]) ).
fof(f17960,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ),
inference(cnf_transformation,[],[f6084]) ).
fof(f6084,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ),
inference(rectify,[],[f5190]) ).
fof(f5190,axiom,
! [X124,X99] :
( X99 = X124
| ~ hBOOL(hAPP(hAPP(c_fequal,X99),X124)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(f30515,plain,
spl573_513,
inference(avatar_split_clause,[],[f17539,f30513]) ).
fof(f30513,plain,
( spl573_513
<=> ! [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,[spl573_513])]) ).
fof(f17539,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,[],[f5720]) ).
fof(f5720,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,[],[f3907]) ).
fof(f3907,axiom,
! [X169,X7] : c_Relation_Orefl__on(X7,c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X7,X169)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__rtrancl) ).
fof(f30511,plain,
spl573_512,
inference(avatar_split_clause,[],[f17538,f30509]) ).
fof(f30509,plain,
( spl573_512
<=> ! [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,[spl573_512])]) ).
fof(f17538,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X0)),
inference(cnf_transformation,[],[f5719]) ).
fof(f5719,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X0)),
inference(rectify,[],[f1886]) ).
fof(f1886,axiom,
! [X148,X7] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X7,tc_HOL_Obool)),X148),X148)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(f30507,plain,
spl573_511,
inference(avatar_split_clause,[],[f17537,f30505]) ).
fof(f30505,plain,
( spl573_511
<=> ! [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,[spl573_511])]) ).
fof(f17537,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,[],[f5718]) ).
fof(f5718,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,[],[f2658]) ).
fof(f2658,axiom,
! [X157,X154] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X154),X157))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
fof(f30503,plain,
spl573_510,
inference(avatar_split_clause,[],[f17536,f30501]) ).
fof(f30501,plain,
( spl573_510
<=> ! [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,[spl573_510])]) ).
fof(f17536,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,[],[f5717]) ).
fof(f5717,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,[],[f2663]) ).
fof(f2663,axiom,
! [X157,X154] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X154),X157))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastLessThan__int) ).
fof(f30499,plain,
( spl573_509
| ~ spl573_224
| ~ spl573_388 ),
inference(avatar_split_clause,[],[f30309,f29954,f29203,f30497]) ).
fof(f30497,plain,
( spl573_509
<=> ! [X0] : sP2(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_509])]) ).
fof(f29203,plain,
( spl573_224
<=> ! [X1] : sP2(hAPP(c_Int_Onat,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_224])]) ).
fof(f29954,plain,
( spl573_388
<=> ! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_388])]) ).
fof(f30309,plain,
( ! [X0] : sP2(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ spl573_224
| ~ spl573_388 ),
inference(superposition,[],[f29204,f29955]) ).
fof(f29955,plain,
( ! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0
| ~ spl573_388 ),
inference(avatar_component_clause,[],[f29954]) ).
fof(f29204,plain,
( ! [X1] : sP2(hAPP(c_Int_Onat,X1),X1)
| ~ spl573_224 ),
inference(avatar_component_clause,[],[f29203]) ).
fof(f30495,plain,
spl573_508,
inference(avatar_split_clause,[],[f17535,f30493]) ).
fof(f30493,plain,
( spl573_508
<=> ! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_508])]) ).
fof(f17535,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(cnf_transformation,[],[f5716]) ).
fof(f5716,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(rectify,[],[f2417]) ).
fof(f2417,axiom,
! [X77,X7] : hAPP(c_Set_Oimage(X7,X7,c_COMBI(X7)),X77) = X77,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__ident) ).
fof(f30491,plain,
spl573_507,
inference(avatar_split_clause,[],[f17534,f30489]) ).
fof(f30489,plain,
( spl573_507
<=> ! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_507])]) ).
fof(f17534,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(cnf_transformation,[],[f5715]) ).
fof(f5715,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(rectify,[],[f3718]) ).
fof(f3718,axiom,
! [X77,X7] : hAPP(c_Set_Oimage(X7,X7,c_Fun_Oid(X7)),X77) = X77,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__id) ).
fof(f30487,plain,
spl573_506,
inference(avatar_split_clause,[],[f17532,f30485]) ).
fof(f30485,plain,
( spl573_506
<=> ! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_506])]) ).
fof(f17532,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(cnf_transformation,[],[f5713]) ).
fof(f5713,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(rectify,[],[f3456]) ).
fof(f3456,axiom,
! [X77,X7] : hAPP(c_Set_Ovimage(X7,X7,c_COMBI(X7)),X77) = X77,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__ident) ).
fof(f30483,plain,
spl573_505,
inference(avatar_split_clause,[],[f17531,f30481]) ).
fof(f30481,plain,
( spl573_505
<=> ! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_505])]) ).
fof(f17531,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(cnf_transformation,[],[f5712]) ).
fof(f5712,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(rectify,[],[f3713]) ).
fof(f3713,axiom,
! [X148,X7] : hAPP(c_Set_Ovimage(X7,X7,c_Fun_Oid(X7)),X148) = X148,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vimage__id) ).
fof(f30479,plain,
spl573_504,
inference(avatar_split_clause,[],[f17528,f30477]) ).
fof(f30477,plain,
( spl573_504
<=> ! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_504])]) ).
fof(f17528,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0,
inference(cnf_transformation,[],[f5709]) ).
fof(f5709,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0,
inference(rectify,[],[f4571]) ).
fof(f4571,axiom,
! [X291,X13] : hAPP(hAPP(c_List_Oappend(X13),c_List_Olist_ONil(X13)),X291) = X291,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Nil) ).
fof(f30475,plain,
spl573_503,
inference(avatar_split_clause,[],[f17527,f30473]) ).
fof(f30473,plain,
( spl573_503
<=> ! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_503])]) ).
fof(f17527,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0,
inference(cnf_transformation,[],[f5708]) ).
fof(f5708,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0,
inference(rectify,[],[f4569]) ).
fof(f4569,axiom,
! [X290,X13] : hAPP(hAPP(c_List_Oappend(X13),X290),c_List_Olist_ONil(X13)) = X290,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_append__Nil2) ).
fof(f30471,plain,
spl573_502,
inference(avatar_split_clause,[],[f17526,f30469]) ).
fof(f30469,plain,
( spl573_502
<=> ! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_502])]) ).
fof(f17526,plain,
! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0,
inference(cnf_transformation,[],[f5707]) ).
fof(f5707,plain,
! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0,
inference(rectify,[],[f4934]) ).
fof(f4934,axiom,
! [X290,X13] : hAPP(c_List_Orev(X13),hAPP(c_List_Orev(X13),X290)) = X290,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__rev__ident) ).
fof(f30467,plain,
spl573_501,
inference(avatar_split_clause,[],[f17525,f30465]) ).
fof(f30465,plain,
( spl573_501
<=> ! [X0,X1] : hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_501])]) ).
fof(f17525,plain,
! [X0,X1] : hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X0)) = X0,
inference(cnf_transformation,[],[f5706]) ).
fof(f5706,plain,
! [X0,X1] : hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X0)) = X0,
inference(rectify,[],[f328]) ).
fof(f328,axiom,
! [X61,X13] : hAPP(c_Option_Othe(X13),hAPP(c_Option_Ooption_OSome(X13),X61)) = X61,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the_Osimps) ).
fof(f30463,plain,
spl573_500,
inference(avatar_split_clause,[],[f17523,f30461]) ).
fof(f30461,plain,
( spl573_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,[spl573_500])]) ).
fof(f17523,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(cnf_transformation,[],[f5704]) ).
fof(f5704,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(rectify,[],[f3906]) ).
fof(f3906,axiom,
! [X169,X7] : c_Transitive__Closure_Ortrancl(X7,X169) = c_Transitive__Closure_Ortrancl(X7,c_Transitive__Closure_Ortrancl(X7,X169)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
fof(f30459,plain,
spl573_499,
inference(avatar_split_clause,[],[f17520,f30457]) ).
fof(f30457,plain,
( spl573_499
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_499])]) ).
fof(f17520,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5701]) ).
fof(f5701,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f4814]) ).
fof(f4814,axiom,
! [X5,X7] : c_List_Olist_ONil(X7) = hAPP(c_List_Ofilter(X7,X5),c_List_Olist_ONil(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_filter_Osimps_I1_J) ).
fof(f30455,plain,
( spl573_498
| ~ spl573_225
| ~ spl573_388 ),
inference(avatar_split_clause,[],[f30308,f29954,f29207,f30453]) ).
fof(f30453,plain,
( spl573_498
<=> ! [X0] : sP3(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_498])]) ).
fof(f29207,plain,
( spl573_225
<=> ! [X0] : sP3(hAPP(c_Int_Onat,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_225])]) ).
fof(f30308,plain,
( ! [X0] : sP3(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ spl573_225
| ~ spl573_388 ),
inference(superposition,[],[f29208,f29955]) ).
fof(f29208,plain,
( ! [X0] : sP3(hAPP(c_Int_Onat,X0),X0)
| ~ spl573_225 ),
inference(avatar_component_clause,[],[f29207]) ).
fof(f30451,plain,
spl573_497,
inference(avatar_split_clause,[],[f17333,f30449]) ).
fof(f30449,plain,
( spl573_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,[spl573_497])]) ).
fof(f17333,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,[],[f10416]) ).
fof(f10416,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,[],[f10415]) ).
fof(f10415,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,[],[f5583]) ).
fof(f5583,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,[],[f3174]) ).
fof(f3174,axiom,
! [X7] :
( ( class_Orderings_Olinorder(X7)
& class_Lattices_Osemilattice__inf(X7) )
=> c_Orderings_Oord__class_Omin(X7) = c_Lattices_Osemilattice__inf__class_Oinf(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__min) ).
fof(f30447,plain,
spl573_496,
inference(avatar_split_clause,[],[f17332,f30445]) ).
fof(f30445,plain,
( spl573_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,[spl573_496])]) ).
fof(f17332,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,[],[f10414]) ).
fof(f10414,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,[],[f10413]) ).
fof(f10413,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,[],[f5582]) ).
fof(f5582,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,[],[f2300]) ).
fof(f2300,axiom,
! [X7] :
( ( class_Orderings_Olinorder(X7)
& class_Lattices_Osemilattice__sup(X7) )
=> c_Orderings_Oord__class_Omax(X7) = c_Lattices_Osemilattice__sup__class_Osup(X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__max) ).
fof(f30443,plain,
spl573_495,
inference(avatar_split_clause,[],[f17279,f30441]) ).
fof(f30441,plain,
( spl573_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,[spl573_495])]) ).
fof(f17279,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,[],[f10362]) ).
fof(f10362,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,[],[f5534]) ).
fof(f5534,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,[],[f1902]) ).
fof(f1902,axiom,
! [X7] :
( class_Orderings_Oord(X7)
=> c_Orderings_Oord__class_Omin(X7) = c_Orderings_Oord_Omin(X7,c_Orderings_Oord__class_Oless__eq(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__ord__min) ).
fof(f30439,plain,
spl573_494,
inference(avatar_split_clause,[],[f17278,f30437]) ).
fof(f30437,plain,
( spl573_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,[spl573_494])]) ).
fof(f17278,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,[],[f10361]) ).
fof(f10361,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,[],[f5533]) ).
fof(f5533,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,[],[f1967]) ).
fof(f1967,axiom,
! [X7] :
( class_Orderings_Oord(X7)
=> c_Orderings_Oord__class_Omax(X7) = c_Orderings_Oord_Omax(X7,c_Orderings_Oord__class_Oless__eq(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__ord__max) ).
fof(f30435,plain,
spl573_493,
inference(avatar_split_clause,[],[f17234,f30433]) ).
fof(f30433,plain,
( spl573_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,[spl573_493])]) ).
fof(f17234,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,[],[f10317]) ).
fof(f10317,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,[],[f5489]) ).
fof(f5489,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,[],[f1345]) ).
fof(f1345,axiom,
! [X13] :
( class_Int_Onumber__ring(X13)
=> c_Groups_Ozero__class_Ozero(X13) = hAPP(c_Int_Onumber__class_Onumber__of(X13),c_Int_OPls) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__Pls) ).
fof(f30430,plain,
spl573_492,
inference(avatar_split_clause,[],[f17233,f30428]) ).
fof(f17233,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,[],[f10316]) ).
fof(f10316,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,[],[f5488]) ).
fof(f5488,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,[],[f1418]) ).
fof(f1418,axiom,
! [X13] :
( class_Int_Onumber__ring(X13)
=> ~ c_Int_Oiszero(X13,hAPP(c_Int_Onumber__class_Onumber__of(X13),c_Int_OBit1(c_Int_OPls))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__iszero__Numeral1) ).
fof(f30426,plain,
spl573_491,
inference(avatar_split_clause,[],[f17223,f30424]) ).
fof(f30424,plain,
( spl573_491
<=> ! [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,[spl573_491])]) ).
fof(f17223,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,[],[f10306]) ).
fof(f10306,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,[],[f5478]) ).
fof(f5478,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,[],[f680]) ).
fof(f680,axiom,
! [X13] :
( class_Groups_Osgn__if(X13)
=> c_Groups_Ozero__class_Ozero(X13) = c_Groups_Osgn__class_Osgn(X13,c_Groups_Ozero__class_Ozero(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sgn0) ).
fof(f30422,plain,
spl573_490,
inference(avatar_split_clause,[],[f17053,f30420]) ).
fof(f30420,plain,
( spl573_490
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_490])]) ).
fof(f17053,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))),
inference(cnf_transformation,[],[f5321]) ).
fof(f5321,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))),
inference(rectify,[],[f268]) ).
fof(f268,axiom,
! [X12] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),hAPP(c_Nat_OSuc,X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lessI) ).
fof(f30418,plain,
spl573_489,
inference(avatar_split_clause,[],[f17052,f30416]) ).
fof(f30416,plain,
( spl573_489
<=> ! [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,[spl573_489])]) ).
fof(f17052,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,[],[f5320]) ).
fof(f5320,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f568]) ).
fof(f568,axiom,
! [X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X12) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1) ).
fof(f30414,plain,
spl573_488,
inference(avatar_split_clause,[],[f17051,f30412]) ).
fof(f30412,plain,
( spl573_488
<=> ! [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,[spl573_488])]) ).
fof(f17051,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,[],[f5319]) ).
fof(f5319,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
inference(rectify,[],[f441]) ).
fof(f441,axiom,
! [X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X97) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1) ).
fof(f30410,plain,
spl573_487,
inference(avatar_split_clause,[],[f17047,f30408]) ).
fof(f30408,plain,
( spl573_487
<=> ! [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,[spl573_487])]) ).
fof(f17047,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,[],[f5315]) ).
fof(f5315,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(rectify,[],[f566]) ).
fof(f566,axiom,
! [X12] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X12),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__1__right) ).
fof(f30406,plain,
spl573_486,
inference(avatar_split_clause,[],[f17046,f30404]) ).
fof(f30404,plain,
( spl573_486
<=> ! [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,[spl573_486])]) ).
fof(f17046,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,[],[f5314]) ).
fof(f5314,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
inference(rectify,[],[f436]) ).
fof(f436,axiom,
! [X97] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X97),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__1__right) ).
fof(f30402,plain,
spl573_485,
inference(avatar_split_clause,[],[f17041,f30400]) ).
fof(f17041,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,[],[f5309]) ).
fof(f5309,plain,
! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = X0,
inference(rectify,[],[f447]) ).
fof(f447,axiom,
! [X97] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X97)) = X97,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__zminus) ).
fof(f30398,plain,
spl573_484,
inference(avatar_split_clause,[],[f17040,f30396]) ).
fof(f30396,plain,
( spl573_484
<=> ! [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,[spl573_484])]) ).
fof(f17040,plain,
! [X0] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)) = X0,
inference(cnf_transformation,[],[f5308]) ).
fof(f5308,plain,
! [X0] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)) = X0,
inference(rectify,[],[f2276]) ).
fof(f2276,axiom,
! [X157] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X157)) = X157,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__lessThan) ).
fof(f30394,plain,
spl573_483,
inference(avatar_split_clause,[],[f17037,f30392]) ).
fof(f30390,plain,
spl573_482,
inference(avatar_split_clause,[],[f17036,f30388]) ).
fof(f30388,plain,
( spl573_482
<=> ! [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,[spl573_482])]) ).
fof(f17036,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,[],[f5304]) ).
fof(f5304,plain,
! [X0] : c_List_Olist_ONil(tc_List_Olist(X0)) = c_List_Otranspose(X0,c_List_Olist_ONil(tc_List_Olist(X0))),
inference(rectify,[],[f4830]) ).
fof(f4830,axiom,
! [X13] : c_List_Olist_ONil(tc_List_Olist(X13)) = c_List_Otranspose(X13,c_List_Olist_ONil(tc_List_Olist(X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transpose_Osimps_I1_J) ).
fof(f30385,plain,
spl573_481,
inference(avatar_split_clause,[],[f17027,f30383]) ).
fof(f30383,plain,
( spl573_481
<=> ! [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,[spl573_481])]) ).
fof(f17027,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X0)),
inference(cnf_transformation,[],[f5295]) ).
fof(f5295,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X0)),
inference(rectify,[],[f650]) ).
fof(f650,axiom,
! [X12] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X12)),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__le__n) ).
fof(f30381,plain,
spl573_480,
inference(avatar_split_clause,[],[f17026,f30379]) ).
fof(f30379,plain,
( spl573_480
<=> ! [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,[spl573_480])]) ).
fof(f17026,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,[],[f5294]) ).
fof(f5294,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,[],[f2461]) ).
fof(f2461,axiom,
! [X7] : c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UNIV__not__empty) ).
fof(f30377,plain,
spl573_479,
inference(avatar_split_clause,[],[f16905,f30374]) ).
fof(f30374,plain,
( spl573_479
<=> 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,[spl573_479])]) ).
fof(f16905,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,[],[f3417]) ).
fof(f3417,axiom,
c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition__code__numeral) ).
fof(f30372,plain,
spl573_478,
inference(avatar_split_clause,[],[f16904,f30369]) ).
fof(f30369,plain,
( spl573_478
<=> 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,[spl573_478])]) ).
fof(f16904,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,[],[f3412]) ).
fof(f3412,axiom,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__int) ).
fof(f30367,plain,
( spl573_477
| ~ spl573_315
| ~ spl573_475 ),
inference(avatar_split_clause,[],[f30349,f30336,f29617,f30364]) ).
fof(f30364,plain,
( spl573_477
<=> c_Nat__Transfer_Ois__nat(c_Int_OBit1(c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_477])]) ).
fof(f29617,plain,
( spl573_315
<=> c_Nat__Transfer_Ois__nat(c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_315])]) ).
fof(f30349,plain,
( c_Nat__Transfer_Ois__nat(c_Int_OBit1(c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl573_315
| ~ spl573_475 ),
inference(superposition,[],[f29619,f30338]) ).
fof(f29619,plain,
( c_Nat__Transfer_Ois__nat(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))
| ~ spl573_315 ),
inference(avatar_component_clause,[],[f29617]) ).
fof(f30345,plain,
( ~ spl573_27
| ~ spl573_476
| ~ spl573_244
| ~ spl573_397 ),
inference(avatar_split_clause,[],[f30317,f29990,f29295,f30342,f28229]) ).
fof(f30342,plain,
( spl573_476
<=> c_Int_Oiszero(tc_Int_Oint,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_476])]) ).
fof(f29990,plain,
( spl573_397
<=> ! [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,[spl573_397])]) ).
fof(f30317,plain,
( ~ c_Int_Oiszero(tc_Int_Oint,c_Int_OMin)
| ~ class_Int_Onumber__ring(tc_Int_Oint)
| ~ spl573_244
| ~ spl573_397 ),
inference(superposition,[],[f29991,f29296]) ).
fof(f29991,plain,
( ! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) )
| ~ spl573_397 ),
inference(avatar_component_clause,[],[f29990]) ).
fof(f30339,plain,
( spl573_475
| ~ spl573_244
| ~ spl573_383 ),
inference(avatar_split_clause,[],[f30304,f29932,f29295,f30336]) ).
fof(f29932,plain,
( spl573_383
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_383])]) ).
fof(f30304,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_OBit1(c_Int_OPls)
| ~ spl573_244
| ~ spl573_383 ),
inference(superposition,[],[f29934,f29296]) ).
fof(f29934,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))
| ~ spl573_383 ),
inference(avatar_component_clause,[],[f29932]) ).
fof(f30325,plain,
( ~ spl573_474
| ~ spl573_350
| spl573_380 ),
inference(avatar_split_clause,[],[f30301,f29917,f29766,f30322]) ).
fof(f30322,plain,
( spl573_474
<=> class_Finite__Set_Ofinite(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_474])]) ).
fof(f29917,plain,
( spl573_380
<=> 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,[spl573_380])]) ).
fof(f30301,plain,
( ~ class_Finite__Set_Ofinite(tc_Nat_Onat)
| ~ spl573_350
| spl573_380 ),
inference(resolution,[],[f29919,f29767]) ).
fof(f29919,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| spl573_380 ),
inference(avatar_component_clause,[],[f29917]) ).
fof(f30314,plain,
( ~ spl573_473
| ~ spl573_350
| spl573_379 ),
inference(avatar_split_clause,[],[f30300,f29912,f29766,f30311]) ).
fof(f30311,plain,
( spl573_473
<=> class_Finite__Set_Ofinite(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_473])]) ).
fof(f29912,plain,
( spl573_379
<=> 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,[spl573_379])]) ).
fof(f30300,plain,
( ~ class_Finite__Set_Ofinite(tc_Int_Oint)
| ~ spl573_350
| spl573_379 ),
inference(resolution,[],[f29914,f29767]) ).
fof(f29914,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool))))
| spl573_379 ),
inference(avatar_component_clause,[],[f29912]) ).
fof(f30299,plain,
spl573_472,
inference(avatar_split_clause,[],[f27373,f30297]) ).
fof(f30297,plain,
( spl573_472
<=> ! [X2,X1] :
( ~ sP39(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,c_Int_OPls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_472])]) ).
fof(f27373,plain,
! [X2,X1] :
( ~ sP39(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,c_Int_OPls)) ),
inference(forward_demodulation,[],[f27372,f16829]) ).
fof(f27372,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,c_Int_OPls))
| ~ sP39(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(forward_demodulation,[],[f24859,f16829]) ).
fof(f24859,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP39(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(equality_resolution,[],[f20831]) ).
fof(f20831,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f15605]) ).
fof(f15605,plain,
! [X0,X1,X2] :
( ( sP39(X0,X1,X2)
| ~ sP38(X2,X1,X0)
| ~ sP37(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP38(X2,X1,X0)
& sP37(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP39(X0,X1,X2) ) ),
inference(flattening,[],[f15604]) ).
fof(f15604,plain,
! [X0,X1,X2] :
( ( sP39(X0,X1,X2)
| ~ sP38(X2,X1,X0)
| ~ sP37(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP38(X2,X1,X0)
& sP37(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP39(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14411]) ).
fof(f14411,plain,
! [X0,X1,X2] :
( sP39(X0,X1,X2)
<=> ( sP38(X2,X1,X0)
& sP37(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,[sP39])]) ).
fof(f30295,plain,
spl573_471,
inference(avatar_split_clause,[],[f27347,f30293]) ).
fof(f30293,plain,
( spl573_471
<=> ! [X2,X1] :
( ~ sP34(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_471])]) ).
fof(f27347,plain,
! [X2,X1] :
( ~ sP34(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,X1)) ),
inference(forward_demodulation,[],[f24833,f16829]) ).
fof(f24833,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,X1))
| ~ sP34(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(equality_resolution,[],[f20748]) ).
fof(f20748,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ sP34(X0,X1,X2) ),
inference(cnf_transformation,[],[f15549]) ).
fof(f15549,plain,
! [X0,X1,X2] :
( ( sP34(X0,X1,X2)
| ~ sP33(X2,X1,X0)
| ~ sP32(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP33(X2,X1,X0)
& sP32(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP34(X0,X1,X2) ) ),
inference(flattening,[],[f15548]) ).
fof(f15548,plain,
! [X0,X1,X2] :
( ( sP34(X0,X1,X2)
| ~ sP33(X2,X1,X0)
| ~ sP32(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP33(X2,X1,X0)
& sP32(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP34(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14403]) ).
fof(f30291,plain,
spl573_470,
inference(avatar_split_clause,[],[f26802,f30289]) ).
fof(f30289,plain,
( spl573_470
<=> ! [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,[spl573_470])]) ).
fof(f26802,plain,
! [X2,X0,X1] : c_Nat_Onat_Onat__case(X2,X1,X0,c_HOL_Obool_Obool__size(c_fTrue)) = X1,
inference(forward_demodulation,[],[f19201,f16841]) ).
fof(f19201,plain,
! [X2,X0,X1] : c_Nat_Onat_Onat__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(cnf_transformation,[],[f6883]) ).
fof(f6883,plain,
! [X0,X1,X2] : c_Nat_Onat_Onat__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rectify,[],[f149]) ).
fof(f149,axiom,
! [X70,X57,X7] : c_Nat_Onat_Onat__case(X7,X57,X70,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X57,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__0) ).
fof(f30287,plain,
spl573_469,
inference(avatar_split_clause,[],[f26801,f30285]) ).
fof(f30285,plain,
( spl573_469
<=> ! [X2,X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X2,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_469])]) ).
fof(f26801,plain,
! [X2,X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X2,X1,X0)),
inference(forward_demodulation,[],[f19198,f16841]) ).
fof(f19198,plain,
! [X2,X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X2,X1,X0)),
inference(cnf_transformation,[],[f6880]) ).
fof(f6880,plain,
! [X0,X1,X2] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X2,X1,X0)),
inference(rectify,[],[f163]) ).
fof(f163,axiom,
! [X56,X74,X75] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(X75,X74,X56)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I8_J) ).
fof(f30283,plain,
spl573_468,
inference(avatar_split_clause,[],[f25633,f30281]) ).
fof(f30281,plain,
( spl573_468
<=> ! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_Option_Ooption_Ooption__size(X1,X0,c_Option_Ooption_ONone(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_468])]) ).
fof(f25633,plain,
! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_Option_Ooption_Ooption__size(X1,X0,c_Option_Ooption_ONone(X1)),
inference(forward_demodulation,[],[f17503,f16841]) ).
fof(f17503,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Option_Ooption_Ooption__size(X1,X0,c_Option_Ooption_ONone(X1)),
inference(cnf_transformation,[],[f5684]) ).
fof(f5684,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Option_Ooption_Ooption__size(X1,X0,c_Option_Ooption_ONone(X1)),
inference(rectify,[],[f326]) ).
fof(f326,axiom,
! [X92,X7] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Option_Ooption_Ooption__size(X7,X92,c_Option_Ooption_ONone(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osize_I1_J) ).
fof(f30279,plain,
spl573_467,
inference(avatar_split_clause,[],[f25361,f30277]) ).
fof(f30277,plain,
( spl573_467
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_467])]) ).
fof(f25361,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Int_OPls),
inference(forward_demodulation,[],[f17193,f16829]) ).
fof(f17193,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,[],[f5461]) ).
fof(f5461,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,[],[f928]) ).
fof(f928,axiom,
! [X88] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X88,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X88
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X88),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DIVISION__BY__ZERO) ).
fof(f30275,plain,
spl573_466,
inference(avatar_split_clause,[],[f25292,f30273]) ).
fof(f30271,plain,
spl573_465,
inference(avatar_split_clause,[],[f25287,f30269]) ).
fof(f30269,plain,
( spl573_465
<=> ! [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,[spl573_465])]) ).
fof(f25287,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,[],[f25286,f25195]) ).
fof(f25286,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,[],[f17077,f16841]) ).
fof(f17077,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,[],[f5345]) ).
fof(f5345,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,[],[f2056]) ).
fof(f2056,axiom,
! [X96] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X96)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd__1__left) ).
fof(f30267,plain,
spl573_464,
inference(avatar_split_clause,[],[f25280,f30265]) ).
fof(f30265,plain,
( spl573_464
<=> ! [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,[spl573_464])]) ).
fof(f25280,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,[],[f25279,f25195]) ).
fof(f25279,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,[],[f17062,f16841]) ).
fof(f17062,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,[],[f5330]) ).
fof(f5330,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,[],[f920]) ).
fof(f920,axiom,
! [X85] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X85,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__1) ).
fof(f30263,plain,
spl573_463,
inference(avatar_split_clause,[],[f25271,f30261]) ).
fof(f30261,plain,
( spl573_463
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OPls),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_463])]) ).
fof(f25271,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OPls),X0),
inference(forward_demodulation,[],[f17055,f16829]) ).
fof(f17055,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,[],[f5323]) ).
fof(f5323,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,[],[f902]) ).
fof(f902,axiom,
! [X100] : 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)),X100),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zdiv__zero) ).
fof(f30259,plain,
( spl573_462
| ~ spl573_208
| ~ spl573_257 ),
inference(avatar_split_clause,[],[f29528,f29347,f29132,f30257]) ).
fof(f30257,plain,
( spl573_462
<=> ! [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,[spl573_462])]) ).
fof(f29132,plain,
( spl573_208
<=> c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_208])]) ).
fof(f29347,plain,
( spl573_257
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_257])]) ).
fof(f29528,plain,
( ! [X0] : c_Fun_Oinj__on(tc_Int_Oint,tc_Int_Oint,c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)
| ~ spl573_208
| ~ spl573_257 ),
inference(superposition,[],[f29348,f29134]) ).
fof(f29134,plain,
( c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint)
| ~ spl573_208 ),
inference(avatar_component_clause,[],[f29132]) ).
fof(f29348,plain,
( ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0)
| ~ spl573_257 ),
inference(avatar_component_clause,[],[f29347]) ).
fof(f30255,plain,
spl573_461,
inference(avatar_split_clause,[],[f25257,f30253]) ).
fof(f30253,plain,
( spl573_461
<=> ! [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,[spl573_461])]) ).
fof(f25257,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,[],[f17020,f16841]) ).
fof(f17020,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,[],[f5288]) ).
fof(f5288,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,[],[f558]) ).
fof(f558,axiom,
! [X12] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
fof(f30251,plain,
spl573_460,
inference(avatar_split_clause,[],[f25251,f30249]) ).
fof(f30249,plain,
( spl573_460
<=> ! [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,[spl573_460])]) ).
fof(f25251,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f17002,f16841]) ).
fof(f17002,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,[],[f5270]) ).
fof(f5270,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rectify,[],[f267]) ).
fof(f267,axiom,
! [X12] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__zeroE) ).
fof(f30247,plain,
spl573_459,
inference(avatar_split_clause,[],[f25210,f30244]) ).
fof(f30244,plain,
( spl573_459
<=> 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,[spl573_459])]) ).
fof(f25210,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,[],[f16902,f16829]) ).
fof(f16902,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,[],[f741]) ).
fof(f741,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J) ).
fof(f30242,plain,
spl573_458,
inference(avatar_split_clause,[],[f25209,f30239]) ).
fof(f30239,plain,
( spl573_458
<=> 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,[spl573_458])]) ).
fof(f25209,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,[],[f16901,f16829]) ).
fof(f16901,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,[],[f530]) ).
fof(f530,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__less__1) ).
fof(f30237,plain,
spl573_457,
inference(avatar_split_clause,[],[f25203,f30234]) ).
fof(f30234,plain,
( spl573_457
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_457])]) ).
fof(f25203,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(forward_demodulation,[],[f16895,f16841]) ).
fof(f16895,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,[],[f1674]) ).
fof(f1674,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osize_I3_J) ).
fof(f30232,plain,
spl573_456,
inference(avatar_split_clause,[],[f24971,f30230]) ).
fof(f30230,plain,
( spl573_456
<=> ! [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,[spl573_456])]) ).
fof(f24971,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,[],[f22068]) ).
fof(f22068,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,[],[f15975]) ).
fof(f30228,plain,
spl573_455,
inference(avatar_split_clause,[],[f24640,f30226]) ).
fof(f30226,plain,
( spl573_455
<=> ! [X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_455])]) ).
fof(f24640,plain,
! [X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)),
inference(equality_resolution,[],[f18800]) ).
fof(f18800,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),X0)
| c_List_Olist_ONil(X1) != X0 ),
inference(cnf_transformation,[],[f14864]) ).
fof(f30224,plain,
spl573_454,
inference(avatar_split_clause,[],[f23743,f30221]) ).
fof(f30221,plain,
( spl573_454
<=> 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,[spl573_454])]) ).
fof(f23743,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin),
inference(definition_unfolding,[],[f16826,f17039]) ).
fof(f16826,plain,
c_Int_OPls = c_Int_Osucc(c_Int_OMin),
inference(cnf_transformation,[],[f1360]) ).
fof(f1360,axiom,
c_Int_OPls = c_Int_Osucc(c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Min) ).
fof(f30219,plain,
spl573_453,
inference(avatar_split_clause,[],[f22728,f30217]) ).
fof(f30217,plain,
( spl573_453
<=> ! [X2,X4,X0,X3,X1] :
( sP66(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_453])]) ).
fof(f22728,plain,
! [X2,X3,X0,X1,X4] :
( sP66(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ),
inference(cnf_transformation,[],[f14460]) ).
fof(f14460,plain,
! [X0,X1,X2,X3,X4] :
( sP66(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ),
inference(definition_folding,[],[f13696,f14459,f14458]) ).
fof(f14458,plain,
! [X0,X1,X4,X2,X3] :
( sP65(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,[sP65])]) ).
fof(f14459,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)))
<=> sP65(X0,X1,X4,X2,X3) )
| ~ sP66(X3,X2,X4,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP66])]) ).
fof(f13696,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,[],[f9426]) ).
fof(f9426,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,[],[f2198]) ).
fof(f2198,axiom,
! [X133,X4,X27,X76,X7] :
( class_Orderings_Oorder(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X7,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X76,X27)),c_SetInterval_Oord__class_OatLeastAtMost(X7,X4,X133)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X4),X133))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X27),X133))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X4),X76)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X27),X133))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X4),X76)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X76),X27)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastatMost__psubset__iff) ).
fof(f30215,plain,
spl573_452,
inference(avatar_split_clause,[],[f22380,f30213]) ).
fof(f30213,plain,
( spl573_452
<=> ! [X2,X4,X0,X3,X1] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OAss(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_452])]) ).
fof(f22380,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OAss(X4,X3),
inference(cnf_transformation,[],[f9133]) ).
fof(f9133,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OAss(X4,X3),
inference(rectify,[],[f147]) ).
fof(f147,axiom,
! [X51,X52,X53,X56,X75] : c_Com_Ocom_OCond(X53,X52,X51) != c_Com_Ocom_OAss(X75,X56),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I26_J) ).
fof(f30211,plain,
spl573_451,
inference(avatar_split_clause,[],[f22378,f30209]) ).
fof(f30209,plain,
( spl573_451
<=> ! [X2,X4,X0,X3,X1] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OSemi(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_451])]) ).
fof(f22378,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OSemi(X4,X3),
inference(cnf_transformation,[],[f9131]) ).
fof(f9131,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OSemi(X4,X3),
inference(rectify,[],[f26]) ).
fof(f26,axiom,
! [X51,X52,X53,X54,X55] : c_Com_Ocom_OCond(X53,X52,X51) != c_Com_Ocom_OSemi(X55,X54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I44_J) ).
fof(f30207,plain,
spl573_450,
inference(avatar_split_clause,[],[f22375,f30205]) ).
fof(f30205,plain,
( spl573_450
<=> ! [X4,X0,X3,X2,X1] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OCall(X4,X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_450])]) ).
fof(f22375,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OCall(X4,X3,X2),
inference(cnf_transformation,[],[f9128]) ).
fof(f9128,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OCall(X4,X3,X2),
inference(rectify,[],[f153]) ).
fof(f153,axiom,
! [X56,X75,X53,X78,X79] : c_Com_Ocom_OCall(X79,X78,X53) != c_Com_Ocom_OAss(X75,X56),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I33_J) ).
fof(f30203,plain,
spl573_449,
inference(avatar_split_clause,[],[f22374,f30201]) ).
fof(f30201,plain,
( spl573_449
<=> ! [X4,X0,X3,X2,X1] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OLocal(X4,X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_449])]) ).
fof(f22374,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OLocal(X4,X3,X2),
inference(cnf_transformation,[],[f9127]) ).
fof(f9127,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OLocal(X4,X3,X2),
inference(rectify,[],[f152]) ).
fof(f152,axiom,
! [X56,X75,X35,X53,X80] : c_Com_Ocom_OLocal(X80,X53,X35) != c_Com_Ocom_OAss(X75,X56),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I23_J) ).
fof(f30199,plain,
spl573_448,
inference(avatar_split_clause,[],[f22372,f30197]) ).
fof(f30197,plain,
( spl573_448
<=> ! [X2,X4,X0,X3,X1] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_448])]) ).
fof(f22372,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3),
inference(cnf_transformation,[],[f9125]) ).
fof(f9125,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X54,X55,X56,X35,X53] : c_Com_Ocom_OWhile(X53,X35) != c_Com_Ocom_OCond(X56,X55,X54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I53_J) ).
fof(f30195,plain,
spl573_447,
inference(avatar_split_clause,[],[f22370,f30193]) ).
fof(f30193,plain,
( spl573_447
<=> ! [X2,X4,X0,X3,X1] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_447])]) ).
fof(f22370,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3),
inference(cnf_transformation,[],[f9123]) ).
fof(f9123,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3),
inference(rectify,[],[f80]) ).
fof(f80,axiom,
! [X38,X56,X73,X35,X53] : c_Com_Ocom_OWhile(X53,X35) != c_Com_Ocom_OLocal(X73,X56,X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I39_J) ).
fof(f30191,plain,
spl573_446,
inference(avatar_split_clause,[],[f22368,f30189]) ).
fof(f30189,plain,
( spl573_446
<=> ! [X2,X4,X0,X3,X1] : c_Com_Ocom_OCall(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_446])]) ).
fof(f22368,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OCall(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3),
inference(cnf_transformation,[],[f9121]) ).
fof(f9121,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OCall(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3),
inference(rectify,[],[f81]) ).
fof(f81,axiom,
! [X53,X78,X79,X38,X56] : c_Com_Ocom_OWhile(X56,X38) != c_Com_Ocom_OCall(X79,X78,X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I60_J) ).
fof(f30187,plain,
spl573_445,
inference(avatar_split_clause,[],[f22366,f30185]) ).
fof(f30185,plain,
( spl573_445
<=> ! [X2,X4,X0,X3,X1] : c_Com_Ocom_OCall(X2,X1,X0) != c_Com_Ocom_OSemi(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_445])]) ).
fof(f22366,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OCall(X2,X1,X0) != c_Com_Ocom_OSemi(X4,X3),
inference(cnf_transformation,[],[f9119]) ).
fof(f9119,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OCall(X2,X1,X0) != c_Com_Ocom_OSemi(X4,X3),
inference(rectify,[],[f89]) ).
fof(f89,axiom,
! [X53,X78,X79,X54,X55] : c_Com_Ocom_OSemi(X55,X54) != c_Com_Ocom_OCall(X79,X78,X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I50_J) ).
fof(f30183,plain,
spl573_444,
inference(avatar_split_clause,[],[f22364,f30181]) ).
fof(f30181,plain,
( spl573_444
<=> ! [X4,X0,X3,X2,X1] : c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OLocal(X4,X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_444])]) ).
fof(f22364,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OLocal(X4,X3,X2),
inference(cnf_transformation,[],[f9117]) ).
fof(f9117,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OLocal(X4,X3,X2),
inference(rectify,[],[f86]) ).
fof(f86,axiom,
! [X51,X52,X38,X56,X73] : c_Com_Ocom_OSemi(X52,X51) != c_Com_Ocom_OLocal(X73,X56,X38),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I34_J) ).
fof(f30179,plain,
spl573_443,
inference(avatar_split_clause,[],[f21069,f30177]) ).
fof(f30177,plain,
( spl573_443
<=> ! [X2,X0,X1,X3] : hAPP(c_Com_Ocom_OBODY,X0) != c_Com_Ocom_OCond(X3,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_443])]) ).
fof(f21069,plain,
! [X2,X3,X0,X1] : hAPP(c_Com_Ocom_OBODY,X0) != c_Com_Ocom_OCond(X3,X2,X1),
inference(cnf_transformation,[],[f8173]) ).
fof(f8173,plain,
! [X0,X1,X2,X3] : hAPP(c_Com_Ocom_OBODY,X0) != c_Com_Ocom_OCond(X3,X2,X1),
inference(rectify,[],[f134]) ).
fof(f134,axiom,
! [X78,X54,X55,X56] : c_Com_Ocom_OCond(X56,X55,X54) != hAPP(c_Com_Ocom_OBODY,X78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I54_J) ).
fof(f30175,plain,
spl573_442,
inference(avatar_split_clause,[],[f21066,f30173]) ).
fof(f30173,plain,
( spl573_442
<=> ! [X2,X0,X1,X3] : c_Com_Ocom_OLocal(X2,X1,X0) != hAPP(c_Com_Ocom_OBODY,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_442])]) ).
fof(f21066,plain,
! [X2,X3,X0,X1] : c_Com_Ocom_OLocal(X2,X1,X0) != hAPP(c_Com_Ocom_OBODY,X3),
inference(cnf_transformation,[],[f8170]) ).
fof(f8170,plain,
! [X0,X1,X2,X3] : c_Com_Ocom_OLocal(X2,X1,X0) != hAPP(c_Com_Ocom_OBODY,X3),
inference(rectify,[],[f139]) ).
fof(f139,axiom,
! [X38,X56,X73,X78] : c_Com_Ocom_OLocal(X73,X56,X38) != hAPP(c_Com_Ocom_OBODY,X78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I41_J) ).
fof(f30171,plain,
( ~ spl573_134
| spl573_441
| ~ spl573_211
| ~ spl573_249 ),
inference(avatar_split_clause,[],[f29521,f29315,f29147,f30168,f28764]) ).
fof(f28764,plain,
( spl573_134
<=> class_Rings_Osemiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_134])]) ).
fof(f30168,plain,
( spl573_441
<=> c_Int_Oiszero(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_441])]) ).
fof(f29147,plain,
( spl573_211
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_211])]) ).
fof(f29521,plain,
( c_Int_Oiszero(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue))
| ~ class_Rings_Osemiring__1(tc_Nat_Onat)
| ~ spl573_211
| ~ spl573_249 ),
inference(superposition,[],[f29316,f29149]) ).
fof(f29149,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue)
| ~ spl573_211 ),
inference(avatar_component_clause,[],[f29147]) ).
fof(f30166,plain,
spl573_440,
inference(avatar_split_clause,[],[f21065,f30164]) ).
fof(f30164,plain,
( spl573_440
<=> ! [X2,X0,X1,X3] : c_Com_Ocom_OCall(X2,X1,X0) != hAPP(c_Com_Ocom_OBODY,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_440])]) ).
fof(f21065,plain,
! [X2,X3,X0,X1] : c_Com_Ocom_OCall(X2,X1,X0) != hAPP(c_Com_Ocom_OBODY,X3),
inference(cnf_transformation,[],[f8169]) ).
fof(f8169,plain,
! [X0,X1,X2,X3] : c_Com_Ocom_OCall(X2,X1,X0) != hAPP(c_Com_Ocom_OBODY,X3),
inference(rectify,[],[f140]) ).
fof(f140,axiom,
! [X53,X78,X79,X74] : c_Com_Ocom_OCall(X79,X78,X53) != hAPP(c_Com_Ocom_OBODY,X74),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I62_J) ).
fof(f30162,plain,
spl573_439,
inference(avatar_split_clause,[],[f20833,f30160]) ).
fof(f30160,plain,
( spl573_439
<=> ! [X2,X0,X1] :
( sP38(X2,X1,X0)
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_439])]) ).
fof(f20833,plain,
! [X2,X0,X1] :
( sP38(X2,X1,X0)
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f15605]) ).
fof(f30158,plain,
spl573_438,
inference(avatar_split_clause,[],[f20832,f30156]) ).
fof(f30156,plain,
( spl573_438
<=> ! [X2,X0,X1] :
( sP37(X2,X1,X0)
| ~ sP39(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_438])]) ).
fof(f20832,plain,
! [X2,X0,X1] :
( sP37(X2,X1,X0)
| ~ sP39(X0,X1,X2) ),
inference(cnf_transformation,[],[f15605]) ).
fof(f30154,plain,
spl573_437,
inference(avatar_split_clause,[],[f20750,f30152]) ).
fof(f30152,plain,
( spl573_437
<=> ! [X2,X0,X1] :
( sP33(X2,X1,X0)
| ~ sP34(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_437])]) ).
fof(f20750,plain,
! [X2,X0,X1] :
( sP33(X2,X1,X0)
| ~ sP34(X0,X1,X2) ),
inference(cnf_transformation,[],[f15549]) ).
fof(f30150,plain,
spl573_436,
inference(avatar_split_clause,[],[f20749,f30148]) ).
fof(f30148,plain,
( spl573_436
<=> ! [X2,X0,X1] :
( sP32(X2,X1,X0)
| ~ sP34(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_436])]) ).
fof(f20749,plain,
! [X2,X0,X1] :
( sP32(X2,X1,X0)
| ~ sP34(X0,X1,X2) ),
inference(cnf_transformation,[],[f15549]) ).
fof(f30146,plain,
spl573_435,
inference(avatar_split_clause,[],[f20713,f30144]) ).
fof(f30144,plain,
( spl573_435
<=> ! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP29(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_435])]) ).
fof(f20713,plain,
! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP29(X0,X2,X1) ),
inference(cnf_transformation,[],[f15520]) ).
fof(f15520,plain,
! [X0,X1,X2] :
( ( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP29(X0,X2,X1) )
& ( sP29(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14397]) ).
fof(f14397,plain,
! [X0,X1,X2] :
( c_Relation_Orefl__on(X2,X1,X0)
<=> sP29(X0,X2,X1) ),
inference(definition_folding,[],[f12514,f14396]) ).
fof(f14396,plain,
! [X0,X2,X1] :
( sP29(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,[sP29])]) ).
fof(f12514,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,[],[f8058]) ).
fof(f8058,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,[],[f3315]) ).
fof(f3315,axiom,
! [X169,X148,X7] :
( c_Relation_Orefl__on(X7,X148,X169)
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X7),X2),X148))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X2),X2)),X169)) )
& ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),X2),X169))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X7,X7,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X7,tc_HOL_Obool),tc_fun(X7,tc_HOL_Obool)),X7),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X7)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X7),c_fconj),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X148)))),hAPP(hAPP(c_COMBC(X7,tc_fun(X7,tc_HOL_Obool),tc_HOL_Obool),c_member(X7)),X148))),X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def_H) ).
fof(f30142,plain,
spl573_434,
inference(avatar_split_clause,[],[f20712,f30140]) ).
fof(f30140,plain,
( spl573_434
<=> ! [X2,X0,X1] :
( sP29(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_434])]) ).
fof(f20712,plain,
! [X2,X0,X1] :
( sP29(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f15520]) ).
fof(f30138,plain,
spl573_433,
inference(avatar_split_clause,[],[f20697,f30136]) ).
fof(f30136,plain,
( spl573_433
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0)
| ~ sP28(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_433])]) ).
fof(f20697,plain,
! [X2,X0,X1] :
( c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0)
| ~ sP28(X2,X0,X1) ),
inference(cnf_transformation,[],[f15503]) ).
fof(f15503,plain,
! [X0,X1,X2] :
( ( c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0)
| ~ sP28(X2,X0,X1) )
& ( sP28(X2,X0,X1)
| ~ c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14395]) ).
fof(f14395,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0)
<=> sP28(X2,X0,X1) ),
inference(definition_folding,[],[f12511,f14394]) ).
fof(f14394,plain,
! [X2,X0,X1] :
( sP28(X2,X0,X1)
<=> ! [X3] :
( ! [X5] :
( c_Hoare__Mirabelle_Otriple__valid(X2,X3,X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X2)),X5),X0)) )
| ? [X4] :
( ~ c_Hoare__Mirabelle_Otriple__valid(X2,X3,X4)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X2)),X4),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP28])]) ).
fof(f12511,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0)
<=> ! [X3] :
( ! [X5] :
( c_Hoare__Mirabelle_Otriple__valid(X2,X3,X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X2)),X5),X0)) )
| ? [X4] :
( ~ c_Hoare__Mirabelle_Otriple__valid(X2,X3,X4)
& hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X2)),X4),X1)) ) ) ),
inference(ennf_transformation,[],[f8055]) ).
fof(f8055,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0)
<=> ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X2)),X4),X1))
=> c_Hoare__Mirabelle_Otriple__valid(X2,X3,X4) )
=> ! [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X2)),X5),X0))
=> c_Hoare__Mirabelle_Otriple__valid(X2,X3,X5) ) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X15,X16,X7] :
( c_Hoare__Mirabelle_Ohoare__valids(X7,X16,X15)
<=> ! [X17] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X7)),X2),X16))
=> c_Hoare__Mirabelle_Otriple__valid(X7,X17,X2) )
=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(X7)),X2),X15))
=> c_Hoare__Mirabelle_Otriple__valid(X7,X17,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__valids__def) ).
fof(f30134,plain,
spl573_432,
inference(avatar_split_clause,[],[f20696,f30132]) ).
fof(f30132,plain,
( spl573_432
<=> ! [X2,X0,X1] :
( sP28(X2,X0,X1)
| ~ c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_432])]) ).
fof(f20696,plain,
! [X2,X0,X1] :
( sP28(X2,X0,X1)
| ~ c_Hoare__Mirabelle_Ohoare__valids(X2,X1,X0) ),
inference(cnf_transformation,[],[f15503]) ).
fof(f30130,plain,
spl573_431,
inference(avatar_split_clause,[],[f20295,f30128]) ).
fof(f30128,plain,
( spl573_431
<=> ! [X2,X0,X1] :
( X0 = X2
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_431])]) ).
fof(f20295,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X2,X1,X0) ),
inference(cnf_transformation,[],[f12151]) ).
fof(f12151,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X2,X1,X0) ),
inference(ennf_transformation,[],[f7793]) ).
fof(f7793,plain,
! [X0,X1,X2] :
( c_Natural_Oevaln(c_Com_Ocom_OSKIP,X2,X1,X0)
=> X0 = X2 ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X11,X12,X14] :
( c_Natural_Oevaln(c_Com_Ocom_OSKIP,X14,X12,X11)
=> X11 = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I1_J) ).
fof(f30126,plain,
spl573_430,
inference(avatar_split_clause,[],[f19202,f30124]) ).
fof(f30124,plain,
( spl573_430
<=> ! [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,[spl573_430])]) ).
fof(f19202,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,[],[f6884]) ).
fof(f6884,plain,
! [X0,X1,X2] : c_Fun_Oinj__on(X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(rectify,[],[f3346]) ).
fof(f3346,axiom,
! [X1,X58,X7] : c_Fun_Oinj__on(X7,X58,X1,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__empty) ).
fof(f30122,plain,
spl573_429,
inference(avatar_split_clause,[],[f19200,f30120]) ).
fof(f30120,plain,
( spl573_429
<=> ! [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,[spl573_429])]) ).
fof(f19200,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,[],[f6882]) ).
fof(f6882,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,[],[f1737]) ).
fof(f1737,axiom,
! [X70,X57,X7] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(X7,X57,X70,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X57,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Orecs_I1_J) ).
fof(f30118,plain,
spl573_428,
inference(avatar_split_clause,[],[f19199,f30116]) ).
fof(f30116,plain,
( spl573_428
<=> ! [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,[spl573_428])]) ).
fof(f19199,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,[],[f6881]) ).
fof(f6881,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,[],[f1675]) ).
fof(f1675,axiom,
! [X70,X57,X7] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X7,X57,X70,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X57,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osimps_I4_J) ).
fof(f30114,plain,
spl573_427,
inference(avatar_split_clause,[],[f19196,f30112]) ).
fof(f30112,plain,
( spl573_427
<=> ! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2) != X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_427])]) ).
fof(f19196,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2) != X2,
inference(cnf_transformation,[],[f6878]) ).
fof(f6878,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2) != X2,
inference(rectify,[],[f4401]) ).
fof(f4401,axiom,
! [X61,X13,X290] : hAPP(hAPP(c_List_Olist_OCons(X13),X61),X290) != X290,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Cons__self) ).
fof(f30110,plain,
spl573_426,
inference(avatar_split_clause,[],[f18753,f30108]) ).
fof(f30108,plain,
( spl573_426
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| ~ sP3(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_426])]) ).
fof(f18753,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| ~ sP3(X1,X0) ),
inference(cnf_transformation,[],[f14817]) ).
fof(f14817,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onat,X0) = X1
| ~ sP3(X1,X0) )
& ( sP3(X1,X0)
| hAPP(c_Int_Onat,X0) != X1 ) ),
inference(nnf_transformation,[],[f14353]) ).
fof(f14353,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
<=> sP3(X1,X0) ),
inference(definition_folding,[],[f11239,f14352]) ).
fof(f11239,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,[],[f6703]) ).
fof(f6703,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,[],[f797]) ).
fof(f797,axiom,
! [X122,X95] :
( hAPP(c_Int_Onat,X122) = X95
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X122))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X95 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X122))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) = X122 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__iff2) ).
fof(f30106,plain,
spl573_425,
inference(avatar_split_clause,[],[f18745,f30104]) ).
fof(f30104,plain,
( spl573_425
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_425])]) ).
fof(f18745,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f14813]) ).
fof(f14813,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onat,X1) = X0
| ~ sP2(X0,X1) )
& ( sP2(X0,X1)
| hAPP(c_Int_Onat,X1) != X0 ) ),
inference(nnf_transformation,[],[f14351]) ).
fof(f14351,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
<=> sP2(X0,X1) ),
inference(definition_folding,[],[f11238,f14350]) ).
fof(f11238,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,[],[f6702]) ).
fof(f6702,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,[],[f798]) ).
fof(f798,axiom,
! [X95,X122] :
( hAPP(c_Int_Onat,X122) = X95
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X122))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X95 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X122))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X95) = X122 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__iff) ).
fof(f30102,plain,
spl573_424,
inference(avatar_split_clause,[],[f18736,f30100]) ).
fof(f30100,plain,
( spl573_424
<=> ! [X0,X1] :
( X0 = X1
| c_Int_OBit1(X0) != c_Int_OBit1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_424])]) ).
fof(f18736,plain,
! [X0,X1] :
( X0 = X1
| c_Int_OBit1(X0) != c_Int_OBit1(X1) ),
inference(cnf_transformation,[],[f14810]) ).
fof(f14810,plain,
! [X0,X1] :
( ( c_Int_OBit1(X0) = c_Int_OBit1(X1)
| X0 != X1 )
& ( X0 = X1
| c_Int_OBit1(X0) != c_Int_OBit1(X1) ) ),
inference(nnf_transformation,[],[f6701]) ).
fof(f6701,plain,
! [X0,X1] :
( c_Int_OBit1(X0) = c_Int_OBit1(X1)
<=> X0 = X1 ),
inference(rectify,[],[f1384]) ).
fof(f1384,axiom,
! [X154,X94] :
( c_Int_OBit1(X94) = c_Int_OBit1(X154)
<=> X94 = X154 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I51_J) ).
fof(f30098,plain,
spl573_423,
inference(avatar_split_clause,[],[f18662,f30096]) ).
fof(f30096,plain,
( spl573_423
<=> ! [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,[spl573_423])]) ).
fof(f18662,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11204]) ).
fof(f11204,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11203]) ).
fof(f11203,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6661]) ).
fof(f6661,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,
! [X327,X326] :
( ( class_Finite__Set_Ofinite(X327)
& class_Finite__Set_Ofinite(X326) )
=> class_Finite__Set_Ofinite(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Finite__Set_Ofinite) ).
fof(f30094,plain,
spl573_422,
inference(avatar_split_clause,[],[f18661,f30092]) ).
fof(f30092,plain,
( spl573_422
<=> ! [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,[spl573_422])]) ).
fof(f18661,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11202]) ).
fof(f11202,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11201]) ).
fof(f11201,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6660]) ).
fof(f6660,plain,
! [X0,X1] :
( ( class_Finite__Set_Ofinite(X0)
& class_Finite__Set_Ofinite(X1) )
=> class_Finite__Set_Ofinite(tc_prod(X1,X0)) ),
inference(rectify,[],[f5140]) ).
fof(f5140,axiom,
! [X327,X326] :
( ( class_Finite__Set_Ofinite(X327)
& class_Finite__Set_Ofinite(X326) )
=> class_Finite__Set_Ofinite(tc_prod(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Finite__Set_Ofinite) ).
fof(f30090,plain,
spl573_421,
inference(avatar_split_clause,[],[f18660,f30088]) ).
fof(f30088,plain,
( spl573_421
<=> ! [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,[spl573_421])]) ).
fof(f18660,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11200]) ).
fof(f11200,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11199]) ).
fof(f11199,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6659]) ).
fof(f6659,plain,
! [X0,X1] :
( ( class_Finite__Set_Ofinite(X0)
& class_Finite__Set_Ofinite(X1) )
=> class_Finite__Set_Ofinite(tc_sum(X1,X0)) ),
inference(rectify,[],[f5138]) ).
fof(f5138,axiom,
! [X327,X326] :
( ( class_Finite__Set_Ofinite(X327)
& class_Finite__Set_Ofinite(X326) )
=> class_Finite__Set_Ofinite(tc_sum(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum__Finite__Set_Ofinite) ).
fof(f30086,plain,
spl573_420,
inference(avatar_split_clause,[],[f18655,f30084]) ).
fof(f30084,plain,
( spl573_420
<=> ! [X0,X1] :
( class_Smallcheck_Osmall(tc_prod(X1,X0))
| ~ class_Smallcheck_Osmall(X0)
| ~ class_Smallcheck_Osmall(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_420])]) ).
fof(f18655,plain,
! [X0,X1] :
( class_Smallcheck_Osmall(tc_prod(X1,X0))
| ~ class_Smallcheck_Osmall(X0)
| ~ class_Smallcheck_Osmall(X1) ),
inference(cnf_transformation,[],[f11192]) ).
fof(f11192,plain,
! [X0,X1] :
( class_Smallcheck_Osmall(tc_prod(X1,X0))
| ~ class_Smallcheck_Osmall(X0)
| ~ class_Smallcheck_Osmall(X1) ),
inference(flattening,[],[f11191]) ).
fof(f11191,plain,
! [X0,X1] :
( class_Smallcheck_Osmall(tc_prod(X1,X0))
| ~ class_Smallcheck_Osmall(X0)
| ~ class_Smallcheck_Osmall(X1) ),
inference(ennf_transformation,[],[f6655]) ).
fof(f6655,plain,
! [X0,X1] :
( ( class_Smallcheck_Osmall(X0)
& class_Smallcheck_Osmall(X1) )
=> class_Smallcheck_Osmall(tc_prod(X1,X0)) ),
inference(rectify,[],[f5141]) ).
fof(f5141,axiom,
! [X327,X326] :
( ( class_Smallcheck_Osmall(X327)
& class_Smallcheck_Osmall(X326) )
=> class_Smallcheck_Osmall(tc_prod(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_prod__Smallcheck_Osmall) ).
fof(f30082,plain,
spl573_419,
inference(avatar_split_clause,[],[f18321,f30080]) ).
fof(f30080,plain,
( spl573_419
<=> ! [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,[spl573_419])]) ).
fof(f18321,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,[],[f10818]) ).
fof(f10818,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,[],[f10817]) ).
fof(f10817,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,[],[f6384]) ).
fof(f6384,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,[],[f1612]) ).
fof(f1612,axiom,
! [X60,X61] :
( c_Nat__Transfer_Ois__nat(X61)
=> ( c_Nat__Transfer_Ois__nat(X60)
=> c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X61,X60)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) ).
fof(f30078,plain,
spl573_418,
inference(avatar_split_clause,[],[f18025,f30076]) ).
fof(f30076,plain,
( spl573_418
<=> ! [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,[spl573_418])]) ).
fof(f18025,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,[],[f10515]) ).
fof(f10515,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,[],[f6133]) ).
fof(f6133,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,[],[f3347]) ).
fof(f3347,axiom,
! [X148,X7] :
( class_Groups_Oordered__ab__group__add(X7)
=> c_Fun_Oinj__on(X7,X7,c_Groups_Ouminus__class_Ouminus(X7),X148) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__uminus) ).
fof(f30074,plain,
spl573_417,
inference(avatar_split_clause,[],[f17962,f30072]) ).
fof(f30072,plain,
( spl573_417
<=> ! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_417])]) ).
fof(f17962,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(cnf_transformation,[],[f6086]) ).
fof(f6086,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(rectify,[],[f5197]) ).
fof(f5197,axiom,
! [X3,X5] :
( hBOOL(X5)
| ~ hBOOL(hAPP(hAPP(c_fconj,X5),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__2) ).
fof(f30070,plain,
spl573_416,
inference(avatar_split_clause,[],[f17961,f30068]) ).
fof(f30068,plain,
( spl573_416
<=> ! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_416])]) ).
fof(f17961,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(cnf_transformation,[],[f6085]) ).
fof(f6085,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(rectify,[],[f5198]) ).
fof(f5198,axiom,
! [X3,X5] :
( hBOOL(X3)
| ~ hBOOL(hAPP(hAPP(c_fconj,X5),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fconj__3) ).
fof(f30066,plain,
spl573_415,
inference(avatar_split_clause,[],[f17956,f30064]) ).
fof(f30064,plain,
( spl573_415
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_415])]) ).
fof(f17956,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ),
inference(cnf_transformation,[],[f6080]) ).
fof(f6080,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ),
inference(rectify,[],[f5202]) ).
fof(f5202,axiom,
! [X3,X5] :
( hBOOL(hAPP(hAPP(c_fimplies,X5),X3))
| hBOOL(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__1) ).
fof(f30062,plain,
spl573_414,
inference(avatar_split_clause,[],[f17955,f30060]) ).
fof(f30060,plain,
( spl573_414
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_414])]) ).
fof(f17955,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6079]) ).
fof(f6079,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5203]) ).
fof(f5203,axiom,
! [X5,X3] :
( hBOOL(hAPP(hAPP(c_fimplies,X5),X3))
| ~ hBOOL(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fimplies__2) ).
fof(f30058,plain,
spl573_413,
inference(avatar_split_clause,[],[f17954,f30056]) ).
fof(f30056,plain,
( spl573_413
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_413])]) ).
fof(f17954,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6078]) ).
fof(f6078,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5200]) ).
fof(f5200,axiom,
! [X5,X3] :
( hBOOL(hAPP(hAPP(c_fdisj,X5),X3))
| ~ hBOOL(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__2) ).
fof(f30054,plain,
spl573_412,
inference(avatar_split_clause,[],[f17953,f30052]) ).
fof(f30052,plain,
( spl573_412
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_412])]) ).
fof(f17953,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6077]) ).
fof(f6077,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5199]) ).
fof(f5199,axiom,
! [X3,X5] :
( hBOOL(hAPP(hAPP(c_fdisj,X5),X3))
| ~ hBOOL(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fdisj__1) ).
fof(f30050,plain,
spl573_411,
inference(avatar_split_clause,[],[f17518,f30048]) ).
fof(f30048,plain,
( spl573_411
<=> ! [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,[spl573_411])]) ).
fof(f17518,plain,
! [X0,X1] : c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X0),
inference(cnf_transformation,[],[f5699]) ).
fof(f5699,plain,
! [X0,X1] : c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X0),
inference(rectify,[],[f4908]) ).
fof(f4908,axiom,
! [X148,X7] : c_Fun_Oinj__on(tc_List_Olist(X7),tc_List_Olist(X7),c_List_Orev(X7),X148),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__rev) ).
fof(f30046,plain,
( spl573_410
| spl573_207
| ~ spl573_374 ),
inference(avatar_split_clause,[],[f29909,f29870,f29127,f30043]) ).
fof(f30043,plain,
( spl573_410
<=> sP7(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_410])]) ).
fof(f29127,plain,
( spl573_207
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_207])]) ).
fof(f29870,plain,
( spl573_374
<=> ! [X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP7(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_374])]) ).
fof(f29909,plain,
( sP7(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| spl573_207
| ~ spl573_374 ),
inference(resolution,[],[f29871,f29129]) ).
fof(f29129,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| spl573_207 ),
inference(avatar_component_clause,[],[f29127]) ).
fof(f29871,plain,
( ! [X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP7(X1,X1) )
| ~ spl573_374 ),
inference(avatar_component_clause,[],[f29870]) ).
fof(f30041,plain,
spl573_409,
inference(avatar_split_clause,[],[f17516,f30039]) ).
fof(f30039,plain,
( spl573_409
<=> ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_409])]) ).
fof(f17516,plain,
! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))),
inference(cnf_transformation,[],[f5697]) ).
fof(f5697,plain,
! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))),
inference(rectify,[],[f2550]) ).
fof(f2550,axiom,
! [X76,X7] : c_Hoare__Mirabelle_Ohoare__derivs(X7,X76,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X7),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_hoare__derivs_Oequations_I1_J) ).
fof(f30037,plain,
spl573_408,
inference(avatar_split_clause,[],[f17514,f30035]) ).
fof(f30035,plain,
( spl573_408
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_408])]) ).
fof(f17514,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X0))),
inference(cnf_transformation,[],[f5695]) ).
fof(f5695,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X0))),
inference(rectify,[],[f4286]) ).
fof(f4286,axiom,
! [X283,X7] : hBOOL(hAPP(c_Finite__Set_Ofinite(X7),hAPP(c_List_Oset(X7),X283))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__set) ).
fof(f30033,plain,
spl573_407,
inference(avatar_split_clause,[],[f17513,f30031]) ).
fof(f30031,plain,
( spl573_407
<=> ! [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,[spl573_407])]) ).
fof(f17513,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,[],[f5694]) ).
fof(f5694,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f2660]) ).
fof(f2660,axiom,
! [X157,X154] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X154,X157))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).
fof(f30029,plain,
spl573_406,
inference(avatar_split_clause,[],[f17512,f30027]) ).
fof(f30027,plain,
( spl573_406
<=> ! [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,[spl573_406])]) ).
fof(f17512,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,[],[f5693]) ).
fof(f5693,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f2664]) ).
fof(f2664,axiom,
! [X157,X154] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X154,X157))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost) ).
fof(f30025,plain,
spl573_405,
inference(avatar_split_clause,[],[f17511,f30023]) ).
fof(f30023,plain,
( spl573_405
<=> ! [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,[spl573_405])]) ).
fof(f17511,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,[],[f5692]) ).
fof(f5692,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f2667]) ).
fof(f2667,axiom,
! [X157,X154] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X154,X157))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan) ).
fof(f30021,plain,
spl573_404,
inference(avatar_split_clause,[],[f17510,f30019]) ).
fof(f30019,plain,
( spl573_404
<=> ! [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,[spl573_404])]) ).
fof(f17510,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,[],[f5691]) ).
fof(f5691,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f2659]) ).
fof(f2659,axiom,
! [X157,X154] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X154,X157))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atLeastAtMost__int) ).
fof(f30017,plain,
spl573_403,
inference(avatar_split_clause,[],[f17509,f30015]) ).
fof(f30015,plain,
( spl573_403
<=> ! [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,[spl573_403])]) ).
fof(f17509,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,[],[f5690]) ).
fof(f5690,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f2665]) ).
fof(f2665,axiom,
! [X157,X154] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X154,X157))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost__int) ).
fof(f30013,plain,
spl573_402,
inference(avatar_split_clause,[],[f17508,f30011]) ).
fof(f30011,plain,
( spl573_402
<=> ! [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,[spl573_402])]) ).
fof(f17508,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,[],[f5689]) ).
fof(f5689,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f2666]) ).
fof(f2666,axiom,
! [X157,X154] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X154,X157))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan__int) ).
fof(f30009,plain,
spl573_401,
inference(avatar_split_clause,[],[f17507,f30007]) ).
fof(f30007,plain,
( spl573_401
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_401])]) ).
fof(f17507,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5688]) ).
fof(f5688,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4452]) ).
fof(f4452,axiom,
! [X61,X13] : c_List_Olist_ONil(X13) = c_List_Oremove1(X13,X61,c_List_Olist_ONil(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_remove1_Osimps_I1_J) ).
fof(f30005,plain,
spl573_400,
inference(avatar_split_clause,[],[f17506,f30003]) ).
fof(f30003,plain,
( spl573_400
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_400])]) ).
fof(f17506,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5687]) ).
fof(f5687,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4972]) ).
fof(f4972,axiom,
! [X5,X7] : c_List_Olist_ONil(X7) = c_List_OtakeWhile(X7,X5,c_List_Olist_ONil(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).
fof(f30001,plain,
( ~ spl573_399
| ~ spl573_290
| ~ spl573_370 ),
inference(avatar_split_clause,[],[f29904,f29852,f29483,f29998]) ).
fof(f29998,plain,
( spl573_399
<=> c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_399])]) ).
fof(f29483,plain,
( spl573_290
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_290])]) ).
fof(f29852,plain,
( spl573_370
<=> 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,[spl573_370])]) ).
fof(f29904,plain,
( c_HOL_Obool_Obool__size(c_fTrue) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ spl573_290
| ~ spl573_370 ),
inference(superposition,[],[f29484,f29854]) ).
fof(f29854,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))
| ~ spl573_370 ),
inference(avatar_component_clause,[],[f29852]) ).
fof(f29484,plain,
( ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0)
| ~ spl573_290 ),
inference(avatar_component_clause,[],[f29483]) ).
fof(f29996,plain,
spl573_398,
inference(avatar_split_clause,[],[f17232,f29994]) ).
fof(f17232,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,[],[f10315]) ).
fof(f10315,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,[],[f5487]) ).
fof(f5487,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls)) ),
inference(rectify,[],[f1359]) ).
fof(f1359,axiom,
! [X13] :
( class_Int_Onumber__ring(X13)
=> c_Int_Oiszero(X13,hAPP(c_Int_Onumber__class_Onumber__of(X13),c_Int_OPls)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__Numeral0) ).
fof(f29992,plain,
spl573_397,
inference(avatar_split_clause,[],[f17231,f29990]) ).
fof(f17231,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,[],[f10314]) ).
fof(f10314,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,[],[f5486]) ).
fof(f5486,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin)) ),
inference(rectify,[],[f1301]) ).
fof(f1301,axiom,
! [X13] :
( class_Int_Onumber__ring(X13)
=> ~ c_Int_Oiszero(X13,hAPP(c_Int_Onumber__class_Onumber__of(X13),c_Int_OMin)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nonzero__number__of__Min) ).
fof(f29988,plain,
spl573_396,
inference(avatar_split_clause,[],[f17024,f29986]) ).
fof(f29986,plain,
( spl573_396
<=> ! [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,[spl573_396])]) ).
fof(f17024,plain,
! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f5292]) ).
fof(f5292,plain,
! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f3745]) ).
fof(f3745,axiom,
! [X7] : c_Wellfounded_Owf(X7,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X7,X7),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__empty) ).
fof(f29984,plain,
spl573_395,
inference(avatar_split_clause,[],[f17022,f29982]) ).
fof(f29982,plain,
( spl573_395
<=> ! [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,[spl573_395])]) ).
fof(f17022,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5290]) ).
fof(f5290,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(rectify,[],[f2678]) ).
fof(f2678,axiom,
! [X7] : hBOOL(hAPP(c_Finite__Set_Ofinite(X7),c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).
fof(f29980,plain,
spl573_394,
inference(avatar_split_clause,[],[f17019,f29978]) ).
fof(f29978,plain,
( spl573_394
<=> ! [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,[spl573_394])]) ).
fof(f17019,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0))),
inference(cnf_transformation,[],[f5287]) ).
fof(f5287,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0))),
inference(rectify,[],[f2661]) ).
fof(f2661,axiom,
! [X94] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X94))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__lessThan) ).
fof(f29976,plain,
spl573_393,
inference(avatar_split_clause,[],[f17018,f29974]) ).
fof(f29974,plain,
( spl573_393
<=> ! [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,[spl573_393])]) ).
fof(f17018,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0))),
inference(cnf_transformation,[],[f5286]) ).
fof(f5286,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0))),
inference(rectify,[],[f2662]) ).
fof(f2662,axiom,
! [X94] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X94))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__atMost) ).
fof(f29972,plain,
spl573_392,
inference(avatar_split_clause,[],[f17017,f29970]) ).
fof(f29970,plain,
( spl573_392
<=> ! [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,[spl573_392])]) ).
fof(f17017,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,[],[f5285]) ).
fof(f5285,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,[],[f2344]) ).
fof(f2344,axiom,
! [X190] : 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)),X190)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) ).
fof(f29968,plain,
spl573_391,
inference(avatar_split_clause,[],[f17016,f29966]) ).
fof(f29966,plain,
( spl573_391
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_391])]) ).
fof(f17016,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(cnf_transformation,[],[f5284]) ).
fof(f5284,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(rectify,[],[f1337]) ).
fof(f1337,axiom,
! [X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X96),c_Int_OPls) = X96,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls__right) ).
fof(f29964,plain,
spl573_390,
inference(avatar_split_clause,[],[f17015,f29962]) ).
fof(f29962,plain,
( spl573_390
<=> ! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_390])]) ).
fof(f17015,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(cnf_transformation,[],[f5283]) ).
fof(f5283,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(rectify,[],[f1339]) ).
fof(f1339,axiom,
! [X96] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X96),c_Int_OPls) = X96,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I1_J) ).
fof(f29960,plain,
spl573_389,
inference(avatar_split_clause,[],[f17014,f29958]) ).
fof(f29958,plain,
( spl573_389
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_389])]) ).
fof(f17014,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0,
inference(cnf_transformation,[],[f5282]) ).
fof(f5282,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0,
inference(rectify,[],[f1336]) ).
fof(f1336,axiom,
! [X96] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X96) = X96,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(f29956,plain,
spl573_388,
inference(avatar_split_clause,[],[f17013,f29954]) ).
fof(f17013,plain,
! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0,
inference(cnf_transformation,[],[f5281]) ).
fof(f5281,plain,
! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0,
inference(rectify,[],[f479]) ).
fof(f479,axiom,
! [X12] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X12)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__int) ).
fof(f29952,plain,
spl573_387,
inference(avatar_split_clause,[],[f17010,f29950]) ).
fof(f29950,plain,
( spl573_387
<=> ! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_387])]) ).
fof(f17010,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5278]) ).
fof(f5278,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)),
inference(rectify,[],[f4921]) ).
fof(f4921,axiom,
! [X13] : c_List_Olist_ONil(X13) = hAPP(c_List_Orev(X13),c_List_Olist_ONil(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev_Osimps_I1_J) ).
fof(f29948,plain,
spl573_386,
inference(avatar_split_clause,[],[f17009,f29946]) ).
fof(f29946,plain,
( spl573_386
<=> ! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_386])]) ).
fof(f17009,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5277]) ).
fof(f5277,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)),
inference(rectify,[],[f4701]) ).
fof(f4701,axiom,
! [X13] : c_List_Olist_ONil(X13) = hAPP(c_List_Otl(X13),c_List_Olist_ONil(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tl_Osimps_I1_J) ).
fof(f29944,plain,
spl573_385,
inference(avatar_split_clause,[],[f17005,f29942]) ).
fof(f29942,plain,
( spl573_385
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_385])]) ).
fof(f17005,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0),
inference(cnf_transformation,[],[f5273]) ).
fof(f5273,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0),
inference(rectify,[],[f1338]) ).
fof(f1338,axiom,
! [X128] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X128),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__Pls) ).
fof(f29940,plain,
spl573_384,
inference(avatar_split_clause,[],[f16890,f29937]) ).
fof(f29937,plain,
( spl573_384
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_384])]) ).
fof(f16890,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,[],[f1414]) ).
fof(f1414,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Numeral1__eq1__nat) ).
fof(f29935,plain,
spl573_383,
inference(avatar_split_clause,[],[f16889,f29932]) ).
fof(f16889,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,[],[f1413]) ).
fof(f1413,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__num__one) ).
fof(f29930,plain,
spl573_382,
inference(avatar_split_clause,[],[f16887,f29927]) ).
fof(f29927,plain,
( spl573_382
<=> 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,[spl573_382])]) ).
fof(f16887,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,[],[f752]) ).
fof(f752,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__1) ).
fof(f29925,plain,
spl573_381,
inference(avatar_split_clause,[],[f16886,f29922]) ).
fof(f29922,plain,
( spl573_381
<=> 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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_381])]) ).
fof(f16886,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,[],[f1557]) ).
fof(f1557,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__code__numeral__code) ).
fof(f29920,plain,
~ spl573_380,
inference(avatar_split_clause,[],[f16883,f29917]) ).
fof(f16883,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,[],[f2673]) ).
fof(f2673,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__nat) ).
fof(f29915,plain,
~ spl573_379,
inference(avatar_split_clause,[],[f16882,f29912]) ).
fof(f16882,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,[],[f2762]) ).
fof(f2762,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_infinite__UNIV__int) ).
fof(f29901,plain,
( spl573_378
| ~ spl573_224
| ~ spl573_311 ),
inference(avatar_split_clause,[],[f29879,f29596,f29203,f29898]) ).
fof(f29898,plain,
( spl573_378
<=> sP2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_378])]) ).
fof(f29879,plain,
( sP2(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl573_224
| ~ spl573_311 ),
inference(superposition,[],[f29204,f29598]) ).
fof(f29895,plain,
( spl573_377
| ~ spl573_225
| ~ spl573_311 ),
inference(avatar_split_clause,[],[f29878,f29596,f29207,f29892]) ).
fof(f29892,plain,
( spl573_377
<=> sP3(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_377])]) ).
fof(f29878,plain,
( sP3(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl573_225
| ~ spl573_311 ),
inference(superposition,[],[f29208,f29598]) ).
fof(f29884,plain,
( spl573_376
| ~ spl573_213
| ~ spl573_276 ),
inference(avatar_split_clause,[],[f29539,f29423,f29158,f29881]) ).
fof(f29881,plain,
( spl573_376
<=> sP1(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_376])]) ).
fof(f29158,plain,
( spl573_213
<=> c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_213])]) ).
fof(f29423,plain,
( spl573_276
<=> ! [X0,X1] :
( sP1(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_276])]) ).
fof(f29539,plain,
( sP1(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl573_213
| ~ spl573_276 ),
inference(resolution,[],[f29424,f29160]) ).
fof(f29160,plain,
( c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl573_213 ),
inference(avatar_component_clause,[],[f29158]) ).
fof(f29424,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,X0)
| sP1(X1,X0) )
| ~ spl573_276 ),
inference(avatar_component_clause,[],[f29423]) ).
fof(f29877,plain,
( spl573_375
| ~ spl573_213
| ~ spl573_275 ),
inference(avatar_split_clause,[],[f29531,f29419,f29158,f29874]) ).
fof(f29874,plain,
( spl573_375
<=> c_Wellfounded_Oacyclic(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_375])]) ).
fof(f29419,plain,
( spl573_275
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_275])]) ).
fof(f29531,plain,
( c_Wellfounded_Oacyclic(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl573_213
| ~ spl573_275 ),
inference(resolution,[],[f29420,f29160]) ).
fof(f29420,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,X0)
| c_Wellfounded_Oacyclic(X1,X0) )
| ~ spl573_275 ),
inference(avatar_component_clause,[],[f29419]) ).
fof(f29872,plain,
spl573_374,
inference(avatar_split_clause,[],[f26543,f29870]) ).
fof(f26543,plain,
! [X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP7(X1,X1) ),
inference(forward_demodulation,[],[f24678,f16979]) ).
fof(f24678,plain,
! [X1] :
( sP7(X1,X1)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(equality_resolution,[],[f18933]) ).
fof(f18933,plain,
! [X0,X1] :
( sP7(X0,X1)
| X0 != X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(cnf_transformation,[],[f14953]) ).
fof(f29868,plain,
spl573_373,
inference(avatar_split_clause,[],[f25632,f29866]) ).
fof(f29866,plain,
( spl573_373
<=> ! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_373])]) ).
fof(f25632,plain,
! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X1,X0)),
inference(forward_demodulation,[],[f17492,f16841]) ).
fof(f17492,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X1,X0)),
inference(cnf_transformation,[],[f5673]) ).
fof(f5673,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X1,X0)),
inference(rectify,[],[f164]) ).
fof(f164,axiom,
! [X56,X75] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X75,X56)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I2_J) ).
fof(f29864,plain,
spl573_372,
inference(avatar_split_clause,[],[f25250,f29862]) ).
fof(f29862,plain,
( spl573_372
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_372])]) ).
fof(f25250,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X0)),
inference(forward_demodulation,[],[f16988,f16841]) ).
fof(f16988,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X0)),
inference(cnf_transformation,[],[f5256]) ).
fof(f5256,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X0)),
inference(rectify,[],[f165]) ).
fof(f165,axiom,
! [X93] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,X93)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I7_J) ).
fof(f29860,plain,
spl573_371,
inference(avatar_split_clause,[],[f25199,f29857]) ).
fof(f29857,plain,
( spl573_371
<=> 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,[spl573_371])]) ).
fof(f29855,plain,
spl573_370,
inference(avatar_split_clause,[],[f25195,f29852]) ).
fof(f29850,plain,
spl573_369,
inference(avatar_split_clause,[],[f25193,f29847]) ).
fof(f29847,plain,
( spl573_369
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_369])]) ).
fof(f25193,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
inference(forward_demodulation,[],[f16871,f16841]) ).
fof(f16871,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,[],[f1350]) ).
fof(f1350,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I113_J) ).
fof(f29845,plain,
spl573_368,
inference(avatar_split_clause,[],[f25192,f29842]) ).
fof(f29842,plain,
( spl573_368
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_368])]) ).
fof(f25192,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
inference(forward_demodulation,[],[f16870,f16841]) ).
fof(f16870,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
inference(cnf_transformation,[],[f227]) ).
fof(f227,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I4_J) ).
fof(f29840,plain,
spl573_367,
inference(avatar_split_clause,[],[f25191,f29837]) ).
fof(f29837,plain,
( spl573_367
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_367])]) ).
fof(f25191,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
inference(forward_demodulation,[],[f16869,f16841]) ).
fof(f16869,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
inference(cnf_transformation,[],[f228]) ).
fof(f228,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I3_J) ).
fof(f29835,plain,
spl573_366,
inference(avatar_split_clause,[],[f25190,f29832]) ).
fof(f29832,plain,
( spl573_366
<=> hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_366])]) ).
fof(f25190,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f16868,f16841]) ).
fof(f16868,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP),
inference(cnf_transformation,[],[f166]) ).
fof(f166,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I9_J) ).
fof(f29830,plain,
spl573_365,
inference(avatar_split_clause,[],[f25184,f29827]) ).
fof(f29825,plain,
spl573_364,
inference(avatar_split_clause,[],[f25144,f29823]) ).
fof(f29823,plain,
( spl573_364
<=> ! [X3,X4,X5,X1] : sP85(X5,X1,X4,X3,X4,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_364])]) ).
fof(f25144,plain,
! [X3,X1,X4,X5] : sP85(X5,X1,X4,X3,X4,X5),
inference(equality_resolution,[],[f25143]) ).
fof(f25143,plain,
! [X2,X3,X1,X4,X5] :
( sP85(X5,X1,X2,X3,X4,X5)
| X2 != X4 ),
inference(equality_resolution,[],[f23657]) ).
fof(f23657,plain,
! [X2,X3,X0,X1,X4,X5] :
( sP85(X0,X1,X2,X3,X4,X5)
| X0 != X5
| X2 != X4 ),
inference(cnf_transformation,[],[f16611]) ).
fof(f29821,plain,
spl573_363,
inference(avatar_split_clause,[],[f24650,f29819]) ).
fof(f29819,plain,
( spl573_363
<=> ! [X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_363])]) ).
fof(f24650,plain,
! [X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)),
inference(equality_resolution,[],[f18837]) ).
fof(f18837,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f14886]) ).
fof(f14886,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,[],[f14885]) ).
fof(f14885,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,[],[f6736]) ).
fof(f6736,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,[],[f671]) ).
fof(f671,axiom,
! [X122,X121] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X121),X122))
<=> ( X121 != X122
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X121),X122)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zless__le) ).
fof(f29817,plain,
spl573_362,
inference(avatar_split_clause,[],[f21349,f29815]) ).
fof(f29815,plain,
( spl573_362
<=> ! [X0,X3,X2,X1] :
( sP49(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_362])]) ).
fof(f21349,plain,
! [X2,X3,X0,X1] :
( sP49(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f14430]) ).
fof(f14430,plain,
! [X0,X1,X2,X3] :
( sP49(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f12593,f14429,f14428]) ).
fof(f14428,plain,
! [X1,X0,X3,X2] :
( sP48(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,[sP48])]) ).
fof(f14429,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)))
<=> sP48(X1,X0,X3,X2) )
| ~ sP49(X2,X3,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP49])]) ).
fof(f12593,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,[],[f8447]) ).
fof(f8447,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,[],[f506]) ).
fof(f506,axiom,
! [X27,X76,X4,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X4),X76)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X4),X27)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X27),X76))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X4),c_Groups_Ozero__class_Ozero(X7))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X76),X27))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(f29813,plain,
spl573_361,
inference(avatar_split_clause,[],[f21340,f29811]) ).
fof(f29811,plain,
( spl573_361
<=> ! [X0,X3,X2,X1] :
( sP47(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_361])]) ).
fof(f21340,plain,
! [X2,X3,X0,X1] :
( sP47(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f14427]) ).
fof(f14427,plain,
! [X0,X1,X2,X3] :
( sP47(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f12592,f14426,f14425]) ).
fof(f14425,plain,
! [X2,X0,X3,X1] :
( sP46(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,[sP46])]) ).
fof(f14426,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)))
<=> sP46(X2,X0,X3,X1) )
| ~ sP47(X1,X3,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP47])]) ).
fof(f12592,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),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,[],[f8446]) ).
fof(f8446,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,[],[f505]) ).
fof(f505,axiom,
! [X27,X4,X76,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X76),X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X27),X4)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X27),X76))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X4),c_Groups_Ozero__class_Ozero(X7))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),X76),X27))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X7),c_Groups_Ozero__class_Ozero(X7)),X4)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(f29809,plain,
spl573_360,
inference(avatar_split_clause,[],[f21063,f29807]) ).
fof(f29807,plain,
( spl573_360
<=> ! [X2,X0,X1,X3] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_360])]) ).
fof(f21063,plain,
! [X2,X3,X0,X1] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OWhile(X3,X2),
inference(cnf_transformation,[],[f8167]) ).
fof(f8167,plain,
! [X0,X1,X2,X3] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OWhile(X3,X2),
inference(rectify,[],[f146]) ).
fof(f146,axiom,
! [X56,X75,X35,X53] : c_Com_Ocom_OWhile(X53,X35) != c_Com_Ocom_OAss(X75,X56),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I29_J) ).
fof(f29804,plain,
spl573_359,
inference(avatar_split_clause,[],[f21061,f29802]) ).
fof(f29802,plain,
( spl573_359
<=> ! [X2,X0,X1,X3] : c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_359])]) ).
fof(f21061,plain,
! [X2,X3,X0,X1] : c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OWhile(X3,X2),
inference(cnf_transformation,[],[f8165]) ).
fof(f8165,plain,
! [X0,X1,X2,X3] : c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OWhile(X3,X2),
inference(rectify,[],[f31]) ).
fof(f31,axiom,
! [X54,X55,X35,X53] : c_Com_Ocom_OSemi(X55,X54) != c_Com_Ocom_OWhile(X53,X35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I47_J) ).
fof(f29800,plain,
spl573_358,
inference(avatar_split_clause,[],[f21059,f29798]) ).
fof(f29798,plain,
( spl573_358
<=> ! [X2,X0,X1,X3] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_358])]) ).
fof(f21059,plain,
! [X2,X3,X0,X1] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OSemi(X3,X2),
inference(cnf_transformation,[],[f8163]) ).
fof(f8163,plain,
! [X0,X1,X2,X3] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OSemi(X3,X2),
inference(rectify,[],[f151]) ).
fof(f151,axiom,
! [X56,X75,X51,X52] : c_Com_Ocom_OSemi(X52,X51) != c_Com_Ocom_OAss(X75,X56),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I25_J) ).
fof(f29796,plain,
spl573_357,
inference(avatar_split_clause,[],[f19997,f29794]) ).
fof(f29794,plain,
( spl573_357
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X1)
| ~ sP16(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_357])]) ).
fof(f19997,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X1)
| ~ sP16(X0,X1,X2) ),
inference(cnf_transformation,[],[f15233]) ).
fof(f15233,plain,
! [X0,X1,X2] :
( ( sP16(X0,X1,X2)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK208(X0,X1,X2)),sK209(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK209(X0,X1,X2)),hAPP(c_List_Oset(X0),X1)))
& hBOOL(hAPP(hAPP(c_member(X0),sK208(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) )
| ~ sP16(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK208,sK209])],[f15230,f15232,f15231]) ).
fof(f15231,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),sK208(X0,X1,X2)),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X1))) )
& hBOOL(hAPP(hAPP(c_member(X0),sK208(X0,X1,X2)),hAPP(c_List_Oset(X0),X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15232,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK208(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),sK208(X0,X1,X2)),sK209(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK209(X0,X1,X2)),hAPP(c_List_Oset(X0),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15230,plain,
! [X0,X1,X2] :
( ( sP16(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) )
| ~ sP16(X0,X1,X2) ) ),
inference(rectify,[],[f15229]) ).
fof(f15229,plain,
! [X2,X0,X1] :
( ( sP16(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) )
| ~ sP16(X2,X0,X1) ) ),
inference(flattening,[],[f15228]) ).
fof(f15228,plain,
! [X2,X0,X1] :
( ( sP16(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) )
| ~ sP16(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f14375]) ).
fof(f14375,plain,
! [X2,X0,X1] :
( sP16(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,[sP16])]) ).
fof(f29792,plain,
spl573_356,
inference(avatar_split_clause,[],[f19996,f29790]) ).
fof(f29790,plain,
( spl573_356
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X2)
| ~ sP16(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_356])]) ).
fof(f19996,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X2)
| ~ sP16(X0,X1,X2) ),
inference(cnf_transformation,[],[f15233]) ).
fof(f29788,plain,
spl573_355,
inference(avatar_split_clause,[],[f19194,f29786]) ).
fof(f29786,plain,
( spl573_355
<=> ! [X2,X0,X1] : hAPP(c_Com_Ocom_OBODY,X0) != c_Com_Ocom_OWhile(X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_355])]) ).
fof(f19194,plain,
! [X2,X0,X1] : hAPP(c_Com_Ocom_OBODY,X0) != c_Com_Ocom_OWhile(X2,X1),
inference(cnf_transformation,[],[f6876]) ).
fof(f6876,plain,
! [X0,X1,X2] : hAPP(c_Com_Ocom_OBODY,X0) != c_Com_Ocom_OWhile(X2,X1),
inference(rectify,[],[f132]) ).
fof(f132,axiom,
! [X78,X38,X56] : c_Com_Ocom_OWhile(X56,X38) != hAPP(c_Com_Ocom_OBODY,X78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I58_J) ).
fof(f29784,plain,
spl573_354,
inference(avatar_split_clause,[],[f19192,f29782]) ).
fof(f29782,plain,
( spl573_354
<=> ! [X2,X0,X1] : c_Com_Ocom_OAss(X1,X0) != hAPP(c_Com_Ocom_OBODY,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_354])]) ).
fof(f19192,plain,
! [X2,X0,X1] : c_Com_Ocom_OAss(X1,X0) != hAPP(c_Com_Ocom_OBODY,X2),
inference(cnf_transformation,[],[f6874]) ).
fof(f6874,plain,
! [X0,X1,X2] : c_Com_Ocom_OAss(X1,X0) != hAPP(c_Com_Ocom_OBODY,X2),
inference(rectify,[],[f114]) ).
fof(f114,axiom,
! [X56,X75,X78] : c_Com_Ocom_OAss(X75,X56) != hAPP(c_Com_Ocom_OBODY,X78),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I31_J) ).
fof(f29780,plain,
spl573_353,
inference(avatar_split_clause,[],[f19190,f29778]) ).
fof(f29778,plain,
( spl573_353
<=> ! [X2,X0,X1] : hAPP(c_Com_Ocom_OBODY,X0) != c_Com_Ocom_OSemi(X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_353])]) ).
fof(f19190,plain,
! [X2,X0,X1] : hAPP(c_Com_Ocom_OBODY,X0) != c_Com_Ocom_OSemi(X2,X1),
inference(cnf_transformation,[],[f6872]) ).
fof(f6872,plain,
! [X0,X1,X2] : hAPP(c_Com_Ocom_OBODY,X0) != c_Com_Ocom_OSemi(X2,X1),
inference(rectify,[],[f136]) ).
fof(f136,axiom,
! [X91,X89,X90] : hAPP(c_Com_Ocom_OBODY,X91) != c_Com_Ocom_OSemi(X90,X89),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I48_J) ).
fof(f29776,plain,
spl573_352,
inference(avatar_split_clause,[],[f18702,f29774]) ).
fof(f29774,plain,
( spl573_352
<=> ! [X0,X1] :
( c_Option_Ooption_ONone(X1) = X0
| ~ c_Option_Ois__none(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_352])]) ).
fof(f18702,plain,
! [X0,X1] :
( c_Option_Ooption_ONone(X1) = X0
| ~ c_Option_Ois__none(X1,X0) ),
inference(cnf_transformation,[],[f14770]) ).
fof(f14770,plain,
! [X0,X1] :
( ( c_Option_Ois__none(X1,X0)
| c_Option_Ooption_ONone(X1) != X0 )
& ( c_Option_Ooption_ONone(X1) = X0
| ~ c_Option_Ois__none(X1,X0) ) ),
inference(nnf_transformation,[],[f6688]) ).
fof(f6688,plain,
! [X0,X1] :
( c_Option_Ois__none(X1,X0)
<=> c_Option_Ooption_ONone(X1) = X0 ),
inference(rectify,[],[f344]) ).
fof(f344,axiom,
! [X99,X7] :
( c_Option_Ois__none(X7,X99)
<=> c_Option_Ooption_ONone(X7) = X99 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_is__none__def) ).
fof(f29772,plain,
spl573_351,
inference(avatar_split_clause,[],[f18317,f29770]) ).
fof(f29770,plain,
( spl573_351
<=> ! [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,[spl573_351])]) ).
fof(f18317,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,[],[f10813]) ).
fof(f10813,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,[],[f6381]) ).
fof(f6381,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,[],[f2345]) ).
fof(f2345,axiom,
! [X124,X99] :
( c_Nat__Transfer_Ois__nat(X99)
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X99,X124)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_SetInterval_Otransfer__int__nat__set__function__closures) ).
fof(f29768,plain,
spl573_350,
inference(avatar_split_clause,[],[f18303,f29766]) ).
fof(f18303,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f10793]) ).
fof(f10793,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6370]) ).
fof(f6370,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(X1)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(rectify,[],[f2689]) ).
fof(f2689,axiom,
! [X148,X7] :
( class_Finite__Set_Ofinite(X7)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X7),X148)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__code) ).
fof(f29763,plain,
spl573_349,
inference(avatar_split_clause,[],[f17502,f29761]) ).
fof(f29761,plain,
( spl573_349
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_349])]) ).
fof(f17502,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X0),
inference(cnf_transformation,[],[f5683]) ).
fof(f5683,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X0),
inference(rectify,[],[f3408]) ).
fof(f3408,axiom,
! [X148,X7] : c_Fun_Oinj__on(X7,tc_Option_Ooption(X7),c_Option_Ooption_OSome(X7),X148),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Some) ).
fof(f29759,plain,
spl573_348,
inference(avatar_split_clause,[],[f17500,f29757]) ).
fof(f29757,plain,
( spl573_348
<=> ! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_348])]) ).
fof(f17500,plain,
! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5681]) ).
fof(f5681,plain,
! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(rectify,[],[f4449]) ).
fof(f4449,axiom,
! [X169,X7] : c_List_Olistrelp(X7,X169,c_List_Olist_ONil(X7),c_List_Olist_ONil(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_listrelp_Oequations_I1_J) ).
fof(f29755,plain,
spl573_347,
inference(avatar_split_clause,[],[f17499,f29753]) ).
fof(f17499,plain,
! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(cnf_transformation,[],[f5680]) ).
fof(f5680,plain,
! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(rectify,[],[f3995]) ).
fof(f3995,axiom,
! [X169,X7] : c_Relation_Ototal__on(X7,c_Orderings_Obot__class_Obot(tc_fun(X7,tc_HOL_Obool)),X169),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__empty) ).
fof(f29751,plain,
spl573_346,
inference(avatar_split_clause,[],[f17498,f29749]) ).
fof(f17498,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)),
inference(cnf_transformation,[],[f5679]) ).
fof(f5679,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)),
inference(rectify,[],[f2419]) ).
fof(f2419,axiom,
! [X99,X7] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X7,tc_HOL_Obool)),X99)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_top1I) ).
fof(f29747,plain,
spl573_345,
inference(avatar_split_clause,[],[f17496,f29745]) ).
fof(f29745,plain,
( spl573_345
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_345])]) ).
fof(f17496,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))),
inference(cnf_transformation,[],[f5677]) ).
fof(f5677,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))),
inference(rectify,[],[f4326]) ).
fof(f4326,axiom,
! [X115,X116] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X116,X115))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct__upto) ).
fof(f29743,plain,
spl573_344,
inference(avatar_split_clause,[],[f17495,f29741]) ).
fof(f29741,plain,
( spl573_344
<=> ! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_344])]) ).
fof(f17495,plain,
! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0,
inference(cnf_transformation,[],[f5676]) ).
fof(f5676,plain,
! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0,
inference(rectify,[],[f2046]) ).
fof(f2046,axiom,
! [X99,X7] : c_HOL_OThe(X7,hAPP(c_fequal,X99)) = X99,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__sym__eq__trivial) ).
fof(f29739,plain,
spl573_343,
inference(avatar_split_clause,[],[f17494,f29737]) ).
fof(f29737,plain,
( spl573_343
<=> ! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_343])]) ).
fof(f17494,plain,
! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0,
inference(cnf_transformation,[],[f5675]) ).
fof(f5675,plain,
! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0,
inference(rectify,[],[f3850]) ).
fof(f3850,axiom,
! [X99,X7] : c_Hilbert__Choice_OEps(X7,hAPP(c_fequal,X99)) = X99,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).
fof(f29735,plain,
spl573_342,
inference(avatar_split_clause,[],[f17493,f29733]) ).
fof(f29733,plain,
( spl573_342
<=> ! [X0,X1] : hAPP(c_New__DSequence_Opos__empty(X1),X0) = c_Lazy__Sequence_Oempty(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_342])]) ).
fof(f17493,plain,
! [X0,X1] : hAPP(c_New__DSequence_Opos__empty(X1),X0) = c_Lazy__Sequence_Oempty(X1),
inference(cnf_transformation,[],[f5674]) ).
fof(f5674,plain,
! [X0,X1] : hAPP(c_New__DSequence_Opos__empty(X1),X0) = c_Lazy__Sequence_Oempty(X1),
inference(rectify,[],[f2021]) ).
fof(f2021,axiom,
! [X200,X13] : hAPP(c_New__DSequence_Opos__empty(X13),X200) = c_Lazy__Sequence_Oempty(X13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
fof(f29731,plain,
spl573_341,
inference(avatar_split_clause,[],[f17490,f29729]) ).
fof(f29729,plain,
( spl573_341
<=> ! [X0,X1] : hAPP(c_Option_Ooption_OSome(X1),X0) != c_Option_Ooption_ONone(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_341])]) ).
fof(f17490,plain,
! [X0,X1] : hAPP(c_Option_Ooption_OSome(X1),X0) != c_Option_Ooption_ONone(X1),
inference(cnf_transformation,[],[f5671]) ).
fof(f5671,plain,
! [X0,X1] : hAPP(c_Option_Ooption_OSome(X1),X0) != c_Option_Ooption_ONone(X1),
inference(rectify,[],[f329]) ).
fof(f329,axiom,
! [X120,X13] : c_Option_Ooption_ONone(X13) != hAPP(c_Option_Ooption_OSome(X13),X120),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I2_J) ).
fof(f29727,plain,
spl573_340,
inference(avatar_split_clause,[],[f17344,f29725]) ).
fof(f29725,plain,
( spl573_340
<=> ! [X0] :
( c_Int_OMin = X0
| c_Int_OMin != c_Int_OBit1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_340])]) ).
fof(f17344,plain,
! [X0] :
( c_Int_OMin = X0
| c_Int_OMin != c_Int_OBit1(X0) ),
inference(cnf_transformation,[],[f14521]) ).
fof(f14521,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,[],[f5589]) ).
fof(f5589,plain,
! [X0] :
( c_Int_OMin = c_Int_OBit1(X0)
<=> c_Int_OMin = X0 ),
inference(rectify,[],[f1392]) ).
fof(f1392,axiom,
! [X154] :
( c_Int_OMin = c_Int_OBit1(X154)
<=> c_Int_OMin = X154 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).
fof(f29723,plain,
( spl573_339
| ~ spl573_298 ),
inference(avatar_split_clause,[],[f29548,f29516,f29720]) ).
fof(f29720,plain,
( spl573_339
<=> sP7(c_Int_OPls,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_339])]) ).
fof(f29516,plain,
( spl573_298
<=> ! [X1] :
( c_Int_OPls != X1
| sP7(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_298])]) ).
fof(f29548,plain,
( sP7(c_Int_OPls,c_Int_OPls)
| ~ spl573_298 ),
inference(equality_resolution,[],[f29517]) ).
fof(f29517,plain,
( ! [X1] :
( c_Int_OPls != X1
| sP7(X1,X1) )
| ~ spl573_298 ),
inference(avatar_component_clause,[],[f29516]) ).
fof(f29718,plain,
spl573_338,
inference(avatar_split_clause,[],[f17334,f29716]) ).
fof(f29716,plain,
( spl573_338
<=> ! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_338])]) ).
fof(f17334,plain,
! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ),
inference(cnf_transformation,[],[f10417]) ).
fof(f10417,plain,
! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ),
inference(ennf_transformation,[],[f10105]) ).
fof(f10105,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,[],[f5584]) ).
fof(f5584,plain,
! [X0] :
( c_List_Onat__list(X0)
<=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ),
inference(rectify,[],[f4329]) ).
fof(f4329,axiom,
! [X154] :
( c_List_Onat__list(X154)
<=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X154)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__list__def) ).
fof(f29714,plain,
spl573_337,
inference(avatar_split_clause,[],[f17277,f29712]) ).
fof(f17277,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,[],[f10360]) ).
fof(f10360,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,[],[f5532]) ).
fof(f5532,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,[],[f3626]) ).
fof(f3626,axiom,
! [X7] :
( class_Lattices_Osemilattice__inf(X7)
=> c_Finite__Set_Ofun__left__comm__idem(X7,X7,c_Lattices_Osemilattice__inf__class_Oinf(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__inf) ).
fof(f29710,plain,
spl573_336,
inference(avatar_split_clause,[],[f17276,f29708]) ).
fof(f17276,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,[],[f10359]) ).
fof(f10359,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,[],[f5531]) ).
fof(f5531,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,[],[f3637]) ).
fof(f3637,axiom,
! [X7] :
( class_Lattices_Osemilattice__sup(X7)
=> c_Finite__Set_Ofun__left__comm__idem(X7,X7,c_Lattices_Osemilattice__sup__class_Osup(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__sup) ).
fof(f29706,plain,
spl573_335,
inference(avatar_split_clause,[],[f17271,f29704]) ).
fof(f29704,plain,
( spl573_335
<=> ! [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,[spl573_335])]) ).
fof(f17271,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10354]) ).
fof(f10354,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5526]) ).
fof(f5526,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0)) ),
inference(rectify,[],[f3644]) ).
fof(f3644,axiom,
! [X7] :
( class_Orderings_Olinorder(X7)
=> c_Finite__Set_Ofun__left__comm__idem(X7,X7,c_Orderings_Oord__class_Omin(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofun__left__comm__idem__inf) ).
fof(f29702,plain,
spl573_334,
inference(avatar_split_clause,[],[f17270,f29700]) ).
fof(f29700,plain,
( spl573_334
<=> ! [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,[spl573_334])]) ).
fof(f17270,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10353]) ).
fof(f10353,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5525]) ).
fof(f5525,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0)) ),
inference(rectify,[],[f3643]) ).
fof(f3643,axiom,
! [X7] :
( class_Orderings_Olinorder(X7)
=> c_Finite__Set_Ofun__left__comm__idem(X7,X7,c_Orderings_Oord__class_Omax(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__max_Ofun__left__comm__idem__sup) ).
fof(f29698,plain,
spl573_333,
inference(avatar_split_clause,[],[f17252,f29696]) ).
fof(f29696,plain,
( spl573_333
<=> ! [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,[spl573_333])]) ).
fof(f17252,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,[],[f10335]) ).
fof(f10335,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,[],[f5507]) ).
fof(f5507,plain,
! [X0] :
( class_Groups_Oab__semigroup__mult(X0)
=> c_Finite__Set_Ofun__left__comm(X0,X0,c_Groups_Otimes__class_Otimes(X0)) ),
inference(rectify,[],[f4064]) ).
fof(f4064,axiom,
! [X7] :
( class_Groups_Oab__semigroup__mult(X7)
=> c_Finite__Set_Ofun__left__comm(X7,X7,c_Groups_Otimes__class_Otimes(X7)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm) ).
fof(f29694,plain,
spl573_332,
inference(avatar_split_clause,[],[f17249,f29692]) ).
fof(f29692,plain,
( spl573_332
<=> ! [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,[spl573_332])]) ).
fof(f17249,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(cnf_transformation,[],[f10332]) ).
fof(f10332,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(ennf_transformation,[],[f5504]) ).
fof(f5504,plain,
! [X0] :
( class_Rings_Ozero__neq__one(X0)
=> c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) ),
inference(rectify,[],[f476]) ).
fof(f476,axiom,
! [X13] :
( class_Rings_Ozero__neq__one(X13)
=> c_Groups_Ozero__class_Ozero(X13) != c_Groups_Oone__class_Oone(X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__neq__zero) ).
fof(f29690,plain,
spl573_331,
inference(avatar_split_clause,[],[f17001,f29688]) ).
fof(f29688,plain,
( spl573_331
<=> ! [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,[spl573_331])]) ).
fof(f17001,plain,
! [X0] : c_Finite__Set_Ofun__left__comm__idem(X0,tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0)),
inference(cnf_transformation,[],[f5269]) ).
fof(f5269,plain,
! [X0] : c_Finite__Set_Ofun__left__comm__idem(X0,tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0)),
inference(rectify,[],[f3628]) ).
fof(f3628,axiom,
! [X7] : c_Finite__Set_Ofun__left__comm__idem(X7,tc_fun(X7,tc_HOL_Obool),c_Set_Oinsert(X7)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__left__comm__idem__insert) ).
fof(f29686,plain,
spl573_330,
inference(avatar_split_clause,[],[f17000,f29684]) ).
fof(f17000,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f5268]) ).
fof(f5268,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f814]) ).
fof(f814,axiom,
! [X12] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X12),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__refl) ).
fof(f29682,plain,
spl573_329,
inference(avatar_split_clause,[],[f16999,f29680]) ).
fof(f16999,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)),
inference(cnf_transformation,[],[f5267]) ).
fof(f5267,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)),
inference(rectify,[],[f573]) ).
fof(f573,axiom,
! [X128] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X128),X128)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zle__refl) ).
fof(f29678,plain,
spl573_328,
inference(avatar_split_clause,[],[f16998,f29676]) ).
fof(f16998,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f5266]) ).
fof(f5266,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f2054]) ).
fof(f2054,axiom,
! [X61] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X61),X61)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dvd_Oorder__refl) ).
fof(f29674,plain,
spl573_327,
inference(avatar_split_clause,[],[f16996,f29672]) ).
fof(f16996,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X0),X0)),
inference(cnf_transformation,[],[f5264]) ).
fof(f5264,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X0),X0)),
inference(rectify,[],[f130]) ).
fof(f130,axiom,
! [X88] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X88),X88)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I1_J) ).
fof(f29670,plain,
spl573_326,
inference(avatar_split_clause,[],[f16994,f29668]) ).
fof(f29668,plain,
( spl573_326
<=> ! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_326])]) ).
fof(f16994,plain,
! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0,
inference(cnf_transformation,[],[f5262]) ).
fof(f5262,plain,
! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0,
inference(rectify,[],[f1975]) ).
fof(f1975,axiom,
! [X61] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X61)) = X61,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__inverse) ).
fof(f29666,plain,
spl573_325,
inference(avatar_split_clause,[],[f16993,f29664]) ).
fof(f16993,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0,
inference(cnf_transformation,[],[f5261]) ).
fof(f5261,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0,
inference(rectify,[],[f1973]) ).
fof(f1973,axiom,
! [X12] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X12)) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__of__of__nat) ).
fof(f29662,plain,
spl573_324,
inference(avatar_split_clause,[],[f16992,f29660]) ).
fof(f29660,plain,
( spl573_324
<=> ! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_324])]) ).
fof(f16992,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0,
inference(cnf_transformation,[],[f5260]) ).
fof(f5260,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0,
inference(rectify,[],[f3062]) ).
fof(f3062,axiom,
! [X99] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X99)) = X99,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inverse) ).
fof(f29658,plain,
spl573_323,
inference(avatar_split_clause,[],[f16986,f29656]) ).
fof(f29656,plain,
( spl573_323
<=> ! [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,[spl573_323])]) ).
fof(f16986,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,[],[f5254]) ).
fof(f5254,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,[],[f1709]) ).
fof(f1709,axiom,
! [X96] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Quickcheck_Obeyond(X96,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_beyond__zero) ).
fof(f29654,plain,
spl573_322,
inference(avatar_split_clause,[],[f16983,f29652]) ).
fof(f29652,plain,
( spl573_322
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_322])]) ).
fof(f16983,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f5251]) ).
fof(f5251,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f276]) ).
fof(f276,axiom,
! [X12] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X12),X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__not__refl) ).
fof(f29650,plain,
spl573_321,
inference(avatar_split_clause,[],[f16982,f29648]) ).
fof(f29648,plain,
( spl573_321
<=> ! [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,[spl573_321])]) ).
fof(f16982,plain,
! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(cnf_transformation,[],[f5250]) ).
fof(f5250,plain,
! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(rectify,[],[f1277]) ).
fof(f1277,axiom,
! [X12] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__int) ).
fof(f29646,plain,
spl573_320,
inference(avatar_split_clause,[],[f16880,f29643]) ).
fof(f16880,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f1354]) ).
fof(f1354,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I23_J) ).
fof(f29641,plain,
spl573_319,
inference(avatar_split_clause,[],[f16878,f29638]) ).
fof(f16878,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f1356]) ).
fof(f1356,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I6_J) ).
fof(f29636,plain,
( spl573_318
| ~ spl573_190
| ~ spl573_276 ),
inference(avatar_split_clause,[],[f29538,f29423,f29045,f29633]) ).
fof(f29633,plain,
( spl573_318
<=> sP1(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_318])]) ).
fof(f29045,plain,
( spl573_190
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_190])]) ).
fof(f29538,plain,
( sP1(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl573_190
| ~ spl573_276 ),
inference(resolution,[],[f29424,f29047]) ).
fof(f29047,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl573_190 ),
inference(avatar_component_clause,[],[f29045]) ).
fof(f29631,plain,
( spl573_317
| ~ spl573_244
| ~ spl573_316 ),
inference(avatar_split_clause,[],[f29626,f29622,f29295,f29628]) ).
fof(f29628,plain,
( spl573_317
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_317])]) ).
fof(f29622,plain,
( spl573_316
<=> 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,[spl573_316])]) ).
fof(f29626,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))
| ~ spl573_244
| ~ spl573_316 ),
inference(forward_demodulation,[],[f29624,f29296]) ).
fof(f29624,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)))
| ~ spl573_316 ),
inference(avatar_component_clause,[],[f29622]) ).
fof(f29625,plain,
spl573_316,
inference(avatar_split_clause,[],[f16877,f29622]) ).
fof(f16877,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
inference(cnf_transformation,[],[f1310]) ).
fof(f1310,axiom,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__number__of__Min) ).
fof(f29620,plain,
( spl573_315
| ~ spl573_244
| ~ spl573_314 ),
inference(avatar_split_clause,[],[f29615,f29611,f29295,f29617]) ).
fof(f29611,plain,
( spl573_314
<=> c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_314])]) ).
fof(f29615,plain,
( c_Nat__Transfer_Ois__nat(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))
| ~ spl573_244
| ~ spl573_314 ),
inference(forward_demodulation,[],[f29613,f29296]) ).
fof(f29613,plain,
( c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))
| ~ spl573_314 ),
inference(avatar_component_clause,[],[f29611]) ).
fof(f29614,plain,
spl573_314,
inference(avatar_split_clause,[],[f16876,f29611]) ).
fof(f16876,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f1667]) ).
fof(f1667,axiom,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J) ).
fof(f29609,plain,
spl573_313,
inference(avatar_split_clause,[],[f16874,f29606]) ).
fof(f16874,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin,
inference(cnf_transformation,[],[f1308]) ).
fof(f1308,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int_OMin__def) ).
fof(f29604,plain,
spl573_312,
inference(avatar_split_clause,[],[f16864,f29601]) ).
fof(f16864,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,[],[f1650]) ).
fof(f1650,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__code__numeral__code) ).
fof(f29599,plain,
spl573_311,
inference(avatar_split_clause,[],[f16862,f29596]) ).
fof(f16862,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f754]) ).
fof(f754,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I2_J) ).
fof(f29594,plain,
spl573_310,
inference(avatar_split_clause,[],[f16861,f29591]) ).
fof(f16861,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,[],[f1717]) ).
fof(f1717,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__code__numeral__def) ).
fof(f29589,plain,
( spl573_309
| ~ spl573_189
| ~ spl573_276 ),
inference(avatar_split_clause,[],[f29537,f29423,f29040,f29586]) ).
fof(f29586,plain,
( spl573_309
<=> sP1(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_309])]) ).
fof(f29040,plain,
( spl573_189
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_189])]) ).
fof(f29537,plain,
( sP1(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl573_189
| ~ spl573_276 ),
inference(resolution,[],[f29424,f29042]) ).
fof(f29042,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl573_189 ),
inference(avatar_component_clause,[],[f29040]) ).
fof(f29584,plain,
spl573_308,
inference(avatar_split_clause,[],[f16860,f29581]) ).
fof(f29581,plain,
( spl573_308
<=> c_Int_OBit1(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_308])]) ).
fof(f16860,plain,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin),
inference(cnf_transformation,[],[f1417]) ).
fof(f1417,axiom,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Min) ).
fof(f29579,plain,
spl573_307,
inference(avatar_split_clause,[],[f16859,f29576]) ).
fof(f29576,plain,
( spl573_307
<=> 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,[spl573_307])]) ).
fof(f16859,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,[],[f2981]) ).
fof(f2981,axiom,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__less__def) ).
fof(f29574,plain,
spl573_306,
inference(avatar_split_clause,[],[f16858,f29571]) ).
fof(f29571,plain,
( spl573_306
<=> 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,[spl573_306])]) ).
fof(f16858,plain,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f2974]) ).
fof(f2974,axiom,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__strict__def) ).
fof(f29569,plain,
spl573_305,
inference(avatar_split_clause,[],[f16857,f29566]) ).
fof(f29566,plain,
( spl573_305
<=> 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,[spl573_305])]) ).
fof(f16857,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f2976]) ).
fof(f2976,axiom,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__strict__def) ).
fof(f29564,plain,
~ spl573_304,
inference(avatar_split_clause,[],[f16856,f29561]) ).
fof(f16856,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f1353]) ).
fof(f1353,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I20_J) ).
fof(f29559,plain,
~ spl573_303,
inference(avatar_split_clause,[],[f16854,f29556]) ).
fof(f29556,plain,
( spl573_303
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_303])]) ).
fof(f16854,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f1355]) ).
fof(f1355,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I3_J) ).
fof(f29553,plain,
~ spl573_302,
inference(avatar_split_clause,[],[f16852,f29550]) ).
fof(f29550,plain,
( spl573_302
<=> 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,[spl573_302])]) ).
fof(f16852,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(cnf_transformation,[],[f1358]) ).
fof(f1358,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__number__of__Pls) ).
fof(f29544,plain,
( spl573_301
| ~ spl573_190
| ~ spl573_275 ),
inference(avatar_split_clause,[],[f29530,f29419,f29045,f29541]) ).
fof(f29541,plain,
( spl573_301
<=> c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_301])]) ).
fof(f29530,plain,
( c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl573_190
| ~ spl573_275 ),
inference(resolution,[],[f29420,f29047]) ).
fof(f29536,plain,
( spl573_300
| ~ spl573_189
| ~ spl573_275 ),
inference(avatar_split_clause,[],[f29529,f29419,f29040,f29533]) ).
fof(f29533,plain,
( spl573_300
<=> c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_300])]) ).
fof(f29529,plain,
( c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl573_189
| ~ spl573_275 ),
inference(resolution,[],[f29420,f29042]) ).
fof(f29527,plain,
( ~ spl573_133
| spl573_299
| ~ spl573_197
| ~ spl573_249 ),
inference(avatar_split_clause,[],[f29520,f29315,f29078,f29524,f28759]) ).
fof(f28759,plain,
( spl573_133
<=> class_Rings_Osemiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_133])]) ).
fof(f29524,plain,
( spl573_299
<=> c_Int_Oiszero(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_299])]) ).
fof(f29520,plain,
( c_Int_Oiszero(tc_Int_Oint,c_Int_OPls)
| ~ class_Rings_Osemiring__1(tc_Int_Oint)
| ~ spl573_197
| ~ spl573_249 ),
inference(superposition,[],[f29316,f29080]) ).
fof(f29518,plain,
spl573_298,
inference(avatar_split_clause,[],[f26542,f29516]) ).
fof(f26542,plain,
! [X1] :
( c_Int_OPls != X1
| sP7(X1,X1) ),
inference(forward_demodulation,[],[f26541,f16829]) ).
fof(f26541,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
| sP7(X1,X1) ),
inference(forward_demodulation,[],[f24677,f16979]) ).
fof(f24677,plain,
! [X1] :
( sP7(X1,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ),
inference(equality_resolution,[],[f18934]) ).
fof(f18934,plain,
! [X0,X1] :
( sP7(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,[],[f14953]) ).
fof(f29514,plain,
spl573_297,
inference(avatar_split_clause,[],[f25775,f29512]) ).
fof(f29512,plain,
( spl573_297
<=> ! [X0] : c_Nitpick_Onat__gcd(X0,c_HOL_Obool_Obool__size(c_fTrue)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_297])]) ).
fof(f25775,plain,
! [X0] : c_Nitpick_Onat__gcd(X0,c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f24550,f16841]) ).
fof(f24550,plain,
! [X0] : c_Nitpick_Onat__gcd(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(equality_resolution,[],[f17863]) ).
fof(f17863,plain,
! [X0,X1] :
( c_Nitpick_Onat__gcd(X0,X1) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f10431]) ).
fof(f10431,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,[],[f6037]) ).
fof(f6037,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,[],[f1119]) ).
fof(f1119,axiom,
! [X61,X60] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X60
=> c_Nitpick_Onat__gcd(X61,X60) = c_Nitpick_Onat__gcd(X60,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X61,X60)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X60
=> c_Nitpick_Onat__gcd(X61,X60) = X61 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__gcd_Osimps) ).
fof(f29510,plain,
spl573_296,
inference(avatar_split_clause,[],[f25364,f29507]) ).
fof(f29507,plain,
( spl573_296
<=> 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,[spl573_296])]) ).
fof(f25364,plain,
c_Int_OPls = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(forward_demodulation,[],[f24527,f16829]) ).
fof(f24527,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,[],[f17195]) ).
fof(f17195,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,[],[f10293]) ).
fof(f10293,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,[],[f5462]) ).
fof(f5462,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,[],[f1556]) ).
fof(f1556,axiom,
! [X96] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X96
=> ( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X96,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,X96) = 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),X96),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,X96,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,X96) = 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),X96),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) = X96
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X96) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__of__code) ).
fof(f29505,plain,
spl573_295,
inference(avatar_split_clause,[],[f25360,f29503]) ).
fof(f29503,plain,
( spl573_295
<=> ! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_295])]) ).
fof(f25360,plain,
! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(forward_demodulation,[],[f17194,f16829]) ).
fof(f17194,plain,
! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f5461]) ).
fof(f29501,plain,
spl573_294,
inference(avatar_split_clause,[],[f25273,f29499]) ).
fof(f29499,plain,
( spl573_294
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_294])]) ).
fof(f25273,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin),
inference(forward_demodulation,[],[f25272,f16829]) ).
fof(f25272,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,[],[f17056,f16979]) ).
fof(f17056,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,[],[f5324]) ).
fof(f5324,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,[],[f1316]) ).
fof(f1316,axiom,
! [X88] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X88,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__minus1__right) ).
fof(f29497,plain,
spl573_293,
inference(avatar_split_clause,[],[f25263,f29495]) ).
fof(f29495,plain,
( spl573_293
<=> ! [X0] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_293])]) ).
fof(f25263,plain,
! [X0] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) = X0,
inference(forward_demodulation,[],[f17038,f16979]) ).
fof(f17038,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,[],[f5306]) ).
fof(f5306,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,[],[f1221]) ).
fof(f1221,axiom,
! [X128] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X128) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X128),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__number__of__def) ).
fof(f29493,plain,
spl573_292,
inference(avatar_split_clause,[],[f25254,f29491]) ).
fof(f29491,plain,
( spl573_292
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OPls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_292])]) ).
fof(f25254,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OPls,X0),
inference(forward_demodulation,[],[f17006,f16829]) ).
fof(f17006,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,[],[f5274]) ).
fof(f5274,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,[],[f853]) ).
fof(f853,axiom,
! [X100] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X100),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zero) ).
fof(f29489,plain,
spl573_291,
inference(avatar_split_clause,[],[f25249,f29487]) ).
fof(f29487,plain,
( spl573_291
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_291])]) ).
fof(f25249,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(forward_demodulation,[],[f16987,f16829]) ).
fof(f16987,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f5255]) ).
fof(f5255,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(rectify,[],[f854]) ).
fof(f854,axiom,
! [X88] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X88,X88),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__self) ).
fof(f29485,plain,
spl573_290,
inference(avatar_split_clause,[],[f25242,f29483]) ).
fof(f25242,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0),
inference(forward_demodulation,[],[f16968,f16841]) ).
fof(f16968,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X0),
inference(cnf_transformation,[],[f5236]) ).
fof(f5236,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X0),
inference(rectify,[],[f121]) ).
fof(f121,axiom,
! [X85] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X85),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__neq__Zero) ).
fof(f29481,plain,
~ spl573_289,
inference(avatar_split_clause,[],[f25206,f29478]) ).
fof(f29478,plain,
( spl573_289
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl573_289])]) ).
fof(f25206,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != c_Int_OPls,
inference(forward_demodulation,[],[f16899,f25185]) ).
fof(f25185,plain,
c_Int_OPls = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(forward_demodulation,[],[f16865,f16829]) ).
fof(f16865,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,[],[f1351]) ).
fof(f1351,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__is__num__zero) ).
fof(f16899,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,[],[f1357]) ).
fof(f1357,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/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__Pls__Min) ).
fof(f29476,plain,
spl573_288,
inference(avatar_split_clause,[],[f25187,f29473]) ).
fof(f29473,plain,
( spl573_288
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_288])]) ).
fof(f25187,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OPls),
inference(forward_demodulation,[],[f25186,f16841]) ).
fof(f25186,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(forward_demodulation,[],[f16866,f16829]) ).
fof(f16866,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f503]) ).
fof(f503,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__nat__int__numerals_I1_J) ).
fof(f29471,plain,
spl573_287,
inference(avatar_split_clause,[],[f25183,f29468]) ).
fof(f29468,plain,
( spl573_287
<=> 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,[spl573_287])]) ).
fof(f25183,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Nat_Onat_Onat__size(c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f16851,f16841]) ).
fof(f16851,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,[],[f211]) ).
fof(f211,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Osize_I1_J) ).
fof(f29466,plain,
spl573_286,
inference(avatar_split_clause,[],[f25182,f29463]) ).
fof(f29463,plain,
( spl573_286
<=> c_HOL_Obool_Obool__size(c_fTrue) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_286])]) ).
fof(f25182,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(forward_demodulation,[],[f16850,f16841]) ).
fof(f16850,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,[],[f1673]) ).
fof(f1673,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral_Osize_I1_J) ).
fof(f29461,plain,
spl573_285,
inference(avatar_split_clause,[],[f24558,f29459]) ).
fof(f24558,plain,
! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_resolution,[],[f17957]) ).
fof(f17957,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f6081]) ).
fof(f6081,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
| X0 != X1 ),
inference(rectify,[],[f5191]) ).
fof(f5191,axiom,
! [X124,X99] :
( hBOOL(hAPP(hAPP(c_fequal,X99),X124))
| X99 != X124 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(f29457,plain,
spl573_284,
inference(avatar_split_clause,[],[f24543,f29455]) ).
fof(f29455,plain,
( spl573_284
<=> ! [X1] : c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_284])]) ).
fof(f24543,plain,
! [X1] : c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X1),
inference(equality_resolution,[],[f17851]) ).
fof(f17851,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f10426]) ).
fof(f10426,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,[],[f6032]) ).
fof(f6032,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,[],[f1679]) ).
fof(f1679,axiom,
! [X96,X136] :
( ( X96 != X136
=> c_Random_Oinc__shift(X136,X96) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X96),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) )
& ( X96 = X136
=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X136,X96) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inc__shift__def) ).
fof(f29453,plain,
spl573_283,
inference(avatar_split_clause,[],[f20002,f29451]) ).
fof(f29451,plain,
( spl573_283
<=> ! [X2,X0,X1] :
( sP17(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_283])]) ).
fof(f20002,plain,
! [X2,X0,X1] :
( sP17(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f14377]) ).
fof(f14377,plain,
! [X0,X1,X2] :
( sP17(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(definition_folding,[],[f11839,f14376,f14375]) ).
fof(f14376,plain,
! [X1,X0,X2] :
( ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Oappend(X2),X1),X0))
<=> sP16(X2,X0,X1) )
| ~ sP17(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f11839,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,[],[f7576]) ).
fof(f7576,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,[],[f4859]) ).
fof(f4859,axiom,
! [X282,X283,X7] :
( class_Orderings_Olinorder(X7)
=> ( c_List_Olinorder__class_Osorted(X7,hAPP(hAPP(c_List_Oappend(X7),X283),X282))
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X7),X2),hAPP(c_List_Oset(X7),X283)))
=> ! [X202] :
( hBOOL(hAPP(hAPP(c_member(X7),X202),hAPP(c_List_Oset(X7),X282)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X2),X202)) ) )
& c_List_Olinorder__class_Osorted(X7,X282)
& c_List_Olinorder__class_Osorted(X7,X283) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__append) ).
fof(f29449,plain,
spl573_282,
inference(avatar_split_clause,[],[f19553,f29447]) ).
fof(f29447,plain,
( spl573_282
<=> ! [X2,X0,X1] :
( sP15(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_282])]) ).
fof(f19553,plain,
! [X2,X0,X1] :
( sP15(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f14374]) ).
fof(f14374,plain,
! [X0,X1,X2] :
( sP15(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f11303,f14373,f14372]) ).
fof(f14372,plain,
! [X0,X2,X1] :
( sP14(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,[sP14])]) ).
fof(f14373,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)))
<=> sP14(X0,X2,X1) )
| ~ sP15(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f11303,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,[],[f7222]) ).
fof(f7222,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,[],[f704]) ).
fof(f704,axiom,
! [X27,X76,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X76),X27)),c_Groups_Ozero__class_Ozero(X7)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X27))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X76),c_Groups_Ozero__class_Ozero(X7))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X27),c_Groups_Ozero__class_Ozero(X7)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X76)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__le__0__iff) ).
fof(f29445,plain,
spl573_281,
inference(avatar_split_clause,[],[f19544,f29443]) ).
fof(f29443,plain,
( spl573_281
<=> ! [X2,X0,X1] :
( sP13(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_281])]) ).
fof(f19544,plain,
! [X2,X0,X1] :
( sP13(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f14371]) ).
fof(f14371,plain,
! [X0,X1,X2] :
( sP13(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f11302,f14370,f14369]) ).
fof(f14369,plain,
! [X2,X0,X1] :
( sP12(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,[sP12])]) ).
fof(f14370,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)))
<=> sP12(X2,X0,X1) )
| ~ sP13(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f11302,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,[],[f7221]) ).
fof(f7221,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,[],[f705]) ).
fof(f705,axiom,
! [X27,X76,X7] :
( class_Rings_Olinordered__ring__strict(X7)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X7),X76),X27)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X27),c_Groups_Ozero__class_Ozero(X7)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),X76),c_Groups_Ozero__class_Ozero(X7))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X27))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X7),c_Groups_Ozero__class_Ozero(X7)),X76)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zero__le__mult__iff) ).
fof(f29441,plain,
spl573_280,
inference(avatar_split_clause,[],[f19188,f29439]) ).
fof(f29439,plain,
( spl573_280
<=> ! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X2,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_280])]) ).
fof(f19188,plain,
! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X2,X1,X0),
inference(cnf_transformation,[],[f6870]) ).
fof(f6870,plain,
! [X0,X1,X2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X2,X1,X0),
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X51,X52,X53] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X53,X52,X51),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I14_J) ).
fof(f29437,plain,
spl573_279,
inference(avatar_split_clause,[],[f19185,f29435]) ).
fof(f29435,plain,
( spl573_279
<=> ! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X2,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_279])]) ).
fof(f19185,plain,
! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X2,X1,X0),
inference(cnf_transformation,[],[f6867]) ).
fof(f6867,plain,
! [X0,X1,X2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X2,X1,X0),
inference(rectify,[],[f91]) ).
fof(f91,axiom,
! [X53,X78,X79] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(X79,X78,X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I21_J) ).
fof(f29433,plain,
spl573_278,
inference(avatar_split_clause,[],[f19184,f29431]) ).
fof(f29431,plain,
( spl573_278
<=> ! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X2,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_278])]) ).
fof(f19184,plain,
! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X2,X1,X0),
inference(cnf_transformation,[],[f6866]) ).
fof(f6866,plain,
! [X0,X1,X2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X2,X1,X0),
inference(rectify,[],[f90]) ).
fof(f90,axiom,
! [X35,X53,X80] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X80,X53,X35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I11_J) ).
fof(f29429,plain,
spl573_277,
inference(avatar_split_clause,[],[f18729,f29427]) ).
fof(f29427,plain,
( spl573_277
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ sP1(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_277])]) ).
fof(f18729,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ sP1(X1,X0) ),
inference(cnf_transformation,[],[f14803]) ).
fof(f14803,plain,
! [X0,X1] :
( ( c_Wellfounded_Owf(X1,X0)
| ~ sP1(X1,X0) )
& ( sP1(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
inference(nnf_transformation,[],[f14349]) ).
fof(f14349,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> sP1(X1,X0) ),
inference(definition_folding,[],[f11237,f14348]) ).
fof(f14348,plain,
! [X1,X0] :
( sP1(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,[sP1])]) ).
fof(f11237,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,[],[f6697]) ).
fof(f6697,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,[],[f4224]) ).
fof(f4224,axiom,
! [X169,X7] :
( c_Wellfounded_Owf(X7,X169)
<=> ! [X265] :
( ? [X2] : hBOOL(hAPP(hAPP(c_member(X7),X2),X265))
=> ? [X2] :
( ! [X113] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X113),X2)),X169))
=> ~ hBOOL(hAPP(hAPP(c_member(X7),X113),X265)) )
& hBOOL(hAPP(hAPP(c_member(X7),X2),X265)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
fof(f29425,plain,
spl573_276,
inference(avatar_split_clause,[],[f18728,f29423]) ).
fof(f18728,plain,
! [X0,X1] :
( sP1(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f14803]) ).
fof(f29421,plain,
spl573_275,
inference(avatar_split_clause,[],[f18334,f29419]) ).
fof(f18334,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10837]) ).
fof(f10837,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6396]) ).
fof(f6396,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f3830]) ).
fof(f3830,axiom,
! [X169,X7] :
( c_Wellfounded_Owf(X7,X169)
=> c_Wellfounded_Oacyclic(X7,X169) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acyclic) ).
fof(f29417,plain,
spl573_274,
inference(avatar_split_clause,[],[f18293,f29415]) ).
fof(f29415,plain,
( spl573_274
<=> ! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_274])]) ).
fof(f18293,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f10783]) ).
fof(f10783,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f6363]) ).
fof(f6363,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> class_Orderings_Oorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f4996]) ).
fof(f4996,axiom,
! [X326,X327] :
( class_Orderings_Oorder(X327)
=> class_Orderings_Oorder(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(f29413,plain,
spl573_273,
inference(avatar_split_clause,[],[f18292,f29411]) ).
fof(f29411,plain,
( spl573_273
<=> ! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_273])]) ).
fof(f18292,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(cnf_transformation,[],[f10782]) ).
fof(f10782,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(ennf_transformation,[],[f6362]) ).
fof(f6362,plain,
! [X0,X1] :
( class_Orderings_Oord(X1)
=> class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(rectify,[],[f4998]) ).
fof(f4998,axiom,
! [X326,X327] :
( class_Orderings_Oord(X327)
=> class_Orderings_Oord(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(f29409,plain,
spl573_272,
inference(avatar_split_clause,[],[f18289,f29407]) ).
fof(f29407,plain,
( spl573_272
<=> ! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_272])]) ).
fof(f18289,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10779]) ).
fof(f10779,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6359]) ).
fof(f6359,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> class_Orderings_Opreorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f4993]) ).
fof(f4993,axiom,
! [X326,X327] :
( class_Orderings_Opreorder(X327)
=> class_Orderings_Opreorder(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(f29405,plain,
spl573_271,
inference(avatar_split_clause,[],[f18288,f29403]) ).
fof(f29403,plain,
( spl573_271
<=> ! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_271])]) ).
fof(f18288,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(cnf_transformation,[],[f10778]) ).
fof(f10778,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(ennf_transformation,[],[f6358]) ).
fof(f6358,plain,
! [X0,X1] :
( class_Groups_Ominus(X1)
=> class_Groups_Ominus(tc_fun(X0,X1)) ),
inference(rectify,[],[f5001]) ).
fof(f5001,axiom,
! [X326,X327] :
( class_Groups_Ominus(X327)
=> class_Groups_Ominus(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(f29401,plain,
spl573_270,
inference(avatar_split_clause,[],[f18278,f29399]) ).
fof(f29399,plain,
( spl573_270
<=> ! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_270])]) ).
fof(f18278,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10763]) ).
fof(f10763,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6348]) ).
fof(f6348,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Olattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4995]) ).
fof(f4995,axiom,
! [X326,X327] :
( class_Lattices_Olattice(X327)
=> class_Lattices_Olattice(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
fof(f29397,plain,
spl573_269,
inference(avatar_split_clause,[],[f18277,f29395]) ).
fof(f29395,plain,
( spl573_269
<=> ! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_269])]) ).
fof(f18277,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10762]) ).
fof(f10762,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6347]) ).
fof(f6347,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__inf(tc_fun(X0,X1)) ),
inference(rectify,[],[f4990]) ).
fof(f4990,axiom,
! [X326,X327] :
( class_Lattices_Olattice(X327)
=> class_Lattices_Osemilattice__inf(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
fof(f29393,plain,
spl573_268,
inference(avatar_split_clause,[],[f18276,f29391]) ).
fof(f29391,plain,
( spl573_268
<=> ! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_268])]) ).
fof(f18276,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10761]) ).
fof(f10761,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6346]) ).
fof(f6346,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__sup(tc_fun(X0,X1)) ),
inference(rectify,[],[f4989]) ).
fof(f4989,axiom,
! [X326,X327] :
( class_Lattices_Olattice(X327)
=> class_Lattices_Osemilattice__sup(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).
fof(f29389,plain,
spl573_267,
inference(avatar_split_clause,[],[f18271,f29387]) ).
fof(f29387,plain,
( spl573_267
<=> ! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_267])]) ).
fof(f18271,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(cnf_transformation,[],[f10756]) ).
fof(f10756,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(ennf_transformation,[],[f6341]) ).
fof(f6341,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(X1)
=> class_Lattices_Odistrib__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4991]) ).
fof(f4991,axiom,
! [X326,X327] :
( class_Lattices_Odistrib__lattice(X327)
=> class_Lattices_Odistrib__lattice(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).
fof(f29385,plain,
spl573_266,
inference(avatar_split_clause,[],[f18181,f29383]) ).
fof(f29383,plain,
( spl573_266
<=> ! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_266])]) ).
fof(f18181,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(cnf_transformation,[],[f10654]) ).
fof(f10654,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(ennf_transformation,[],[f6258]) ).
fof(f6258,plain,
! [X0,X1] :
( class_Orderings_Obot(X1)
=> class_Orderings_Obot(tc_fun(X0,X1)) ),
inference(rectify,[],[f4999]) ).
fof(f4999,axiom,
! [X326,X327] :
( class_Orderings_Obot(X327)
=> class_Orderings_Obot(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
fof(f29381,plain,
spl573_265,
inference(avatar_split_clause,[],[f18178,f29379]) ).
fof(f29379,plain,
( spl573_265
<=> ! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_265])]) ).
fof(f18178,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(cnf_transformation,[],[f10651]) ).
fof(f10651,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(ennf_transformation,[],[f6255]) ).
fof(f6255,plain,
! [X0,X1] :
( class_Groups_Ouminus(X1)
=> class_Groups_Ouminus(tc_fun(X0,X1)) ),
inference(rectify,[],[f5000]) ).
fof(f5000,axiom,
! [X326,X327] :
( class_Groups_Ouminus(X327)
=> class_Groups_Ouminus(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(f29377,plain,
spl573_264,
inference(avatar_split_clause,[],[f18163,f29375]) ).
fof(f29375,plain,
( spl573_264
<=> ! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_264])]) ).
fof(f18163,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(cnf_transformation,[],[f10634]) ).
fof(f10634,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(ennf_transformation,[],[f6242]) ).
fof(f6242,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(X1)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4986]) ).
fof(f4986,axiom,
! [X326,X327] :
( class_Complete__Lattice_Ocomplete__lattice(X327)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Complete__Lattice_Ocomplete__lattice) ).
fof(f29373,plain,
spl573_263,
inference(avatar_split_clause,[],[f18157,f29371]) ).
fof(f29371,plain,
( spl573_263
<=> ! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_263])]) ).
fof(f18157,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f10628]) ).
fof(f10628,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f6236]) ).
fof(f6236,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
inference(rectify,[],[f4992]) ).
fof(f4992,axiom,
! [X326,X327] :
( class_Lattices_Oboolean__algebra(X327)
=> class_Lattices_Oboolean__algebra(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(f29369,plain,
spl573_262,
inference(avatar_split_clause,[],[f18147,f29367]) ).
fof(f29367,plain,
( spl573_262
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_262])]) ).
fof(f18147,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10618]) ).
fof(f10618,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6226]) ).
fof(f6226,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice__top(tc_fun(X0,X1)) ),
inference(rectify,[],[f4987]) ).
fof(f4987,axiom,
! [X326,X327] :
( class_Lattices_Obounded__lattice(X327)
=> class_Lattices_Obounded__lattice__top(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__top) ).
fof(f29365,plain,
spl573_261,
inference(avatar_split_clause,[],[f18146,f29363]) ).
fof(f29363,plain,
( spl573_261
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_261])]) ).
fof(f18146,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10617]) ).
fof(f10617,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6225]) ).
fof(f6225,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1)) ),
inference(rectify,[],[f4988]) ).
fof(f4988,axiom,
! [X326,X327] :
( class_Lattices_Obounded__lattice(X327)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).
fof(f29361,plain,
spl573_260,
inference(avatar_split_clause,[],[f18145,f29359]) ).
fof(f29359,plain,
( spl573_260
<=> ! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_260])]) ).
fof(f18145,plain,
! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ),
inference(cnf_transformation,[],[f10616]) ).
fof(f10616,plain,
! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ),
inference(ennf_transformation,[],[f6224]) ).
fof(f6224,plain,
! [X0,X1] :
( class_Orderings_Otop(X1)
=> class_Orderings_Otop(tc_fun(X0,X1)) ),
inference(rectify,[],[f4997]) ).
fof(f4997,axiom,
! [X326,X327] :
( class_Orderings_Otop(X327)
=> class_Orderings_Otop(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Otop) ).
fof(f29357,plain,
spl573_259,
inference(avatar_split_clause,[],[f18144,f29355]) ).
fof(f29355,plain,
( spl573_259
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_259])]) ).
fof(f18144,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10615]) ).
fof(f10615,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6223]) ).
fof(f6223,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4985]) ).
fof(f4985,axiom,
! [X326,X327] :
( class_Lattices_Obounded__lattice(X327)
=> class_Lattices_Obounded__lattice(tc_fun(X326,X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
fof(f29353,plain,
spl573_258,
inference(avatar_split_clause,[],[f17489,f29351]) ).
fof(f29351,plain,
( spl573_258
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_258])]) ).
fof(f17489,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0),
inference(cnf_transformation,[],[f5670]) ).
fof(f5670,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0),
inference(rectify,[],[f3359]) ).
fof(f3359,axiom,
! [X148,X7] : c_Fun_Oinj__on(X7,X7,c_COMBI(X7),X148),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id2) ).
fof(f29349,plain,
spl573_257,
inference(avatar_split_clause,[],[f17488,f29347]) ).
fof(f17488,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0),
inference(cnf_transformation,[],[f5669]) ).
fof(f5669,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0),
inference(rectify,[],[f3705]) ).
fof(f3705,axiom,
! [X148,X7] : c_Fun_Oinj__on(X7,X7,c_Fun_Oid(X7),X148),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__id) ).
fof(f29345,plain,
spl573_256,
inference(avatar_split_clause,[],[f17483,f29343]) ).
fof(f29343,plain,
( spl573_256
<=> ! [X0,X1] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_256])]) ).
fof(f17483,plain,
! [X0,X1] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X1,X0))),
inference(cnf_transformation,[],[f5664]) ).
fof(f5664,plain,
! [X0,X1] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X1,X0))),
inference(rectify,[],[f143]) ).
fof(f143,axiom,
! [X44,X46] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(X46,X44))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I2_J) ).
fof(f29341,plain,
spl573_255,
inference(avatar_split_clause,[],[f17482,f29339]) ).
fof(f29339,plain,
( spl573_255
<=> ! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_255])]) ).
fof(f29337,plain,
spl573_254,
inference(avatar_split_clause,[],[f17481,f29335]) ).
fof(f29335,plain,
( spl573_254
<=> ! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_254])]) ).
fof(f17481,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f5662]) ).
fof(f5662,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(rectify,[],[f5185]) ).
fof(f5185,axiom,
! [X104,X13] : hAPP(c_COMBI(X13),X104) = X104,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(f29333,plain,
spl573_253,
inference(avatar_split_clause,[],[f17479,f29331]) ).
fof(f29331,plain,
( spl573_253
<=> ! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_253])]) ).
fof(f17479,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0,
inference(cnf_transformation,[],[f5660]) ).
fof(f5660,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0,
inference(rectify,[],[f3709]) ).
fof(f3709,axiom,
! [X254,X13] : hAPP(c_Fun_Oid(X13),X254) = X254,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_id__def) ).
fof(f29329,plain,
spl573_252,
inference(avatar_split_clause,[],[f17478,f29327]) ).
fof(f29327,plain,
( spl573_252
<=> ! [X0,X1] : ~ c_Option_Ois__none(X1,hAPP(c_Option_Ooption_OSome(X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_252])]) ).
fof(f17478,plain,
! [X0,X1] : ~ c_Option_Ois__none(X1,hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(cnf_transformation,[],[f5659]) ).
fof(f5659,plain,
! [X0,X1] : ~ c_Option_Ois__none(X1,hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(rectify,[],[f343]) ).
fof(f343,axiom,
! [X61,X7] : ~ c_Option_Ois__none(X7,hAPP(c_Option_Ooption_OSome(X7),X61)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_is__none__code_I2_J) ).
fof(f29325,plain,
spl573_251,
inference(avatar_split_clause,[],[f17463,f29323]) ).
fof(f29323,plain,
( spl573_251
<=> ! [X0] : hAPP(c_Int_OAbs__Integ,sK109(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_251])]) ).
fof(f17463,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,sK109(X0)) = X0,
inference(cnf_transformation,[],[f14611]) ).
fof(f14611,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])],[f10424,f14610]) ).
fof(f14610,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(f10424,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,[],[f5645]) ).
fof(f5645,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,[],[f3841]) ).
fof(f3841,axiom,
! [X99] :
~ ! [X113] :
( hAPP(c_Int_OAbs__Integ,X113) = X99
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X113),c_Int_OInteg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Abs__Integ__cases) ).
fof(f29321,plain,
spl573_250,
inference(avatar_split_clause,[],[f17268,f29319]) ).
fof(f29319,plain,
( spl573_250
<=> ! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_250])]) ).
fof(f17268,plain,
! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10351]) ).
fof(f10351,plain,
! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5523]) ).
fof(f5523,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0)) ),
inference(rectify,[],[f4842]) ).
fof(f4842,axiom,
! [X13] :
( class_Orderings_Olinorder(X13)
=> c_List_Olinorder__class_Osorted(X13,c_List_Olist_ONil(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted_ONil) ).
fof(f29317,plain,
spl573_249,
inference(avatar_split_clause,[],[f17256,f29315]) ).
fof(f17256,plain,
! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10339]) ).
fof(f10339,plain,
! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5511]) ).
fof(f5511,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f1305]) ).
fof(f1305,axiom,
! [X13] :
( class_Rings_Osemiring__1(X13)
=> c_Int_Oiszero(X13,c_Groups_Ozero__class_Ozero(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_iszero__0) ).
fof(f29313,plain,
spl573_248,
inference(avatar_split_clause,[],[f17255,f29311]) ).
fof(f29311,plain,
( spl573_248
<=> ! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_248])]) ).
fof(f17255,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10338]) ).
fof(f10338,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5510]) ).
fof(f5510,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f1306]) ).
fof(f1306,axiom,
! [X13] :
( class_Rings_Osemiring__1(X13)
=> ~ c_Int_Oiszero(X13,c_Groups_Oone__class_Oone(X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__iszero__1) ).
fof(f29309,plain,
spl573_247,
inference(avatar_split_clause,[],[f17220,f29307]) ).
fof(f29307,plain,
( spl573_247
<=> ! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_247])]) ).
fof(f17220,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ),
inference(cnf_transformation,[],[f5474]) ).
fof(f5474,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ),
inference(rectify,[],[f5194]) ).
fof(f5194,axiom,
! [X5] :
( ~ hBOOL(X5)
| ~ hBOOL(hAPP(c_fNot,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(f29305,plain,
spl573_246,
inference(avatar_split_clause,[],[f17219,f29303]) ).
fof(f29303,plain,
( spl573_246
<=> ! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_246])]) ).
fof(f17219,plain,
! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f5473]) ).
fof(f5473,plain,
! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f5195]) ).
fof(f5195,axiom,
! [X5] :
( hBOOL(hAPP(c_fNot,X5))
| hBOOL(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).
fof(f29301,plain,
spl573_245,
inference(avatar_split_clause,[],[f16980,f29299]) ).
fof(f29299,plain,
( spl573_245
<=> ! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_245])]) ).
fof(f16980,plain,
! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))),
inference(cnf_transformation,[],[f5248]) ).
fof(f5248,plain,
! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))),
inference(rectify,[],[f4451]) ).
fof(f4451,axiom,
! [X13] : hBOOL(hAPP(c_List_Odistinct(X13),c_List_Olist_ONil(X13))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distinct_Osimps_I1_J) ).
fof(f29297,plain,
spl573_244,
inference(avatar_split_clause,[],[f16979,f29295]) ).
fof(f29293,plain,
spl573_243,
inference(avatar_split_clause,[],[f16978,f29291]) ).
fof(f29291,plain,
( spl573_243
<=> ! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_243])]) ).
fof(f16978,plain,
! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f5246]) ).
fof(f5246,plain,
! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0,
inference(rectify,[],[f209]) ).
fof(f209,axiom,
! [X12] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X12) = X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__size) ).
fof(f29289,plain,
spl573_242,
inference(avatar_split_clause,[],[f16848,f29286]) ).
fof(f29286,plain,
( spl573_242
<=> c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_242])]) ).
fof(f16848,plain,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
inference(cnf_transformation,[],[f1340]) ).
fof(f1340,axiom,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__Pls) ).
fof(f29284,plain,
spl573_241,
inference(avatar_split_clause,[],[f16847,f29281]) ).
fof(f29281,plain,
( spl573_241
<=> c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_241])]) ).
fof(f16847,plain,
c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies),
inference(cnf_transformation,[],[f4262]) ).
fof(f4262,axiom,
c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_body__def) ).
fof(f29279,plain,
( spl573_240
| ~ spl573_212 ),
inference(avatar_split_clause,[],[f29156,f29152,f29276]) ).
fof(f29276,plain,
( spl573_240
<=> c_Nat__Transfer_Onat__set(c_Option_Oset(tc_Int_Oint,c_Option_Ooption_ONone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_240])]) ).
fof(f29152,plain,
( spl573_212
<=> c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_212])]) ).
fof(f29156,plain,
( c_Nat__Transfer_Onat__set(c_Option_Oset(tc_Int_Oint,c_Option_Ooption_ONone(tc_Int_Oint)))
| ~ spl573_212 ),
inference(forward_demodulation,[],[f29154,f17037]) ).
fof(f29154,plain,
( c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))
| ~ spl573_212 ),
inference(avatar_component_clause,[],[f29152]) ).
fof(f29274,plain,
spl573_239,
inference(avatar_split_clause,[],[f27385,f29272]) ).
fof(f29272,plain,
( spl573_239
<=> ! [X0,X1] : sP40(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_239])]) ).
fof(f27385,plain,
! [X0,X1] : sP40(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f24862,f16841]) ).
fof(f24862,plain,
! [X0,X1] : sP40(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f20851]) ).
fof(f20851,plain,
! [X2,X0,X1] :
( sP40(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f15623]) ).
fof(f29270,plain,
spl573_238,
inference(avatar_split_clause,[],[f27359,f29268]) ).
fof(f29268,plain,
( spl573_238
<=> ! [X0,X1] : sP35(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_238])]) ).
fof(f27359,plain,
! [X0,X1] : sP35(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f24836,f16841]) ).
fof(f24836,plain,
! [X0,X1] : sP35(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f20768]) ).
fof(f20768,plain,
! [X2,X0,X1] :
( sP35(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f15565]) ).
fof(f29266,plain,
spl573_237,
inference(avatar_split_clause,[],[f26610,f29263]) ).
fof(f29263,plain,
( spl573_237
<=> sP11(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_237])]) ).
fof(f26610,plain,
sP11(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f26609,f25195]) ).
fof(f26609,plain,
sP11(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f24696,f16841]) ).
fof(f24696,plain,
sP11(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f24695]) ).
fof(f24695,plain,
! [X1] :
( sP11(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,[],[f19026]) ).
fof(f19026,plain,
! [X0,X1] :
( sP11(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,[],[f15004]) ).
fof(f29261,plain,
spl573_236,
inference(avatar_split_clause,[],[f26608,f29258]) ).
fof(f29258,plain,
( spl573_236
<=> sP11(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_236])]) ).
fof(f26608,plain,
sP11(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f26607,f25195]) ).
fof(f26607,plain,
sP11(hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f24694,f16841]) ).
fof(f24694,plain,
sP11(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f24693]) ).
fof(f24693,plain,
! [X1] :
( sP11(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,[],[f19027]) ).
fof(f19027,plain,
! [X0,X1] :
( sP11(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,[],[f15004]) ).
fof(f29256,plain,
spl573_235,
inference(avatar_split_clause,[],[f26590,f29253]) ).
fof(f29253,plain,
( spl573_235
<=> sP10(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_235])]) ).
fof(f26590,plain,
sP10(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f26589,f25195]) ).
fof(f26589,plain,
sP10(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f24692,f16841]) ).
fof(f24692,plain,
sP10(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f24691]) ).
fof(f24691,plain,
! [X1] :
( sP10(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,[],[f19018]) ).
fof(f19018,plain,
! [X0,X1] :
( sP10(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,[],[f15001]) ).
fof(f29251,plain,
spl573_234,
inference(avatar_split_clause,[],[f26588,f29248]) ).
fof(f29248,plain,
( spl573_234
<=> sP10(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_234])]) ).
fof(f26588,plain,
sP10(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f26587,f25195]) ).
fof(f26587,plain,
sP10(hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f24690,f16841]) ).
fof(f24690,plain,
sP10(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f24689]) ).
fof(f24689,plain,
! [X1] :
( sP10(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,[],[f19019]) ).
fof(f19019,plain,
! [X0,X1] :
( sP10(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,[],[f15001]) ).
fof(f29246,plain,
spl573_233,
inference(avatar_split_clause,[],[f25370,f29243]) ).
fof(f29243,plain,
( spl573_233
<=> c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_233])]) ).
fof(f25370,plain,
c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls),
inference(forward_demodulation,[],[f24528,f16829]) ).
fof(f24528,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,[],[f17198]) ).
fof(f17198,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,[],[f10294]) ).
fof(f10294,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,[],[f5463]) ).
fof(f5463,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,[],[f552]) ).
fof(f552,axiom,
! [X116] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X116
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X116))
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,X116) = 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)),X116))
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X116) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X116
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X116) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zsgn__def) ).
fof(f29241,plain,
spl573_232,
inference(avatar_split_clause,[],[f25181,f29238]) ).
fof(f29238,plain,
( spl573_232
<=> c_HOL_Obool_Obool__size(c_fTrue) = c_Orderings_Obot__class_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_232])]) ).
fof(f25181,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
inference(forward_demodulation,[],[f16844,f16841]) ).
fof(f16844,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f2551]) ).
fof(f2551,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__nat__def) ).
fof(f29236,plain,
spl573_231,
inference(avatar_split_clause,[],[f25180,f29233]) ).
fof(f29233,plain,
( spl573_231
<=> c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_231])]) ).
fof(f25180,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f16843,f16841]) ).
fof(f16843,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP),
inference(cnf_transformation,[],[f162]) ).
fof(f162,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osize_I1_J) ).
fof(f29231,plain,
spl573_230,
inference(avatar_split_clause,[],[f25179,f29228]) ).
fof(f29228,plain,
( spl573_230
<=> c_HOL_Obool_Obool__size(c_fFalse) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_230])]) ).
fof(f25179,plain,
c_HOL_Obool_Obool__size(c_fFalse) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f16842,f16841]) ).
fof(f16842,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
inference(cnf_transformation,[],[f225]) ).
fof(f225,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bool_Osize_I2_J) ).
fof(f29226,plain,
spl573_229,
inference(avatar_split_clause,[],[f25092,f29224]) ).
fof(f29224,plain,
( spl573_229
<=> ! [X2,X3] : sP77(X3,X2,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_229])]) ).
fof(f25092,plain,
! [X2,X3] : sP77(X3,X2,X2,X3),
inference(equality_resolution,[],[f25091]) ).
fof(f25091,plain,
! [X2,X3,X1] :
( sP77(X3,X1,X2,X3)
| X1 != X2 ),
inference(equality_resolution,[],[f23157]) ).
fof(f23157,plain,
! [X2,X3,X0,X1] :
( sP77(X0,X1,X2,X3)
| X0 != X3
| X1 != X2 ),
inference(cnf_transformation,[],[f16463]) ).
fof(f29222,plain,
spl573_228,
inference(avatar_split_clause,[],[f25090,f29220]) ).
fof(f29220,plain,
( spl573_228
<=> ! [X1,X3] : sP77(X1,X1,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_228])]) ).
fof(f25090,plain,
! [X3,X1] : sP77(X1,X1,X3,X3),
inference(equality_resolution,[],[f25089]) ).
fof(f25089,plain,
! [X2,X3,X1] :
( sP77(X1,X1,X2,X3)
| X2 != X3 ),
inference(equality_resolution,[],[f23158]) ).
fof(f23158,plain,
! [X2,X3,X0,X1] :
( sP77(X0,X1,X2,X3)
| X0 != X1
| X2 != X3 ),
inference(cnf_transformation,[],[f16463]) ).
fof(f29218,plain,
spl573_227,
inference(avatar_split_clause,[],[f24876,f29216]) ).
fof(f29216,plain,
( spl573_227
<=> ! [X0,X1] : sP44(X0,X1,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_227])]) ).
fof(f24876,plain,
! [X0,X1] : sP44(X0,X1,c_List_Olist_ONil(X1)),
inference(equality_resolution,[],[f20927]) ).
fof(f20927,plain,
! [X2,X0,X1] :
( sP44(X0,X1,X2)
| c_List_Olist_ONil(X1) != X2 ),
inference(cnf_transformation,[],[f15678]) ).
fof(f15678,plain,
! [X0,X1,X2] :
( ( sP44(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)),sK346(X0,X1,X2)),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),sK345(X0,X1,X2)),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),sK345(X0,X1,X2)),sK346(X0,X1,X2)) = X2 )
| c_List_Olist_ONil(X1) = X2
| ~ sP44(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK345,sK346])],[f15676,f15677]) ).
fof(f15677,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)),sK346(X0,X1,X2)),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),sK345(X0,X1,X2)),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),sK345(X0,X1,X2)),sK346(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f15676,plain,
! [X0,X1,X2] :
( ( sP44(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
| ~ sP44(X0,X1,X2) ) ),
inference(rectify,[],[f15675]) ).
fof(f15675,plain,
! [X0,X2,X1] :
( ( sP44(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
| ~ sP44(X0,X2,X1) ) ),
inference(flattening,[],[f15674]) ).
fof(f15674,plain,
! [X0,X2,X1] :
( ( sP44(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
| ~ sP44(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f14421]) ).
fof(f14421,plain,
! [X0,X2,X1] :
( sP44(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,[sP44])]) ).
fof(f29214,plain,
spl573_226,
inference(avatar_split_clause,[],[f24662,f29211]) ).
fof(f29211,plain,
( spl573_226
<=> sP5(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_226])]) ).
fof(f24662,plain,
sP5(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(equality_resolution,[],[f24661]) ).
fof(f24661,plain,
! [X1] :
( sP5(c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ),
inference(equality_resolution,[],[f18881]) ).
fof(f18881,plain,
! [X0,X1] :
( sP5(X0,X1)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ),
inference(cnf_transformation,[],[f14920]) ).
fof(f29209,plain,
spl573_225,
inference(avatar_split_clause,[],[f24630,f29207]) ).
fof(f24630,plain,
! [X0] : sP3(hAPP(c_Int_Onat,X0),X0),
inference(equality_resolution,[],[f18752]) ).
fof(f18752,plain,
! [X0,X1] :
( sP3(X1,X0)
| hAPP(c_Int_Onat,X0) != X1 ),
inference(cnf_transformation,[],[f14817]) ).
fof(f29205,plain,
spl573_224,
inference(avatar_split_clause,[],[f24625,f29203]) ).
fof(f24625,plain,
! [X1] : sP2(hAPP(c_Int_Onat,X1),X1),
inference(equality_resolution,[],[f18744]) ).
fof(f18744,plain,
! [X0,X1] :
( sP2(X0,X1)
| hAPP(c_Int_Onat,X1) != X0 ),
inference(cnf_transformation,[],[f14813]) ).
fof(f29201,plain,
spl573_223,
inference(avatar_split_clause,[],[f17476,f29199]) ).
fof(f29199,plain,
( spl573_223
<=> ! [X0,X1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_223])]) ).
fof(f17476,plain,
! [X0,X1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X0,X1),
inference(cnf_transformation,[],[f5657]) ).
fof(f5657,plain,
! [X0,X1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X0,X1),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X12,X14] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X14,X12,X14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OSkip) ).
fof(f29197,plain,
spl573_222,
inference(avatar_split_clause,[],[f17474,f29195]) ).
fof(f29195,plain,
( spl573_222
<=> ! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_222])]) ).
fof(f17474,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)),
inference(cnf_transformation,[],[f5655]) ).
fof(f5655,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)),
inference(rectify,[],[f4873]) ).
fof(f4873,axiom,
! [X115,X116] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X116,X115)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__upto) ).
fof(f29193,plain,
spl573_221,
inference(avatar_split_clause,[],[f17470,f29191]) ).
fof(f29191,plain,
( spl573_221
<=> ! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_221])]) ).
fof(f17470,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X0),
inference(cnf_transformation,[],[f5651]) ).
fof(f5651,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X0),
inference(rectify,[],[f29]) ).
fof(f29,axiom,
! [X35,X53] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X53,X35),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I17_J) ).
fof(f29189,plain,
spl573_220,
inference(avatar_split_clause,[],[f17467,f29187]) ).
fof(f29187,plain,
( spl573_220
<=> ! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_220])]) ).
fof(f17467,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X0),
inference(cnf_transformation,[],[f5648]) ).
fof(f5648,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X0),
inference(rectify,[],[f22]) ).
fof(f22,axiom,
! [X49,X50] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X50,X49),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I12_J) ).
fof(f29185,plain,
spl573_219,
inference(avatar_split_clause,[],[f17466,f29183]) ).
fof(f29183,plain,
( spl573_219
<=> ! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_219])]) ).
fof(f17466,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X0),
inference(cnf_transformation,[],[f5647]) ).
fof(f5647,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X0),
inference(rectify,[],[f157]) ).
fof(f157,axiom,
! [X53,X79] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X79,X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I9_J) ).
fof(f29181,plain,
spl573_218,
inference(avatar_split_clause,[],[f17280,f29179]) ).
fof(f29179,plain,
( spl573_218
<=> ! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_218])]) ).
fof(f17280,plain,
! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(cnf_transformation,[],[f10363]) ).
fof(f10363,plain,
! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(ennf_transformation,[],[f5535]) ).
fof(f5535,plain,
! [X0] :
( class_Finite__Set_Ofinite(X0)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X0)) ),
inference(rectify,[],[f5139]) ).
fof(f5139,axiom,
! [X327] :
( class_Finite__Set_Ofinite(X327)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X327)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Option__Ooption__Finite__Set_Ofinite) ).
fof(f29177,plain,
spl573_217,
inference(avatar_split_clause,[],[f16967,f29175]) ).
fof(f29175,plain,
( spl573_217
<=> ! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_217])]) ).
fof(f16967,plain,
! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0),
inference(cnf_transformation,[],[f5235]) ).
fof(f5235,plain,
! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0),
inference(rectify,[],[f3407]) ).
fof(f3407,axiom,
! [X215] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X215),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__Suc) ).
fof(f29173,plain,
spl573_216,
inference(avatar_split_clause,[],[f16965,f29171]) ).
fof(f29171,plain,
( spl573_216
<=> ! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_216])]) ).
fof(f16965,plain,
! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f5233]) ).
fof(f5233,plain,
! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(rectify,[],[f1577]) ).
fof(f1577,axiom,
! [X97] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X97)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) ).
fof(f29169,plain,
spl573_215,
inference(avatar_split_clause,[],[f16962,f29167]) ).
fof(f29167,plain,
( spl573_215
<=> ! [X0] : hAPP(c_Nat_OSuc,X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl573_215])]) ).
fof(f16962,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(cnf_transformation,[],[f5230]) ).
fof(f5230,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X12] : hAPP(c_Nat_OSuc,X12) != X12,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
fof(f29165,plain,
spl573_214,
inference(avatar_split_clause,[],[f16958,f29163]) ).
fof(f29163,plain,
( spl573_214
<=> ! [X0] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_214])]) ).
fof(f16958,plain,
! [X0] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X0),
inference(cnf_transformation,[],[f5226]) ).
fof(f5226,plain,
! [X0] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X0),
inference(rectify,[],[f142]) ).
fof(f142,axiom,
! [X91] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,X91),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I19_J) ).
fof(f29161,plain,
spl573_213,
inference(avatar_split_clause,[],[f16846,f29158]) ).
fof(f16846,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f3762]) ).
fof(f3762,axiom,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pair__less) ).
fof(f29155,plain,
spl573_212,
inference(avatar_split_clause,[],[f16845,f29152]) ).
fof(f16845,plain,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
inference(cnf_transformation,[],[f2548]) ).
fof(f2548,axiom,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J) ).
fof(f29150,plain,
spl573_211,
inference(avatar_split_clause,[],[f16841,f29147]) ).
fof(f29145,plain,
spl573_210,
inference(avatar_split_clause,[],[f16839,f29142]) ).
fof(f16839,plain,
c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),
inference(cnf_transformation,[],[f3301]) ).
fof(f3301,axiom,
c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__nat__def) ).
fof(f29140,plain,
spl573_209,
inference(avatar_split_clause,[],[f16838,f29137]) ).
fof(f16838,plain,
c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),
inference(cnf_transformation,[],[f2362]) ).
fof(f2362,axiom,
c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__nat__def) ).
fof(f29135,plain,
spl573_208,
inference(avatar_split_clause,[],[f16837,f29132]) ).
fof(f16837,plain,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
inference(cnf_transformation,[],[f3708]) ).
fof(f3708,axiom,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__int__eq__id) ).
fof(f29130,plain,
~ spl573_207,
inference(avatar_split_clause,[],[f16833,f29127]) ).
fof(f16833,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f1278]) ).
fof(f1278,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__1) ).
fof(f29125,plain,
spl573_206,
inference(avatar_split_clause,[],[f16631,f29122]) ).
fof(f16631,plain,
c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H),
inference(cnf_transformation,[],[f5210]) ).
fof(f5210,axiom,
c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
fof(f29120,plain,
spl573_205,
inference(avatar_split_clause,[],[f16630,f29117]) ).
fof(f16630,plain,
c_Natural_Oevaln(v_c,v_s,v_n,v_s1),
inference(cnf_transformation,[],[f5209]) ).
fof(f5209,axiom,
c_Natural_Oevaln(v_c,v_s,v_n,v_s1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
fof(f29114,plain,
spl573_204,
inference(avatar_split_clause,[],[f26451,f29111]) ).
fof(f29111,plain,
( spl573_204
<=> sP3(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_204])]) ).
fof(f26451,plain,
sP3(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls),
inference(forward_demodulation,[],[f26450,f25199]) ).
fof(f26450,plain,
sP3(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,[],[f24627,f16841]) ).
fof(f24627,plain,
sP3(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,[],[f24626]) ).
fof(f24626,plain,
! [X1] :
( sP3(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,[],[f18751]) ).
fof(f18751,plain,
! [X0,X1] :
( sP3(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,[],[f14816]) ).
fof(f29109,plain,
spl573_203,
inference(avatar_split_clause,[],[f26443,f29106]) ).
fof(f29106,plain,
( spl573_203
<=> sP2(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_203])]) ).
fof(f26443,plain,
sP2(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls),
inference(forward_demodulation,[],[f26442,f25199]) ).
fof(f26442,plain,
sP2(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,[],[f24622,f16841]) ).
fof(f24622,plain,
sP2(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,[],[f24621]) ).
fof(f24621,plain,
! [X1] :
( sP2(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,[],[f18743]) ).
fof(f18743,plain,
! [X0,X1] :
( sP2(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,[],[f14812]) ).
fof(f29104,plain,
~ spl573_202,
inference(avatar_split_clause,[],[f25178,f29101]) ).
fof(f29101,plain,
( spl573_202
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_202])]) ).
fof(f25178,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)),
inference(forward_demodulation,[],[f16834,f16829]) ).
fof(f16834,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(cnf_transformation,[],[f1276]) ).
fof(f1276,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__neg__0) ).
fof(f29099,plain,
~ spl573_201,
inference(avatar_split_clause,[],[f25177,f29096]) ).
fof(f29096,plain,
( spl573_201
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl573_201])]) ).
fof(f25177,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Int_OPls,
inference(forward_demodulation,[],[f16832,f16829]) ).
fof(f16832,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f490]) ).
fof(f490,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(f29094,plain,
spl573_200,
inference(avatar_split_clause,[],[f16957,f29092]) ).
fof(f29092,plain,
( spl573_200
<=> ! [X0] : c_Option_Ois__none(X0,c_Option_Ooption_ONone(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_200])]) ).
fof(f16957,plain,
! [X0] : c_Option_Ois__none(X0,c_Option_Ooption_ONone(X0)),
inference(cnf_transformation,[],[f5225]) ).
fof(f5225,plain,
! [X0] : c_Option_Ois__none(X0,c_Option_Ooption_ONone(X0)),
inference(rectify,[],[f345]) ).
fof(f345,axiom,
! [X13] : c_Option_Ois__none(X13,c_Option_Ooption_ONone(X13)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_is__none__code_I1_J) ).
fof(f29090,plain,
spl573_199,
inference(avatar_split_clause,[],[f16953,f29088]) ).
fof(f29088,plain,
( spl573_199
<=> ! [X0] : c_Int_OPls != c_Int_OBit1(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_199])]) ).
fof(f16953,plain,
! [X0] : c_Int_OPls != c_Int_OBit1(X0),
inference(cnf_transformation,[],[f5221]) ).
fof(f5221,plain,
! [X0] : c_Int_OPls != c_Int_OBit1(X0),
inference(rectify,[],[f1390]) ).
fof(f1390,axiom,
! [X96] : c_Int_OPls != c_Int_OBit1(X96),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I46_J) ).
fof(f29086,plain,
spl573_198,
inference(avatar_split_clause,[],[f16830,f29083]) ).
fof(f29083,plain,
( spl573_198
<=> hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_198])]) ).
fof(f16830,plain,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
inference(cnf_transformation,[],[f76]) ).
fof(f76,axiom,
hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I1_J) ).
fof(f29081,plain,
spl573_197,
inference(avatar_split_clause,[],[f16829,f29078]) ).
fof(f29076,plain,
spl573_196,
inference(avatar_split_clause,[],[f16828,f29073]) ).
fof(f29073,plain,
( spl573_196
<=> c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral ),
introduced(avatar_definition,[new_symbols(naming,[spl573_196])]) ).
fof(f29071,plain,
spl573_195,
inference(avatar_split_clause,[],[f16825,f29068]) ).
fof(f29068,plain,
( spl573_195
<=> c_Int_OMin = c_Int_OBit1(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_195])]) ).
fof(f16825,plain,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
inference(cnf_transformation,[],[f1391]) ).
fof(f1391,axiom,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__Min) ).
fof(f29066,plain,
spl573_194,
inference(avatar_split_clause,[],[f16823,f29063]) ).
fof(f29063,plain,
( spl573_194
<=> c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_194])]) ).
fof(f16823,plain,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f1697]) ).
fof(f1697,axiom,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Code__Numeral_Oof__nat__code) ).
fof(f29061,plain,
spl573_193,
inference(avatar_split_clause,[],[f26500,f29059]) ).
fof(f29059,plain,
( spl573_193
<=> ! [X0] : sP6(X0,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_193])]) ).
fof(f26500,plain,
! [X0] : sP6(X0,c_Int_OPls),
inference(forward_demodulation,[],[f24667,f16829]) ).
fof(f24667,plain,
! [X0] : sP6(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(equality_resolution,[],[f18895]) ).
fof(f18895,plain,
! [X0,X1] :
( sP6(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ),
inference(cnf_transformation,[],[f14928]) ).
fof(f14928,plain,
! [X0,X1] :
( ( sP6(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
| ~ sP6(X0,X1) ) ),
inference(rectify,[],[f14927]) ).
fof(f14927,plain,
! [X1,X0] :
( ( sP6(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
| ~ sP6(X1,X0) ) ),
inference(flattening,[],[f14926]) ).
fof(f14926,plain,
! [X1,X0] :
( ( sP6(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
| ~ sP6(X1,X0) ) ),
inference(nnf_transformation,[],[f14358]) ).
fof(f29057,plain,
spl573_192,
inference(avatar_split_clause,[],[f26493,f29054]) ).
fof(f29054,plain,
( spl573_192
<=> sP5(c_Int_OMin,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_192])]) ).
fof(f26493,plain,
sP5(c_Int_OMin,c_Int_OMin),
inference(forward_demodulation,[],[f24660,f16979]) ).
fof(f24660,plain,
sP5(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,[],[f24659]) ).
fof(f24659,plain,
! [X1] :
( sP5(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,[],[f18882]) ).
fof(f18882,plain,
! [X0,X1] :
( sP5(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,[],[f14920]) ).
fof(f29052,plain,
spl573_191,
inference(avatar_split_clause,[],[f16950,f29050]) ).
fof(f29050,plain,
( spl573_191
<=> ! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_191])]) ).
fof(f16950,plain,
! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal),
inference(cnf_transformation,[],[f5218]) ).
fof(f5218,plain,
! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal),
inference(rectify,[],[f3364]) ).
fof(f3364,axiom,
! [X7] : c_Equiv__Relations_Oequivp(X7,c_fequal),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_identity__equivp) ).
fof(f29048,plain,
spl573_190,
inference(avatar_split_clause,[],[f16822,f29045]) ).
fof(f16822,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f3743]) ).
fof(f3743,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__less__than) ).
fof(f29043,plain,
spl573_189,
inference(avatar_split_clause,[],[f16821,f29040]) ).
fof(f16821,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f3781]) ).
fof(f3781,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
fof(f29038,plain,
( spl573_188
| ~ spl573_187 ),
inference(avatar_split_clause,[],[f29033,f29029,f29035]) ).
fof(f29035,plain,
( spl573_188
<=> c_Nat__Transfer_Ois__nat(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_188])]) ).
fof(f29029,plain,
( spl573_187
<=> c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_187])]) ).
fof(f29033,plain,
( c_Nat__Transfer_Ois__nat(c_Int_OPls)
| ~ spl573_187 ),
inference(forward_demodulation,[],[f29031,f16829]) ).
fof(f29031,plain,
( c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl573_187 ),
inference(avatar_component_clause,[],[f29029]) ).
fof(f29032,plain,
spl573_187,
inference(avatar_split_clause,[],[f16820,f29029]) ).
fof(f16820,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f1575]) ).
fof(f1575,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J) ).
fof(f29027,plain,
spl573_186,
inference(avatar_split_clause,[],[f16819,f29024]) ).
fof(f29024,plain,
( spl573_186
<=> c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_186])]) ).
fof(f16819,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f1578]) ).
fof(f1578,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J) ).
fof(f29022,plain,
~ spl573_185,
inference(avatar_split_clause,[],[f16817,f29019]) ).
fof(f29019,plain,
( spl573_185
<=> c_Int_OMin = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl573_185])]) ).
fof(f16817,plain,
c_Int_OMin != c_Int_OPls,
inference(cnf_transformation,[],[f1342]) ).
fof(f1342,axiom,
c_Int_OMin != c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I40_J) ).
fof(f29017,plain,
spl573_184,
inference(avatar_split_clause,[],[f16629,f29014]) ).
fof(f16629,plain,
v_P(v_Z,v_s),
inference(cnf_transformation,[],[f5208]) ).
fof(f5208,axiom,
v_P(v_Z,v_s),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
fof(f29012,plain,
spl573_183,
inference(avatar_split_clause,[],[f16816,f29009]) ).
fof(f29009,plain,
( spl573_183
<=> hBOOL(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_183])]) ).
fof(f16816,plain,
hBOOL(c_fTrue),
inference(cnf_transformation,[],[f5193]) ).
fof(f5193,axiom,
hBOOL(c_fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fTrue__1) ).
fof(f29007,plain,
spl573_182,
inference(avatar_split_clause,[],[f16815,f29004]) ).
fof(f29004,plain,
( spl573_182
<=> class_Finite__Set_Ofinite(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_182])]) ).
fof(f16815,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(cnf_transformation,[],[f5130]) ).
fof(f5130,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(f29002,plain,
spl573_181,
inference(avatar_split_clause,[],[f16814,f28999]) ).
fof(f28999,plain,
( spl573_181
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_181])]) ).
fof(f16814,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5142]) ).
fof(f5142,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(f28997,plain,
spl573_180,
inference(avatar_split_clause,[],[f16813,f28994]) ).
fof(f28994,plain,
( spl573_180
<=> class_Orderings_Oorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_180])]) ).
fof(f16813,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f5132]) ).
fof(f5132,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(f28992,plain,
spl573_179,
inference(avatar_split_clause,[],[f16812,f28989]) ).
fof(f28989,plain,
( spl573_179
<=> class_Orderings_Oorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_179])]) ).
fof(f16812,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5112]) ).
fof(f5112,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(f28987,plain,
spl573_178,
inference(avatar_split_clause,[],[f16811,f28984]) ).
fof(f28984,plain,
( spl573_178
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_178])]) ).
fof(f16811,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5057]) ).
fof(f5057,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(f28982,plain,
spl573_177,
inference(avatar_split_clause,[],[f16810,f28979]) ).
fof(f28979,plain,
( spl573_177
<=> class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_177])]) ).
fof(f16810,plain,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5176]) ).
fof(f5176,axiom,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oorder) ).
fof(f28977,plain,
spl573_176,
inference(avatar_split_clause,[],[f16809,f28974]) ).
fof(f28974,plain,
( spl573_176
<=> class_Orderings_Oord(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_176])]) ).
fof(f16809,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f5134]) ).
fof(f5134,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(f28972,plain,
spl573_175,
inference(avatar_split_clause,[],[f16808,f28969]) ).
fof(f28969,plain,
( spl573_175
<=> class_Orderings_Oord(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_175])]) ).
fof(f16808,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f5114]) ).
fof(f5114,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(f28967,plain,
spl573_174,
inference(avatar_split_clause,[],[f16807,f28964]) ).
fof(f28964,plain,
( spl573_174
<=> class_Orderings_Oord(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_174])]) ).
fof(f16807,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(cnf_transformation,[],[f5061]) ).
fof(f5061,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(f28962,plain,
spl573_173,
inference(avatar_split_clause,[],[f16806,f28959]) ).
fof(f28959,plain,
( spl573_173
<=> class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_173])]) ).
fof(f16806,plain,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5178]) ).
fof(f5178,axiom,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oord) ).
fof(f28957,plain,
spl573_172,
inference(avatar_split_clause,[],[f16805,f28954]) ).
fof(f28954,plain,
( spl573_172
<=> class_Orderings_Opreorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_172])]) ).
fof(f16805,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f5129]) ).
fof(f5129,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(f28952,plain,
spl573_171,
inference(avatar_split_clause,[],[f16804,f28949]) ).
fof(f28949,plain,
( spl573_171
<=> class_Orderings_Opreorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_171])]) ).
fof(f16804,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5104]) ).
fof(f5104,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(f28947,plain,
spl573_170,
inference(avatar_split_clause,[],[f16803,f28944]) ).
fof(f28944,plain,
( spl573_170
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_170])]) ).
fof(f16803,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5044]) ).
fof(f5044,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(f28942,plain,
spl573_169,
inference(avatar_split_clause,[],[f16802,f28939]) ).
fof(f28939,plain,
( spl573_169
<=> class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_169])]) ).
fof(f16802,plain,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5169]) ).
fof(f5169,axiom,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder) ).
fof(f28937,plain,
spl573_168,
inference(avatar_split_clause,[],[f16801,f28934]) ).
fof(f28934,plain,
( spl573_168
<=> class_Groups_Ominus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_168])]) ).
fof(f16801,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(cnf_transformation,[],[f5137]) ).
fof(f5137,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(f28932,plain,
spl573_167,
inference(avatar_split_clause,[],[f16800,f28929]) ).
fof(f28929,plain,
( spl573_167
<=> class_Groups_Ominus(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_167])]) ).
fof(f16800,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(cnf_transformation,[],[f5116]) ).
fof(f5116,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(f28927,plain,
spl573_166,
inference(avatar_split_clause,[],[f16799,f28924]) ).
fof(f28924,plain,
( spl573_166
<=> class_Groups_Ominus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_166])]) ).
fof(f16799,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(cnf_transformation,[],[f5066]) ).
fof(f5066,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(f28922,plain,
spl573_165,
inference(avatar_split_clause,[],[f16798,f28919]) ).
fof(f28919,plain,
( spl573_165
<=> class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_165])]) ).
fof(f16798,plain,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5179]) ).
fof(f5179,axiom,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ominus) ).
fof(f28917,plain,
spl573_164,
inference(avatar_split_clause,[],[f16797,f28914]) ).
fof(f28914,plain,
( spl573_164
<=> class_Lattices_Olattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_164])]) ).
fof(f16797,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5131]) ).
fof(f5131,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
fof(f28912,plain,
spl573_163,
inference(avatar_split_clause,[],[f16796,f28909]) ).
fof(f28909,plain,
( spl573_163
<=> class_Lattices_Olattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_163])]) ).
fof(f16796,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f5110]) ).
fof(f5110,axiom,
class_Lattices_Olattice(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
fof(f28907,plain,
spl573_162,
inference(avatar_split_clause,[],[f16795,f28904]) ).
fof(f28904,plain,
( spl573_162
<=> class_Lattices_Olattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_162])]) ).
fof(f16795,plain,
class_Lattices_Olattice(tc_Int_Oint),
inference(cnf_transformation,[],[f5052]) ).
fof(f5052,axiom,
class_Lattices_Olattice(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Olattice) ).
fof(f28902,plain,
spl573_161,
inference(avatar_split_clause,[],[f16794,f28899]) ).
fof(f28899,plain,
( spl573_161
<=> class_Lattices_Osemilattice__inf(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_161])]) ).
fof(f16794,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(cnf_transformation,[],[f5126]) ).
fof(f5126,axiom,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
fof(f28897,plain,
spl573_160,
inference(avatar_split_clause,[],[f16793,f28894]) ).
fof(f16793,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(cnf_transformation,[],[f5089]) ).
fof(f5089,axiom,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
fof(f28892,plain,
spl573_159,
inference(avatar_split_clause,[],[f16792,f28889]) ).
fof(f28889,plain,
( spl573_159
<=> class_Lattices_Osemilattice__inf(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_159])]) ).
fof(f16792,plain,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
inference(cnf_transformation,[],[f5025]) ).
fof(f5025,axiom,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__inf) ).
fof(f28887,plain,
spl573_158,
inference(avatar_split_clause,[],[f16791,f28884]) ).
fof(f28884,plain,
( spl573_158
<=> class_Lattices_Osemilattice__sup(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_158])]) ).
fof(f16791,plain,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
inference(cnf_transformation,[],[f5125]) ).
fof(f5125,axiom,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
fof(f28882,plain,
spl573_157,
inference(avatar_split_clause,[],[f16790,f28879]) ).
fof(f16790,plain,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
inference(cnf_transformation,[],[f5088]) ).
fof(f5088,axiom,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
fof(f28877,plain,
spl573_156,
inference(avatar_split_clause,[],[f16789,f28874]) ).
fof(f28874,plain,
( spl573_156
<=> class_Lattices_Osemilattice__sup(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_156])]) ).
fof(f16789,plain,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
inference(cnf_transformation,[],[f5024]) ).
fof(f5024,axiom,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__sup) ).
fof(f28872,plain,
spl573_155,
inference(avatar_split_clause,[],[f16788,f28869]) ).
fof(f28869,plain,
( spl573_155
<=> class_Lattices_Odistrib__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_155])]) ).
fof(f16788,plain,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5127]) ).
fof(f5127,axiom,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
fof(f28867,plain,
spl573_154,
inference(avatar_split_clause,[],[f16787,f28864]) ).
fof(f28864,plain,
( spl573_154
<=> class_Lattices_Odistrib__lattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_154])]) ).
fof(f16787,plain,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f5090]) ).
fof(f5090,axiom,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Odistrib__lattice) ).
fof(f28862,plain,
spl573_153,
inference(avatar_split_clause,[],[f16786,f28859]) ).
fof(f28859,plain,
( spl573_153
<=> class_Lattices_Odistrib__lattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_153])]) ).
fof(f16786,plain,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
inference(cnf_transformation,[],[f5026]) ).
fof(f5026,axiom,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Odistrib__lattice) ).
fof(f28857,plain,
spl573_152,
inference(avatar_split_clause,[],[f16785,f28854]) ).
fof(f28854,plain,
( spl573_152
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_152])]) ).
fof(f16785,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5105]) ).
fof(f5105,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(f28852,plain,
spl573_151,
inference(avatar_split_clause,[],[f16784,f28849]) ).
fof(f28849,plain,
( spl573_151
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_151])]) ).
fof(f16784,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5045]) ).
fof(f5045,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(f28847,plain,
spl573_150,
inference(avatar_split_clause,[],[f16783,f28844]) ).
fof(f28844,plain,
( spl573_150
<=> class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_150])]) ).
fof(f16783,plain,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5170]) ).
fof(f5170,axiom,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) ).
fof(f28842,plain,
spl573_149,
inference(avatar_split_clause,[],[f16782,f28839]) ).
fof(f28839,plain,
( spl573_149
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_149])]) ).
fof(f16782,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5096]) ).
fof(f5096,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(f28837,plain,
spl573_148,
inference(avatar_split_clause,[],[f16781,f28834]) ).
fof(f28834,plain,
( spl573_148
<=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_148])]) ).
fof(f16781,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5033]) ).
fof(f5033,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(f28832,plain,
spl573_147,
inference(avatar_split_clause,[],[f16780,f28829]) ).
fof(f28829,plain,
( spl573_147
<=> class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_147])]) ).
fof(f16780,plain,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5162]) ).
fof(f5162,axiom,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) ).
fof(f28827,plain,
spl573_146,
inference(avatar_split_clause,[],[f16779,f28824]) ).
fof(f28824,plain,
( spl573_146
<=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_146])]) ).
fof(f16779,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(cnf_transformation,[],[f5099]) ).
fof(f5099,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(f28822,plain,
spl573_145,
inference(avatar_split_clause,[],[f16778,f28819]) ).
fof(f28819,plain,
( spl573_145
<=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_145])]) ).
fof(f16778,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f5097]) ).
fof(f5097,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(f28817,plain,
spl573_144,
inference(avatar_split_clause,[],[f16777,f28814]) ).
fof(f28814,plain,
( spl573_144
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_144])]) ).
fof(f16777,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f5038]) ).
fof(f5038,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
fof(f28812,plain,
spl573_143,
inference(avatar_split_clause,[],[f16776,f28809]) ).
fof(f28809,plain,
( spl573_143
<=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_143])]) ).
fof(f16776,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5036]) ).
fof(f5036,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(f28807,plain,
spl573_142,
inference(avatar_split_clause,[],[f16775,f28804]) ).
fof(f28804,plain,
( spl573_142
<=> class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_142])]) ).
fof(f16775,plain,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5165]) ).
fof(f5165,axiom,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) ).
fof(f28802,plain,
spl573_141,
inference(avatar_split_clause,[],[f16774,f28799]) ).
fof(f28799,plain,
( spl573_141
<=> class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_141])]) ).
fof(f16774,plain,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5163]) ).
fof(f5163,axiom,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).
fof(f28797,plain,
spl573_140,
inference(avatar_split_clause,[],[f16773,f28794]) ).
fof(f28794,plain,
( spl573_140
<=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_140])]) ).
fof(f16773,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5092]) ).
fof(f5092,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(f28792,plain,
spl573_139,
inference(avatar_split_clause,[],[f16772,f28789]) ).
fof(f28789,plain,
( spl573_139
<=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_139])]) ).
fof(f16772,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5028]) ).
fof(f5028,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(f28787,plain,
spl573_138,
inference(avatar_split_clause,[],[f16771,f28784]) ).
fof(f28784,plain,
( spl573_138
<=> class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_138])]) ).
fof(f16771,plain,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5158]) ).
fof(f5158,axiom,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult) ).
fof(f28782,plain,
spl573_137,
inference(avatar_split_clause,[],[f16770,f28779]) ).
fof(f28779,plain,
( spl573_137
<=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_137])]) ).
fof(f16770,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f5087]) ).
fof(f5087,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(f28777,plain,
spl573_136,
inference(avatar_split_clause,[],[f16769,f28774]) ).
fof(f28774,plain,
( spl573_136
<=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_136])]) ).
fof(f16769,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(cnf_transformation,[],[f5023]) ).
fof(f5023,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(f28772,plain,
spl573_135,
inference(avatar_split_clause,[],[f16768,f28769]) ).
fof(f28769,plain,
( spl573_135
<=> class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_135])]) ).
fof(f16768,plain,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5156]) ).
fof(f5156,axiom,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) ).
fof(f28767,plain,
spl573_134,
inference(avatar_split_clause,[],[f16767,f28764]) ).
fof(f16767,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f5108]) ).
fof(f5108,axiom,
class_Rings_Osemiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
fof(f28762,plain,
spl573_133,
inference(avatar_split_clause,[],[f16766,f28759]) ).
fof(f16766,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5050]) ).
fof(f5050,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
fof(f28757,plain,
spl573_132,
inference(avatar_split_clause,[],[f16765,f28754]) ).
fof(f16765,plain,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5173]) ).
fof(f5173,axiom,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).
fof(f28752,plain,
spl573_131,
inference(avatar_split_clause,[],[f16764,f28749]) ).
fof(f28749,plain,
( spl573_131
<=> class_Int_Onumber(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_131])]) ).
fof(f16764,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(cnf_transformation,[],[f5119]) ).
fof(f5119,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
fof(f28747,plain,
spl573_130,
inference(avatar_split_clause,[],[f16763,f28744]) ).
fof(f28744,plain,
( spl573_130
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_130])]) ).
fof(f16763,plain,
class_Int_Onumber(tc_Int_Oint),
inference(cnf_transformation,[],[f5071]) ).
fof(f5071,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
fof(f28742,plain,
spl573_129,
inference(avatar_split_clause,[],[f16762,f28739]) ).
fof(f28739,plain,
( spl573_129
<=> class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_129])]) ).
fof(f16762,plain,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5182]) ).
fof(f5182,axiom,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Int_Onumber) ).
fof(f28737,plain,
spl573_128,
inference(avatar_split_clause,[],[f16761,f28734]) ).
fof(f28734,plain,
( spl573_128
<=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_128])]) ).
fof(f16761,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f5079]) ).
fof(f5079,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(f28732,plain,
spl573_127,
inference(avatar_split_clause,[],[f16760,f28729]) ).
fof(f28729,plain,
( spl573_127
<=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_127])]) ).
fof(f16760,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5008]) ).
fof(f5008,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(f28727,plain,
spl573_126,
inference(avatar_split_clause,[],[f16759,f28724]) ).
fof(f28724,plain,
( spl573_126
<=> class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_126])]) ).
fof(f16759,plain,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5148]) ).
fof(f5148,axiom,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) ).
fof(f28722,plain,
spl573_125,
inference(avatar_split_clause,[],[f16758,f28719]) ).
fof(f28719,plain,
( spl573_125
<=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_125])]) ).
fof(f16758,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5081]) ).
fof(f5081,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__comm__monoid__add) ).
fof(f28717,plain,
spl573_124,
inference(avatar_split_clause,[],[f16757,f28714]) ).
fof(f28714,plain,
( spl573_124
<=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_124])]) ).
fof(f16757,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5011]) ).
fof(f5011,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__comm__monoid__add) ).
fof(f28712,plain,
spl573_123,
inference(avatar_split_clause,[],[f16756,f28709]) ).
fof(f28709,plain,
( spl573_123
<=> class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_123])]) ).
fof(f16756,plain,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5150]) ).
fof(f5150,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add) ).
fof(f28707,plain,
spl573_122,
inference(avatar_split_clause,[],[f16755,f28704]) ).
fof(f28704,plain,
( spl573_122
<=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_122])]) ).
fof(f16755,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5106]) ).
fof(f5106,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(f28702,plain,
spl573_121,
inference(avatar_split_clause,[],[f16754,f28699]) ).
fof(f28699,plain,
( spl573_121
<=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_121])]) ).
fof(f16754,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5046]) ).
fof(f5046,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(f28697,plain,
spl573_120,
inference(avatar_split_clause,[],[f16753,f28694]) ).
fof(f28694,plain,
( spl573_120
<=> class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_120])]) ).
fof(f16753,plain,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5171]) ).
fof(f5171,axiom,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) ).
fof(f28692,plain,
spl573_119,
inference(avatar_split_clause,[],[f16752,f28689]) ).
fof(f28689,plain,
( spl573_119
<=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_119])]) ).
fof(f16752,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5091]) ).
fof(f5091,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(f28687,plain,
spl573_118,
inference(avatar_split_clause,[],[f16751,f28684]) ).
fof(f28684,plain,
( spl573_118
<=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_118])]) ).
fof(f16751,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5107]) ).
fof(f5107,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(f28682,plain,
spl573_117,
inference(avatar_split_clause,[],[f16750,f28679]) ).
fof(f28679,plain,
( spl573_117
<=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_117])]) ).
fof(f16750,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5027]) ).
fof(f5027,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(f28677,plain,
spl573_116,
inference(avatar_split_clause,[],[f16749,f28674]) ).
fof(f28674,plain,
( spl573_116
<=> class_Groups_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_116])]) ).
fof(f16749,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5048]) ).
fof(f5048,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(f28672,plain,
spl573_115,
inference(avatar_split_clause,[],[f16748,f28669]) ).
fof(f28669,plain,
( spl573_115
<=> class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_115])]) ).
fof(f16748,plain,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5172]) ).
fof(f5172,axiom,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) ).
fof(f28667,plain,
spl573_114,
inference(avatar_split_clause,[],[f16747,f28664]) ).
fof(f28664,plain,
( spl573_114
<=> class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_114])]) ).
fof(f16747,plain,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5157]) ).
fof(f5157,axiom,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) ).
fof(f28662,plain,
spl573_113,
inference(avatar_split_clause,[],[f16746,f28659]) ).
fof(f28659,plain,
( spl573_113
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_113])]) ).
fof(f16746,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[],[f5076]) ).
fof(f5076,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f28657,plain,
spl573_112,
inference(avatar_split_clause,[],[f16745,f28654]) ).
fof(f28654,plain,
( spl573_112
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_112])]) ).
fof(f16745,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[],[f5004]) ).
fof(f5004,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f28652,plain,
spl573_111,
inference(avatar_split_clause,[],[f16744,f28649]) ).
fof(f28649,plain,
( spl573_111
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_111])]) ).
fof(f16744,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5145]) ).
fof(f5145,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f28647,plain,
spl573_110,
inference(avatar_split_clause,[],[f16743,f28644]) ).
fof(f28644,plain,
( spl573_110
<=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_110])]) ).
fof(f16743,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f5109]) ).
fof(f5109,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(f28642,plain,
spl573_109,
inference(avatar_split_clause,[],[f16742,f28639]) ).
fof(f28639,plain,
( spl573_109
<=> class_Rings_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_109])]) ).
fof(f16742,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5051]) ).
fof(f5051,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(f28637,plain,
spl573_108,
inference(avatar_split_clause,[],[f16741,f28634]) ).
fof(f28634,plain,
( spl573_108
<=> class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_108])]) ).
fof(f16741,plain,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5174]) ).
fof(f5174,axiom,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).
fof(f28632,plain,
spl573_107,
inference(avatar_split_clause,[],[f16740,f28629]) ).
fof(f28629,plain,
( spl573_107
<=> class_Power_Opower(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_107])]) ).
fof(f16740,plain,
class_Power_Opower(tc_Nat_Onat),
inference(cnf_transformation,[],[f5117]) ).
fof(f5117,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(f28627,plain,
spl573_106,
inference(avatar_split_clause,[],[f16739,f28624]) ).
fof(f28624,plain,
( spl573_106
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_106])]) ).
fof(f16739,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5075]) ).
fof(f5075,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f28622,plain,
spl573_105,
inference(avatar_split_clause,[],[f16738,f28619]) ).
fof(f28619,plain,
( spl573_105
<=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_105])]) ).
fof(f16738,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5080]) ).
fof(f5080,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oordered__ab__semigroup__add) ).
fof(f28617,plain,
spl573_104,
inference(avatar_split_clause,[],[f16737,f28614]) ).
fof(f28614,plain,
( spl573_104
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_104])]) ).
fof(f16737,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5003]) ).
fof(f5003,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f28612,plain,
spl573_103,
inference(avatar_split_clause,[],[f16736,f28609]) ).
fof(f28609,plain,
( spl573_103
<=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_103])]) ).
fof(f16736,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5009]) ).
fof(f5009,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add) ).
fof(f28607,plain,
spl573_102,
inference(avatar_split_clause,[],[f16735,f28604]) ).
fof(f28604,plain,
( spl573_102
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_102])]) ).
fof(f16735,plain,
class_Power_Opower(tc_Int_Oint),
inference(cnf_transformation,[],[f5067]) ).
fof(f5067,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(f28602,plain,
spl573_101,
inference(avatar_split_clause,[],[f16734,f28599]) ).
fof(f28599,plain,
( spl573_101
<=> class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_101])]) ).
fof(f16734,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5149]) ).
fof(f5149,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) ).
fof(f28597,plain,
spl573_100,
inference(avatar_split_clause,[],[f16733,f28594]) ).
fof(f28594,plain,
( spl573_100
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_100])]) ).
fof(f16733,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5144]) ).
fof(f5144,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f28592,plain,
spl573_99,
inference(avatar_split_clause,[],[f16732,f28589]) ).
fof(f28589,plain,
( spl573_99
<=> class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_99])]) ).
fof(f16732,plain,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5180]) ).
fof(f5180,axiom,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).
fof(f28587,plain,
spl573_98,
inference(avatar_split_clause,[],[f16731,f28584]) ).
fof(f28584,plain,
( spl573_98
<=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_98])]) ).
fof(f16731,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5083]) ).
fof(f5083,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(f28582,plain,
spl573_97,
inference(avatar_split_clause,[],[f16730,f28579]) ).
fof(f28579,plain,
( spl573_97
<=> class_Rings_Odvd(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_97])]) ).
fof(f16730,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(cnf_transformation,[],[f5121]) ).
fof(f5121,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(f28577,plain,
spl573_96,
inference(avatar_split_clause,[],[f16729,f28574]) ).
fof(f28574,plain,
( spl573_96
<=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_96])]) ).
fof(f16729,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5015]) ).
fof(f5015,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(f28572,plain,
spl573_95,
inference(avatar_split_clause,[],[f16728,f28569]) ).
fof(f28569,plain,
( spl573_95
<=> class_Rings_Odvd(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_95])]) ).
fof(f16728,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(cnf_transformation,[],[f5073]) ).
fof(f5073,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(f28567,plain,
spl573_94,
inference(avatar_split_clause,[],[f16727,f28564]) ).
fof(f28564,plain,
( spl573_94
<=> class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_94])]) ).
fof(f16727,plain,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5152]) ).
fof(f5152,axiom,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) ).
fof(f28562,plain,
spl573_93,
inference(avatar_split_clause,[],[f16726,f28559]) ).
fof(f28559,plain,
( spl573_93
<=> class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_93])]) ).
fof(f16726,plain,
class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5184]) ).
fof(f5184,axiom,
class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Odvd) ).
fof(f28557,plain,
spl573_92,
inference(avatar_split_clause,[],[f16725,f28554]) ).
fof(f28554,plain,
( spl573_92
<=> class_Orderings_Obot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_92])]) ).
fof(f16725,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(cnf_transformation,[],[f5135]) ).
fof(f5135,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(f28552,plain,
spl573_91,
inference(avatar_split_clause,[],[f16724,f28549]) ).
fof(f28549,plain,
( spl573_91
<=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_91])]) ).
fof(f16724,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(cnf_transformation,[],[f5095]) ).
fof(f5095,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(f28547,plain,
spl573_90,
inference(avatar_split_clause,[],[f16723,f28544]) ).
fof(f28544,plain,
( spl573_90
<=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_90])]) ).
fof(f16723,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5094]) ).
fof(f5094,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(f28542,plain,
spl573_89,
inference(avatar_split_clause,[],[f16722,f28539]) ).
fof(f28539,plain,
( spl573_89
<=> class_Orderings_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_89])]) ).
fof(f16722,plain,
class_Orderings_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f5115]) ).
fof(f5115,axiom,
class_Orderings_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
fof(f28537,plain,
spl573_88,
inference(avatar_split_clause,[],[f16721,f28534]) ).
fof(f28534,plain,
( spl573_88
<=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_88])]) ).
fof(f16721,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5085]) ).
fof(f5085,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(f28532,plain,
spl573_87,
inference(avatar_split_clause,[],[f16720,f28529]) ).
fof(f28529,plain,
( spl573_87
<=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_87])]) ).
fof(f16720,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5032]) ).
fof(f5032,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(f28527,plain,
spl573_86,
inference(avatar_split_clause,[],[f16719,f28524]) ).
fof(f28524,plain,
( spl573_86
<=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_86])]) ).
fof(f16719,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5021]) ).
fof(f5021,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(f28522,plain,
spl573_85,
inference(avatar_split_clause,[],[f16718,f28519]) ).
fof(f28519,plain,
( spl573_85
<=> class_Smallcheck_Osmall(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_85])]) ).
fof(f16718,plain,
class_Smallcheck_Osmall(tc_Int_Oint),
inference(cnf_transformation,[],[f5049]) ).
fof(f5049,axiom,
class_Smallcheck_Osmall(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Smallcheck_Osmall) ).
fof(f28517,plain,
spl573_84,
inference(avatar_split_clause,[],[f16717,f28514]) ).
fof(f28514,plain,
( spl573_84
<=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_84])]) ).
fof(f16717,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5030]) ).
fof(f5030,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(f28512,plain,
spl573_83,
inference(avatar_split_clause,[],[f16716,f28509]) ).
fof(f28509,plain,
( spl573_83
<=> class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_83])]) ).
fof(f16716,plain,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5161]) ).
fof(f5161,axiom,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) ).
fof(f28507,plain,
spl573_82,
inference(avatar_split_clause,[],[f16715,f28504]) ).
fof(f28504,plain,
( spl573_82
<=> class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_82])]) ).
fof(f16715,plain,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5154]) ).
fof(f5154,axiom,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) ).
fof(f28502,plain,
spl573_81,
inference(avatar_split_clause,[],[f16714,f28499]) ).
fof(f28499,plain,
( spl573_81
<=> class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_81])]) ).
fof(f16714,plain,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5160]) ).
fof(f5160,axiom,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) ).
fof(f28497,plain,
spl573_80,
inference(avatar_split_clause,[],[f16713,f28494]) ).
fof(f28494,plain,
( spl573_80
<=> class_Smallcheck_Osmall(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_80])]) ).
fof(f16713,plain,
class_Smallcheck_Osmall(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5143]) ).
fof(f5143,axiom,
class_Smallcheck_Osmall(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Smallcheck_Osmall) ).
fof(f28492,plain,
spl573_79,
inference(avatar_split_clause,[],[f16712,f28489]) ).
fof(f28489,plain,
( spl573_79
<=> class_Groups_Ouminus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_79])]) ).
fof(f16712,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(cnf_transformation,[],[f5136]) ).
fof(f5136,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(f28487,plain,
spl573_78,
inference(avatar_split_clause,[],[f16711,f28484]) ).
fof(f28484,plain,
( spl573_78
<=> class_Rings_Omult__zero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_78])]) ).
fof(f16711,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(cnf_transformation,[],[f5111]) ).
fof(f5111,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(f28482,plain,
spl573_77,
inference(avatar_split_clause,[],[f16710,f28479]) ).
fof(f28479,plain,
( spl573_77
<=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_77])]) ).
fof(f16710,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(cnf_transformation,[],[f5103]) ).
fof(f5103,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(f28477,plain,
spl573_76,
inference(avatar_split_clause,[],[f16709,f28474]) ).
fof(f28474,plain,
( spl573_76
<=> class_Rings_Osemiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_76])]) ).
fof(f16709,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5113]) ).
fof(f5113,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(f28472,plain,
spl573_75,
inference(avatar_split_clause,[],[f16708,f28469]) ).
fof(f28469,plain,
( spl573_75
<=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_75])]) ).
fof(f16708,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(cnf_transformation,[],[f5042]) ).
fof(f5042,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(f28467,plain,
spl573_74,
inference(avatar_split_clause,[],[f16707,f28464]) ).
fof(f28464,plain,
( spl573_74
<=> class_Rings_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_74])]) ).
fof(f16707,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5060]) ).
fof(f5060,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(f28462,plain,
spl573_73,
inference(avatar_split_clause,[],[f16706,f28459]) ).
fof(f28459,plain,
( spl573_73
<=> class_Groups_Ouminus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_73])]) ).
fof(f16706,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(cnf_transformation,[],[f5062]) ).
fof(f5062,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(f28457,plain,
spl573_72,
inference(avatar_split_clause,[],[f16705,f28454]) ).
fof(f28454,plain,
( spl573_72
<=> class_Rings_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_72])]) ).
fof(f16705,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(cnf_transformation,[],[f5055]) ).
fof(f5055,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(f28452,plain,
spl573_71,
inference(avatar_split_clause,[],[f16704,f28449]) ).
fof(f28449,plain,
( spl573_71
<=> class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_71])]) ).
fof(f16704,plain,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5168]) ).
fof(f5168,axiom,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one) ).
fof(f28447,plain,
spl573_70,
inference(avatar_split_clause,[],[f16703,f28444]) ).
fof(f28444,plain,
( spl573_70
<=> class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_70])]) ).
fof(f16703,plain,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5177]) ).
fof(f5177,axiom,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring) ).
fof(f28442,plain,
spl573_69,
inference(avatar_split_clause,[],[f16702,f28439]) ).
fof(f28439,plain,
( spl573_69
<=> class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_69])]) ).
fof(f16702,plain,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5175]) ).
fof(f5175,axiom,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero) ).
fof(f28437,plain,
spl573_68,
inference(avatar_split_clause,[],[f16701,f28434]) ).
fof(f28434,plain,
( spl573_68
<=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_68])]) ).
fof(f16701,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5093]) ).
fof(f5093,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(f28432,plain,
spl573_67,
inference(avatar_split_clause,[],[f16700,f28429]) ).
fof(f28429,plain,
( spl573_67
<=> class_Nat_Osemiring__char__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_67])]) ).
fof(f16700,plain,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f5102]) ).
fof(f5102,axiom,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).
fof(f28427,plain,
spl573_66,
inference(avatar_split_clause,[],[f16699,f28424]) ).
fof(f28424,plain,
( spl573_66
<=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_66])]) ).
fof(f16699,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5086]) ).
fof(f5086,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(f28422,plain,
spl573_65,
inference(avatar_split_clause,[],[f16698,f28419]) ).
fof(f28419,plain,
( spl573_65
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_65])]) ).
fof(f16698,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5078]) ).
fof(f5078,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add) ).
fof(f28417,plain,
spl573_64,
inference(avatar_split_clause,[],[f16697,f28414]) ).
fof(f28414,plain,
( spl573_64
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_64])]) ).
fof(f16697,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5007]) ).
fof(f5007,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__semigroup__add) ).
fof(f28412,plain,
spl573_63,
inference(avatar_split_clause,[],[f16696,f28409]) ).
fof(f28409,plain,
( spl573_63
<=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_63])]) ).
fof(f16696,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5029]) ).
fof(f5029,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(f28407,plain,
spl573_62,
inference(avatar_split_clause,[],[f16695,f28404]) ).
fof(f28404,plain,
( spl573_62
<=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_62])]) ).
fof(f16695,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5022]) ).
fof(f5022,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(f28402,plain,
spl573_61,
inference(avatar_split_clause,[],[f16694,f28399]) ).
fof(f28399,plain,
( spl573_61
<=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_61])]) ).
fof(f16694,plain,
class_Nat_Osemiring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5040]) ).
fof(f5040,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).
fof(f28397,plain,
spl573_60,
inference(avatar_split_clause,[],[f16693,f28394]) ).
fof(f28394,plain,
( spl573_60
<=> class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_60])]) ).
fof(f16693,plain,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5167]) ).
fof(f5167,axiom,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0) ).
fof(f28392,plain,
spl573_59,
inference(avatar_split_clause,[],[f16692,f28389]) ).
fof(f28389,plain,
( spl573_59
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_59])]) ).
fof(f16692,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5147]) ).
fof(f5147,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) ).
fof(f28387,plain,
spl573_58,
inference(avatar_split_clause,[],[f16691,f28384]) ).
fof(f28384,plain,
( spl573_58
<=> class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_58])]) ).
fof(f16691,plain,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5155]) ).
fof(f5155,axiom,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) ).
fof(f28382,plain,
spl573_57,
inference(avatar_split_clause,[],[f16690,f28379]) ).
fof(f28379,plain,
( spl573_57
<=> class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_57])]) ).
fof(f16690,plain,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5159]) ).
fof(f5159,axiom,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) ).
fof(f28377,plain,
spl573_56,
inference(avatar_split_clause,[],[f16689,f28374]) ).
fof(f28374,plain,
( spl573_56
<=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_56])]) ).
fof(f16689,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5100]) ).
fof(f5100,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(f28372,plain,
spl573_55,
inference(avatar_split_clause,[],[f16688,f28369]) ).
fof(f28369,plain,
( spl573_55
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_55])]) ).
fof(f16688,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f5077]) ).
fof(f5077,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict) ).
fof(f28367,plain,
spl573_54,
inference(avatar_split_clause,[],[f16687,f28364]) ).
fof(f28364,plain,
( spl573_54
<=> class_Groups_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_54])]) ).
fof(f16687,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f5120]) ).
fof(f5120,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(f28362,plain,
spl573_53,
inference(avatar_split_clause,[],[f16686,f28359]) ).
fof(f28359,plain,
( spl573_53
<=> class_Groups_Osemigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_53])]) ).
fof(f16686,plain,
class_Groups_Osemigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5098]) ).
fof(f5098,axiom,
class_Groups_Osemigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Osemigroup__add) ).
fof(f28357,plain,
spl573_52,
inference(avatar_split_clause,[],[f16685,f28354]) ).
fof(f28354,plain,
( spl573_52
<=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_52])]) ).
fof(f16685,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5084]) ).
fof(f5084,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(f28352,plain,
spl573_51,
inference(avatar_split_clause,[],[f16684,f28349]) ).
fof(f28349,plain,
( spl573_51
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_51])]) ).
fof(f16684,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5082]) ).
fof(f5082,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add) ).
fof(f28347,plain,
spl573_50,
inference(avatar_split_clause,[],[f16683,f28344]) ).
fof(f28344,plain,
( spl573_50
<=> class_Groups_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_50])]) ).
fof(f16683,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f5118]) ).
fof(f5118,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(f28342,plain,
spl573_49,
inference(avatar_split_clause,[],[f16682,f28339]) ).
fof(f28339,plain,
( spl573_49
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_49])]) ).
fof(f16682,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5013]) ).
fof(f5013,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__ab__semigroup__add) ).
fof(f28337,plain,
spl573_48,
inference(avatar_split_clause,[],[f16681,f28334]) ).
fof(f28334,plain,
( spl573_48
<=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_48])]) ).
fof(f16681,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5018]) ).
fof(f5018,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(f28332,plain,
spl573_47,
inference(avatar_split_clause,[],[f16680,f28329]) ).
fof(f28329,plain,
( spl573_47
<=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_47])]) ).
fof(f16680,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5039]) ).
fof(f5039,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(f28327,plain,
spl573_46,
inference(avatar_split_clause,[],[f16679,f28324]) ).
fof(f28324,plain,
( spl573_46
<=> class_Groups_Osemigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_46])]) ).
fof(f16679,plain,
class_Groups_Osemigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5037]) ).
fof(f5037,axiom,
class_Groups_Osemigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osemigroup__add) ).
fof(f28322,plain,
spl573_45,
inference(avatar_split_clause,[],[f16678,f28319]) ).
fof(f28319,plain,
( spl573_45
<=> class_Groups_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_45])]) ).
fof(f16678,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f5068]) ).
fof(f5068,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(f28317,plain,
spl573_44,
inference(avatar_split_clause,[],[f16677,f28314]) ).
fof(f28314,plain,
( spl573_44
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_44])]) ).
fof(f16677,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5005]) ).
fof(f5005,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(f28312,plain,
spl573_43,
inference(avatar_split_clause,[],[f16676,f28309]) ).
fof(f28309,plain,
( spl573_43
<=> class_Groups_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_43])]) ).
fof(f16676,plain,
class_Groups_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f5072]) ).
fof(f5072,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(f28307,plain,
spl573_42,
inference(avatar_split_clause,[],[f16675,f28304]) ).
fof(f28304,plain,
( spl573_42
<=> class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_42])]) ).
fof(f16675,plain,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5166]) ).
fof(f5166,axiom,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring) ).
fof(f28302,plain,
spl573_41,
inference(avatar_split_clause,[],[f16674,f28299]) ).
fof(f28299,plain,
( spl573_41
<=> class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_41])]) ).
fof(f16674,plain,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5183]) ).
fof(f5183,axiom,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oone) ).
fof(f28297,plain,
spl573_40,
inference(avatar_split_clause,[],[f16673,f28294]) ).
fof(f28294,plain,
( spl573_40
<=> class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_40])]) ).
fof(f16673,plain,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5164]) ).
fof(f5164,axiom,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add) ).
fof(f28292,plain,
spl573_39,
inference(avatar_split_clause,[],[f16672,f28289]) ).
fof(f28289,plain,
( spl573_39
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_39])]) ).
fof(f16672,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5151]) ).
fof(f5151,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) ).
fof(f28287,plain,
spl573_38,
inference(avatar_split_clause,[],[f16671,f28284]) ).
fof(f28284,plain,
( spl573_38
<=> class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_38])]) ).
fof(f16671,plain,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5181]) ).
fof(f5181,axiom,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ozero) ).
fof(f28282,plain,
spl573_37,
inference(avatar_split_clause,[],[f16670,f28279]) ).
fof(f28279,plain,
( spl573_37
<=> class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_37])]) ).
fof(f16670,plain,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5153]) ).
fof(f5153,axiom,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) ).
fof(f28277,plain,
spl573_36,
inference(avatar_split_clause,[],[f16669,f28274]) ).
fof(f28274,plain,
( spl573_36
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_36])]) ).
fof(f16669,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5146]) ).
fof(f5146,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict) ).
fof(f28272,plain,
spl573_35,
inference(avatar_split_clause,[],[f16668,f28269]) ).
fof(f28269,plain,
( spl573_35
<=> class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_35])]) ).
fof(f16668,plain,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5122]) ).
fof(f5122,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
fof(f28267,plain,
spl573_34,
inference(avatar_split_clause,[],[f16667,f28264]) ).
fof(f28264,plain,
( spl573_34
<=> class_Lattices_Oboolean__algebra(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_34])]) ).
fof(f16667,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(cnf_transformation,[],[f5128]) ).
fof(f5128,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(f28262,plain,
spl573_33,
inference(avatar_split_clause,[],[f16666,f28259]) ).
fof(f28259,plain,
( spl573_33
<=> class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_33])]) ).
fof(f16666,plain,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
inference(cnf_transformation,[],[f5124]) ).
fof(f5124,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(f28257,plain,
spl573_32,
inference(avatar_split_clause,[],[f16665,f28254]) ).
fof(f28254,plain,
( spl573_32
<=> class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_32])]) ).
fof(f16665,plain,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
inference(cnf_transformation,[],[f5123]) ).
fof(f5123,axiom,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
fof(f28252,plain,
spl573_31,
inference(avatar_split_clause,[],[f16664,f28249]) ).
fof(f28249,plain,
( spl573_31
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_31])]) ).
fof(f16664,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(cnf_transformation,[],[f5074]) ).
fof(f5074,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f28247,plain,
spl573_30,
inference(avatar_split_clause,[],[f16663,f28244]) ).
fof(f28244,plain,
( spl573_30
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_30])]) ).
fof(f16663,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(cnf_transformation,[],[f5002]) ).
fof(f5002,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(f28242,plain,
spl573_29,
inference(avatar_split_clause,[],[f16662,f28239]) ).
fof(f28239,plain,
( spl573_29
<=> class_Lattices_Obounded__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_29])]) ).
fof(f16662,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/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
fof(f28237,plain,
spl573_28,
inference(avatar_split_clause,[],[f16661,f28234]) ).
fof(f28234,plain,
( spl573_28
<=> class_Orderings_Otop(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_28])]) ).
fof(f16661,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(cnf_transformation,[],[f5133]) ).
fof(f5133,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
fof(f28232,plain,
spl573_27,
inference(avatar_split_clause,[],[f16660,f28229]) ).
fof(f16660,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5059]) ).
fof(f5059,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
fof(f28227,plain,
spl573_26,
inference(avatar_split_clause,[],[f16659,f28224]) ).
fof(f28224,plain,
( spl573_26
<=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_26])]) ).
fof(f16659,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(cnf_transformation,[],[f5035]) ).
fof(f5035,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(f28222,plain,
spl573_25,
inference(avatar_split_clause,[],[f16658,f28219]) ).
fof(f16658,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f5010]) ).
fof(f5010,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add__abs) ).
fof(f28217,plain,
spl573_24,
inference(avatar_split_clause,[],[f16657,f28214]) ).
fof(f28214,plain,
( spl573_24
<=> class_Rings_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_24])]) ).
fof(f16657,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5065]) ).
fof(f5065,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(f28212,plain,
spl573_23,
inference(avatar_split_clause,[],[f16656,f28209]) ).
fof(f28209,plain,
( spl573_23
<=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_23])]) ).
fof(f16656,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5020]) ).
fof(f5020,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__group__add) ).
fof(f28207,plain,
spl573_22,
inference(avatar_split_clause,[],[f16655,f28204]) ).
fof(f28204,plain,
( spl573_22
<=> class_Groups_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_22])]) ).
fof(f16655,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5053]) ).
fof(f5053,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(f28202,plain,
spl573_21,
inference(avatar_split_clause,[],[f16654,f28199]) ).
fof(f28199,plain,
( spl573_21
<=> class_Groups_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_21])]) ).
fof(f16654,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5041]) ).
fof(f5041,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(f28197,plain,
spl573_20,
inference(avatar_split_clause,[],[f16653,f28194]) ).
fof(f28194,plain,
( spl573_20
<=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_20])]) ).
fof(f16653,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5012]) ).
fof(f5012,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Olinordered__ab__group__add) ).
fof(f28192,plain,
spl573_19,
inference(avatar_split_clause,[],[f16652,f28189]) ).
fof(f28189,plain,
( spl573_19
<=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_19])]) ).
fof(f16652,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5016]) ).
fof(f5016,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(f28187,plain,
spl573_18,
inference(avatar_split_clause,[],[f16651,f28184]) ).
fof(f28184,plain,
( spl573_18
<=> class_Rings_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_18])]) ).
fof(f16651,plain,
class_Rings_Oring(tc_Int_Oint),
inference(cnf_transformation,[],[f5069]) ).
fof(f5069,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(f28182,plain,
spl573_17,
inference(avatar_split_clause,[],[f16650,f28179]) ).
fof(f28179,plain,
( spl573_17
<=> class_Divides_Oring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_17])]) ).
fof(f16650,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f5054]) ).
fof(f5054,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
fof(f28177,plain,
spl573_16,
inference(avatar_split_clause,[],[f16649,f28174]) ).
fof(f28174,plain,
( spl573_16
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_16])]) ).
fof(f16649,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5058]) ).
fof(f5058,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(f28172,plain,
spl573_15,
inference(avatar_split_clause,[],[f16648,f28169]) ).
fof(f28169,plain,
( spl573_15
<=> class_Rings_Oordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_15])]) ).
fof(f16648,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5043]) ).
fof(f5043,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(f28167,plain,
spl573_14,
inference(avatar_split_clause,[],[f16647,f28164]) ).
fof(f28164,plain,
( spl573_14
<=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_14])]) ).
fof(f16647,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5047]) ).
fof(f5047,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(f28162,plain,
spl573_13,
inference(avatar_split_clause,[],[f16646,f28159]) ).
fof(f28159,plain,
( spl573_13
<=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_13])]) ).
fof(f16646,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5014]) ).
fof(f5014,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1__no__zero__divisors) ).
fof(f28157,plain,
spl573_12,
inference(avatar_split_clause,[],[f16645,f28154]) ).
fof(f28154,plain,
( spl573_12
<=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_12])]) ).
fof(f16645,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5034]) ).
fof(f5034,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(f28152,plain,
spl573_11,
inference(avatar_split_clause,[],[f16644,f28149]) ).
fof(f28149,plain,
( spl573_11
<=> class_Rings_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_11])]) ).
fof(f16644,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(cnf_transformation,[],[f5070]) ).
fof(f5070,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(f28147,plain,
spl573_10,
inference(avatar_split_clause,[],[f16643,f28144]) ).
fof(f28144,plain,
( spl573_10
<=> class_Groups_Osgn__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_10])]) ).
fof(f16643,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(cnf_transformation,[],[f5063]) ).
fof(f5063,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).
fof(f28142,plain,
spl573_9,
inference(avatar_split_clause,[],[f16642,f28139]) ).
fof(f28139,plain,
( spl573_9
<=> class_Rings_Ocomm__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_9])]) ).
fof(f16642,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5056]) ).
fof(f5056,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(f28137,plain,
spl573_8,
inference(avatar_split_clause,[],[f16641,f28134]) ).
fof(f28134,plain,
( spl573_8
<=> class_Orderings_Owellorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_8])]) ).
fof(f16641,plain,
class_Orderings_Owellorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5101]) ).
fof(f5101,axiom,
class_Orderings_Owellorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).
fof(f28132,plain,
spl573_7,
inference(avatar_split_clause,[],[f16640,f28129]) ).
fof(f28129,plain,
( spl573_7
<=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_7])]) ).
fof(f16640,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5006]) ).
fof(f5006,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__strict) ).
fof(f28127,plain,
spl573_6,
inference(avatar_split_clause,[],[f16639,f28124]) ).
fof(f28124,plain,
( spl573_6
<=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_6])]) ).
fof(f16639,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5019]) ).
fof(f5019,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(f28122,plain,
spl573_5,
inference(avatar_split_clause,[],[f16638,f28119]) ).
fof(f28119,plain,
( spl573_5
<=> class_Groups_Oabs__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_5])]) ).
fof(f16638,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(cnf_transformation,[],[f5064]) ).
fof(f5064,axiom,
class_Groups_Oabs__if(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).
fof(f28117,plain,
spl573_4,
inference(avatar_split_clause,[],[f16637,f28114]) ).
fof(f28114,plain,
( spl573_4
<=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_4])]) ).
fof(f16637,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5017]) ).
fof(f5017,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__no__zero__divisors) ).
fof(f28112,plain,
spl573_3,
inference(avatar_split_clause,[],[f16636,f28109]) ).
fof(f28109,plain,
( spl573_3
<=> class_Rings_Oordered__ring__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_3])]) ).
fof(f16636,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f5031]) ).
fof(f5031,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(f28107,plain,
~ spl573_2,
inference(avatar_split_clause,[],[f16635,f28104]) ).
fof(f28104,plain,
( spl573_2
<=> hBOOL(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl573_2])]) ).
fof(f16635,plain,
~ hBOOL(c_fFalse),
inference(cnf_transformation,[],[f5192]) ).
fof(f5192,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__1) ).
fof(f28102,plain,
~ spl573_1,
inference(avatar_split_clause,[],[f16628,f28099]) ).
fof(f16628,plain,
~ v_R(v_Z,v_s_H),
inference(cnf_transformation,[],[f5213]) ).
fof(f5213,plain,
~ v_R(v_Z,v_s_H),
inference(flattening,[],[f5212]) ).
fof(f5212,negated_conjecture,
~ v_R(v_Z,v_s_H),
inference(negated_conjecture,[],[f5211]) ).
fof(f5211,conjecture,
v_R(v_Z,v_s_H),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : SWW344+1 : TPTP v8.1.2. Released v5.2.0.
% 0.02/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30 % Computer : n006.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri May 3 19:23:08 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.30 % (10560)Running in auto input_syntax mode. Trying TPTP
% 0.68/0.86 % (10568)WARNING: value z3 for option sas not known
% 0.68/0.86 % (10569)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.68/0.86 % (10566)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.68/0.86 % (10567)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.68/0.86 % (10571)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)
% 0.68/0.86 % (10570)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)
% 0.68/0.87 % (10572)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.68/0.87 % (10568)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)
% 8.52/2.01 % (10570)First to succeed.
% 9.19/2.09 % (10570)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-10560"
% 9.25/2.09 % (10570)Refutation found. Thanks to Tanya!
% 9.25/2.09 % SZS status Theorem for theBenchmark
% 9.25/2.09 % SZS output start Proof for theBenchmark
% See solution above
% 9.32/2.13 % (10570)------------------------------
% 9.32/2.13 % (10570)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 9.32/2.13 % (10570)Termination reason: Refutation
% 9.32/2.13
% 9.32/2.13 % (10570)Memory used [KB]: 22604
% 9.32/2.13 % (10570)Time elapsed: 1.220 s
% 9.32/2.13 % (10570)Instructions burned: 2437 (million)
% 9.32/2.13 % (10560)Success in time 1.815 s
%------------------------------------------------------------------------------