TSTP Solution File: SWW358+1 by SnakeForV-SAT---1.0
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%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SWW358+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n025.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 : Wed Aug 31 19:19:09 EDT 2022
% Result : Theorem 85.10s 11.42s
% Output : Refutation 85.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 881
% Syntax : Number of formulae : 2701 (1339 unt; 0 def)
% Number of atoms : 5338 (1955 equ)
% Maximal formula atoms : 16 ( 1 avg)
% Number of connectives : 4134 (1497 ~;1545 |; 343 &)
% ( 525 <=>; 224 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 550 ( 548 usr; 453 prp; 0-5 aty)
% Number of functors : 135 ( 135 usr; 42 con; 0-6 aty)
% Number of variables : 1404 (1375 !; 29 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f36806,plain,
$false,
inference(avatar_smt_refutation,[],[f28932,f28937,f28942,f28948,f28953,f28958,f28964,f28972,f28977,f28982,f28987,f28995,f29005,f29013,f29018,f29023,f29034,f29040,f29045,f29052,f29058,f29066,f29072,f29079,f29084,f29089,f29095,f29100,f29108,f29115,f29122,f29127,f29134,f29139,f29145,f29150,f29155,f29160,f29165,f29171,f29176,f29183,f29196,f29202,f29208,f29215,f29220,f29225,f29230,f29236,f29242,f29248,f29257,f29274,f29279,f29358,f29359,f29365,f29378,f29391,f29397,f29406,f29411,f29416,f29422,f29433,f29438,f29443,f29448,f29452,f29462,f29467,f29478,f29485,f29493,f29506,f29511,f29516,f29583,f29594,f29600,f29605,f29610,f29616,f29623,f29637,f29648,f29654,f29660,f29673,f29678,f29705,f29707,f29715,f29792,f29807,f29818,f29824,f29832,f29841,f29854,f29859,f29864,f29871,f29890,f29909,f29915,f29926,f29939,f29955,f29960,f29974,f29980,f29986,f30000,f30010,f30019,f30041,f30052,f30068,f30087,f30102,f30109,f30113,f30120,f30131,f30140,f30156,f30169,f30174,f30183,f30191,f30205,f30217,f30222,f30238,f30248,f30269,f30284,f30296,f30308,f30313,f30319,f30324,f30332,f30493,f30522,f30529,f30534,f30542,f30571,f30576,f30581,f30594,f30599,f30605,f30613,f30643,f30646,f30652,f30658,f30663,f30680,f30692,f30709,f30724,f30755,f30762,f30767,f30772,f30785,f30824,f30840,f30861,f30872,f30878,f30883,f30889,f30930,f30938,f30944,f30949,f30967,f30974,f30988,f30993,f30999,f31004,f31028,f31036,f31042,f31049,f31057,f31068,f31073,f31078,f31083,f31095,f31119,f31136,f31141,f31147,f31152,f31161,f31166,f31177,f31182,f31187,f31200,f31214,f31221,f31230,f31240,f31247,f31254,f31268,f31273,f31280,f31290,f31299,f31304,f31318,f31328,f31333,f31348,f31370,f31375,f31383,f31395,f31401,f31406,f31434,f31439,f31445,f31457,f31472,f31522,f31527,f31535,f31542,f31579,f31584,f31589,f31614,f31621,f31624,f31629,f31641,f31678,f31786,f31802,f31809,f31814,f31819,f31838,f31848,f31855,f31864,f31871,f31892,f31905,f31953,f31963,f31968,f31983,f31991,f32035,f32041,f32051,f32059,f32064,f32070,f32076,f32146,f32153,f32173,f32186,f32191,f32207,f32216,f32221,f32233,f32244,f32262,f32283,f32319,f32326,f32336,f32349,f32354,f32360,f32372,f32374,f32415,f32429,f32477,f32520,f32546,f32562,f32582,f33023,f33034,f33041,f33052,f33057,f33262,f33298,f33303,f33305,f33315,f33317,f33322,f33355,f33398,f33452,f33457,f33462,f33496,f33501,f33517,f33522,f33527,f33538,f33581,f33606,f33607,f33629,f33636,f33647,f33654,f33659,f33848,f33855,f33867,f33894,f33900,f33940,f33960,f33965,f33986,f34040,f34053,f34060,f34069,f34082,f34099,f34107,f34117,f34133,f34194,f34201,f34214,f34219,f34226,f34236,f34256,f34267,f34281,f34303,f34323,f34328,f34350,f34361,f34371,f34381,f34400,f34407,f34418,f34449,f34455,f34497,f34517,f34858,f34866,f34882,f34887,f34896,f34905,f34916,f34921,f34938,f34943,f34955,f34961,f35422,f35524,f35547,f35570,f35605,f35681,f35687,f35690,f35697,f35709,f35716,f35722,f35727,f35733,f35739,f35745,f35752,f35758,f35764,f35770,f35776,f35782,f35788,f35794,f35800,f35810,f35816,f35823,f35826,f35832,f35839,f35846,f35853,f35860,f35868,f35879,f35885,f35891,f35898,f35904,f35910,f35914,f35922,f35930,f35936,f35945,f35953,f35959,f35966,f35998,f36009,f36024,f36040,f36071,f36078,f36145,f36184,f36201,f36206,f36236,f36297,f36431,f36439,f36444,f36449,f36476,f36484,f36493,f36495,f36522,f36558,f36562,f36567,f36570,f36572,f36593,f36603,f36605,f36625,f36628,f36646,f36711,f36717,f36721,f36725,f36756,f36763,f36767,f36777,f36778,f36783,f36784,f36789,f36798,f36805]) ).
fof(f36805,plain,
( spl559_51
| ~ spl559_420
| ~ spl559_452
| ~ spl559_117
| ~ spl559_336 ),
inference(avatar_split_clause,[],[f36800,f34104,f30016,f36802,f36006,f29233]) ).
fof(f29233,plain,
( spl559_51
<=> v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_51])]) ).
fof(f36006,plain,
( spl559_420
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_420])]) ).
fof(f36802,plain,
( spl559_452
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),v_G))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_452])]) ).
fof(f30016,plain,
( spl559_117
<=> hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_117])]) ).
fof(f34104,plain,
( spl559_336
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_336])]) ).
fof(f36800,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),v_G)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)
| ~ spl559_117
| ~ spl559_336 ),
inference(forward_demodulation,[],[f36539,f30018]) ).
fof(f30018,plain,
( hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))
| ~ spl559_117 ),
inference(avatar_component_clause,[],[f30016]) ).
fof(f36539,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)
| ~ spl559_336 ),
inference(resolution,[],[f34106,f23849]) ).
fof(f23849,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X0),X1)),hAPP(c_Finite__Set_Ocard(X0),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| X1 = X2 ),
inference(cnf_transformation,[],[f17416]) ).
fof(f17416,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X0),X1)),hAPP(c_Finite__Set_Ocard(X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| X1 = X2 ),
inference(rectify,[],[f10696]) ).
fof(f10696,plain,
! [X1,X2,X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| X0 = X2 ),
inference(flattening,[],[f10695]) ).
fof(f10695,plain,
! [X1,X2,X0] :
( X0 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(ennf_transformation,[],[f7148]) ).
fof(f7148,plain,
! [X1,X2,X0] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X0)))
=> X0 = X2 ) ) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X10,X8,X9] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X9))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X10),X9))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X8),X9)),hAPP(c_Finite__Set_Ocard(X8),X10)))
=> X9 = X10 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__seteq) ).
fof(f34106,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ spl559_336 ),
inference(avatar_component_clause,[],[f34104]) ).
fof(f36798,plain,
( ~ spl559_420
| ~ spl559_450
| spl559_451
| ~ spl559_336 ),
inference(avatar_split_clause,[],[f36538,f34104,f36795,f36791,f36006]) ).
fof(f36791,plain,
( spl559_450
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_450])]) ).
fof(f36795,plain,
( spl559_451
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_451])]) ).
fof(f36538,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ spl559_336 ),
inference(resolution,[],[f34106,f23151]) ).
fof(f23151,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X0,tc_HOL_Obool)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X0),X2)),hAPP(c_Finite__Set_Ocard(X0),X1))) ),
inference(cnf_transformation,[],[f16889]) ).
fof(f16889,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X0,tc_HOL_Obool)),X2),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X0),X2)),hAPP(c_Finite__Set_Ocard(X0),X1))) ),
inference(rectify,[],[f11722]) ).
fof(f11722,plain,
! [X0,X2,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X0,tc_HOL_Obool)),X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X0),X1)),hAPP(c_Finite__Set_Ocard(X0),X2))) ),
inference(flattening,[],[f11721]) ).
fof(f11721,plain,
! [X2,X1,X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X0,tc_HOL_Obool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X0),X1)),hAPP(c_Finite__Set_Ocard(X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2)) ),
inference(ennf_transformation,[],[f8520]) ).
fof(f8520,plain,
! [X2,X1,X0] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X0),X1)),hAPP(c_Finite__Set_Ocard(X0),X2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X0,tc_HOL_Obool)),X1),X2)) ) ) ),
inference(rectify,[],[f308]) ).
fof(f308,axiom,
! [X8,X10,X9] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X9))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X10),X9))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X8),X10)),hAPP(c_Finite__Set_Ocard(X8),X9)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X8,tc_HOL_Obool)),X10),X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__psubset) ).
fof(f36789,plain,
( spl559_51
| ~ spl559_420
| ~ spl559_449
| ~ spl559_336 ),
inference(avatar_split_clause,[],[f36208,f34104,f36786,f36006,f29233]) ).
fof(f36786,plain,
( spl559_449
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_449])]) ).
fof(f36208,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)
| ~ spl559_336 ),
inference(resolution,[],[f23849,f34106]) ).
fof(f36784,plain,
( ~ spl559_420
| spl559_448
| ~ spl559_336 ),
inference(avatar_split_clause,[],[f36541,f34104,f36780,f36006]) ).
fof(f36780,plain,
( spl559_448
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_448])]) ).
fof(f36541,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ spl559_336 ),
inference(resolution,[],[f34106,f26662]) ).
fof(f26662,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X2))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X0)),hAPP(c_Finite__Set_Ocard(X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(cnf_transformation,[],[f19568]) ).
fof(f19568,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X0)),hAPP(c_Finite__Set_Ocard(X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X2)) ),
inference(rectify,[],[f13434]) ).
fof(f13434,plain,
! [X1,X2,X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X1)),hAPP(c_Finite__Set_Ocard(X2),X0)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0)) ),
inference(flattening,[],[f13433]) ).
fof(f13433,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X1)),hAPP(c_Finite__Set_Ocard(X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0)) ),
inference(ennf_transformation,[],[f8545]) ).
fof(f8545,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0))
=> ( 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__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X1)),hAPP(c_Finite__Set_Ocard(X2),X0))) ) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X9,X10,X8] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X9))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X10),X9))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X8),X10)),hAPP(c_Finite__Set_Ocard(X8),X9))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__mono) ).
fof(f36783,plain,
( spl559_448
| ~ spl559_420
| ~ spl559_336 ),
inference(avatar_split_clause,[],[f36156,f34104,f36006,f36780]) ).
fof(f36156,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))))
| ~ spl559_336 ),
inference(resolution,[],[f26662,f34106]) ).
fof(f36778,plain,
( ~ spl559_271
| spl559_447 ),
inference(avatar_contradiction_clause,[],[f36773]) ).
fof(f36773,plain,
( $false
| ~ spl559_271
| spl559_447 ),
inference(resolution,[],[f36762,f34568]) ).
fof(f34568,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),X0))
| ~ spl559_271 ),
inference(backward_demodulation,[],[f22026,f32172]) ).
fof(f32172,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat)
| ~ spl559_271 ),
inference(avatar_component_clause,[],[f32170]) ).
fof(f32170,plain,
( spl559_271
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_271])]) ).
fof(f22026,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,[],[f9220]) ).
fof(f9220,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,[],[f361]) ).
fof(f361,axiom,
! [X54] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X54)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le0) ).
fof(f36762,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| spl559_447 ),
inference(avatar_component_clause,[],[f36760]) ).
fof(f36760,plain,
( spl559_447
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_447])]) ).
fof(f36777,plain,
spl559_447,
inference(avatar_contradiction_clause,[],[f36774]) ).
fof(f36774,plain,
( $false
| spl559_447 ),
inference(resolution,[],[f36762,f28578]) ).
fof(f28578,plain,
! [X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X1)),
inference(equality_resolution,[],[f23536]) ).
fof(f23536,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f17175]) ).
fof(f17175,plain,
! [X0,X1] :
( ( X0 = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| ( X0 != X1
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) ) ),
inference(flattening,[],[f17174]) ).
fof(f17174,plain,
! [X0,X1] :
( ( X0 = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0))
| ( X0 != X1
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) ) ) ),
inference(nnf_transformation,[],[f8454]) ).
fof(f8454,plain,
! [X0,X1] :
( ( X0 = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),X0)) )
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X1),X0)) ),
inference(rectify,[],[f329]) ).
fof(f329,axiom,
! [X56,X53] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X53),X56))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X53),X56))
| X53 = X56 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(f36767,plain,
( ~ spl559_447
| spl559_51
| ~ spl559_420
| ~ spl559_336
| ~ spl559_435
| ~ spl559_439 ),
inference(avatar_split_clause,[],[f36766,f36519,f36441,f34104,f36006,f29233,f36760]) ).
fof(f36441,plain,
( spl559_435
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(t_a),v_G) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_435])]) ).
fof(f36519,plain,
( spl559_439
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_439])]) ).
fof(f36766,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ spl559_336
| ~ spl559_435
| ~ spl559_439 ),
inference(forward_demodulation,[],[f36765,f36521]) ).
fof(f36521,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))
| ~ spl559_439 ),
inference(avatar_component_clause,[],[f36519]) ).
fof(f36765,plain,
( v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ spl559_336
| ~ spl559_435 ),
inference(forward_demodulation,[],[f36208,f36442]) ).
fof(f36442,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(t_a),v_G)
| ~ spl559_435 ),
inference(avatar_component_clause,[],[f36441]) ).
fof(f36763,plain,
( ~ spl559_447
| spl559_51
| ~ spl559_420
| ~ spl559_336
| ~ spl559_435
| ~ spl559_439 ),
inference(avatar_split_clause,[],[f36758,f36519,f36441,f34104,f36006,f29233,f36760]) ).
fof(f36758,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ spl559_336
| ~ spl559_435
| ~ spl559_439 ),
inference(forward_demodulation,[],[f36757,f36521]) ).
fof(f36757,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)
| ~ spl559_336
| ~ spl559_435 ),
inference(forward_demodulation,[],[f36539,f36442]) ).
fof(f36756,plain,
( ~ spl559_149
| spl559_420 ),
inference(avatar_split_clause,[],[f36754,f36006,f30539]) ).
fof(f30539,plain,
( spl559_149
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_149])]) ).
fof(f36754,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U))
| spl559_420 ),
inference(resolution,[],[f36008,f25368]) ).
fof(f25368,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X0,X3,X1),X2)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2)) ),
inference(cnf_transformation,[],[f18617]) ).
fof(f18617,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X3),hAPP(c_Set_Oimage(X0,X3,X1),X2))) ),
inference(rectify,[],[f14008]) ).
fof(f14008,plain,
! [X2,X3,X1,X0] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X0),hAPP(c_Set_Oimage(X2,X0,X3),X1))) ),
inference(ennf_transformation,[],[f6096]) ).
fof(f6096,plain,
! [X1,X0,X3,X2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X0),hAPP(c_Set_Oimage(X2,X0,X3),X1))) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X6,X7,X8,X5] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X7))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X6),hAPP(c_Set_Oimage(X8,X6,X5),X7))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__imageI) ).
fof(f36008,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| spl559_420 ),
inference(avatar_component_clause,[],[f36006]) ).
fof(f36725,plain,
spl559_437,
inference(avatar_contradiction_clause,[],[f36724]) ).
fof(f36724,plain,
( $false
| spl559_437 ),
inference(resolution,[],[f36475,f25231]) ).
fof(f25231,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X1)),
inference(cnf_transformation,[],[f8073]) ).
fof(f8073,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X1)),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X8,X10] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X10),X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
fof(f36475,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),v_G))
| spl559_437 ),
inference(avatar_component_clause,[],[f36473]) ).
fof(f36473,plain,
( spl559_437
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),v_G)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_437])]) ).
fof(f36721,plain,
~ spl559_423,
inference(avatar_contradiction_clause,[],[f36719]) ).
fof(f36719,plain,
( $false
| ~ spl559_423 ),
inference(resolution,[],[f36074,f26813]) ).
fof(f26813,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f7323]) ).
fof(f7323,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(rectify,[],[f116]) ).
fof(f116,axiom,
! [X8] : hBOOL(hAPP(c_Finite__Set_Ofinite(X8),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite_Oequations_I1_J) ).
fof(f36074,plain,
( ! [X0] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))
| ~ spl559_423 ),
inference(avatar_component_clause,[],[f36073]) ).
fof(f36073,plain,
( spl559_423
<=> ! [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,[spl559_423])]) ).
fof(f36717,plain,
( spl559_446
| spl559_233
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f36712,f32170,f31469,f36714]) ).
fof(f36714,plain,
( spl559_446
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_446])]) ).
fof(f31469,plain,
( spl559_233
<=> 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,[spl559_233])]) ).
fof(f36712,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| spl559_233
| ~ spl559_271 ),
inference(resolution,[],[f31471,f34709]) ).
fof(f34709,plain,
( ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0) )
| ~ spl559_271 ),
inference(backward_demodulation,[],[f26822,f32172]) ).
fof(f26822,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0) ),
inference(cnf_transformation,[],[f19689]) ).
fof(f19689,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(rectify,[],[f11541]) ).
fof(f11541,plain,
! [X1,X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X1)
| hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1)) ),
inference(ennf_transformation,[],[f8831]) ).
fof(f8831,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X1) ),
inference(rectify,[],[f513]) ).
fof(f513,axiom,
! [X8,X10] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X10))
=> hAPP(c_Finite__Set_Ocard(X8),X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__infinite) ).
fof(f31471,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| spl559_233 ),
inference(avatar_component_clause,[],[f31469]) ).
fof(f36711,plain,
( spl559_445
| spl559_176
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f36706,f32170,f30927,f36708]) ).
fof(f36708,plain,
( spl559_445
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_445])]) ).
fof(f30927,plain,
( spl559_176
<=> 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,[spl559_176])]) ).
fof(f36706,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))
| spl559_176
| ~ spl559_271 ),
inference(resolution,[],[f30929,f34709]) ).
fof(f30929,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool))))
| spl559_176 ),
inference(avatar_component_clause,[],[f30927]) ).
fof(f36646,plain,
( ~ spl559_149
| spl559_444
| ~ spl559_149
| ~ spl559_271
| ~ spl559_417
| ~ spl559_418 ),
inference(avatar_split_clause,[],[f36642,f35995,f35991,f32170,f30539,f36644,f30539]) ).
fof(f36644,plain,
( spl559_444
<=> ! [X0,X3,X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Com_Opname,X0,X2),v_U)),X1))
| ~ c_Fun_Oinj__on(X0,tc_Com_Opname,X3,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Com_Opname,tc_HOL_Obool)),hAPP(c_Set_Oimage(X0,tc_Com_Opname,X3),X1)),v_U))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_444])]) ).
fof(f35991,plain,
( spl559_417
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_417])]) ).
fof(f35995,plain,
( spl559_418
<=> v_U = c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_418])]) ).
fof(f36642,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Com_Opname,X0,X2),v_U)),X1))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Com_Opname,tc_HOL_Obool)),hAPP(c_Set_Oimage(X0,tc_Com_Opname,X3),X1)),v_U))
| ~ c_Fun_Oinj__on(X0,tc_Com_Opname,X3,X1) )
| ~ spl559_149
| ~ spl559_271
| ~ spl559_417
| ~ spl559_418 ),
inference(forward_demodulation,[],[f36637,f35992]) ).
fof(f35992,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)
| ~ spl559_417 ),
inference(avatar_component_clause,[],[f35991]) ).
fof(f36637,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Com_Opname,X0,X2),v_U)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Com_Opname,tc_HOL_Obool)),hAPP(c_Set_Oimage(X0,tc_Com_Opname,X3),X1)),v_U))
| ~ c_Fun_Oinj__on(X0,tc_Com_Opname,X3,X1)
| hAPP(c_Finite__Set_Ocard(X0),X1) = hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U) )
| ~ spl559_149
| ~ spl559_271
| ~ spl559_417
| ~ spl559_418 ),
inference(resolution,[],[f36480,f26552]) ).
fof(f26552,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_Fun_Oinj__on(X2,X5,X1,X4)
| hAPP(c_Finite__Set_Ocard(X2),X4) = hAPP(c_Finite__Set_Ocard(X5),X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X5,X1),X4)),X0))
| ~ c_Fun_Oinj__on(X5,X2,X3,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X2,X3),X0)),X4)) ),
inference(cnf_transformation,[],[f19487]) ).
fof(f19487,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X5),X0))
| ~ c_Fun_Oinj__on(X5,X2,X3,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X5,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X5,X1),X4)),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X4))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X5,X2,X3),X0)),X4))
| ~ c_Fun_Oinj__on(X2,X5,X1,X4)
| hAPP(c_Finite__Set_Ocard(X2),X4) = hAPP(c_Finite__Set_Ocard(X5),X0) ),
inference(rectify,[],[f12529]) ).
fof(f12529,plain,
! [X0,X5,X4,X3,X1,X2] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0))
| ~ c_Fun_Oinj__on(X2,X4,X3,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X2,X5),X1)),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X4,X3),X0)),X1))
| ~ c_Fun_Oinj__on(X4,X2,X5,X1)
| hAPP(c_Finite__Set_Ocard(X2),X0) = hAPP(c_Finite__Set_Ocard(X4),X1) ),
inference(flattening,[],[f12528]) ).
fof(f12528,plain,
! [X0,X3,X5,X2,X1,X4] :
( hAPP(c_Finite__Set_Ocard(X2),X0) = hAPP(c_Finite__Set_Ocard(X4),X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X2,X5),X1)),X0))
| ~ c_Fun_Oinj__on(X4,X2,X5,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X4,X3),X0)),X1))
| ~ c_Fun_Oinj__on(X2,X4,X3,X0) ),
inference(ennf_transformation,[],[f5233]) ).
fof(f5233,plain,
! [X0,X3,X5,X2,X1,X4] :
( c_Fun_Oinj__on(X2,X4,X3,X0)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),hAPP(c_Set_Oimage(X2,X4,X3),X0)),X1))
=> ( c_Fun_Oinj__on(X4,X2,X5,X1)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),hAPP(c_Set_Oimage(X4,X2,X5),X1)),X0))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X1))
=> hAPP(c_Finite__Set_Ocard(X2),X0) = hAPP(c_Finite__Set_Ocard(X4),X1) ) ) ) ) ) ),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X10,X9,X8,X1,X6,X0] :
( c_Fun_Oinj__on(X8,X6,X1,X10)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool)),hAPP(c_Set_Oimage(X8,X6,X1),X10)),X9))
=> ( c_Fun_Oinj__on(X6,X8,X0,X9)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),hAPP(c_Set_Oimage(X6,X8,X0),X9)),X10))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X10))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X9))
=> hAPP(c_Finite__Set_Ocard(X8),X10) = hAPP(c_Finite__Set_Ocard(X6),X9) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__bij__eq) ).
fof(f36480,plain,
( ! [X10,X11] : c_Fun_Oinj__on(tc_Com_Opname,X10,X11,v_U)
| ~ spl559_149
| ~ spl559_271
| ~ spl559_417
| ~ spl559_418 ),
inference(trivial_inequality_removal,[],[f36479]) ).
fof(f36479,plain,
( ! [X10,X11] :
( c_Fun_Oinj__on(tc_Com_Opname,X10,X11,v_U)
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) != c_Orderings_Obot__class_Obot(tc_Nat_Onat) )
| ~ spl559_149
| ~ spl559_271
| ~ spl559_417
| ~ spl559_418 ),
inference(forward_demodulation,[],[f36469,f34741]) ).
fof(f34741,plain,
( ! [X1] : c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))
| ~ spl559_271 ),
inference(backward_demodulation,[],[f28392,f32172]) ).
fof(f28392,plain,
! [X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(equality_resolution,[],[f21364]) ).
fof(f21364,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0 ),
inference(cnf_transformation,[],[f15577]) ).
fof(f15577,plain,
! [X0,X1] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Finite__Set_Ocard(X1),X0) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0)
| ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0
& hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ) ) ),
inference(flattening,[],[f15576]) ).
fof(f15576,plain,
! [X0,X1] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Finite__Set_Ocard(X1),X0) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0)
| ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0
& hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ) ) ),
inference(nnf_transformation,[],[f7093]) ).
fof(f7093,plain,
! [X0,X1] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) )
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0) ),
inference(rectify,[],[f523]) ).
fof(f523,axiom,
! [X10,X8] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = X10
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X10)) )
<=> hAPP(c_Finite__Set_Ocard(X8),X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__eq__0__iff) ).
fof(f36469,plain,
( ! [X10,X11] :
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) != hAPP(c_Finite__Set_Ocard(X10),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_HOL_Obool)))
| c_Fun_Oinj__on(tc_Com_Opname,X10,X11,v_U) )
| ~ spl559_149
| ~ spl559_417
| ~ spl559_418 ),
inference(backward_demodulation,[],[f36239,f36455]) ).
fof(f36455,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Com_Opname,X0,X1),v_U)
| ~ spl559_418 ),
inference(superposition,[],[f25092,f35997]) ).
fof(f35997,plain,
( v_U = c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))
| ~ spl559_418 ),
inference(avatar_component_clause,[],[f35995]) ).
fof(f25092,plain,
! [X2,X0,X1] : hAPP(c_Set_Oimage(X0,X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(cnf_transformation,[],[f18393]) ).
fof(f18393,plain,
! [X0,X1,X2] : hAPP(c_Set_Oimage(X0,X2,X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)),
inference(rectify,[],[f9591]) ).
fof(f9591,plain,
! [X1,X2,X0] : hAPP(c_Set_Oimage(X1,X0,X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),
inference(rectify,[],[f119]) ).
fof(f119,axiom,
! [X8,X6,X1] : c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = hAPP(c_Set_Oimage(X6,X8,X1),c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_image__empty) ).
fof(f36239,plain,
( ! [X10,X11] :
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) != hAPP(c_Finite__Set_Ocard(X10),hAPP(c_Set_Oimage(tc_Com_Opname,X10,X11),v_U))
| c_Fun_Oinj__on(tc_Com_Opname,X10,X11,v_U) )
| ~ spl559_149
| ~ spl559_417 ),
inference(backward_demodulation,[],[f36081,f35992]) ).
fof(f36081,plain,
( ! [X10,X11] :
( c_Fun_Oinj__on(tc_Com_Opname,X10,X11,v_U)
| hAPP(c_Finite__Set_Ocard(X10),hAPP(c_Set_Oimage(tc_Com_Opname,X10,X11),v_U)) != hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U) )
| ~ spl559_149 ),
inference(resolution,[],[f25182,f30541]) ).
fof(f30541,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U))
| ~ spl559_149 ),
inference(avatar_component_clause,[],[f30539]) ).
fof(f25182,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X2,X3,X0),X1)) != hAPP(c_Finite__Set_Ocard(X2),X1)
| c_Fun_Oinj__on(X2,X3,X0,X1) ),
inference(cnf_transformation,[],[f18472]) ).
fof(f18472,plain,
! [X0,X1,X2,X3] :
( ( ( c_Fun_Oinj__on(X2,X3,X0,X1)
| hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X2,X3,X0),X1)) != hAPP(c_Finite__Set_Ocard(X2),X1) )
& ( hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X2,X3,X0),X1)) = hAPP(c_Finite__Set_Ocard(X2),X1)
| ~ c_Fun_Oinj__on(X2,X3,X0,X1) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(rectify,[],[f18471]) ).
fof(f18471,plain,
! [X1,X0,X2,X3] :
( ( ( c_Fun_Oinj__on(X2,X3,X1,X0)
| hAPP(c_Finite__Set_Ocard(X2),X0) != hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X2,X3,X1),X0)) )
& ( hAPP(c_Finite__Set_Ocard(X2),X0) = hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X2,X3,X1),X0))
| ~ c_Fun_Oinj__on(X2,X3,X1,X0) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0)) ),
inference(nnf_transformation,[],[f12421]) ).
fof(f12421,plain,
! [X1,X0,X2,X3] :
( ( c_Fun_Oinj__on(X2,X3,X1,X0)
<=> hAPP(c_Finite__Set_Ocard(X2),X0) = hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X2,X3,X1),X0)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0)) ),
inference(ennf_transformation,[],[f7701]) ).
fof(f7701,plain,
! [X3,X1,X2,X0] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0))
=> ( c_Fun_Oinj__on(X2,X3,X1,X0)
<=> hAPP(c_Finite__Set_Ocard(X2),X0) = hAPP(c_Finite__Set_Ocard(X3),hAPP(c_Set_Oimage(X2,X3,X1),X0)) ) ),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X10,X1,X8,X6] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X10))
=> ( c_Fun_Oinj__on(X8,X6,X1,X10)
<=> hAPP(c_Finite__Set_Ocard(X8),X10) = hAPP(c_Finite__Set_Ocard(X6),hAPP(c_Set_Oimage(X8,X6,X1),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inj__on__iff__eq__card) ).
fof(f36628,plain,
( spl559_443
| ~ spl559_271
| ~ spl559_417
| ~ spl559_428 ),
inference(avatar_split_clause,[],[f36627,f36203,f35991,f32170,f36600]) ).
fof(f36600,plain,
( spl559_443
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_443])]) ).
fof(f36203,plain,
( spl559_428
<=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_428])]) ).
fof(f36627,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_271
| ~ spl559_417
| ~ spl559_428 ),
inference(forward_demodulation,[],[f36611,f34703]) ).
fof(f34703,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),X0)
| ~ spl559_271 ),
inference(backward_demodulation,[],[f26659,f32172]) ).
fof(f26659,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,[],[f6931]) ).
fof(f6931,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,[],[f478]) ).
fof(f478,axiom,
! [X54] : 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)),X54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__0__eq__0) ).
fof(f36611,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl559_417
| ~ spl559_428 ),
inference(backward_demodulation,[],[f36205,f35992]) ).
fof(f36205,plain,
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)
| ~ spl559_428 ),
inference(avatar_component_clause,[],[f36203]) ).
fof(f36625,plain,
( spl559_442
| ~ spl559_417
| ~ spl559_438 ),
inference(avatar_split_clause,[],[f36620,f36490,f35991,f36590]) ).
fof(f36590,plain,
( spl559_442
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_442])]) ).
fof(f36490,plain,
( spl559_438
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_438])]) ).
fof(f36620,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ spl559_417
| ~ spl559_438 ),
inference(backward_demodulation,[],[f36492,f35992]) ).
fof(f36492,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)))
| ~ spl559_438 ),
inference(avatar_component_clause,[],[f36490]) ).
fof(f36605,plain,
( spl559_439
| ~ spl559_117
| ~ spl559_435 ),
inference(avatar_split_clause,[],[f36573,f36441,f30016,f36519]) ).
fof(f36573,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))
| ~ spl559_117
| ~ spl559_435 ),
inference(backward_demodulation,[],[f30018,f36442]) ).
fof(f36603,plain,
( spl559_443
| ~ spl559_271
| ~ spl559_434
| ~ spl559_435 ),
inference(avatar_split_clause,[],[f36598,f36441,f36436,f32170,f36600]) ).
fof(f36436,plain,
( spl559_434
<=> hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_434])]) ).
fof(f36598,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_271
| ~ spl559_434
| ~ spl559_435 ),
inference(forward_demodulation,[],[f36587,f34703]) ).
fof(f36587,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl559_434
| ~ spl559_435 ),
inference(backward_demodulation,[],[f36438,f36442]) ).
fof(f36438,plain,
( hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl559_434 ),
inference(avatar_component_clause,[],[f36436]) ).
fof(f36593,plain,
( spl559_442
| ~ spl559_431
| ~ spl559_435 ),
inference(avatar_split_clause,[],[f36586,f36441,f36424,f36590]) ).
fof(f36424,plain,
( spl559_431
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(t_a),v_G))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_431])]) ).
fof(f36586,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ spl559_431
| ~ spl559_435 ),
inference(backward_demodulation,[],[f36426,f36442]) ).
fof(f36426,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(t_a),v_G)))
| ~ spl559_431 ),
inference(avatar_component_clause,[],[f36424]) ).
fof(f36572,plain,
( spl559_435
| ~ spl559_117
| ~ spl559_271
| ~ spl559_418 ),
inference(avatar_split_clause,[],[f36571,f35995,f32170,f30016,f36441]) ).
fof(f36571,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(t_a),v_G)
| ~ spl559_117
| ~ spl559_271
| ~ spl559_418 ),
inference(forward_demodulation,[],[f36458,f34741]) ).
fof(f36458,plain,
( hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(c_Finite__Set_Ocard(t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)))
| ~ spl559_117
| ~ spl559_418 ),
inference(backward_demodulation,[],[f30018,f36455]) ).
fof(f36570,plain,
( spl559_435
| ~ spl559_117
| ~ spl559_271
| ~ spl559_418 ),
inference(avatar_split_clause,[],[f36527,f35995,f32170,f30016,f36441]) ).
fof(f36527,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(t_a),v_G)
| ~ spl559_117
| ~ spl559_271
| ~ spl559_418 ),
inference(forward_demodulation,[],[f36458,f34741]) ).
fof(f36567,plain,
( spl559_427
| spl559_441
| ~ spl559_149 ),
inference(avatar_split_clause,[],[f36247,f30539,f36564,f36199]) ).
fof(f36199,plain,
( spl559_427
<=> ! [X8] : ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X8),v_U)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_427])]) ).
fof(f36564,plain,
( spl559_441
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_441])]) ).
fof(f36247,plain,
( ! [X8] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X8),v_U)) )
| ~ spl559_149 ),
inference(resolution,[],[f31195,f30541]) ).
fof(f31195,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X0)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Finite__Set_Ocard(X2),X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0)) ),
inference(forward_subsumption_demodulation,[],[f31194,f30249]) ).
fof(f30249,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(c_fequal,X0))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X2)) ),
inference(forward_demodulation,[],[f23133,f29718]) ).
fof(f29718,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,[],[f26972,f26067]) ).
fof(f26067,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(cnf_transformation,[],[f8627]) ).
fof(f8627,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(rectify,[],[f3035]) ).
fof(f3035,axiom,
! [X28,X8] : hAPP(c_Set_OCollect(X8),X28) = X28,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Collect__def) ).
fof(f26972,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X0)) = hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(cnf_transformation,[],[f19803]) ).
fof(f19803,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X0)) = hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))),
inference(rectify,[],[f8466]) ).
fof(f8466,plain,
! [X1,X0] : hAPP(c_Set_OCollect(X0),hAPP(c_fequal,X1)) = hAPP(hAPP(c_Set_Oinsert(X0),X1),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(rectify,[],[f3051]) ).
fof(f3051,axiom,
! [X8,X30] : hAPP(hAPP(c_Set_Oinsert(X8),X30),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X8),hAPP(c_fequal,X30)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__conv2) ).
fof(f23133,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(cnf_transformation,[],[f12008]) ).
fof(f12008,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X2)) ),
inference(flattening,[],[f12007]) ).
fof(f12007,plain,
! [X0,X1,X2] :
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2)) ),
inference(ennf_transformation,[],[f8247]) ).
fof(f8247,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X2))
=> ( hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ) ),
inference(rectify,[],[f197]) ).
fof(f197,axiom,
! [X14,X8,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X10))
=> ( hBOOL(hAPP(hAPP(c_member(X8),X14),X10))
=> hAPP(c_Finite__Set_Ocard(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X10),hAPP(hAPP(c_Set_Oinsert(X8),X14),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X8),X10)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__singleton) ).
fof(f31194,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X0),hAPP(c_fequal,X1)))),hAPP(c_Finite__Set_Ocard(X2),X0))) ),
inference(forward_demodulation,[],[f23161,f29718]) ).
fof(f23161,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X0),hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X2),X0))) ),
inference(cnf_transformation,[],[f16899]) ).
fof(f16899,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X0),hAPP(hAPP(c_Set_Oinsert(X2),X1),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X2),X0))) ),
inference(rectify,[],[f11797]) ).
fof(f11797,plain,
! [X0,X2,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X0),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X0))) ),
inference(flattening,[],[f11796]) ).
fof(f11796,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X0),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(ennf_transformation,[],[f9021]) ).
fof(f9021,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
=> ( hBOOL(hAPP(hAPP(c_member(X1),X2),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X0),hAPP(hAPP(c_Set_Oinsert(X1),X2),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X1),X0))) ) ),
inference(rectify,[],[f198]) ).
fof(f198,axiom,
! [X10,X8,X14] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X10))
=> ( hBOOL(hAPP(hAPP(c_member(X8),X14),X10))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X10),hAPP(hAPP(c_Set_Oinsert(X8),X14),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(X8),X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff1__less) ).
fof(f36562,plain,
( spl559_440
| spl559_417
| ~ spl559_271
| ~ spl559_427 ),
inference(avatar_split_clause,[],[f36557,f36199,f32170,f35991,f36560]) ).
fof(f36560,plain,
( spl559_440
<=> ! [X0] : hAPP(c_Finite__Set_Ocard(tc_Com_Opname),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),X0),v_U)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_440])]) ).
fof(f36557,plain,
( ! [X0] :
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)
| hAPP(c_Finite__Set_Ocard(tc_Com_Opname),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),X0),v_U)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)) )
| ~ spl559_271
| ~ spl559_427 ),
inference(resolution,[],[f36200,f34738]) ).
fof(f34738,plain,
( ! [X0,X6,X5] :
( hBOOL(hAPP(hAPP(c_member(X0),X5),X6))
| hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X0),X6)) = hAPP(c_Finite__Set_Ocard(X0),hAPP(hAPP(c_Set_Oinsert(X0),X5),X6))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X6) )
| ~ spl559_271 ),
inference(backward_demodulation,[],[f28332,f32172]) ).
fof(f28332,plain,
! [X0,X6,X5] :
( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X0),X6)) = hAPP(c_Finite__Set_Ocard(X0),hAPP(hAPP(c_Set_Oinsert(X0),X5),X6))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X6)
| hBOOL(hAPP(hAPP(c_member(X0),X5),X6)) ),
inference(equality_resolution,[],[f28331]) ).
fof(f28331,plain,
! [X2,X0,X6,X5] :
( hAPP(c_Finite__Set_Ocard(X0),X2) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X0),X6))
| hBOOL(hAPP(hAPP(c_member(X0),X5),X6))
| hAPP(hAPP(c_Set_Oinsert(X0),X5),X6) != X2
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X6) ),
inference(equality_resolution,[],[f20706]) ).
fof(f20706,plain,
! [X2,X0,X1,X6,X5] :
( hAPP(c_Finite__Set_Ocard(X0),X2) = hAPP(c_Nat_OSuc,X1)
| hAPP(c_Finite__Set_Ocard(X0),X6) != X1
| hBOOL(hAPP(hAPP(c_member(X0),X5),X6))
| hAPP(hAPP(c_Set_Oinsert(X0),X5),X6) != X2
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ),
inference(cnf_transformation,[],[f15083]) ).
fof(f15083,plain,
! [X0,X1,X2] :
( ( ( hAPP(c_Finite__Set_Ocard(X0),sK59(X0,X1,X2)) = X1
& ~ hBOOL(hAPP(hAPP(c_member(X0),sK58(X0,X1,X2)),sK59(X0,X1,X2)))
& hAPP(hAPP(c_Set_Oinsert(X0),sK58(X0,X1,X2)),sK59(X0,X1,X2)) = X2
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = sK59(X0,X1,X2) ) )
| hAPP(c_Finite__Set_Ocard(X0),X2) != hAPP(c_Nat_OSuc,X1) )
& ( hAPP(c_Finite__Set_Ocard(X0),X2) = hAPP(c_Nat_OSuc,X1)
| ! [X5,X6] :
( hAPP(c_Finite__Set_Ocard(X0),X6) != X1
| hBOOL(hAPP(hAPP(c_member(X0),X5),X6))
| hAPP(hAPP(c_Set_Oinsert(X0),X5),X6) != X2
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != X6 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK58,sK59])],[f15081,f15082]) ).
fof(f15082,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( hAPP(c_Finite__Set_Ocard(X0),X4) = X1
& ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X4))
& hAPP(hAPP(c_Set_Oinsert(X0),X3),X4) = X2
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X4 ) )
=> ( hAPP(c_Finite__Set_Ocard(X0),sK59(X0,X1,X2)) = X1
& ~ hBOOL(hAPP(hAPP(c_member(X0),sK58(X0,X1,X2)),sK59(X0,X1,X2)))
& hAPP(hAPP(c_Set_Oinsert(X0),sK58(X0,X1,X2)),sK59(X0,X1,X2)) = X2
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = sK59(X0,X1,X2) ) ) ),
introduced(choice_axiom,[]) ).
fof(f15081,plain,
! [X0,X1,X2] :
( ( ? [X3,X4] :
( hAPP(c_Finite__Set_Ocard(X0),X4) = X1
& ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X4))
& hAPP(hAPP(c_Set_Oinsert(X0),X3),X4) = X2
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X4 ) )
| hAPP(c_Finite__Set_Ocard(X0),X2) != hAPP(c_Nat_OSuc,X1) )
& ( hAPP(c_Finite__Set_Ocard(X0),X2) = hAPP(c_Nat_OSuc,X1)
| ! [X5,X6] :
( hAPP(c_Finite__Set_Ocard(X0),X6) != X1
| hBOOL(hAPP(hAPP(c_member(X0),X5),X6))
| hAPP(hAPP(c_Set_Oinsert(X0),X5),X6) != X2
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != X6 ) ) ) ),
inference(rectify,[],[f15080]) ).
fof(f15080,plain,
! [X0,X1,X2] :
( ( ? [X3,X4] :
( hAPP(c_Finite__Set_Ocard(X0),X4) = X1
& ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X4))
& hAPP(hAPP(c_Set_Oinsert(X0),X3),X4) = X2
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X4 ) )
| hAPP(c_Finite__Set_Ocard(X0),X2) != hAPP(c_Nat_OSuc,X1) )
& ( hAPP(c_Finite__Set_Ocard(X0),X2) = hAPP(c_Nat_OSuc,X1)
| ! [X3,X4] :
( hAPP(c_Finite__Set_Ocard(X0),X4) != X1
| hBOOL(hAPP(hAPP(c_member(X0),X3),X4))
| hAPP(hAPP(c_Set_Oinsert(X0),X3),X4) != X2
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != X4 ) ) ) ),
inference(nnf_transformation,[],[f14087]) ).
fof(f14087,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( hAPP(c_Finite__Set_Ocard(X0),X4) = X1
& ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X4))
& hAPP(hAPP(c_Set_Oinsert(X0),X3),X4) = X2
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X4 ) )
<=> hAPP(c_Finite__Set_Ocard(X0),X2) = hAPP(c_Nat_OSuc,X1) ),
inference(ennf_transformation,[],[f8263]) ).
fof(f8263,plain,
! [X1,X0,X2] :
( hAPP(c_Finite__Set_Ocard(X0),X2) = hAPP(c_Nat_OSuc,X1)
<=> ? [X4,X3] :
( ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X4))
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X4 )
& hAPP(c_Finite__Set_Ocard(X0),X4) = X1
& hAPP(hAPP(c_Set_Oinsert(X0),X3),X4) = X2 ) ),
inference(rectify,[],[f538]) ).
fof(f538,axiom,
! [X8,X44,X10] :
( hAPP(c_Finite__Set_Ocard(X8),X10) = hAPP(c_Nat_OSuc,X44)
<=> ? [X76,X77] :
( hAPP(hAPP(c_Set_Oinsert(X8),X76),X77) = X10
& ~ hBOOL(hAPP(hAPP(c_member(X8),X76),X77))
& hAPP(c_Finite__Set_Ocard(X8),X77) = X44
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X44
=> c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = X77 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__eq) ).
fof(f36200,plain,
( ! [X8] : ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X8),v_U))
| ~ spl559_427 ),
inference(avatar_component_clause,[],[f36199]) ).
fof(f36558,plain,
( spl559_417
| ~ spl559_149
| ~ spl559_271
| ~ spl559_427 ),
inference(avatar_split_clause,[],[f36556,f36199,f32170,f30539,f35991]) ).
fof(f36556,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)
| ~ spl559_271
| ~ spl559_427 ),
inference(resolution,[],[f36200,f34665]) ).
fof(f34665,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),sK426(X0,X1)),X1))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1)) )
| ~ spl559_271 ),
inference(backward_demodulation,[],[f25403,f32172]) ).
fof(f25403,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| hBOOL(hAPP(hAPP(c_member(X0),sK426(X0,X1)),X1)) ),
inference(cnf_transformation,[],[f18647]) ).
fof(f18647,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X1)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(X0),sK426(X0,X1)),X1)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK426])],[f18645,f18646]) ).
fof(f18646,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(hAPP(c_member(X0),X2),X1))
=> hBOOL(hAPP(hAPP(c_member(X0),sK426(X0,X1)),X1)) ),
introduced(choice_axiom,[]) ).
fof(f18645,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X1)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [X2] : hBOOL(hAPP(hAPP(c_member(X0),X2),X1)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1)) ),
inference(rectify,[],[f12885]) ).
fof(f12885,plain,
! [X1,X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [X2] : hBOOL(hAPP(hAPP(c_member(X1),X2),X0)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(flattening,[],[f12884]) ).
fof(f12884,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0)
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [X2] : hBOOL(hAPP(hAPP(c_member(X1),X2),X0)) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(ennf_transformation,[],[f5680]) ).
fof(f5680,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
=> ( ( ? [X2] : hBOOL(hAPP(hAPP(c_member(X1),X2),X0))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X1),X0) ) ),
inference(rectify,[],[f581]) ).
fof(f581,axiom,
! [X10,X8] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X10))
=> ( ( ? [X2] : hBOOL(hAPP(hAPP(c_member(X8),X2),X10))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> hAPP(c_Finite__Set_Ocard(X8),X10) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Oneutral) ).
fof(f36522,plain,
( spl559_439
| ~ spl559_117
| ~ spl559_435 ),
inference(avatar_split_clause,[],[f36498,f36441,f30016,f36519]) ).
fof(f36498,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))
| ~ spl559_117
| ~ spl559_435 ),
inference(backward_demodulation,[],[f30018,f36442]) ).
fof(f36495,plain,
( spl559_435
| ~ spl559_117
| ~ spl559_271
| ~ spl559_418 ),
inference(avatar_split_clause,[],[f36483,f35995,f32170,f30016,f36441]) ).
fof(f36483,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(t_a),v_G)
| ~ spl559_117
| ~ spl559_271
| ~ spl559_418 ),
inference(forward_demodulation,[],[f36458,f34741]) ).
fof(f36493,plain,
( spl559_418
| spl559_438
| ~ spl559_149
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f36047,f32170,f30539,f36490,f35995]) ).
fof(f36047,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)))
| v_U = c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))
| ~ spl559_149
| ~ spl559_271 ),
inference(resolution,[],[f34615,f30541]) ).
fof(f34615,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X0)))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 )
| ~ spl559_271 ),
inference(backward_demodulation,[],[f23506,f32172]) ).
fof(f23506,plain,
! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X0))) ),
inference(cnf_transformation,[],[f17152]) ).
fof(f17152,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
& c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0 )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X0))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X0)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 ) ),
inference(flattening,[],[f17151]) ).
fof(f17151,plain,
! [X0,X1] :
( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
& c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0 )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X0))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X0)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 ) ),
inference(nnf_transformation,[],[f7987]) ).
fof(f7987,plain,
! [X0,X1] :
( ( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
& c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0 )
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X1),X0))) ),
inference(rectify,[],[f527]) ).
fof(f527,axiom,
! [X10,X8] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(X8),X10)))
<=> ( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) != X10
& hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__gt__0__iff) ).
fof(f36484,plain,
( spl559_435
| ~ spl559_117
| ~ spl559_271
| ~ spl559_418 ),
inference(avatar_split_clause,[],[f36483,f35995,f32170,f30016,f36441]) ).
fof(f36476,plain,
( ~ spl559_437
| ~ spl559_418
| spl559_421
| ~ spl559_432 ),
inference(avatar_split_clause,[],[f36471,f36428,f36021,f35995,f36473]) ).
fof(f36021,plain,
( spl559_421
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)),v_G)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_421])]) ).
fof(f36428,plain,
( spl559_432
<=> c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)) = v_G ),
introduced(avatar_definition,[new_symbols(naming,[spl559_432])]) ).
fof(f36471,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),v_G))
| ~ spl559_418
| spl559_421
| ~ spl559_432 ),
inference(forward_demodulation,[],[f36463,f36430]) ).
fof(f36430,plain,
( c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)) = v_G
| ~ spl559_432 ),
inference(avatar_component_clause,[],[f36428]) ).
fof(f36463,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool))),v_G))
| ~ spl559_418
| spl559_421 ),
inference(backward_demodulation,[],[f36023,f36455]) ).
fof(f36023,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)),v_G))
| spl559_421 ),
inference(avatar_component_clause,[],[f36021]) ).
fof(f36449,plain,
( spl559_436
| spl559_433
| ~ spl559_419 ),
inference(avatar_split_clause,[],[f36418,f36002,f36433,f36446]) ).
fof(f36446,plain,
( spl559_436
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Finite__Set_Ocard(t_a),v_G))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_436])]) ).
fof(f36433,plain,
( spl559_433
<=> ! [X38] : ~ hBOOL(hAPP(hAPP(c_member(t_a),X38),v_G)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_433])]) ).
fof(f36002,plain,
( spl559_419
<=> hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_G)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_419])]) ).
fof(f36418,plain,
( ! [X35] :
( ~ hBOOL(hAPP(hAPP(c_member(t_a),X35),v_G))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Finite__Set_Ocard(t_a),v_G))) )
| ~ spl559_419 ),
inference(resolution,[],[f36004,f31195]) ).
fof(f36004,plain,
( hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_G))
| ~ spl559_419 ),
inference(avatar_component_clause,[],[f36002]) ).
fof(f36444,plain,
( ~ spl559_435
| spl559_432
| ~ spl559_271
| ~ spl559_419 ),
inference(avatar_split_clause,[],[f36421,f36002,f32170,f36428,f36441]) ).
fof(f36421,plain,
( c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)) = v_G
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) != hAPP(c_Finite__Set_Ocard(t_a),v_G)
| ~ spl559_271
| ~ spl559_419 ),
inference(resolution,[],[f36004,f34550]) ).
fof(f34550,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) != hAPP(c_Finite__Set_Ocard(X1),X0)
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 )
| ~ spl559_271 ),
inference(backward_demodulation,[],[f21365,f32172]) ).
fof(f21365,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Finite__Set_Ocard(X1),X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 ),
inference(cnf_transformation,[],[f15577]) ).
fof(f36439,plain,
( spl559_433
| spl559_434
| ~ spl559_419 ),
inference(avatar_split_clause,[],[f36420,f36002,f36436,f36433]) ).
fof(f36420,plain,
( ! [X38] :
( hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_member(t_a),X38),v_G)) )
| ~ spl559_419 ),
inference(resolution,[],[f36004,f33614]) ).
fof(f33614,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X0),X1))
| hAPP(c_Finite__Set_Ocard(X2),X1) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X1)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(forward_subsumption_demodulation,[],[f33613,f30249]) ).
fof(f33613,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X0),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| hAPP(c_Finite__Set_Ocard(X2),X1) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(c_fequal,X0)))) ),
inference(forward_demodulation,[],[f22707,f29718]) ).
fof(f22707,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X0),X1))
| hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X2),X1) ),
inference(cnf_transformation,[],[f16559]) ).
fof(f16559,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X0),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(X2),X1) ),
inference(rectify,[],[f11552]) ).
fof(f11552,plain,
! [X2,X1,X0] :
( ~ hBOOL(hAPP(hAPP(c_member(X0),X2),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| hAPP(c_Finite__Set_Ocard(X0),X1) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))))) ),
inference(flattening,[],[f11551]) ).
fof(f11551,plain,
! [X0,X1,X2] :
( hAPP(c_Finite__Set_Ocard(X0),X1) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X2),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1)) ),
inference(ennf_transformation,[],[f7591]) ).
fof(f7591,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
=> ( hBOOL(hAPP(hAPP(c_member(X0),X2),X1))
=> hAPP(c_Finite__Set_Ocard(X0),X1) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(hAPP(c_Set_Oinsert(X0),X2),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))))) ) ),
inference(rectify,[],[f201]) ).
fof(f201,axiom,
! [X8,X10,X14] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X10))
=> ( hBOOL(hAPP(hAPP(c_member(X8),X14),X10))
=> hAPP(c_Finite__Set_Ocard(X8),X10) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X10),hAPP(hAPP(c_Set_Oinsert(X8),X14),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Suc__Diff1) ).
fof(f36431,plain,
( spl559_431
| spl559_432
| ~ spl559_271
| ~ spl559_419 ),
inference(avatar_split_clause,[],[f36422,f36002,f32170,f36428,f36424]) ).
fof(f36422,plain,
( c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_HOL_Obool)) = v_G
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(t_a),v_G)))
| ~ spl559_271
| ~ spl559_419 ),
inference(resolution,[],[f36004,f34615]) ).
fof(f36297,plain,
( spl559_430
| ~ spl559_419
| ~ spl559_117
| ~ spl559_271
| ~ spl559_336 ),
inference(avatar_split_clause,[],[f36292,f34104,f32170,f30016,f36002,f36294]) ).
fof(f36294,plain,
( spl559_430
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(t_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)),v_G)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_430])]) ).
fof(f36292,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_G))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(t_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)),v_G))
| ~ spl559_117
| ~ spl559_271
| ~ spl559_336 ),
inference(forward_demodulation,[],[f36291,f34713]) ).
fof(f34713,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0)
| ~ spl559_271 ),
inference(backward_demodulation,[],[f26859,f32172]) ).
fof(f26859,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,[],[f7943]) ).
fof(f7943,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0),
inference(rectify,[],[f480]) ).
fof(f480,axiom,
! [X55] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X55),X55),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__self__eq__0) ).
fof(f36291,plain,
( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),v_G)),hAPP(c_Finite__Set_Ocard(t_a),v_G)) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(t_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)),v_G))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_G))
| ~ spl559_117
| ~ spl559_336 ),
inference(forward_demodulation,[],[f36288,f30018]) ).
fof(f36288,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_G))
| hAPP(c_Finite__Set_Ocard(t_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(t_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)),v_G)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),hAPP(c_Finite__Set_Ocard(t_a),v_G))
| ~ spl559_336 ),
inference(resolution,[],[f22323,f34106]) ).
fof(f22323,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0))
| hAPP(c_Finite__Set_Ocard(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X0),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X0)),hAPP(c_Finite__Set_Ocard(X2),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(cnf_transformation,[],[f16279]) ).
fof(f16279,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0))
| hAPP(c_Finite__Set_Ocard(X2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool)),X0),X1)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X2),X0)),hAPP(c_Finite__Set_Ocard(X2),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(rectify,[],[f10860]) ).
fof(f10860,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X2))
| hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X0)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(flattening,[],[f10859]) ).
fof(f10859,plain,
! [X1,X2,X0] :
( hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X0)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(ennf_transformation,[],[f5909]) ).
fof(f5909,plain,
! [X1,X2,X0] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X2))
=> hAPP(c_Finite__Set_Ocard(X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X1,tc_HOL_Obool)),X2),X0)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X1),X2)),hAPP(c_Finite__Set_Ocard(X1),X0)) ) ),
inference(rectify,[],[f192]) ).
fof(f192,axiom,
! [X9,X8,X10] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X9))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X9),X10))
=> hAPP(c_Finite__Set_Ocard(X8),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool)),X10),X9)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X8),X10)),hAPP(c_Finite__Set_Ocard(X8),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__Diff__subset) ).
fof(f36236,plain,
( spl559_429
| spl559_417
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f36224,f32170,f35991,f36234]) ).
fof(f36234,plain,
( spl559_429
<=> ! [X0] :
( v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X0)))
| hAPP(c_Finite__Set_Ocard(tc_Com_Opname),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),X0),v_U)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_429])]) ).
fof(f36224,plain,
( ! [X0] :
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)
| v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X0)))
| hAPP(c_Finite__Set_Ocard(tc_Com_Opname),hAPP(hAPP(c_Set_Oinsert(tc_Com_Opname),X0),v_U)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)) )
| ~ spl559_271 ),
inference(resolution,[],[f34738,f21897]) ).
fof(f21897,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_U))
| v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X0))) ),
inference(cnf_transformation,[],[f10830]) ).
fof(f10830,plain,
! [X0] :
( v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_U)) ),
inference(ennf_transformation,[],[f6645]) ).
fof(f6645,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X0),v_U))
=> v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X0))) ),
inference(rectify,[],[f47]) ).
fof(f47,axiom,
! [X29] :
( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X29),v_U))
=> v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(X29))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I4_J) ).
fof(f36206,plain,
( spl559_427
| spl559_428
| ~ spl559_149 ),
inference(avatar_split_clause,[],[f36193,f30539,f36203,f36199]) ).
fof(f36193,plain,
( ! [X8] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X8),v_U)) )
| ~ spl559_149 ),
inference(resolution,[],[f33614,f30541]) ).
fof(f36201,plain,
( spl559_427
| spl559_364
| ~ spl559_149
| ~ spl559_271
| ~ spl559_361
| ~ spl559_417 ),
inference(avatar_split_clause,[],[f36197,f35991,f34863,f32170,f30539,f34890,f36199]) ).
fof(f34890,plain,
( spl559_364
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_364])]) ).
fof(f34863,plain,
( spl559_361
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_361])]) ).
fof(f36197,plain,
( ! [X8] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat)
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X8),v_U)) )
| ~ spl559_149
| ~ spl559_271
| ~ spl559_361
| ~ spl559_417 ),
inference(forward_demodulation,[],[f36196,f34865]) ).
fof(f34865,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_361 ),
inference(avatar_component_clause,[],[f34863]) ).
fof(f36196,plain,
( ! [X8] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X8),v_U))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) )
| ~ spl559_149
| ~ spl559_271
| ~ spl559_417 ),
inference(forward_demodulation,[],[f36195,f34703]) ).
fof(f36195,plain,
( ! [X8] :
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),X8),v_U)) )
| ~ spl559_149
| ~ spl559_417 ),
inference(forward_demodulation,[],[f36193,f35992]) ).
fof(f36184,plain,
( spl559_426
| ~ spl559_336 ),
inference(avatar_split_clause,[],[f36174,f34104,f36181]) ).
fof(f36181,plain,
( spl559_426
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Com_Opname,tc_HOL_Obool)),sK151(t_a,v_G,tc_Com_Opname,v_U,v_mgt__call)),v_U)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_426])]) ).
fof(f36174,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Com_Opname,tc_HOL_Obool)),sK151(t_a,v_G,tc_Com_Opname,v_U,v_mgt__call)),v_U))
| ~ spl559_336 ),
inference(resolution,[],[f22107,f34106]) ).
fof(f22107,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(X2,X0,X4),X3)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),sK151(X0,X1,X2,X3,X4)),X3)) ),
inference(cnf_transformation,[],[f16108]) ).
fof(f16108,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(X2,X0,X4),X3)))
| ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),X3))
| hAPP(c_Set_Oimage(X2,X0,X4),X5) != X1 ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),sK151(X0,X1,X2,X3,X4)),X3))
& hAPP(c_Set_Oimage(X2,X0,X4),sK151(X0,X1,X2,X3,X4)) = X1 )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(X2,X0,X4),X3))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK151])],[f16106,f16107]) ).
fof(f16107,plain,
! [X0,X1,X2,X3,X4] :
( ? [X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X6),X3))
& hAPP(c_Set_Oimage(X2,X0,X4),X6) = X1 )
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),sK151(X0,X1,X2,X3,X4)),X3))
& hAPP(c_Set_Oimage(X2,X0,X4),sK151(X0,X1,X2,X3,X4)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f16106,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(X2,X0,X4),X3)))
| ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X5),X3))
| hAPP(c_Set_Oimage(X2,X0,X4),X5) != X1 ) )
& ( ? [X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X6),X3))
& hAPP(c_Set_Oimage(X2,X0,X4),X6) = X1 )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(X2,X0,X4),X3))) ) ),
inference(rectify,[],[f16105]) ).
fof(f16105,plain,
! [X1,X4,X3,X0,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X3,X1,X2),X0)))
| ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X5),X0))
| hAPP(c_Set_Oimage(X3,X1,X2),X5) != X4 ) )
& ( ? [X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X5),X0))
& hAPP(c_Set_Oimage(X3,X1,X2),X5) = X4 )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X3,X1,X2),X0))) ) ),
inference(nnf_transformation,[],[f7968]) ).
fof(f7968,plain,
! [X1,X4,X3,X0,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X4),hAPP(c_Set_Oimage(X3,X1,X2),X0)))
<=> ? [X5] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool)),X5),X0))
& hAPP(c_Set_Oimage(X3,X1,X2),X5) = X4 ) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X10,X8,X1,X6,X9] :
( ? [X13] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool)),X13),X10))
& hAPP(c_Set_Oimage(X6,X8,X1),X13) = X9 )
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X9),hAPP(c_Set_Oimage(X6,X8,X1),X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__image__iff) ).
fof(f36145,plain,
( spl559_425
| ~ spl559_336 ),
inference(avatar_split_clause,[],[f36135,f34104,f36142]) ).
fof(f36142,plain,
( spl559_425
<=> v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),sK151(t_a,v_G,tc_Com_Opname,v_U,v_mgt__call)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_425])]) ).
fof(f36135,plain,
( v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),sK151(t_a,v_G,tc_Com_Opname,v_U,v_mgt__call))
| ~ spl559_336 ),
inference(resolution,[],[f22106,f34106]) ).
fof(f22106,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(c_Set_Oimage(X2,X0,X4),X3)))
| hAPP(c_Set_Oimage(X2,X0,X4),sK151(X0,X1,X2,X3,X4)) = X1 ),
inference(cnf_transformation,[],[f16108]) ).
fof(f36078,plain,
( spl559_423
| spl559_424 ),
inference(avatar_split_clause,[],[f36070,f36076,f36073]) ).
fof(f36076,plain,
( spl559_424
<=> ! [X1,X3] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_424])]) ).
fof(f36070,plain,
! [X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X3),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X3)) ),
inference(superposition,[],[f20831,f25092]) ).
fof(f20831,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X0,X4,X1),X3)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X3)) ),
inference(cnf_transformation,[],[f15176]) ).
fof(f15176,plain,
! [X0,X1,X2,X3,X4] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X0,X4,X1),X3)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X2)) ),
inference(rectify,[],[f11851]) ).
fof(f11851,plain,
! [X4,X1,X2,X3,X0] :
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X4,X0,X1),X3)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2)) ),
inference(flattening,[],[f11850]) ).
fof(f11850,plain,
! [X0,X3,X4,X2,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X4,X0,X1),X3)))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3)) ),
inference(ennf_transformation,[],[f7326]) ).
fof(f7326,plain,
! [X0,X3,X4,X2,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X3))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),hAPP(c_Set_Oimage(X4,X0,X1),X3)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2)) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X6,X1,X9,X10,X8] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X10))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X6,tc_HOL_Obool)),X9),hAPP(c_Set_Oimage(X8,X6,X1),X10)))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X6),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__surj) ).
fof(f36071,plain,
( spl559_419
| ~ spl559_149
| ~ spl559_336 ),
inference(avatar_split_clause,[],[f36068,f34104,f30539,f36002]) ).
fof(f36068,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U))
| hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_G))
| ~ spl559_336 ),
inference(resolution,[],[f20831,f34106]) ).
fof(f36040,plain,
( ~ spl559_149
| spl559_422
| spl559_417
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f36033,f32170,f35991,f36037,f30539]) ).
fof(f36037,plain,
( spl559_422
<=> v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(sK426(tc_Com_Opname,v_U)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_422])]) ).
fof(f36033,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)
| v_wt(c_Option_Othe(tc_Com_Ocom,c_Com_Obody(sK426(tc_Com_Opname,v_U))))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U))
| ~ spl559_271 ),
inference(resolution,[],[f34665,f21897]) ).
fof(f36024,plain,
( ~ spl559_421
| spl559_51
| ~ spl559_336 ),
inference(avatar_split_clause,[],[f36019,f34104,f29233,f36021]) ).
fof(f36019,plain,
( v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)),v_G))
| ~ spl559_336 ),
inference(resolution,[],[f21324,f34106]) ).
fof(f21324,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X1))
| X1 = X2 ),
inference(cnf_transformation,[],[f15543]) ).
fof(f15543,plain,
! [X0,X1,X2] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2)) )
| X1 != X2 )
& ( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2)) ) ),
inference(rectify,[],[f15542]) ).
fof(f15542,plain,
! [X0,X2,X1] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X1)) )
| X1 != X2 )
& ( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X1)) ) ),
inference(flattening,[],[f15541]) ).
fof(f15541,plain,
! [X0,X2,X1] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X1)) )
| X1 != X2 )
& ( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X1)) ) ),
inference(nnf_transformation,[],[f5672]) ).
fof(f5672,plain,
! [X0,X2,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X1),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X1)) )
<=> X1 = X2 ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X8,X9,X10] :
( X9 = X10
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X9),X10))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X10),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
fof(f36009,plain,
( spl559_419
| ~ spl559_420
| ~ spl559_336 ),
inference(avatar_split_clause,[],[f35999,f34104,f36006,f36002]) ).
fof(f35999,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)))
| hBOOL(hAPP(c_Finite__Set_Ofinite(t_a),v_G))
| ~ spl559_336 ),
inference(resolution,[],[f21084,f34106]) ).
fof(f21084,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2)) ),
inference(cnf_transformation,[],[f15359]) ).
fof(f15359,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool)),X2),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2)) ),
inference(rectify,[],[f11989]) ).
fof(f11989,plain,
! [X2,X1,X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X0),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0)) ),
inference(flattening,[],[f11988]) ).
fof(f11988,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X0),X1)) ),
inference(ennf_transformation,[],[f8686]) ).
fof(f8686,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X0),X1))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X0)) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X10,X9,X8] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool)),X10),X9))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X9))
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_finite__subset) ).
fof(f35998,plain,
( ~ spl559_417
| spl559_418
| ~ spl559_149
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35988,f32170,f30539,f35995,f35991]) ).
fof(f35988,plain,
( v_U = c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) != hAPP(c_Finite__Set_Ocard(tc_Com_Opname),v_U)
| ~ spl559_149
| ~ spl559_271 ),
inference(resolution,[],[f34550,f30541]) ).
fof(f35966,plain,
( spl559_416
| ~ spl559_336 ),
inference(avatar_split_clause,[],[f35960,f34104,f35963]) ).
fof(f35963,plain,
( spl559_416
<=> v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),v_G) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_416])]) ).
fof(f35960,plain,
( v_P(hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),v_G)
| ~ spl559_336 ),
inference(resolution,[],[f21728,f34106]) ).
fof(f21728,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X1),X0))
| v_P(X0,X1) ),
inference(cnf_transformation,[],[f12167]) ).
fof(f12167,plain,
! [X0,X1] :
( v_P(X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X1),X0)) ),
inference(ennf_transformation,[],[f5344]) ).
fof(f5344,plain,
! [X1,X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X1),X0))
=> v_P(X0,X1) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X3,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),X4),X3))
=> v_P(X3,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I1_J) ).
fof(f35959,plain,
( spl559_415
| ~ spl559_356
| ~ spl559_412 ),
inference(avatar_split_clause,[],[f35954,f35933,f34415,f35956]) ).
fof(f35956,plain,
( spl559_415
<=> hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_415])]) ).
fof(f34415,plain,
( spl559_356
<=> hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_356])]) ).
fof(f35933,plain,
( spl559_412
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_412])]) ).
fof(f35954,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl559_356
| ~ spl559_412 ),
inference(backward_demodulation,[],[f34417,f35935]) ).
fof(f35935,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl559_412 ),
inference(avatar_component_clause,[],[f35933]) ).
fof(f34417,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)))
| ~ spl559_356 ),
inference(avatar_component_clause,[],[f34415]) ).
fof(f35953,plain,
( spl559_414
| ~ spl559_361
| ~ spl559_409 ),
inference(avatar_split_clause,[],[f35948,f35907,f34863,f35950]) ).
fof(f35950,plain,
( spl559_414
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_414])]) ).
fof(f35907,plain,
( spl559_409
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_409])]) ).
fof(f35948,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl559_361
| ~ spl559_409 ),
inference(forward_demodulation,[],[f35909,f34865]) ).
fof(f35909,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))))
| ~ spl559_409 ),
inference(avatar_component_clause,[],[f35907]) ).
fof(f35945,plain,
( spl559_413
| ~ spl559_271
| ~ spl559_351
| ~ spl559_361 ),
inference(avatar_split_clause,[],[f35940,f34863,f34358,f32170,f35942]) ).
fof(f35942,plain,
( spl559_413
<=> hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_413])]) ).
fof(f34358,plain,
( spl559_351
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_351])]) ).
fof(f35940,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)))
| ~ spl559_271
| ~ spl559_351
| ~ spl559_361 ),
inference(forward_demodulation,[],[f35939,f34865]) ).
fof(f35939,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)))
| ~ spl559_271
| ~ spl559_351 ),
inference(forward_demodulation,[],[f34360,f32172]) ).
fof(f34360,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)))
| ~ spl559_351 ),
inference(avatar_component_clause,[],[f34358]) ).
fof(f35936,plain,
( spl559_412
| ~ spl559_361
| ~ spl559_388 ),
inference(avatar_split_clause,[],[f35931,f35761,f34863,f35933]) ).
fof(f35761,plain,
( spl559_388
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_388])]) ).
fof(f35931,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl559_361
| ~ spl559_388 ),
inference(forward_demodulation,[],[f35763,f34865]) ).
fof(f35763,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)))
| ~ spl559_388 ),
inference(avatar_component_clause,[],[f35761]) ).
fof(f35930,plain,
( ~ spl559_411
| spl559_366
| ~ spl559_387 ),
inference(avatar_split_clause,[],[f35923,f35755,f34902,f35927]) ).
fof(f35927,plain,
( spl559_411
<=> 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,[spl559_411])]) ).
fof(f34902,plain,
( spl559_366
<=> 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_Orderings_Obot__class_Obot(tc_Nat_Onat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_366])]) ).
fof(f35755,plain,
( spl559_387
<=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_387])]) ).
fof(f35923,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)))
| spl559_366
| ~ spl559_387 ),
inference(backward_demodulation,[],[f34904,f35757]) ).
fof(f35757,plain,
( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_387 ),
inference(avatar_component_clause,[],[f35755]) ).
fof(f34904,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_Orderings_Obot__class_Obot(tc_Nat_Onat))))
| spl559_366 ),
inference(avatar_component_clause,[],[f34902]) ).
fof(f35922,plain,
( ~ spl559_410
| ~ spl559_361
| spl559_381 ),
inference(avatar_split_clause,[],[f35917,f35713,f34863,f35919]) ).
fof(f35919,plain,
( spl559_410
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_410])]) ).
fof(f35713,plain,
( spl559_381
<=> hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_381])]) ).
fof(f35917,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_361
| spl559_381 ),
inference(forward_demodulation,[],[f35715,f34865]) ).
fof(f35715,plain,
( hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| spl559_381 ),
inference(avatar_component_clause,[],[f35713]) ).
fof(f35914,plain,
( spl559_380
| ~ spl559_361
| ~ spl559_404 ),
inference(avatar_split_clause,[],[f35912,f35876,f34863,f35706]) ).
fof(f35706,plain,
( spl559_380
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_380])]) ).
fof(f35876,plain,
( spl559_404
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_404])]) ).
fof(f35912,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| ~ spl559_361
| ~ spl559_404 ),
inference(backward_demodulation,[],[f35878,f34865]) ).
fof(f35878,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_404 ),
inference(avatar_component_clause,[],[f35876]) ).
fof(f35910,plain,
( spl559_409
| ~ spl559_271
| ~ spl559_354 ),
inference(avatar_split_clause,[],[f35905,f34397,f32170,f35907]) ).
fof(f34397,plain,
( spl559_354
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_354])]) ).
fof(f35905,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))))
| ~ spl559_271
| ~ spl559_354 ),
inference(forward_demodulation,[],[f34399,f32172]) ).
fof(f34399,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))
| ~ spl559_354 ),
inference(avatar_component_clause,[],[f34397]) ).
fof(f35904,plain,
( spl559_408
| ~ spl559_146
| ~ spl559_372 ),
inference(avatar_split_clause,[],[f35899,f34958,f30519,f35901]) ).
fof(f35901,plain,
( spl559_408
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_408])]) ).
fof(f30519,plain,
( spl559_146
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl559_146])]) ).
fof(f34958,plain,
( spl559_372
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_372])]) ).
fof(f35899,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls)
| ~ spl559_146
| ~ spl559_372 ),
inference(forward_demodulation,[],[f34960,f30521]) ).
fof(f30521,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls
| ~ spl559_146 ),
inference(avatar_component_clause,[],[f30519]) ).
fof(f34960,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl559_372 ),
inference(avatar_component_clause,[],[f34958]) ).
fof(f35898,plain,
( spl559_407
| ~ spl559_271
| ~ spl559_352 ),
inference(avatar_split_clause,[],[f35893,f34368,f32170,f35895]) ).
fof(f35895,plain,
( spl559_407
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_407])]) ).
fof(f34368,plain,
( spl559_352
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_352])]) ).
fof(f35893,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))
| ~ spl559_271
| ~ spl559_352 ),
inference(forward_demodulation,[],[f34370,f32172]) ).
fof(f34370,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))
| ~ spl559_352 ),
inference(avatar_component_clause,[],[f34368]) ).
fof(f35891,plain,
( spl559_406
| ~ spl559_80
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35886,f32170,f29580,f35888]) ).
fof(f35888,plain,
( spl559_406
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_406])]) ).
fof(f29580,plain,
( spl559_80
<=> 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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_80])]) ).
fof(f35886,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| ~ spl559_80
| ~ spl559_271 ),
inference(forward_demodulation,[],[f29582,f32172]) ).
fof(f29582,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))
| ~ spl559_80 ),
inference(avatar_component_clause,[],[f29580]) ).
fof(f35885,plain,
( spl559_405
| ~ spl559_54
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35880,f32170,f29254,f35882]) ).
fof(f35882,plain,
( spl559_405
<=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_405])]) ).
fof(f29254,plain,
( spl559_54
<=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_54])]) ).
fof(f35880,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ spl559_54
| ~ spl559_271 ),
inference(forward_demodulation,[],[f29256,f32172]) ).
fof(f29256,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl559_54 ),
inference(avatar_component_clause,[],[f29254]) ).
fof(f35879,plain,
( spl559_404
| ~ spl559_108
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35874,f32170,f29923,f35876]) ).
fof(f29923,plain,
( spl559_108
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_108])]) ).
fof(f35874,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_108
| ~ spl559_271 ),
inference(forward_demodulation,[],[f35873,f32172]) ).
fof(f35873,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| ~ spl559_108 ),
inference(forward_demodulation,[],[f35872,f28163]) ).
fof(f28163,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(definition_unfolding,[],[f26615,f20937]) ).
fof(f20937,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f9785]) ).
fof(f9785,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(rectify,[],[f933]) ).
fof(f933,axiom,
! [X61] : c_Int_Osucc(X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__def) ).
fof(f26615,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(cnf_transformation,[],[f6158]) ).
fof(f6158,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(rectify,[],[f1568]) ).
fof(f1568,axiom,
! [X61] : c_Int_Osucc(X61) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X61),c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I2_J) ).
fof(f35872,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl559_108 ),
inference(forward_demodulation,[],[f35871,f24320]) ).
fof(f24320,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1),
inference(cnf_transformation,[],[f6439]) ).
fof(f6439,plain,
! [X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1),
inference(rectify,[],[f786]) ).
fof(f786,axiom,
! [X90,X16] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X90),X16) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X16),X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__commute) ).
fof(f35871,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))
| ~ spl559_108 ),
inference(forward_demodulation,[],[f35870,f25821]) ).
fof(f25821,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0,
inference(cnf_transformation,[],[f5792]) ).
fof(f5792,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0,
inference(rectify,[],[f882]) ).
fof(f882,axiom,
! [X61] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X61) = X61,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Pls) ).
fof(f35870,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))
| ~ spl559_108 ),
inference(forward_demodulation,[],[f29925,f22937]) ).
fof(f22937,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),
inference(cnf_transformation,[],[f16737]) ).
fof(f16737,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)),
inference(rectify,[],[f6723]) ).
fof(f6723,plain,
! [X0,X2,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)),
inference(rectify,[],[f787]) ).
fof(f787,axiom,
! [X11,X16,X15] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),X16)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X15),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X11),X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__left__commute) ).
fof(f29925,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))
| ~ spl559_108 ),
inference(avatar_component_clause,[],[f29923]) ).
fof(f35868,plain,
( spl559_403
| ~ spl559_72
| ~ spl559_146
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35863,f32170,f30519,f29464,f35865]) ).
fof(f35865,plain,
( spl559_403
<=> c_Int_OPls = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_403])]) ).
fof(f29464,plain,
( spl559_72
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_72])]) ).
fof(f35863,plain,
( c_Int_OPls = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))))
| ~ spl559_72
| ~ spl559_146
| ~ spl559_271 ),
inference(forward_demodulation,[],[f35862,f30521]) ).
fof(f35862,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))))
| ~ spl559_72
| ~ spl559_271 ),
inference(forward_demodulation,[],[f35861,f32172]) ).
fof(f35861,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ spl559_72 ),
inference(forward_demodulation,[],[f29466,f29718]) ).
fof(f29466,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))
| ~ spl559_72 ),
inference(avatar_component_clause,[],[f29464]) ).
fof(f35860,plain,
( spl559_402
| ~ spl559_77
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35855,f32170,f29503,f35857]) ).
fof(f35857,plain,
( spl559_402
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_402])]) ).
fof(f29503,plain,
( spl559_77
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_77])]) ).
fof(f35855,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))))
| ~ spl559_77
| ~ spl559_271 ),
inference(forward_demodulation,[],[f35854,f32172]) ).
fof(f35854,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ spl559_77 ),
inference(forward_demodulation,[],[f29505,f29718]) ).
fof(f29505,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))
| ~ spl559_77 ),
inference(avatar_component_clause,[],[f29503]) ).
fof(f35853,plain,
( spl559_401
| ~ spl559_18
| ~ spl559_146
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35848,f32170,f30519,f29037,f35850]) ).
fof(f35850,plain,
( spl559_401
<=> c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_401])]) ).
fof(f29037,plain,
( spl559_18
<=> 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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_18])]) ).
fof(f35848,plain,
( c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_18
| ~ spl559_146
| ~ spl559_271 ),
inference(forward_demodulation,[],[f35847,f30521]) ).
fof(f35847,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_18
| ~ spl559_271 ),
inference(forward_demodulation,[],[f29039,f32172]) ).
fof(f29039,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))
| ~ spl559_18 ),
inference(avatar_component_clause,[],[f29037]) ).
fof(f35846,plain,
( spl559_400
| ~ spl559_146
| ~ spl559_315 ),
inference(avatar_split_clause,[],[f35841,f33603,f30519,f35843]) ).
fof(f35843,plain,
( spl559_400
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_400])]) ).
fof(f33603,plain,
( spl559_315
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_315])]) ).
fof(f35841,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))
| ~ spl559_146
| ~ spl559_315 ),
inference(forward_demodulation,[],[f35840,f30521]) ).
fof(f35840,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))
| ~ spl559_315 ),
inference(forward_demodulation,[],[f33605,f28163]) ).
fof(f33605,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl559_315 ),
inference(avatar_component_clause,[],[f33603]) ).
fof(f35839,plain,
( spl559_399
| ~ spl559_21 ),
inference(avatar_split_clause,[],[f35834,f29055,f35836]) ).
fof(f35836,plain,
( spl559_399
<=> c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_399])]) ).
fof(f29055,plain,
( spl559_21
<=> c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_21])]) ).
fof(f35834,plain,
( c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),c_Int_OMin)
| ~ spl559_21 ),
inference(forward_demodulation,[],[f29057,f28163]) ).
fof(f29057,plain,
( c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OMin)
| ~ spl559_21 ),
inference(avatar_component_clause,[],[f29055]) ).
fof(f35832,plain,
( spl559_398
| ~ spl559_189 ),
inference(avatar_split_clause,[],[f35827,f31046,f35829]) ).
fof(f35829,plain,
( spl559_398
<=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_398])]) ).
fof(f31046,plain,
( spl559_189
<=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_189])]) ).
fof(f35827,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),c_Int_OPls)
| ~ spl559_189 ),
inference(forward_demodulation,[],[f31048,f28163]) ).
fof(f31048,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls)
| ~ spl559_189 ),
inference(avatar_component_clause,[],[f31046]) ).
fof(f35826,plain,
( spl559_380
| ~ spl559_244 ),
inference(avatar_split_clause,[],[f35825,f31638,f35706]) ).
fof(f31638,plain,
( spl559_244
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_244])]) ).
fof(f35825,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| ~ spl559_244 ),
inference(forward_demodulation,[],[f35824,f28163]) ).
fof(f35824,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl559_244 ),
inference(forward_demodulation,[],[f31640,f25821]) ).
fof(f31640,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl559_244 ),
inference(avatar_component_clause,[],[f31638]) ).
fof(f35823,plain,
( spl559_397
| ~ spl559_53
| ~ spl559_163 ),
inference(avatar_split_clause,[],[f35817,f30706,f29245,f35820]) ).
fof(f35820,plain,
( spl559_397
<=> 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,[spl559_397])]) ).
fof(f29245,plain,
( spl559_53
<=> c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral ),
introduced(avatar_definition,[new_symbols(naming,[spl559_53])]) ).
fof(f30706,plain,
( spl559_163
<=> 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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_163])]) ).
fof(f35817,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))
| ~ spl559_53
| ~ spl559_163 ),
inference(backward_demodulation,[],[f30708,f29247]) ).
fof(f29247,plain,
( c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral
| ~ spl559_53 ),
inference(avatar_component_clause,[],[f29245]) ).
fof(f30708,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))
| ~ spl559_163 ),
inference(avatar_component_clause,[],[f30706]) ).
fof(f35816,plain,
( ~ spl559_396
| ~ spl559_146
| spl559_335 ),
inference(avatar_split_clause,[],[f35811,f34096,f30519,f35813]) ).
fof(f35813,plain,
( spl559_396
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl559_396])]) ).
fof(f34096,plain,
( spl559_335
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_335])]) ).
fof(f35811,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Int_OPls
| ~ spl559_146
| spl559_335 ),
inference(forward_demodulation,[],[f34098,f30521]) ).
fof(f34098,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| spl559_335 ),
inference(avatar_component_clause,[],[f34096]) ).
fof(f35810,plain,
( spl559_395
| ~ spl559_251 ),
inference(avatar_split_clause,[],[f35805,f31835,f35807]) ).
fof(f35807,plain,
( spl559_395
<=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_395])]) ).
fof(f31835,plain,
( spl559_251
<=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_251])]) ).
fof(f35805,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))
| ~ spl559_251 ),
inference(forward_demodulation,[],[f35804,f28163]) ).
fof(f35804,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl559_251 ),
inference(forward_demodulation,[],[f35803,f25821]) ).
fof(f35803,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl559_251 ),
inference(forward_demodulation,[],[f35802,f25821]) ).
fof(f35802,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl559_251 ),
inference(forward_demodulation,[],[f35801,f25821]) ).
fof(f35801,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl559_251 ),
inference(forward_demodulation,[],[f31837,f25821]) ).
fof(f31837,plain,
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl559_251 ),
inference(avatar_component_clause,[],[f31835]) ).
fof(f35800,plain,
( spl559_394
| ~ spl559_271
| ~ spl559_278 ),
inference(avatar_split_clause,[],[f35795,f32241,f32170,f35797]) ).
fof(f35797,plain,
( spl559_394
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),c_List_Olist_ONil(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_394])]) ).
fof(f32241,plain,
( spl559_278
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),c_List_Olist_ONil(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_278])]) ).
fof(f35795,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),c_List_Olist_ONil(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_271
| ~ spl559_278 ),
inference(forward_demodulation,[],[f32243,f32172]) ).
fof(f32243,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),c_List_Olist_ONil(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl559_278 ),
inference(avatar_component_clause,[],[f32241]) ).
fof(f35794,plain,
( spl559_393
| ~ spl559_271
| ~ spl559_294 ),
inference(avatar_split_clause,[],[f35789,f33020,f32170,f35791]) ).
fof(f35791,plain,
( spl559_393
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_393])]) ).
fof(f33020,plain,
( spl559_294
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_294])]) ).
fof(f35789,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_271
| ~ spl559_294 ),
inference(forward_demodulation,[],[f33022,f32172]) ).
fof(f33022,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl559_294 ),
inference(avatar_component_clause,[],[f33020]) ).
fof(f35788,plain,
( spl559_392
| ~ spl559_121
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35783,f32170,f30084,f35785]) ).
fof(f35785,plain,
( spl559_392
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = 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,[spl559_392])]) ).
fof(f30084,plain,
( spl559_121
<=> 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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_121])]) ).
fof(f35783,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| ~ spl559_121
| ~ spl559_271 ),
inference(forward_demodulation,[],[f30086,f32172]) ).
fof(f30086,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))
| ~ spl559_121 ),
inference(avatar_component_clause,[],[f30084]) ).
fof(f35782,plain,
( spl559_391
| ~ spl559_115
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35777,f32170,f29997,f35779]) ).
fof(f35779,plain,
( spl559_391
<=> hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_391])]) ).
fof(f29997,plain,
( spl559_115
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_115])]) ).
fof(f35777,plain,
( hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ spl559_115
| ~ spl559_271 ),
inference(forward_demodulation,[],[f29999,f32172]) ).
fof(f29999,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl559_115 ),
inference(avatar_component_clause,[],[f29997]) ).
fof(f35776,plain,
( spl559_390
| ~ spl559_32
| ~ spl559_146 ),
inference(avatar_split_clause,[],[f35771,f30519,f29119,f35773]) ).
fof(f35773,plain,
( spl559_390
<=> 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,[spl559_390])]) ).
fof(f29119,plain,
( spl559_32
<=> 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))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_32])]) ).
fof(f35771,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)))
| ~ spl559_32
| ~ spl559_146 ),
inference(forward_demodulation,[],[f29121,f30521]) ).
fof(f29121,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)))
| ~ spl559_32 ),
inference(avatar_component_clause,[],[f29119]) ).
fof(f35770,plain,
( spl559_389
| ~ spl559_265
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35765,f32170,f32056,f35767]) ).
fof(f35767,plain,
( spl559_389
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_389])]) ).
fof(f32056,plain,
( spl559_265
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_265])]) ).
fof(f35765,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl559_265
| ~ spl559_271 ),
inference(forward_demodulation,[],[f32058,f32172]) ).
fof(f32058,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| ~ spl559_265 ),
inference(avatar_component_clause,[],[f32056]) ).
fof(f35764,plain,
( spl559_388
| ~ spl559_271
| ~ spl559_326 ),
inference(avatar_split_clause,[],[f35759,f33937,f32170,f35761]) ).
fof(f33937,plain,
( spl559_326
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_326])]) ).
fof(f35759,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)))
| ~ spl559_271
| ~ spl559_326 ),
inference(forward_demodulation,[],[f33939,f32172]) ).
fof(f33939,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)))
| ~ spl559_326 ),
inference(avatar_component_clause,[],[f33937]) ).
fof(f35758,plain,
( spl559_387
| ~ spl559_16
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35753,f32170,f29020,f35755]) ).
fof(f29020,plain,
( spl559_16
<=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_16])]) ).
fof(f35753,plain,
( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_16
| ~ spl559_271 ),
inference(forward_demodulation,[],[f29022,f32172]) ).
fof(f29022,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))
| ~ spl559_16 ),
inference(avatar_component_clause,[],[f29020]) ).
fof(f35752,plain,
( spl559_386
| ~ spl559_240
| ~ spl559_263 ),
inference(avatar_split_clause,[],[f35747,f32038,f31586,f35749]) ).
fof(f35749,plain,
( spl559_386
<=> c_Divides_OnegateSnd = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Int_Oring__1__class_Oof__int(tc_Int_Oint)))),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_386])]) ).
fof(f31586,plain,
( spl559_240
<=> c_Divides_OnegateSnd = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Fun_Oid(tc_Int_Oint)))),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_240])]) ).
fof(f32038,plain,
( spl559_263
<=> c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_263])]) ).
fof(f35747,plain,
( c_Divides_OnegateSnd = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Int_Oring__1__class_Oof__int(tc_Int_Oint)))),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))
| ~ spl559_240
| ~ spl559_263 ),
inference(forward_demodulation,[],[f31588,f32040]) ).
fof(f32040,plain,
( c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint)
| ~ spl559_263 ),
inference(avatar_component_clause,[],[f32038]) ).
fof(f31588,plain,
( c_Divides_OnegateSnd = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Fun_Oid(tc_Int_Oint)))),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))
| ~ spl559_240 ),
inference(avatar_component_clause,[],[f31586]) ).
fof(f35745,plain,
( spl559_385
| ~ spl559_196
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35740,f32170,f31116,f35742]) ).
fof(f35742,plain,
( spl559_385
<=> hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_385])]) ).
fof(f31116,plain,
( spl559_196
<=> hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_196])]) ).
fof(f35740,plain,
( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_196
| ~ spl559_271 ),
inference(forward_demodulation,[],[f31118,f32172]) ).
fof(f31118,plain,
( hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
| ~ spl559_196 ),
inference(avatar_component_clause,[],[f31116]) ).
fof(f35739,plain,
( spl559_384
| ~ spl559_39
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35734,f32170,f29157,f35736]) ).
fof(f35736,plain,
( spl559_384
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_384])]) ).
fof(f29157,plain,
( spl559_39
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_39])]) ).
fof(f35734,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue)
| ~ spl559_39
| ~ spl559_271 ),
inference(forward_demodulation,[],[f29159,f32172]) ).
fof(f29159,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue)
| ~ spl559_39 ),
inference(avatar_component_clause,[],[f29157]) ).
fof(f35733,plain,
( spl559_383
| ~ spl559_154
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35728,f32170,f30596,f35730]) ).
fof(f35730,plain,
( spl559_383
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_383])]) ).
fof(f30596,plain,
( spl559_154
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_154])]) ).
fof(f35728,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse)
| ~ spl559_154
| ~ spl559_271 ),
inference(forward_demodulation,[],[f30598,f32172]) ).
fof(f30598,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse)
| ~ spl559_154 ),
inference(avatar_component_clause,[],[f30596]) ).
fof(f35727,plain,
( ~ spl559_364
| spl559_224
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35726,f32170,f31377,f34890]) ).
fof(f31377,plain,
( spl559_224
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_224])]) ).
fof(f35726,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Orderings_Obot__class_Obot(tc_Nat_Onat)
| spl559_224
| ~ spl559_271 ),
inference(forward_demodulation,[],[f31379,f32172]) ).
fof(f31379,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| spl559_224 ),
inference(avatar_component_clause,[],[f31377]) ).
fof(f35722,plain,
( spl559_382
| ~ spl559_146
| ~ spl559_302 ),
inference(avatar_split_clause,[],[f35717,f33319,f30519,f35719]) ).
fof(f35719,plain,
( spl559_382
<=> c_Nitpick_OFrac = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_382])]) ).
fof(f33319,plain,
( spl559_302
<=> c_Nitpick_OFrac = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_302])]) ).
fof(f35717,plain,
( c_Nitpick_OFrac = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl559_146
| ~ spl559_302 ),
inference(forward_demodulation,[],[f33321,f30521]) ).
fof(f33321,plain,
( c_Nitpick_OFrac = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl559_302 ),
inference(avatar_component_clause,[],[f33319]) ).
fof(f35716,plain,
( ~ spl559_381
| ~ spl559_271
| spl559_280 ),
inference(avatar_split_clause,[],[f35711,f32316,f32170,f35713]) ).
fof(f32316,plain,
( spl559_280
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_280])]) ).
fof(f35711,plain,
( hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_271
| spl559_280 ),
inference(forward_demodulation,[],[f32317,f32172]) ).
fof(f32317,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| spl559_280 ),
inference(avatar_component_clause,[],[f32316]) ).
fof(f35709,plain,
( spl559_380
| ~ spl559_113 ),
inference(avatar_split_clause,[],[f35704,f29977,f35706]) ).
fof(f29977,plain,
( spl559_113
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_113])]) ).
fof(f35704,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| ~ spl559_113 ),
inference(forward_demodulation,[],[f35703,f28163]) ).
fof(f35703,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl559_113 ),
inference(forward_demodulation,[],[f35702,f24320]) ).
fof(f35702,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))
| ~ spl559_113 ),
inference(forward_demodulation,[],[f35701,f25821]) ).
fof(f35701,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))
| ~ spl559_113 ),
inference(forward_demodulation,[],[f29979,f22937]) ).
fof(f29979,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))
| ~ spl559_113 ),
inference(avatar_component_clause,[],[f29977]) ).
fof(f35697,plain,
( spl559_379
| ~ spl559_1
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f35692,f32170,f28929,f35694]) ).
fof(f35694,plain,
( spl559_379
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_379])]) ).
fof(f28929,plain,
( spl559_1
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_1])]) ).
fof(f35692,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat)))
| ~ spl559_1
| ~ spl559_271 ),
inference(forward_demodulation,[],[f28931,f32172]) ).
fof(f28931,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ spl559_1 ),
inference(avatar_component_clause,[],[f28929]) ).
fof(f35690,plain,
( ~ spl559_73
| spl559_69 ),
inference(avatar_split_clause,[],[f35689,f29445,f29475]) ).
fof(f29475,plain,
( spl559_73
<=> c_Int_OPls = c_Int_OMin ),
introduced(avatar_definition,[new_symbols(naming,[spl559_73])]) ).
fof(f29445,plain,
( spl559_69
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_69])]) ).
fof(f35689,plain,
( c_Int_OPls != c_Int_OMin
| spl559_69 ),
inference(forward_demodulation,[],[f35688,f26803]) ).
fof(f26803,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(cnf_transformation,[],[f9898]) ).
fof(f9898,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(rectify,[],[f805]) ).
fof(f805,axiom,
! [X61] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X61) = X61,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of__is__id) ).
fof(f35688,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != c_Int_OMin
| spl559_69 ),
inference(forward_demodulation,[],[f29447,f26803]) ).
fof(f29447,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
| spl559_69 ),
inference(avatar_component_clause,[],[f29445]) ).
fof(f35687,plain,
( spl559_378
| ~ spl559_146
| ~ spl559_339 ),
inference(avatar_split_clause,[],[f35682,f34191,f30519,f35684]) ).
fof(f35684,plain,
( spl559_378
<=> 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,[spl559_378])]) ).
fof(f34191,plain,
( spl559_339
<=> 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))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_339])]) ).
fof(f35682,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl559_146
| ~ spl559_339 ),
inference(forward_demodulation,[],[f34193,f30521]) ).
fof(f34193,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)))
| ~ spl559_339 ),
inference(avatar_component_clause,[],[f34191]) ).
fof(f35681,plain,
( spl559_377
| ~ spl559_271
| ~ spl559_300 ),
inference(avatar_split_clause,[],[f35676,f33300,f32170,f35678]) ).
fof(f35678,plain,
( spl559_377
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_377])]) ).
fof(f33300,plain,
( spl559_300
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_300])]) ).
fof(f35676,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse)
| ~ spl559_271
| ~ spl559_300 ),
inference(forward_demodulation,[],[f33302,f32172]) ).
fof(f33302,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse)
| ~ spl559_300 ),
inference(avatar_component_clause,[],[f33300]) ).
fof(f35605,plain,
( spl559_376
| ~ spl559_146
| ~ spl559_174 ),
inference(avatar_split_clause,[],[f35300,f30880,f30519,f35602]) ).
fof(f35602,plain,
( spl559_376
<=> 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,[spl559_376])]) ).
fof(f30880,plain,
( spl559_174
<=> 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))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_174])]) ).
fof(f35300,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl559_146
| ~ spl559_174 ),
inference(backward_demodulation,[],[f30882,f30521]) ).
fof(f30882,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)))
| ~ spl559_174 ),
inference(avatar_component_clause,[],[f30880]) ).
fof(f35570,plain,
( spl559_334
| ~ spl559_90
| ~ spl559_146 ),
inference(avatar_split_clause,[],[f35266,f30519,f29657,f34079]) ).
fof(f34079,plain,
( spl559_334
<=> c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_334])]) ).
fof(f29657,plain,
( spl559_90
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_90])]) ).
fof(f35266,plain,
( c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)
| ~ spl559_90
| ~ spl559_146 ),
inference(backward_demodulation,[],[f29659,f30521]) ).
fof(f29659,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl559_90 ),
inference(avatar_component_clause,[],[f29657]) ).
fof(f35547,plain,
( spl559_375
| ~ spl559_91
| ~ spl559_146 ),
inference(avatar_split_clause,[],[f35268,f30519,f29670,f35544]) ).
fof(f35544,plain,
( spl559_375
<=> c_Nat__Transfer_Ois__nat(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_375])]) ).
fof(f29670,plain,
( spl559_91
<=> c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_91])]) ).
fof(f35268,plain,
( c_Nat__Transfer_Ois__nat(c_Int_OPls)
| ~ spl559_91
| ~ spl559_146 ),
inference(backward_demodulation,[],[f29672,f30521]) ).
fof(f29672,plain,
( c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl559_91 ),
inference(avatar_component_clause,[],[f29670]) ).
fof(f35524,plain,
( spl559_374
| ~ spl559_146
| ~ spl559_340 ),
inference(avatar_split_clause,[],[f35386,f34198,f30519,f35521]) ).
fof(f35521,plain,
( spl559_374
<=> c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_374])]) ).
fof(f34198,plain,
( spl559_340
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_340])]) ).
fof(f35386,plain,
( c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls)
| ~ spl559_146
| ~ spl559_340 ),
inference(backward_demodulation,[],[f34200,f30521]) ).
fof(f34200,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))
| ~ spl559_340 ),
inference(avatar_component_clause,[],[f34198]) ).
fof(f35422,plain,
( spl559_373
| ~ spl559_146
| ~ spl559_254 ),
inference(avatar_split_clause,[],[f35323,f31861,f30519,f35419]) ).
fof(f35419,plain,
( spl559_373
<=> 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,[spl559_373])]) ).
fof(f31861,plain,
( spl559_254
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_254])]) ).
fof(f35323,plain,
( c_Int_OPls = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| ~ spl559_146
| ~ spl559_254 ),
inference(backward_demodulation,[],[f31863,f30521]) ).
fof(f31863,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))
| ~ spl559_254 ),
inference(avatar_component_clause,[],[f31861]) ).
fof(f34961,plain,
( spl559_372
| ~ spl559_236
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f34783,f32170,f31532,f34958]) ).
fof(f31532,plain,
( spl559_236
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_236])]) ).
fof(f34783,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl559_236
| ~ spl559_271 ),
inference(backward_demodulation,[],[f31534,f32172]) ).
fof(f31534,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl559_236 ),
inference(avatar_component_clause,[],[f31532]) ).
fof(f34955,plain,
( spl559_371
| ~ spl559_271
| ~ spl559_325 ),
inference(avatar_split_clause,[],[f34831,f33897,f32170,f34952]) ).
fof(f34952,plain,
( spl559_371
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_371])]) ).
fof(f33897,plain,
( spl559_325
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_325])]) ).
fof(f34831,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue)
| ~ spl559_271
| ~ spl559_325 ),
inference(backward_demodulation,[],[f33899,f32172]) ).
fof(f33899,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue)
| ~ spl559_325 ),
inference(avatar_component_clause,[],[f33897]) ).
fof(f34943,plain,
( spl559_370
| ~ spl559_170
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f34778,f32170,f30821,f34940]) ).
fof(f34940,plain,
( spl559_370
<=> c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_370])]) ).
fof(f30821,plain,
( spl559_170
<=> 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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_170])]) ).
fof(f34778,plain,
( c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_170
| ~ spl559_271 ),
inference(backward_demodulation,[],[f30823,f32172]) ).
fof(f30823,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))
| ~ spl559_170 ),
inference(avatar_component_clause,[],[f30821]) ).
fof(f34938,plain,
( spl559_369
| ~ spl559_252
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f34784,f32170,f31845,f34935]) ).
fof(f34935,plain,
( spl559_369
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_369])]) ).
fof(f31845,plain,
( spl559_252
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_252])]) ).
fof(f34784,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_252
| ~ spl559_271 ),
inference(backward_demodulation,[],[f31847,f32172]) ).
fof(f31847,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl559_252 ),
inference(avatar_component_clause,[],[f31845]) ).
fof(f34921,plain,
( spl559_368
| ~ spl559_209
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f34780,f32170,f31227,f34918]) ).
fof(f34918,plain,
( spl559_368
<=> hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) = hAPP(c_fequal,c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_368])]) ).
fof(f31227,plain,
( spl559_209
<=> hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_fequal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_209])]) ).
fof(f34780,plain,
( hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) = hAPP(c_fequal,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_209
| ~ spl559_271 ),
inference(backward_demodulation,[],[f31229,f32172]) ).
fof(f31229,plain,
( hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_fequal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl559_209 ),
inference(avatar_component_clause,[],[f31227]) ).
fof(f34916,plain,
( spl559_367
| ~ spl559_78
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f34767,f32170,f29508,f34913]) ).
fof(f34913,plain,
( spl559_367
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_367])]) ).
fof(f29508,plain,
( spl559_78
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_78])]) ).
fof(f34767,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ spl559_78
| ~ spl559_271 ),
inference(backward_demodulation,[],[f29510,f32172]) ).
fof(f29510,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ spl559_78 ),
inference(avatar_component_clause,[],[f29508]) ).
fof(f34905,plain,
( ~ spl559_366
| spl559_14
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f34764,f32170,f29010,f34902]) ).
fof(f29010,plain,
( spl559_14
<=> 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)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_14])]) ).
fof(f34764,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_Orderings_Obot__class_Obot(tc_Nat_Onat))))
| spl559_14
| ~ spl559_271 ),
inference(backward_demodulation,[],[f29012,f32172]) ).
fof(f29012,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))))
| spl559_14 ),
inference(avatar_component_clause,[],[f29010]) ).
fof(f34896,plain,
( ~ spl559_364
| spl559_365
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f34888,f32170,f34894,f34890]) ).
fof(f34894,plain,
( spl559_365
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_365])]) ).
fof(f34888,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Orderings_Obot__class_Obot(tc_Nat_Onat) )
| ~ spl559_271 ),
inference(forward_subsumption_demodulation,[],[f34827,f34850]) ).
fof(f34850,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),X0))
| c_Orderings_Obot__class_Obot(tc_Nat_Onat) = X0 )
| ~ spl559_271 ),
inference(forward_demodulation,[],[f34563,f32172]) ).
fof(f34563,plain,
( ! [X0] :
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) )
| ~ spl559_271 ),
inference(backward_demodulation,[],[f21872,f32172]) ).
fof(f21872,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ),
inference(cnf_transformation,[],[f15955]) ).
fof(f15955,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) ) ),
inference(nnf_transformation,[],[f6090]) ).
fof(f6090,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(rectify,[],[f472]) ).
fof(f472,axiom,
! [X56] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X56
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X56)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neq0__conv) ).
fof(f34827,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)))) )
| ~ spl559_271 ),
inference(backward_demodulation,[],[f33768,f32172]) ).
fof(f33768,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(forward_demodulation,[],[f33767,f23833]) ).
fof(f23833,plain,
! [X0,X1] : hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X0)) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X0,X1)),
inference(cnf_transformation,[],[f6190]) ).
fof(f6190,plain,
! [X0,X1] : hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X1),X0)) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X0,X1)),
inference(rectify,[],[f2162]) ).
fof(f2162,axiom,
! [X49,X48] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X49,X48)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X48),X49)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__greaterThanAtMost__int) ).
fof(f33767,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))) ),
inference(forward_demodulation,[],[f33766,f23833]) ).
fof(f33766,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))))) ),
inference(forward_demodulation,[],[f33757,f28163]) ).
fof(f33757,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) ),
inference(backward_demodulation,[],[f33277,f28163]) ).
fof(f33277,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
inference(forward_demodulation,[],[f33232,f33119]) ).
fof(f33119,plain,
! [X0] : hAPP(c_Int_Onat,X0) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),
inference(forward_demodulation,[],[f22082,f26803]) ).
fof(f22082,plain,
! [X0] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f7349]) ).
fof(f7349,plain,
! [X0] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),
inference(rectify,[],[f966]) ).
fof(f966,axiom,
! [X82] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__def) ).
fof(f33232,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
inference(backward_demodulation,[],[f32987,f33119]) ).
fof(f32987,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
inference(forward_demodulation,[],[f32986,f25821]) ).
fof(f32986,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(forward_demodulation,[],[f32985,f22937]) ).
fof(f32985,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
inference(forward_demodulation,[],[f32984,f25821]) ).
fof(f32984,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(forward_demodulation,[],[f32983,f22937]) ).
fof(f32983,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) ),
inference(forward_demodulation,[],[f32982,f25821]) ).
fof(f32982,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) ),
inference(forward_demodulation,[],[f32981,f25821]) ).
fof(f32981,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
inference(forward_demodulation,[],[f32980,f20419]) ).
fof(f20419,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)),
inference(cnf_transformation,[],[f14872]) ).
fof(f14872,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X2)),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X1)),
inference(rectify,[],[f7542]) ).
fof(f7542,plain,
! [X0,X2,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X1)),X2),
inference(rectify,[],[f788]) ).
fof(f788,axiom,
! [X100,X99,X98] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X100),X99)),X98) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X100),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X99),X98)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zadd__assoc) ).
fof(f32980,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) ),
inference(forward_demodulation,[],[f32979,f20419]) ).
fof(f32979,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) ),
inference(forward_demodulation,[],[f32978,f27261]) ).
fof(f27261,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),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_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
inference(definition_unfolding,[],[f20666,f21744]) ).
fof(f21744,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0) = c_Int_OBit0(X0),
inference(cnf_transformation,[],[f8845]) ).
fof(f8845,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0) = c_Int_OBit0(X0),
inference(rectify,[],[f1126]) ).
fof(f1126,axiom,
! [X61] : c_Int_OBit0(X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),X61),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__def) ).
fof(f20666,plain,
! [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_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X0)),
inference(cnf_transformation,[],[f9311]) ).
fof(f9311,plain,
! [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_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X0)),
inference(rectify,[],[f1218]) ).
fof(f1218,axiom,
! [X91] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(X91)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X91)),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))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__Bit0) ).
fof(f32978,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),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(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) ),
inference(forward_demodulation,[],[f32977,f27261]) ).
fof(f32977,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),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))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),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)))) ),
inference(forward_demodulation,[],[f32616,f25821]) ).
fof(f32616,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),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)))))) ),
inference(backward_demodulation,[],[f30478,f25821]) ).
fof(f30478,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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)))))) ),
inference(forward_demodulation,[],[f30477,f24320]) ).
fof(f30477,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),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)))))) ),
inference(forward_demodulation,[],[f30476,f24320]) ).
fof(f30476,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),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(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),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)))))) ),
inference(forward_demodulation,[],[f30365,f22937]) ).
fof(f30365,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),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(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),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)))))) ),
inference(backward_demodulation,[],[f29964,f22937]) ).
fof(f29964,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),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(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),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)))))) ),
inference(forward_demodulation,[],[f29963,f20419]) ).
fof(f29963,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),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))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),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)))) ),
inference(forward_demodulation,[],[f29962,f20419]) ).
fof(f29962,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),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))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),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)))) ),
inference(forward_demodulation,[],[f29961,f27261]) ).
fof(f29961,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),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)))) ),
inference(forward_demodulation,[],[f27373,f27261]) ).
fof(f27373,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))) ),
inference(definition_unfolding,[],[f21415,f21744,f20132,f21744,f20132]) ).
fof(f20132,plain,
! [X0] : c_Int_OBit1(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0),
inference(cnf_transformation,[],[f8719]) ).
fof(f8719,plain,
! [X0] : c_Int_OBit1(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0),
inference(rectify,[],[f970]) ).
fof(f970,axiom,
! [X61] : c_Int_OBit1(X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X61)),X61),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__def) ).
fof(f21415,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(cnf_transformation,[],[f15613]) ).
fof(f15613,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
inference(nnf_transformation,[],[f7230]) ).
fof(f7230,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
inference(rectify,[],[f1515]) ).
fof(f1515,axiom,
! [X53] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X53,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X53,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod2__gr__0) ).
fof(f34887,plain,
( spl559_363
| ~ spl559_28
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f34765,f32170,f29097,f34884]) ).
fof(f34884,plain,
( spl559_363
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_363])]) ).
fof(f29097,plain,
( spl559_28
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_28])]) ).
fof(f34765,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Obot__class_Obot(tc_Nat_Onat)))))
| ~ spl559_28
| ~ spl559_271 ),
inference(backward_demodulation,[],[f29099,f32172]) ).
fof(f29099,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| ~ spl559_28 ),
inference(avatar_component_clause,[],[f29097]) ).
fof(f34882,plain,
( spl559_362
| ~ spl559_158
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f34777,f32170,f30649,f34879]) ).
fof(f34879,plain,
( spl559_362
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_362])]) ).
fof(f30649,plain,
( spl559_158
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_158])]) ).
fof(f34777,plain,
( c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)
| ~ spl559_158
| ~ spl559_271 ),
inference(backward_demodulation,[],[f30651,f32172]) ).
fof(f30651,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)
| ~ spl559_158 ),
inference(avatar_component_clause,[],[f30649]) ).
fof(f34866,plain,
( spl559_361
| ~ spl559_156
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f34776,f32170,f30610,f34863]) ).
fof(f30610,plain,
( spl559_156
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_156])]) ).
fof(f34776,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_156
| ~ spl559_271 ),
inference(backward_demodulation,[],[f30612,f32172]) ).
fof(f30612,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ spl559_156 ),
inference(avatar_component_clause,[],[f30610]) ).
fof(f34858,plain,
( spl559_360
| ~ spl559_144
| ~ spl559_271 ),
inference(avatar_split_clause,[],[f34774,f32170,f30329,f34855]) ).
fof(f34855,plain,
( spl559_360
<=> c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_360])]) ).
fof(f30329,plain,
( spl559_144
<=> 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)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_144])]) ).
fof(f34774,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| ~ spl559_144
| ~ spl559_271 ),
inference(backward_demodulation,[],[f30331,f32172]) ).
fof(f30331,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))
| ~ spl559_144 ),
inference(avatar_component_clause,[],[f30329]) ).
fof(f34517,plain,
( spl559_359
| ~ spl559_48 ),
inference(avatar_split_clause,[],[f34512,f29217,f34514]) ).
fof(f34514,plain,
( spl559_359
<=> c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_359])]) ).
fof(f29217,plain,
( spl559_48
<=> c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_48])]) ).
fof(f34512,plain,
( c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))
| ~ spl559_48 ),
inference(forward_demodulation,[],[f29219,f29718]) ).
fof(f29219,plain,
( c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool))))
| ~ spl559_48 ),
inference(avatar_component_clause,[],[f29217]) ).
fof(f34497,plain,
( spl559_338
| ~ spl559_156
| ~ spl559_249 ),
inference(avatar_split_clause,[],[f34489,f31811,f30610,f34130]) ).
fof(f34130,plain,
( spl559_338
<=> 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,[spl559_338])]) ).
fof(f31811,plain,
( spl559_249
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_249])]) ).
fof(f34489,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl559_156
| ~ spl559_249 ),
inference(backward_demodulation,[],[f31813,f30612]) ).
fof(f31813,plain,
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl559_249 ),
inference(avatar_component_clause,[],[f31811]) ).
fof(f34455,plain,
( ~ spl559_358
| spl559_136 ),
inference(avatar_split_clause,[],[f34450,f30242,f34452]) ).
fof(f34452,plain,
( spl559_358
<=> c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olist_ONil(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_358])]) ).
fof(f30242,plain,
( spl559_136
<=> c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),c_List_Olist_ONil(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_136])]) ).
fof(f34450,plain,
( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olist_ONil(tc_Nat_Onat))
| spl559_136 ),
inference(forward_demodulation,[],[f30244,f23952]) ).
fof(f23952,plain,
! [X0] : hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)) = c_List_Olist_ONil(X0),
inference(cnf_transformation,[],[f9609]) ).
fof(f9609,plain,
! [X0] : hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)) = c_List_Olist_ONil(X0),
inference(rectify,[],[f4427]) ).
fof(f4427,axiom,
! [X12] : c_List_Olist_ONil(X12) = hAPP(c_List_Orev(X12),c_List_Olist_ONil(X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev_Osimps_I1_J) ).
fof(f30244,plain,
( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),c_List_Olist_ONil(tc_Nat_Onat)))
| spl559_136 ),
inference(avatar_component_clause,[],[f30242]) ).
fof(f34449,plain,
( spl559_357
| ~ spl559_60 ),
inference(avatar_split_clause,[],[f34444,f29375,f34446]) ).
fof(f34446,plain,
( spl559_357
<=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_357])]) ).
fof(f29375,plain,
( spl559_60
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),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)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_60])]) ).
fof(f34444,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,c_Int_OMin,c_Groups_Oone__class_Oone(tc_Int_Oint)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34443,f23833]) ).
fof(f34443,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34442,f28163]) ).
fof(f34442,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34441,f25821]) ).
fof(f34441,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34440,f22937]) ).
fof(f34440,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34439,f25821]) ).
fof(f34439,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34438,f20419]) ).
fof(f34438,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34437,f28163]) ).
fof(f34437,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34436,f33119]) ).
fof(f34436,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34435,f33144]) ).
fof(f33144,plain,
! [X0] : hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onat,X0)),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))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0)),
inference(backward_demodulation,[],[f27261,f33119]) ).
fof(f34435,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),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))))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34434,f25821]) ).
fof(f34434,plain,
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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))))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34433,f25821]) ).
fof(f34433,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34432,f22937]) ).
fof(f34432,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),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)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34431,f24320]) ).
fof(f34431,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),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)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34430,f25821]) ).
fof(f34430,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),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)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34429,f22937]) ).
fof(f34429,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),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)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34428,f25821]) ).
fof(f34428,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),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)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34427,f22937]) ).
fof(f34427,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),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)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34426,f25821]) ).
fof(f34426,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),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)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34425,f22937]) ).
fof(f34425,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),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)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34424,f26803]) ).
fof(f34424,plain,
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),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)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f34423,f22937]) ).
fof(f34423,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),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))))
| ~ spl559_60 ),
inference(forward_demodulation,[],[f29377,f33119]) ).
fof(f29377,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),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))))
| ~ spl559_60 ),
inference(avatar_component_clause,[],[f29375]) ).
fof(f34418,plain,
( spl559_356
| ~ spl559_132 ),
inference(avatar_split_clause,[],[f34413,f30202,f34415]) ).
fof(f30202,plain,
( spl559_132
<=> hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_132])]) ).
fof(f34413,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)))
| ~ spl559_132 ),
inference(forward_demodulation,[],[f34412,f27519]) ).
fof(f27519,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X0)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X0)),
inference(definition_unfolding,[],[f22412,f21744,f21744]) ).
fof(f22412,plain,
! [X0] : c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X0)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X0)),
inference(cnf_transformation,[],[f9310]) ).
fof(f9310,plain,
! [X0] : c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X0)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X0)),
inference(rectify,[],[f1196]) ).
fof(f1196,axiom,
! [X64] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(X64)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),X64)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_diff__bin__simps_I3_J) ).
fof(f34412,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))
| ~ spl559_132 ),
inference(forward_demodulation,[],[f34411,f33684]) ).
fof(f33684,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0))),
inference(backward_demodulation,[],[f31102,f28163]) ).
fof(f31102,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0))),
inference(forward_demodulation,[],[f31101,f20419]) ).
fof(f31101,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0)),
inference(forward_demodulation,[],[f27590,f24320]) ).
fof(f27590,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(definition_unfolding,[],[f22870,f21744,f20937,f20937,f20132]) ).
fof(f22870,plain,
! [X0] : c_Int_OBit0(c_Int_Osucc(X0)) = c_Int_Osucc(c_Int_OBit1(X0)),
inference(cnf_transformation,[],[f7627]) ).
fof(f7627,plain,
! [X0] : c_Int_OBit0(c_Int_Osucc(X0)) = c_Int_Osucc(c_Int_OBit1(X0)),
inference(rectify,[],[f1216]) ).
fof(f1216,axiom,
! [X61] : c_Int_Osucc(c_Int_OBit1(X61)) = c_Int_OBit0(c_Int_Osucc(X61)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Bit1) ).
fof(f34411,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))
| ~ spl559_132 ),
inference(forward_demodulation,[],[f34410,f25821]) ).
fof(f34410,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ spl559_132 ),
inference(forward_demodulation,[],[f34409,f22937]) ).
fof(f34409,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ spl559_132 ),
inference(forward_demodulation,[],[f34408,f25821]) ).
fof(f34408,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))
| ~ spl559_132 ),
inference(forward_demodulation,[],[f30204,f22937]) ).
fof(f30204,plain,
( hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))
| ~ spl559_132 ),
inference(avatar_component_clause,[],[f30202]) ).
fof(f34407,plain,
( spl559_355
| ~ spl559_290 ),
inference(avatar_split_clause,[],[f34402,f32517,f34404]) ).
fof(f34404,plain,
( spl559_355
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_355])]) ).
fof(f32517,plain,
( spl559_290
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_290])]) ).
fof(f34402,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| ~ spl559_290 ),
inference(forward_demodulation,[],[f34401,f28163]) ).
fof(f34401,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl559_290 ),
inference(forward_demodulation,[],[f32519,f25821]) ).
fof(f32519,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl559_290 ),
inference(avatar_component_clause,[],[f32517]) ).
fof(f34400,plain,
( spl559_354
| ~ spl559_257 ),
inference(avatar_split_clause,[],[f34395,f31950,f34397]) ).
fof(f31950,plain,
( spl559_257
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_257])]) ).
fof(f34395,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)))
| ~ spl559_257 ),
inference(forward_demodulation,[],[f34394,f28163]) ).
fof(f34394,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl559_257 ),
inference(forward_demodulation,[],[f34393,f25821]) ).
fof(f34393,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl559_257 ),
inference(forward_demodulation,[],[f34392,f25821]) ).
fof(f34392,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl559_257 ),
inference(forward_demodulation,[],[f34391,f25821]) ).
fof(f34391,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl559_257 ),
inference(forward_demodulation,[],[f31952,f25821]) ).
fof(f31952,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))))
| ~ spl559_257 ),
inference(avatar_component_clause,[],[f31950]) ).
fof(f34381,plain,
( spl559_353
| ~ spl559_247 ),
inference(avatar_split_clause,[],[f34376,f31799,f34378]) ).
fof(f34378,plain,
( spl559_353
<=> hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_353])]) ).
fof(f31799,plain,
( spl559_247
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_247])]) ).
fof(f34376,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))
| ~ spl559_247 ),
inference(forward_demodulation,[],[f34375,f28163]) ).
fof(f34375,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl559_247 ),
inference(forward_demodulation,[],[f34374,f25821]) ).
fof(f34374,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl559_247 ),
inference(forward_demodulation,[],[f34373,f25821]) ).
fof(f34373,plain,
( hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl559_247 ),
inference(forward_demodulation,[],[f34372,f25821]) ).
fof(f34372,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl559_247 ),
inference(forward_demodulation,[],[f31801,f25821]) ).
fof(f31801,plain,
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ spl559_247 ),
inference(avatar_component_clause,[],[f31799]) ).
fof(f34371,plain,
( spl559_352
| ~ spl559_217 ),
inference(avatar_split_clause,[],[f34366,f31315,f34368]) ).
fof(f31315,plain,
( spl559_217
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_217])]) ).
fof(f34366,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin))
| ~ spl559_217 ),
inference(forward_demodulation,[],[f34365,f28163]) ).
fof(f34365,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ spl559_217 ),
inference(forward_demodulation,[],[f34364,f25821]) ).
fof(f34364,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
| ~ spl559_217 ),
inference(forward_demodulation,[],[f34363,f25821]) ).
fof(f34363,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))
| ~ spl559_217 ),
inference(forward_demodulation,[],[f34362,f25821]) ).
fof(f34362,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))
| ~ spl559_217 ),
inference(forward_demodulation,[],[f31317,f25821]) ).
fof(f31317,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))
| ~ spl559_217 ),
inference(avatar_component_clause,[],[f31315]) ).
fof(f34361,plain,
( spl559_351
| ~ spl559_139 ),
inference(avatar_split_clause,[],[f34356,f30281,f34358]) ).
fof(f30281,plain,
( spl559_139
<=> hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_139])]) ).
fof(f34356,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)))
| ~ spl559_139 ),
inference(forward_demodulation,[],[f34355,f27519]) ).
fof(f34355,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))
| ~ spl559_139 ),
inference(forward_demodulation,[],[f34354,f33684]) ).
fof(f34354,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))
| ~ spl559_139 ),
inference(forward_demodulation,[],[f34353,f25821]) ).
fof(f34353,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ spl559_139 ),
inference(forward_demodulation,[],[f34352,f22937]) ).
fof(f34352,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))
| ~ spl559_139 ),
inference(forward_demodulation,[],[f34351,f25821]) ).
fof(f34351,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))
| ~ spl559_139 ),
inference(forward_demodulation,[],[f30283,f22937]) ).
fof(f30283,plain,
( hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))
| ~ spl559_139 ),
inference(avatar_component_clause,[],[f30281]) ).
fof(f34350,plain,
spl559_350,
inference(avatar_split_clause,[],[f34345,f34347]) ).
fof(f34347,plain,
( spl559_350
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin),c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_350])]) ).
fof(f34345,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin),c_Int_OPls))),
inference(forward_demodulation,[],[f34344,f31881]) ).
fof(f31881,plain,
! [X0,X1] : hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),X1))) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0)),
inference(forward_demodulation,[],[f21458,f24320]) ).
fof(f21458,plain,
! [X0,X1] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f9239]) ).
fof(f9239,plain,
! [X0,X1] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),X1)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(rectify,[],[f2239]) ).
fof(f2239,axiom,
! [X48,X49] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X49,X48)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X48),X49)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__atLeastAtMost__int) ).
fof(f34344,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))),
inference(forward_demodulation,[],[f34343,f27519]) ).
fof(f34343,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))),
inference(forward_demodulation,[],[f34342,f33684]) ).
fof(f34342,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(forward_demodulation,[],[f34341,f20419]) ).
fof(f34341,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f34340,f25821]) ).
fof(f34340,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f34339,f22937]) ).
fof(f34339,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f34338,f22937]) ).
fof(f34338,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f34337,f25821]) ).
fof(f34337,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f34336,f22937]) ).
fof(f34336,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f34335,f22937]) ).
fof(f34335,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f34334,f20419]) ).
fof(f34334,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f34333,f26803]) ).
fof(f34333,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f34332,f20419]) ).
fof(f34332,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f34331,f20419]) ).
fof(f34331,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f27269,f33119]) ).
fof(f27269,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(definition_unfolding,[],[f20725,f20132,f20132,f20132,f20132]) ).
fof(f20725,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f1014]) ).
fof(f1014,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I4_J) ).
fof(f34328,plain,
spl559_349,
inference(avatar_split_clause,[],[f23596,f34325]) ).
fof(f34325,plain,
( spl559_349
<=> v_wt(v_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_349])]) ).
fof(f23596,plain,
v_wt(v_c),
inference(cnf_transformation,[],[f5227]) ).
fof(f5227,axiom,
v_wt(v_c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
fof(f34323,plain,
spl559_348,
inference(avatar_split_clause,[],[f21608,f34320]) ).
fof(f34320,plain,
( spl559_348
<=> class_Groups_Ouminus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_348])]) ).
fof(f21608,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(cnf_transformation,[],[f5139]) ).
fof(f5139,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(f34303,plain,
spl559_347,
inference(avatar_split_clause,[],[f34298,f34300]) ).
fof(f34300,plain,
( spl559_347
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_347])]) ).
fof(f34298,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))))),
inference(forward_demodulation,[],[f34297,f27519]) ).
fof(f34297,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))))),
inference(forward_demodulation,[],[f34296,f33684]) ).
fof(f34296,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f34295,f20419]) ).
fof(f34295,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f34294,f25821]) ).
fof(f34294,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f34293,f22937]) ).
fof(f34293,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f34292,f22937]) ).
fof(f34292,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f34291,f25821]) ).
fof(f34291,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))),
inference(forward_demodulation,[],[f34290,f22937]) ).
fof(f34290,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))),
inference(forward_demodulation,[],[f34289,f22937]) ).
fof(f34289,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))))),
inference(forward_demodulation,[],[f34288,f20419]) ).
fof(f34288,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f34287,f20419]) ).
fof(f34287,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f34286,f20419]) ).
fof(f34286,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f27886,f26803]) ).
fof(f27886,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(definition_unfolding,[],[f24906,f20132,f20132]) ).
fof(f24906,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
inference(cnf_transformation,[],[f1012]) ).
fof(f1012,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).
fof(f34281,plain,
spl559_346,
inference(avatar_split_clause,[],[f20626,f34265]) ).
fof(f34265,plain,
( spl559_346
<=> ! [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,[spl559_346])]) ).
fof(f20626,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,[],[f10127]) ).
fof(f10127,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,[],[f507]) ).
fof(f507,axiom,
! [X54] : hAPP(c_Nat_OSuc,X54) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X54),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(f34267,plain,
( spl559_97
| spl559_346 ),
inference(avatar_split_clause,[],[f34263,f34265,f29805]) ).
fof(f29805,plain,
( spl559_97
<=> ! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_97])]) ).
fof(f34263,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
inference(forward_demodulation,[],[f34262,f20972]) ).
fof(f20972,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,[],[f7110]) ).
fof(f7110,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f374]) ).
fof(f374,axiom,
! [X54] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X54) = X54,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
fof(f34262,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
inference(forward_subsumption_demodulation,[],[f34261,f33149]) ).
fof(f33149,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0) ),
inference(backward_demodulation,[],[f29520,f33119]) ).
fof(f29520,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(backward_demodulation,[],[f21752,f26803]) ).
fof(f21752,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f13284]) ).
fof(f13284,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(ennf_transformation,[],[f9762]) ).
fof(f9762,plain,
! [X0] :
( 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),X0) ),
inference(rectify,[],[f909]) ).
fof(f909,axiom,
! [X82] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__imp__number__of__eq__0) ).
fof(f34261,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,X1)),X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
inference(forward_demodulation,[],[f34260,f33119]) ).
fof(f34260,plain,
! [X0,X1] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
inference(forward_demodulation,[],[f22423,f26803]) ).
fof(f22423,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X0)) ),
inference(cnf_transformation,[],[f10704]) ).
fof(f10704,plain,
! [X0,X1] :
( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1))),X0) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) ),
inference(ennf_transformation,[],[f7777]) ).
fof(f7777,plain,
! [X1,X0] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X0)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X1))),X0) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X0)) ) ),
inference(rectify,[],[f922]) ).
fof(f922,axiom,
! [X54,X82] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)),X54)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X82))),X54) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X54) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)),X54)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__number__of__add) ).
fof(f34256,plain,
spl559_345,
inference(avatar_split_clause,[],[f24808,f34253]) ).
fof(f34253,plain,
( spl559_345
<=> class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_345])]) ).
fof(f24808,plain,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5181]) ).
fof(f5181,axiom,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add) ).
fof(f34236,plain,
spl559_344,
inference(avatar_split_clause,[],[f22517,f34233]) ).
fof(f34233,plain,
( spl559_344
<=> class_Groups_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_344])]) ).
fof(f22517,plain,
class_Groups_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f5074]) ).
fof(f5074,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(f34226,plain,
~ spl559_343,
inference(avatar_split_clause,[],[f22060,f34223]) ).
fof(f34223,plain,
( spl559_343
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_343])]) ).
fof(f22060,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f1548]) ).
fof(f1548,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(f34219,plain,
spl559_342,
inference(avatar_split_clause,[],[f24241,f34216]) ).
fof(f34216,plain,
( spl559_342
<=> class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_342])]) ).
fof(f24241,plain,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5171]) ).
fof(f5171,axiom,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add) ).
fof(f34214,plain,
spl559_341,
inference(avatar_split_clause,[],[f21238,f34211]) ).
fof(f34211,plain,
( spl559_341
<=> 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,[spl559_341])]) ).
fof(f21238,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,[],[f2039]) ).
fof(f2039,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(f34201,plain,
spl559_340,
inference(avatar_split_clause,[],[f28327,f34198]) ).
fof(f28327,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,[],[f20653]) ).
fof(f20653,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,[],[f12544]) ).
fof(f12544,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 )
& ( ( ( 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)) )
& ( ~ 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 ) ),
inference(ennf_transformation,[],[f8685]) ).
fof(f8685,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,[],[f2637]) ).
fof(f2637,axiom,
! [X63] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X63
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X63) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X63
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X63))
=> 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,X63) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X63))
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X63) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zsgn__def) ).
fof(f34194,plain,
spl559_339,
inference(avatar_split_clause,[],[f23253,f34191]) ).
fof(f23253,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,[],[f778]) ).
fof(f778,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(f34133,plain,
spl559_338,
inference(avatar_split_clause,[],[f23708,f34130]) ).
fof(f23708,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f969]) ).
fof(f969,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(f34117,plain,
spl559_337,
inference(avatar_split_clause,[],[f26892,f34114]) ).
fof(f34114,plain,
( spl559_337
<=> class_Rings_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_337])]) ).
fof(f26892,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5062]) ).
fof(f5062,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(f34107,plain,
spl559_336,
inference(avatar_split_clause,[],[f26213,f34104]) ).
fof(f26213,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
inference(cnf_transformation,[],[f5225]) ).
fof(f5225,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a,tc_HOL_Obool)),v_G),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
fof(f34099,plain,
~ spl559_335,
inference(avatar_split_clause,[],[f23346,f34096]) ).
fof(f23346,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f806]) ).
fof(f806,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__0__neq__1) ).
fof(f34082,plain,
spl559_334,
inference(avatar_split_clause,[],[f25936,f34079]) ).
fof(f25936,plain,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
inference(cnf_transformation,[],[f1133]) ).
fof(f1133,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(f34069,plain,
spl559_333,
inference(avatar_split_clause,[],[f20482,f34066]) ).
fof(f34066,plain,
( spl559_333
<=> class_Groups_Oabs__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_333])]) ).
fof(f20482,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(cnf_transformation,[],[f5066]) ).
fof(f5066,axiom,
class_Groups_Oabs__if(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).
fof(f34060,plain,
spl559_332,
inference(avatar_split_clause,[],[f26251,f34057]) ).
fof(f34057,plain,
( spl559_332
<=> class_Rings_Osemiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_332])]) ).
fof(f26251,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5052]) ).
fof(f5052,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__1) ).
fof(f34053,plain,
spl559_331,
inference(avatar_split_clause,[],[f26891,f34050]) ).
fof(f34050,plain,
( spl559_331
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_331])]) ).
fof(f26891,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f5041]) ).
fof(f5041,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Osemiring__div) ).
fof(f34040,plain,
spl559_330,
inference(avatar_split_clause,[],[f25373,f34037]) ).
fof(f34037,plain,
( spl559_330
<=> class_Rings_Oordered__ring__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_330])]) ).
fof(f25373,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f5034]) ).
fof(f5034,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
fof(f33986,plain,
spl559_329,
inference(avatar_split_clause,[],[f23612,f33983]) ).
fof(f33983,plain,
( spl559_329
<=> class_Rings_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_329])]) ).
fof(f23612,plain,
class_Rings_Oring(tc_Int_Oint),
inference(cnf_transformation,[],[f5071]) ).
fof(f5071,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(f33965,plain,
spl559_328,
inference(avatar_split_clause,[],[f23796,f33962]) ).
fof(f33962,plain,
( spl559_328
<=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_328])]) ).
fof(f23796,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5037]) ).
fof(f5037,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring) ).
fof(f33960,plain,
spl559_327,
inference(avatar_split_clause,[],[f33955,f33957]) ).
fof(f33957,plain,
( spl559_327
<=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_327])]) ).
fof(f33955,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(forward_demodulation,[],[f33954,f28163]) ).
fof(f33954,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f33953,f24320]) ).
fof(f33953,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),
inference(forward_demodulation,[],[f33952,f25821]) ).
fof(f33952,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))),
inference(forward_demodulation,[],[f33951,f22937]) ).
fof(f33951,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(forward_demodulation,[],[f27781,f20419]) ).
fof(f27781,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),
inference(definition_unfolding,[],[f24161,f20132]) ).
fof(f24161,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,[],[f1617]) ).
fof(f1617,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(f33940,plain,
spl559_326,
inference(avatar_split_clause,[],[f33935,f33937]) ).
fof(f33935,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin))),
inference(forward_demodulation,[],[f33934,f27519]) ).
fof(f33934,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin))),
inference(forward_demodulation,[],[f33933,f33684]) ).
fof(f33933,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),
inference(forward_demodulation,[],[f33932,f20419]) ).
fof(f33932,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),
inference(forward_demodulation,[],[f33931,f25821]) ).
fof(f33931,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f33930,f22937]) ).
fof(f33930,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f33929,f25821]) ).
fof(f33929,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f33928,f22937]) ).
fof(f33928,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f33927,f20419]) ).
fof(f33927,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f27282,f20419]) ).
fof(f27282,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),
inference(definition_unfolding,[],[f20839,f21744,f20132]) ).
fof(f20839,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(cnf_transformation,[],[f1260]) ).
fof(f1260,axiom,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_semiring__norm_I115_J) ).
fof(f33900,plain,
spl559_325,
inference(avatar_split_clause,[],[f24581,f33897]) ).
fof(f24581,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
inference(cnf_transformation,[],[f3704]) ).
fof(f3704,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(f33894,plain,
spl559_324,
inference(avatar_split_clause,[],[f33889,f33891]) ).
fof(f33891,plain,
( spl559_324
<=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_324])]) ).
fof(f33889,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OMin)))),
inference(forward_demodulation,[],[f33888,f27519]) ).
fof(f33888,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))),
inference(forward_demodulation,[],[f33887,f33684]) ).
fof(f33887,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(forward_demodulation,[],[f33886,f20419]) ).
fof(f33886,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f33885,f25821]) ).
fof(f33885,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f33884,f22937]) ).
fof(f33884,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f33883,f22937]) ).
fof(f33883,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f33882,f25821]) ).
fof(f33882,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f33881,f22937]) ).
fof(f33881,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f33880,f22937]) ).
fof(f33880,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f33879,f20419]) ).
fof(f33879,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f33878,f20419]) ).
fof(f33878,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f33877,f20419]) ).
fof(f33877,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),
inference(forward_demodulation,[],[f28180,f26803]) ).
fof(f28180,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(definition_unfolding,[],[f26710,f20132,f20132]) ).
fof(f26710,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,[],[f1660]) ).
fof(f1660,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(f33867,plain,
( spl559_97
| spl559_323 ),
inference(avatar_split_clause,[],[f33863,f33865,f29805]) ).
fof(f33865,plain,
( spl559_323
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_323])]) ).
fof(f33863,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_subsumption_demodulation,[],[f33862,f33149]) ).
fof(f33862,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hAPP(c_Int_Onat,X1) = hAPP(c_Int_Onat,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f33861,f33119]) ).
fof(f33861,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ),
inference(forward_demodulation,[],[f33860,f33119]) ).
fof(f33860,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ),
inference(forward_demodulation,[],[f33859,f26803]) ).
fof(f33859,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f33858,f26803]) ).
fof(f33858,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ),
inference(forward_demodulation,[],[f21553,f26803]) ).
fof(f21553,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| 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),X0))) ),
inference(cnf_transformation,[],[f15714]) ).
fof(f15714,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& 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),X0)
& 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),X1)))
& X0 != X1 ) )
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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),X0)
| ~ 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),X1)))
| X0 = X1 ) )
| 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),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ) ),
inference(flattening,[],[f15713]) ).
fof(f15713,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& 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),X0)
& 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),X1)))
& X0 != X1 ) )
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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),X0)
| ~ 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),X1)))
| X0 = X1 ) )
| 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),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ) ),
inference(nnf_transformation,[],[f12384]) ).
fof(f12384,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ 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),X0)
| ~ 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),X1)))
| X0 = X1 ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ) ),
inference(ennf_transformation,[],[f5252]) ).
fof(f5252,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
<=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ 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)))
=> 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 ) ) ) ) ),
inference(rectify,[],[f918]) ).
fof(f918,axiom,
! [X95,X111] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X95) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X111)
<=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X95)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X111)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X95)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X111)))
=> X95 = X111 )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X111)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X95) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__nat__number__of) ).
fof(f33855,plain,
spl559_322,
inference(avatar_split_clause,[],[f20475,f33852]) ).
fof(f33852,plain,
( spl559_322
<=> c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_322])]) ).
fof(f20475,plain,
c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f1558]) ).
fof(f1558,axiom,
c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int_OMin__def) ).
fof(f33848,plain,
spl559_321,
inference(avatar_split_clause,[],[f23932,f33845]) ).
fof(f33845,plain,
( spl559_321
<=> 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,[spl559_321])]) ).
fof(f23932,plain,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f2164]) ).
fof(f2164,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(f33659,plain,
spl559_320,
inference(avatar_split_clause,[],[f21655,f33656]) ).
fof(f33656,plain,
( spl559_320
<=> class_Nat_Osize(tc_Code__Evaluation_Oterm) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_320])]) ).
fof(f21655,plain,
class_Nat_Osize(tc_Code__Evaluation_Oterm),
inference(cnf_transformation,[],[f5160]) ).
fof(f5160,axiom,
class_Nat_Osize(tc_Code__Evaluation_Oterm),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Evaluation__Oterm__Nat_Osize) ).
fof(f33654,plain,
spl559_319,
inference(avatar_split_clause,[],[f24805,f33651]) ).
fof(f33651,plain,
( spl559_319
<=> class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_319])]) ).
fof(f24805,plain,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5198]) ).
fof(f5198,axiom,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ozero) ).
fof(f33647,plain,
( ~ spl559_224
| spl559_318 ),
inference(avatar_split_clause,[],[f25404,f33645,f31377]) ).
fof(f33645,plain,
( spl559_318
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_318])]) ).
fof(f25404,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),X1)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(cnf_transformation,[],[f18647]) ).
fof(f33636,plain,
spl559_317,
inference(avatar_split_clause,[],[f22819,f33633]) ).
fof(f33633,plain,
( spl559_317
<=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_317])]) ).
fof(f22819,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5024]) ).
fof(f5024,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
fof(f33629,plain,
spl559_316,
inference(avatar_split_clause,[],[f26198,f33626]) ).
fof(f33626,plain,
( spl559_316
<=> class_Rings_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_316])]) ).
fof(f26198,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(cnf_transformation,[],[f5057]) ).
fof(f5057,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(f33607,plain,
spl559_146,
inference(avatar_split_clause,[],[f20408,f30519]) ).
fof(f20408,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
inference(cnf_transformation,[],[f878]) ).
fof(f878,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pls__def) ).
fof(f33606,plain,
spl559_315,
inference(avatar_split_clause,[],[f33601,f33603]) ).
fof(f33601,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f33600,f25821]) ).
fof(f33600,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(forward_demodulation,[],[f33599,f22937]) ).
fof(f33599,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(forward_demodulation,[],[f33598,f24320]) ).
fof(f33598,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))),
inference(forward_demodulation,[],[f33597,f25821]) ).
fof(f33597,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))),
inference(forward_demodulation,[],[f33596,f22937]) ).
fof(f33596,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))),
inference(forward_demodulation,[],[f33595,f22937]) ).
fof(f33595,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))),
inference(forward_demodulation,[],[f33594,f20419]) ).
fof(f33594,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f33593,f25821]) ).
fof(f33593,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f33592,f22937]) ).
fof(f33592,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f33591,f25821]) ).
fof(f33591,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f33590,f22937]) ).
fof(f33590,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f33589,f20419]) ).
fof(f33589,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f33588,f20419]) ).
fof(f33588,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f27348,f26803]) ).
fof(f27348,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(definition_unfolding,[],[f21207,f21744,f20132]) ).
fof(f21207,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(cnf_transformation,[],[f1262]) ).
fof(f1262,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).
fof(f33581,plain,
spl559_314,
inference(avatar_split_clause,[],[f21786,f33578]) ).
fof(f33578,plain,
( spl559_314
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_314])]) ).
fof(f21786,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f5079]) ).
fof(f5079,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(f33538,plain,
spl559_313,
inference(avatar_split_clause,[],[f23911,f33535]) ).
fof(f33535,plain,
( spl559_313
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_313])]) ).
fof(f23911,plain,
class_Int_Onumber(tc_Int_Oint),
inference(cnf_transformation,[],[f5073]) ).
fof(f5073,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber) ).
fof(f33527,plain,
spl559_312,
inference(avatar_split_clause,[],[f28167,f33524]) ).
fof(f33524,plain,
( spl559_312
<=> 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,[spl559_312])]) ).
fof(f28167,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)),
inference(definition_unfolding,[],[f26652,f20937]) ).
fof(f26652,plain,
c_Int_OPls = c_Int_Osucc(c_Int_OMin),
inference(cnf_transformation,[],[f1567]) ).
fof(f1567,axiom,
c_Int_OPls = c_Int_Osucc(c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Min) ).
fof(f33522,plain,
spl559_311,
inference(avatar_split_clause,[],[f21729,f33519]) ).
fof(f33519,plain,
( spl559_311
<=> class_Nat_Osize(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_311])]) ).
fof(f21729,plain,
class_Nat_Osize(tc_Nat_Onat),
inference(cnf_transformation,[],[f5124]) ).
fof(f5124,axiom,
class_Nat_Osize(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osize) ).
fof(f33517,plain,
spl559_310,
inference(avatar_split_clause,[],[f25177,f33514]) ).
fof(f33514,plain,
( spl559_310
<=> class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_310])]) ).
fof(f25177,plain,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5182]) ).
fof(f5182,axiom,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div) ).
fof(f33501,plain,
spl559_309,
inference(avatar_split_clause,[],[f21848,f33498]) ).
fof(f33498,plain,
( spl559_309
<=> class_Groups_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_309])]) ).
fof(f21848,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f5070]) ).
fof(f5070,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(f33496,plain,
spl559_308,
inference(avatar_split_clause,[],[f23344,f33493]) ).
fof(f33493,plain,
( spl559_308
<=> class_Nat_Osize(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_308])]) ).
fof(f23344,plain,
class_Nat_Osize(tc_HOL_Obool),
inference(cnf_transformation,[],[f5142]) ).
fof(f5142,axiom,
class_Nat_Osize(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Nat_Osize) ).
fof(f33462,plain,
spl559_307,
inference(avatar_split_clause,[],[f23986,f33459]) ).
fof(f33459,plain,
( spl559_307
<=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_307])]) ).
fof(f23986,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f5111]) ).
fof(f5111,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(f33457,plain,
spl559_306,
inference(avatar_split_clause,[],[f25027,f33454]) ).
fof(f33454,plain,
( spl559_306
<=> class_Groups_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_306])]) ).
fof(f25027,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f5122]) ).
fof(f5122,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(f33452,plain,
spl559_305,
inference(avatar_split_clause,[],[f20053,f33449]) ).
fof(f33449,plain,
( spl559_305
<=> class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_305])]) ).
fof(f20053,plain,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5175]) ).
fof(f5175,axiom,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult) ).
fof(f33398,plain,
spl559_304,
inference(avatar_split_clause,[],[f23213,f33395]) ).
fof(f33395,plain,
( spl559_304
<=> 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,[spl559_304])]) ).
fof(f23213,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,[],[f2904]) ).
fof(f2904,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(f33355,plain,
spl559_303,
inference(avatar_split_clause,[],[f22808,f33352]) ).
fof(f33352,plain,
( spl559_303
<=> class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_303])]) ).
fof(f22808,plain,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5184]) ).
fof(f5184,axiom,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0) ).
fof(f33322,plain,
spl559_302,
inference(avatar_split_clause,[],[f28136,f33319]) ).
fof(f28136,plain,
c_Nitpick_OFrac = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(definition_unfolding,[],[f26459,f22094]) ).
fof(f22094,plain,
! [X2,X0,X1] : c_Product__Type_Oprod_Oprod__case(X0,X2,X1) = c_Product__Type_Ointernal__split(X0,X2,X1),
inference(cnf_transformation,[],[f16094]) ).
fof(f16094,plain,
! [X0,X1,X2] : c_Product__Type_Oprod_Oprod__case(X0,X2,X1) = c_Product__Type_Ointernal__split(X0,X2,X1),
inference(rectify,[],[f7468]) ).
fof(f7468,plain,
! [X0,X2,X1] : c_Product__Type_Oprod_Oprod__case(X0,X1,X2) = c_Product__Type_Ointernal__split(X0,X1,X2),
inference(rectify,[],[f3700]) ).
fof(f3700,axiom,
! [X8,X6,X22] : c_Product__Type_Oprod_Oprod__case(X8,X6,X22) = c_Product__Type_Ointernal__split(X8,X6,X22),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__def) ).
fof(f26459,plain,
c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(cnf_transformation,[],[f1716]) ).
fof(f1716,axiom,
c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),c_fequal)),c_Nitpick_Oint__gcd))),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_OFrac__def) ).
fof(f33317,plain,
spl559_236,
inference(avatar_split_clause,[],[f22526,f31532]) ).
fof(f22526,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f958]) ).
fof(f958,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_nat__0) ).
fof(f33315,plain,
spl559_301,
inference(avatar_split_clause,[],[f24468,f33312]) ).
fof(f33312,plain,
( spl559_301
<=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_301])]) ).
fof(f24468,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5019]) ).
fof(f5019,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(f33305,plain,
( spl559_18
| spl559_299 ),
inference(avatar_split_clause,[],[f33304,f33260,f29037]) ).
fof(f33260,plain,
( spl559_299
<=> ! [X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_299])]) ).
fof(f33304,plain,
! [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_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(forward_subsumption_demodulation,[],[f24238,f28765]) ).
fof(f28765,plain,
! [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) = hAPP(c_Int_Onat,X0) ),
inference(equality_resolution,[],[f25691]) ).
fof(f25691,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 ),
inference(cnf_transformation,[],[f18853]) ).
fof(f18853,plain,
! [X0,X1] :
( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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_Int_Onat,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))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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)) ) ) ),
inference(flattening,[],[f18852]) ).
fof(f18852,plain,
! [X0,X1] :
( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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_Int_Onat,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))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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)) ) ) ),
inference(nnf_transformation,[],[f13739]) ).
fof(f13739,plain,
! [X0,X1] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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_Int_Onat,X0) = X1 ),
inference(ennf_transformation,[],[f6740]) ).
fof(f6740,plain,
! [X1,X0] :
( 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))
=> 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 ) ) ),
inference(rectify,[],[f1001]) ).
fof(f1001,axiom,
! [X91,X53] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X53 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X53) = X91 ) )
<=> hAPP(c_Int_Onat,X91) = X53 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__iff2) ).
fof(f24238,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ),
inference(cnf_transformation,[],[f14355]) ).
fof(f14355,plain,
! [X0] :
( ( ~ 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),hAPP(c_Int_Onat,X0)) = 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_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X0)) ) ),
inference(ennf_transformation,[],[f9413]) ).
fof(f9413,plain,
! [X0] :
( ( 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),hAPP(c_Int_Onat,X0)) = 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_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X0)) ) ),
inference(rectify,[],[f986]) ).
fof(f986,axiom,
! [X16] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X16)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X16))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,X16)) = X16 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__nat__eq) ).
fof(f33303,plain,
spl559_300,
inference(avatar_split_clause,[],[f26066,f33300]) ).
fof(f26066,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
inference(cnf_transformation,[],[f4572]) ).
fof(f4572,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(f33298,plain,
spl559_258,
inference(avatar_split_clause,[],[f20471,f31960]) ).
fof(f31960,plain,
( spl559_258
<=> 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,[spl559_258])]) ).
fof(f20471,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,[],[f825]) ).
fof(f825,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_transfer__int__nat__numerals_I2_J) ).
fof(f33262,plain,
( spl559_275
| spl559_299 ),
inference(avatar_split_clause,[],[f33258,f33260,f32214]) ).
fof(f32214,plain,
( spl559_275
<=> ! [X0] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X0)
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_275])]) ).
fof(f33258,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ class_Int_Onumber__ring(X0)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X0) ),
inference(forward_subsumption_demodulation,[],[f33173,f28765]) ).
fof(f33173,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),hAPP(c_Int_Onat,X1)) = c_Groups_Ozero__class_Ozero(X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(backward_demodulation,[],[f30637,f33119]) ).
fof(f30637,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),hAPP(c_Int_Onumber__class_Onumber__of(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(forward_demodulation,[],[f22238,f26803]) ).
fof(f22238,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ class_Int_Onumber__ring(X0)
| c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) ),
inference(cnf_transformation,[],[f13654]) ).
fof(f13654,plain,
! [X0,X1] :
( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(c_Int_Onumber__class_Onumber__of(X0),X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) ) )
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f7783]) ).
fof(f7783,plain,
! [X1,X0] :
( class_Int_Onumber__ring(X0)
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
=> hAPP(c_Int_Onumber__class_Onumber__of(X0),X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
=> c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) ) ) ),
inference(rectify,[],[f814]) ).
fof(f814,axiom,
! [X12,X82] :
( class_Int_Onumber__ring(X12)
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> c_Groups_Ozero__class_Ozero(X12) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X12),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> hAPP(c_Int_Onumber__class_Onumber__of(X12),X82) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X12),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__number__of__lemma) ).
fof(f33057,plain,
spl559_298,
inference(avatar_split_clause,[],[f23920,f33054]) ).
fof(f33054,plain,
( spl559_298
<=> c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_298])]) ).
fof(f23920,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f1629]) ).
fof(f1629,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(f33052,plain,
spl559_297,
inference(avatar_split_clause,[],[f22658,f33049]) ).
fof(f33049,plain,
( spl559_297
<=> class_Lattices_Odistrib__lattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_297])]) ).
fof(f22658,plain,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
inference(cnf_transformation,[],[f5029]) ).
fof(f5029,axiom,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Odistrib__lattice) ).
fof(f33041,plain,
spl559_296,
inference(avatar_split_clause,[],[f22915,f33038]) ).
fof(f33038,plain,
( spl559_296
<=> class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_296])]) ).
fof(f22915,plain,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5188]) ).
fof(f5188,axiom,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult) ).
fof(f33034,plain,
spl559_295,
inference(avatar_split_clause,[],[f27023,f33031]) ).
fof(f33031,plain,
( spl559_295
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_295])]) ).
fof(f27023,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5009]) ).
fof(f5009,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(f33023,plain,
spl559_294,
inference(avatar_split_clause,[],[f33018,f33020]) ).
fof(f33018,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f33017,f28382]) ).
fof(f28382,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(equality_resolution,[],[f21200]) ).
fof(f21200,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f15447]) ).
fof(f15447,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X0)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
inference(rectify,[],[f11338]) ).
fof(f11338,plain,
! [X1,X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(ennf_transformation,[],[f8188]) ).
fof(f8188,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X1)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) ) ),
inference(rectify,[],[f742]) ).
fof(f742,axiom,
! [X55,X54] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X55
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X55),X54) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X55
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X55),X54) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X54),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X55),c_Groups_Oone__class_Oone(tc_Nat_Onat))),X54)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__if) ).
fof(f33017,plain,
! [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)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f28882,f28382]) ).
fof(f28882,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,[],[f26856]) ).
fof(f26856,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,[],[f19720]) ).
fof(f19720,plain,
! [X0,X1,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 )
& ( 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)) ) ),
inference(rectify,[],[f13443]) ).
fof(f13443,plain,
! [X1,X0,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),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ) ),
inference(ennf_transformation,[],[f8637]) ).
fof(f8637,plain,
! [X2,X1,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),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)) ) ),
inference(rectify,[],[f1538]) ).
fof(f1538,axiom,
! [X55,X54,X61] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X61
=> 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),X61),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X54)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X61
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X55),X54) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X55)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X61),X54)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__div__cancel__disj) ).
fof(f32582,plain,
spl559_293,
inference(avatar_split_clause,[],[f21927,f32579]) ).
fof(f32579,plain,
( spl559_293
<=> class_Divides_Oring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_293])]) ).
fof(f21927,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f5056]) ).
fof(f5056,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Divides_Oring__div) ).
fof(f32562,plain,
spl559_292,
inference(avatar_split_clause,[],[f21516,f32559]) ).
fof(f32559,plain,
( spl559_292
<=> class_Lattices_Osemilattice__inf(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_292])]) ).
fof(f21516,plain,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
inference(cnf_transformation,[],[f5028]) ).
fof(f5028,axiom,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__inf) ).
fof(f32546,plain,
spl559_291,
inference(avatar_split_clause,[],[f27345,f32543]) ).
fof(f32543,plain,
( spl559_291
<=> c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_291])]) ).
fof(f27345,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Int_OPls),
inference(definition_unfolding,[],[f21181,f22455]) ).
fof(f22455,plain,
! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X0),
inference(cnf_transformation,[],[f8460]) ).
fof(f8460,plain,
! [X0] : c_Int_Opred(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X0),
inference(rectify,[],[f1563]) ).
fof(f1563,axiom,
! [X61] : c_Int_Opred(X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X61),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min) ).
fof(f21181,plain,
c_Int_OMin = c_Int_Opred(c_Int_OPls),
inference(cnf_transformation,[],[f1561]) ).
fof(f1561,axiom,
c_Int_OMin = c_Int_Opred(c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__Pls) ).
fof(f32520,plain,
spl559_290,
inference(avatar_split_clause,[],[f32515,f32517]) ).
fof(f32515,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f32514,f24320]) ).
fof(f32514,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))),
inference(forward_demodulation,[],[f32513,f22937]) ).
fof(f32513,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(forward_demodulation,[],[f27244,f20419]) ).
fof(f27244,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),
inference(definition_unfolding,[],[f20553,f20132]) ).
fof(f20553,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,[],[f994]) ).
fof(f994,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(f32477,plain,
spl559_289,
inference(avatar_split_clause,[],[f20767,f32474]) ).
fof(f32474,plain,
( spl559_289
<=> class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_289])]) ).
fof(f20767,plain,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
inference(cnf_transformation,[],[f5126]) ).
fof(f5126,axiom,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__top) ).
fof(f32429,plain,
spl559_288,
inference(avatar_split_clause,[],[f23268,f32426]) ).
fof(f32426,plain,
( spl559_288
<=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_288])]) ).
fof(f23268,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5013]) ).
fof(f5013,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(f32415,plain,
spl559_287,
inference(avatar_split_clause,[],[f22660,f32412]) ).
fof(f32412,plain,
( spl559_287
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_287])]) ).
fof(f22660,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5107]) ).
fof(f5107,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(f32374,plain,
spl559_158,
inference(avatar_split_clause,[],[f26001,f30649]) ).
fof(f26001,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,[],[f893]) ).
fof(f893,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(f32372,plain,
spl559_286,
inference(avatar_split_clause,[],[f22545,f32369]) ).
fof(f32369,plain,
( spl559_286
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_286])]) ).
fof(f22545,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[],[f5078]) ).
fof(f5078,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(f32360,plain,
spl559_285,
inference(avatar_split_clause,[],[f25972,f32357]) ).
fof(f32357,plain,
( spl559_285
<=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_285])]) ).
fof(f25972,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5083]) ).
fof(f5083,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(f32354,plain,
spl559_284,
inference(avatar_split_clause,[],[f26294,f32351]) ).
fof(f32351,plain,
( spl559_284
<=> class_Lattices_Olattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_284])]) ).
fof(f26294,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f5112]) ).
fof(f5112,axiom,
class_Lattices_Olattice(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
fof(f32349,plain,
spl559_283,
inference(avatar_split_clause,[],[f20660,f32346]) ).
fof(f32346,plain,
( spl559_283
<=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_283])]) ).
fof(f20660,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5050]) ).
fof(f5050,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(f32336,plain,
spl559_282,
inference(avatar_split_clause,[],[f24344,f32333]) ).
fof(f32333,plain,
( spl559_282
<=> class_Rings_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_282])]) ).
fof(f24344,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5053]) ).
fof(f5053,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(f32326,plain,
spl559_281,
inference(avatar_split_clause,[],[f23546,f32323]) ).
fof(f32323,plain,
( spl559_281
<=> class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_281])]) ).
fof(f23546,plain,
class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
inference(cnf_transformation,[],[f5026]) ).
fof(f5026,axiom,
class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lazy__Sequence_Osmall__lazy) ).
fof(f32319,plain,
( spl559_97
| spl559_280 ),
inference(avatar_split_clause,[],[f32314,f32316,f29805]) ).
fof(f32314,plain,
! [X0] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_subsumption_demodulation,[],[f32313,f29520]) ).
fof(f32313,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ),
inference(forward_demodulation,[],[f22913,f26803]) ).
fof(f22913,plain,
! [X0] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f10316]) ).
fof(f10316,plain,
! [X0] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ) ),
inference(ennf_transformation,[],[f9387]) ).
fof(f9387,plain,
! [X0] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ) ),
inference(rectify,[],[f1516]) ).
fof(f1516,axiom,
! [X108] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X108)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X108)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X108))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X108)))
=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X108)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__mod__nat__number__of) ).
fof(f32283,plain,
spl559_279,
inference(avatar_split_clause,[],[f26564,f32280]) ).
fof(f32280,plain,
( spl559_279
<=> class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_279])]) ).
fof(f26564,plain,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5169]) ).
fof(f5169,axiom,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring) ).
fof(f32262,plain,
spl559_40,
inference(avatar_split_clause,[],[f27141,f29162]) ).
fof(f29162,plain,
( spl559_40
<=> c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_40])]) ).
fof(f27141,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls),
inference(definition_unfolding,[],[f20028,f21744]) ).
fof(f20028,plain,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
inference(cnf_transformation,[],[f1123]) ).
fof(f1123,axiom,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit0__Pls) ).
fof(f32244,plain,
spl559_278,
inference(avatar_split_clause,[],[f32239,f32241]) ).
fof(f32239,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),c_List_Olist_ONil(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f32238,f21617]) ).
fof(f21617,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Omap(X0,X2),X1),c_List_Olist_ONil(X0)) = c_List_Olist_ONil(X2),
inference(cnf_transformation,[],[f15758]) ).
fof(f15758,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Omap(X0,X2),X1),c_List_Olist_ONil(X0)) = c_List_Olist_ONil(X2),
inference(rectify,[],[f5797]) ).
fof(f5797,plain,
! [X2,X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Omap(X2,X1),X0),c_List_Olist_ONil(X2)),
inference(rectify,[],[f4116]) ).
fof(f4116,axiom,
! [X1,X8,X6] : c_List_Olist_ONil(X8) = hAPP(hAPP(c_List_Omap(X6,X8),X1),c_List_Olist_ONil(X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map_Osimps_I1_J) ).
fof(f32238,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X0,tc_Nat_Onat),X1),c_List_Olist_ONil(X0)))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f27619,f28520]) ).
fof(f28520,plain,
! [X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),c_List_Olist_ONil(X1)),
inference(equality_resolution,[],[f23007]) ).
fof(f23007,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0)
| c_List_Olist_ONil(X1) != X0 ),
inference(cnf_transformation,[],[f16779]) ).
fof(f16779,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0)
| c_List_Olist_ONil(X1) != X0 )
& ( c_List_Olist_ONil(X1) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X0) ) ),
inference(rectify,[],[f16778]) ).
fof(f16778,plain,
! [X1,X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),X1)
| c_List_Olist_ONil(X0) != X1 )
& ( c_List_Olist_ONil(X0) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),X1) ) ),
inference(nnf_transformation,[],[f9950]) ).
fof(f9950,plain,
! [X1,X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),X1)
<=> c_List_Olist_ONil(X0) = X1 ),
inference(rectify,[],[f3887]) ).
fof(f3887,axiom,
! [X8,X202] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X202)
<=> c_List_Olist_ONil(X8) = X202 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__0__conv) ).
fof(f27619,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X0,tc_Nat_Onat),X1),c_List_Olist_ONil(X0)))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),c_List_Olist_ONil(X0))),
inference(definition_unfolding,[],[f23057,f20844]) ).
fof(f20844,plain,
! [X2,X0,X1] : c_List_Olist_Olist__size(X1,X0,X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X1,tc_Nat_Onat),X0),X2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),
inference(cnf_transformation,[],[f15188]) ).
fof(f15188,plain,
! [X0,X1,X2] : c_List_Olist_Olist__size(X1,X0,X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X1,tc_Nat_Onat),X0),X2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X1)),X2)),
inference(rectify,[],[f9546]) ).
fof(f9546,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X0,tc_Nat_Onat),X2),X1))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),X1)) = c_List_Olist_Olist__size(X0,X2,X1),
inference(rectify,[],[f4174]) ).
fof(f4174,axiom,
! [X8,X202,X1] : c_List_Olist_Olist__size(X8,X1,X202) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(X8,tc_Nat_Onat),X1),X202))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),X202)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list__size__conv__listsum) ).
fof(f23057,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_List_Olist_Olist__size(X0,X1,c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f7695]) ).
fof(f7695,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_List_Olist_Olist__size(X0,X1,c_List_Olist_ONil(X0)),
inference(rectify,[],[f3894]) ).
fof(f3894,axiom,
! [X8,X85] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_List_Olist_Olist__size(X8,X85,c_List_Olist_ONil(X8)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_list_Osize_I1_J) ).
fof(f32233,plain,
spl559_277,
inference(avatar_split_clause,[],[f23731,f32230]) ).
fof(f32230,plain,
( spl559_277
<=> class_Rings_Ocomm__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_277])]) ).
fof(f23731,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5058]) ).
fof(f5058,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(f32221,plain,
spl559_276,
inference(avatar_split_clause,[],[f21319,f32218]) ).
fof(f32218,plain,
( spl559_276
<=> class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_276])]) ).
fof(f21319,plain,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5189]) ).
fof(f5189,axiom,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add) ).
fof(f32216,plain,
( spl559_275
| spl559_97 ),
inference(avatar_split_clause,[],[f32212,f29805,f32214]) ).
fof(f32212,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(X0)
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_subsumption_demodulation,[],[f32211,f29520]) ).
fof(f32211,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1))
| ~ class_Int_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f24100,f26803]) ).
fof(f24100,plain,
! [X0,X1] :
( ~ class_Int_Onumber__ring(X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) ),
inference(cnf_transformation,[],[f17596]) ).
fof(f17596,plain,
! [X0,X1] :
( ( ( hAPP(c_Int_Onumber__class_Onumber__of(X0),X1) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(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),X1)))
| c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) ) )
| ~ class_Int_Onumber__ring(X0) ),
inference(rectify,[],[f14029]) ).
fof(f14029,plain,
! [X1,X0] :
( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),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)))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) = c_Groups_Ozero__class_Ozero(X1) ) )
| ~ class_Int_Onumber__ring(X1) ),
inference(ennf_transformation,[],[f5611]) ).
fof(f5611,plain,
! [X1,X0] :
( class_Int_Onumber__ring(X1)
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) = hAPP(c_Int_Onumber__class_Onumber__of(X1),X0) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(X1),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) = c_Groups_Ozero__class_Ozero(X1) ) ) ),
inference(rectify,[],[f863]) ).
fof(f863,axiom,
! [X82,X12] :
( class_Int_Onumber__ring(X12)
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> c_Groups_Ozero__class_Ozero(X12) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X12),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> hAPP(c_Int_Onumber__class_Onumber__of(X12),X82) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X12),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__number__of__eq) ).
fof(f32207,plain,
spl559_274,
inference(avatar_split_clause,[],[f22019,f32204]) ).
fof(f32204,plain,
( spl559_274
<=> class_Int_Onumber(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_274])]) ).
fof(f22019,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(cnf_transformation,[],[f5121]) ).
fof(f5121,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Int_Onumber) ).
fof(f32191,plain,
spl559_273,
inference(avatar_split_clause,[],[f22909,f32188]) ).
fof(f32188,plain,
( spl559_273
<=> class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_273])]) ).
fof(f22909,plain,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5192]) ).
fof(f5192,axiom,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero) ).
fof(f32186,plain,
spl559_272,
inference(avatar_split_clause,[],[f20765,f32183]) ).
fof(f32183,plain,
( spl559_272
<=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_272])]) ).
fof(f20765,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f5099]) ).
fof(f5099,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__1) ).
fof(f32173,plain,
spl559_271,
inference(avatar_split_clause,[],[f24258,f32170]) ).
fof(f24258,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f364]) ).
fof(f364,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(f32153,plain,
spl559_270,
inference(avatar_split_clause,[],[f20724,f32150]) ).
fof(f32150,plain,
( spl559_270
<=> class_Enum_Oenum(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_270])]) ).
fof(f20724,plain,
class_Enum_Oenum(tc_HOL_Obool),
inference(cnf_transformation,[],[f5141]) ).
fof(f5141,axiom,
class_Enum_Oenum(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Enum_Oenum) ).
fof(f32146,plain,
spl559_269,
inference(avatar_split_clause,[],[f32141,f32143]) ).
fof(f32143,plain,
( spl559_269
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_269])]) ).
fof(f32141,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),c_Int_OMin),
inference(forward_demodulation,[],[f28795,f26803]) ).
fof(f28795,plain,
c_Groups_Oone__class_Oone(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_OMin)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
inference(equality_resolution,[],[f28794]) ).
fof(f28794,plain,
! [X0] :
( c_Groups_Oone__class_Oone(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_OMin)),X0)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0 ),
inference(equality_resolution,[],[f25967]) ).
fof(f25967,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0 ),
inference(cnf_transformation,[],[f19043]) ).
fof(f19043,plain,
! [X0,X1] :
( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0)
| ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0 )
& ( 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) = X1
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 )
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X1),X0) ) ),
inference(rectify,[],[f19042]) ).
fof(f19042,plain,
! [X1,X0] :
( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),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) != X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X0 ) ) )
& ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 )
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1) ) ),
inference(flattening,[],[f19041]) ).
fof(f19041,plain,
! [X1,X0] :
( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),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) != X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X0 ) ) )
& ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 )
| c_Groups_Oone__class_Oone(tc_Int_Oint) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),X1) ) ),
inference(nnf_transformation,[],[f9406]) ).
fof(f9406,plain,
! [X1,X0] :
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),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) = X1
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X0 ) ) ),
inference(rectify,[],[f1586]) ).
fof(f1586,axiom,
! [X53,X56] :
( ( ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X56
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X53 )
| ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X53
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X56 ) )
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X53),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmult__eq__1__iff) ).
fof(f32076,plain,
spl559_268,
inference(avatar_split_clause,[],[f25369,f32073]) ).
fof(f32073,plain,
( spl559_268
<=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_268])]) ).
fof(f25369,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5087]) ).
fof(f5087,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__semigroup__add) ).
fof(f32070,plain,
spl559_267,
inference(avatar_split_clause,[],[f20387,f32067]) ).
fof(f32067,plain,
( spl559_267
<=> class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_267])]) ).
fof(f20387,plain,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5196]) ).
fof(f5196,axiom,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ominus) ).
fof(f32064,plain,
spl559_266,
inference(avatar_split_clause,[],[f23412,f32061]) ).
fof(f32061,plain,
( spl559_266
<=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_266])]) ).
fof(f23412,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5032]) ).
fof(f5032,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__add) ).
fof(f32059,plain,
spl559_265,
inference(avatar_split_clause,[],[f32054,f32056]) ).
fof(f32054,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f28898,f28808]) ).
fof(f28808,plain,
! [X1] : c_Groups_Oone__class_Oone(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,[],[f26058]) ).
fof(f26058,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(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,[],[f19110]) ).
fof(f19110,plain,
! [X0,X1] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f11842]) ).
fof(f11842,plain,
! [X1,X0] :
( ( 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 )
& ( 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)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 ) ),
inference(ennf_transformation,[],[f9882]) ).
fof(f9882,plain,
! [X0,X1] :
( ( 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
=> 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)))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) ) ),
inference(rectify,[],[f1256]) ).
fof(f1256,axiom,
! [X116,X55] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X55
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X116),X55) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X55
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X116),X55) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X116),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X116),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X55),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power__eq__if) ).
fof(f28898,plain,
! [X0] : 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),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(equality_resolution,[],[f27010]) ).
fof(f27010,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),X0),X1)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f19832]) ).
fof(f19832,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = 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),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),X0),X1)))
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ) ),
inference(rectify,[],[f19831]) ).
fof(f19831,plain,
! [X1,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)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))) )
& ( 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)))
| ( ~ 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 ) ) ),
inference(flattening,[],[f19830]) ).
fof(f19830,plain,
! [X1,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)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))) )
& ( 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)))
| ( ~ 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 ) ) ),
inference(nnf_transformation,[],[f7731]) ).
fof(f7731,plain,
! [X1,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)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))) ),
inference(rectify,[],[f1297]) ).
fof(f1297,axiom,
! [X56,X14] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X14))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X56 )
<=> 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),X14),X56))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(f32051,plain,
spl559_264,
inference(avatar_split_clause,[],[f32046,f32048]) ).
fof(f32048,plain,
( spl559_264
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_264])]) ).
fof(f32046,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)),
inference(forward_demodulation,[],[f21044,f26803]) ).
fof(f21044,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
inference(cnf_transformation,[],[f1560]) ).
fof(f1560,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(f32041,plain,
spl559_263,
inference(avatar_split_clause,[],[f22843,f32038]) ).
fof(f22843,plain,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
inference(cnf_transformation,[],[f3108]) ).
fof(f3108,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(f32035,plain,
spl559_262,
inference(avatar_split_clause,[],[f20958,f32032]) ).
fof(f32032,plain,
( spl559_262
<=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_262])]) ).
fof(f20958,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5085]) ).
fof(f5085,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__cancel__semiring) ).
fof(f31991,plain,
spl559_261,
inference(avatar_split_clause,[],[f31986,f31988]) ).
fof(f31988,plain,
( spl559_261
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_261])]) ).
fof(f31986,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Int_OPls)),
inference(forward_demodulation,[],[f26627,f26803]) ).
fof(f26627,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(cnf_transformation,[],[f891]) ).
fof(f891,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_number__of2) ).
fof(f31983,plain,
spl559_260,
inference(avatar_split_clause,[],[f24192,f31980]) ).
fof(f31980,plain,
( spl559_260
<=> class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_260])]) ).
fof(f24192,plain,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5165]) ).
fof(f5165,axiom,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict) ).
fof(f31968,plain,
spl559_259,
inference(avatar_split_clause,[],[f25872,f31965]) ).
fof(f31965,plain,
( spl559_259
<=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_259])]) ).
fof(f25872,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5094]) ).
fof(f5094,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__mult) ).
fof(f31963,plain,
spl559_258,
inference(avatar_split_clause,[],[f20257,f31960]) ).
fof(f20257,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,[],[f844]) ).
fof(f844,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(f31953,plain,
spl559_257,
inference(avatar_split_clause,[],[f31948,f31950]) ).
fof(f31948,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f31947,f22937]) ).
fof(f31947,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f31946,f22937]) ).
fof(f31946,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))))))),
inference(forward_demodulation,[],[f31945,f24320]) ).
fof(f31945,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),
inference(forward_demodulation,[],[f31944,f22937]) ).
fof(f31944,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),
inference(forward_demodulation,[],[f31943,f22937]) ).
fof(f31943,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))))))),
inference(forward_demodulation,[],[f31942,f22937]) ).
fof(f31942,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))))))),
inference(forward_demodulation,[],[f31941,f20419]) ).
fof(f31941,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31940,f22937]) ).
fof(f31940,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31939,f22937]) ).
fof(f31939,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31938,f22937]) ).
fof(f31938,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31937,f22937]) ).
fof(f31937,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31936,f20419]) ).
fof(f31936,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f31935,f20419]) ).
fof(f31935,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f27167,f20419]) ).
fof(f27167,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),
inference(definition_unfolding,[],[f20174,f20132,f20132]) ).
fof(f20174,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(cnf_transformation,[],[f1010]) ).
fof(f1010,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__3__eq__3) ).
fof(f31905,plain,
spl559_256,
inference(avatar_split_clause,[],[f22723,f31902]) ).
fof(f31902,plain,
( spl559_256
<=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_256])]) ).
fof(f22723,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5023]) ).
fof(f5023,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocancel__semigroup__add) ).
fof(f31892,plain,
spl559_156,
inference(avatar_split_clause,[],[f31891,f30610]) ).
fof(f31891,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(backward_demodulation,[],[f28722,f28808]) ).
fof(f28722,plain,
! [X1] : hAPP(c_Nat_OSuc,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,[],[f25184]) ).
fof(f25184,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,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,[],[f18474]) ).
fof(f18474,plain,
! [X0,X1] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| ( hAPP(c_Nat_OSuc,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
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) ) ),
inference(flattening,[],[f18473]) ).
fof(f18473,plain,
! [X0,X1] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
| ( hAPP(c_Nat_OSuc,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
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0) ) ),
inference(nnf_transformation,[],[f5506]) ).
fof(f5506,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)
<=> ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f1295]) ).
fof(f1295,axiom,
! [X53,X14] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X14),X53)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X53
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(f31871,plain,
spl559_255,
inference(avatar_split_clause,[],[f21143,f31868]) ).
fof(f31868,plain,
( spl559_255
<=> class_Nat_Osemiring__char__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_255])]) ).
fof(f21143,plain,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f5104]) ).
fof(f5104,axiom,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Nat_Osemiring__char__0) ).
fof(f31864,plain,
spl559_254,
inference(avatar_split_clause,[],[f28377,f31861]) ).
fof(f28377,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,[],[f21136]) ).
fof(f21136,plain,
! [X0] :
( 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(cnf_transformation,[],[f13513]) ).
fof(f13513,plain,
! [X0] :
( ( 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) )
& ( ( ( 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 ) ),
inference(ennf_transformation,[],[f6753]) ).
fof(f6753,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,[],[f1614]) ).
fof(f1614,axiom,
! [X61] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X61
=> ( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X61,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,X61) = 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),X61),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,X61,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,X61) = 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),X61),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) = X61
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X61) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__of__code) ).
fof(f31855,plain,
( spl559_97
| spl559_253 ),
inference(avatar_split_clause,[],[f31851,f31853,f29805]) ).
fof(f31853,plain,
( spl559_253
<=> ! [X2,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_253])]) ).
fof(f31851,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2)) ),
inference(forward_subsumption_demodulation,[],[f31850,f29520]) ).
fof(f31850,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X2)) ),
inference(forward_demodulation,[],[f31849,f26803]) ).
fof(f31849,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X2))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
inference(forward_demodulation,[],[f21266,f26803]) ).
fof(f21266,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X2))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f15493]) ).
fof(f15493,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X2) )
& ( 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)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X1),X0))),X2) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),X2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X2))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ) ) ),
inference(rectify,[],[f10932]) ).
fof(f10932,plain,
! [X0,X2,X1] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X1) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
| ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0))),X1) )
& ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ) ) ),
inference(ennf_transformation,[],[f6119]) ).
fof(f6119,plain,
! [X2,X0,X1] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X1) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X2)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),X1) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X2),X0))),X1) ) ) ) ),
inference(rectify,[],[f919]) ).
fof(f919,axiom,
! [X108,X61,X82] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X108)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X108)),X61)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)),X61) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X108)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X108)),X61)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X82),X108))),X61) ) ) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X108)),X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X108)),X61)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__number__of__add__left) ).
fof(f31848,plain,
spl559_252,
inference(avatar_split_clause,[],[f24352,f31845]) ).
fof(f24352,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,[],[f1916]) ).
fof(f1916,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(f31838,plain,
spl559_251,
inference(avatar_split_clause,[],[f31833,f31835]) ).
fof(f31833,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),
inference(forward_demodulation,[],[f31832,f22937]) ).
fof(f31832,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),
inference(forward_demodulation,[],[f31831,f24320]) ).
fof(f31831,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31830,f22937]) ).
fof(f31830,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31829,f22937]) ).
fof(f31829,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31828,f20419]) ).
fof(f31828,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f31827,f22937]) ).
fof(f31827,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f31826,f22937]) ).
fof(f31826,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f31825,f20419]) ).
fof(f31825,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f31824,f20419]) ).
fof(f31824,plain,
c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),
inference(forward_demodulation,[],[f27463,f26803]) ).
fof(f27463,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(definition_unfolding,[],[f22057,f21744,f20132]) ).
fof(f22057,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f1669]) ).
fof(f1669,axiom,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J) ).
fof(f31819,plain,
spl559_250,
inference(avatar_split_clause,[],[f21463,f31816]) ).
fof(f31816,plain,
( spl559_250
<=> c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_250])]) ).
fof(f21463,plain,
c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),
inference(cnf_transformation,[],[f2497]) ).
fof(f2497,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(f31814,plain,
spl559_249,
inference(avatar_split_clause,[],[f22328,f31811]) ).
fof(f22328,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f983]) ).
fof(f983,axiom,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1) ).
fof(f31809,plain,
spl559_248,
inference(avatar_split_clause,[],[f24983,f31806]) ).
fof(f31806,plain,
( spl559_248
<=> class_Lattices_Osemilattice__sup(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_248])]) ).
fof(f24983,plain,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
inference(cnf_transformation,[],[f5128]) ).
fof(f5128,axiom,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
fof(f31802,plain,
spl559_247,
inference(avatar_split_clause,[],[f31797,f31799]) ).
fof(f31797,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))) = hAPP(c_Nat_OSuc,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f31796,f22302]) ).
fof(f22302,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,[],[f5661]) ).
fof(f5661,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,[],[f508]) ).
fof(f508,axiom,
! [X54] : hAPP(c_Nat_OSuc,X54) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X54),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__eq__plus1) ).
fof(f31796,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),
inference(forward_demodulation,[],[f31795,f22937]) ).
fof(f31795,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),
inference(forward_demodulation,[],[f31794,f24320]) ).
fof(f31794,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31793,f22937]) ).
fof(f31793,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31792,f22937]) ).
fof(f31792,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31791,f20419]) ).
fof(f31791,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f31790,f22937]) ).
fof(f31790,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f31789,f22937]) ).
fof(f31789,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f31788,f20419]) ).
fof(f31788,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f27606,f20419]) ).
fof(f27606,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),
inference(definition_unfolding,[],[f22977,f21744,f20132]) ).
fof(f22977,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1269]) ).
fof(f1269,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__1__add__1) ).
fof(f31786,plain,
spl559_246,
inference(avatar_split_clause,[],[f26626,f31783]) ).
fof(f31783,plain,
( spl559_246
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_246])]) ).
fof(f26626,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5007]) ).
fof(f5007,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(f31678,plain,
spl559_245,
inference(avatar_split_clause,[],[f22736,f31675]) ).
fof(f31675,plain,
( spl559_245
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_245])]) ).
fof(f22736,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5163]) ).
fof(f5163,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict) ).
fof(f31641,plain,
spl559_244,
inference(avatar_split_clause,[],[f31636,f31638]) ).
fof(f31636,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(forward_demodulation,[],[f31635,f24320]) ).
fof(f31635,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls))),
inference(forward_demodulation,[],[f31634,f22937]) ).
fof(f31634,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(forward_demodulation,[],[f27972,f20419]) ).
fof(f27972,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),
inference(definition_unfolding,[],[f25420,f20132]) ).
fof(f25420,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,[],[f995]) ).
fof(f995,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_nat__numeral__1__eq__1) ).
fof(f31629,plain,
spl559_243,
inference(avatar_split_clause,[],[f21618,f31626]) ).
fof(f31626,plain,
( spl559_243
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_243])]) ).
fof(f21618,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5080]) ).
fof(f5080,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(f31624,plain,
spl559_18,
inference(avatar_split_clause,[],[f26398,f29037]) ).
fof(f26398,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,[],[f817]) ).
fof(f817,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(f31621,plain,
spl559_242,
inference(avatar_split_clause,[],[f22081,f31618]) ).
fof(f31618,plain,
( spl559_242
<=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_242])]) ).
fof(f22081,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5086]) ).
fof(f5086,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__comm__semiring) ).
fof(f31614,plain,
spl559_241,
inference(avatar_split_clause,[],[f26958,f31611]) ).
fof(f31611,plain,
( spl559_241
<=> 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,[spl559_241])]) ).
fof(f26958,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,[],[f4168]) ).
fof(f4168,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(f31589,plain,
spl559_240,
inference(avatar_split_clause,[],[f28227,f31586]) ).
fof(f28227,plain,
c_Divides_OnegateSnd = hAPP(c_Product__Type_Ointernal__split(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Fun_Oid(tc_Int_Oint)))),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),
inference(definition_unfolding,[],[f26945,f27101]) ).
fof(f27101,plain,
! [X2,X3,X0,X1] : hAPP(c_Product__Type_Ointernal__split(X3,X0,tc_prod(X3,X1)),hAPP(hAPP(c_COMBC(X3,tc_fun(X0,X1),tc_fun(X0,tc_prod(X3,X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X3,X1)),tc_fun(tc_fun(X0,X1),tc_fun(X0,tc_prod(X3,X1))),X3),c_COMBB(X1,tc_prod(X3,X1),X0)),hAPP(hAPP(c_COMBB(X3,tc_fun(X1,tc_prod(X3,X1)),X3),c_Product__Type_OPair(X3,X1)),c_Fun_Oid(X3)))),X2)) = c_Product__Type_Oapsnd(X0,X1,X3,X2),
inference(definition_unfolding,[],[f20097,f27100]) ).
fof(f27100,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(c_Product__Type_Ointernal__split(X2,X5,tc_prod(X4,X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X5,X1),tc_fun(X5,tc_prod(X4,X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X4,X1)),tc_fun(tc_fun(X5,X1),tc_fun(X5,tc_prod(X4,X1))),X2),c_COMBB(X1,tc_prod(X4,X1),X5)),hAPP(hAPP(c_COMBB(X4,tc_fun(X1,tc_prod(X4,X1)),X2),c_Product__Type_OPair(X4,X1)),X0))),X3)) = c_Product__Type_Omap__pair(X2,X4,X5,X1,X0,X3),
inference(definition_unfolding,[],[f23164,f22094]) ).
fof(f23164,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(c_Product__Type_Oprod_Oprod__case(X2,X5,tc_prod(X4,X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X5,X1),tc_fun(X5,tc_prod(X4,X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X4,X1)),tc_fun(tc_fun(X5,X1),tc_fun(X5,tc_prod(X4,X1))),X2),c_COMBB(X1,tc_prod(X4,X1),X5)),hAPP(hAPP(c_COMBB(X4,tc_fun(X1,tc_prod(X4,X1)),X2),c_Product__Type_OPair(X4,X1)),X0))),X3)) = c_Product__Type_Omap__pair(X2,X4,X5,X1,X0,X3),
inference(cnf_transformation,[],[f16902]) ).
fof(f16902,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(c_Product__Type_Oprod_Oprod__case(X2,X5,tc_prod(X4,X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X5,X1),tc_fun(X5,tc_prod(X4,X1))),hAPP(hAPP(c_COMBB(tc_fun(X1,tc_prod(X4,X1)),tc_fun(tc_fun(X5,X1),tc_fun(X5,tc_prod(X4,X1))),X2),c_COMBB(X1,tc_prod(X4,X1),X5)),hAPP(hAPP(c_COMBB(X4,tc_fun(X1,tc_prod(X4,X1)),X2),c_Product__Type_OPair(X4,X1)),X0))),X3)) = c_Product__Type_Omap__pair(X2,X4,X5,X1,X0,X3),
inference(rectify,[],[f5261]) ).
fof(f5261,plain,
! [X2,X0,X3,X1,X4,X5] : c_Product__Type_Omap__pair(X3,X4,X5,X0,X2,X1) = hAPP(c_Product__Type_Oprod_Oprod__case(X3,X5,tc_prod(X4,X0)),hAPP(hAPP(c_COMBC(X3,tc_fun(X5,X0),tc_fun(X5,tc_prod(X4,X0))),hAPP(hAPP(c_COMBB(tc_fun(X0,tc_prod(X4,X0)),tc_fun(tc_fun(X5,X0),tc_fun(X5,tc_prod(X4,X0))),X3),c_COMBB(X0,tc_prod(X4,X0),X5)),hAPP(hAPP(c_COMBB(X4,tc_fun(X0,tc_prod(X4,X0)),X3),c_Product__Type_OPair(X4,X0)),X2))),X1)),
inference(rectify,[],[f3007]) ).
fof(f3007,axiom,
! [X140,X0,X1,X8,X22,X6] : c_Product__Type_Omap__pair(X8,X22,X6,X140,X1,X0) = hAPP(c_Product__Type_Oprod_Oprod__case(X8,X6,tc_prod(X22,X140)),hAPP(hAPP(c_COMBC(X8,tc_fun(X6,X140),tc_fun(X6,tc_prod(X22,X140))),hAPP(hAPP(c_COMBB(tc_fun(X140,tc_prod(X22,X140)),tc_fun(tc_fun(X6,X140),tc_fun(X6,tc_prod(X22,X140))),X8),c_COMBB(X140,tc_prod(X22,X140),X6)),hAPP(hAPP(c_COMBB(X22,tc_fun(X140,tc_prod(X22,X140)),X8),c_Product__Type_OPair(X22,X140)),X1))),X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__pair__def) ).
fof(f20097,plain,
! [X2,X3,X0,X1] : c_Product__Type_Omap__pair(X3,X3,X0,X1,c_Fun_Oid(X3),X2) = c_Product__Type_Oapsnd(X0,X1,X3,X2),
inference(cnf_transformation,[],[f6463]) ).
fof(f6463,plain,
! [X0,X1,X2,X3] : c_Product__Type_Omap__pair(X3,X3,X0,X1,c_Fun_Oid(X3),X2) = c_Product__Type_Oapsnd(X0,X1,X3,X2),
inference(rectify,[],[f3111]) ).
fof(f3111,axiom,
! [X6,X22,X1,X8] : c_Product__Type_Oapsnd(X6,X22,X8,X1) = c_Product__Type_Omap__pair(X8,X8,X6,X22,c_Fun_Oid(X8),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_apsnd__def) ).
fof(f26945,plain,
c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
inference(cnf_transformation,[],[f2720]) ).
fof(f2720,axiom,
c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negateSnd__def) ).
fof(f31584,plain,
spl559_239,
inference(avatar_split_clause,[],[f24641,f31581]) ).
fof(f31581,plain,
( spl559_239
<=> class_Nat_Osize(tc_Com_Ocom) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_239])]) ).
fof(f24641,plain,
class_Nat_Osize(tc_Com_Ocom),
inference(cnf_transformation,[],[f5003]) ).
fof(f5003,axiom,
class_Nat_Osize(tc_Com_Ocom),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Com__Ocom__Nat_Osize) ).
fof(f31579,plain,
spl559_238,
inference(avatar_split_clause,[],[f22333,f31576]) ).
fof(f31576,plain,
( spl559_238
<=> class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_238])]) ).
fof(f22333,plain,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5176]) ).
fof(f5176,axiom,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add) ).
fof(f31542,plain,
spl559_237,
inference(avatar_split_clause,[],[f26199,f31539]) ).
fof(f31539,plain,
( spl559_237
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_237])]) ).
fof(f26199,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5164]) ).
fof(f5164,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add) ).
fof(f31535,plain,
spl559_236,
inference(avatar_split_clause,[],[f24750,f31532]) ).
fof(f24750,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f959]) ).
fof(f959,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(f31527,plain,
spl559_235,
inference(avatar_split_clause,[],[f20615,f31524]) ).
fof(f31524,plain,
( spl559_235
<=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_235])]) ).
fof(f20615,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f5081]) ).
fof(f5081,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring__strict) ).
fof(f31522,plain,
spl559_234,
inference(avatar_split_clause,[],[f24070,f31519]) ).
fof(f31519,plain,
( spl559_234
<=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_234])]) ).
fof(f24070,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(cnf_transformation,[],[f5101]) ).
fof(f5101,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Divides_Osemiring__div) ).
fof(f31472,plain,
~ spl559_233,
inference(avatar_split_clause,[],[f25407,f31469]) ).
fof(f25407,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,[],[f2823]) ).
fof(f2823,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(f31457,plain,
( spl559_97
| spl559_232 ),
inference(avatar_split_clause,[],[f31453,f31455,f29805]) ).
fof(f31455,plain,
( spl559_232
<=> ! [X0] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_232])]) ).
fof(f31453,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_subsumption_demodulation,[],[f31452,f29520]) ).
fof(f31452,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f31451,f26803]) ).
fof(f31451,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f20172,f26803]) ).
fof(f20172,plain,
! [X0,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)))
| c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f13161]) ).
fof(f13161,plain,
! [X0,X1] :
( ( ( ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,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))) )
& ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),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),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) ) ),
inference(ennf_transformation,[],[f5582]) ).
fof(f5582,plain,
! [X1,X0] :
( ( 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) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,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),X0)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
=> hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,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)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ) ) ) ),
inference(rectify,[],[f1512]) ).
fof(f1512,axiom,
! [X82,X108] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X108)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X108)))
=> c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X108)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X108))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X108)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X108)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mod__nat__number__of) ).
fof(f31445,plain,
spl559_231,
inference(avatar_split_clause,[],[f24972,f31442]) ).
fof(f31442,plain,
( spl559_231
<=> class_Rings_Osemiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_231])]) ).
fof(f24972,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f5110]) ).
fof(f5110,axiom,
class_Rings_Osemiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__1) ).
fof(f31439,plain,
spl559_230,
inference(avatar_split_clause,[],[f21026,f31436]) ).
fof(f31436,plain,
( spl559_230
<=> class_Groups_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_230])]) ).
fof(f21026,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5055]) ).
fof(f5055,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(f31434,plain,
spl559_229,
inference(avatar_split_clause,[],[f21379,f31431]) ).
fof(f31431,plain,
( spl559_229
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_229])]) ).
fof(f21379,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5077]) ).
fof(f5077,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(f31406,plain,
spl559_228,
inference(avatar_split_clause,[],[f24579,f31403]) ).
fof(f31403,plain,
( spl559_228
<=> 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,[spl559_228])]) ).
fof(f24579,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,[],[f4188]) ).
fof(f4188,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(f31401,plain,
spl559_227,
inference(avatar_split_clause,[],[f24054,f31398]) ).
fof(f31398,plain,
( spl559_227
<=> 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,[spl559_227])]) ).
fof(f24054,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,[],[f4192]) ).
fof(f4192,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(f31395,plain,
spl559_226,
inference(avatar_split_clause,[],[f24576,f31392]) ).
fof(f31392,plain,
( spl559_226
<=> c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_226])]) ).
fof(f24576,plain,
c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f4687]) ).
fof(f4687,axiom,
c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trans__less__than) ).
fof(f31383,plain,
( ~ spl559_224
| spl559_225 ),
inference(avatar_split_clause,[],[f26551,f31381,f31377]) ).
fof(f31381,plain,
( spl559_225
<=> ! [X2,X0,X1] :
( hAPP(c_Finite__Set_Ocard(X0),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X0),X2)),hAPP(c_Finite__Set_Ocard(X0),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_225])]) ).
fof(f26551,plain,
! [X2,X0,X1] :
( hAPP(c_Finite__Set_Ocard(X0),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X0),X2)),hAPP(c_Finite__Set_Ocard(X0),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(cnf_transformation,[],[f19486]) ).
fof(f19486,plain,
! [X0,X1,X2] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(X0),sK524(X0,X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X2),X1))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2))
| hAPP(c_Finite__Set_Ocard(X0),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X0),X2)),hAPP(c_Finite__Set_Ocard(X0),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK524])],[f19484,f19485]) ).
fof(f19485,plain,
! [X0,X1,X2] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X0),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X2),X1)))
=> hBOOL(hAPP(hAPP(c_member(X0),sK524(X0,X1,X2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X2),X1))) ),
introduced(choice_axiom,[]) ).
fof(f19484,plain,
! [X0,X1,X2] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [X3] : hBOOL(hAPP(hAPP(c_member(X0),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X2),X1))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2))
| hAPP(c_Finite__Set_Ocard(X0),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X1)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X0),X2)),hAPP(c_Finite__Set_Ocard(X0),X1))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1)) ),
inference(rectify,[],[f14183]) ).
fof(f14183,plain,
! [X0,X2,X1] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [X3] : hBOOL(hAPP(hAPP(c_member(X0),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),X2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X0),X1)),hAPP(c_Finite__Set_Ocard(X0),X2)) = hAPP(c_Finite__Set_Ocard(X0),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2)) ),
inference(flattening,[],[f14182]) ).
fof(f14182,plain,
! [X1,X2,X0] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X0),X1)),hAPP(c_Finite__Set_Ocard(X0),X2)) = hAPP(c_Finite__Set_Ocard(X0),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X2))
| ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ? [X3] : hBOOL(hAPP(hAPP(c_member(X0),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),X2))) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1)) ),
inference(ennf_transformation,[],[f8509]) ).
fof(f8509,plain,
! [X1,X2,X0] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X1))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X0),X2))
=> ( ( ? [X3] : hBOOL(hAPP(hAPP(c_member(X0),X3),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),X2)))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X0),X1)),hAPP(c_Finite__Set_Ocard(X0),X2)) = hAPP(c_Finite__Set_Ocard(X0),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X2)) ) ) ),
inference(rectify,[],[f2494]) ).
fof(f2494,axiom,
! [X8,X10,X9] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X10))
=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(X8),X9))
=> ( ( ? [X2] : hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X10),X9)))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
=> hAPP(c_Finite__Set_Ocard(X8),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X10),X9)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(X8),X10)),hAPP(c_Finite__Set_Ocard(X8),X9)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card_Ounion__inter__neutral) ).
fof(f31375,plain,
spl559_223,
inference(avatar_split_clause,[],[f20112,f31372]) ).
fof(f31372,plain,
( spl559_223
<=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_223])]) ).
fof(f20112,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5102]) ).
fof(f5102,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(f31370,plain,
spl559_222,
inference(avatar_split_clause,[],[f23369,f31367]) ).
fof(f31367,plain,
( spl559_222
<=> class_Lattices_Olattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_222])]) ).
fof(f23369,plain,
class_Lattices_Olattice(tc_Int_Oint),
inference(cnf_transformation,[],[f5054]) ).
fof(f5054,axiom,
class_Lattices_Olattice(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Olattice) ).
fof(f31348,plain,
~ spl559_221,
inference(avatar_split_clause,[],[f31343,f31345]) ).
fof(f31345,plain,
( spl559_221
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_221])]) ).
fof(f31343,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)),
inference(forward_demodulation,[],[f22004,f26803]) ).
fof(f22004,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(cnf_transformation,[],[f877]) ).
fof(f877,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(f31333,plain,
spl559_220,
inference(avatar_split_clause,[],[f26427,f31330]) ).
fof(f31330,plain,
( spl559_220
<=> c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_220])]) ).
fof(f26427,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)),
inference(cnf_transformation,[],[f2851]) ).
fof(f2851,axiom,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__lessThan__UNIV) ).
fof(f31328,plain,
( spl559_218
| ~ spl559_219 ),
inference(avatar_split_clause,[],[f31320,f31325,f31322]) ).
fof(f31322,plain,
( spl559_218
<=> ! [X1] :
( c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_218])]) ).
fof(f31325,plain,
( spl559_219
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_219])]) ).
fof(f31320,plain,
! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(forward_subsumption_demodulation,[],[f31319,f24680]) ).
fof(f24680,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0) = c_Divides_OposDivAlg(X0,X1) ),
inference(cnf_transformation,[],[f18058]) ).
fof(f18058,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
| hAPP(c_Divides_Oadjust(X1),c_Divides_OposDivAlg(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)))),X1))) = c_Divides_OposDivAlg(X0,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0) = c_Divides_OposDivAlg(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),X0),X1)) ) ) ),
inference(rectify,[],[f11654]) ).
fof(f11654,plain,
! [X1,X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| hAPP(c_Divides_Oadjust(X0),c_Divides_OposDivAlg(X1,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)))),X0))) = c_Divides_OposDivAlg(X1,X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) = c_Divides_OposDivAlg(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),X1),X0)) ) ) ),
inference(flattening,[],[f11653]) ).
fof(f11653,plain,
! [X1,X0] :
( ( hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) = c_Divides_OposDivAlg(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),X1),X0)) ) )
& ( hAPP(c_Divides_Oadjust(X0),c_Divides_OposDivAlg(X1,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)))),X0))) = c_Divides_OposDivAlg(X1,X0)
| 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))) ) ),
inference(ennf_transformation,[],[f8960]) ).
fof(f8960,plain,
! [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),X1),X0)) )
=> hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1) = c_Divides_OposDivAlg(X1,X0) )
& ( ~ ( 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))) )
=> hAPP(c_Divides_Oadjust(X0),c_Divides_OposDivAlg(X1,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)))),X0))) = c_Divides_OposDivAlg(X1,X0) ) ),
inference(rectify,[],[f1872]) ).
fof(f1872,axiom,
! [X19,X18] :
( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18),X19)) )
=> c_Divides_OposDivAlg(X18,X19) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18) )
& ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X19),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X18),X19)) )
=> c_Divides_OposDivAlg(X18,X19) = hAPP(c_Divides_Oadjust(X19),c_Divides_OposDivAlg(X18,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)))),X19))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_posDivAlg_Osimps) ).
fof(f31319,plain,
! [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| 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)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(forward_demodulation,[],[f28562,f24281]) ).
fof(f24281,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,[],[f9165]) ).
fof(f9165,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,[],[f1370]) ).
fof(f1370,axiom,
! [X19] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X19),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zmod__zero) ).
fof(f28562,plain,
! [X1] :
( 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)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)),c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ),
inference(equality_resolution,[],[f27664]) ).
fof(f27664,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != 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)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),X1)),c_Divides_Odiv__class_Omod(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)) ),
inference(definition_unfolding,[],[f23381,f20616]) ).
fof(f20616,plain,
! [X0,X1] : hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)) = c_Divides_Odivmod__int(X1,X0),
inference(cnf_transformation,[],[f9350]) ).
fof(f9350,plain,
! [X0,X1] : hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1),X0)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)) = c_Divides_Odivmod__int(X1,X0),
inference(rectify,[],[f1767]) ).
fof(f1767,axiom,
! [X106,X116] : c_Divides_Odivmod__int(X116,X106) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X116),X106)),c_Divides_Odiv__class_Omod(tc_Int_Oint,X116,X106)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__mod__div) ).
fof(f23381,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != 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_Odivmod__int(X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ),
inference(cnf_transformation,[],[f17064]) ).
fof(f17064,plain,
! [X0,X1] :
( ( ( ( hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))) = c_Divides_Odivmod__int(X0,X1)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& ( c_Divides_OnegDivAlg(X0,X1) = c_Divides_Odivmod__int(X0,X1)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
| 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)),X1))
| ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != 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_Odivmod__int(X0,X1) )
& ( hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))) = c_Divides_Odivmod__int(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ) )
& ( c_Divides_OposDivAlg(X0,X1) = c_Divides_Odivmod__int(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_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ),
inference(rectify,[],[f12737]) ).
fof(f12737,plain,
! [X1,X0] :
( ( ( ( c_Divides_Odivmod__int(X1,X0) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(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_Divides_Odivmod__int(X1,X0) = c_Divides_OnegDivAlg(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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)),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
| 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_Odivmod__int(X1,X0) )
& ( hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0))) = c_Divides_Odivmod__int(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 ) ) )
& ( c_Divides_Odivmod__int(X1,X0) = c_Divides_OposDivAlg(X1,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)),X1)) ) ),
inference(ennf_transformation,[],[f8330]) ).
fof(f8330,plain,
! [X1,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_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> c_Divides_Odivmod__int(X1,X0) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(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_Divides_Odivmod__int(X1,X0) = c_Divides_OnegDivAlg(X1,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_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> c_Divides_Odivmod__int(X1,X0) = c_Divides_OposDivAlg(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_Int_Oint) != X1
=> hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0))) = c_Divides_Odivmod__int(X1,X0) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
=> 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_Odivmod__int(X1,X0) ) ) ) ) ) ),
inference(rectify,[],[f1878]) ).
fof(f1878,axiom,
! [X19,X18] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19))
=> c_Divides_Odivmod__int(X18,X19) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19))
=> c_Divides_Odivmod__int(X18,X19) = c_Divides_OnegDivAlg(X18,X19) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X18))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19))
=> c_Divides_Odivmod__int(X18,X19) = c_Divides_OposDivAlg(X18,X19) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X19))
=> ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X18
=> 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_Odivmod__int(X18,X19) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X18
=> c_Divides_Odivmod__int(X18,X19) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X18),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X19))) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_divmod__int__def) ).
fof(f31318,plain,
spl559_217,
inference(avatar_split_clause,[],[f31313,f31315]) ).
fof(f31313,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),
inference(forward_demodulation,[],[f31312,f22937]) ).
fof(f31312,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))))))),
inference(forward_demodulation,[],[f31311,f24320]) ).
fof(f31311,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31310,f22937]) ).
fof(f31310,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31309,f22937]) ).
fof(f31309,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f31308,f20419]) ).
fof(f31308,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f31307,f22937]) ).
fof(f31307,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f31306,f22937]) ).
fof(f31306,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f31305,f20419]) ).
fof(f31305,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f28129,f20419]) ).
fof(f28129,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),
inference(definition_unfolding,[],[f26411,f21744,f20132]) ).
fof(f26411,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(cnf_transformation,[],[f1261]) ).
fof(f1261,axiom,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_numeral__2__eq__2) ).
fof(f31304,plain,
spl559_216,
inference(avatar_split_clause,[],[f21700,f31301]) ).
fof(f31301,plain,
( spl559_216
<=> class_Orderings_Oorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_216])]) ).
fof(f21700,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f5135]) ).
fof(f5135,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(f31299,plain,
spl559_215,
inference(avatar_split_clause,[],[f24803,f31296]) ).
fof(f31296,plain,
( spl559_215
<=> 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,[spl559_215])]) ).
fof(f24803,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,[],[f2840]) ).
fof(f2840,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(f31290,plain,
spl559_21,
inference(avatar_split_clause,[],[f31289,f29055]) ).
fof(f31289,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OMin),
inference(forward_demodulation,[],[f28255,f27633]) ).
fof(f27633,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),X0),
inference(definition_unfolding,[],[f23148,f22455]) ).
fof(f23148,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OMin) = c_Int_Opred(X0),
inference(cnf_transformation,[],[f9095]) ).
fof(f9095,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OMin) = c_Int_Opred(X0),
inference(rectify,[],[f1562]) ).
fof(f1562,axiom,
! [X61] : c_Int_Opred(X61) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X61),c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__Min__right) ).
fof(f28255,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Int_OMin),
inference(definition_unfolding,[],[f27072,f20132]) ).
fof(f27072,plain,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
inference(cnf_transformation,[],[f1533]) ).
fof(f1533,axiom,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Bit1__Min) ).
fof(f31280,plain,
spl559_214,
inference(avatar_split_clause,[],[f23089,f31277]) ).
fof(f31277,plain,
( spl559_214
<=> class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_214])]) ).
fof(f23089,plain,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5170]) ).
fof(f5170,axiom,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring) ).
fof(f31273,plain,
spl559_40,
inference(avatar_split_clause,[],[f28847,f29162]) ).
fof(f28847,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls),
inference(equality_resolution,[],[f28126]) ).
fof(f28126,plain,
! [X0] :
( c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0)
| c_Int_OPls != X0 ),
inference(definition_unfolding,[],[f26404,f21744]) ).
fof(f26404,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 ),
inference(cnf_transformation,[],[f19372]) ).
fof(f19372,plain,
! [X0] :
( ( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 )
& ( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) ) ),
inference(nnf_transformation,[],[f5258]) ).
fof(f5258,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
<=> c_Int_OPls = X0 ),
inference(rectify,[],[f1122]) ).
fof(f1122,axiom,
! [X49] :
( c_Int_OPls = X49
<=> c_Int_OPls = c_Int_OBit0(X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I38_J) ).
fof(f31268,plain,
spl559_213,
inference(avatar_split_clause,[],[f21019,f31265]) ).
fof(f31265,plain,
( spl559_213
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_213])]) ).
fof(f21019,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5059]) ).
fof(f5059,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(f31254,plain,
spl559_212,
inference(avatar_split_clause,[],[f20481,f31251]) ).
fof(f31251,plain,
( spl559_212
<=> c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_212])]) ).
fof(f20481,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
inference(cnf_transformation,[],[f2035]) ).
fof(f2035,axiom,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omax__strict),c_FunDef_Omax__weak)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__rpair__set) ).
fof(f31247,plain,
spl559_211,
inference(avatar_split_clause,[],[f21741,f31244]) ).
fof(f31244,plain,
( spl559_211
<=> class_Groups_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_211])]) ).
fof(f21741,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5044]) ).
fof(f5044,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(f31240,plain,
spl559_210,
inference(avatar_split_clause,[],[f25316,f31237]) ).
fof(f31237,plain,
( spl559_210
<=> class_Enum_Oenum(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_210])]) ).
fof(f25316,plain,
class_Enum_Oenum(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5158]) ).
fof(f5158,axiom,
class_Enum_Oenum(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Enum_Oenum) ).
fof(f31230,plain,
spl559_209,
inference(avatar_split_clause,[],[f31225,f31227]) ).
fof(f31225,plain,
hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_fequal,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(forward_demodulation,[],[f20648,f29718]) ).
fof(f20648,plain,
hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f2304]) ).
fof(f2304,axiom,
hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atMost__0) ).
fof(f31221,plain,
spl559_208,
inference(avatar_split_clause,[],[f21064,f31218]) ).
fof(f31218,plain,
( spl559_208
<=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_208])]) ).
fof(f21064,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5016]) ).
fof(f5016,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(f31214,plain,
( spl559_97
| spl559_207 ),
inference(avatar_split_clause,[],[f31210,f31212,f29805]) ).
fof(f31212,plain,
( spl559_207
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_207])]) ).
fof(f31210,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ),
inference(forward_subsumption_demodulation,[],[f31209,f29520]) ).
fof(f31209,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f31208,f26803]) ).
fof(f31208,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,X0))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1)) ),
inference(forward_demodulation,[],[f31207,f26803]) ).
fof(f31207,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ),
inference(forward_demodulation,[],[f21547,f26803]) ).
fof(f21547,plain,
! [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),X0)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) ),
inference(cnf_transformation,[],[f15714]) ).
fof(f31200,plain,
spl559_206,
inference(avatar_split_clause,[],[f27731,f31197]) ).
fof(f31197,plain,
( spl559_206
<=> c_Wellfounded_Oless__than = hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)),c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_206])]) ).
fof(f27731,plain,
c_Wellfounded_Oless__than = hAPP(hAPP(c_Relation_Orel__comp(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)),c_Wellfounded_Opred__nat),
inference(definition_unfolding,[],[f23744,f22270]) ).
fof(f22270,plain,
! [X0,X1] : hAPP(hAPP(c_Relation_Orel__comp(X0,X0,X0),c_Transitive__Closure_Ortrancl(X0,X1)),X1) = c_Transitive__Closure_Otrancl(X0,X1),
inference(cnf_transformation,[],[f6060]) ).
fof(f6060,plain,
! [X0,X1] : hAPP(hAPP(c_Relation_Orel__comp(X0,X0,X0),c_Transitive__Closure_Ortrancl(X0,X1)),X1) = c_Transitive__Closure_Otrancl(X0,X1),
inference(rectify,[],[f3385]) ).
fof(f3385,axiom,
! [X8,X137] : c_Transitive__Closure_Otrancl(X8,X137) = hAPP(hAPP(c_Relation_Orel__comp(X8,X8,X8),c_Transitive__Closure_Ortrancl(X8,X137)),X137),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__unfold__right) ).
fof(f23744,plain,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f3329]) ).
fof(f3329,axiom,
c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__than__def) ).
fof(f31187,plain,
spl559_205,
inference(avatar_split_clause,[],[f20374,f31184]) ).
fof(f31184,plain,
( spl559_205
<=> class_Rings_Oordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_205])]) ).
fof(f20374,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5046]) ).
fof(f5046,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(f31182,plain,
spl559_204,
inference(avatar_split_clause,[],[f21280,f31179]) ).
fof(f31179,plain,
( spl559_204
<=> class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_204])]) ).
fof(f21280,plain,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5179]) ).
fof(f5179,axiom,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add) ).
fof(f31177,plain,
spl559_203,
inference(avatar_split_clause,[],[f21760,f31174]) ).
fof(f31174,plain,
( spl559_203
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_203])]) ).
fof(f21760,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5161]) ).
fof(f5161,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(f31166,plain,
spl559_202,
inference(avatar_split_clause,[],[f24025,f31163]) ).
fof(f31163,plain,
( spl559_202
<=> class_Groups_Ominus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_202])]) ).
fof(f24025,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(cnf_transformation,[],[f5140]) ).
fof(f5140,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(f31161,plain,
spl559_201,
inference(avatar_split_clause,[],[f21713,f31158]) ).
fof(f31158,plain,
( spl559_201
<=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_201])]) ).
fof(f21713,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5036]) ).
fof(f5036,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__add) ).
fof(f31152,plain,
spl559_200,
inference(avatar_split_clause,[],[f21081,f31149]) ).
fof(f31149,plain,
( spl559_200
<=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_200])]) ).
fof(f21081,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(cnf_transformation,[],[f5097]) ).
fof(f5097,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ono__zero__divisors) ).
fof(f31147,plain,
spl559_199,
inference(avatar_split_clause,[],[f20554,f31144]) ).
fof(f31144,plain,
( spl559_199
<=> class_Groups_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_199])]) ).
fof(f20554,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f5120]) ).
fof(f5120,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(f31141,plain,
spl559_198,
inference(avatar_split_clause,[],[f22706,f31138]) ).
fof(f31138,plain,
( spl559_198
<=> class_Groups_Osemigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_198])]) ).
fof(f22706,plain,
class_Groups_Osemigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5100]) ).
fof(f5100,axiom,
class_Groups_Osemigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Osemigroup__add) ).
fof(f31136,plain,
spl559_197,
inference(avatar_split_clause,[],[f23083,f31133]) ).
fof(f31133,plain,
( spl559_197
<=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_197])]) ).
fof(f23083,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5033]) ).
fof(f5033,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__semiring) ).
fof(f31119,plain,
spl559_196,
inference(avatar_split_clause,[],[f21600,f31116]) ).
fof(f21600,plain,
hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(cnf_transformation,[],[f2889]) ).
fof(f2889,axiom,
hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_greaterThan__0) ).
fof(f31095,plain,
spl559_195,
inference(avatar_split_clause,[],[f22780,f31092]) ).
fof(f31092,plain,
( spl559_195
<=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_195])]) ).
fof(f22780,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5020]) ).
fof(f5020,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__comm__semiring) ).
fof(f31083,plain,
spl559_194,
inference(avatar_split_clause,[],[f25823,f31080]) ).
fof(f31080,plain,
( spl559_194
<=> class_Orderings_Opreorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_194])]) ).
fof(f25823,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5106]) ).
fof(f5106,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(f31078,plain,
spl559_193,
inference(avatar_split_clause,[],[f22036,f31075]) ).
fof(f31075,plain,
( spl559_193
<=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_193])]) ).
fof(f22036,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5095]) ).
fof(f5095,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__add) ).
fof(f31073,plain,
spl559_192,
inference(avatar_split_clause,[],[f23870,f31070]) ).
fof(f31070,plain,
( spl559_192
<=> class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_192])]) ).
fof(f23870,plain,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5178]) ).
fof(f5178,axiom,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors) ).
fof(f31068,plain,
spl559_191,
inference(avatar_split_clause,[],[f26268,f31065]) ).
fof(f31065,plain,
( spl559_191
<=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_191])]) ).
fof(f26268,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5035]) ).
fof(f5035,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ono__zero__divisors) ).
fof(f31057,plain,
spl559_190,
inference(avatar_split_clause,[],[f25529,f31054]) ).
fof(f31054,plain,
( spl559_190
<=> class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_190])]) ).
fof(f25529,plain,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5195]) ).
fof(f5195,axiom,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oord) ).
fof(f31049,plain,
spl559_189,
inference(avatar_split_clause,[],[f31044,f31046]) ).
fof(f31044,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls),
inference(forward_demodulation,[],[f27292,f24320]) ).
fof(f27292,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls),
inference(definition_unfolding,[],[f20910,f20132]) ).
fof(f20910,plain,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin),
inference(cnf_transformation,[],[f1585]) ).
fof(f1585,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(f31042,plain,
spl559_188,
inference(avatar_split_clause,[],[f22340,f31039]) ).
fof(f31039,plain,
( spl559_188
<=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_188])]) ).
fof(f22340,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5093]) ).
fof(f5093,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Oab__semigroup__mult) ).
fof(f31036,plain,
spl559_187,
inference(avatar_split_clause,[],[f22682,f31033]) ).
fof(f31033,plain,
( spl559_187
<=> class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_187])]) ).
fof(f22682,plain,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5199]) ).
fof(f5199,axiom,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Int_Onumber) ).
fof(f31028,plain,
spl559_186,
inference(avatar_split_clause,[],[f21067,f31025]) ).
fof(f31025,plain,
( spl559_186
<=> class_Orderings_Otop(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_186])]) ).
fof(f21067,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(cnf_transformation,[],[f5136]) ).
fof(f5136,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Otop) ).
fof(f31004,plain,
spl559_185,
inference(avatar_split_clause,[],[f22725,f31001]) ).
fof(f31001,plain,
( spl559_185
<=> class_Lattices_Olattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_185])]) ).
fof(f22725,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5134]) ).
fof(f5134,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
fof(f30999,plain,
spl559_184,
inference(avatar_split_clause,[],[f21759,f30996]) ).
fof(f30996,plain,
( spl559_184
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_184])]) ).
fof(f21759,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[],[f5006]) ).
fof(f5006,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(f30993,plain,
spl559_183,
inference(avatar_split_clause,[],[f20773,f30990]) ).
fof(f30990,plain,
( spl559_183
<=> class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_183])]) ).
fof(f20773,plain,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5183]) ).
fof(f5183,axiom,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring) ).
fof(f30988,plain,
spl559_182,
inference(avatar_split_clause,[],[f23566,f30985]) ).
fof(f30985,plain,
( spl559_182
<=> class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_182])]) ).
fof(f23566,plain,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5180]) ).
fof(f5180,axiom,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1) ).
fof(f30974,plain,
spl559_181,
inference(avatar_split_clause,[],[f21159,f30971]) ).
fof(f30971,plain,
( spl559_181
<=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_181])]) ).
fof(f21159,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5018]) ).
fof(f5018,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__ring__strict) ).
fof(f30967,plain,
spl559_180,
inference(avatar_split_clause,[],[f21807,f30964]) ).
fof(f30964,plain,
( spl559_180
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_180])]) ).
fof(f21807,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f3209]) ).
fof(f3209,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__pred__nat) ).
fof(f30949,plain,
spl559_179,
inference(avatar_split_clause,[],[f20782,f30946]) ).
fof(f30946,plain,
( spl559_179
<=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_179])]) ).
fof(f20782,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5014]) ).
fof(f5014,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(f30944,plain,
spl559_178,
inference(avatar_split_clause,[],[f22226,f30941]) ).
fof(f30941,plain,
( spl559_178
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_178])]) ).
fof(f22226,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5048]) ).
fof(f5048,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(f30938,plain,
spl559_177,
inference(avatar_split_clause,[],[f23997,f30935]) ).
fof(f30935,plain,
( spl559_177
<=> class_Lattices_Odistrib__lattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_177])]) ).
fof(f23997,plain,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f5092]) ).
fof(f5092,axiom,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Odistrib__lattice) ).
fof(f30930,plain,
~ spl559_176,
inference(avatar_split_clause,[],[f25521,f30927]) ).
fof(f25521,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,[],[f2841]) ).
fof(f2841,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(f30889,plain,
spl559_175,
inference(avatar_split_clause,[],[f23482,f30886]) ).
fof(f30886,plain,
( spl559_175
<=> class_Groups_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_175])]) ).
fof(f23482,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5051]) ).
fof(f5051,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(f30883,plain,
spl559_174,
inference(avatar_split_clause,[],[f21619,f30880]) ).
fof(f21619,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,[],[f808]) ).
fof(f808,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(f30878,plain,
( spl559_97
| spl559_156 ),
inference(avatar_split_clause,[],[f30877,f30610,f29805]) ).
fof(f30877,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_subsumption_demodulation,[],[f30876,f29520]) ).
fof(f30876,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ),
inference(forward_demodulation,[],[f26247,f26803]) ).
fof(f26247,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f12063]) ).
fof(f12063,plain,
! [X0] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X0)) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ),
inference(ennf_transformation,[],[f9088]) ).
fof(f9088,plain,
! [X0] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X0)) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ) ),
inference(rectify,[],[f923]) ).
fof(f923,axiom,
! [X82] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(X82)) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__nat__number__of) ).
fof(f30872,plain,
spl559_173,
inference(avatar_split_clause,[],[f20422,f30869]) ).
fof(f30869,plain,
( spl559_173
<=> c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_173])]) ).
fof(f20422,plain,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
inference(cnf_transformation,[],[f1565]) ).
fof(f1565,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(f30861,plain,
spl559_172,
inference(avatar_split_clause,[],[f21599,f30858]) ).
fof(f30858,plain,
( spl559_172
<=> class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_172])]) ).
fof(f21599,plain,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5186]) ).
fof(f5186,axiom,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder) ).
fof(f30840,plain,
spl559_171,
inference(avatar_split_clause,[],[f23002,f30837]) ).
fof(f30837,plain,
( spl559_171
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_171])]) ).
fof(f23002,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f1552]) ).
fof(f1552,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(f30824,plain,
spl559_170,
inference(avatar_split_clause,[],[f25613,f30821]) ).
fof(f25613,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,[],[f2870]) ).
fof(f2870,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(f30785,plain,
spl559_169,
inference(avatar_split_clause,[],[f20781,f30782]) ).
fof(f30782,plain,
( spl559_169
<=> class_Power_Opower(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_169])]) ).
fof(f20781,plain,
class_Power_Opower(tc_Nat_Onat),
inference(cnf_transformation,[],[f5119]) ).
fof(f5119,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(f30772,plain,
spl559_168,
inference(avatar_split_clause,[],[f20401,f30769]) ).
fof(f30769,plain,
( spl559_168
<=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_168])]) ).
fof(f20401,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5008]) ).
fof(f5008,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(f30767,plain,
spl559_167,
inference(avatar_split_clause,[],[f24852,f30764]) ).
fof(f30764,plain,
( spl559_167
<=> class_Nat_Osize(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_167])]) ).
fof(f24852,plain,
class_Nat_Osize(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5159]) ).
fof(f5159,axiom,
class_Nat_Osize(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Nat_Osize) ).
fof(f30762,plain,
spl559_166,
inference(avatar_split_clause,[],[f20427,f30759]) ).
fof(f30759,plain,
( spl559_166
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_166])]) ).
fof(f20427,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5061]) ).
fof(f5061,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Onumber__ring) ).
fof(f30755,plain,
spl559_165,
inference(avatar_split_clause,[],[f19923,f30752]) ).
fof(f30752,plain,
( spl559_165
<=> class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_165])]) ).
fof(f19923,plain,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5125]) ).
fof(f5125,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice) ).
fof(f30724,plain,
spl559_164,
inference(avatar_split_clause,[],[f26795,f30721]) ).
fof(f30721,plain,
( spl559_164
<=> class_Lattices_Oboolean__algebra(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_164])]) ).
fof(f26795,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(cnf_transformation,[],[f5131]) ).
fof(f5131,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(f30709,plain,
spl559_163,
inference(avatar_split_clause,[],[f20321,f30706]) ).
fof(f20321,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,[],[f1622]) ).
fof(f1622,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(f30692,plain,
spl559_162,
inference(avatar_split_clause,[],[f30687,f30689]) ).
fof(f30689,plain,
( spl559_162
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_162])]) ).
fof(f30687,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OPls),
inference(forward_demodulation,[],[f27281,f24320]) ).
fof(f27281,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls),
inference(definition_unfolding,[],[f20821,f20132,f20937]) ).
fof(f20821,plain,
c_Int_OBit1(c_Int_OPls) = c_Int_Osucc(c_Int_OPls),
inference(cnf_transformation,[],[f975]) ).
fof(f975,axiom,
c_Int_OBit1(c_Int_OPls) = c_Int_Osucc(c_Int_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_succ__Pls) ).
fof(f30680,plain,
spl559_161,
inference(avatar_split_clause,[],[f26489,f30677]) ).
fof(f30677,plain,
( spl559_161
<=> class_Orderings_Oord(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_161])]) ).
fof(f26489,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f5116]) ).
fof(f5116,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(f30663,plain,
spl559_160,
inference(avatar_split_clause,[],[f23880,f30660]) ).
fof(f30660,plain,
( spl559_160
<=> class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_160])]) ).
fof(f23880,plain,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5197]) ).
fof(f5197,axiom,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Power_Opower) ).
fof(f30658,plain,
spl559_159,
inference(avatar_split_clause,[],[f23275,f30655]) ).
fof(f30655,plain,
( spl559_159
<=> c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(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,[spl559_159])]) ).
fof(f23275,plain,
c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(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,[],[f2895]) ).
fof(f2895,axiom,
c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(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_Integ__def) ).
fof(f30652,plain,
spl559_158,
inference(avatar_split_clause,[],[f24358,f30649]) ).
fof(f24358,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,[],[f894]) ).
fof(f894,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_nat__number__of__Pls) ).
fof(f30646,plain,
( spl559_97
| spl559_18 ),
inference(avatar_split_clause,[],[f30645,f29037,f29805]) ).
fof(f30645,plain,
! [X0] :
( 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))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_subsumption_demodulation,[],[f30644,f29520]) ).
fof(f30644,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ),
inference(forward_demodulation,[],[f25807,f26803]) ).
fof(f25807,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) ),
inference(cnf_transformation,[],[f14372]) ).
fof(f14372,plain,
! [X0] :
( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) = 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))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ),
inference(ennf_transformation,[],[f7459]) ).
fof(f7459,plain,
! [X0] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) )
& ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ) ),
inference(rectify,[],[f910]) ).
fof(f910,axiom,
! [X82] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__nat__number__of) ).
fof(f30643,plain,
spl559_157,
inference(avatar_split_clause,[],[f22387,f30640]) ).
fof(f30640,plain,
( spl559_157
<=> class_Lattices_Osemilattice__inf(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_157])]) ).
fof(f22387,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(cnf_transformation,[],[f5129]) ).
fof(f5129,axiom,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
fof(f30613,plain,
spl559_156,
inference(avatar_split_clause,[],[f24989,f30610]) ).
fof(f24989,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f518]) ).
fof(f518,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__nat__def) ).
fof(f30605,plain,
spl559_155,
inference(avatar_split_clause,[],[f24082,f30602]) ).
fof(f30602,plain,
( spl559_155
<=> class_Finite__Set_Ofinite(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_155])]) ).
fof(f24082,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(cnf_transformation,[],[f5133]) ).
fof(f5133,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Finite__Set_Ofinite) ).
fof(f30599,plain,
spl559_154,
inference(avatar_split_clause,[],[f24814,f30596]) ).
fof(f24814,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
inference(cnf_transformation,[],[f3703]) ).
fof(f3703,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(f30594,plain,
spl559_153,
inference(avatar_split_clause,[],[f24635,f30591]) ).
fof(f30591,plain,
( spl559_153
<=> 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,[spl559_153])]) ).
fof(f24635,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f2036]) ).
fof(f2036,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(f30581,plain,
spl559_152,
inference(avatar_split_clause,[],[f19922,f30578]) ).
fof(f30578,plain,
( spl559_152
<=> class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_152])]) ).
fof(f19922,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f5012]) ).
fof(f5012,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(f30576,plain,
spl559_151,
inference(avatar_split_clause,[],[f24135,f30573]) ).
fof(f30573,plain,
( spl559_151
<=> class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_151])]) ).
fof(f24135,plain,
class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5156]) ).
fof(f5156,axiom,
class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy) ).
fof(f30571,plain,
spl559_150,
inference(avatar_split_clause,[],[f24469,f30568]) ).
fof(f30568,plain,
( spl559_150
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_150])]) ).
fof(f24469,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5047]) ).
fof(f5047,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(f30542,plain,
spl559_149,
inference(avatar_split_clause,[],[f21636,f30539]) ).
fof(f21636,plain,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)),
inference(cnf_transformation,[],[f5224]) ).
fof(f5224,axiom,
hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),v_U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f30534,plain,
spl559_148,
inference(avatar_split_clause,[],[f25452,f30531]) ).
fof(f30531,plain,
( spl559_148
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_148])]) ).
fof(f25452,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5157]) ).
fof(f5157,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Product____Type__Ounit__Finite__Set_Ofinite) ).
fof(f30529,plain,
spl559_147,
inference(avatar_split_clause,[],[f30524,f30526]) ).
fof(f30526,plain,
( spl559_147
<=> c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_147])]) ).
fof(f30524,plain,
c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(forward_demodulation,[],[f26957,f29718]) ).
fof(f26957,plain,
c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f2041]) ).
fof(f2041,axiom,
c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__weak__def) ).
fof(f30522,plain,
spl559_146,
inference(avatar_split_clause,[],[f30517,f30519]) ).
fof(f30517,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
inference(forward_demodulation,[],[f23298,f26803]) ).
fof(f23298,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,[],[f895]) ).
fof(f895,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(f30493,plain,
spl559_145,
inference(avatar_split_clause,[],[f20754,f30490]) ).
fof(f30490,plain,
( spl559_145
<=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_145])]) ).
fof(f20754,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(cnf_transformation,[],[f5038]) ).
fof(f5038,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__idom) ).
fof(f30332,plain,
spl559_144,
inference(avatar_split_clause,[],[f25640,f30329]) ).
fof(f25640,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,[],[f2432]) ).
fof(f2432,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(f30324,plain,
spl559_143,
inference(avatar_split_clause,[],[f24453,f30321]) ).
fof(f30321,plain,
( spl559_143
<=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_143])]) ).
fof(f24453,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(cnf_transformation,[],[f5105]) ).
fof(f5105,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(f30319,plain,
spl559_142,
inference(avatar_split_clause,[],[f30314,f30316]) ).
fof(f30316,plain,
( spl559_142
<=> c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_142])]) ).
fof(f30314,plain,
c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat))),
inference(forward_demodulation,[],[f28149,f26067]) ).
fof(f28149,plain,
c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
inference(definition_unfolding,[],[f26524,f22094]) ).
fof(f26524,plain,
c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
inference(cnf_transformation,[],[f3169]) ).
fof(f3169,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__less) ).
fof(f30313,plain,
spl559_141,
inference(avatar_split_clause,[],[f19952,f30310]) ).
fof(f30310,plain,
( spl559_141
<=> class_Lattices_Osemilattice__sup(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_141])]) ).
fof(f19952,plain,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
inference(cnf_transformation,[],[f5027]) ).
fof(f5027,axiom,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Lattices_Osemilattice__sup) ).
fof(f30308,plain,
spl559_21,
inference(avatar_split_clause,[],[f30307,f29055]) ).
fof(f30307,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OMin),
inference(forward_demodulation,[],[f28755,f27633]) ).
fof(f28755,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Int_OMin),
inference(equality_resolution,[],[f28006]) ).
fof(f28006,plain,
! [X0] :
( c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0)
| c_Int_OMin != X0 ),
inference(definition_unfolding,[],[f25566,f20132]) ).
fof(f25566,plain,
! [X0] :
( c_Int_OMin = c_Int_OBit1(X0)
| c_Int_OMin != X0 ),
inference(cnf_transformation,[],[f18758]) ).
fof(f18758,plain,
! [X0] :
( ( c_Int_OMin = X0
| c_Int_OMin != c_Int_OBit1(X0) )
& ( c_Int_OMin = c_Int_OBit1(X0)
| c_Int_OMin != X0 ) ),
inference(nnf_transformation,[],[f5509]) ).
fof(f5509,plain,
! [X0] :
( c_Int_OMin = X0
<=> c_Int_OMin = c_Int_OBit1(X0) ),
inference(rectify,[],[f1532]) ).
fof(f1532,axiom,
! [X49] :
( c_Int_OMin = X49
<=> c_Int_OBit1(X49) = c_Int_OMin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I43_J) ).
fof(f30296,plain,
spl559_140,
inference(avatar_split_clause,[],[f26472,f30293]) ).
fof(f30293,plain,
( spl559_140
<=> c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_140])]) ).
fof(f26472,plain,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f4160]) ).
fof(f4160,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(f30284,plain,
spl559_139,
inference(avatar_split_clause,[],[f30279,f30281]) ).
fof(f30279,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f30278,f20419]) ).
fof(f30278,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f30277,f20419]) ).
fof(f30277,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f30276,f20419]) ).
fof(f30276,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),
inference(forward_demodulation,[],[f27520,f26803]) ).
fof(f27520,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(definition_unfolding,[],[f22413,f21744,f20132]) ).
fof(f22413,plain,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f1272]) ).
fof(f1272,axiom,
hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__2) ).
fof(f30269,plain,
spl559_138,
inference(avatar_split_clause,[],[f26999,f30266]) ).
fof(f30266,plain,
( spl559_138
<=> class_Groups_Ominus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_138])]) ).
fof(f26999,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(cnf_transformation,[],[f5068]) ).
fof(f5068,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(f30248,plain,
( ~ spl559_136
| spl559_137 ),
inference(avatar_split_clause,[],[f30240,f30246,f30242]) ).
fof(f30246,plain,
( spl559_137
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X0))),c_List_Otranspose(X0,c_List_Olist_ONil(tc_List_Olist(X0)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_137])]) ).
fof(f30240,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X0))),c_List_Otranspose(X0,c_List_Olist_ONil(tc_List_Olist(X0))))
| ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),c_List_Olist_ONil(tc_Nat_Onat))) ),
inference(forward_demodulation,[],[f28268,f21617]) ).
fof(f28268,plain,
! [X0] :
( ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X0),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X0))),c_List_Olist_ONil(tc_List_Olist(X0)))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X0))),c_List_Otranspose(X0,c_List_Olist_ONil(tc_List_Olist(X0)))) ),
inference(equality_resolution,[],[f19998]) ).
fof(f19998,plain,
! [X0,X1] :
( c_List_Olist_ONil(tc_List_Olist(X0)) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X0))),c_List_Otranspose(X0,X1))
| ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X0),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X0))),X1))) ),
inference(cnf_transformation,[],[f13719]) ).
fof(f13719,plain,
! [X0,X1] :
( ( ( c_List_Olist_ONil(tc_List_Olist(X0)) = X1
| hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X0)),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X0))),c_List_Otranspose(X0,X1)) )
& ( c_List_Olist_ONil(tc_List_Olist(X0)) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X0))),c_List_Otranspose(X0,X1)) ) )
| ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X0),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X0))),X1))) ),
inference(ennf_transformation,[],[f7680]) ).
fof(f7680,plain,
! [X1,X0] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X0),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X0))),X1)))
=> ( ( c_List_Olist_ONil(tc_List_Olist(X0)) = X1
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X0))),c_List_Otranspose(X0,X1)) )
& ( c_List_Olist_ONil(tc_List_Olist(X0)) != X1
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X0)),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X0))),c_List_Otranspose(X0,X1)) ) ) ),
inference(rectify,[],[f4460]) ).
fof(f4460,axiom,
! [X8,X202] :
( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(X8),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(X8))),X202)))
=> ( ( c_List_Olist_ONil(tc_List_Olist(X8)) = X202
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8))),c_List_Otranspose(X8,X202)) )
& ( c_List_Olist_ONil(tc_List_Olist(X8)) != X202
=> hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(X8))),c_List_Otranspose(X8,X202)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X8)),hAPP(hAPP(c_List_Onth(tc_List_Olist(X8)),X202),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_length__transpose__sorted) ).
fof(f30238,plain,
spl559_135,
inference(avatar_split_clause,[],[f20448,f30235]) ).
fof(f30235,plain,
( spl559_135
<=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_135])]) ).
fof(f20448,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5021]) ).
fof(f5021,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
fof(f30222,plain,
spl559_134,
inference(avatar_split_clause,[],[f22256,f30219]) ).
fof(f30219,plain,
( spl559_134
<=> class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_134])]) ).
fof(f22256,plain,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5187]) ).
fof(f5187,axiom,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder) ).
fof(f30217,plain,
spl559_133,
inference(avatar_split_clause,[],[f28084,f30214]) ).
fof(f30214,plain,
( spl559_133
<=> c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_133])]) ).
fof(f28084,plain,
c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Ointernal__split(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
inference(definition_unfolding,[],[f26193,f22094]) ).
fof(f26193,plain,
c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
inference(cnf_transformation,[],[f3204]) ).
fof(f3204,axiom,
c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_fequal)),c_Nat_OSuc))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__nat__def) ).
fof(f30205,plain,
spl559_132,
inference(avatar_split_clause,[],[f30200,f30202]) ).
fof(f30200,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))),
inference(forward_demodulation,[],[f30199,f20419]) ).
fof(f30199,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f30198,f20419]) ).
fof(f30198,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f27566,f20419]) ).
fof(f27566,plain,
hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),
inference(definition_unfolding,[],[f22713,f21744,f20132]) ).
fof(f22713,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))),
inference(cnf_transformation,[],[f2887]) ).
fof(f2887,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Finite__Set_Ocard(tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_card__UNIV__bool) ).
fof(f30191,plain,
spl559_131,
inference(avatar_split_clause,[],[f22719,f30188]) ).
fof(f30188,plain,
( spl559_131
<=> class_Orderings_Oord(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_131])]) ).
fof(f22719,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f5137]) ).
fof(f5137,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(f30183,plain,
spl559_130,
inference(avatar_split_clause,[],[f26500,f30180]) ).
fof(f30180,plain,
( spl559_130
<=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_130])]) ).
fof(f26500,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5010]) ).
fof(f5010,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__strict) ).
fof(f30174,plain,
spl559_129,
inference(avatar_split_clause,[],[f21682,f30171]) ).
fof(f30171,plain,
( spl559_129
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_129])]) ).
fof(f21682,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5162]) ).
fof(f5162,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(f30169,plain,
spl559_128,
inference(avatar_split_clause,[],[f25980,f30166]) ).
fof(f30166,plain,
( spl559_128
<=> class_Rings_Omult__zero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_128])]) ).
fof(f25980,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(cnf_transformation,[],[f5113]) ).
fof(f5113,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(f30156,plain,
~ spl559_127,
inference(avatar_split_clause,[],[f20215,f30153]) ).
fof(f30153,plain,
( spl559_127
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_127])]) ).
fof(f20215,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(cnf_transformation,[],[f892]) ).
fof(f892,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I1_J) ).
fof(f30140,plain,
spl559_126,
inference(avatar_split_clause,[],[f26664,f30137]) ).
fof(f30137,plain,
( spl559_126
<=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_126])]) ).
fof(f26664,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5042]) ).
fof(f5042,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(f30131,plain,
spl559_125,
inference(avatar_split_clause,[],[f28780,f30128]) ).
fof(f30128,plain,
( spl559_125
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_125])]) ).
fof(f28780,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(equality_resolution,[],[f25871]) ).
fof(f25871,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f18971]) ).
fof(f18971,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
inference(nnf_transformation,[],[f7752]) ).
fof(f7752,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f4894]) ).
fof(f4894,axiom,
! [X53] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X53
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X53),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__dvd__1__iff__1) ).
fof(f30120,plain,
spl559_124,
inference(avatar_split_clause,[],[f23741,f30117]) ).
fof(f30117,plain,
( spl559_124
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_124])]) ).
fof(f23741,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(cnf_transformation,[],[f5004]) ).
fof(f5004,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(f30113,plain,
spl559_45,
inference(avatar_split_clause,[],[f30112,f29199]) ).
fof(f29199,plain,
( spl559_45
<=> c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_45])]) ).
fof(f30112,plain,
c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(forward_demodulation,[],[f28565,f25637]) ).
fof(f25637,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,[],[f6471]) ).
fof(f6471,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,[],[f2281]) ).
fof(f2281,axiom,
! [X53] : c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X53),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_atLeastLessThan0) ).
fof(f28565,plain,
! [X1] : 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,X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f27670]) ).
fof(f27670,plain,
! [X0,X1] :
( 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,X1),X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(definition_unfolding,[],[f23400,f25412]) ).
fof(f25412,plain,
! [X0,X1] : c_List_Oupt(X0,X1) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),X1)),
inference(cnf_transformation,[],[f18651]) ).
fof(f18651,plain,
! [X0,X1] : c_List_Oupt(X0,X1) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X0),X1)),
inference(rectify,[],[f7367]) ).
fof(f7367,plain,
! [X1,X0] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0)) = c_List_Oupt(X1,X0),
inference(rectify,[],[f4369]) ).
fof(f4369,axiom,
! [X56,X53] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X53),X56)) = c_List_Oupt(X53,X56),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sorted__list__of__set__range) ).
fof(f23400,plain,
! [X0,X1] :
( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X1,X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f17076]) ).
fof(f17076,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1))
| c_List_Olist_ONil(tc_Nat_Onat) != c_List_Oupt(X1,X0) )
& ( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X1,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1)) ) ) ),
inference(flattening,[],[f17075]) ).
fof(f17075,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1))
| c_List_Olist_ONil(tc_Nat_Onat) != c_List_Oupt(X1,X0) )
& ( c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X1,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1)) ) ) ),
inference(nnf_transformation,[],[f8702]) ).
fof(f8702,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X1)) )
<=> c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X1,X0) ),
inference(rectify,[],[f4366]) ).
fof(f4366,axiom,
! [X74,X46] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X74),X46))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X74 )
<=> c_List_Oupt(X46,X74) = c_List_Olist_ONil(tc_Nat_Onat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__eq__Nil__conv) ).
fof(f30109,plain,
spl559_123,
inference(avatar_split_clause,[],[f21275,f30106]) ).
fof(f30106,plain,
( spl559_123
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_123])]) ).
fof(f21275,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5098]) ).
fof(f5098,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ocomm__monoid__add) ).
fof(f30102,plain,
~ spl559_122,
inference(avatar_split_clause,[],[f23095,f30099]) ).
fof(f30099,plain,
( spl559_122
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_122])]) ).
fof(f23095,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f886]) ).
fof(f886,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(f30087,plain,
spl559_121,
inference(avatar_split_clause,[],[f26781,f30084]) ).
fof(f26781,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,[],[f1888]) ).
fof(f1888,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(f30068,plain,
spl559_120,
inference(avatar_split_clause,[],[f22098,f30065]) ).
fof(f30065,plain,
( spl559_120
<=> class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_120])]) ).
fof(f22098,plain,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
inference(cnf_transformation,[],[f5127]) ).
fof(f5127,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(f30052,plain,
spl559_119,
inference(avatar_split_clause,[],[f21333,f30049]) ).
fof(f30049,plain,
( spl559_119
<=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_119])]) ).
fof(f21333,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5022]) ).
fof(f5022,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(f30041,plain,
spl559_118,
inference(avatar_split_clause,[],[f21672,f30038]) ).
fof(f30038,plain,
( spl559_118
<=> class_Lattices_Osemilattice__sup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_118])]) ).
fof(f21672,plain,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
inference(cnf_transformation,[],[f5090]) ).
fof(f5090,axiom,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
fof(f30019,plain,
spl559_117,
inference(avatar_split_clause,[],[f21154,f30016]) ).
fof(f21154,plain,
hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)),
inference(cnf_transformation,[],[f5226]) ).
fof(f5226,axiom,
hAPP(c_Finite__Set_Ocard(t_a),v_G) = hAPP(c_Finite__Set_Ocard(t_a),hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
fof(f30010,plain,
spl559_116,
inference(avatar_split_clause,[],[f21028,f30007]) ).
fof(f30007,plain,
( spl559_116
<=> class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_116])]) ).
fof(f21028,plain,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5185]) ).
fof(f5185,axiom,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one) ).
fof(f30000,plain,
spl559_115,
inference(avatar_split_clause,[],[f28854,f29997]) ).
fof(f28854,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f28853]) ).
fof(f28853,plain,
! [X0] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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)) != X0 ),
inference(equality_resolution,[],[f26504]) ).
fof(f26504,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),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 ),
inference(cnf_transformation,[],[f19453]) ).
fof(f19453,plain,
! [X0,X1] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),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 )
& ( ( 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 )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ) ),
inference(rectify,[],[f19452]) ).
fof(f19452,plain,
! [X1,X0] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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 )
& ( ( 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 )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) ) ),
inference(flattening,[],[f19451]) ).
fof(f19451,plain,
! [X1,X0] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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 )
& ( ( 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 )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) ) ),
inference(nnf_transformation,[],[f9531]) ).
fof(f9531,plain,
! [X1,X0] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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 ) ),
inference(rectify,[],[f697]) ).
fof(f697,axiom,
! [X53,X56] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X56
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X53 )
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mult__eq__1__iff) ).
fof(f29986,plain,
spl559_114,
inference(avatar_split_clause,[],[f22571,f29983]) ).
fof(f29983,plain,
( spl559_114
<=> class_Groups_Ominus(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_114])]) ).
fof(f22571,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(cnf_transformation,[],[f5118]) ).
fof(f5118,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(f29980,plain,
spl559_113,
inference(avatar_split_clause,[],[f29975,f29977]) ).
fof(f29975,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(forward_demodulation,[],[f27985,f20419]) ).
fof(f27985,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),
inference(definition_unfolding,[],[f25483,f20132]) ).
fof(f25483,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,[],[f996]) ).
fof(f996,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(f29974,plain,
spl559_112,
inference(avatar_split_clause,[],[f22983,f29971]) ).
fof(f29971,plain,
( spl559_112
<=> class_Orderings_Oorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_112])]) ).
fof(f22983,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5114]) ).
fof(f5114,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(f29960,plain,
spl559_111,
inference(avatar_split_clause,[],[f21918,f29957]) ).
fof(f29957,plain,
( spl559_111
<=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_111])]) ).
fof(f21918,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5108]) ).
fof(f5108,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(f29955,plain,
spl559_110,
inference(avatar_split_clause,[],[f20205,f29952]) ).
fof(f29952,plain,
( spl559_110
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_110])]) ).
fof(f20205,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5168]) ).
fof(f5168,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add) ).
fof(f29939,plain,
spl559_109,
inference(avatar_split_clause,[],[f21885,f29936]) ).
fof(f29936,plain,
( spl559_109
<=> class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_109])]) ).
fof(f21885,plain,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5172]) ).
fof(f5172,axiom,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring) ).
fof(f29926,plain,
spl559_108,
inference(avatar_split_clause,[],[f29921,f29923]) ).
fof(f29921,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls))),
inference(forward_demodulation,[],[f27526,f20419]) ).
fof(f27526,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),
inference(definition_unfolding,[],[f22445,f20132]) ).
fof(f22445,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f1011]) ).
fof(f1011,axiom,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(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_numeral__1__eq__Suc__0) ).
fof(f29915,plain,
spl559_107,
inference(avatar_split_clause,[],[f24198,f29912]) ).
fof(f29912,plain,
( spl559_107
<=> class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_107])]) ).
fof(f24198,plain,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5167]) ).
fof(f5167,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add) ).
fof(f29909,plain,
spl559_106,
inference(avatar_split_clause,[],[f20500,f29906]) ).
fof(f29906,plain,
( spl559_106
<=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_106])]) ).
fof(f20500,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5049]) ).
fof(f5049,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(f29890,plain,
spl559_105,
inference(avatar_split_clause,[],[f20418,f29887]) ).
fof(f29887,plain,
( spl559_105
<=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_105])]) ).
fof(f20418,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5011]) ).
fof(f5011,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(f29871,plain,
spl559_104,
inference(avatar_split_clause,[],[f22129,f29868]) ).
fof(f29868,plain,
( spl559_104
<=> 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,[spl559_104])]) ).
fof(f22129,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,[],[f2842]) ).
fof(f2842,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(f29864,plain,
spl559_103,
inference(avatar_split_clause,[],[f24532,f29861]) ).
fof(f29861,plain,
( spl559_103
<=> class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_103])]) ).
fof(f24532,plain,
class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5201]) ).
fof(f5201,axiom,
class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Odvd) ).
fof(f29859,plain,
spl559_102,
inference(avatar_split_clause,[],[f24467,f29856]) ).
fof(f29856,plain,
( spl559_102
<=> class_Groups_Osemigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_102])]) ).
fof(f24467,plain,
class_Groups_Osemigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5040]) ).
fof(f5040,axiom,
class_Groups_Osemigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osemigroup__add) ).
fof(f29854,plain,
spl559_101,
inference(avatar_split_clause,[],[f28754,f29851]) ).
fof(f29851,plain,
( spl559_101
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_101])]) ).
fof(f28754,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f28753]) ).
fof(f28753,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(equality_resolution,[],[f25559]) ).
fof(f25559,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f18752]) ).
fof(f18752,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) ) ),
inference(flattening,[],[f18751]) ).
fof(f18751,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1) ) ),
inference(nnf_transformation,[],[f5773]) ).
fof(f5773,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),X1)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
inference(rectify,[],[f370]) ).
fof(f370,axiom,
! [X53,X56] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X56)
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X56
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X53 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__0) ).
fof(f29841,plain,
spl559_43,
inference(avatar_split_clause,[],[f28741,f29180]) ).
fof(f29180,plain,
( spl559_43
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_43])]) ).
fof(f28741,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f28740]) ).
fof(f28740,plain,
! [X0] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ),
inference(equality_resolution,[],[f25444]) ).
fof(f25444,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ),
inference(cnf_transformation,[],[f18677]) ).
fof(f18677,plain,
! [X0,X1] :
( ( ( 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) = 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)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) )
& ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) ) ),
inference(flattening,[],[f18676]) ).
fof(f18676,plain,
! [X0,X1] :
( ( ( 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) = 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)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) )
& ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) ) ),
inference(nnf_transformation,[],[f8436]) ).
fof(f8436,plain,
! [X0,X1] :
( ( ( 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) = 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)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ),
inference(rectify,[],[f399]) ).
fof(f399,axiom,
! [X56,X53] :
( ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X53
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X56 )
| ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X56
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X53 ) )
<=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X56) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_one__is__add) ).
fof(f29832,plain,
spl559_100,
inference(avatar_split_clause,[],[f29827,f29829]) ).
fof(f29829,plain,
( spl559_100
<=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_100])]) ).
fof(f29827,plain,
hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(forward_demodulation,[],[f29825,f28382]) ).
fof(f29825,plain,
! [X2] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),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)),X2))),
inference(backward_demodulation,[],[f28875,f28382]) ).
fof(f28875,plain,
! [X2,X0] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X2))),
inference(equality_resolution,[],[f26770]) ).
fof(f26770,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f19653]) ).
fof(f19653,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2)))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X2)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X2))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X2))) ) ),
inference(rectify,[],[f19652]) ).
fof(f19652,plain,
! [X0,X2,X1] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))) ) ),
inference(flattening,[],[f19651]) ).
fof(f19651,plain,
! [X0,X2,X1] :
( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2
& ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1))) ) ),
inference(nnf_transformation,[],[f9174]) ).
fof(f9174,plain,
! [X0,X2,X1] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X0)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X1)))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X0),X1)) ) ),
inference(rectify,[],[f4960]) ).
fof(f4960,axiom,
! [X53,X56,X44] :
( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X53)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X44),X56)))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X44
| hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),X53),X56)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
fof(f29824,plain,
spl559_99,
inference(avatar_split_clause,[],[f23979,f29821]) ).
fof(f29821,plain,
( spl559_99
<=> 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,[spl559_99])]) ).
fof(f23979,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,[],[f4163]) ).
fof(f4163,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(f29818,plain,
spl559_98,
inference(avatar_split_clause,[],[f22562,f29815]) ).
fof(f29815,plain,
( spl559_98
<=> c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_98])]) ).
fof(f22562,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)),
inference(cnf_transformation,[],[f2855]) ).
fof(f2855,axiom,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__atLeast__UNIV) ).
fof(f29807,plain,
( spl559_96
| spl559_97 ),
inference(avatar_split_clause,[],[f29800,f29805,f29802]) ).
fof(f29802,plain,
( spl559_96
<=> ! [X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_96])]) ).
fof(f29800,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) ),
inference(forward_subsumption_demodulation,[],[f29799,f29520]) ).
fof(f29799,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,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,X0)) ),
inference(forward_demodulation,[],[f20171,f26803]) ).
fof(f20171,plain,
! [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_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,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,[],[f13161]) ).
fof(f29792,plain,
spl559_95,
inference(avatar_split_clause,[],[f28527,f29789]) ).
fof(f29789,plain,
( spl559_95
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_95])]) ).
fof(f28527,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(equality_resolution,[],[f28526]) ).
fof(f28526,plain,
! [X0] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 ),
inference(equality_resolution,[],[f23058]) ).
fof(f23058,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f16821]) ).
fof(f16821,plain,
! [X0,X1] :
( ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0 )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X1)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0 ) ),
inference(rectify,[],[f16820]) ).
fof(f16820,plain,
! [X1,X0] :
( ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1 ) ),
inference(flattening,[],[f16819]) ).
fof(f16819,plain,
! [X1,X0] :
( ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X0
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != X1 ) ),
inference(nnf_transformation,[],[f7807]) ).
fof(f7807,plain,
! [X1,X0] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X0
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X1 )
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X1),X0) ),
inference(rectify,[],[f648]) ).
fof(f648,axiom,
! [X56,X53] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X53),X56)
<=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = X56
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = X53 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__mult__eq__1__iff) ).
fof(f29715,plain,
spl559_94,
inference(avatar_split_clause,[],[f25611,f29712]) ).
fof(f29712,plain,
( spl559_94
<=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_94])]) ).
fof(f25611,plain,
class_Nat_Osemiring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5043]) ).
fof(f5043,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Nat_Osemiring__char__0) ).
fof(f29707,plain,
~ spl559_73,
inference(avatar_split_clause,[],[f25120,f29475]) ).
fof(f25120,plain,
c_Int_OPls != c_Int_OMin,
inference(cnf_transformation,[],[f1530]) ).
fof(f1530,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I40_J) ).
fof(f29705,plain,
spl559_93,
inference(avatar_split_clause,[],[f21875,f29702]) ).
fof(f29702,plain,
( spl559_93
<=> class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_93])]) ).
fof(f21875,plain,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5173]) ).
fof(f5173,axiom,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom) ).
fof(f29678,plain,
spl559_92,
inference(avatar_split_clause,[],[f20982,f29675]) ).
fof(f29675,plain,
( spl559_92
<=> class_Groups_Osgn__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_92])]) ).
fof(f20982,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(cnf_transformation,[],[f5065]) ).
fof(f5065,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).
fof(f29673,plain,
spl559_91,
inference(avatar_split_clause,[],[f20219,f29670]) ).
fof(f20219,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f1626]) ).
fof(f1626,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(f29660,plain,
spl559_90,
inference(avatar_split_clause,[],[f20726,f29657]) ).
fof(f20726,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f1120]) ).
fof(f1120,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zminus__0) ).
fof(f29654,plain,
spl559_89,
inference(avatar_split_clause,[],[f23084,f29651]) ).
fof(f29651,plain,
( spl559_89
<=> class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_89])]) ).
fof(f23084,plain,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5191]) ).
fof(f5191,axiom,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0) ).
fof(f29648,plain,
~ spl559_88,
inference(avatar_split_clause,[],[f25392,f29645]) ).
fof(f29645,plain,
( spl559_88
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_88])]) ).
fof(f25392,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f1551]) ).
fof(f1551,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(f29637,plain,
spl559_87,
inference(avatar_split_clause,[],[f23865,f29634]) ).
fof(f29634,plain,
( spl559_87
<=> hBOOL(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_87])]) ).
fof(f23865,plain,
hBOOL(c_fTrue),
inference(cnf_transformation,[],[f5212]) ).
fof(f5212,axiom,
hBOOL(c_fTrue),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fTrue__1) ).
fof(f29623,plain,
spl559_86,
inference(avatar_split_clause,[],[f20095,f29620]) ).
fof(f29620,plain,
( spl559_86
<=> class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_86])]) ).
fof(f20095,plain,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5200]) ).
fof(f5200,axiom,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oone) ).
fof(f29616,plain,
spl559_85,
inference(avatar_split_clause,[],[f24583,f29613]) ).
fof(f29613,plain,
( spl559_85
<=> class_Rings_Odvd(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_85])]) ).
fof(f24583,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(cnf_transformation,[],[f5123]) ).
fof(f5123,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(f29610,plain,
spl559_84,
inference(avatar_split_clause,[],[f20573,f29607]) ).
fof(f29607,plain,
( spl559_84
<=> class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_84])]) ).
fof(f20573,plain,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5193]) ).
fof(f5193,axiom,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Orderings_Oorder) ).
fof(f29605,plain,
spl559_83,
inference(avatar_split_clause,[],[f20241,f29602]) ).
fof(f29602,plain,
( spl559_83
<=> 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,[spl559_83])]) ).
fof(f20241,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,[],[f2825]) ).
fof(f2825,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(f29600,plain,
spl559_82,
inference(avatar_split_clause,[],[f26315,f29597]) ).
fof(f29597,plain,
( spl559_82
<=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_82])]) ).
fof(f26315,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5096]) ).
fof(f5096,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Oordered__semiring) ).
fof(f29594,plain,
spl559_81,
inference(avatar_split_clause,[],[f26080,f29591]) ).
fof(f29591,plain,
( spl559_81
<=> class_Rings_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_81])]) ).
fof(f26080,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5067]) ).
fof(f5067,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(f29583,plain,
spl559_80,
inference(avatar_split_clause,[],[f25131,f29580]) ).
fof(f25131,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,[],[f1675]) ).
fof(f1675,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(f29516,plain,
spl559_79,
inference(avatar_split_clause,[],[f25901,f29513]) ).
fof(f29513,plain,
( spl559_79
<=> class_Rings_Osemiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_79])]) ).
fof(f25901,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5115]) ).
fof(f5115,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(f29511,plain,
spl559_78,
inference(avatar_split_clause,[],[f28449,f29508]) ).
fof(f28449,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(equality_resolution,[],[f21990]) ).
fof(f21990,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f16013]) ).
fof(f16013,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
inference(nnf_transformation,[],[f8447]) ).
fof(f8447,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(rectify,[],[f850]) ).
fof(f850,axiom,
! [X56] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X56
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X56)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__le__0__conv) ).
fof(f29506,plain,
spl559_77,
inference(avatar_split_clause,[],[f20069,f29503]) ).
fof(f20069,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(cnf_transformation,[],[f2242]) ).
fof(f2242,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_One__int__def) ).
fof(f29493,plain,
( spl559_75
| spl559_76 ),
inference(avatar_split_clause,[],[f29486,f29491,f29488]) ).
fof(f29488,plain,
( spl559_75
<=> ! [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),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_75])]) ).
fof(f29491,plain,
( spl559_76
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != 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),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_76])]) ).
fof(f29486,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)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(forward_subsumption_demodulation,[],[f21558,f21752]) ).
fof(f21558,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f15714]) ).
fof(f29485,plain,
spl559_74,
inference(avatar_split_clause,[],[f24155,f29482]) ).
fof(f29482,plain,
( spl559_74
<=> class_Lattices_Osemilattice__inf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_74])]) ).
fof(f24155,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(cnf_transformation,[],[f5091]) ).
fof(f5091,axiom,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
fof(f29478,plain,
~ spl559_73,
inference(avatar_split_clause,[],[f22538,f29475]) ).
fof(f22538,plain,
c_Int_OPls != c_Int_OMin,
inference(cnf_transformation,[],[f1529]) ).
fof(f1529,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I37_J) ).
fof(f29467,plain,
spl559_72,
inference(avatar_split_clause,[],[f23523,f29464]) ).
fof(f23523,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
inference(cnf_transformation,[],[f2246]) ).
fof(f2246,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Zero__int__def) ).
fof(f29462,plain,
spl559_71,
inference(avatar_split_clause,[],[f22897,f29459]) ).
fof(f29459,plain,
( spl559_71
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_71])]) ).
fof(f22897,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f3153]) ).
fof(f3153,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__less__than) ).
fof(f29452,plain,
( spl559_70
| spl559_55 ),
inference(avatar_split_clause,[],[f28672,f29268,f29450]) ).
fof(f29450,plain,
( spl559_70
<=> ! [X1] : hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_70])]) ).
fof(f29268,plain,
( spl559_55
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_55])]) ).
fof(f28672,plain,
! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(equality_resolution,[],[f24516]) ).
fof(f24516,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,X0) ),
inference(cnf_transformation,[],[f17926]) ).
fof(f17926,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ( ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 )
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,X0) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| c_Nitpick_Onorm__frac(X1,X0) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X0)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0))) ) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Nitpick_Onorm__frac(X1,X0) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) ) ),
inference(rectify,[],[f13330]) ).
fof(f13330,plain,
! [X1,X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ( ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 )
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X0,X1) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| c_Nitpick_Onorm__frac(X0,X1) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X0),X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))) ) ) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Nitpick_Onorm__frac(X0,X1) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)) ) ),
inference(flattening,[],[f13329]) ).
fof(f13329,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Nitpick_Onorm__frac(X0,X1) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)) )
& ( ( ( c_Nitpick_Onorm__frac(X0,X1) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X0),X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| 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) != X1 )
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X0,X1) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
inference(ennf_transformation,[],[f9170]) ).
fof(f9170,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(X0,X1) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ~ ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
=> c_Nitpick_Onorm__frac(X0,X1) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X0),X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
=> hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X0,X1) ) ) ) ),
inference(rectify,[],[f1783]) ).
fof(f1783,axiom,
! [X30,X31] :
( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X31),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ~ ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X31
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X30 )
=> c_Nitpick_Onorm__frac(X30,X31) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X30),X31)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X31))) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X31
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X30 )
=> c_Nitpick_Onorm__frac(X30,X31) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X31),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(X30,X31) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X31)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_norm__frac_Osimps) ).
fof(f29448,plain,
~ spl559_69,
inference(avatar_split_clause,[],[f26956,f29445]) ).
fof(f26956,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
inference(cnf_transformation,[],[f1557]) ).
fof(f1557,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__number__of__Pls__Min) ).
fof(f29443,plain,
spl559_68,
inference(avatar_split_clause,[],[f24030,f29440]) ).
fof(f29440,plain,
( spl559_68
<=> class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_68])]) ).
fof(f24030,plain,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5174]) ).
fof(f5174,axiom,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult) ).
fof(f29438,plain,
spl559_67,
inference(avatar_split_clause,[],[f20921,f29435]) ).
fof(f29435,plain,
( spl559_67
<=> c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_67])]) ).
fof(f20921,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)),
inference(cnf_transformation,[],[f2852]) ).
fof(f2852,axiom,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UN__atMost__UNIV) ).
fof(f29433,plain,
~ spl559_66,
inference(avatar_split_clause,[],[f22022,f29430]) ).
fof(f29430,plain,
( spl559_66
<=> hBOOL(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_66])]) ).
fof(f22022,plain,
~ hBOOL(c_fFalse),
inference(cnf_transformation,[],[f5211]) ).
fof(f5211,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fFalse__1) ).
fof(f29422,plain,
spl559_65,
inference(avatar_split_clause,[],[f25960,f29419]) ).
fof(f29419,plain,
( spl559_65
<=> class_Orderings_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_65])]) ).
fof(f25960,plain,
class_Orderings_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f5117]) ).
fof(f5117,axiom,
class_Orderings_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
fof(f29416,plain,
spl559_64,
inference(avatar_split_clause,[],[f26538,f29413]) ).
fof(f29413,plain,
( spl559_64
<=> class_Orderings_Opreorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_64])]) ).
fof(f26538,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f5132]) ).
fof(f5132,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(f29411,plain,
spl559_63,
inference(avatar_split_clause,[],[f23276,f29408]) ).
fof(f29408,plain,
( spl559_63
<=> class_Orderings_Owellorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_63])]) ).
fof(f23276,plain,
class_Orderings_Owellorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5103]) ).
fof(f5103,axiom,
class_Orderings_Owellorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).
fof(f29406,plain,
spl559_18,
inference(avatar_split_clause,[],[f23371,f29037]) ).
fof(f23371,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,[],[f827]) ).
fof(f827,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_int__0) ).
fof(f29397,plain,
spl559_62,
inference(avatar_split_clause,[],[f21206,f29394]) ).
fof(f29394,plain,
( spl559_62
<=> class_Lattices_Odistrib__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_62])]) ).
fof(f21206,plain,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5130]) ).
fof(f5130,axiom,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
fof(f29391,plain,
spl559_61,
inference(avatar_split_clause,[],[f20858,f29388]) ).
fof(f29388,plain,
( spl559_61
<=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_61])]) ).
fof(f20858,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(cnf_transformation,[],[f5045]) ).
fof(f5045,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(f29378,plain,
spl559_60,
inference(avatar_split_clause,[],[f29373,f29375]) ).
fof(f29373,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls)))),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)))),
inference(forward_demodulation,[],[f29372,f20419]) ).
fof(f29372,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),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)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))))),
inference(forward_demodulation,[],[f29371,f20419]) ).
fof(f29371,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),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)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(forward_demodulation,[],[f29370,f20419]) ).
fof(f29370,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),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)))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),
inference(forward_demodulation,[],[f27155,f27261]) ).
fof(f27155,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(definition_unfolding,[],[f20084,f21744,f20132,f21744,f20132]) ).
fof(f20084,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f1267]) ).
fof(f1267,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_transfer__int__nat__numerals_I3_J) ).
fof(f29365,plain,
spl559_59,
inference(avatar_split_clause,[],[f23568,f29362]) ).
fof(f29362,plain,
( spl559_59
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_59])]) ).
fof(f23568,plain,
class_Power_Opower(tc_Int_Oint),
inference(cnf_transformation,[],[f5069]) ).
fof(f5069,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(f29359,plain,
spl559_31,
inference(avatar_split_clause,[],[f28767,f29112]) ).
fof(f29112,plain,
( spl559_31
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_31])]) ).
fof(f28767,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f28766]) ).
fof(f28766,plain,
! [X1] :
( hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f25689]) ).
fof(f25689,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f18853]) ).
fof(f29358,plain,
~ spl559_58,
inference(avatar_split_clause,[],[f24524,f29355]) ).
fof(f29355,plain,
( spl559_58
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_58])]) ).
fof(f24524,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(cnf_transformation,[],[f885]) ).
fof(f885,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(f29279,plain,
spl559_57,
inference(avatar_split_clause,[],[f24668,f29276]) ).
fof(f29276,plain,
( spl559_57
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_57])]) ).
fof(f24668,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5084]) ).
fof(f5084,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(f29274,plain,
( spl559_55
| spl559_56 ),
inference(avatar_split_clause,[],[f28762,f29272,f29268]) ).
fof(f29272,plain,
( spl559_56
<=> ! [X1] :
( hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_56])]) ).
fof(f28762,plain,
! [X1] :
( hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(equality_resolution,[],[f25670]) ).
fof(f25670,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
inference(cnf_transformation,[],[f18839]) ).
fof(f18839,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X1),X0)))
| ( ( ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| c_Nitpick_Onorm__frac(X1,X0) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X1),X0)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 )
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X1,X0) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Nitpick_Onorm__frac(X1,X0) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
inference(rectify,[],[f12711]) ).
fof(f12711,plain,
! [X1,X0] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X0),X1)))
| ( ( ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| c_Nitpick_Onorm__frac(X0,X1) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X0),X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1)))
| 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) != X1 )
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X0,X1) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( c_Nitpick_Onorm__frac(X0,X1) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
inference(flattening,[],[f12710]) ).
fof(f12710,plain,
! [X1,X0] :
( ( ( c_Nitpick_Onorm__frac(X0,X1) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ( ( c_Nitpick_Onorm__frac(X0,X1) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X0),X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 )
& ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 )
| hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X0,X1) ) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X0),X1))) ),
inference(ennf_transformation,[],[f9580]) ).
fof(f9580,plain,
! [X1,X0] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X0),X1)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(X0,X1) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X1)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ~ ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 )
=> c_Nitpick_Onorm__frac(X0,X1) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X0),X1)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X1))) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1 )
=> hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Nitpick_Onorm__frac(X0,X1) ) ) ) ) ),
inference(rectify,[],[f1891]) ).
fof(f1891,axiom,
! [X30,X31] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Nitpick_Onorm__frac__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),X30),X31)))
=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X31),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> c_Nitpick_Onorm__frac(X30,X31) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X31)) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X31),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> ( ( ~ ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X31
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X30 )
=> c_Nitpick_Onorm__frac(X30,X31) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,X30),X31)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X30))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X31))) )
& ( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X31
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X30 )
=> c_Nitpick_Onorm__frac(X30,X31) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,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_norm__frac_Opsimps) ).
fof(f29257,plain,
spl559_54,
inference(avatar_split_clause,[],[f28677,f29254]) ).
fof(f28677,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f28676]) ).
fof(f28676,plain,
! [X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f24615]) ).
fof(f24615,plain,
! [X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f18006]) ).
fof(f18006,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(flattening,[],[f18005]) ).
fof(f18005,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) )
& ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(nnf_transformation,[],[f10014]) ).
fof(f10014,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
<=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) ),
inference(rectify,[],[f1195]) ).
fof(f1195,axiom,
! [X56,X53] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X53) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X56))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X56
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X53 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_negative__eq__positive) ).
fof(f29248,plain,
spl559_53,
inference(avatar_split_clause,[],[f22528,f29245]) ).
fof(f22528,plain,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
inference(cnf_transformation,[],[f4202]) ).
fof(f4202,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(f29242,plain,
spl559_52,
inference(avatar_split_clause,[],[f26758,f29239]) ).
fof(f29239,plain,
( spl559_52
<=> class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_52])]) ).
fof(f26758,plain,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5194]) ).
fof(f5194,axiom,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring) ).
fof(f29236,plain,
~ spl559_51,
inference(avatar_split_clause,[],[f26183,f29233]) ).
fof(f26183,plain,
v_G != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
inference(cnf_transformation,[],[f9543]) ).
fof(f9543,plain,
v_G != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
inference(flattening,[],[f5229]) ).
fof(f5229,negated_conjecture,
v_G != hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
inference(negated_conjecture,[],[f5228]) ).
fof(f5228,conjecture,
v_G = hAPP(c_Set_Oimage(tc_Com_Opname,t_a,v_mgt__call),v_U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
fof(f29230,plain,
spl559_50,
inference(avatar_split_clause,[],[f23715,f29227]) ).
fof(f29227,plain,
( spl559_50
<=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_50])]) ).
fof(f23715,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f5089]) ).
fof(f5089,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semidom) ).
fof(f29225,plain,
spl559_49,
inference(avatar_split_clause,[],[f24796,f29222]) ).
fof(f29222,plain,
( spl559_49
<=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_49])]) ).
fof(f24796,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5030]) ).
fof(f5030,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Oab__semigroup__mult) ).
fof(f29220,plain,
spl559_48,
inference(avatar_split_clause,[],[f23933,f29217]) ).
fof(f23933,plain,
c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f2140]) ).
fof(f2140,axiom,
c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__leq)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_max__weak__def) ).
fof(f29215,plain,
spl559_47,
inference(avatar_split_clause,[],[f26288,f29212]) ).
fof(f29212,plain,
( spl559_47
<=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_47])]) ).
fof(f26288,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5017]) ).
fof(f5017,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oordered__cancel__semiring) ).
fof(f29208,plain,
spl559_46,
inference(avatar_split_clause,[],[f22489,f29205]) ).
fof(f29205,plain,
( spl559_46
<=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_46])]) ).
fof(f22489,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5031]) ).
fof(f5031,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ocomm__monoid__mult) ).
fof(f29202,plain,
spl559_45,
inference(avatar_split_clause,[],[f29197,f29199]) ).
fof(f29197,plain,
c_List_Olist_ONil(tc_Nat_Onat) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(backward_demodulation,[],[f27856,f25637]) ).
fof(f27856,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,[],[f24699,f25412]) ).
fof(f24699,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f5322]) ).
fof(f5322,plain,
! [X0] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f4367]) ).
fof(f4367,axiom,
! [X63] : c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oupt(X63,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_upt__0) ).
fof(f29196,plain,
spl559_44,
inference(avatar_split_clause,[],[f20579,f29193]) ).
fof(f29193,plain,
( spl559_44
<=> class_Orderings_Oord(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_44])]) ).
fof(f20579,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(cnf_transformation,[],[f5063]) ).
fof(f5063,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(f29183,plain,
spl559_43,
inference(avatar_split_clause,[],[f28803,f29180]) ).
fof(f28803,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f28802]) ).
fof(f28802,plain,
! [X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f26005]) ).
fof(f26005,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f19070]) ).
fof(f19070,plain,
! [X0,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 )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) )
& ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ( ( 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 ) ) ) ),
inference(flattening,[],[f19069]) ).
fof(f19069,plain,
! [X0,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 )
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) )
& ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| ( ( 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 ) ) ) ),
inference(nnf_transformation,[],[f7611]) ).
fof(f7611,plain,
! [X0,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 ) )
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0) ),
inference(rectify,[],[f398]) ).
fof(f398,axiom,
! [X56,X53] :
( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X53),X56) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X56
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X53 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X53
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X56 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_add__is__1) ).
fof(f29176,plain,
spl559_42,
inference(avatar_split_clause,[],[f24399,f29173]) ).
fof(f29173,plain,
( spl559_42
<=> class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_42])]) ).
fof(f24399,plain,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5177]) ).
fof(f5177,axiom,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring) ).
fof(f29171,plain,
spl559_41,
inference(avatar_split_clause,[],[f22793,f29168]) ).
fof(f29168,plain,
( spl559_41
<=> c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_41])]) ).
fof(f22793,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(cnf_transformation,[],[f868]) ).
fof(f868,axiom,
c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J) ).
fof(f29165,plain,
spl559_40,
inference(avatar_split_clause,[],[f28836,f29162]) ).
fof(f28836,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),c_Int_OPls),
inference(equality_resolution,[],[f28107]) ).
fof(f28107,plain,
! [X0] :
( c_Int_OPls = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0)
| c_Int_OPls != X0 ),
inference(definition_unfolding,[],[f26318,f21744]) ).
fof(f26318,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 ),
inference(cnf_transformation,[],[f19297]) ).
fof(f19297,plain,
! [X0] :
( ( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) )
& ( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 ) ),
inference(nnf_transformation,[],[f7053]) ).
fof(f7053,plain,
! [X0] :
( c_Int_OPls = X0
<=> c_Int_OPls = c_Int_OBit0(X0) ),
inference(rectify,[],[f1121]) ).
fof(f1121,axiom,
! [X44] :
( c_Int_OPls = c_Int_OBit0(X44)
<=> c_Int_OPls = X44 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I44_J) ).
fof(f29160,plain,
spl559_39,
inference(avatar_split_clause,[],[f23087,f29157]) ).
fof(f23087,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
inference(cnf_transformation,[],[f4571]) ).
fof(f4571,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(f29155,plain,
spl559_38,
inference(avatar_split_clause,[],[f27198,f29152]) ).
fof(f29152,plain,
( spl559_38
<=> c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Transitive__Closure_Ortrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_38])]) ).
fof(f27198,plain,
c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Transitive__Closure_Ortrancl(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)))),
inference(definition_unfolding,[],[f20299,f20563]) ).
fof(f20563,plain,
! [X0] : c_Transitive__Closure_Ortrancl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))) = c_Relation_OId(X0),
inference(cnf_transformation,[],[f8480]) ).
fof(f8480,plain,
! [X0] : c_Transitive__Closure_Ortrancl(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))) = c_Relation_OId(X0),
inference(rectify,[],[f3375]) ).
fof(f3375,axiom,
! [X8] : c_Relation_OId(X8) = c_Transitive__Closure_Ortrancl(X8,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X8),tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__empty) ).
fof(f20299,plain,
c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
inference(cnf_transformation,[],[f3397]) ).
fof(f3397,axiom,
c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_HOL_Obool)),c_FunDef_Opair__less),c_Relation_OId(tc_prod(tc_Nat_Onat,tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__leq__def) ).
fof(f29150,plain,
spl559_37,
inference(avatar_split_clause,[],[f20696,f29147]) ).
fof(f29147,plain,
( spl559_37
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_37])]) ).
fof(f20696,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5060]) ).
fof(f5060,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(f29145,plain,
spl559_36,
inference(avatar_split_clause,[],[f21675,f29142]) ).
fof(f29142,plain,
( spl559_36
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_36])]) ).
fof(f21675,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(cnf_transformation,[],[f5076]) ).
fof(f5076,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(f29139,plain,
spl559_35,
inference(avatar_split_clause,[],[f23393,f29136]) ).
fof(f29136,plain,
( spl559_35
<=> class_Groups_Ouminus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_35])]) ).
fof(f23393,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(cnf_transformation,[],[f5064]) ).
fof(f5064,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(f29134,plain,
spl559_34,
inference(avatar_split_clause,[],[f26537,f29131]) ).
fof(f29131,plain,
( spl559_34
<=> class_Rings_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_34])]) ).
fof(f26537,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(cnf_transformation,[],[f5072]) ).
fof(f5072,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(f29127,plain,
spl559_33,
inference(avatar_split_clause,[],[f25411,f29124]) ).
fof(f29124,plain,
( spl559_33
<=> c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_33])]) ).
fof(f25411,plain,
c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),
inference(cnf_transformation,[],[f2147]) ).
fof(f2147,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(f29122,plain,
spl559_32,
inference(avatar_split_clause,[],[f28369,f29119]) ).
fof(f28369,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,[],[f21024]) ).
fof(f21024,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,[],[f15314]) ).
fof(f15314,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint))) )
& ( 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(nnf_transformation,[],[f8395]) ).
fof(f8395,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X0)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(rectify,[],[f2695]) ).
fof(f2695,axiom,
! [X23] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X23
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),X23)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_zabs__less__one__iff) ).
fof(f29115,plain,
spl559_31,
inference(avatar_split_clause,[],[f28487,f29112]) ).
fof(f28487,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f28486]) ).
fof(f28486,plain,
! [X1] :
( hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)) = X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f22594]) ).
fof(f22594,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f16473]) ).
fof(f16473,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onat,X0) = X1
| ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != X0
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_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)) )
& ( 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_Int_Onat,X0) != X1 ) ),
inference(rectify,[],[f16472]) ).
fof(f16472,plain,
! [X1,X0] :
( ( hAPP(c_Int_Onat,X1) = X0
| ( 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)) )
& ( 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_Int_Onat,X1) != X0 ) ),
inference(flattening,[],[f16471]) ).
fof(f16471,plain,
! [X1,X0] :
( ( hAPP(c_Int_Onat,X1) = X0
| ( 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)) )
& ( 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_Int_Onat,X1) != X0 ) ),
inference(nnf_transformation,[],[f11426]) ).
fof(f11426,plain,
! [X1,X0] :
( hAPP(c_Int_Onat,X1) = X0
<=> ( ( 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)) ) ) ),
inference(ennf_transformation,[],[f5384]) ).
fof(f5384,plain,
! [X1,X0] :
( 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))
=> 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 ) ) ),
inference(rectify,[],[f1000]) ).
fof(f1000,axiom,
! [X53,X91] :
( hAPP(c_Int_Onat,X91) = X53
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X53 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X91))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X53) = X91 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__eq__iff) ).
fof(f29108,plain,
( spl559_29
| spl559_30 ),
inference(avatar_split_clause,[],[f29101,f29106,f29103]) ).
fof(f29103,plain,
( spl559_29
<=> ! [X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_29])]) ).
fof(f29106,plain,
( spl559_30
<=> ! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_30])]) ).
fof(f29101,plain,
! [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_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) ),
inference(forward_subsumption_demodulation,[],[f20179,f21752]) ).
fof(f20179,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),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),X0))) ),
inference(cnf_transformation,[],[f14282]) ).
fof(f14282,plain,
! [X0,X1] :
( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| hBOOL(hAPP(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)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) ) ),
inference(ennf_transformation,[],[f6859]) ).
fof(f6859,plain,
! [X0,X1] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)) ) ),
inference(rectify,[],[f1607]) ).
fof(f1607,axiom,
! [X82,X108] :
( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X108)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X108))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X82)))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X82)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X108)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_div__nat__number__of) ).
fof(f29100,plain,
spl559_28,
inference(avatar_split_clause,[],[f28530,f29097]) ).
fof(f28530,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))),
inference(equality_resolution,[],[f28529]) ).
fof(f28529,plain,
! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f23098]) ).
fof(f23098,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f16850]) ).
fof(f16850,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(rectify,[],[f16849]) ).
fof(f16849,plain,
! [X1,X0] :
( ( ( 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__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
inference(flattening,[],[f16848]) ).
fof(f16848,plain,
! [X1,X0] :
( ( ( 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__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) ),
inference(nnf_transformation,[],[f7194]) ).
fof(f7194,plain,
! [X1,X0] :
( ( 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__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1)))) ),
inference(rectify,[],[f1237]) ).
fof(f1237,axiom,
! [X56,X53] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X56)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X53))))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X53
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X56 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__zle__neg) ).
fof(f29095,plain,
spl559_27,
inference(avatar_split_clause,[],[f20576,f29092]) ).
fof(f29092,plain,
( spl559_27
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_27])]) ).
fof(f20576,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5015]) ).
fof(f5015,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(f29089,plain,
spl559_26,
inference(avatar_split_clause,[],[f24421,f29086]) ).
fof(f29086,plain,
( spl559_26
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_26])]) ).
fof(f24421,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(cnf_transformation,[],[f1546]) ).
fof(f1546,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bin__less__0__simps_I2_J) ).
fof(f29084,plain,
spl559_25,
inference(avatar_split_clause,[],[f27863,f29081]) ).
fof(f29081,plain,
( spl559_25
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_25])]) ).
fof(f27863,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OPls)),c_Int_OPls)))),
inference(definition_unfolding,[],[f24754,f20132,f20132,f20132,f20132]) ).
fof(f24754,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f957]) ).
fof(f957,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,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_transfer__nat__int__numerals_I4_J) ).
fof(f29079,plain,
spl559_24,
inference(avatar_split_clause,[],[f24295,f29076]) ).
fof(f29076,plain,
( spl559_24
<=> class_Lattices_Obounded__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_24])]) ).
fof(f24295,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(f29072,plain,
spl559_23,
inference(avatar_split_clause,[],[f26349,f29069]) ).
fof(f29069,plain,
( spl559_23
<=> c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_23])]) ).
fof(f26349,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)),
inference(cnf_transformation,[],[f3589]) ).
fof(f3589,axiom,
c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_INT__greaterThan__UNIV) ).
fof(f29066,plain,
spl559_22,
inference(avatar_split_clause,[],[f25176,f29063]) ).
fof(f29063,plain,
( spl559_22
<=> class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_22])]) ).
fof(f25176,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5166]) ).
fof(f5166,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add) ).
fof(f29058,plain,
spl559_21,
inference(avatar_split_clause,[],[f29053,f29055]) ).
fof(f29053,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Int_OMin),
inference(forward_demodulation,[],[f28262,f27633]) ).
fof(f28262,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Int_OMin)),c_Int_OMin),
inference(equality_resolution,[],[f27129]) ).
fof(f27129,plain,
! [X0] :
( c_Int_OMin = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0)),X0)
| c_Int_OMin != X0 ),
inference(definition_unfolding,[],[f19937,f20132]) ).
fof(f19937,plain,
! [X0] :
( c_Int_OMin = c_Int_OBit1(X0)
| c_Int_OMin != X0 ),
inference(cnf_transformation,[],[f14515]) ).
fof(f14515,plain,
! [X0] :
( ( c_Int_OMin = X0
| c_Int_OMin != c_Int_OBit1(X0) )
& ( c_Int_OMin = c_Int_OBit1(X0)
| c_Int_OMin != X0 ) ),
inference(nnf_transformation,[],[f9385]) ).
fof(f9385,plain,
! [X0] :
( c_Int_OMin = X0
<=> c_Int_OMin = c_Int_OBit1(X0) ),
inference(rectify,[],[f1531]) ).
fof(f1531,axiom,
! [X44] :
( c_Int_OMin = X44
<=> c_Int_OBit1(X44) = c_Int_OMin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rel__simps_I47_J) ).
fof(f29052,plain,
spl559_20,
inference(avatar_split_clause,[],[f28743,f29049]) ).
fof(f29049,plain,
( spl559_20
<=> hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_20])]) ).
fof(f28743,plain,
hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f28742]) ).
fof(f28742,plain,
! [X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f25443]) ).
fof(f25443,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X1),X0)
| 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,[],[f18677]) ).
fof(f29045,plain,
spl559_19,
inference(avatar_split_clause,[],[f22474,f29042]) ).
fof(f29042,plain,
( spl559_19
<=> c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_19])]) ).
fof(f22474,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f3167]) ).
fof(f3167,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(f29040,plain,
spl559_18,
inference(avatar_split_clause,[],[f28414,f29037]) ).
fof(f28414,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(equality_resolution,[],[f21544]) ).
fof(f21544,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f15711]) ).
fof(f15711,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,[],[f7170]) ).
fof(f7170,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,[],[f826]) ).
fof(f826,axiom,
! [X56] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X56
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__eq__0__conv) ).
fof(f29034,plain,
spl559_17,
inference(avatar_split_clause,[],[f23938,f29031]) ).
fof(f29031,plain,
( spl559_17
<=> class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_17])]) ).
fof(f23938,plain,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5190]) ).
fof(f5190,axiom,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1) ).
fof(f29023,plain,
spl559_16,
inference(avatar_split_clause,[],[f23763,f29020]) ).
fof(f23763,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,[],[f4162]) ).
fof(f4162,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(f29018,plain,
spl559_15,
inference(avatar_split_clause,[],[f26759,f29015]) ).
fof(f29015,plain,
( spl559_15
<=> class_Orderings_Obot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_15])]) ).
fof(f26759,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(cnf_transformation,[],[f5138]) ).
fof(f5138,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(f29013,plain,
~ spl559_14,
inference(avatar_split_clause,[],[f28881,f29010]) ).
fof(f28881,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,[],[f26836]) ).
fof(f26836,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,[],[f19702]) ).
fof(f19702,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0))
| hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 )
& ( 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(nnf_transformation,[],[f7795]) ).
fof(f7795,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0))
<=> hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0 ),
inference(rectify,[],[f4175]) ).
fof(f4175,axiom,
! [X46] :
( hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X46
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X46)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_code__numeral__not__eq__zero) ).
fof(f29005,plain,
spl559_13,
inference(avatar_split_clause,[],[f23038,f29002]) ).
fof(f29002,plain,
( spl559_13
<=> c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_13])]) ).
fof(f23038,plain,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
inference(cnf_transformation,[],[f2034]) ).
fof(f2034,axiom,
c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool),tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),tc_HOL_Obool)),c_FunDef_Omin__strict),c_FunDef_Omin__weak)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_min__rpair__set) ).
fof(f28995,plain,
spl559_12,
inference(avatar_split_clause,[],[f23552,f28992]) ).
fof(f28992,plain,
( spl559_12
<=> 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,[spl559_12])]) ).
fof(f23552,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,[],[f1656]) ).
fof(f1656,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(f28987,plain,
spl559_11,
inference(avatar_split_clause,[],[f23463,f28984]) ).
fof(f28984,plain,
( spl559_11
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_11])]) ).
fof(f23463,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5005]) ).
fof(f5005,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(f28982,plain,
spl559_10,
inference(avatar_split_clause,[],[f27037,f28979]) ).
fof(f28979,plain,
( spl559_10
<=> class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_10])]) ).
fof(f27037,plain,
class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5202]) ).
fof(f5202,axiom,
class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Code____Numeral__Ocode____numeral__Nat_Osize) ).
fof(f28977,plain,
spl559_9,
inference(avatar_split_clause,[],[f23050,f28974]) ).
fof(f28974,plain,
( spl559_9
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_9])]) ).
fof(f23050,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f1547]) ).
fof(f1547,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(f28972,plain,
spl559_8,
inference(avatar_split_clause,[],[f22648,f28969]) ).
fof(f28969,plain,
( spl559_8
<=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_8])]) ).
fof(f22648,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5109]) ).
fof(f5109,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(f28964,plain,
spl559_7,
inference(avatar_split_clause,[],[f24677,f28961]) ).
fof(f28961,plain,
( spl559_7
<=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_7])]) ).
fof(f24677,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(cnf_transformation,[],[f5025]) ).
fof(f5025,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semidom) ).
fof(f28958,plain,
spl559_6,
inference(avatar_split_clause,[],[f23929,f28955]) ).
fof(f28955,plain,
( spl559_6
<=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_6])]) ).
fof(f23929,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5039]) ).
fof(f5039,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__1) ).
fof(f28953,plain,
spl559_5,
inference(avatar_split_clause,[],[f22056,f28950]) ).
fof(f28950,plain,
( spl559_5
<=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_5])]) ).
fof(f22056,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5088]) ).
fof(f5088,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
fof(f28948,plain,
spl559_4,
inference(avatar_split_clause,[],[f22715,f28945]) ).
fof(f28945,plain,
( spl559_4
<=> c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_4])]) ).
fof(f22715,plain,
c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))),
inference(cnf_transformation,[],[f4554]) ).
fof(f4554,axiom,
c_FunDef_Ois__measure(tc_Int_Oint,hAPP(c_Fun_Ocomp(tc_Int_Oint,tc_Nat_Onat,tc_Int_Oint,c_Int_Onat),c_Groups_Oabs__class_Oabs(tc_Int_Oint))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_measure__function__int) ).
fof(f28942,plain,
spl559_3,
inference(avatar_split_clause,[],[f26096,f28939]) ).
fof(f28939,plain,
( spl559_3
<=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_3])]) ).
fof(f26096,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5082]) ).
fof(f5082,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(f28937,plain,
spl559_2,
inference(avatar_split_clause,[],[f23345,f28934]) ).
fof(f28934,plain,
( spl559_2
<=> class_Rings_Odvd(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl559_2])]) ).
fof(f23345,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(cnf_transformation,[],[f5075]) ).
fof(f5075,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
fof(f28932,plain,
spl559_1,
inference(avatar_split_clause,[],[f24609,f28929]) ).
fof(f24609,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f851]) ).
fof(f851,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_int__Suc0__eq__1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW358+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 20:41:30 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.56/0.83 % (24836)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/50Mi)
% 0.56/0.84 % (24844)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/100Mi)
% 0.56/0.85 % (24848)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/498Mi)
% 0.56/0.85 % (24829)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/51Mi)
% 0.56/0.85 % (24840)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/68Mi)
% 0.56/0.86 % (24832)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/51Mi)
% 0.56/0.88 % (24828)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/37Mi)
% 0.56/0.88 % (24827)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/50Mi)
% 0.56/0.89 % (24826)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/191324Mi)
% 0.56/0.89 % (24854)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/439Mi)
% 0.56/0.89 % (24830)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/51Mi)
% 0.56/0.89 % (24831)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/48Mi)
% 0.56/0.90 % (24846)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/176Mi)
% 0.56/0.90 % (24835)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/51Mi)
% 0.56/0.90 % (24837)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/100Mi)
% 0.56/0.90 % (24834)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/2Mi)
% 0.56/0.90 % (24839)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/99Mi)
% 0.56/0.90 % (24834)Instruction limit reached!
% 0.56/0.90 % (24834)------------------------------
% 0.56/0.90 % (24834)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.56/0.90 % (24834)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.56/0.90 % (24834)Termination reason: Unknown
% 0.56/0.90 % (24834)Termination phase: shuffling
% 0.56/0.90
% 0.56/0.90 % (24834)Memory used [KB]: 6652
% 0.56/0.90 % (24834)Time elapsed: 0.003 s
% 0.56/0.90 % (24834)Instructions burned: 2 (million)
% 0.56/0.90 % (24834)------------------------------
% 0.56/0.90 % (24834)------------------------------
% 0.56/0.90 % (24833)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/7Mi)
% 0.56/0.90 % (24836)Instruction limit reached!
% 0.56/0.90 % (24836)------------------------------
% 0.56/0.90 % (24836)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.56/0.91 % (24838)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/101Mi)
% 0.56/0.91 % (24850)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/482Mi)
% 0.56/0.91 % (24836)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.56/0.91 % (24836)Termination reason: Unknown
% 0.56/0.91 % (24836)Termination phase: Preprocessing 1
% 0.56/0.91
% 0.56/0.91 % (24836)Memory used [KB]: 10106
% 0.56/0.91 % (24836)Time elapsed: 0.047 s
% 0.56/0.91 % (24836)Instructions burned: 50 (million)
% 0.56/0.91 % (24836)------------------------------
% 0.56/0.91 % (24836)------------------------------
% 0.56/0.91 % (24847)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/138Mi)
% 0.56/0.91 % (24843)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/59Mi)
% 0.56/0.91 % (24841)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/75Mi)
% 0.56/0.91 % (24855)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/355Mi)
% 0.56/0.91 % (24853)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/177Mi)
% 0.56/0.91 % (24845)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/100Mi)
% 0.56/0.91 % (24842)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/99Mi)
% 0.56/0.92 % (24851)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/500Mi)
% 0.56/0.92 % (24852)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/68Mi)
% 0.56/0.92 % (24849)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/467Mi)
% 0.70/0.94 % (24829)Instruction limit reached!
% 0.70/0.94 % (24829)------------------------------
% 0.70/0.94 % (24829)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.70/0.94 % (24833)Instruction limit reached!
% 0.70/0.94 % (24833)------------------------------
% 0.70/0.94 % (24833)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.70/0.94 % (24833)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.70/0.94 % (24833)Termination reason: Unknown
% 0.70/0.94 % (24833)Termination phase: shuffling
% 0.70/0.94
% 0.70/0.94 % (24833)Memory used [KB]: 7164
% 0.70/0.94 % (24833)Time elapsed: 0.010 s
% 0.70/0.94 % (24833)Instructions burned: 7 (million)
% 0.70/0.94 % (24833)------------------------------
% 0.70/0.94 % (24833)------------------------------
% 0.70/0.96 % (24829)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.70/0.96 % (24829)Termination reason: Unknown
% 0.70/0.96 % (24829)Termination phase: Preprocessing 1
% 0.70/0.96
% 0.70/0.96 % (24829)Memory used [KB]: 10234
% 0.70/0.96 % (24829)Time elapsed: 0.044 s
% 0.70/0.96 % (24829)Instructions burned: 52 (million)
% 0.70/0.96 % (24829)------------------------------
% 0.70/0.96 % (24829)------------------------------
% 0.75/0.96 % (24832)Instruction limit reached!
% 0.75/0.96 % (24832)------------------------------
% 0.75/0.96 % (24832)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.75/0.98 % (24832)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.75/0.98 % (24832)Termination reason: Unknown
% 0.75/0.98 % (24832)Termination phase: Preprocessing 1
% 0.75/0.98
% 0.75/0.98 % (24832)Memory used [KB]: 10106
% 0.75/0.98 % (24832)Time elapsed: 0.045 s
% 0.75/0.98 % (24832)Instructions burned: 51 (million)
% 0.75/0.98 % (24832)------------------------------
% 0.75/0.98 % (24832)------------------------------
% 0.75/0.99 % (24844)Instruction limit reached!
% 0.75/0.99 % (24844)------------------------------
% 0.75/0.99 % (24844)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.75/0.99 % (24844)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.75/0.99 % (24844)Termination reason: Unknown
% 0.75/0.99 % (24844)Termination phase: Preprocessing 1
% 0.75/0.99
% 0.75/0.99 % (24844)Memory used [KB]: 12025
% 0.75/0.99 % (24844)Time elapsed: 0.113 s
% 0.75/0.99 % (24844)Instructions burned: 100 (million)
% 0.75/0.99 % (24844)------------------------------
% 0.75/0.99 % (24844)------------------------------
% 0.75/0.99 % (24840)Instruction limit reached!
% 0.75/0.99 % (24840)------------------------------
% 0.75/0.99 % (24840)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.75/0.99 % (24840)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.75/0.99 % (24840)Termination reason: Unknown
% 0.75/0.99 % (24840)Termination phase: Preprocessing 1
% 0.75/0.99
% 0.75/0.99 % (24840)Memory used [KB]: 10746
% 0.75/0.99 % (24840)Time elapsed: 0.057 s
% 0.75/0.99 % (24840)Instructions burned: 68 (million)
% 0.75/0.99 % (24840)------------------------------
% 0.75/0.99 % (24840)------------------------------
% 0.75/1.01 % (24828)Instruction limit reached!
% 0.75/1.01 % (24828)------------------------------
% 0.75/1.01 % (24828)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.75/1.01 % (24828)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.75/1.01 % (24828)Termination reason: Unknown
% 0.75/1.01 % (24828)Termination phase: SInE selection
% 0.75/1.01
% 0.75/1.01 % (24828)Memory used [KB]: 7291
% 0.75/1.01 % (24828)Time elapsed: 0.037 s
% 0.75/1.01 % (24828)Instructions burned: 37 (million)
% 0.75/1.01 % (24828)------------------------------
% 0.75/1.01 % (24828)------------------------------
% 1.18/1.03 % (24827)Instruction limit reached!
% 1.18/1.03 % (24827)------------------------------
% 1.18/1.03 % (24827)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.18/1.03 % (24827)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.18/1.03 % (24827)Termination reason: Unknown
% 1.18/1.03 % (24827)Termination phase: Preprocessing 1
% 1.18/1.03
% 1.18/1.03 % (24827)Memory used [KB]: 10106
% 1.18/1.03 % (24827)Time elapsed: 0.041 s
% 1.18/1.03 % (24827)Instructions burned: 50 (million)
% 1.18/1.03 % (24827)------------------------------
% 1.18/1.03 % (24827)------------------------------
% 1.18/1.03 % (24831)Instruction limit reached!
% 1.18/1.03 % (24831)------------------------------
% 1.18/1.03 % (24831)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.18/1.03 % (24831)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.18/1.03 % (24831)Termination reason: Unknown
% 1.18/1.03 % (24831)Termination phase: Preprocessing 1
% 1.18/1.03
% 1.18/1.03 % (24831)Memory used [KB]: 9978
% 1.18/1.03 % (24831)Time elapsed: 0.040 s
% 1.18/1.03 % (24831)Instructions burned: 48 (million)
% 1.18/1.03 % (24831)------------------------------
% 1.18/1.03 % (24831)------------------------------
% 1.18/1.03 % (24835)Instruction limit reached!
% 1.18/1.03 % (24835)------------------------------
% 1.18/1.03 % (24835)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.18/1.03 % (24835)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.18/1.03 % (24835)Termination reason: Unknown
% 1.18/1.03 % (24835)Termination phase: Preprocessing 1
% 1.18/1.03
% 1.18/1.03 % (24835)Memory used [KB]: 10106
% 1.18/1.03 % (24835)Time elapsed: 0.041 s
% 1.18/1.03 % (24835)Instructions burned: 51 (million)
% 1.18/1.03 % (24835)------------------------------
% 1.18/1.03 % (24835)------------------------------
% 1.18/1.04 % (24856)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=388:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/388Mi)
% 1.18/1.05 % (24843)Instruction limit reached!
% 1.18/1.05 % (24843)------------------------------
% 1.18/1.05 % (24843)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.18/1.05 % (24843)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.18/1.05 % (24843)Termination reason: Unknown
% 1.18/1.05 % (24843)Termination phase: Preprocessing 1
% 1.18/1.05
% 1.18/1.05 % (24843)Memory used [KB]: 10490
% 1.18/1.05 % (24843)Time elapsed: 0.050 s
% 1.18/1.05 % (24843)Instructions burned: 59 (million)
% 1.18/1.05 % (24843)------------------------------
% 1.18/1.05 % (24843)------------------------------
% 1.18/1.06 % (24830)Instruction limit reached!
% 1.18/1.06 % (24830)------------------------------
% 1.18/1.06 % (24830)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.18/1.06 % (24830)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.18/1.06 % (24830)Termination reason: Unknown
% 1.18/1.06 % (24830)Termination phase: Preprocessing 1
% 1.18/1.06
% 1.18/1.06 % (24830)Memory used [KB]: 7803
% 1.18/1.06 % (24830)Time elapsed: 0.048 s
% 1.18/1.06 % (24830)Instructions burned: 51 (million)
% 1.18/1.06 % (24830)------------------------------
% 1.18/1.06 % (24830)------------------------------
% 1.18/1.09 % (24852)Instruction limit reached!
% 1.18/1.09 % (24852)------------------------------
% 1.18/1.09 % (24852)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.32/1.11 % (24852)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.32/1.11 % (24852)Termination reason: Unknown
% 3.32/1.11 % (24852)Termination phase: Preprocessing 1
% 3.32/1.11
% 3.32/1.11 % (24852)Memory used [KB]: 10746
% 3.32/1.11 % (24852)Time elapsed: 0.055 s
% 3.32/1.11 % (24852)Instructions burned: 68 (million)
% 3.32/1.11 % (24852)------------------------------
% 3.32/1.11 % (24852)------------------------------
% 3.32/1.12 % (24841)Instruction limit reached!
% 3.32/1.12 % (24841)------------------------------
% 3.32/1.12 % (24841)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.32/1.12 % (24841)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.32/1.12 % (24841)Termination reason: Unknown
% 3.32/1.12 % (24841)Termination phase: Preprocessing 1
% 3.32/1.12
% 3.32/1.12 % (24841)Memory used [KB]: 11129
% 3.32/1.12 % (24841)Time elapsed: 0.062 s
% 3.32/1.12 % (24841)Instructions burned: 75 (million)
% 3.32/1.12 % (24841)------------------------------
% 3.32/1.12 % (24841)------------------------------
% 3.32/1.14 % (24839)Instruction limit reached!
% 3.32/1.14 % (24839)------------------------------
% 3.32/1.14 % (24839)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.32/1.14 % (24839)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.32/1.14 % (24839)Termination reason: Unknown
% 3.32/1.14 % (24839)Termination phase: Preprocessing 1
% 3.32/1.14
% 3.32/1.14 % (24839)Memory used [KB]: 12025
% 3.32/1.14 % (24839)Time elapsed: 0.088 s
% 3.32/1.14 % (24839)Instructions burned: 99 (million)
% 3.32/1.14 % (24839)------------------------------
% 3.32/1.14 % (24839)------------------------------
% 3.32/1.15 % (24842)Instruction limit reached!
% 3.32/1.15 % (24842)------------------------------
% 3.32/1.15 % (24842)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.32/1.15 % (24842)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.32/1.15 % (24842)Termination reason: Unknown
% 3.32/1.15 % (24842)Termination phase: Preprocessing 1
% 3.32/1.15
% 3.32/1.15 % (24842)Memory used [KB]: 12025
% 3.32/1.15 % (24842)Time elapsed: 0.103 s
% 3.32/1.15 % (24842)Instructions burned: 100 (million)
% 3.32/1.15 % (24842)------------------------------
% 3.32/1.15 % (24842)------------------------------
% 3.32/1.17 % (24857)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=211:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/211Mi)
% 3.90/1.18 % (24891)ott+10_1:50_bsr=unit_only:drc=off:fd=preordered:sp=frequency:i=747:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/747Mi)
% 3.90/1.18 % (24837)Instruction limit reached!
% 3.90/1.18 % (24837)------------------------------
% 3.90/1.18 % (24837)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.90/1.18 % (24837)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.90/1.18 % (24837)Termination reason: Unknown
% 3.90/1.18 % (24837)Termination phase: shuffling
% 3.90/1.18
% 3.90/1.18 % (24837)Memory used [KB]: 12153
% 3.90/1.18 % (24837)Time elapsed: 0.083 s
% 3.90/1.18 % (24837)Instructions burned: 100 (million)
% 3.90/1.18 % (24837)------------------------------
% 3.90/1.18 % (24837)------------------------------
% 3.90/1.19 % (24838)Instruction limit reached!
% 3.90/1.19 % (24838)------------------------------
% 3.90/1.19 % (24838)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.90/1.19 % (24838)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.90/1.19 % (24838)Termination reason: Unknown
% 3.90/1.19 % (24838)Termination phase: shuffling
% 3.90/1.19
% 3.90/1.19 % (24838)Memory used [KB]: 12153
% 3.90/1.19 % (24838)Time elapsed: 0.082 s
% 3.90/1.19 % (24838)Instructions burned: 101 (million)
% 3.90/1.19 % (24838)------------------------------
% 3.90/1.19 % (24838)------------------------------
% 3.90/1.20 % (24845)Instruction limit reached!
% 3.90/1.20 % (24845)------------------------------
% 3.90/1.20 % (24845)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.90/1.20 % (24845)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.90/1.20 % (24845)Termination reason: Unknown
% 3.90/1.20 % (24845)Termination phase: Preprocessing 1
% 3.90/1.20
% 3.90/1.20 % (24845)Memory used [KB]: 8571
% 3.90/1.20 % (24845)Time elapsed: 0.085 s
% 3.90/1.20 % (24845)Instructions burned: 101 (million)
% 3.90/1.20 % (24845)------------------------------
% 3.90/1.20 % (24845)------------------------------
% 3.90/1.20 % (24893)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/68Mi)
% 3.90/1.20 % (24888)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/90Mi)
% 4.15/1.22 % (24847)Instruction limit reached!
% 4.15/1.22 % (24847)------------------------------
% 4.15/1.22 % (24847)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 4.15/1.22 % (24847)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 4.15/1.22 % (24847)Termination reason: Unknown
% 4.15/1.22 % (24847)Termination phase: Preprocessing 3
% 4.15/1.22
% 4.15/1.22 % (24847)Memory used [KB]: 14711
% 4.15/1.22 % (24847)Time elapsed: 0.161 s
% 4.15/1.22 % (24847)Instructions burned: 138 (million)
% 4.15/1.22 % (24847)------------------------------
% 4.15/1.22 % (24847)------------------------------
% 4.15/1.23 % (24889)ott+1_1:2_i=920:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/920Mi)
% 4.31/1.24 % (24899)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=4958:si=on:rawr=on:rtra=on_0 on theBenchmark for (2992ds/4958Mi)
% 4.31/1.24 WARNING Broken Constraint: if sine_depth(2) has been set then sine_selection(off) is not equal to off
% 4.31/1.24 % (24895)ott+11_4:1_br=off:fde=none:s2a=on:sd=2:sp=frequency:urr=on:i=981:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/981Mi)
% 4.31/1.26 % (24894)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=940:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/940Mi)
% 4.31/1.27 % (24896)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/90Mi)
% 4.31/1.27 % (24890)ott+1_1:7_bd=off:i=934:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/934Mi)
% 4.31/1.30 % (24853)Instruction limit reached!
% 4.31/1.30 % (24853)------------------------------
% 4.31/1.30 % (24853)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 4.31/1.30 % (24853)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 4.31/1.30 % (24853)Termination reason: Unknown
% 4.31/1.30 % (24853)Termination phase: Preprocessing 3
% 4.31/1.30
% 4.31/1.30 % (24853)Memory used [KB]: 15991
% 4.31/1.30 % (24853)Time elapsed: 0.141 s
% 4.31/1.30 % (24853)Instructions burned: 177 (million)
% 4.31/1.30 % (24853)------------------------------
% 4.31/1.30 % (24853)------------------------------
% 4.31/1.30 % (24892)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=655:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/655Mi)
% 4.31/1.32 % (24898)dis+10_1:2_atotf=0.3:i=3735:si=on:rawr=on:rtra=on_0 on theBenchmark for (2992ds/3735Mi)
% 4.80/1.34 % (24893)Instruction limit reached!
% 4.80/1.34 % (24893)------------------------------
% 4.80/1.34 % (24893)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 4.80/1.34 % (24893)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 4.80/1.34 % (24893)Termination reason: Unknown
% 4.80/1.34 % (24893)Termination phase: Preprocessing 1
% 4.80/1.34
% 4.80/1.34 % (24893)Memory used [KB]: 10746
% 4.80/1.34 % (24893)Time elapsed: 0.054 s
% 4.80/1.34 % (24893)Instructions burned: 69 (million)
% 4.80/1.34 % (24893)------------------------------
% 4.80/1.34 % (24893)------------------------------
% 5.14/1.40 % (24846)Instruction limit reached!
% 5.14/1.40 % (24846)------------------------------
% 5.14/1.40 % (24846)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 5.14/1.40 % (24846)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 5.14/1.40 % (24846)Termination reason: Unknown
% 5.14/1.40 % (24846)Termination phase: Unused predicate definition removal
% 5.14/1.40
% 5.14/1.40 % (24846)Memory used [KB]: 12665
% 5.14/1.40 % (24846)Time elapsed: 0.142 s
% 5.14/1.40 % (24846)Instructions burned: 178 (million)
% 5.14/1.40 % (24846)------------------------------
% 5.14/1.40 % (24846)------------------------------
% 5.14/1.42 % (24901)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=4959:si=on:rawr=on:rtra=on_0 on theBenchmark for (2992ds/4959Mi)
% 5.14/1.43 % (24897)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=2016:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/2016Mi)
% 5.14/1.44 % (24914)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=2134:si=on:rawr=on:rtra=on_0 on theBenchmark for (2991ds/2134Mi)
% 5.14/1.46 % (24888)Instruction limit reached!
% 5.14/1.46 % (24888)------------------------------
% 5.14/1.46 % (24888)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 5.14/1.46 % (24888)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 5.14/1.46 % (24888)Termination reason: Unknown
% 5.14/1.46 % (24888)Termination phase: Preprocessing 1
% 5.14/1.46
% 5.14/1.46 % (24888)Memory used [KB]: 10362
% 5.14/1.46 % (24888)Time elapsed: 0.080 s
% 5.14/1.46 % (24888)Instructions burned: 91 (million)
% 5.14/1.46 % (24888)------------------------------
% 5.14/1.46 % (24888)------------------------------
% 5.56/1.48 % (24921)ott-1_1:1_sp=const_frequency:i=2891:si=on:rawr=on:rtra=on_0 on theBenchmark for (2991ds/2891Mi)
% 5.56/1.49 % (24906)ott+3_1:1_atotf=0.2:fsr=off:kws=precedence:sp=weighted_frequency:spb=intro:tgt=ground:i=4931:si=on:rawr=on:rtra=on_0 on theBenchmark for (2991ds/4931Mi)
% 5.72/1.52 % (24902)ott+10_1:1_kws=precedence:tgt=ground:i=4756:si=on:rawr=on:rtra=on_0 on theBenchmark for (2992ds/4756Mi)
% 5.72/1.53 % (24966)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2990ds/90Mi)
% 5.84/1.53 % (24908)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2991ds/68Mi)
% 5.84/1.54 % (24968)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=2016:si=on:rawr=on:rtra=on_0 on theBenchmark for (2989ds/2016Mi)
% 5.84/1.54 % (24912)ott+11_9:8_amm=off:bsd=on:etr=on:fsd=on:fsr=off:lma=on:newcnf=on:nm=0:nwc=3.0:s2a=on:s2agt=10:sas=z3:tha=some:i=1824:si=on:rawr=on:rtra=on_0 on theBenchmark for (2991ds/1824Mi)
% 6.30/1.64 % (24896)Instruction limit reached!
% 6.30/1.64 % (24896)------------------------------
% 6.30/1.64 % (24896)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.30/1.64 % (24896)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.30/1.64 % (24896)Termination reason: Unknown
% 6.30/1.64 % (24896)Termination phase: Preprocessing 1
% 6.30/1.64
% 6.30/1.64 % (24896)Memory used [KB]: 10362
% 6.30/1.64 % (24896)Time elapsed: 0.076 s
% 6.30/1.64 % (24896)Instructions burned: 91 (million)
% 6.30/1.64 % (24896)------------------------------
% 6.30/1.64 % (24896)------------------------------
% 6.30/1.68 % (24952)dis+2_1:64_add=large:bce=on:bd=off:i=4585:si=on:rawr=on:rtra=on_0 on theBenchmark for (2990ds/4585Mi)
% 6.30/1.72 % (24966)Instruction limit reached!
% 6.30/1.72 % (24966)------------------------------
% 6.30/1.72 % (24966)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.30/1.72 % (24966)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.30/1.72 % (24966)Termination reason: Unknown
% 6.30/1.72 % (24966)Termination phase: Preprocessing 1
% 6.30/1.72
% 6.30/1.72 % (24966)Memory used [KB]: 10362
% 6.30/1.72 % (24966)Time elapsed: 0.076 s
% 6.30/1.72 % (24966)Instructions burned: 91 (million)
% 6.30/1.72 % (24966)------------------------------
% 6.30/1.72 % (24966)------------------------------
% 8.21/1.73 % (24855)Instruction limit reached!
% 8.21/1.73 % (24855)------------------------------
% 8.21/1.73 % (24855)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 8.21/1.73 % (24855)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 8.21/1.73 % (24855)Termination reason: Unknown
% 8.21/1.73 % (24855)Termination phase: Property scanning
% 8.21/1.73
% 8.21/1.73 % (24855)Memory used [KB]: 22003
% 8.21/1.73 % (24855)Time elapsed: 0.266 s
% 8.21/1.73 % (24855)Instructions burned: 356 (million)
% 8.21/1.73 % (24855)------------------------------
% 8.21/1.73 % (24855)------------------------------
% 8.21/1.75 % (24856)Instruction limit reached!
% 8.21/1.75 % (24856)------------------------------
% 8.21/1.75 % (24856)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 8.21/1.75 % (24856)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 8.21/1.75 % (24856)Termination reason: Unknown
% 8.21/1.75 % (24856)Termination phase: Property scanning
% 8.21/1.75
% 8.21/1.75 % (24856)Memory used [KB]: 22003
% 8.21/1.75 % (24856)Time elapsed: 0.278 s
% 8.21/1.75 % (24856)Instructions burned: 389 (million)
% 8.21/1.75 % (24856)------------------------------
% 8.21/1.75 % (24856)------------------------------
% 8.21/1.75 % (24857)Instruction limit reached!
% 8.21/1.75 % (24857)------------------------------
% 8.21/1.75 % (24857)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 8.21/1.75 % (24857)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 8.21/1.75 % (24857)Termination reason: Unknown
% 8.21/1.75 % (24857)Termination phase: Preprocessing 3
% 8.21/1.75
% 8.21/1.75 % (24857)Memory used [KB]: 17142
% 8.21/1.75 % (24857)Time elapsed: 0.168 s
% 8.21/1.75 % (24857)Instructions burned: 212 (million)
% 8.21/1.75 % (24857)------------------------------
% 8.21/1.75 % (24857)------------------------------
% 8.21/1.78 % (24973)dis+10_1:2_atotf=0.3:i=8004:si=on:rawr=on:rtra=on_0 on theBenchmark for (2988ds/8004Mi)
% 8.21/1.79 % (24908)Instruction limit reached!
% 8.21/1.79 % (24908)------------------------------
% 8.21/1.79 % (24908)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 8.21/1.79 % (24908)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 8.21/1.79 % (24908)Termination reason: Unknown
% 8.21/1.79 % (24908)Termination phase: Preprocessing 1
% 8.21/1.79
% 8.21/1.79 % (24908)Memory used [KB]: 10874
% 8.21/1.79 % (24908)Time elapsed: 0.045 s
% 8.21/1.79 % (24908)Instructions burned: 69 (million)
% 8.21/1.79 % (24908)------------------------------
% 8.21/1.79 % (24908)------------------------------
% 8.88/1.85 % (24854)Instruction limit reached!
% 8.88/1.85 % (24854)------------------------------
% 8.88/1.85 % (24854)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 8.88/1.85 % (24854)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 8.88/1.85 % (24854)Termination reason: Unknown
% 8.88/1.85 % (24854)Termination phase: Property scanning
% 8.88/1.85
% 8.88/1.85 % (24854)Memory used [KB]: 22003
% 8.88/1.85 % (24854)Time elapsed: 0.309 s
% 8.88/1.85 % (24854)Instructions burned: 439 (million)
% 8.88/1.85 % (24854)------------------------------
% 8.88/1.85 % (24854)------------------------------
% 8.88/1.86 % (24895)Instruction limit reached!
% 8.88/1.86 % (24895)------------------------------
% 8.88/1.86 % (24895)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 8.88/1.86 % (24895)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 8.88/1.86 % (24895)Termination reason: Unknown
% 8.88/1.86 % (24895)Termination phase: Saturation
% 8.88/1.86
% 8.88/1.86 % (24895)Memory used [KB]: 31342
% 8.88/1.86 % (24895)Time elapsed: 0.593 s
% 8.88/1.86 % (24895)Instructions burned: 981 (million)
% 8.88/1.86 % (24895)------------------------------
% 8.88/1.86 % (24895)------------------------------
% 8.88/1.90 % (24989)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=9877:si=on:rawr=on:rtra=on_0 on theBenchmark for (2986ds/9877Mi)
% 9.56/1.91 % (24990)ins+10_1:16_bce=on:fde=unused:igpr=on:igs=35:igwr=on:sp=const_frequency:tgt=full:to=lpo:i=9902:si=on:rawr=on:rtra=on_0 on theBenchmark for (2986ds/9902Mi)
% 9.56/1.93 % (24849)Instruction limit reached!
% 9.56/1.93 % (24849)------------------------------
% 9.56/1.93 % (24849)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 9.56/1.93 % (24849)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 9.56/1.93 % (24849)Termination reason: Unknown
% 9.56/1.93 % (24849)Termination phase: Property scanning
% 9.56/1.93
% 9.56/1.93 % (24849)Memory used [KB]: 22003
% 9.56/1.93 % (24849)Time elapsed: 0.321 s
% 9.56/1.93 % (24849)Instructions burned: 467 (million)
% 9.56/1.93 % (24849)------------------------------
% 9.56/1.93 % (24849)------------------------------
% 9.56/1.93 % (24993)ott+11_9:8_amm=off:bsd=on:etr=on:fsd=on:fsr=off:lma=on:newcnf=on:nm=0:nwc=3.0:s2a=on:s2agt=10:sas=z3:tha=some:i=1824:si=on:rawr=on:rtra=on_0 on theBenchmark for (2986ds/1824Mi)
% 9.56/1.97 % (24985)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=9965:si=on:rawr=on:rtra=on_0 on theBenchmark for (2986ds/9965Mi)
% 9.98/2.00 % (24994)dis+2_1:64_add=large:bce=on:bd=off:i=9989:si=on:rawr=on:rtra=on_0 on theBenchmark for (2986ds/9989Mi)
% 9.98/2.04 % (24998)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2985ds/90Mi)
% 9.98/2.07 % (24999)ott+3_1:1_abs=on:anc=none:bs=on:fsr=off:spb=goal_then_units:i=44001:si=on:rawr=on:rtra=on_0 on theBenchmark for (2984ds/44001Mi)
% 10.40/2.10 % (24851)Instruction limit reached!
% 10.40/2.10 % (24851)------------------------------
% 10.40/2.10 % (24851)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 10.40/2.10 % (24851)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 10.40/2.10 % (24851)Termination reason: Unknown
% 10.40/2.10 % (24851)Termination phase: Equality resolution with deletion
% 10.40/2.10
% 10.40/2.10 % (24851)Memory used [KB]: 22387
% 10.40/2.10 % (24851)Time elapsed: 0.343 s
% 10.40/2.10 % (24851)Instructions burned: 500 (million)
% 10.40/2.10 % (24851)------------------------------
% 10.40/2.10 % (24851)------------------------------
% 10.40/2.12 % (24996)ott-11_1:32_i=9707:si=on:rawr=on:rtra=on_0 on theBenchmark for (2985ds/9707Mi)
% 10.40/2.13 % (25004)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=4958:si=on:rawr=on:rtra=on_0 on theBenchmark for (2984ds/4958Mi)
% 10.94/2.23 % (24998)Instruction limit reached!
% 10.94/2.23 % (24998)------------------------------
% 10.94/2.23 % (24998)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 10.94/2.24 % (24850)Instruction limit reached!
% 10.94/2.24 % (24850)------------------------------
% 10.94/2.24 % (24850)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 10.94/2.24 % (24850)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 10.94/2.24 % (24998)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 10.94/2.24 % (24998)Termination reason: Unknown
% 10.94/2.24 % (24998)Termination phase: Preprocessing 1
% 10.94/2.24
% 10.94/2.24 % (24998)Memory used [KB]: 10362
% 10.94/2.24 % (24998)Time elapsed: 0.070 s
% 10.94/2.24 % (24998)Instructions burned: 90 (million)
% 10.94/2.24 % (24998)------------------------------
% 10.94/2.24 % (24998)------------------------------
% 10.94/2.24 % (24850)Termination reason: Unknown
% 10.94/2.24 % (24850)Termination phase: Function definition elimination
% 10.94/2.24
% 10.94/2.24 % (24850)Memory used [KB]: 22259
% 10.94/2.24 % (24850)Time elapsed: 0.308 s
% 10.94/2.24 % (24850)Instructions burned: 482 (million)
% 10.94/2.24 % (24850)------------------------------
% 10.94/2.24 % (24850)------------------------------
% 10.94/2.29 % (25013)ott+1_27:428_av=off:awrs=converge:awrsf=8:bsr=unit_only:drc=off:fd=preordered:newcnf=on:nwc=1.5:skr=on:slsq=on:slsqc=2:slsql=off:slsqr=1,4:sp=reverse_frequency:uwa=one_side_constant:i=35256:si=on:rawr=on:rtra=on_0 on theBenchmark for (2982ds/35256Mi)
% 10.94/2.29 % (24848)Instruction limit reached!
% 10.94/2.29 % (24848)------------------------------
% 10.94/2.29 % (24848)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 10.94/2.29 % (24848)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 10.94/2.29 % (24848)Termination reason: Unknown
% 10.94/2.29 % (24848)Termination phase: Function definition elimination
% 10.94/2.29
% 10.94/2.29 % (24848)Memory used [KB]: 22131
% 10.94/2.29 % (24848)Time elapsed: 0.335 s
% 10.94/2.29 % (24848)Instructions burned: 499 (million)
% 10.94/2.29 % (24848)------------------------------
% 10.94/2.29 % (24848)------------------------------
% 11.56/2.38 % (24891)Instruction limit reached!
% 11.56/2.38 % (24891)------------------------------
% 11.56/2.38 % (24891)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 11.56/2.38 % (24891)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 11.56/2.38 % (24891)Termination reason: Unknown
% 11.56/2.38 % (24891)Termination phase: Saturation
% 11.56/2.38
% 11.56/2.38 % (24891)Memory used [KB]: 28144
% 11.56/2.38 % (24891)Time elapsed: 0.439 s
% 11.56/2.38 % (24891)Instructions burned: 747 (million)
% 11.56/2.38 % (24891)------------------------------
% 11.56/2.38 % (24891)------------------------------
% 11.56/2.39 % (25030)dis+1002_1:1_fde=unused:nwc=10.0:s2a=on:s2at=3.0:sac=on:i=32293:si=on:rawr=on:rtra=on_0 on theBenchmark for (2981ds/32293Mi)
% 11.56/2.39 % (25032)ott+21_1:28_afr=on:anc=all_dependent:bs=on:bsr=unit_only:nicw=on:sp=const_frequency:uhcvi=on:i=37001:si=on:rawr=on:rtra=on_0 on theBenchmark for (2981ds/37001Mi)
% 13.33/2.43 % (25057)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=10187:si=on:rawr=on:rtra=on_0 on theBenchmark for (2980ds/10187Mi)
% 14.17/2.55 % (25094)ott+3_1:1_atotf=0.2:fsr=off:kws=precedence:sp=weighted_frequency:spb=intro:tgt=ground:i=29337:si=on:rawr=on:rtra=on_0 on theBenchmark for (2979ds/29337Mi)
% 15.68/2.73 % (24892)Instruction limit reached!
% 15.68/2.73 % (24892)------------------------------
% 15.68/2.73 % (24892)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 15.68/2.73 % (24892)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 15.68/2.73 % (24892)Termination reason: Unknown
% 15.68/2.73 % (24892)Termination phase: Property scanning
% 15.68/2.73
% 15.68/2.73 % (24892)Memory used [KB]: 22771
% 15.68/2.73 % (24892)Time elapsed: 0.370 s
% 15.68/2.73 % (24892)Instructions burned: 656 (million)
% 15.68/2.73 % (24892)------------------------------
% 15.68/2.73 % (24892)------------------------------
% 16.58/2.89 % (25222)ins+10_1:16_bce=on:fde=unused:igpr=on:igs=35:igwr=on:sp=const_frequency:tgt=full:to=lpo:i=10147:si=on:rawr=on:rtra=on_0 on theBenchmark for (2976ds/10147Mi)
% 17.31/2.94 % (24894)Instruction limit reached!
% 17.31/2.94 % (24894)------------------------------
% 17.31/2.94 % (24894)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 17.31/2.94 % (24894)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 17.31/2.94 % (24894)Termination reason: Unknown
% 17.31/2.94 % (24894)Termination phase: Saturation
% 17.31/2.94
% 17.31/2.94 % (24894)Memory used [KB]: 29040
% 17.31/2.94 % (24894)Time elapsed: 1.856 s
% 17.31/2.94 % (24894)Instructions burned: 941 (million)
% 17.31/2.94 % (24894)------------------------------
% 17.31/2.94 % (24894)------------------------------
% 18.04/3.03 % (24889)Instruction limit reached!
% 18.04/3.03 % (24889)------------------------------
% 18.04/3.03 % (24889)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 18.04/3.03 % (24889)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 18.04/3.03 % (24889)Termination reason: Unknown
% 18.04/3.03 % (24889)Termination phase: Saturation
% 18.04/3.03
% 18.04/3.03 % (24889)Memory used [KB]: 30958
% 18.04/3.03 % (24889)Time elapsed: 0.480 s
% 18.04/3.03 % (24889)Instructions burned: 920 (million)
% 18.04/3.03 % (24889)------------------------------
% 18.04/3.03 % (24889)------------------------------
% 18.04/3.06 % (24890)Instruction limit reached!
% 18.04/3.06 % (24890)------------------------------
% 18.04/3.06 % (24890)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 18.04/3.06 % (24890)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 18.04/3.06 % (24890)Termination reason: Unknown
% 18.04/3.06 % (24890)Termination phase: Saturation
% 18.04/3.06
% 18.04/3.06 % (24890)Memory used [KB]: 29295
% 18.04/3.06 % (24890)Time elapsed: 0.454 s
% 18.04/3.06 % (24890)Instructions burned: 935 (million)
% 18.04/3.06 % (24890)------------------------------
% 18.04/3.06 % (24890)------------------------------
% 18.04/3.10 % (25248)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=38056:si=on:rawr=on:rtra=on_0 on theBenchmark for (2974ds/38056Mi)
% 19.02/3.13 % (25249)fmb+10_1:1_dr=on:fmbsr=2.0:newcnf=on:nm=2:i=33239:si=on:rawr=on:rtra=on_0 on theBenchmark for (2973ds/33239Mi)
% 19.78/3.22 % (25250)fmb+10_1:1_fmbas=predicate:gsp=on:nm=2:i=20987:si=on:rawr=on:rtra=on_0 on theBenchmark for (2972ds/20987Mi)
% 25.95/4.03 % (24968)Instruction limit reached!
% 25.95/4.03 % (24968)------------------------------
% 25.95/4.03 % (24968)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 25.95/4.03 % (24968)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 25.95/4.03 % (24968)Termination reason: Unknown
% 25.95/4.03 % (24968)Termination phase: Saturation
% 25.95/4.03
% 25.95/4.03 % (24968)Memory used [KB]: 28016
% 25.95/4.03 % (24968)Time elapsed: 2.504 s
% 25.95/4.03 % (24968)Instructions burned: 2018 (million)
% 25.95/4.03 % (24968)------------------------------
% 25.95/4.03 % (24968)------------------------------
% 26.99/4.19 % (25251)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=49917:si=on:rawr=on:rtra=on_0 on theBenchmark for (2963ds/49917Mi)
% 29.19/4.47 % (24897)Instruction limit reached!
% 29.19/4.47 % (24897)------------------------------
% 29.19/4.47 % (24897)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 29.19/4.47 % (24897)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 29.19/4.47 % (24897)Termination reason: Unknown
% 29.19/4.47 % (24897)Termination phase: Saturation
% 29.19/4.47
% 29.19/4.47 % (24897)Memory used [KB]: 30958
% 29.19/4.47 % (24897)Time elapsed: 3.330 s
% 29.19/4.47 % (24897)Instructions burned: 2016 (million)
% 29.19/4.47 % (24897)------------------------------
% 29.19/4.47 % (24897)------------------------------
% 30.17/4.51 % (24912)Instruction limit reached!
% 30.17/4.51 % (24912)------------------------------
% 30.17/4.51 % (24912)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 30.20/4.52 % (24912)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 30.20/4.52 % (24912)Termination reason: Unknown
% 30.20/4.52 % (24912)Termination phase: Saturation
% 30.20/4.52
% 30.20/4.52 % (24912)Memory used [KB]: 29295
% 30.20/4.52 % (24912)Time elapsed: 1.009 s
% 30.20/4.52 % (24912)Instructions burned: 1826 (million)
% 30.20/4.52 % (24912)------------------------------
% 30.20/4.52 % (24912)------------------------------
% 30.86/4.61 % (25252)dis+2_1:64_add=large:bce=on:bd=off:i=19144:si=on:rawr=on:rtra=on_0 on theBenchmark for (2958ds/19144Mi)
% 30.86/4.65 % (25253)dis+10_1:128_bd=off:lcm=predicate:sac=on:sp=reverse_arity:urr=on:i=27492:si=on:rawr=on:rtra=on_0 on theBenchmark for (2958ds/27492Mi)
% 31.48/4.71 % (24993)Instruction limit reached!
% 31.48/4.71 % (24993)------------------------------
% 31.48/4.71 % (24993)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 31.48/4.71 % (24993)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 31.48/4.71 % (24993)Termination reason: Unknown
% 31.48/4.71 % (24993)Termination phase: Saturation
% 31.48/4.71
% 31.48/4.71 % (24993)Memory used [KB]: 28656
% 31.48/4.71 % (24993)Time elapsed: 0.938 s
% 31.48/4.71 % (24993)Instructions burned: 1824 (million)
% 31.48/4.71 % (24993)------------------------------
% 31.48/4.71 % (24993)------------------------------
% 32.43/4.86 % (25254)ott-11_1:32_i=6101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2956ds/6101Mi)
% 34.05/5.00 % (24914)Instruction limit reached!
% 34.05/5.00 % (24914)------------------------------
% 34.05/5.00 % (24914)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 34.05/5.00 % (24914)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 34.05/5.00 % (24914)Termination reason: Unknown
% 34.05/5.00 % (24914)Termination phase: Saturation
% 34.05/5.00
% 34.05/5.00 % (24914)Memory used [KB]: 47078
% 34.05/5.00 % (24914)Time elapsed: 3.723 s
% 34.05/5.00 % (24914)Instructions burned: 2134 (million)
% 34.05/5.00 % (24914)------------------------------
% 34.05/5.00 % (24914)------------------------------
% 34.91/5.16 % (25255)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2953ds/90Mi)
% 36.34/5.34 % (25255)Instruction limit reached!
% 36.34/5.34 % (25255)------------------------------
% 36.34/5.34 % (25255)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 36.34/5.35 % (25255)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 36.34/5.35 % (25255)Termination reason: Unknown
% 36.34/5.35 % (25255)Termination phase: Preprocessing 1
% 36.34/5.35
% 36.34/5.35 % (25255)Memory used [KB]: 10362
% 36.34/5.35 % (25255)Time elapsed: 0.056 s
% 36.34/5.35 % (25255)Instructions burned: 91 (million)
% 36.34/5.35 % (25255)------------------------------
% 36.34/5.35 % (25255)------------------------------
% 38.03/5.51 % (25256)ott+11_1:128_av=off:bd=off:bsr=unit_only:fd=preordered:to=lpo:updr=off:i=91600:si=on:rawr=on:rtra=on_0 on theBenchmark for (2949ds/91600Mi)
% 44.37/6.36 % (24921)Instruction limit reached!
% 44.37/6.36 % (24921)------------------------------
% 44.37/6.36 % (24921)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 44.37/6.38 % (24921)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 44.37/6.38 % (24921)Termination reason: Unknown
% 44.37/6.38 % (24921)Termination phase: Saturation
% 44.37/6.38
% 44.37/6.38 % (24921)Memory used [KB]: 43240
% 44.37/6.38 % (24921)Time elapsed: 4.952 s
% 44.37/6.38 % (24921)Instructions burned: 2891 (million)
% 44.37/6.38 % (24921)------------------------------
% 44.37/6.38 % (24921)------------------------------
% 46.01/6.52 % (25257)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=7127:si=on:rawr=on:rtra=on_0 on theBenchmark for (2939ds/7127Mi)
% 53.26/7.48 % (24898)Instruction limit reached!
% 53.26/7.48 % (24898)------------------------------
% 53.26/7.48 % (24898)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 53.26/7.48 % (24898)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 53.26/7.48 % (24898)Termination reason: Unknown
% 53.26/7.48 % (24898)Termination phase: Saturation
% 53.26/7.48
% 53.26/7.48 % (24898)Memory used [KB]: 62301
% 53.26/7.48 % (24898)Time elapsed: 6.215 s
% 53.26/7.48 % (24898)Instructions burned: 3735 (million)
% 53.26/7.48 % (24898)------------------------------
% 53.26/7.48 % (24898)------------------------------
% 54.67/7.63 % (25258)ott+1_27:428_av=off:awrs=converge:awrsf=8:bsr=unit_only:drc=off:fd=preordered:newcnf=on:nwc=1.5:skr=on:slsq=on:slsqc=2:slsql=off:slsqr=1,4:sp=reverse_frequency:uwa=one_side_constant:i=35256:si=on:rawr=on:rtra=on_0 on theBenchmark for (2928ds/35256Mi)
% 64.48/8.83 % (24899)Instruction limit reached!
% 64.48/8.83 % (24899)------------------------------
% 64.48/8.83 % (24899)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 64.48/8.84 % (24899)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 64.48/8.84 % (24899)Termination reason: Unknown
% 64.48/8.84 % (24899)Termination phase: Saturation
% 64.48/8.84
% 64.48/8.84 % (24899)Memory used [KB]: 38890
% 64.48/8.84 % (24899)Time elapsed: 2.818 s
% 64.48/8.84 % (24899)Instructions burned: 4959 (million)
% 64.48/8.84 % (24899)------------------------------
% 64.48/8.84 % (24899)------------------------------
% 65.19/8.95 % (25259)dis+1002_1:1_fde=unused:nwc=10.0:s2a=on:s2at=3.0:sac=on:i=32293:si=on:rawr=on:rtra=on_0 on theBenchmark for (2915ds/32293Mi)
% 66.81/9.13 % (24952)Instruction limit reached!
% 66.81/9.13 % (24952)------------------------------
% 66.81/9.13 % (24952)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 66.81/9.13 % (24952)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 66.81/9.13 % (24952)Termination reason: Unknown
% 66.81/9.13 % (24952)Termination phase: Saturation
% 66.81/9.13
% 66.81/9.13 % (24952)Memory used [KB]: 49380
% 66.81/9.13 % (24952)Time elapsed: 7.765 s
% 66.81/9.13 % (24952)Instructions burned: 4585 (million)
% 66.81/9.13 % (24952)------------------------------
% 66.81/9.13 % (24952)------------------------------
% 67.55/9.26 % (25260)ott+3_1:1_atotf=0.2:fsr=off:kws=precedence:sp=weighted_frequency:spb=intro:tgt=ground:i=29337:si=on:rawr=on:rtra=on_0 on theBenchmark for (2912ds/29337Mi)
% 73.84/10.02 % (24902)Instruction limit reached!
% 73.84/10.02 % (24902)------------------------------
% 73.84/10.02 % (24902)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 73.84/10.02 % (24902)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 73.84/10.02 % (24902)Termination reason: Unknown
% 73.84/10.02 % (24902)Termination phase: Saturation
% 73.84/10.02
% 73.84/10.02 % (24902)Memory used [KB]: 55137
% 73.84/10.02 % (24902)Time elapsed: 6.256 s
% 73.84/10.02 % (24902)Instructions burned: 4756 (million)
% 73.84/10.02 % (24902)------------------------------
% 73.84/10.02 % (24902)------------------------------
% 74.69/10.15 % (25261)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=99860:si=on:rawr=on:rtra=on_0 on theBenchmark for (2903ds/99860Mi)
% 76.19/10.36 % (25004)Instruction limit reached!
% 76.19/10.36 % (25004)------------------------------
% 76.19/10.36 % (25004)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 76.19/10.37 % (25004)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 76.19/10.37 % (25004)Termination reason: Unknown
% 76.19/10.37 % (25004)Termination phase: Saturation
% 76.19/10.37
% 76.19/10.37 % (25004)Memory used [KB]: 39146
% 76.19/10.37 % (25004)Time elapsed: 2.445 s
% 76.19/10.37 % (25004)Instructions burned: 4959 (million)
% 76.19/10.37 % (25004)------------------------------
% 76.19/10.37 % (25004)------------------------------
% 77.12/10.47 % (24901)Instruction limit reached!
% 77.12/10.47 % (24901)------------------------------
% 77.12/10.47 % (24901)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 77.12/10.49 % (24901)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 77.12/10.49 % (24901)Termination reason: Unknown
% 77.12/10.49 % (24901)Termination phase: Saturation
% 77.12/10.49
% 77.12/10.49 % (24901)Memory used [KB]: 80467
% 77.12/10.49 % (24901)Time elapsed: 9.283 s
% 77.12/10.49 % (24901)Instructions burned: 4960 (million)
% 77.12/10.49 % (24901)------------------------------
% 77.12/10.49 % (24901)------------------------------
% 77.91/10.53 % (25262)fmb+10_1:1_fmbas=expand:i=96985:si=on:rawr=on:rtra=on_0 on theBenchmark for (2899ds/96985Mi)
% 78.64/10.65 % (25263)fmb+10_1:1_bce=on:dr=on:fmbsr=1.47:gsp=on:nm=2:skr=on:i=99648:si=on:rawr=on:rtra=on_0 on theBenchmark for (2898ds/99648Mi)
% 82.74/11.12 % (24906)Instruction limit reached!
% 82.74/11.12 % (24906)------------------------------
% 82.74/11.12 % (24906)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 82.74/11.14 % (24906)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 82.74/11.14 % (24906)Termination reason: Unknown
% 82.74/11.14 % (24906)Termination phase: Saturation
% 82.74/11.14
% 82.74/11.14 % (24906)Memory used [KB]: 93004
% 82.74/11.14 % (24906)Time elapsed: 9.876 s
% 82.74/11.14 % (24906)Instructions burned: 4932 (million)
% 82.74/11.14 % (24906)------------------------------
% 82.74/11.14 % (24906)------------------------------
% 83.52/11.27 % (25264)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=99882:si=on:rawr=on:rtra=on_0 on theBenchmark for (2892ds/99882Mi)
% 83.52/11.28 % (24985)First to succeed.
% 85.10/11.42 % (24985)Refutation found. Thanks to Tanya!
% 85.10/11.42 % SZS status Theorem for theBenchmark
% 85.10/11.42 % SZS output start Proof for theBenchmark
% See solution above
% 85.10/11.46 % (24985)------------------------------
% 85.10/11.46 % (24985)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 85.10/11.46 % (24985)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 85.10/11.46 % (24985)Termination reason: Refutation
% 85.10/11.46
% 85.10/11.46 % (24985)Memory used [KB]: 40681
% 85.10/11.46 % (24985)Time elapsed: 9.514 s
% 85.10/11.46 % (24985)Instructions burned: 5965 (million)
% 85.10/11.46 % (24985)------------------------------
% 85.10/11.46 % (24985)------------------------------
% 85.10/11.46 % (24823)Success in time 11.072 s
%------------------------------------------------------------------------------