TSTP Solution File: SWW317+1 by Vampire-SAT---4.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.9
% Problem : SWW317+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d SAT
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:50:29 EDT 2024
% Result : Theorem 5.72s 1.50s
% Output : Refutation 5.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1512
% Syntax : Number of formulae : 4097 (2071 unt; 0 def)
% Number of atoms : 7983 (2084 equ)
% Maximal formula atoms : 12 ( 1 avg)
% Number of connectives : 5998 (2112 ~;1823 |; 737 &)
% ( 971 <=>; 355 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 945 ( 943 usr; 778 prp; 0-6 aty)
% Number of functors : 211 ( 211 usr; 38 con; 0-5 aty)
% Number of variables : 4957 (4790 !; 167 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33153,plain,
$false,
inference(avatar_sat_refutation,[],[f28812,f28817,f28822,f28827,f28832,f28837,f28842,f28847,f28852,f28857,f28862,f28867,f28872,f28877,f28882,f28887,f28892,f28897,f28902,f28907,f28912,f28917,f28922,f28927,f28932,f28937,f28942,f28947,f28952,f28957,f28962,f28967,f28972,f28977,f28982,f28987,f28992,f28997,f29002,f29007,f29012,f29017,f29022,f29027,f29032,f29037,f29042,f29047,f29052,f29057,f29062,f29067,f29072,f29077,f29082,f29087,f29092,f29097,f29102,f29107,f29112,f29117,f29122,f29127,f29132,f29137,f29142,f29147,f29152,f29157,f29162,f29167,f29172,f29177,f29182,f29187,f29192,f29197,f29202,f29207,f29212,f29217,f29222,f29227,f29232,f29237,f29242,f29247,f29252,f29257,f29262,f29267,f29272,f29277,f29282,f29287,f29292,f29297,f29302,f29307,f29312,f29317,f29322,f29327,f29332,f29337,f29342,f29347,f29352,f29357,f29362,f29367,f29372,f29377,f29382,f29387,f29392,f29397,f29402,f29407,f29412,f29417,f29422,f29427,f29432,f29437,f29442,f29447,f29452,f29457,f29462,f29467,f29472,f29477,f29482,f29487,f29492,f29497,f29502,f29507,f29512,f29517,f29522,f29527,f29532,f29537,f29542,f29547,f29552,f29557,f29562,f29567,f29572,f29577,f29582,f29587,f29592,f29597,f29602,f29607,f29612,f29617,f29622,f29627,f29632,f29637,f29642,f29647,f29652,f29657,f29662,f29667,f29672,f29677,f29682,f29687,f29692,f29697,f29702,f29707,f29712,f29717,f29722,f29727,f29732,f29737,f29742,f29747,f29752,f29757,f29762,f29767,f29772,f29777,f29782,f29787,f29792,f29797,f29802,f29807,f29813,f29818,f29823,f29827,f29831,f29835,f29839,f29843,f29847,f29851,f29855,f29859,f29863,f29868,f29872,f29877,f29882,f29887,f29892,f29897,f29901,f29905,f29909,f29913,f29917,f29921,f29926,f29931,f29936,f29941,f29947,f29953,f29958,f29963,f29968,f29973,f29978,f29983,f29989,f29993,f29997,f30001,f30005,f30009,f30013,f30017,f30021,f30025,f30029,f30033,f30037,f30041,f30045,f30049,f30053,f30057,f30062,f30066,f30070,f30074,f30079,f30084,f30089,f30094,f30099,f30104,f30109,f30114,f30118,f30122,f30127,f30132,f30136,f30140,f30144,f30148,f30152,f30156,f30160,f30164,f30168,f30172,f30176,f30180,f30184,f30188,f30192,f30196,f30200,f30204,f30208,f30212,f30216,f30220,f30224,f30228,f30232,f30236,f30240,f30244,f30248,f30252,f30256,f30260,f30264,f30268,f30272,f30276,f30280,f30284,f30288,f30292,f30296,f30300,f30305,f30310,f30315,f30320,f30324,f30328,f30332,f30336,f30340,f30344,f30348,f30352,f30357,f30361,f30365,f30373,f30395,f30406,f30414,f30420,f30426,f30431,f30437,f30442,f30448,f30453,f30458,f30463,f30468,f30473,f30478,f30483,f30488,f30493,f30498,f30503,f30509,f30514,f30519,f30523,f30527,f30531,f30535,f30539,f30543,f30547,f30552,f30556,f30560,f30564,f30568,f30572,f30576,f30580,f30584,f30588,f30592,f30596,f30600,f30605,f30609,f30613,f30617,f30621,f30625,f30629,f30633,f30637,f30641,f30645,f30650,f30654,f30658,f30662,f30666,f30670,f30674,f30678,f30682,f30686,f30692,f30697,f30702,f30707,f30712,f30717,f30722,f30726,f30730,f30737,f30743,f30752,f30758,f30765,f30776,f30781,f30786,f30791,f30795,f30800,f30805,f30810,f30815,f30819,f30823,f30828,f30832,f30836,f30840,f30844,f30848,f30852,f30856,f30860,f30864,f30868,f30873,f30877,f30881,f30885,f30889,f30893,f30897,f30901,f30905,f30909,f30913,f30917,f30921,f30925,f30929,f30933,f30937,f30941,f30945,f30949,f30953,f30957,f30961,f30965,f30969,f30973,f30977,f30981,f30985,f30989,f30993,f30997,f31001,f31005,f31009,f31013,f31017,f31021,f31025,f31029,f31033,f31037,f31041,f31045,f31049,f31053,f31057,f31061,f31065,f31069,f31073,f31077,f31081,f31085,f31090,f31094,f31098,f31102,f31107,f31112,f31117,f31121,f31125,f31129,f31133,f31137,f31141,f31145,f31149,f31153,f31157,f31161,f31165,f31178,f31189,f31204,f31208,f31217,f31222,f31227,f31231,f31235,f31240,f31244,f31248,f31252,f31256,f31260,f31264,f31268,f31272,f31276,f31280,f31284,f31288,f31292,f31296,f31300,f31304,f31309,f31313,f31317,f31321,f31325,f31329,f31333,f31337,f31341,f31345,f31349,f31354,f31358,f31362,f31366,f31370,f31374,f31378,f31382,f31386,f31390,f31394,f31399,f31403,f31407,f31411,f31415,f31419,f31423,f31427,f31431,f31435,f31439,f31444,f31448,f31452,f31456,f31460,f31464,f31468,f31472,f31476,f31480,f31484,f31489,f31493,f31498,f31502,f31506,f31510,f31514,f31518,f31522,f31526,f31530,f31535,f31539,f31543,f31548,f31553,f31557,f31561,f31565,f31569,f31573,f31577,f31582,f31586,f31590,f31594,f31598,f31602,f31607,f31611,f31615,f31619,f31623,f31627,f31631,f31635,f31639,f31643,f31647,f31651,f31655,f31660,f31664,f31668,f31672,f31676,f31893,f31921,f31926,f31931,f31936,f31941,f31945,f31949,f31953,f31957,f31961,f31965,f31969,f31973,f31977,f31981,f31986,f31990,f31994,f31998,f32002,f32006,f32010,f32014,f32018,f32022,f32026,f32031,f32035,f32039,f32043,f32047,f32051,f32055,f32059,f32063,f32067,f32071,f32075,f32079,f32083,f32087,f32091,f32095,f32099,f32103,f32107,f32111,f32115,f32119,f32123,f32127,f32131,f32135,f32139,f32143,f32147,f32151,f32155,f32159,f32163,f32167,f32171,f32175,f32179,f32183,f32187,f32191,f32195,f32199,f32203,f32207,f32211,f32215,f32219,f32223,f32227,f32231,f32235,f32239,f32243,f32247,f32251,f32255,f32259,f32263,f32267,f32271,f32275,f32279,f32283,f32287,f32296,f32300,f32304,f32308,f32312,f32316,f32320,f32324,f32328,f32333,f32339,f32344,f32350,f32356,f32363,f32368,f32374,f32378,f32382,f32387,f32391,f32395,f32399,f32403,f32407,f32411,f32415,f32419,f32423,f32424,f32428,f32432,f32436,f32440,f32444,f32448,f32452,f32456,f32460,f32464,f32469,f32473,f32477,f32481,f32485,f32489,f32493,f32497,f32501,f32505,f32509,f32513,f32517,f32521,f32525,f32530,f32566,f32606,f32992,f33009,f33024,f33034,f33079,f33117,f33143,f33152]) ).
fof(f33152,plain,
( spl625_232
| ~ spl625_764 ),
inference(avatar_contradiction_clause,[],[f33151]) ).
fof(f33151,plain,
( $false
| spl625_232
| ~ spl625_764 ),
inference(resolution,[],[f32516,f29952]) ).
fof(f29952,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)))
| spl625_232 ),
inference(avatar_component_clause,[],[f29950]) ).
fof(f29950,plain,
( spl625_232
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_232])]) ).
fof(f32516,plain,
( ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(X2,X0,c_Com_Ocom_OSKIP,X0)))
| ~ spl625_764 ),
inference(avatar_component_clause,[],[f32515]) ).
fof(f32515,plain,
( spl625_764
<=> ! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(X2,X0,c_Com_Ocom_OSKIP,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_764])]) ).
fof(f33143,plain,
( ~ spl625_777
| ~ spl625_353
| ~ spl625_687 ),
inference(avatar_split_clause,[],[f32863,f32189,f30516,f33140]) ).
fof(f33140,plain,
( spl625_777
<=> sP29(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_777])]) ).
fof(f30516,plain,
( spl625_353
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_353])]) ).
fof(f32189,plain,
( spl625_687
<=> ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP29(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_687])]) ).
fof(f32863,plain,
( ~ sP29(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint))
| ~ spl625_353
| ~ spl625_687 ),
inference(resolution,[],[f32190,f30518]) ).
fof(f30518,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls))
| ~ spl625_353 ),
inference(avatar_component_clause,[],[f30516]) ).
fof(f32190,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP29(X0,X1,X2) )
| ~ spl625_687 ),
inference(avatar_component_clause,[],[f32189]) ).
fof(f33117,plain,
( ~ spl625_776
| ~ spl625_352
| ~ spl625_687 ),
inference(avatar_split_clause,[],[f32862,f32189,f30511,f33114]) ).
fof(f33114,plain,
( spl625_776
<=> sP29(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_776])]) ).
fof(f30511,plain,
( spl625_352
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_352])]) ).
fof(f32862,plain,
( ~ sP29(c_Int_OPls,c_Int_OMin,c_Orderings_Oord__class_Oless(tc_Int_Oint))
| ~ spl625_352
| ~ spl625_687 ),
inference(resolution,[],[f32190,f30513]) ).
fof(f30513,plain,
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls))
| ~ spl625_352 ),
inference(avatar_component_clause,[],[f30511]) ).
fof(f33079,plain,
( spl625_775
| ~ spl625_363
| ~ spl625_687 ),
inference(avatar_split_clause,[],[f32839,f32189,f30558,f33077]) ).
fof(f33077,plain,
( spl625_775
<=> ! [X0] : ~ sP29(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_775])]) ).
fof(f30558,plain,
( spl625_363
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_363])]) ).
fof(f32839,plain,
( ! [X0] : ~ sP29(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat))
| ~ spl625_363
| ~ spl625_687 ),
inference(resolution,[],[f32190,f30559]) ).
fof(f30559,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0))
| ~ spl625_363 ),
inference(avatar_component_clause,[],[f30558]) ).
fof(f33034,plain,
( spl625_774
| ~ spl625_362
| ~ spl625_687 ),
inference(avatar_split_clause,[],[f32838,f32189,f30554,f33032]) ).
fof(f33032,plain,
( spl625_774
<=> ! [X0] : ~ sP29(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_774])]) ).
fof(f30554,plain,
( spl625_362
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_362])]) ).
fof(f32838,plain,
( ! [X0] : ~ sP29(X0,X0,c_Orderings_Oord__class_Oless__eq(tc_Int_Oint))
| ~ spl625_362
| ~ spl625_687 ),
inference(resolution,[],[f32190,f30555]) ).
fof(f30555,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0))
| ~ spl625_362 ),
inference(avatar_component_clause,[],[f30554]) ).
fof(f33024,plain,
( spl625_773
| ~ spl625_515
| ~ spl625_728 ),
inference(avatar_split_clause,[],[f32369,f32365,f31246,f33021]) ).
fof(f33021,plain,
( spl625_773
<=> hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) = c_Option_Oset(tc_Nat_Onat,c_Option_Ooption_ONone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_773])]) ).
fof(f31246,plain,
( spl625_515
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Option_Oset(X0,c_Option_Ooption_ONone(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_515])]) ).
fof(f32365,plain,
( spl625_728
<=> c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_728])]) ).
fof(f32369,plain,
( hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) = c_Option_Oset(tc_Nat_Onat,c_Option_Ooption_ONone(tc_Nat_Onat))
| ~ spl625_515
| ~ spl625_728 ),
inference(forward_demodulation,[],[f32367,f31247]) ).
fof(f31247,plain,
( ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Option_Oset(X0,c_Option_Ooption_ONone(X0))
| ~ spl625_515 ),
inference(avatar_component_clause,[],[f31246]) ).
fof(f32367,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue))
| ~ spl625_728 ),
inference(avatar_component_clause,[],[f32365]) ).
fof(f33009,plain,
( spl625_772
| ~ spl625_361
| ~ spl625_687 ),
inference(avatar_split_clause,[],[f32837,f32189,f30550,f33007]) ).
fof(f33007,plain,
( spl625_772
<=> ! [X0] : ~ sP29(X0,X0,c_Natural_Oevalc(c_Com_Ocom_OSKIP)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_772])]) ).
fof(f30550,plain,
( spl625_361
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_361])]) ).
fof(f32837,plain,
( ! [X0] : ~ sP29(X0,X0,c_Natural_Oevalc(c_Com_Ocom_OSKIP))
| ~ spl625_361
| ~ spl625_687 ),
inference(resolution,[],[f32190,f30551]) ).
fof(f30551,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X0),X0))
| ~ spl625_361 ),
inference(avatar_component_clause,[],[f30550]) ).
fof(f32992,plain,
( spl625_771
| ~ spl625_313
| ~ spl625_687 ),
inference(avatar_split_clause,[],[f32836,f32189,f30294,f32990]) ).
fof(f32990,plain,
( spl625_771
<=> ! [X0] : ~ sP29(X0,X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_771])]) ).
fof(f30294,plain,
( spl625_313
<=> ! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_313])]) ).
fof(f32836,plain,
( ! [X0] : ~ sP29(X0,X0,c_fequal)
| ~ spl625_313
| ~ spl625_687 ),
inference(resolution,[],[f32190,f30295]) ).
fof(f30295,plain,
( ! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1))
| ~ spl625_313 ),
inference(avatar_component_clause,[],[f30294]) ).
fof(f32606,plain,
( spl625_769
| ~ spl625_770
| ~ spl625_600
| ~ spl625_653 ),
inference(avatar_split_clause,[],[f32578,f32053,f31596,f32603,f32599]) ).
fof(f32599,plain,
( spl625_769
<=> c_Nat__Transfer_Ois__nat(c_Orderings_Otop__class_Otop(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_769])]) ).
fof(f32603,plain,
( spl625_770
<=> class_Orderings_Otop(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_770])]) ).
fof(f31596,plain,
( spl625_600
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| c_Nat__Transfer_Ois__nat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_600])]) ).
fof(f32053,plain,
( spl625_653
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_653])]) ).
fof(f32578,plain,
( ~ class_Orderings_Otop(tc_Int_Oint)
| c_Nat__Transfer_Ois__nat(c_Orderings_Otop__class_Otop(tc_Int_Oint))
| ~ spl625_600
| ~ spl625_653 ),
inference(resolution,[],[f32054,f31597]) ).
fof(f31597,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| c_Nat__Transfer_Ois__nat(X0) )
| ~ spl625_600 ),
inference(avatar_component_clause,[],[f31596]) ).
fof(f32054,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) )
| ~ spl625_653 ),
inference(avatar_component_clause,[],[f32053]) ).
fof(f32566,plain,
( spl625_768
| ~ spl625_378
| ~ spl625_561 ),
inference(avatar_split_clause,[],[f31770,f31433,f30619,f32564]) ).
fof(f32564,plain,
( spl625_768
<=> ! [X0,X1] : sP7(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_768])]) ).
fof(f30619,plain,
( spl625_378
<=> ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_378])]) ).
fof(f31433,plain,
( spl625_561
<=> ! [X0,X1] :
( sP7(X1,X0)
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_561])]) ).
fof(f31770,plain,
( ! [X0,X1] : sP7(c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),X1)
| ~ spl625_378
| ~ spl625_561 ),
inference(resolution,[],[f31434,f30620]) ).
fof(f30620,plain,
( ! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0))
| ~ spl625_378 ),
inference(avatar_component_clause,[],[f30619]) ).
fof(f31434,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| sP7(X1,X0) )
| ~ spl625_561 ),
inference(avatar_component_clause,[],[f31433]) ).
fof(f32530,plain,
( spl625_767
| ~ spl625_384
| ~ spl625_626 ),
inference(avatar_split_clause,[],[f32526,f31943,f30643,f32528]) ).
fof(f32528,plain,
( spl625_767
<=> ! [X0] : ~ class_Finite__Set_Ofinite(tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_767])]) ).
fof(f30643,plain,
( spl625_384
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_384])]) ).
fof(f31943,plain,
( spl625_626
<=> ! [X0] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X0)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X0),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_626])]) ).
fof(f32526,plain,
( ! [X0] : ~ class_Finite__Set_Ofinite(tc_List_Olist(X0))
| ~ spl625_384
| ~ spl625_626 ),
inference(resolution,[],[f31944,f30644]) ).
fof(f30644,plain,
( ! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) )
| ~ spl625_384 ),
inference(avatar_component_clause,[],[f30643]) ).
fof(f31944,plain,
( ! [X0] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X0)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X0),tc_HOL_Obool))))
| ~ spl625_626 ),
inference(avatar_component_clause,[],[f31943]) ).
fof(f32525,plain,
spl625_766,
inference(avatar_split_clause,[],[f27654,f32523]) ).
fof(f32523,plain,
( spl625_766
<=> ! [X2,X0,X1] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_HOL_Obool_Obool__size(c_fTrue),X0) = X0
| ~ class_Rings_Osemiring__1(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_766])]) ).
fof(f27654,plain,
! [X2,X0,X1] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_HOL_Obool_Obool__size(c_fTrue),X0) = X0
| ~ class_Rings_Osemiring__1(X2) ),
inference(forward_demodulation,[],[f19959,f17032]) ).
fof(f17032,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
inference(cnf_transformation,[],[f4934]) ).
fof(f4934,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f19959,plain,
! [X2,X0,X1] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0
| ~ class_Rings_Osemiring__1(X2) ),
inference(cnf_transformation,[],[f11549]) ).
fof(f11549,plain,
! [X0,X1,X2] :
( c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0
| ~ class_Rings_Osemiring__1(X2) ),
inference(ennf_transformation,[],[f7429]) ).
fof(f7429,plain,
! [X0,X1,X2] :
( class_Rings_Osemiring__1(X2)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X2,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0) = X0 ),
inference(rectify,[],[f1834]) ).
fof(f1834,axiom,
! [X147,X202,X4] :
( class_Rings_Osemiring__1(X4)
=> c_Nat_Osemiring__1__class_Oof__nat__aux(X4,X202,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X147) = X147 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32521,plain,
spl625_765,
inference(avatar_split_clause,[],[f27440,f32519]) ).
fof(f32519,plain,
( spl625_765
<=> ! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_765])]) ).
fof(f27440,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)),
inference(forward_demodulation,[],[f27439,f26111]) ).
fof(f26111,plain,
! [X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f26110,f25523]) ).
fof(f25523,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17055,f17032]) ).
fof(f17055,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1609]) ).
fof(f1609,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f26110,plain,
! [X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f17986,f17032]) ).
fof(f17986,plain,
! [X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f6002]) ).
fof(f6002,plain,
! [X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rectify,[],[f1723]) ).
fof(f1723,axiom,
! [X193,X194] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(X194,X193)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X194)),c_Com_Ocom_Ocom__size(X193))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f27439,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f27438,f25523]) ).
fof(f27438,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f19509,f17032]) ).
fof(f19509,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)),
inference(cnf_transformation,[],[f7044]) ).
fof(f7044,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X1)),c_Com_Ocom_Ocom__size(X0))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X2,X1,X0)),
inference(rectify,[],[f1778]) ).
fof(f1778,axiom,
! [X57,X58,X53] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(X53,X58,X57)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X58)),c_Com_Ocom_Ocom__size(X57))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32517,plain,
spl625_764,
inference(avatar_split_clause,[],[f27425,f32515]) ).
fof(f27425,plain,
! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(X2,X0,c_Com_Ocom_OSKIP,X0))),
inference(forward_demodulation,[],[f19478,f26086]) ).
fof(f26086,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,[],[f17905,f17702]) ).
fof(f17702,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(cnf_transformation,[],[f5718]) ).
fof(f5718,plain,
! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0,
inference(rectify,[],[f202]) ).
fof(f202,axiom,
! [X5,X4] : hAPP(c_Set_OCollect(X4),X5) = X5,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17905,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X0)),
inference(cnf_transformation,[],[f5921]) ).
fof(f5921,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X1),hAPP(c_fequal,X0)),
inference(rectify,[],[f201]) ).
fof(f201,axiom,
! [X6,X4] : hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = hAPP(c_Set_OCollect(X4),hAPP(c_fequal,X6)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f19478,plain,
! [X2,X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X0,c_Com_Ocom_OSKIP,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f7013]) ).
fof(f7013,plain,
! [X0,X1,X2] : c_Hoare__Mirabelle_Ohoare__derivs(X2,X1,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X2)),c_Hoare__Mirabelle_Otriple_Otriple(X2,X0,c_Com_Ocom_OSKIP,X0)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X2),tc_HOL_Obool)))),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X7,X8,X4] : c_Hoare__Mirabelle_Ohoare__derivs(X4,X8,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(X4)),c_Hoare__Mirabelle_Otriple_Otriple(X4,X7,c_Com_Ocom_OSKIP,X7)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32513,plain,
spl625_763,
inference(avatar_split_clause,[],[f27419,f32511]) ).
fof(f32511,plain,
( spl625_763
<=> ! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)) = hAPP(c_Nat_OSuc,c_Com_Ocom_Ocom__size(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_763])]) ).
fof(f27419,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)) = hAPP(c_Nat_OSuc,c_Com_Ocom_Ocom__size(X0)),
inference(forward_demodulation,[],[f27418,f17286]) ).
fof(f17286,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f5389]) ).
fof(f5389,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(rectify,[],[f1400]) ).
fof(f1400,axiom,
! [X88] : hAPP(c_Nat_OSuc,X88) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X88),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f27418,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X0)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f27417,f25523]) ).
fof(f27417,plain,
! [X2,X0,X1] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X0)),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f19436,f17032]) ).
fof(f19436,plain,
! [X2,X0,X1] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X0)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)),
inference(cnf_transformation,[],[f6971]) ).
fof(f6971,plain,
! [X0,X1,X2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X0)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X2,X1,X0)),
inference(rectify,[],[f1722]) ).
fof(f1722,axiom,
! [X13,X53,X70] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(X70,X53,X13)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(X13)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32509,plain,
( spl625_762
| ~ spl625_384
| ~ spl625_561 ),
inference(avatar_split_clause,[],[f31769,f31433,f30643,f32507]) ).
fof(f32507,plain,
( spl625_762
<=> ! [X0,X1] :
( sP7(c_Finite__Set_Ofinite(X0),X1)
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_762])]) ).
fof(f31769,plain,
( ! [X0,X1] :
( sP7(c_Finite__Set_Ofinite(X0),X1)
| ~ class_Finite__Set_Ofinite(X0) )
| ~ spl625_384
| ~ spl625_561 ),
inference(resolution,[],[f31434,f30644]) ).
fof(f32505,plain,
spl625_761,
inference(avatar_split_clause,[],[f27187,f32503]) ).
fof(f32503,plain,
( spl625_761
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) != hAPP(c_Int_Onat,X1)
| sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_761])]) ).
fof(f27187,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) != hAPP(c_Int_Onat,X1)
| sP11(X0,X1) ),
inference(forward_demodulation,[],[f27186,f25669]) ).
fof(f25669,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X0),
inference(forward_demodulation,[],[f17294,f17178]) ).
fof(f17178,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(cnf_transformation,[],[f5281]) ).
fof(f5281,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0,
inference(rectify,[],[f2379]) ).
fof(f2379,axiom,
! [X112] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X112) = X112,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17294,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f5397]) ).
fof(f5397,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),
inference(rectify,[],[f2421]) ).
fof(f2421,axiom,
! [X190] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X190) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X190)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f27186,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) != hAPP(c_Int_Onat,X1)
| sP11(X0,X1) ),
inference(forward_demodulation,[],[f19164,f25669]) ).
fof(f19164,plain,
! [X0,X1] :
( sP11(X0,X1)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) ),
inference(cnf_transformation,[],[f15033]) ).
fof(f15033,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
| ~ sP11(X0,X1) )
& ( sP11(X0,X1)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1) ) ),
inference(nnf_transformation,[],[f14423]) ).
fof(f14423,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
<=> sP11(X0,X1) ),
inference(definition_folding,[],[f11276,f14422,f14421]) ).
fof(f14421,plain,
! [X1,X0] :
( sP10(X1,X0)
<=> ( ( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f14422,plain,
! [X0,X1] :
( sP11(X0,X1)
<=> ( ( sP10(X1,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f11276,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
<=> ( ( ( ( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) ) ),
inference(ennf_transformation,[],[f6826]) ).
fof(f6826,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
<=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> X0 = X1 )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ) ) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
inference(rectify,[],[f2546]) ).
fof(f2546,axiom,
! [X235,X102] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X102) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X235)
<=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X102)))
=> ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X235)))
=> X102 = X235 )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X235)))
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X102) ) ) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X102)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X235)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32501,plain,
spl625_760,
inference(avatar_split_clause,[],[f27185,f32499]) ).
fof(f32499,plain,
( spl625_760
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) = hAPP(c_Int_Onat,X1)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_760])]) ).
fof(f27185,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = hAPP(c_Int_Onat,X1)
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f27184,f25669]) ).
fof(f27184,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X1)
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f19165,f25669]) ).
fof(f19165,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X1)
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f15033]) ).
fof(f32497,plain,
spl625_759,
inference(avatar_split_clause,[],[f27183,f32495]) ).
fof(f32495,plain,
( spl625_759
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Int_OPls = X0
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_759])]) ).
fof(f27183,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| c_Int_OPls = X0
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f27182,f17178]) ).
fof(f27182,plain,
! [X0,X1] :
( c_Int_OPls = X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f27181,f17021]) ).
fof(f17021,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
inference(cnf_transformation,[],[f2565]) ).
fof(f2565,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f27181,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f19158,f17178]) ).
fof(f19158,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f15032]) ).
fof(f15032,plain,
! [X0,X1] :
( ( sP10(X0,X1)
| ( X0 != X1
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
& ( ( ( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
| ~ sP10(X0,X1) ) ),
inference(rectify,[],[f15031]) ).
fof(f15031,plain,
! [X1,X0] :
( ( sP10(X1,X0)
| ( X0 != X1
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
& ( ( ( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
| ~ sP10(X1,X0) ) ),
inference(flattening,[],[f15030]) ).
fof(f15030,plain,
! [X1,X0] :
( ( sP10(X1,X0)
| ( X0 != X1
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
| ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
& ( ( ( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ) )
| ~ sP10(X1,X0) ) ),
inference(nnf_transformation,[],[f14421]) ).
fof(f32493,plain,
spl625_758,
inference(avatar_split_clause,[],[f27180,f32491]) ).
fof(f32491,plain,
( spl625_758
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| X0 = X1
| ~ sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_758])]) ).
fof(f27180,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| X0 = X1
| ~ sP10(X0,X1) ),
inference(forward_demodulation,[],[f19159,f17178]) ).
fof(f19159,plain,
! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP10(X0,X1) ),
inference(cnf_transformation,[],[f15032]) ).
fof(f32489,plain,
spl625_757,
inference(avatar_split_clause,[],[f27179,f32487]) ).
fof(f32487,plain,
( spl625_757
<=> ! [X0,X1] :
( c_Int_OPls != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_757])]) ).
fof(f27179,plain,
! [X0,X1] :
( c_Int_OPls != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X0,X1) ),
inference(forward_demodulation,[],[f27178,f17021]) ).
fof(f27178,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X0,X1) ),
inference(forward_demodulation,[],[f27177,f17178]) ).
fof(f27177,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ),
inference(forward_demodulation,[],[f19161,f17178]) ).
fof(f19161,plain,
! [X0,X1] :
( sP10(X0,X1)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f15032]) ).
fof(f32485,plain,
spl625_756,
inference(avatar_split_clause,[],[f27170,f32483]) ).
fof(f32483,plain,
( spl625_756
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X1,X0)
| ~ sP11(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_756])]) ).
fof(f27170,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X1,X0)
| ~ sP11(X0,X1) ),
inference(forward_demodulation,[],[f19153,f17178]) ).
fof(f19153,plain,
! [X0,X1] :
( sP10(X1,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1)))
| ~ sP11(X0,X1) ),
inference(cnf_transformation,[],[f15029]) ).
fof(f15029,plain,
! [X0,X1] :
( ( sP11(X0,X1)
| ( ~ sP10(X1,X0)
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
& ( ( ( sP10(X1,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
| ~ sP11(X0,X1) ) ),
inference(flattening,[],[f15028]) ).
fof(f15028,plain,
! [X0,X1] :
( ( sP11(X0,X1)
| ( ~ sP10(X1,X0)
& ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
& ( ( ( sP10(X1,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ) )
| ~ sP11(X0,X1) ) ),
inference(nnf_transformation,[],[f14422]) ).
fof(f32481,plain,
spl625_755,
inference(avatar_split_clause,[],[f27166,f32479]) ).
fof(f32479,plain,
( spl625_755
<=> ! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X0,X1)
| ~ sP10(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_755])]) ).
fof(f27166,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP11(X0,X1)
| ~ sP10(X1,X0) ),
inference(forward_demodulation,[],[f19156,f17178]) ).
fof(f19156,plain,
! [X0,X1] :
( sP11(X0,X1)
| ~ sP10(X1,X0)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(cnf_transformation,[],[f15029]) ).
fof(f32477,plain,
spl625_754,
inference(avatar_split_clause,[],[f27154,f32475]) ).
fof(f32475,plain,
( spl625_754
<=> ! [X0,X1,X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0
| ~ hBOOL(hAPP(X0,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_754])]) ).
fof(f27154,plain,
! [X3,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0
| ~ hBOOL(hAPP(X0,X3)) ),
inference(forward_demodulation,[],[f19137,f17702]) ).
fof(f19137,plain,
! [X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X3))
| hAPP(c_Set_OCollect(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ),
inference(cnf_transformation,[],[f15017]) ).
fof(f15017,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| hBOOL(hAPP(X0,sK186(X0))) )
& ( ! [X3] : ~ hBOOL(hAPP(X0,X3))
| hAPP(c_Set_OCollect(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK186])],[f15015,f15016]) ).
fof(f15016,plain,
! [X0] :
( ? [X2] : hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X0,sK186(X0))) ),
introduced(choice_axiom,[]) ).
fof(f15015,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ? [X2] : hBOOL(hAPP(X0,X2)) )
& ( ! [X3] : ~ hBOOL(hAPP(X0,X3))
| hAPP(c_Set_OCollect(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ) ),
inference(rectify,[],[f15014]) ).
fof(f15014,plain,
! [X0,X1] :
( ( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ? [X2] : hBOOL(hAPP(X0,X2)) )
& ( ! [X2] : ~ hBOOL(hAPP(X0,X2))
| hAPP(c_Set_OCollect(X1),X0) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ) ),
inference(nnf_transformation,[],[f6819]) ).
fof(f6819,plain,
! [X0,X1] :
( hAPP(c_Set_OCollect(X1),X0) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
<=> ! [X2] : ~ hBOOL(hAPP(X0,X2)) ),
inference(rectify,[],[f206]) ).
fof(f206,axiom,
! [X5,X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_Set_OCollect(X4),X5)
<=> ! [X2] : ~ hBOOL(hAPP(X5,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32473,plain,
spl625_753,
inference(avatar_split_clause,[],[f27135,f32471]) ).
fof(f32471,plain,
( spl625_753
<=> ! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_753])]) ).
fof(f27135,plain,
! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP8(X0,X1) ),
inference(forward_demodulation,[],[f19109,f17178]) ).
fof(f19109,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f15001]) ).
fof(f15001,plain,
! [X0,X1] :
( ( sP8(X0,X1)
| ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ) ) )
& ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 )
| ~ sP8(X0,X1) ) ),
inference(flattening,[],[f15000]) ).
fof(f15000,plain,
! [X0,X1] :
( ( sP8(X0,X1)
| ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ) ) )
& ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 )
| ~ sP8(X0,X1) ) ),
inference(nnf_transformation,[],[f14417]) ).
fof(f14417,plain,
! [X0,X1] :
( sP8(X0,X1)
<=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
& hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1 )
| ( c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
& c_Groups_Oone__class_Oone(tc_Int_Oint) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f32469,plain,
spl625_752,
inference(avatar_split_clause,[],[f27134,f32467]) ).
fof(f32467,plain,
( spl625_752
<=> ! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_752])]) ).
fof(f27134,plain,
! [X0,X1] :
( c_Int_OMin = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP8(X0,X1) ),
inference(forward_demodulation,[],[f19110,f17178]) ).
fof(f19110,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X1
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f15001]) ).
fof(f32464,plain,
spl625_751,
inference(avatar_split_clause,[],[f27133,f32462]) ).
fof(f32462,plain,
( spl625_751
<=> ! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_751])]) ).
fof(f27133,plain,
! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP8(X0,X1) ),
inference(forward_demodulation,[],[f19111,f17178]) ).
fof(f19111,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X1
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f15001]) ).
fof(f32460,plain,
spl625_750,
inference(avatar_split_clause,[],[f27132,f32458]) ).
fof(f32458,plain,
( spl625_750
<=> ! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP8(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_750])]) ).
fof(f27132,plain,
! [X0,X1] :
( c_Int_OMin = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP8(X0,X1) ),
inference(forward_demodulation,[],[f19112,f17178]) ).
fof(f19112,plain,
! [X0,X1] :
( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) = X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) = X0
| ~ sP8(X0,X1) ),
inference(cnf_transformation,[],[f15001]) ).
fof(f32456,plain,
spl625_749,
inference(avatar_split_clause,[],[f26595,f32454]) ).
fof(f32454,plain,
( spl625_749
<=> ! [X0,X1] :
( hAPP(c_fequal,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0)
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_749])]) ).
fof(f26595,plain,
! [X0,X1] :
( hAPP(c_fequal,X0) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(forward_demodulation,[],[f18554,f26086]) ).
fof(f18554,plain,
! [X0,X1] :
( hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f10853]) ).
fof(f10853,plain,
! [X0,X1] :
( hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0)
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f6446]) ).
fof(f6446,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X1,X0,X0) ),
inference(rectify,[],[f3118]) ).
fof(f3118,axiom,
! [X6,X4] :
( class_Orderings_Oorder(X4)
=> hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastAtMost(X4,X6,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32452,plain,
spl625_748,
inference(avatar_split_clause,[],[f26229,f32450]) ).
fof(f32450,plain,
( spl625_748
<=> ! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_748])]) ).
fof(f26229,plain,
! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f24892,f17032]) ).
fof(f24892,plain,
! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f18104]) ).
fof(f18104,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f10484]) ).
fof(f10484,plain,
! [X0,X1] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(ennf_transformation,[],[f6111]) ).
fof(f6111,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X1),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X0),X1) ) ),
inference(rectify,[],[f1926]) ).
fof(f1926,axiom,
! [X210,X93] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X93
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X210),X93) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X210),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X210),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X93),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X93
=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X210),X93) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32448,plain,
spl625_747,
inference(avatar_split_clause,[],[f26087,f32446]) ).
fof(f32446,plain,
( spl625_747
<=> ! [X0,X1] : hAPP(c_fequal,X0) = c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_747])]) ).
fof(f26087,plain,
! [X0,X1] : hAPP(c_fequal,X0) = c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(forward_demodulation,[],[f17906,f26086]) ).
fof(f17906,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(cnf_transformation,[],[f5922]) ).
fof(f5922,plain,
! [X0,X1] : hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = c_Option_Oset(X1,hAPP(c_Option_Ooption_OSome(X1),X0)),
inference(rectify,[],[f837]) ).
fof(f837,axiom,
! [X20,X4] : hAPP(hAPP(c_Set_Oinsert(X4),X20),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))) = c_Option_Oset(X4,hAPP(c_Option_Ooption_OSome(X4),X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32444,plain,
spl625_746,
inference(avatar_split_clause,[],[f26064,f32442]) ).
fof(f32442,plain,
( spl625_746
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_746])]) ).
fof(f26064,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0),
inference(forward_demodulation,[],[f17768,f17032]) ).
fof(f17768,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f5784]) ).
fof(f5784,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(rectify,[],[f3955]) ).
fof(f3955,axiom,
! [X263,X23] : c_List_Olist_ONil(X23) = hAPP(hAPP(c_List_Otake(X23),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X263),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32440,plain,
spl625_745,
inference(avatar_split_clause,[],[f25959,f32438]) ).
fof(f32438,plain,
( spl625_745
<=> ! [X0] :
( c_Int_OPls != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_HOL_Obool_Obool__size(c_fTrue) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_745])]) ).
fof(f25959,plain,
! [X0] :
( c_Int_OPls != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_HOL_Obool_Obool__size(c_fTrue) = X0 ),
inference(forward_demodulation,[],[f25958,f17021]) ).
fof(f25958,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) ),
inference(forward_demodulation,[],[f17574,f17032]) ).
fof(f17574,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f14595]) ).
fof(f14595,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) ) ),
inference(nnf_transformation,[],[f5642]) ).
fof(f5642,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ),
inference(rectify,[],[f1728]) ).
fof(f1728,axiom,
! [X78] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X78)
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X78 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32436,plain,
spl625_744,
inference(avatar_split_clause,[],[f25938,f32434]) ).
fof(f32434,plain,
( spl625_744
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK93(X0)))
| c_Nat__Transfer_Onat__set(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_744])]) ).
fof(f25938,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),sK93(X0)))
| c_Nat__Transfer_Onat__set(X0) ),
inference(forward_demodulation,[],[f17545,f17021]) ).
fof(f17545,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK93(X0))) ),
inference(cnf_transformation,[],[f14573]) ).
fof(f14573,plain,
! [X0] :
( ( c_Nat__Transfer_Onat__set(X0)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK93(X0)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK93(X0)),X0)) ) )
& ( ! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X0)) )
| ~ c_Nat__Transfer_Onat__set(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK93])],[f14571,f14572]) ).
fof(f14572,plain,
! [X0] :
( ? [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X0)) )
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK93(X0)))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK93(X0)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14571,plain,
! [X0] :
( ( c_Nat__Transfer_Onat__set(X0)
| ? [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X0)) ) )
& ( ! [X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X0)) )
| ~ c_Nat__Transfer_Onat__set(X0) ) ),
inference(rectify,[],[f14570]) ).
fof(f14570,plain,
! [X0] :
( ( c_Nat__Transfer_Onat__set(X0)
| ? [X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X0)) ) )
& ( ! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X0)) )
| ~ c_Nat__Transfer_Onat__set(X0) ) ),
inference(nnf_transformation,[],[f10469]) ).
fof(f10469,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(X0)
<=> ! [X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X0)) ) ),
inference(ennf_transformation,[],[f5628]) ).
fof(f5628,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(X0)
<=> ! [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X1),X0))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ),
inference(rectify,[],[f2587]) ).
fof(f2587,axiom,
! [X117] :
( c_Nat__Transfer_Onat__set(X117)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),X2),X117))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32432,plain,
spl625_743,
inference(avatar_split_clause,[],[f25838,f32430]) ).
fof(f32430,plain,
( spl625_743
<=> ! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_743])]) ).
fof(f25838,plain,
! [X0] :
( c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f17502,f17032]) ).
fof(f17502,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(cnf_transformation,[],[f10427]) ).
fof(f10427,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0)
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(ennf_transformation,[],[f5591]) ).
fof(f5591,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X0) ),
inference(rectify,[],[f2541]) ).
fof(f2541,axiom,
! [X30] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X30))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,X30) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32428,plain,
spl625_742,
inference(avatar_split_clause,[],[f25826,f32426]) ).
fof(f32426,plain,
( spl625_742
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_HOL_Obool_Obool__size(c_fTrue))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_742])]) ).
fof(f25826,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_HOL_Obool_Obool__size(c_fTrue))
| ~ class_Rings_Osemiring__1(X0) ),
inference(forward_demodulation,[],[f17462,f17032]) ).
fof(f17462,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10388]) ).
fof(f10388,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5552]) ).
fof(f5552,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(rectify,[],[f1752]) ).
fof(f1752,axiom,
! [X23] :
( class_Rings_Osemiring__1(X23)
=> c_Groups_Ozero__class_Ozero(X23) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X23),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32424,plain,
( ~ spl625_127
| ~ spl625_279
| spl625_713 ),
inference(avatar_split_clause,[],[f32383,f32293,f30158,f29439]) ).
fof(f29439,plain,
( spl625_127
<=> class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_127])]) ).
fof(f30158,plain,
( spl625_279
<=> ! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_279])]) ).
fof(f32293,plain,
( spl625_713
<=> c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_713])]) ).
fof(f32383,plain,
( ~ class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral)
| ~ spl625_279
| spl625_713 ),
inference(resolution,[],[f32294,f30159]) ).
fof(f30159,plain,
( ! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) )
| ~ spl625_279 ),
inference(avatar_component_clause,[],[f30158]) ).
fof(f32294,plain,
( ~ c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| spl625_713 ),
inference(avatar_component_clause,[],[f32293]) ).
fof(f32423,plain,
spl625_741,
inference(avatar_split_clause,[],[f25686,f32421]) ).
fof(f32421,plain,
( spl625_741
<=> ! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_741])]) ).
fof(f25686,plain,
! [X0] : c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0),
inference(forward_demodulation,[],[f25685,f25523]) ).
fof(f25685,plain,
! [X0] : hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),X0),
inference(forward_demodulation,[],[f17325,f17032]) ).
fof(f17325,plain,
! [X0] : hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
inference(cnf_transformation,[],[f5428]) ).
fof(f5428,plain,
! [X0] : hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X0),
inference(rectify,[],[f1965]) ).
fof(f1965,axiom,
! [X88] : hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),X88),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32419,plain,
spl625_740,
inference(avatar_split_clause,[],[f25674,f32417]) ).
fof(f32417,plain,
( spl625_740
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_740])]) ).
fof(f25674,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(forward_demodulation,[],[f17302,f17021]) ).
fof(f17302,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(cnf_transformation,[],[f5405]) ).
fof(f5405,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(rectify,[],[f1864]) ).
fof(f1864,axiom,
! [X30] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32415,plain,
spl625_739,
inference(avatar_split_clause,[],[f25670,f32413]) ).
fof(f32413,plain,
( spl625_739
<=> ! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X0)) = hAPP(c_Int_Onat,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_739])]) ).
fof(f25670,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X0)) = hAPP(c_Int_Onat,X0),
inference(forward_demodulation,[],[f17297,f25669]) ).
fof(f17297,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X0)),
inference(cnf_transformation,[],[f5400]) ).
fof(f5400,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X0)),
inference(rectify,[],[f4644]) ).
fof(f4644,axiom,
! [X112] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),X112)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X112),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32411,plain,
spl625_738,
inference(avatar_split_clause,[],[f25665,f32409]) ).
fof(f32409,plain,
( spl625_738
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_738])]) ).
fof(f25665,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Int_OPls)),
inference(forward_demodulation,[],[f17282,f17021]) ).
fof(f17282,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(cnf_transformation,[],[f5385]) ).
fof(f5385,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(rectify,[],[f1787]) ).
fof(f1787,axiom,
! [X112] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X112)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32407,plain,
spl625_737,
inference(avatar_split_clause,[],[f25664,f32405]) ).
fof(f32405,plain,
( spl625_737
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),hAPP(c_Nat_OSuc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_737])]) ).
fof(f25664,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),hAPP(c_Nat_OSuc,X0))),
inference(forward_demodulation,[],[f17281,f17032]) ).
fof(f17281,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X0))),
inference(cnf_transformation,[],[f5384]) ).
fof(f5384,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X0))),
inference(rectify,[],[f1418]) ).
fof(f1418,axiom,
! [X88] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,X88))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32403,plain,
spl625_736,
inference(avatar_split_clause,[],[f25661,f32401]) ).
fof(f32401,plain,
( spl625_736
<=> ! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_736])]) ).
fof(f25661,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue),X0),
inference(forward_demodulation,[],[f17275,f17032]) ).
fof(f17275,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(cnf_transformation,[],[f5378]) ).
fof(f5378,plain,
! [X0] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X0),
inference(rectify,[],[f3184]) ).
fof(f3184,axiom,
! [X78] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X78) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X78),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32399,plain,
spl625_735,
inference(avatar_split_clause,[],[f25660,f32397]) ).
fof(f32397,plain,
( spl625_735
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Finite__Set_Ocard(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_735])]) ).
fof(f25660,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Finite__Set_Ocard(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(forward_demodulation,[],[f17268,f17032]) ).
fof(f17268,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(cnf_transformation,[],[f5371]) ).
fof(f5371,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),
inference(rectify,[],[f1594]) ).
fof(f1594,axiom,
! [X4] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(X4),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32395,plain,
spl625_734,
inference(avatar_split_clause,[],[f25657,f32393]) ).
fof(f32393,plain,
( spl625_734
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_734])]) ).
fof(f25657,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0),
inference(forward_demodulation,[],[f17266,f17032]) ).
fof(f17266,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f5369]) ).
fof(f5369,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(rectify,[],[f1508]) ).
fof(f1508,axiom,
! [X88] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X88),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32391,plain,
spl625_733,
inference(avatar_split_clause,[],[f25656,f32389]) ).
fof(f32389,plain,
( spl625_733
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_733])]) ).
fof(f25656,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0),
inference(forward_demodulation,[],[f17265,f17032]) ).
fof(f17265,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f5368]) ).
fof(f5368,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(rectify,[],[f1499]) ).
fof(f1499,axiom,
! [X88] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X88),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32387,plain,
spl625_732,
inference(avatar_split_clause,[],[f25655,f32385]) ).
fof(f32385,plain,
( spl625_732
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_732])]) ).
fof(f25655,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0),
inference(forward_demodulation,[],[f17264,f17032]) ).
fof(f17264,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(cnf_transformation,[],[f5367]) ).
fof(f5367,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0),
inference(rectify,[],[f1430]) ).
fof(f1430,axiom,
! [X88] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X88),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32382,plain,
spl625_731,
inference(avatar_split_clause,[],[f25654,f32380]) ).
fof(f32380,plain,
( spl625_731
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_731])]) ).
fof(f25654,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17263,f17032]) ).
fof(f17263,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f5366]) ).
fof(f5366,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f1507]) ).
fof(f1507,axiom,
! [X93] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X93),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32378,plain,
spl625_730,
inference(avatar_split_clause,[],[f25653,f32376]) ).
fof(f32376,plain,
( spl625_730
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_730])]) ).
fof(f25653,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17262,f17032]) ).
fof(f17262,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f5365]) ).
fof(f5365,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(rectify,[],[f1431]) ).
fof(f1431,axiom,
! [X88] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),X88),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32374,plain,
spl625_729,
inference(avatar_split_clause,[],[f25571,f32371]) ).
fof(f32371,plain,
( spl625_729
<=> 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,[spl625_729])]) ).
fof(f25571,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),
inference(forward_demodulation,[],[f17108,f17020]) ).
fof(f17020,plain,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
inference(cnf_transformation,[],[f4654]) ).
fof(f4654,axiom,
c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17108,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),
inference(cnf_transformation,[],[f2855]) ).
fof(f2855,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32368,plain,
spl625_728,
inference(avatar_split_clause,[],[f25570,f32365]) ).
fof(f25570,plain,
c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17105,f17032]) ).
fof(f17105,plain,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
inference(cnf_transformation,[],[f1709]) ).
fof(f1709,axiom,
hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32363,plain,
spl625_727,
inference(avatar_split_clause,[],[f25565,f32360]) ).
fof(f32360,plain,
( spl625_727
<=> c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_727])]) ).
fof(f25565,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17103,f17032]) ).
fof(f17103,plain,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f3063]) ).
fof(f3063,axiom,
c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32356,plain,
( spl625_726
| ~ spl625_349
| ~ spl625_517
| ~ spl625_725 ),
inference(avatar_split_clause,[],[f32351,f32347,f31254,f30495,f32353]) ).
fof(f32353,plain,
( spl625_726
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_726])]) ).
fof(f30495,plain,
( spl625_349
<=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin ),
introduced(avatar_definition,[new_symbols(naming,[spl625_349])]) ).
fof(f31254,plain,
( spl625_517
<=> ! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_517])]) ).
fof(f32347,plain,
( spl625_725
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_725])]) ).
fof(f32351,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl625_349
| ~ spl625_517
| ~ spl625_725 ),
inference(forward_demodulation,[],[f32349,f31687]) ).
fof(f31687,plain,
( c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)
| ~ spl625_349
| ~ spl625_517 ),
inference(superposition,[],[f31255,f30497]) ).
fof(f30497,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin
| ~ spl625_349 ),
inference(avatar_component_clause,[],[f30495]) ).
fof(f31255,plain,
( ! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = X0
| ~ spl625_517 ),
inference(avatar_component_clause,[],[f31254]) ).
fof(f32349,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))
| ~ spl625_725 ),
inference(avatar_component_clause,[],[f32347]) ).
fof(f32350,plain,
spl625_725,
inference(avatar_split_clause,[],[f25546,f32347]) ).
fof(f25546,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)),
inference(forward_demodulation,[],[f25545,f25522]) ).
fof(f25522,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin),
inference(forward_demodulation,[],[f24007,f17019]) ).
fof(f17019,plain,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
inference(cnf_transformation,[],[f2652]) ).
fof(f2652,axiom,
c_Int_OPls = c_Int_OBit0(c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f24007,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin),
inference(definition_unfolding,[],[f17052,f23983]) ).
fof(f23983,plain,
! [X0] : c_Int_OBit1(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin),
inference(definition_unfolding,[],[f17174,f17237]) ).
fof(f17237,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(cnf_transformation,[],[f5340]) ).
fof(f5340,plain,
! [X0] : c_Int_Osucc(X0) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OMin),
inference(rectify,[],[f2816]) ).
fof(f2816,axiom,
! [X112] : c_Int_Osucc(X112) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X112),c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17174,plain,
! [X0] : c_Int_OBit1(X0) = c_Int_Osucc(c_Int_OBit0(X0)),
inference(cnf_transformation,[],[f5277]) ).
fof(f5277,plain,
! [X0] : c_Int_OBit1(X0) = c_Int_Osucc(c_Int_OBit0(X0)),
inference(rectify,[],[f2686]) ).
fof(f2686,axiom,
! [X112] : c_Int_OBit1(X112) = c_Int_Osucc(c_Int_OBit0(X112)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17052,plain,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin),
inference(cnf_transformation,[],[f2829]) ).
fof(f2829,axiom,
c_Int_OBit1(c_Int_OPls) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f25545,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(forward_demodulation,[],[f24013,f17019]) ).
fof(f24013,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin)),
inference(definition_unfolding,[],[f17084,f23983]) ).
fof(f17084,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f2603]) ).
fof(f2603,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32344,plain,
spl625_724,
inference(avatar_split_clause,[],[f25544,f32341]) ).
fof(f32341,plain,
( spl625_724
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_724])]) ).
fof(f25544,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)),
inference(forward_demodulation,[],[f25543,f25522]) ).
fof(f25543,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(forward_demodulation,[],[f24012,f17019]) ).
fof(f24012,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin)),
inference(definition_unfolding,[],[f17083,f23983]) ).
fof(f17083,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f2601]) ).
fof(f2601,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32339,plain,
( spl625_723
| ~ spl625_349
| ~ spl625_517
| ~ spl625_722 ),
inference(avatar_split_clause,[],[f32334,f32330,f31254,f30495,f32336]) ).
fof(f32336,plain,
( spl625_723
<=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_723])]) ).
fof(f32330,plain,
( spl625_722
<=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_722])]) ).
fof(f32334,plain,
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl625_349
| ~ spl625_517
| ~ spl625_722 ),
inference(forward_demodulation,[],[f32332,f31687]) ).
fof(f32332,plain,
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin))
| ~ spl625_722 ),
inference(avatar_component_clause,[],[f32330]) ).
fof(f32333,plain,
spl625_722,
inference(avatar_split_clause,[],[f25542,f32330]) ).
fof(f25542,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)),
inference(forward_demodulation,[],[f25541,f25522]) ).
fof(f25541,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,[],[f24011,f17019]) ).
fof(f24011,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin)),
inference(definition_unfolding,[],[f17080,f23983]) ).
fof(f17080,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
inference(cnf_transformation,[],[f2857]) ).
fof(f2857,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32328,plain,
spl625_721,
inference(avatar_split_clause,[],[f25483,f32326]) ).
fof(f32326,plain,
( spl625_721
<=> ! [X4,X0,X5,X3,X1] :
( X0 = X5
| ~ sP89(X0,X1,X4,X3,X4,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_721])]) ).
fof(f25483,plain,
! [X3,X0,X1,X4,X5] :
( X0 = X5
| ~ sP89(X0,X1,X4,X3,X4,X5) ),
inference(equality_resolution,[],[f23916]) ).
fof(f23916,plain,
! [X2,X3,X0,X1,X4,X5] :
( X2 != X4
| X0 = X5
| ~ sP89(X0,X1,X2,X3,X4,X5) ),
inference(cnf_transformation,[],[f16793]) ).
fof(f16793,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( sP89(X0,X1,X2,X3,X4,X5)
| ( ( hAPP(c_Option_Ooption_OSome(X1),X0) != hAPP(X3,X2)
| X2 = X4 )
& ( X0 != X5
| X2 != X4 ) ) )
& ( ( hAPP(c_Option_Ooption_OSome(X1),X0) = hAPP(X3,X2)
& X2 != X4 )
| ( X0 = X5
& X2 = X4 )
| ~ sP89(X0,X1,X2,X3,X4,X5) ) ),
inference(rectify,[],[f16792]) ).
fof(f16792,plain,
! [X0,X5,X1,X4,X3,X2] :
( ( sP89(X0,X5,X1,X4,X3,X2)
| ( ( hAPP(X4,X1) != hAPP(c_Option_Ooption_OSome(X5),X0)
| X1 = X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( hAPP(X4,X1) = hAPP(c_Option_Ooption_OSome(X5),X0)
& X1 != X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP89(X0,X5,X1,X4,X3,X2) ) ),
inference(flattening,[],[f16791]) ).
fof(f16791,plain,
! [X0,X5,X1,X4,X3,X2] :
( ( sP89(X0,X5,X1,X4,X3,X2)
| ( ( hAPP(X4,X1) != hAPP(c_Option_Ooption_OSome(X5),X0)
| X1 = X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( hAPP(X4,X1) = hAPP(c_Option_Ooption_OSome(X5),X0)
& X1 != X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP89(X0,X5,X1,X4,X3,X2) ) ),
inference(nnf_transformation,[],[f14561]) ).
fof(f14561,plain,
! [X0,X5,X1,X4,X3,X2] :
( sP89(X0,X5,X1,X4,X3,X2)
<=> ( ( hAPP(X4,X1) = hAPP(c_Option_Ooption_OSome(X5),X0)
& X1 != X3 )
| ( X0 = X2
& X1 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP89])]) ).
fof(f32324,plain,
spl625_720,
inference(avatar_split_clause,[],[f24974,f32322]) ).
fof(f32322,plain,
( spl625_720
<=> ! [X0,X3] :
( hBOOL(hAPP(X0,X3))
| ~ sP7(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_720])]) ).
fof(f24974,plain,
! [X3,X0] :
( hBOOL(hAPP(X0,X3))
| ~ sP7(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3)) ),
inference(equality_resolution,[],[f19020]) ).
fof(f19020,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(X0,X3))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3) != X1
| ~ sP7(X0,X1) ),
inference(cnf_transformation,[],[f14932]) ).
fof(f14932,plain,
! [X0,X1] :
( ( sP7(X0,X1)
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( ~ hBOOL(hAPP(X0,sK177(X0,X1)))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK177(X0,X1)) = X1 ) )
& ( ( ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [X3] :
( hBOOL(hAPP(X0,X3))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3) != X1 ) )
| ~ sP7(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK177])],[f14930,f14931]) ).
fof(f14931,plain,
! [X0,X1] :
( ? [X2] :
( ~ hBOOL(hAPP(X0,X2))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X1 )
=> ( ~ hBOOL(hAPP(X0,sK177(X0,X1)))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK177(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f14930,plain,
! [X0,X1] :
( ( sP7(X0,X1)
| ( ~ hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ? [X2] :
( ~ hBOOL(hAPP(X0,X2))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X1 ) )
& ( ( ( hBOOL(hAPP(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [X3] :
( hBOOL(hAPP(X0,X3))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X3) != X1 ) )
| ~ sP7(X0,X1) ) ),
inference(rectify,[],[f14929]) ).
fof(f14929,plain,
! [X1,X0] :
( ( sP7(X1,X0)
| ( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ? [X2] :
( ~ hBOOL(hAPP(X1,X2))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X0 ) )
& ( ( ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [X2] :
( hBOOL(hAPP(X1,X2))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) != X0 ) )
| ~ sP7(X1,X0) ) ),
inference(flattening,[],[f14928]) ).
fof(f14928,plain,
! [X1,X0] :
( ( sP7(X1,X0)
| ( ~ hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ? [X2] :
( ~ hBOOL(hAPP(X1,X2))
& hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X0 ) )
& ( ( ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [X2] :
( hBOOL(hAPP(X1,X2))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) != X0 ) )
| ~ sP7(X1,X0) ) ),
inference(nnf_transformation,[],[f14415]) ).
fof(f14415,plain,
! [X1,X0] :
( sP7(X1,X0)
<=> ( ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [X2] :
( hBOOL(hAPP(X1,X2))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) != X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f32320,plain,
spl625_719,
inference(avatar_split_clause,[],[f24909,f32318]) ).
fof(f32318,plain,
( spl625_719
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_719])]) ).
fof(f24909,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Groups_Ouminus__class_Ouminus(X1),c_Groups_Ozero__class_Ozero(X1))
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(equality_resolution,[],[f18231]) ).
fof(f18231,plain,
! [X0,X1] :
( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) = X0
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f14675]) ).
fof(f14675,plain,
! [X0,X1] :
( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) = X0
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) != X0 ) )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(nnf_transformation,[],[f10547]) ).
fof(f10547,plain,
! [X0,X1] :
( ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) = X0
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Groups_Olinordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f6186]) ).
fof(f6186,plain,
! [X0,X1] :
( class_Groups_Olinordered__ab__group__add(X1)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X1),X0) = X0
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f1479]) ).
fof(f1479,axiom,
! [X6,X4] :
( class_Groups_Olinordered__ab__group__add(X4)
=> ( hAPP(c_Groups_Ouminus__class_Ouminus(X4),X6) = X6
<=> c_Groups_Ozero__class_Ozero(X4) = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32316,plain,
spl625_718,
inference(avatar_split_clause,[],[f24138,f32314]) ).
fof(f32314,plain,
( spl625_718
<=> ! [X0,X1] : c_Int_OBit0(X0) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_718])]) ).
fof(f24138,plain,
! [X0,X1] : c_Int_OBit0(X0) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X1)),c_Int_OMin),
inference(definition_unfolding,[],[f17689,f23983]) ).
fof(f17689,plain,
! [X0,X1] : c_Int_OBit0(X0) != c_Int_OBit1(X1),
inference(cnf_transformation,[],[f5705]) ).
fof(f5705,plain,
! [X0,X1] : c_Int_OBit0(X0) != c_Int_OBit1(X1),
inference(rectify,[],[f2654]) ).
fof(f2654,axiom,
! [X124,X112] : c_Int_OBit1(X112) != c_Int_OBit0(X124),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32312,plain,
spl625_717,
inference(avatar_split_clause,[],[f24036,f32310]) ).
fof(f32310,plain,
( spl625_717
<=> ! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_717])]) ).
fof(f24036,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0))),
inference(definition_unfolding,[],[f17157,f17270]) ).
fof(f17270,plain,
! [X0] : c_Code__Numeral_OSuc__code__numeral(X0) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0))),
inference(cnf_transformation,[],[f5373]) ).
fof(f5373,plain,
! [X0] : c_Code__Numeral_OSuc__code__numeral(X0) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X0))),
inference(rectify,[],[f4649]) ).
fof(f4649,axiom,
! [X112] : c_Code__Numeral_OSuc__code__numeral(X112) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,X112))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17157,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X0),
inference(cnf_transformation,[],[f5260]) ).
fof(f5260,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X0),
inference(rectify,[],[f3032]) ).
fof(f3032,axiom,
! [X239] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(X239),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32308,plain,
spl625_716,
inference(avatar_split_clause,[],[f23311,f32306]) ).
fof(f32306,plain,
( spl625_716
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,X3))
| ~ sP76(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_716])]) ).
fof(f23311,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X1,X3))
| ~ sP76(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16547]) ).
fof(f16547,plain,
! [X0,X1,X2,X3,X4] :
( ( sP76(X0,X1,X2,X3,X4)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X2,X1),X6) != X0
| ~ hBOOL(hAPP(X1,X3))
| ( hBOOL(hAPP(X1,sK555(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK555(X1,X2,X5)),hAPP(c_List_Oset(X2),X5))) )
| hAPP(hAPP(c_List_Oappend(X2),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X6)) != X4 ) )
& ( ( hAPP(c_List_Ofilter(X2,X1),sK557(X0,X1,X2,X3,X4)) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),sK556(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK556(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK557(X0,X1,X2,X3,X4))) = X4 )
| ~ sP76(X0,X1,X2,X3,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK555,sK556,sK557])],[f16544,f16546,f16545]) ).
fof(f16545,plain,
! [X1,X2,X5] :
( ? [X7] :
( hBOOL(hAPP(X1,X7))
& hBOOL(hAPP(hAPP(c_member(X2),X7),hAPP(c_List_Oset(X2),X5))) )
=> ( hBOOL(hAPP(X1,sK555(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK555(X1,X2,X5)),hAPP(c_List_Oset(X2),X5))) ) ),
introduced(choice_axiom,[]) ).
fof(f16546,plain,
! [X0,X1,X2,X3,X4] :
( ? [X8,X9] :
( hAPP(c_List_Ofilter(X2,X1),X9) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),X8))) )
& hAPP(hAPP(c_List_Oappend(X2),X8),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X9)) = X4 )
=> ( hAPP(c_List_Ofilter(X2,X1),sK557(X0,X1,X2,X3,X4)) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),sK556(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK556(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK557(X0,X1,X2,X3,X4))) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f16544,plain,
! [X0,X1,X2,X3,X4] :
( ( sP76(X0,X1,X2,X3,X4)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X2,X1),X6) != X0
| ~ hBOOL(hAPP(X1,X3))
| ? [X7] :
( hBOOL(hAPP(X1,X7))
& hBOOL(hAPP(hAPP(c_member(X2),X7),hAPP(c_List_Oset(X2),X5))) )
| hAPP(hAPP(c_List_Oappend(X2),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X6)) != X4 ) )
& ( ? [X8,X9] :
( hAPP(c_List_Ofilter(X2,X1),X9) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),X8))) )
& hAPP(hAPP(c_List_Oappend(X2),X8),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X9)) = X4 )
| ~ sP76(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16543]) ).
fof(f16543,plain,
! [X0,X3,X4,X1,X2] :
( ( sP76(X0,X3,X4,X1,X2)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X4,X3),X6) != X0
| ~ hBOOL(hAPP(X3,X1))
| ? [X7] :
( hBOOL(hAPP(X3,X7))
& hBOOL(hAPP(hAPP(c_member(X4),X7),hAPP(c_List_Oset(X4),X5))) )
| hAPP(hAPP(c_List_Oappend(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X1),X6)) != X2 ) )
& ( ? [X5,X6] :
( hAPP(c_List_Ofilter(X4,X3),X6) = X0
& hBOOL(hAPP(X3,X1))
& ! [X7] :
( ~ hBOOL(hAPP(X3,X7))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X7),hAPP(c_List_Oset(X4),X5))) )
& hAPP(hAPP(c_List_Oappend(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X1),X6)) = X2 )
| ~ sP76(X0,X3,X4,X1,X2) ) ),
inference(nnf_transformation,[],[f14535]) ).
fof(f14535,plain,
! [X0,X3,X4,X1,X2] :
( sP76(X0,X3,X4,X1,X2)
<=> ? [X5,X6] :
( hAPP(c_List_Ofilter(X4,X3),X6) = X0
& hBOOL(hAPP(X3,X1))
& ! [X7] :
( ~ hBOOL(hAPP(X3,X7))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X7),hAPP(c_List_Oset(X4),X5))) )
& hAPP(hAPP(c_List_Oappend(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X1),X6)) = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP76])]) ).
fof(f32304,plain,
spl625_715,
inference(avatar_split_clause,[],[f23303,f32302]) ).
fof(f32302,plain,
( spl625_715
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X1,X3))
| ~ sP75(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_715])]) ).
fof(f23303,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X1,X3))
| ~ sP75(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16541]) ).
fof(f16541,plain,
! [X0,X1,X2,X3,X4] :
( ( sP75(X0,X1,X2,X3,X4)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X2,X1),X6) != X0
| ~ hBOOL(hAPP(X1,X3))
| ( hBOOL(hAPP(X1,sK552(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK552(X1,X2,X5)),hAPP(c_List_Oset(X2),X5))) )
| hAPP(hAPP(c_List_Oappend(X2),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X6)) != X4 ) )
& ( ( hAPP(c_List_Ofilter(X2,X1),sK554(X0,X1,X2,X3,X4)) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),sK553(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK553(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK554(X0,X1,X2,X3,X4))) = X4 )
| ~ sP75(X0,X1,X2,X3,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK552,sK553,sK554])],[f16538,f16540,f16539]) ).
fof(f16539,plain,
! [X1,X2,X5] :
( ? [X7] :
( hBOOL(hAPP(X1,X7))
& hBOOL(hAPP(hAPP(c_member(X2),X7),hAPP(c_List_Oset(X2),X5))) )
=> ( hBOOL(hAPP(X1,sK552(X1,X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),sK552(X1,X2,X5)),hAPP(c_List_Oset(X2),X5))) ) ),
introduced(choice_axiom,[]) ).
fof(f16540,plain,
! [X0,X1,X2,X3,X4] :
( ? [X8,X9] :
( hAPP(c_List_Ofilter(X2,X1),X9) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),X8))) )
& hAPP(hAPP(c_List_Oappend(X2),X8),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X9)) = X4 )
=> ( hAPP(c_List_Ofilter(X2,X1),sK554(X0,X1,X2,X3,X4)) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),sK553(X0,X1,X2,X3,X4)))) )
& hAPP(hAPP(c_List_Oappend(X2),sK553(X0,X1,X2,X3,X4)),hAPP(hAPP(c_List_Olist_OCons(X2),X3),sK554(X0,X1,X2,X3,X4))) = X4 ) ),
introduced(choice_axiom,[]) ).
fof(f16538,plain,
! [X0,X1,X2,X3,X4] :
( ( sP75(X0,X1,X2,X3,X4)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X2,X1),X6) != X0
| ~ hBOOL(hAPP(X1,X3))
| ? [X7] :
( hBOOL(hAPP(X1,X7))
& hBOOL(hAPP(hAPP(c_member(X2),X7),hAPP(c_List_Oset(X2),X5))) )
| hAPP(hAPP(c_List_Oappend(X2),X5),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X6)) != X4 ) )
& ( ? [X8,X9] :
( hAPP(c_List_Ofilter(X2,X1),X9) = X0
& hBOOL(hAPP(X1,X3))
& ! [X10] :
( ~ hBOOL(hAPP(X1,X10))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X10),hAPP(c_List_Oset(X2),X8))) )
& hAPP(hAPP(c_List_Oappend(X2),X8),hAPP(hAPP(c_List_Olist_OCons(X2),X3),X9)) = X4 )
| ~ sP75(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16537]) ).
fof(f16537,plain,
! [X2,X1,X4,X3,X0] :
( ( sP75(X2,X1,X4,X3,X0)
| ! [X5,X6] :
( hAPP(c_List_Ofilter(X4,X1),X6) != X2
| ~ hBOOL(hAPP(X1,X3))
| ? [X7] :
( hBOOL(hAPP(X1,X7))
& hBOOL(hAPP(hAPP(c_member(X4),X7),hAPP(c_List_Oset(X4),X5))) )
| hAPP(hAPP(c_List_Oappend(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6)) != X0 ) )
& ( ? [X5,X6] :
( hAPP(c_List_Ofilter(X4,X1),X6) = X2
& hBOOL(hAPP(X1,X3))
& ! [X7] :
( ~ hBOOL(hAPP(X1,X7))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X7),hAPP(c_List_Oset(X4),X5))) )
& hAPP(hAPP(c_List_Oappend(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6)) = X0 )
| ~ sP75(X2,X1,X4,X3,X0) ) ),
inference(nnf_transformation,[],[f14533]) ).
fof(f14533,plain,
! [X2,X1,X4,X3,X0] :
( sP75(X2,X1,X4,X3,X0)
<=> ? [X5,X6] :
( hAPP(c_List_Ofilter(X4,X1),X6) = X2
& hBOOL(hAPP(X1,X3))
& ! [X7] :
( ~ hBOOL(hAPP(X1,X7))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X7),hAPP(c_List_Oset(X4),X5))) )
& hAPP(hAPP(c_List_Oappend(X4),X5),hAPP(hAPP(c_List_Olist_OCons(X4),X3),X6)) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP75])]) ).
fof(f32300,plain,
spl625_714,
inference(avatar_split_clause,[],[f23241,f32298]) ).
fof(f32298,plain,
( spl625_714
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,X4))
| ~ sP72(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_714])]) ).
fof(f23241,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,X4))
| ~ sP72(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16499]) ).
fof(f16499,plain,
! [X0,X1,X2,X3,X4] :
( ( sP72(X0,X1,X2,X3,X4)
| ! [X5] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X5,X1,X0)
| ~ c_Natural_Oevaln(X2,X4,X1,X5) )
| ~ hBOOL(hAPP(X3,X4)) )
& ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),sK547(X0,X1,X2,X3,X4),X1,X0)
& c_Natural_Oevaln(X2,X4,X1,sK547(X0,X1,X2,X3,X4))
& hBOOL(hAPP(X3,X4)) )
| ~ sP72(X0,X1,X2,X3,X4) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK547])],[f16497,f16498]) ).
fof(f16498,plain,
! [X0,X1,X2,X3,X4] :
( ? [X6] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X6,X1,X0)
& c_Natural_Oevaln(X2,X4,X1,X6) )
=> ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),sK547(X0,X1,X2,X3,X4),X1,X0)
& c_Natural_Oevaln(X2,X4,X1,sK547(X0,X1,X2,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f16497,plain,
! [X0,X1,X2,X3,X4] :
( ( sP72(X0,X1,X2,X3,X4)
| ! [X5] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X5,X1,X0)
| ~ c_Natural_Oevaln(X2,X4,X1,X5) )
| ~ hBOOL(hAPP(X3,X4)) )
& ( ( ? [X6] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X6,X1,X0)
& c_Natural_Oevaln(X2,X4,X1,X6) )
& hBOOL(hAPP(X3,X4)) )
| ~ sP72(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f16496]) ).
fof(f16496,plain,
! [X0,X1,X3,X4,X2] :
( ( sP72(X0,X1,X3,X4,X2)
| ! [X5] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
| ~ c_Natural_Oevaln(X3,X2,X1,X5) )
| ~ hBOOL(hAPP(X4,X2)) )
& ( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) )
| ~ sP72(X0,X1,X3,X4,X2) ) ),
inference(flattening,[],[f16495]) ).
fof(f16495,plain,
! [X0,X1,X3,X4,X2] :
( ( sP72(X0,X1,X3,X4,X2)
| ! [X5] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
| ~ c_Natural_Oevaln(X3,X2,X1,X5) )
| ~ hBOOL(hAPP(X4,X2)) )
& ( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) )
| ~ sP72(X0,X1,X3,X4,X2) ) ),
inference(nnf_transformation,[],[f14527]) ).
fof(f14527,plain,
! [X0,X1,X3,X4,X2] :
( sP72(X0,X1,X3,X4,X2)
<=> ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP72])]) ).
fof(f32296,plain,
( ~ spl625_712
| spl625_713
| ~ spl625_348
| ~ spl625_432 ),
inference(avatar_split_clause,[],[f31182,f30875,f30490,f32293,f32289]) ).
fof(f32289,plain,
( spl625_712
<=> class_Int_Onumber__ring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_712])]) ).
fof(f30490,plain,
( spl625_348
<=> 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,[spl625_348])]) ).
fof(f30875,plain,
( spl625_432
<=> ! [X0] :
( c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_432])]) ).
fof(f31182,plain,
( c_Int_Oiszero(tc_Code__Numeral_Ocode__numeral,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))
| ~ class_Int_Onumber__ring(tc_Code__Numeral_Ocode__numeral)
| ~ spl625_348
| ~ spl625_432 ),
inference(superposition,[],[f30876,f30492]) ).
fof(f30492,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)
| ~ spl625_348 ),
inference(avatar_component_clause,[],[f30490]) ).
fof(f30876,plain,
( ! [X0] :
( c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) )
| ~ spl625_432 ),
inference(avatar_component_clause,[],[f30875]) ).
fof(f32287,plain,
spl625_711,
inference(avatar_split_clause,[],[f23019,f32285]) ).
fof(f32285,plain,
( spl625_711
<=> ! [X4,X0,X3,X2,X1] :
( hBOOL(hAPP(X3,X4))
| ~ sP69(X0,X1,X2,X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_711])]) ).
fof(f23019,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,X4))
| ~ sP69(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f16389]) ).
fof(f16389,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),sK501(X0,X1,X2,X3,X4),X1,X0)
& c_Natural_Oevaln(X2,X4,X1,sK501(X0,X1,X2,X3,X4))
& hBOOL(hAPP(X3,X4)) )
| ~ sP69(X0,X1,X2,X3,X4) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK501])],[f16387,f16388]) ).
fof(f16388,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X5,X1,X0)
& c_Natural_Oevaln(X2,X4,X1,X5) )
=> ( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),sK501(X0,X1,X2,X3,X4),X1,X0)
& c_Natural_Oevaln(X2,X4,X1,sK501(X0,X1,X2,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f16387,plain,
! [X0,X1,X2,X3,X4] :
( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X3,X2),X5,X1,X0)
& c_Natural_Oevaln(X2,X4,X1,X5) )
& hBOOL(hAPP(X3,X4)) )
| ~ sP69(X0,X1,X2,X3,X4) ),
inference(rectify,[],[f16386]) ).
fof(f16386,plain,
! [X0,X1,X3,X4,X2] :
( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) )
| ~ sP69(X0,X1,X3,X4,X2) ),
inference(nnf_transformation,[],[f14521]) ).
fof(f14521,plain,
! [X0,X1,X3,X4,X2] :
( ( ? [X5] :
( c_Natural_Oevaln(c_Com_Ocom_OWhile(X4,X3),X5,X1,X0)
& c_Natural_Oevaln(X3,X2,X1,X5) )
& hBOOL(hAPP(X4,X2)) )
| ~ sP69(X0,X1,X3,X4,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP69])]) ).
fof(f32283,plain,
spl625_710,
inference(avatar_split_clause,[],[f22573,f32281]) ).
fof(f32281,plain,
( spl625_710
<=> ! [X0,X3,X2,X1] :
( sP65(X0,X1,X2,X3)
| ~ sP66(X0,X1,X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_710])]) ).
fof(f22573,plain,
! [X2,X3,X0,X1] :
( sP65(X0,X1,X2,X3)
| ~ sP66(X0,X1,X3,X2) ),
inference(cnf_transformation,[],[f16316]) ).
fof(f16316,plain,
! [X0,X1,X2,X3] :
( ( sP65(X0,X1,X2,X3)
| ~ sP66(X0,X1,X3,X2) )
& ( sP66(X0,X1,X3,X2)
| ~ sP65(X0,X1,X2,X3) ) ),
inference(nnf_transformation,[],[f14517]) ).
fof(f14517,plain,
! [X0,X1,X2,X3] :
( sP65(X0,X1,X2,X3)
<=> sP66(X0,X1,X3,X2) ),
inference(definition_folding,[],[f9160,f14516,f14515]) ).
fof(f14515,plain,
! [X0,X1,X2,X3] :
( sP65(X0,X1,X2,X3)
<=> ? [X4] :
( hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP65])]) ).
fof(f14516,plain,
! [X0,X1,X3,X2] :
( sP66(X0,X1,X3,X2)
<=> ( ? [X5] :
( hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X1)) )
| ? [X6] :
( hBOOL(hAPP(X0,X6))
& hBOOL(hAPP(hAPP(c_member(X3),X6),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP66])]) ).
fof(f9160,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( hBOOL(hAPP(X0,X4))
& hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))) )
<=> ( ? [X5] :
( hBOOL(hAPP(X0,X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X1)) )
| ? [X6] :
( hBOOL(hAPP(X0,X6))
& hBOOL(hAPP(hAPP(c_member(X3),X6),X2)) ) ) ),
inference(rectify,[],[f244]) ).
fof(f244,axiom,
! [X5,X21,X19,X4] :
( ? [X2] :
( hBOOL(hAPP(X5,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X19),X21))) )
<=> ( ? [X2] :
( hBOOL(hAPP(X5,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),X21)) )
| ? [X2] :
( hBOOL(hAPP(X5,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),X19)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32279,plain,
spl625_709,
inference(avatar_split_clause,[],[f22572,f32277]) ).
fof(f32277,plain,
( spl625_709
<=> ! [X0,X3,X2,X1] :
( sP66(X0,X1,X3,X2)
| ~ sP65(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_709])]) ).
fof(f22572,plain,
! [X2,X3,X0,X1] :
( sP66(X0,X1,X3,X2)
| ~ sP65(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16316]) ).
fof(f32275,plain,
spl625_708,
inference(avatar_split_clause,[],[f22288,f32273]) ).
fof(f32273,plain,
( spl625_708
<=> ! [X2,X0,X1,X3] :
( X0 = X2
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_708])]) ).
fof(f22288,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ),
inference(cnf_transformation,[],[f16104]) ).
fof(f16104,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OWhile(X1,X0) = c_Com_Ocom_OWhile(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ) ),
inference(flattening,[],[f16103]) ).
fof(f16103,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OWhile(X1,X0) = c_Com_Ocom_OWhile(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ) ),
inference(nnf_transformation,[],[f9070]) ).
fof(f9070,plain,
! [X0,X1,X2,X3] :
( c_Com_Ocom_OWhile(X1,X0) = c_Com_Ocom_OWhile(X3,X2)
<=> ( X0 = X2
& X1 = X3 ) ),
inference(rectify,[],[f79]) ).
fof(f79,axiom,
! [X10,X51,X13,X53] :
( c_Com_Ocom_OWhile(X51,X10) = c_Com_Ocom_OWhile(X53,X13)
<=> ( X10 = X13
& X51 = X53 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32271,plain,
spl625_707,
inference(avatar_split_clause,[],[f22287,f32269]) ).
fof(f32269,plain,
( spl625_707
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_707])]) ).
fof(f22287,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OWhile(X3,X2) ),
inference(cnf_transformation,[],[f16104]) ).
fof(f32267,plain,
spl625_706,
inference(avatar_split_clause,[],[f22285,f32265]) ).
fof(f32265,plain,
( spl625_706
<=> ! [X2,X0,X1,X3] :
( X0 = X2
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_706])]) ).
fof(f22285,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ),
inference(cnf_transformation,[],[f16102]) ).
fof(f16102,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OAss(X1,X0) = c_Com_Ocom_OAss(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ) ),
inference(flattening,[],[f16101]) ).
fof(f16101,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OAss(X1,X0) = c_Com_Ocom_OAss(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ) ),
inference(nnf_transformation,[],[f9069]) ).
fof(f9069,plain,
! [X0,X1,X2,X3] :
( c_Com_Ocom_OAss(X1,X0) = c_Com_Ocom_OAss(X3,X2)
<=> ( X0 = X2
& X1 = X3 ) ),
inference(rectify,[],[f80]) ).
fof(f80,axiom,
! [X51,X52,X53,X54] :
( c_Com_Ocom_OAss(X52,X51) = c_Com_Ocom_OAss(X54,X53)
<=> ( X51 = X53
& X52 = X54 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32263,plain,
spl625_705,
inference(avatar_split_clause,[],[f22284,f32261]) ).
fof(f32261,plain,
( spl625_705
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_705])]) ).
fof(f22284,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OAss(X3,X2) ),
inference(cnf_transformation,[],[f16102]) ).
fof(f32259,plain,
spl625_704,
inference(avatar_split_clause,[],[f22282,f32257]) ).
fof(f32257,plain,
( spl625_704
<=> ! [X2,X0,X1,X3] :
( X0 = X2
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_704])]) ).
fof(f22282,plain,
! [X2,X3,X0,X1] :
( X0 = X2
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ),
inference(cnf_transformation,[],[f16100]) ).
fof(f16100,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OSemi(X1,X0) = c_Com_Ocom_OSemi(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ) ),
inference(flattening,[],[f16099]) ).
fof(f16099,plain,
! [X0,X1,X2,X3] :
( ( c_Com_Ocom_OSemi(X1,X0) = c_Com_Ocom_OSemi(X3,X2)
| X0 != X2
| X1 != X3 )
& ( ( X0 = X2
& X1 = X3 )
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ) ),
inference(nnf_transformation,[],[f9068]) ).
fof(f9068,plain,
! [X0,X1,X2,X3] :
( c_Com_Ocom_OSemi(X1,X0) = c_Com_Ocom_OSemi(X3,X2)
<=> ( X0 = X2
& X1 = X3 ) ),
inference(rectify,[],[f81]) ).
fof(f81,axiom,
! [X55,X56,X57,X58] :
( c_Com_Ocom_OSemi(X56,X55) = c_Com_Ocom_OSemi(X58,X57)
<=> ( X55 = X57
& X56 = X58 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32255,plain,
spl625_703,
inference(avatar_split_clause,[],[f22281,f32253]) ).
fof(f32253,plain,
( spl625_703
<=> ! [X0,X3,X2,X1] :
( X1 = X3
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_703])]) ).
fof(f22281,plain,
! [X2,X3,X0,X1] :
( X1 = X3
| c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ),
inference(cnf_transformation,[],[f16100]) ).
fof(f32251,plain,
spl625_702,
inference(avatar_split_clause,[],[f22272,f32249]) ).
fof(f32249,plain,
( spl625_702
<=> ! [X0,X3,X2,X1] :
( sP56(X2,X0,X3,X1)
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_702])]) ).
fof(f22272,plain,
! [X2,X3,X0,X1] :
( sP56(X2,X0,X3,X1)
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16091]) ).
fof(f16091,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
| ~ sP56(X2,X0,X3,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = X0
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)) )
& ( ( sP56(X2,X0,X3,X1)
& c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) != X0
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)) )
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
inference(flattening,[],[f16090]) ).
fof(f16090,plain,
! [X0,X1,X2,X3] :
( ( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
| ~ sP56(X2,X0,X3,X1)
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = X0
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)) )
& ( ( sP56(X2,X0,X3,X1)
& c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) != X0
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)) )
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14499]) ).
fof(f14499,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
<=> ( sP56(X2,X0,X3,X1)
& c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) != X0
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)) ) ),
inference(definition_folding,[],[f13451,f14498]) ).
fof(f14498,plain,
! [X2,X0,X3,X1] :
( sP56(X2,X0,X3,X1)
<=> ! [X4] :
( ? [X5] :
( hBOOL(hAPP(hAPP(X2,X4),X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP56])]) ).
fof(f13451,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
<=> ( ! [X4] :
( ? [X5] :
( hBOOL(hAPP(hAPP(X2,X4),X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),X1)) )
& c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) != X0
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)) ) ),
inference(ennf_transformation,[],[f9065]) ).
fof(f9065,plain,
! [X0,X1,X2,X3] :
( c_Wellfounded_Omax__extp(X3,X2,X1,X0)
<=> ( ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X3),X4),X1))
=> ? [X5] :
( hBOOL(hAPP(hAPP(X2,X4),X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) ) )
& c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) != X0
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1)) ) ),
inference(rectify,[],[f3342]) ).
fof(f3342,axiom,
! [X7,X8,X42,X4] :
( c_Wellfounded_Omax__extp(X4,X42,X8,X7)
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),X8))
=> ? [X118] :
( hBOOL(hAPP(hAPP(X42,X2),X118))
& hBOOL(hAPP(hAPP(c_member(X4),X118),X7)) ) )
& c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) != X7
& hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X7))
& hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X8)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32247,plain,
( spl625_701
| ~ spl625_255
| ~ spl625_421 ),
inference(avatar_split_clause,[],[f31173,f30830,f30051,f32245]) ).
fof(f32245,plain,
( spl625_701
<=> ! [X0] : sP5(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_701])]) ).
fof(f30051,plain,
( spl625_255
<=> ! [X0] : sP5(hAPP(c_Int_Onat,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_255])]) ).
fof(f30830,plain,
( spl625_421
<=> ! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_421])]) ).
fof(f31173,plain,
( ! [X0] : sP5(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ spl625_255
| ~ spl625_421 ),
inference(superposition,[],[f30052,f30831]) ).
fof(f30831,plain,
( ! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0
| ~ spl625_421 ),
inference(avatar_component_clause,[],[f30830]) ).
fof(f30052,plain,
( ! [X0] : sP5(hAPP(c_Int_Onat,X0),X0)
| ~ spl625_255 ),
inference(avatar_component_clause,[],[f30051]) ).
fof(f32243,plain,
spl625_700,
inference(avatar_split_clause,[],[f22270,f32241]) ).
fof(f32241,plain,
( spl625_700
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_700])]) ).
fof(f22270,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X0))
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16091]) ).
fof(f32239,plain,
spl625_699,
inference(avatar_split_clause,[],[f22269,f32237]) ).
fof(f32237,plain,
( spl625_699
<=> ! [X0,X3,X2,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_699])]) ).
fof(f22269,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X3),X1))
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16091]) ).
fof(f32235,plain,
spl625_698,
inference(avatar_split_clause,[],[f21298,f32233]) ).
fof(f32233,plain,
( spl625_698
<=> ! [X0,X3,X2,X1] : c_Nitpick_Ofold__graph_H(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_698])]) ).
fof(f21298,plain,
! [X2,X3,X0,X1] : c_Nitpick_Ofold__graph_H(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),X0),
inference(cnf_transformation,[],[f8237]) ).
fof(f8237,plain,
! [X0,X1,X2,X3] : c_Nitpick_Ofold__graph_H(X3,X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)),X0),
inference(rectify,[],[f538]) ).
fof(f538,axiom,
! [X116,X1,X24,X4] : c_Nitpick_Ofold__graph_H(X4,X24,X1,X116,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X116),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32231,plain,
spl625_697,
inference(avatar_split_clause,[],[f21297,f32229]) ).
fof(f32229,plain,
( spl625_697
<=> ! [X2,X0,X1,X3] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_697])]) ).
fof(f21297,plain,
! [X2,X3,X0,X1] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0,
inference(cnf_transformation,[],[f8236]) ).
fof(f8236,plain,
! [X0,X1,X2,X3] : hAPP(c_List_Ofoldl(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X0,
inference(rectify,[],[f4209]) ).
fof(f4209,axiom,
! [X6,X1,X24,X4] : hAPP(c_List_Ofoldl(X4,X24,X1,X6),c_List_Olist_ONil(X24)) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32227,plain,
spl625_696,
inference(avatar_split_clause,[],[f21296,f32225]) ).
fof(f32225,plain,
( spl625_696
<=> ! [X2,X0,X1,X3] : hAPP(c_Option_Ooption_Ooption__case(X3,X2,X1,X0),c_Option_Ooption_ONone(X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_696])]) ).
fof(f21296,plain,
! [X2,X3,X0,X1] : hAPP(c_Option_Ooption_Ooption__case(X3,X2,X1,X0),c_Option_Ooption_ONone(X2)) = X1,
inference(cnf_transformation,[],[f8235]) ).
fof(f8235,plain,
! [X0,X1,X2,X3] : hAPP(c_Option_Ooption_Ooption__case(X3,X2,X1,X0),c_Option_Ooption_ONone(X2)) = X1,
inference(rectify,[],[f1179]) ).
fof(f1179,axiom,
! [X67,X25,X24,X4] : hAPP(c_Option_Ooption_Ooption__case(X4,X24,X25,X67),c_Option_Ooption_ONone(X24)) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32223,plain,
spl625_695,
inference(avatar_split_clause,[],[f21295,f32221]) ).
fof(f32221,plain,
( spl625_695
<=> ! [X2,X0,X1,X3] : hAPP(c_List_Olist_Olist__case(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_695])]) ).
fof(f21295,plain,
! [X2,X3,X0,X1] : hAPP(c_List_Olist_Olist__case(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X1,
inference(cnf_transformation,[],[f8234]) ).
fof(f8234,plain,
! [X0,X1,X2,X3] : hAPP(c_List_Olist_Olist__case(X3,X2,X1,X0),c_List_Olist_ONil(X2)) = X1,
inference(rectify,[],[f4034]) ).
fof(f4034,axiom,
! [X67,X25,X24,X4] : hAPP(c_List_Olist_Olist__case(X4,X24,X25,X67),c_List_Olist_ONil(X24)) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32219,plain,
spl625_694,
inference(avatar_split_clause,[],[f21294,f32217]) ).
fof(f32217,plain,
( spl625_694
<=> ! [X0,X3,X2,X1] : hAPP(X1,X0) = c_Com_Ovname_Ovname__rec(X3,X2,X1,c_Com_Ovname_OLoc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_694])]) ).
fof(f21294,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0) = c_Com_Ovname_Ovname__rec(X3,X2,X1,c_Com_Ovname_OLoc(X0)),
inference(cnf_transformation,[],[f8233]) ).
fof(f8233,plain,
! [X0,X1,X2,X3] : hAPP(X1,X0) = c_Com_Ovname_Ovname__rec(X3,X2,X1,c_Com_Ovname_OLoc(X0)),
inference(rectify,[],[f114]) ).
fof(f114,axiom,
! [X70,X67,X25,X4] : c_Com_Ovname_Ovname__rec(X4,X25,X67,c_Com_Ovname_OLoc(X70)) = hAPP(X67,X70),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32215,plain,
spl625_693,
inference(avatar_split_clause,[],[f21292,f32213]) ).
fof(f32213,plain,
( spl625_693
<=> ! [X0,X3,X2,X1] : hAPP(X2,X0) = c_Com_Ovname_Ovname__case(X3,X2,X1,c_Com_Ovname_OGlb(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_693])]) ).
fof(f21292,plain,
! [X2,X3,X0,X1] : hAPP(X2,X0) = c_Com_Ovname_Ovname__case(X3,X2,X1,c_Com_Ovname_OGlb(X0)),
inference(cnf_transformation,[],[f8231]) ).
fof(f8231,plain,
! [X0,X1,X2,X3] : hAPP(X2,X0) = c_Com_Ovname_Ovname__case(X3,X2,X1,c_Com_Ovname_OGlb(X0)),
inference(rectify,[],[f180]) ).
fof(f180,axiom,
! [X103,X67,X25,X4] : c_Com_Ovname_Ovname__case(X4,X25,X67,c_Com_Ovname_OGlb(X103)) = hAPP(X25,X103),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32211,plain,
spl625_692,
inference(avatar_split_clause,[],[f21291,f32209]) ).
fof(f32209,plain,
( spl625_692
<=> ! [X0,X3,X2,X1] : hAPP(X1,X0) = c_Com_Ovname_Ovname__case(X3,X2,X1,c_Com_Ovname_OLoc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_692])]) ).
fof(f21291,plain,
! [X2,X3,X0,X1] : hAPP(X1,X0) = c_Com_Ovname_Ovname__case(X3,X2,X1,c_Com_Ovname_OLoc(X0)),
inference(cnf_transformation,[],[f8230]) ).
fof(f8230,plain,
! [X0,X1,X2,X3] : hAPP(X1,X0) = c_Com_Ovname_Ovname__case(X3,X2,X1,c_Com_Ovname_OLoc(X0)),
inference(rectify,[],[f115]) ).
fof(f115,axiom,
! [X70,X67,X25,X4] : hAPP(X67,X70) = c_Com_Ovname_Ovname__case(X4,X25,X67,c_Com_Ovname_OLoc(X70)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32207,plain,
spl625_691,
inference(avatar_split_clause,[],[f21290,f32205]) ).
fof(f32205,plain,
( spl625_691
<=> ! [X0,X3,X2,X1] : hAPP(X2,X0) = c_Com_Ovname_Ovname__rec(X3,X2,X1,c_Com_Ovname_OGlb(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_691])]) ).
fof(f21290,plain,
! [X2,X3,X0,X1] : hAPP(X2,X0) = c_Com_Ovname_Ovname__rec(X3,X2,X1,c_Com_Ovname_OGlb(X0)),
inference(cnf_transformation,[],[f8229]) ).
fof(f8229,plain,
! [X0,X1,X2,X3] : hAPP(X2,X0) = c_Com_Ovname_Ovname__rec(X3,X2,X1,c_Com_Ovname_OGlb(X0)),
inference(rectify,[],[f181]) ).
fof(f181,axiom,
! [X103,X67,X25,X4] : hAPP(X25,X103) = c_Com_Ovname_Ovname__rec(X4,X25,X67,c_Com_Ovname_OGlb(X103)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32203,plain,
( spl625_690
| ~ spl625_256
| ~ spl625_421 ),
inference(avatar_split_clause,[],[f31172,f30830,f30055,f32201]) ).
fof(f32201,plain,
( spl625_690
<=> ! [X0] : sP6(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_690])]) ).
fof(f30055,plain,
( spl625_256
<=> ! [X1] : sP6(hAPP(c_Int_Onat,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_256])]) ).
fof(f31172,plain,
( ! [X0] : sP6(X0,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))
| ~ spl625_256
| ~ spl625_421 ),
inference(superposition,[],[f30056,f30831]) ).
fof(f30056,plain,
( ! [X1] : sP6(hAPP(c_Int_Onat,X1),X1)
| ~ spl625_256 ),
inference(avatar_component_clause,[],[f30055]) ).
fof(f32199,plain,
spl625_689,
inference(avatar_split_clause,[],[f20954,f32197]) ).
fof(f32197,plain,
( spl625_689
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP33(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_689])]) ).
fof(f20954,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP33(X1,X0,X2) ),
inference(cnf_transformation,[],[f15630]) ).
fof(f15630,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
| ~ sP33(X1,X0,X2) )
& ( sP33(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ) ),
inference(nnf_transformation,[],[f14459]) ).
fof(f14459,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
<=> sP33(X1,X0,X2) ),
inference(definition_folding,[],[f12546,f14458,f14457]) ).
fof(f14457,plain,
! [X0,X1] :
( sP32(X0,X1)
<=> ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP32])]) ).
fof(f14458,plain,
! [X1,X0,X2] :
( sP33(X1,X0,X2)
<=> ( ( sP32(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X0)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)) = X2 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP33])]) ).
fof(f12546,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
<=> ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0))) )
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0))) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X0)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X0)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)) = X2 ) ),
inference(ennf_transformation,[],[f8116]) ).
fof(f8116,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X1),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0))) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0))) ) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X0) )
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X0)),X1)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X0)) = X2 ) ),
inference(rectify,[],[f2409]) ).
fof(f2409,axiom,
! [X230,X78,X123] :
( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X123,X78),X230))
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X78
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X78))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X230)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X78),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X230))) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X78))
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X230)),X78))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X230))) ) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X78
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X230) )
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),X230)),X78)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),X230)) = X123 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32195,plain,
spl625_688,
inference(avatar_split_clause,[],[f20953,f32193]) ).
fof(f32193,plain,
( spl625_688
<=> ! [X2,X0,X1] :
( sP33(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_688])]) ).
fof(f20953,plain,
! [X2,X0,X1] :
( sP33(X1,X0,X2)
| ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(X2,X1),X0)) ),
inference(cnf_transformation,[],[f15630]) ).
fof(f32191,plain,
spl625_687,
inference(avatar_split_clause,[],[f20830,f32189]) ).
fof(f20830,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
| ~ sP29(X0,X1,X2) ),
inference(cnf_transformation,[],[f15514]) ).
fof(f15514,plain,
! [X0,X1,X2] :
( ( ~ hBOOL(hAPP(hAPP(X2,X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X1)) )
| ~ sP29(X0,X1,X2) ),
inference(rectify,[],[f15513]) ).
fof(f15513,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) )
| ~ sP29(X2,X1,X0) ),
inference(nnf_transformation,[],[f14451]) ).
fof(f14451,plain,
! [X2,X1,X0] :
( ( ~ hBOOL(hAPP(hAPP(X0,X1),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X2),X1)) )
| ~ sP29(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP29])]) ).
fof(f32187,plain,
spl625_686,
inference(avatar_split_clause,[],[f20514,f32185]) ).
fof(f32185,plain,
( spl625_686
<=> ! [X0,X1] :
( sK246(X0,X1) != sK247(X0,X1)
| ~ sP24(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_686])]) ).
fof(f20514,plain,
! [X0,X1] :
( sK246(X0,X1) != sK247(X0,X1)
| ~ sP24(X0,X1) ),
inference(cnf_transformation,[],[f15395]) ).
fof(f15395,plain,
! [X0,X1] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),sK246(X0,X1)),sK247(X0,X1))
& sK246(X0,X1) != sK247(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK247(X0,X1)),X1))
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK246(X0,X1)),X1)) )
| ~ sP24(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK246,sK247])],[f15392,f15394,f15393]) ).
fof(f15393,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X2),X3)
& X2 != X3
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),X3),X1)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),X2),X1)) )
=> ( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),sK246(X0,X1)),X3)
& sK246(X0,X1) != X3
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),X3),X1)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK246(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15394,plain,
! [X0,X1] :
( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),sK246(X0,X1)),X3)
& sK246(X0,X1) != X3
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),X3),X1)) )
=> ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),sK246(X0,X1)),sK247(X0,X1))
& sK246(X0,X1) != sK247(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),sK247(X0,X1)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f15392,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X2),X3)
& X2 != X3
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),X3),X1)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_HOL_Obool)),X2),X1)) )
| ~ sP24(X0,X1) ),
inference(rectify,[],[f15391]) ).
fof(f15391,plain,
! [X2,X1] :
( ? [X4] :
( ? [X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)
& X4 != X5
& hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X5),X1)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X4),X1)) )
| ~ sP24(X2,X1) ),
inference(nnf_transformation,[],[f14443]) ).
fof(f14443,plain,
! [X2,X1] :
( ? [X4] :
( ? [X5] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X4),X5)
& X4 != X5
& hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X5),X1)) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(X2,tc_HOL_Obool)),X4),X1)) )
| ~ sP24(X2,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP24])]) ).
fof(f32183,plain,
spl625_685,
inference(avatar_split_clause,[],[f20506,f32181]) ).
fof(f32181,plain,
( spl625_685
<=> ! [X2,X0,X1] :
( c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_685])]) ).
fof(f20506,plain,
! [X2,X0,X1] :
( c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0) ),
inference(cnf_transformation,[],[f12198]) ).
fof(f12198,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0)
| ~ c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0) ),
inference(ennf_transformation,[],[f7851]) ).
fof(f7851,plain,
! [X0,X1,X2] :
( c_Hoare__Mirabelle_Otriple__valid(X2,hAPP(c_Nat_OSuc,X1),X0)
=> c_Hoare__Mirabelle_Otriple__valid(X2,X1,X0) ),
inference(rectify,[],[f1335]) ).
fof(f1335,axiom,
! [X91,X88,X23] :
( c_Hoare__Mirabelle_Otriple__valid(X23,hAPP(c_Nat_OSuc,X88),X91)
=> c_Hoare__Mirabelle_Otriple__valid(X23,X88,X91) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32179,plain,
spl625_684,
inference(avatar_split_clause,[],[f19393,f32177]) ).
fof(f32177,plain,
( spl625_684
<=> ! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_684])]) ).
fof(f19393,plain,
! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0,
inference(cnf_transformation,[],[f6928]) ).
fof(f6928,plain,
! [X0,X1,X2] : hAPP(c_Fun_Ocomp(X2,X2,X1,c_Fun_Oid(X2)),X0) = X0,
inference(rectify,[],[f3479]) ).
fof(f3479,axiom,
! [X0,X4,X24] : hAPP(c_Fun_Ocomp(X24,X24,X4,c_Fun_Oid(X24)),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32175,plain,
spl625_683,
inference(avatar_split_clause,[],[f19392,f32173]) ).
fof(f32173,plain,
( spl625_683
<=> ! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_683])]) ).
fof(f19392,plain,
! [X2,X0,X1] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0,
inference(cnf_transformation,[],[f6927]) ).
fof(f6927,plain,
! [X0,X1,X2] : hAPP(c_Fun_Ocomp(X2,X1,X2,X0),c_Fun_Oid(X2)) = X0,
inference(rectify,[],[f3480]) ).
fof(f3480,axiom,
! [X1,X24,X4] : hAPP(c_Fun_Ocomp(X4,X24,X4,X1),c_Fun_Oid(X4)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32171,plain,
spl625_682,
inference(avatar_split_clause,[],[f19391,f32169]) ).
fof(f32169,plain,
( spl625_682
<=> ! [X2,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_682])]) ).
fof(f19391,plain,
! [X2,X0,X1] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X0)),
inference(cnf_transformation,[],[f6926]) ).
fof(f6926,plain,
! [X0,X1,X2] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X0)),
inference(rectify,[],[f1697]) ).
fof(f1697,axiom,
! [X20,X1,X4] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32167,plain,
spl625_681,
inference(avatar_split_clause,[],[f19094,f32165]) ).
fof(f32165,plain,
( spl625_681
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_681])]) ).
fof(f19094,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) ),
inference(cnf_transformation,[],[f14992]) ).
fof(f14992,plain,
! [X0,X1] :
( ( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
| ~ c_Wellfounded_Oacyclic(X1,X0) )
& ( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
inference(nnf_transformation,[],[f6805]) ).
fof(f6805,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0))
<=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f4762]) ).
fof(f4762,axiom,
! [X60,X4] :
( c_Wellfounded_Oacyclic(X4,hAPP(c_Relation_Oconverse(X4,X4),X60))
<=> c_Wellfounded_Oacyclic(X4,X60) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32163,plain,
spl625_680,
inference(avatar_split_clause,[],[f19093,f32161]) ).
fof(f32161,plain,
( spl625_680
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_680])]) ).
fof(f19093,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Oacyclic(X1,hAPP(c_Relation_Oconverse(X1,X1),X0)) ),
inference(cnf_transformation,[],[f14992]) ).
fof(f32159,plain,
( spl625_679
| ~ spl625_234
| ~ spl625_286 ),
inference(avatar_split_clause,[],[f30390,f30186,f29960,f32157]) ).
fof(f32157,plain,
( spl625_679
<=> ! [X0] : c_Fun_Oinj__on(tc_Int_Oint,tc_Int_Oint,c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_679])]) ).
fof(f29960,plain,
( spl625_234
<=> c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_234])]) ).
fof(f30186,plain,
( spl625_286
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_286])]) ).
fof(f30390,plain,
( ! [X0] : c_Fun_Oinj__on(tc_Int_Oint,tc_Int_Oint,c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0)
| ~ spl625_234
| ~ spl625_286 ),
inference(superposition,[],[f30187,f29962]) ).
fof(f29962,plain,
( c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint)
| ~ spl625_234 ),
inference(avatar_component_clause,[],[f29960]) ).
fof(f30187,plain,
( ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0)
| ~ spl625_286 ),
inference(avatar_component_clause,[],[f30186]) ).
fof(f32155,plain,
spl625_678,
inference(avatar_split_clause,[],[f19050,f32153]) ).
fof(f32153,plain,
( spl625_678
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Oof__nat,X0) != hAPP(c_Code__Numeral_Oof__nat,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_678])]) ).
fof(f19050,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Oof__nat,X0) != hAPP(c_Code__Numeral_Oof__nat,X1) ),
inference(cnf_transformation,[],[f14954]) ).
fof(f14954,plain,
! [X0,X1] :
( ( hAPP(c_Code__Numeral_Oof__nat,X0) = hAPP(c_Code__Numeral_Oof__nat,X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Code__Numeral_Oof__nat,X0) != hAPP(c_Code__Numeral_Oof__nat,X1) ) ),
inference(nnf_transformation,[],[f6786]) ).
fof(f6786,plain,
! [X0,X1] :
( hAPP(c_Code__Numeral_Oof__nat,X0) = hAPP(c_Code__Numeral_Oof__nat,X1)
<=> X0 = X1 ),
inference(rectify,[],[f4623]) ).
fof(f4623,axiom,
! [X123,X78] :
( hAPP(c_Code__Numeral_Oof__nat,X78) = hAPP(c_Code__Numeral_Oof__nat,X123)
<=> X78 = X123 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32151,plain,
spl625_677,
inference(avatar_split_clause,[],[f19046,f32149]) ).
fof(f32149,plain,
( spl625_677
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Onat__of,X0) != hAPP(c_Code__Numeral_Onat__of,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_677])]) ).
fof(f19046,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Code__Numeral_Onat__of,X0) != hAPP(c_Code__Numeral_Onat__of,X1) ),
inference(cnf_transformation,[],[f14952]) ).
fof(f14952,plain,
! [X0,X1] :
( ( hAPP(c_Code__Numeral_Onat__of,X0) = hAPP(c_Code__Numeral_Onat__of,X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Code__Numeral_Onat__of,X0) != hAPP(c_Code__Numeral_Onat__of,X1) ) ),
inference(nnf_transformation,[],[f6784]) ).
fof(f6784,plain,
! [X0,X1] :
( hAPP(c_Code__Numeral_Onat__of,X0) = hAPP(c_Code__Numeral_Onat__of,X1)
<=> X0 = X1 ),
inference(rectify,[],[f4642]) ).
fof(f4642,axiom,
! [X153,X59] :
( hAPP(c_Code__Numeral_Onat__of,X59) = hAPP(c_Code__Numeral_Onat__of,X153)
<=> X59 = X153 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32147,plain,
spl625_676,
inference(avatar_split_clause,[],[f19044,f32145]) ).
fof(f32145,plain,
( spl625_676
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Int_ORep__Integ,X0) != hAPP(c_Int_ORep__Integ,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_676])]) ).
fof(f19044,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Int_ORep__Integ,X0) != hAPP(c_Int_ORep__Integ,X1) ),
inference(cnf_transformation,[],[f14951]) ).
fof(f14951,plain,
! [X0,X1] :
( ( hAPP(c_Int_ORep__Integ,X0) = hAPP(c_Int_ORep__Integ,X1)
| X0 != X1 )
& ( X0 = X1
| hAPP(c_Int_ORep__Integ,X0) != hAPP(c_Int_ORep__Integ,X1) ) ),
inference(nnf_transformation,[],[f6783]) ).
fof(f6783,plain,
! [X0,X1] :
( hAPP(c_Int_ORep__Integ,X0) = hAPP(c_Int_ORep__Integ,X1)
<=> X0 = X1 ),
inference(rectify,[],[f2536]) ).
fof(f2536,axiom,
! [X34,X20] :
( hAPP(c_Int_ORep__Integ,X20) = hAPP(c_Int_ORep__Integ,X34)
<=> X20 = X34 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32143,plain,
spl625_675,
inference(avatar_split_clause,[],[f19007,f32141]) ).
fof(f32141,plain,
( spl625_675
<=> ! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != c_List_Oremdups(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_675])]) ).
fof(f19007,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != c_List_Oremdups(X1,X0) ),
inference(cnf_transformation,[],[f14916]) ).
fof(f14916,plain,
! [X0,X1] :
( ( c_List_Olist_ONil(X1) = c_List_Oremdups(X1,X0)
| c_List_Olist_ONil(X1) != X0 )
& ( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != c_List_Oremdups(X1,X0) ) ),
inference(nnf_transformation,[],[f6769]) ).
fof(f6769,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = c_List_Oremdups(X1,X0)
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f4210]) ).
fof(f4210,axiom,
! [X20,X4] :
( c_List_Olist_ONil(X4) = c_List_Oremdups(X4,X20)
<=> c_List_Olist_ONil(X4) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32139,plain,
spl625_674,
inference(avatar_split_clause,[],[f18995,f32137]) ).
fof(f32137,plain,
( spl625_674
<=> ! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| c_List_Oremdups(X1,X0) != X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_674])]) ).
fof(f18995,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| c_List_Oremdups(X1,X0) != X0 ),
inference(cnf_transformation,[],[f14904]) ).
fof(f14904,plain,
! [X0,X1] :
( ( c_List_Oremdups(X1,X0) = X0
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) )
& ( hBOOL(hAPP(c_List_Odistinct(X1),X0))
| c_List_Oremdups(X1,X0) != X0 ) ),
inference(nnf_transformation,[],[f6765]) ).
fof(f6765,plain,
! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
<=> hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(rectify,[],[f4201]) ).
fof(f4201,axiom,
! [X258,X4] :
( c_List_Oremdups(X4,X258) = X258
<=> hBOOL(hAPP(c_List_Odistinct(X4),X258)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32135,plain,
spl625_673,
inference(avatar_split_clause,[],[f18931,f32133]) ).
fof(f32133,plain,
( spl625_673
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ~ hBOOL(hAPP(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_673])]) ).
fof(f18931,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ~ hBOOL(hAPP(X1,X2)) ),
inference(cnf_transformation,[],[f11261]) ).
fof(f11261,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1)))
| ! [X2] : ~ hBOOL(hAPP(X1,X2)) ),
inference(ennf_transformation,[],[f6739]) ).
fof(f6739,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(X1,X2))
=> hBOOL(hAPP(X1,c_Hilbert__Choice_OEps(X0,X1))) ),
inference(rectify,[],[f3885]) ).
fof(f3885,axiom,
! [X4,X5] :
( ? [X48] : hBOOL(hAPP(X5,X48))
=> hBOOL(hAPP(X5,c_Hilbert__Choice_OEps(X4,X5))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32131,plain,
spl625_672,
inference(avatar_split_clause,[],[f18662,f32129]) ).
fof(f32129,plain,
( spl625_672
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_672])]) ).
fof(f18662,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X0)) ),
inference(cnf_transformation,[],[f10957]) ).
fof(f10957,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X0)) ),
inference(ennf_transformation,[],[f6525]) ).
fof(f6525,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X1),X0))
=> X0 = X1 ),
inference(rectify,[],[f135]) ).
fof(f135,axiom,
! [X91,X92] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X92),X91))
=> X91 = X92 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32127,plain,
spl625_671,
inference(avatar_split_clause,[],[f18658,f32125]) ).
fof(f32125,plain,
( spl625_671
<=> ! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_671])]) ).
fof(f18658,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ),
inference(cnf_transformation,[],[f10953]) ).
fof(f10953,plain,
! [X0,X1] :
( X0 = X1
| hAPP(c_Nat_OSuc,X0) != hAPP(c_Nat_OSuc,X1) ),
inference(ennf_transformation,[],[f6522]) ).
fof(f6522,plain,
! [X0,X1] :
( hAPP(c_Nat_OSuc,X0) = hAPP(c_Nat_OSuc,X1)
=> X0 = X1 ),
inference(rectify,[],[f1266]) ).
fof(f1266,axiom,
! [X29,X22] :
( hAPP(c_Nat_OSuc,X22) = hAPP(c_Nat_OSuc,X29)
=> X22 = X29 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32123,plain,
spl625_670,
inference(avatar_split_clause,[],[f18648,f32121]) ).
fof(f32121,plain,
( spl625_670
<=> ! [X0,X1] :
( sK142(X0,X1) != sK143(X0,X1)
| ~ sP2(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_670])]) ).
fof(f18648,plain,
! [X0,X1] :
( sK142(X0,X1) != sK143(X0,X1)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f14788]) ).
fof(f14788,plain,
! [X0,X1] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(c_List_Oset(X0),sK142(X0,X1))),hAPP(c_List_Oset(X0),sK143(X0,X1)))
& sK142(X0,X1) != sK143(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),sK143(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1)))
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),sK142(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
| ~ sP2(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK142,sK143])],[f14785,f14787,f14786]) ).
fof(f14786,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(c_List_Oset(X0),X2)),hAPP(c_List_Oset(X0),X3))
& X2 != X3
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),X3),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),X2),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
=> ( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(c_List_Oset(X0),sK142(X0,X1))),hAPP(c_List_Oset(X0),X3))
& sK142(X0,X1) != X3
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),X3),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),sK142(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f14787,plain,
! [X0,X1] :
( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(c_List_Oset(X0),sK142(X0,X1))),hAPP(c_List_Oset(X0),X3))
& sK142(X0,X1) != X3
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),X3),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
=> ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(c_List_Oset(X0),sK142(X0,X1))),hAPP(c_List_Oset(X0),sK143(X0,X1)))
& sK142(X0,X1) != sK143(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),sK143(X0,X1)),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f14785,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(c_List_Oset(X0),X2)),hAPP(c_List_Oset(X0),X3))
& X2 != X3
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),X3),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X0)),X2),hAPP(c_List_Oset(tc_List_Olist(X0)),X1))) )
| ~ sP2(X0,X1) ),
inference(rectify,[],[f14784]) ).
fof(f14784,plain,
! [X1,X0] :
( ? [X3] :
( ? [X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),hAPP(c_List_Oset(X1),X4))
& X3 != X4
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) )
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) )
| ~ sP2(X1,X0) ),
inference(nnf_transformation,[],[f14405]) ).
fof(f14405,plain,
! [X1,X0] :
( ? [X3] :
( ? [X4] :
( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(c_List_Oset(X1),X3)),hAPP(c_List_Oset(X1),X4))
& X3 != X4
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) )
& hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X3),hAPP(c_List_Oset(tc_List_Olist(X1)),X0))) )
| ~ sP2(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f32119,plain,
spl625_669,
inference(avatar_split_clause,[],[f18635,f32117]) ).
fof(f32117,plain,
( spl625_669
<=> ! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_669])]) ).
fof(f18635,plain,
! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(cnf_transformation,[],[f10935]) ).
fof(f10935,plain,
! [X0,X1] :
( c_List_Oremdups(X1,X0) = X0
| ~ hBOOL(hAPP(c_List_Odistinct(X1),X0)) ),
inference(ennf_transformation,[],[f6507]) ).
fof(f6507,plain,
! [X0,X1] :
( hBOOL(hAPP(c_List_Odistinct(X1),X0))
=> c_List_Oremdups(X1,X0) = X0 ),
inference(rectify,[],[f4200]) ).
fof(f4200,axiom,
! [X263,X23] :
( hBOOL(hAPP(c_List_Odistinct(X23),X263))
=> c_List_Oremdups(X23,X263) = X263 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32115,plain,
( spl625_668
| ~ spl625_224
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30381,f30166,f29911,f32113]) ).
fof(f32113,plain,
( spl625_668
<=> ! [X0,X1] : c_fequal = c_HOL_Oequal__class_Oequal(tc_sum(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_668])]) ).
fof(f29911,plain,
( spl625_224
<=> ! [X0,X1] : class_HOL_Oequal(tc_sum(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_224])]) ).
fof(f30166,plain,
( spl625_281
<=> ! [X0] :
( c_fequal = c_HOL_Oequal__class_Oequal(X0)
| ~ class_HOL_Oequal(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_281])]) ).
fof(f30381,plain,
( ! [X0,X1] : c_fequal = c_HOL_Oequal__class_Oequal(tc_sum(X0,X1))
| ~ spl625_224
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29912]) ).
fof(f29912,plain,
( ! [X0,X1] : class_HOL_Oequal(tc_sum(X1,X0))
| ~ spl625_224 ),
inference(avatar_component_clause,[],[f29911]) ).
fof(f30167,plain,
( ! [X0] :
( ~ class_HOL_Oequal(X0)
| c_fequal = c_HOL_Oequal__class_Oequal(X0) )
| ~ spl625_281 ),
inference(avatar_component_clause,[],[f30166]) ).
fof(f32111,plain,
spl625_667,
inference(avatar_split_clause,[],[f18612,f32109]) ).
fof(f32109,plain,
( spl625_667
<=> ! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_667])]) ).
fof(f18612,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10912]) ).
fof(f10912,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6488]) ).
fof(f6488,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omax__ext(X1,X0)) ),
inference(rectify,[],[f3358]) ).
fof(f3358,axiom,
! [X60,X4] :
( c_Wellfounded_Owf(X4,X60)
=> c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Omax__ext(X4,X60)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32107,plain,
spl625_666,
inference(avatar_split_clause,[],[f18611,f32105]) ).
fof(f32105,plain,
( spl625_666
<=> ! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_666])]) ).
fof(f18611,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10911]) ).
fof(f10911,plain,
! [X0,X1] :
( c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6487]) ).
fof(f6487,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Owf(tc_fun(X1,tc_HOL_Obool),c_Wellfounded_Omin__ext(X1,X0)) ),
inference(rectify,[],[f3350]) ).
fof(f3350,axiom,
! [X60,X4] :
( c_Wellfounded_Owf(X4,X60)
=> c_Wellfounded_Owf(tc_fun(X4,tc_HOL_Obool),c_Wellfounded_Omin__ext(X4,X60)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32103,plain,
spl625_665,
inference(avatar_split_clause,[],[f18540,f32101]) ).
fof(f32101,plain,
( spl625_665
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_665])]) ).
fof(f18540,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10834]) ).
fof(f10834,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6432]) ).
fof(f6432,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0 ),
inference(rectify,[],[f361]) ).
fof(f361,axiom,
! [X22,X23] :
( class_Lattices_Olattice(X23)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23),X22),X22) = X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32099,plain,
spl625_664,
inference(avatar_split_clause,[],[f18539,f32097]) ).
fof(f32097,plain,
( spl625_664
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_664])]) ).
fof(f18539,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10833]) ).
fof(f10833,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6431]) ).
fof(f6431,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0 ),
inference(rectify,[],[f398]) ).
fof(f398,axiom,
! [X22,X23] :
( class_Lattices_Olattice(X23)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23),X22),X22) = X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32095,plain,
spl625_663,
inference(avatar_split_clause,[],[f18534,f32093]) ).
fof(f32093,plain,
( spl625_663
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__inf(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_663])]) ).
fof(f18534,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(cnf_transformation,[],[f10828]) ).
fof(f10828,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(ennf_transformation,[],[f6426]) ).
fof(f6426,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0 ),
inference(rectify,[],[f369]) ).
fof(f369,axiom,
! [X22,X23] :
( class_Lattices_Osemilattice__inf(X23)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X23),X22),X22) = X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32091,plain,
spl625_662,
inference(avatar_split_clause,[],[f18532,f32089]) ).
fof(f32089,plain,
( spl625_662
<=> ! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_662])]) ).
fof(f18532,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(cnf_transformation,[],[f10826]) ).
fof(f10826,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__sup(X1) ),
inference(ennf_transformation,[],[f6424]) ).
fof(f6424,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0 ),
inference(rectify,[],[f329]) ).
fof(f329,axiom,
! [X32,X23] :
( class_Lattices_Osemilattice__sup(X23)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X23),X32),X32) = X32 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32087,plain,
spl625_661,
inference(avatar_split_clause,[],[f18494,f32085]) ).
fof(f32085,plain,
( spl625_661
<=> ! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X0))
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_661])]) ).
fof(f18494,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X0))
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10790]) ).
fof(f10790,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X0))
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ class_Orderings_Olinorder(X1) ),
inference(flattening,[],[f10789]) ).
fof(f10789,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X0))
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6404]) ).
fof(f6404,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> ( c_List_Olinorder__class_Osorted(X1,X0)
=> c_List_Olinorder__class_Osorted(X1,c_List_Oremdups(X1,X0)) ) ),
inference(rectify,[],[f4266]) ).
fof(f4266,axiom,
! [X124,X23] :
( class_Orderings_Olinorder(X23)
=> ( c_List_Olinorder__class_Osorted(X23,X124)
=> c_List_Olinorder__class_Osorted(X23,c_List_Oremdups(X23,X124)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32083,plain,
spl625_660,
inference(avatar_split_clause,[],[f18480,f32081]) ).
fof(f32081,plain,
( spl625_660
<=> ! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X0))
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_660])]) ).
fof(f18480,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X0))
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10775]) ).
fof(f10775,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X0))
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6390]) ).
fof(f6390,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> c_List_Olinorder__class_Osorted(X1,c_List_Olinorder__class_Osort__key(X1,X1,c_COMBI(X1),X0)) ),
inference(rectify,[],[f4369]) ).
fof(f4369,axiom,
! [X258,X4] :
( class_Orderings_Olinorder(X4)
=> c_List_Olinorder__class_Osorted(X4,c_List_Olinorder__class_Osort__key(X4,X4,c_COMBI(X4),X258)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32079,plain,
spl625_659,
inference(avatar_split_clause,[],[f18478,f32077]) ).
fof(f32077,plain,
( spl625_659
<=> ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_659])]) ).
fof(f18478,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10773]) ).
fof(f10773,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6388]) ).
fof(f6388,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X1),X0),X0) = X0 ),
inference(rectify,[],[f1432]) ).
fof(f1432,axiom,
! [X22,X23] :
( class_Orderings_Olinorder(X23)
=> hAPP(hAPP(c_Orderings_Oord__class_Omin(X23),X22),X22) = X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32075,plain,
spl625_658,
inference(avatar_split_clause,[],[f18476,f32073]) ).
fof(f32073,plain,
( spl625_658
<=> ! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_658])]) ).
fof(f18476,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10771]) ).
fof(f10771,plain,
! [X0,X1] :
( hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6386]) ).
fof(f6386,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X1),X0),X0) = X0 ),
inference(rectify,[],[f2100]) ).
fof(f2100,axiom,
! [X22,X23] :
( class_Orderings_Olinorder(X23)
=> hAPP(hAPP(c_Orderings_Oord__class_Omax(X23),X22),X22) = X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32071,plain,
( spl625_657
| ~ spl625_225
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30380,f30166,f29915,f32069]) ).
fof(f32069,plain,
( spl625_657
<=> ! [X0,X1] : c_fequal = c_HOL_Oequal__class_Oequal(tc_prod(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_657])]) ).
fof(f29915,plain,
( spl625_225
<=> ! [X0,X1] : class_HOL_Oequal(tc_prod(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_225])]) ).
fof(f30380,plain,
( ! [X0,X1] : c_fequal = c_HOL_Oequal__class_Oequal(tc_prod(X0,X1))
| ~ spl625_225
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29916]) ).
fof(f29916,plain,
( ! [X0,X1] : class_HOL_Oequal(tc_prod(X1,X0))
| ~ spl625_225 ),
inference(avatar_component_clause,[],[f29915]) ).
fof(f32067,plain,
spl625_656,
inference(avatar_split_clause,[],[f18458,f32065]) ).
fof(f32065,plain,
( spl625_656
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_656])]) ).
fof(f18458,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f10752]) ).
fof(f10752,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f6369]) ).
fof(f6369,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,c_Groups_Ozero__class_Ozero(X1),X0) ),
inference(rectify,[],[f2107]) ).
fof(f2107,axiom,
! [X32,X23] :
( class_Divides_Osemiring__div(X23)
=> c_Groups_Ozero__class_Ozero(X23) = c_Divides_Odiv__class_Omod(X23,c_Groups_Ozero__class_Ozero(X23),X32) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32063,plain,
spl625_655,
inference(avatar_split_clause,[],[f18457,f32061]) ).
fof(f32061,plain,
( spl625_655
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_655])]) ).
fof(f18457,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f10751]) ).
fof(f10751,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1))
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f6368]) ).
fof(f6368,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Oone__class_Oone(X1)) ),
inference(rectify,[],[f2161]) ).
fof(f2161,axiom,
! [X32,X23] :
( class_Divides_Osemiring__div(X23)
=> c_Groups_Ozero__class_Ozero(X23) = c_Divides_Odiv__class_Omod(X23,X32,c_Groups_Oone__class_Oone(X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32059,plain,
spl625_654,
inference(avatar_split_clause,[],[f18426,f32057]) ).
fof(f32057,plain,
( spl625_654
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Obot__class_Obot(X1)),X0))
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_654])]) ).
fof(f18426,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Obot__class_Obot(X1)),X0))
| ~ class_Orderings_Obot(X1) ),
inference(cnf_transformation,[],[f10719]) ).
fof(f10719,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Obot__class_Obot(X1)),X0))
| ~ class_Orderings_Obot(X1) ),
inference(ennf_transformation,[],[f6338]) ).
fof(f6338,plain,
! [X0,X1] :
( class_Orderings_Obot(X1)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),c_Orderings_Obot__class_Obot(X1)),X0)) ),
inference(rectify,[],[f45]) ).
fof(f45,axiom,
! [X22,X23] :
( class_Orderings_Obot(X23)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23),c_Orderings_Obot__class_Obot(X23)),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32055,plain,
spl625_653,
inference(avatar_split_clause,[],[f18385,f32053]) ).
fof(f18385,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ),
inference(cnf_transformation,[],[f10670]) ).
fof(f10670,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),c_Orderings_Otop__class_Otop(X1)))
| ~ class_Orderings_Otop(X1) ),
inference(ennf_transformation,[],[f6299]) ).
fof(f6299,plain,
! [X0,X1] :
( class_Orderings_Otop(X1)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),c_Orderings_Otop__class_Otop(X1))) ),
inference(rectify,[],[f1092]) ).
fof(f1092,axiom,
! [X22,X23] :
( class_Orderings_Otop(X23)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23),X22),c_Orderings_Otop__class_Otop(X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32051,plain,
spl625_652,
inference(avatar_split_clause,[],[f18196,f32049]) ).
fof(f32049,plain,
( spl625_652
<=> ! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_652])]) ).
fof(f18196,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ),
inference(cnf_transformation,[],[f6155]) ).
fof(f6155,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X1),X0)) ),
inference(rectify,[],[f5240]) ).
fof(f5240,axiom,
! [X37,X5] :
( hBOOL(X37)
| ~ hBOOL(X5)
| ~ hBOOL(hAPP(hAPP(c_fimplies,X5),X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32047,plain,
spl625_651,
inference(avatar_split_clause,[],[f18195,f32045]) ).
fof(f32045,plain,
( spl625_651
<=> ! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_651])]) ).
fof(f18195,plain,
! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ),
inference(cnf_transformation,[],[f6154]) ).
fof(f6154,plain,
! [X0,X1] :
( hBOOL(X0)
| hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X1),X0)) ),
inference(rectify,[],[f5237]) ).
fof(f5237,axiom,
! [X37,X5] :
( hBOOL(X37)
| hBOOL(X5)
| ~ hBOOL(hAPP(hAPP(c_fdisj,X5),X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32043,plain,
spl625_650,
inference(avatar_split_clause,[],[f18189,f32041]) ).
fof(f32041,plain,
( spl625_650
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_650])]) ).
fof(f18189,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6148]) ).
fof(f6148,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fconj,X1),X0))
| ~ hBOOL(X0)
| ~ hBOOL(X1) ),
inference(rectify,[],[f5232]) ).
fof(f5232,axiom,
! [X37,X5] :
( hBOOL(hAPP(hAPP(c_fconj,X5),X37))
| ~ hBOOL(X37)
| ~ hBOOL(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32039,plain,
spl625_649,
inference(avatar_split_clause,[],[f17778,f32037]) ).
fof(f32037,plain,
( spl625_649
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_649])]) ).
fof(f17778,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)),X1)),
inference(cnf_transformation,[],[f5794]) ).
fof(f5794,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X1,X0)),X1)),
inference(rectify,[],[f2255]) ).
fof(f2255,axiom,
! [X88,X93] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,X93,X88)),X93)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32035,plain,
spl625_648,
inference(avatar_split_clause,[],[f17776,f32033]) ).
fof(f32033,plain,
( spl625_648
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_648])]) ).
fof(f17776,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5792]) ).
fof(f5792,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f1012]) ).
fof(f1012,axiom,
! [X20,X4] : hBOOL(hAPP(hAPP(c_member(X4),X20),c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32031,plain,
spl625_647,
inference(avatar_split_clause,[],[f17774,f32029]) ).
fof(f32029,plain,
( spl625_647
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_647])]) ).
fof(f17774,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(cnf_transformation,[],[f5790]) ).
fof(f5790,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(rectify,[],[f235]) ).
fof(f235,axiom,
! [X19,X4] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool)),X19),X19) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32026,plain,
spl625_646,
inference(avatar_split_clause,[],[f17773,f32024]) ).
fof(f32024,plain,
( spl625_646
<=> ! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_646])]) ).
fof(f17773,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(cnf_transformation,[],[f5789]) ).
fof(f5789,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(rectify,[],[f388]) ).
fof(f388,axiom,
! [X19,X4] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,tc_HOL_Obool)),X19),X19) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32022,plain,
spl625_645,
inference(avatar_split_clause,[],[f17772,f32020]) ).
fof(f32020,plain,
( spl625_645
<=> ! [X0,X1] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_645])]) ).
fof(f17772,plain,
! [X0,X1] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X0)) = X0,
inference(cnf_transformation,[],[f5788]) ).
fof(f5788,plain,
! [X0,X1] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X1,tc_HOL_Obool),hAPP(c_Set_OPow(X1),X0)) = X0,
inference(rectify,[],[f3834]) ).
fof(f3834,axiom,
! [X19,X4] : c_Complete__Lattice_OSup__class_OSup(tc_fun(X4,tc_HOL_Obool),hAPP(c_Set_OPow(X4),X19)) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32018,plain,
spl625_644,
inference(avatar_split_clause,[],[f17771,f32016]) ).
fof(f32016,plain,
( spl625_644
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),X0),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_644])]) ).
fof(f17771,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5787]) ).
fof(f5787,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Otake(X1),X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f3957]) ).
fof(f3957,axiom,
! [X88,X23] : c_List_Olist_ONil(X23) = hAPP(hAPP(c_List_Otake(X23),X88),c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32014,plain,
spl625_643,
inference(avatar_split_clause,[],[f17770,f32012]) ).
fof(f32012,plain,
( spl625_643
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Odrop(X1),X0),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_643])]) ).
fof(f17770,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Odrop(X1),X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5786]) ).
fof(f5786,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(hAPP(c_List_Odrop(X1),X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f4135]) ).
fof(f4135,axiom,
! [X88,X23] : c_List_Olist_ONil(X23) = hAPP(hAPP(c_List_Odrop(X23),X88),c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32010,plain,
spl625_642,
inference(avatar_split_clause,[],[f17766,f32008]) ).
fof(f32008,plain,
( spl625_642
<=> ! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_642])]) ).
fof(f17766,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5782]) ).
fof(f5782,plain,
! [X0,X1] : ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))),
inference(rectify,[],[f227]) ).
fof(f227,axiom,
! [X6,X4] : ~ hBOOL(hAPP(hAPP(c_member(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f32006,plain,
spl625_641,
inference(avatar_split_clause,[],[f17544,f32004]) ).
fof(f32004,plain,
( spl625_641
<=> ! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK93(X0)),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_641])]) ).
fof(f17544,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(X0)
| hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK93(X0)),X0)) ),
inference(cnf_transformation,[],[f14573]) ).
fof(f32002,plain,
spl625_640,
inference(avatar_split_clause,[],[f17461,f32000]) ).
fof(f32000,plain,
( spl625_640
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_640])]) ).
fof(f17461,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10387]) ).
fof(f10387,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5551]) ).
fof(f5551,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> c_Groups_Oone__class_Oone(X0) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(rectify,[],[f1759]) ).
fof(f1759,axiom,
! [X23] :
( class_Rings_Osemiring__1(X23)
=> c_Groups_Oone__class_Oone(X23) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(X23),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31998,plain,
spl625_639,
inference(avatar_split_clause,[],[f17457,f31996]) ).
fof(f31996,plain,
( spl625_639
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_List_Omonoid__add__class_Olistsum(X0),c_List_Olist_ONil(X0))
| ~ class_Groups_Omonoid__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_639])]) ).
fof(f17457,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_List_Omonoid__add__class_Olistsum(X0),c_List_Olist_ONil(X0))
| ~ class_Groups_Omonoid__add(X0) ),
inference(cnf_transformation,[],[f10383]) ).
fof(f10383,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_List_Omonoid__add__class_Olistsum(X0),c_List_Olist_ONil(X0))
| ~ class_Groups_Omonoid__add(X0) ),
inference(ennf_transformation,[],[f5547]) ).
fof(f5547,plain,
! [X0] :
( class_Groups_Omonoid__add(X0)
=> c_Groups_Ozero__class_Ozero(X0) = hAPP(c_List_Omonoid__add__class_Olistsum(X0),c_List_Olist_ONil(X0)) ),
inference(rectify,[],[f3945]) ).
fof(f3945,axiom,
! [X23] :
( class_Groups_Omonoid__add(X23)
=> c_Groups_Ozero__class_Ozero(X23) = hAPP(c_List_Omonoid__add__class_Olistsum(X23),c_List_Olist_ONil(X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31994,plain,
spl625_638,
inference(avatar_split_clause,[],[f17447,f31992]) ).
fof(f31992,plain,
( spl625_638
<=> ! [X0] :
( c_Orderings_Obot__class_Obot(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0))
| ~ class_Lattices_Oboolean__algebra(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_638])]) ).
fof(f17447,plain,
! [X0] :
( c_Orderings_Obot__class_Obot(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0))
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[],[f10373]) ).
fof(f10373,plain,
! [X0] :
( c_Orderings_Obot__class_Obot(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0))
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(ennf_transformation,[],[f5537]) ).
fof(f5537,plain,
! [X0] :
( class_Lattices_Oboolean__algebra(X0)
=> c_Orderings_Obot__class_Obot(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Otop__class_Otop(X0)) ),
inference(rectify,[],[f1150]) ).
fof(f1150,axiom,
! [X23] :
( class_Lattices_Oboolean__algebra(X23)
=> c_Orderings_Obot__class_Obot(X23) = hAPP(c_Groups_Ouminus__class_Ouminus(X23),c_Orderings_Otop__class_Otop(X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31990,plain,
spl625_637,
inference(avatar_split_clause,[],[f17446,f31988]) ).
fof(f31988,plain,
( spl625_637
<=> ! [X0] :
( c_Orderings_Otop__class_Otop(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0))
| ~ class_Lattices_Oboolean__algebra(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_637])]) ).
fof(f17446,plain,
! [X0] :
( c_Orderings_Otop__class_Otop(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0))
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(cnf_transformation,[],[f10372]) ).
fof(f10372,plain,
! [X0] :
( c_Orderings_Otop__class_Otop(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0))
| ~ class_Lattices_Oboolean__algebra(X0) ),
inference(ennf_transformation,[],[f5536]) ).
fof(f5536,plain,
! [X0] :
( class_Lattices_Oboolean__algebra(X0)
=> c_Orderings_Otop__class_Otop(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Orderings_Obot__class_Obot(X0)) ),
inference(rectify,[],[f1149]) ).
fof(f1149,axiom,
! [X23] :
( class_Lattices_Oboolean__algebra(X23)
=> c_Orderings_Otop__class_Otop(X23) = hAPP(c_Groups_Ouminus__class_Ouminus(X23),c_Orderings_Obot__class_Obot(X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31986,plain,
( ~ spl625_129
| spl625_636
| ~ spl625_237
| ~ spl625_279 ),
inference(avatar_split_clause,[],[f30368,f30158,f29975,f31983,f29449]) ).
fof(f29449,plain,
( spl625_129
<=> class_Rings_Osemiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_129])]) ).
fof(f31983,plain,
( spl625_636
<=> c_Int_Oiszero(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_636])]) ).
fof(f29975,plain,
( spl625_237
<=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_237])]) ).
fof(f30368,plain,
( c_Int_Oiszero(tc_Nat_Onat,c_HOL_Obool_Obool__size(c_fTrue))
| ~ class_Rings_Osemiring__1(tc_Nat_Onat)
| ~ spl625_237
| ~ spl625_279 ),
inference(superposition,[],[f30159,f29977]) ).
fof(f29977,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue)
| ~ spl625_237 ),
inference(avatar_component_clause,[],[f29975]) ).
fof(f31981,plain,
spl625_635,
inference(avatar_split_clause,[],[f17434,f31979]) ).
fof(f31979,plain,
( spl625_635
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_635])]) ).
fof(f17434,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(cnf_transformation,[],[f10360]) ).
fof(f10360,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Olinordered__idom(X0) ),
inference(ennf_transformation,[],[f5524]) ).
fof(f5524,plain,
! [X0] :
( class_Rings_Olinordered__idom(X0)
=> c_Groups_Oone__class_Oone(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f3264]) ).
fof(f3264,axiom,
! [X23] :
( class_Rings_Olinordered__idom(X23)
=> c_Groups_Oone__class_Oone(X23) = hAPP(c_Groups_Oabs__class_Oabs(X23),c_Groups_Oone__class_Oone(X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31977,plain,
spl625_634,
inference(avatar_split_clause,[],[f17433,f31975]) ).
fof(f31975,plain,
( spl625_634
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_634])]) ).
fof(f17433,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(cnf_transformation,[],[f10359]) ).
fof(f10359,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Oordered__ab__group__add__abs(X0) ),
inference(ennf_transformation,[],[f5523]) ).
fof(f5523,plain,
! [X0] :
( class_Groups_Oordered__ab__group__add__abs(X0)
=> c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Oabs__class_Oabs(X0),c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f3251]) ).
fof(f3251,axiom,
! [X23] :
( class_Groups_Oordered__ab__group__add__abs(X23)
=> c_Groups_Ozero__class_Ozero(X23) = hAPP(c_Groups_Oabs__class_Oabs(X23),c_Groups_Ozero__class_Ozero(X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31973,plain,
spl625_633,
inference(avatar_split_clause,[],[f17429,f31971]) ).
fof(f31971,plain,
( spl625_633
<=> ! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Rings_Oring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_633])]) ).
fof(f17429,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Rings_Oring__1(X0) ),
inference(cnf_transformation,[],[f10355]) ).
fof(f10355,plain,
! [X0] :
( c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ class_Rings_Oring__1(X0) ),
inference(ennf_transformation,[],[f5519]) ).
fof(f5519,plain,
! [X0] :
( class_Rings_Oring__1(X0)
=> c_Groups_Oone__class_Oone(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(rectify,[],[f2814]) ).
fof(f2814,axiom,
! [X23] :
( class_Rings_Oring__1(X23)
=> c_Groups_Oone__class_Oone(X23) = hAPP(c_Int_Oring__1__class_Oof__int(X23),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31969,plain,
spl625_632,
inference(avatar_split_clause,[],[f17428,f31967]) ).
fof(f31967,plain,
( spl625_632
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Ogroup__add(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_632])]) ).
fof(f17428,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Ogroup__add(X0) ),
inference(cnf_transformation,[],[f10354]) ).
fof(f10354,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Ogroup__add(X0) ),
inference(ennf_transformation,[],[f5518]) ).
fof(f5518,plain,
! [X0] :
( class_Groups_Ogroup__add(X0)
=> c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Groups_Ouminus__class_Ouminus(X0),c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f1477]) ).
fof(f1477,axiom,
! [X23] :
( class_Groups_Ogroup__add(X23)
=> c_Groups_Ozero__class_Ozero(X23) = hAPP(c_Groups_Ouminus__class_Ouminus(X23),c_Groups_Ozero__class_Ozero(X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31965,plain,
spl625_631,
inference(avatar_split_clause,[],[f17278,f31963]) ).
fof(f31963,plain,
( spl625_631
<=> ! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_631])]) ).
fof(f17278,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)),
inference(cnf_transformation,[],[f5381]) ).
fof(f5381,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_COMBI(X0)),
inference(rectify,[],[f3612]) ).
fof(f3612,axiom,
! [X4] : hAPP(c_List_Omap(X4,X4),c_COMBI(X4)) = c_Fun_Oid(tc_List_Olist(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31961,plain,
spl625_630,
inference(avatar_split_clause,[],[f17277,f31959]) ).
fof(f31959,plain,
( spl625_630
<=> ! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_630])]) ).
fof(f17277,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)),
inference(cnf_transformation,[],[f5380]) ).
fof(f5380,plain,
! [X0] : c_Fun_Oid(tc_List_Olist(X0)) = hAPP(c_List_Omap(X0,X0),c_Fun_Oid(X0)),
inference(rectify,[],[f3611]) ).
fof(f3611,axiom,
! [X4] : hAPP(c_List_Omap(X4,X4),c_Fun_Oid(X4)) = c_Fun_Oid(tc_List_Olist(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31957,plain,
spl625_629,
inference(avatar_split_clause,[],[f17276,f31955]) ).
fof(f31955,plain,
( spl625_629
<=> ! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_Fun_Oid(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_629])]) ).
fof(f17276,plain,
! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_Fun_Oid(X0)),
inference(cnf_transformation,[],[f5379]) ).
fof(f5379,plain,
! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_Fun_Oid(X0)),
inference(rectify,[],[f3562]) ).
fof(f3562,axiom,
! [X4] : hAPP(c_Option_Omap(X4,X4),c_Fun_Oid(X4)) = c_Fun_Oid(tc_Option_Ooption(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31953,plain,
spl625_628,
inference(avatar_split_clause,[],[f17274,f31951]) ).
fof(f31951,plain,
( spl625_628
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_List_Oset(X0),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_628])]) ).
fof(f17274,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_List_Oset(X0),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5377]) ).
fof(f5377,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = hAPP(c_List_Oset(X0),c_List_Olist_ONil(X0)),
inference(rectify,[],[f3950]) ).
fof(f3950,axiom,
! [X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = hAPP(c_List_Oset(X4),c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31949,plain,
spl625_627,
inference(avatar_split_clause,[],[f17273,f31947]) ).
fof(f31947,plain,
( spl625_627
<=> ! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_COMBI(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_627])]) ).
fof(f17273,plain,
! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_COMBI(X0)),
inference(cnf_transformation,[],[f5376]) ).
fof(f5376,plain,
! [X0] : c_Fun_Oid(tc_Option_Ooption(X0)) = hAPP(c_Option_Omap(X0,X0),c_COMBI(X0)),
inference(rectify,[],[f3563]) ).
fof(f3563,axiom,
! [X4] : c_Fun_Oid(tc_Option_Ooption(X4)) = hAPP(c_Option_Omap(X4,X4),c_COMBI(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31945,plain,
spl625_626,
inference(avatar_split_clause,[],[f17259,f31943]) ).
fof(f17259,plain,
! [X0] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X0)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X0),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5362]) ).
fof(f5362,plain,
! [X0] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X0)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X0),tc_HOL_Obool)))),
inference(rectify,[],[f3620]) ).
fof(f3620,axiom,
! [X4] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(X4)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(X4),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31941,plain,
spl625_625,
inference(avatar_split_clause,[],[f17107,f31938]) ).
fof(f31938,plain,
( spl625_625
<=> 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,[spl625_625])]) ).
fof(f17107,plain,
c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
inference(cnf_transformation,[],[f3107]) ).
fof(f3107,axiom,
c_Typedef_Otype__definition(tc_Int_Oint,tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool),c_Int_ORep__Integ,c_Int_OAbs__Integ,c_Int_OInteg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31936,plain,
spl625_624,
inference(avatar_split_clause,[],[f17102,f31933]) ).
fof(f31933,plain,
( spl625_624
<=> 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,[spl625_624])]) ).
fof(f17102,plain,
c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
inference(cnf_transformation,[],[f4621]) ).
fof(f4621,axiom,
c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31931,plain,
spl625_623,
inference(avatar_split_clause,[],[f17101,f31928]) ).
fof(f31928,plain,
( spl625_623
<=> 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,[spl625_623])]) ).
fof(f17101,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))),
inference(cnf_transformation,[],[f1192]) ).
fof(f1192,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit),c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31926,plain,
spl625_622,
inference(avatar_split_clause,[],[f17099,f31923]) ).
fof(f31923,plain,
( spl625_622
<=> 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,[spl625_622])]) ).
fof(f17099,plain,
c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
inference(cnf_transformation,[],[f4645]) ).
fof(f4645,axiom,
c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31921,plain,
spl625_621,
inference(avatar_split_clause,[],[f16811,f31918]) ).
fof(f31918,plain,
( spl625_621
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_621])]) ).
fof(f16811,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)),
inference(cnf_transformation,[],[f5241]) ).
fof(f5241,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G),v_Ga)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31893,plain,
( ~ spl625_620
| spl625_341
| ~ spl625_601 ),
inference(avatar_split_clause,[],[f31882,f31600,f30455,f31890]) ).
fof(f31890,plain,
( spl625_620
<=> c_Nat__Transfer_Ois__nat(c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_620])]) ).
fof(f30455,plain,
( spl625_341
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_341])]) ).
fof(f31600,plain,
( spl625_601
<=> ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| ~ c_Nat__Transfer_Ois__nat(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_601])]) ).
fof(f31882,plain,
( ~ c_Nat__Transfer_Ois__nat(c_Int_OMin)
| spl625_341
| ~ spl625_601 ),
inference(resolution,[],[f31601,f30457]) ).
fof(f30457,plain,
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| spl625_341 ),
inference(avatar_component_clause,[],[f30455]) ).
fof(f31601,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| ~ c_Nat__Transfer_Ois__nat(X0) )
| ~ spl625_601 ),
inference(avatar_component_clause,[],[f31600]) ).
fof(f31676,plain,
spl625_619,
inference(avatar_split_clause,[],[f28464,f31674]) ).
fof(f31674,plain,
( spl625_619
<=> ! [X2,X1,X3] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(c_fequal,X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_619])]) ).
fof(f28464,plain,
! [X2,X3,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(c_fequal,X1)),X1)),
inference(forward_demodulation,[],[f25333,f26086]) ).
fof(f25333,plain,
! [X2,X3,X1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X1)),
inference(equality_resolution,[],[f22458]) ).
fof(f22458,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f16231]) ).
fof(f16231,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0))
| X0 != X1 )
& ( X0 = X1
| ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0)) ) ),
inference(nnf_transformation,[],[f9125]) ).
fof(f9125,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X3,X2,hAPP(hAPP(c_Set_Oinsert(X3),X1),c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))),X0))
<=> X0 = X1 ),
inference(rectify,[],[f1699]) ).
fof(f1699,axiom,
! [X26,X6,X1,X4] :
( hBOOL(hAPP(c_Finite__Set_Ofold1Set(X4,X1,hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),X26))
<=> X6 = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31672,plain,
spl625_618,
inference(avatar_split_clause,[],[f27514,f31670]) ).
fof(f31670,plain,
( spl625_618
<=> ! [X0,X1] : c_List_Olast(X1,c_List_Oinsert(X1,X0,c_List_Olist_ONil(X1))) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_618])]) ).
fof(f27514,plain,
! [X0,X1] : c_List_Olast(X1,c_List_Oinsert(X1,X0,c_List_Olist_ONil(X1))) = X0,
inference(forward_demodulation,[],[f25049,f17831]) ).
fof(f17831,plain,
! [X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1)) = c_List_Oinsert(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5847]) ).
fof(f5847,plain,
! [X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1)) = c_List_Oinsert(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4546]) ).
fof(f4546,axiom,
! [X22,X23] : hAPP(hAPP(c_List_Olist_OCons(X23),X22),c_List_Olist_ONil(X23)) = c_List_Oinsert(X23,X22,c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f25049,plain,
! [X0,X1] : c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1))) = X0,
inference(equality_resolution,[],[f19664]) ).
fof(f19664,plain,
! [X2,X0,X1] :
( c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2)) = X0
| c_List_Olist_ONil(X1) != X2 ),
inference(cnf_transformation,[],[f11285]) ).
fof(f11285,plain,
! [X0,X1,X2] :
( ( c_List_Olast(X1,X2) = c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2))
| c_List_Olist_ONil(X1) = X2 )
& ( c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2)) = X0
| c_List_Olist_ONil(X1) != X2 ) ),
inference(ennf_transformation,[],[f7198]) ).
fof(f7198,plain,
! [X0,X1,X2] :
( ( c_List_Olist_ONil(X1) != X2
=> c_List_Olast(X1,X2) = c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2)) )
& ( c_List_Olist_ONil(X1) = X2
=> c_List_Olast(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2)) = X0 ) ),
inference(rectify,[],[f4386]) ).
fof(f4386,axiom,
! [X22,X23,X263] :
( ( c_List_Olist_ONil(X23) != X263
=> c_List_Olast(X23,X263) = c_List_Olast(X23,hAPP(hAPP(c_List_Olist_OCons(X23),X22),X263)) )
& ( c_List_Olist_ONil(X23) = X263
=> c_List_Olast(X23,hAPP(hAPP(c_List_Olist_OCons(X23),X22),X263)) = X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31668,plain,
spl625_617,
inference(avatar_split_clause,[],[f27416,f31666]) ).
fof(f31666,plain,
( spl625_617
<=> ! [X2,X0,X1] : hAPP(c_Finite__Set_Ofold1(X2,X1),hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_617])]) ).
fof(f27416,plain,
! [X2,X0,X1] : hAPP(c_Finite__Set_Ofold1(X2,X1),hAPP(c_fequal,X0)) = X0,
inference(forward_demodulation,[],[f19435,f26086]) ).
fof(f19435,plain,
! [X2,X0,X1] : hAPP(c_Finite__Set_Ofold1(X2,X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = X0,
inference(cnf_transformation,[],[f6970]) ).
fof(f6970,plain,
! [X0,X1,X2] : hAPP(c_Finite__Set_Ofold1(X2,X1),hAPP(hAPP(c_Set_Oinsert(X2),X0),c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = X0,
inference(rectify,[],[f3531]) ).
fof(f3531,axiom,
! [X6,X1,X4] : hAPP(c_Finite__Set_Ofold1(X4,X1),hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X6,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31664,plain,
spl625_616,
inference(avatar_split_clause,[],[f27410,f31662]) ).
fof(f31662,plain,
( spl625_616
<=> ! [X2,X0,X1] : hAPP(c_Nat_Onat_Onat__rec(X2,X1,X0),c_HOL_Obool_Obool__size(c_fTrue)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_616])]) ).
fof(f27410,plain,
! [X2,X0,X1] : hAPP(c_Nat_Onat_Onat__rec(X2,X1,X0),c_HOL_Obool_Obool__size(c_fTrue)) = X1,
inference(forward_demodulation,[],[f19390,f17032]) ).
fof(f19390,plain,
! [X2,X0,X1] : hAPP(c_Nat_Onat_Onat__rec(X2,X1,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(cnf_transformation,[],[f6925]) ).
fof(f6925,plain,
! [X0,X1,X2] : hAPP(c_Nat_Onat_Onat__rec(X2,X1,X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rectify,[],[f2891]) ).
fof(f2891,axiom,
! [X67,X25,X4] : hAPP(c_Nat_Onat_Onat__rec(X4,X25,X67),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31660,plain,
spl625_615,
inference(avatar_split_clause,[],[f27305,f31657]) ).
fof(f31657,plain,
( spl625_615
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_615])]) ).
fof(f27305,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(forward_demodulation,[],[f27304,f26229]) ).
fof(f27304,plain,
! [X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_HOL_Obool_Obool__size(c_fTrue)))),
inference(forward_demodulation,[],[f25039,f17032]) ).
fof(f25039,plain,
! [X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
inference(equality_resolution,[],[f19300]) ).
fof(f19300,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ),
inference(cnf_transformation,[],[f15110]) ).
fof(f15110,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))) ) ),
inference(flattening,[],[f15109]) ).
fof(f15109,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)))
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0))) ) ),
inference(nnf_transformation,[],[f6880]) ).
fof(f6880,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),X1),X0)))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)) ) ),
inference(rectify,[],[f1967]) ).
fof(f1967,axiom,
! [X78,X20] :
( 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),X20),X78)))
<=> ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X78
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31655,plain,
spl625_614,
inference(avatar_split_clause,[],[f26592,f31653]) ).
fof(f31653,plain,
( spl625_614
<=> ! [X0,X1] :
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_614])]) ).
fof(f26592,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(forward_demodulation,[],[f18542,f26086]) ).
fof(f18542,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10836]) ).
fof(f10836,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6434]) ).
fof(f6434,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> c_Big__Operators_Olattice__class_OInf__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f859]) ).
fof(f859,axiom,
! [X20,X4] :
( class_Lattices_Olattice(X4)
=> c_Big__Operators_Olattice__class_OInf__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X20),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31651,plain,
spl625_613,
inference(avatar_split_clause,[],[f26591,f31649]) ).
fof(f31649,plain,
( spl625_613
<=> ! [X0,X1] :
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_613])]) ).
fof(f26591,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(forward_demodulation,[],[f18541,f26086]) ).
fof(f18541,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10835]) ).
fof(f10835,plain,
! [X0,X1] :
( c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6433]) ).
fof(f6433,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> c_Big__Operators_Olattice__class_OSup__fin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f858]) ).
fof(f858,axiom,
! [X20,X4] :
( class_Lattices_Olattice(X4)
=> c_Big__Operators_Olattice__class_OSup__fin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X20),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31647,plain,
spl625_612,
inference(avatar_split_clause,[],[f26584,f31645]) ).
fof(f31645,plain,
( spl625_612
<=> ! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_612])]) ).
fof(f26584,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(forward_demodulation,[],[f18483,f26086]) ).
fof(f18483,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10778]) ).
fof(f10778,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6393]) ).
fof(f6393,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> c_Big__Operators_Olinorder__class_OMax(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f1203]) ).
fof(f1203,axiom,
! [X20,X4] :
( class_Orderings_Olinorder(X4)
=> c_Big__Operators_Olinorder__class_OMax(X4,hAPP(hAPP(c_Set_Oinsert(X4),X20),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31643,plain,
spl625_611,
inference(avatar_split_clause,[],[f26583,f31641]) ).
fof(f31641,plain,
( spl625_611
<=> ! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_611])]) ).
fof(f26583,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(forward_demodulation,[],[f18482,f26086]) ).
fof(f18482,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10777]) ).
fof(f10777,plain,
! [X0,X1] :
( c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6392]) ).
fof(f6392,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> c_Big__Operators_Olinorder__class_OMin(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f1202]) ).
fof(f1202,axiom,
! [X20,X4] :
( class_Orderings_Olinorder(X4)
=> c_Big__Operators_Olinorder__class_OMin(X4,hAPP(hAPP(c_Set_Oinsert(X4),X20),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X20 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31639,plain,
spl625_610,
inference(avatar_split_clause,[],[f26582,f31637]) ).
fof(f31637,plain,
( spl625_610
<=> ! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Oinsert(X1,X0,c_List_Olist_ONil(X1)))
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_610])]) ).
fof(f26582,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,c_List_Oinsert(X1,X0,c_List_Olist_ONil(X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(forward_demodulation,[],[f18481,f17831]) ).
fof(f18481,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f10776]) ).
fof(f10776,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1)))
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6391]) ).
fof(f6391,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> c_List_Olinorder__class_Osorted(X1,hAPP(hAPP(c_List_Olist_OCons(X1),X0),c_List_Olist_ONil(X1))) ),
inference(rectify,[],[f4263]) ).
fof(f4263,axiom,
! [X22,X23] :
( class_Orderings_Olinorder(X23)
=> c_List_Olinorder__class_Osorted(X23,hAPP(hAPP(c_List_Olist_OCons(X23),X22),c_List_Olist_ONil(X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31635,plain,
spl625_609,
inference(avatar_split_clause,[],[f26554,f31633]) ).
fof(f31633,plain,
( spl625_609
<=> ! [X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_609])]) ).
fof(f26554,plain,
! [X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(forward_demodulation,[],[f18403,f26086]) ).
fof(f18403,plain,
! [X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(cnf_transformation,[],[f10688]) ).
fof(f10688,plain,
! [X0,X1] :
( c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(ennf_transformation,[],[f6317]) ).
fof(f6317,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(X1)
=> c_Complete__Lattice_OSup__class_OSup(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f3849]) ).
fof(f3849,axiom,
! [X6,X4] :
( class_Complete__Lattice_Ocomplete__lattice(X4)
=> c_Complete__Lattice_OSup__class_OSup(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31631,plain,
spl625_608,
inference(avatar_split_clause,[],[f26553,f31629]) ).
fof(f31629,plain,
( spl625_608
<=> ! [X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_608])]) ).
fof(f26553,plain,
! [X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(c_fequal,X0)) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(forward_demodulation,[],[f18402,f26086]) ).
fof(f18402,plain,
! [X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(cnf_transformation,[],[f10687]) ).
fof(f10687,plain,
! [X0,X1] :
( c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(ennf_transformation,[],[f6316]) ).
fof(f6316,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(X1)
=> c_Complete__Lattice_OInf__class_OInf(X1,hAPP(hAPP(c_Set_Oinsert(X1),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))) = X0 ),
inference(rectify,[],[f4486]) ).
fof(f4486,axiom,
! [X6,X4] :
( class_Complete__Lattice_Ocomplete__lattice(X4)
=> c_Complete__Lattice_OInf__class_OInf(X4,hAPP(hAPP(c_Set_Oinsert(X4),X6),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))) = X6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31627,plain,
spl625_607,
inference(avatar_split_clause,[],[f26446,f31625]) ).
fof(f31625,plain,
( spl625_607
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Int_OPls)
| ~ class_Int_Oring__char__0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_607])]) ).
fof(f26446,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Int_OPls)
| ~ class_Int_Oring__char__0(X1) ),
inference(forward_demodulation,[],[f24907,f17021]) ).
fof(f24907,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Int_Oring__char__0(X1) ),
inference(equality_resolution,[],[f18224]) ).
fof(f18224,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ class_Int_Oring__char__0(X1) ),
inference(cnf_transformation,[],[f14673]) ).
fof(f14673,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| c_Groups_Ozero__class_Ozero(X1) != hAPP(c_Int_Oring__1__class_Oof__int(X1),X0) ) )
| ~ class_Int_Oring__char__0(X1) ),
inference(nnf_transformation,[],[f10540]) ).
fof(f10540,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
| ~ class_Int_Oring__char__0(X1) ),
inference(ennf_transformation,[],[f6181]) ).
fof(f6181,plain,
! [X0,X1] :
( class_Int_Oring__char__0(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = hAPP(c_Int_Oring__1__class_Oof__int(X1),X0)
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
inference(rectify,[],[f2805]) ).
fof(f2805,axiom,
! [X116,X4] :
( class_Int_Oring__char__0(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) = hAPP(c_Int_Oring__1__class_Oof__int(X4),X116)
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X116 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31623,plain,
spl625_606,
inference(avatar_split_clause,[],[f26063,f31621]) ).
fof(f31621,plain,
( spl625_606
<=> ! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_606])]) ).
fof(f26063,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f17750,f17032]) ).
fof(f17750,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f5766]) ).
fof(f5766,plain,
! [X0,X1] : hAPP(hAPP(c_List_Odrop(X1),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f4130]) ).
fof(f4130,axiom,
! [X263,X23] : hAPP(hAPP(c_List_Odrop(X23),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X263) = X263,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31619,plain,
spl625_605,
inference(avatar_split_clause,[],[f26062,f31617]) ).
fof(f31617,plain,
( spl625_605
<=> ! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_605])]) ).
fof(f26062,plain,
! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X1,X0)),
inference(forward_demodulation,[],[f17743,f17032]) ).
fof(f17743,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X1,X0)),
inference(cnf_transformation,[],[f5759]) ).
fof(f5759,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X1,X0)),
inference(rectify,[],[f2055]) ).
fof(f2055,axiom,
! [X53,X54] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(X54,X53)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31615,plain,
spl625_604,
inference(avatar_split_clause,[],[f25982,f31613]) ).
fof(f31613,plain,
( spl625_604
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_604])]) ).
fof(f25982,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0)))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,X0)) ),
inference(forward_demodulation,[],[f25981,f17178]) ).
fof(f25981,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X0)))) ),
inference(forward_demodulation,[],[f17585,f17178]) ).
fof(f17585,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X0)))) ),
inference(cnf_transformation,[],[f14603]) ).
fof(f14603,plain,
! [X0] :
( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X0))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) )
& ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X0)))) ) ),
inference(nnf_transformation,[],[f5647]) ).
fof(f5647,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X0))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(rectify,[],[f2684]) ).
fof(f2684,axiom,
! [X180] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X180))))
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X180))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31611,plain,
spl625_603,
inference(avatar_split_clause,[],[f25980,f31609]) ).
fof(f31609,plain,
( spl625_603
<=> ! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_603])]) ).
fof(f25980,plain,
! [X0] :
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,X0))
| hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0))) ),
inference(forward_demodulation,[],[f25979,f17178]) ).
fof(f25979,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OBit0(X0)))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(forward_demodulation,[],[f17586,f17178]) ).
fof(f17586,plain,
! [X0] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(X0))))
| ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0))) ),
inference(cnf_transformation,[],[f14603]) ).
fof(f31607,plain,
~ spl625_602,
inference(avatar_split_clause,[],[f25949,f31604]) ).
fof(f31604,plain,
( spl625_602
<=> 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,[spl625_602])]) ).
fof(f25949,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))),
inference(forward_demodulation,[],[f25948,f25524]) ).
fof(f25524,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17056,f17032]) ).
fof(f17056,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f4626]) ).
fof(f4626,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f25948,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Code__Numeral_Oof__nat,c_HOL_Obool_Obool__size(c_fTrue)))),
inference(forward_demodulation,[],[f24876,f17032]) ).
fof(f24876,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,[],[f17571]) ).
fof(f17571,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,[],[f14593]) ).
fof(f14593,plain,
! [X0] :
( ( hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0))
| hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0 ) ),
inference(nnf_transformation,[],[f5640]) ).
fof(f5640,plain,
! [X0] :
( hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X0)) ),
inference(rectify,[],[f4631]) ).
fof(f4631,axiom,
! [X147] :
( hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X147
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),X147)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31602,plain,
spl625_601,
inference(avatar_split_clause,[],[f25941,f31600]) ).
fof(f25941,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| ~ c_Nat__Transfer_Ois__nat(X0) ),
inference(forward_demodulation,[],[f17546,f17021]) ).
fof(f17546,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ c_Nat__Transfer_Ois__nat(X0) ),
inference(cnf_transformation,[],[f14574]) ).
fof(f14574,plain,
! [X0] :
( ( c_Nat__Transfer_Ois__nat(X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
| ~ c_Nat__Transfer_Ois__nat(X0) ) ),
inference(nnf_transformation,[],[f5629]) ).
fof(f5629,plain,
! [X0] :
( c_Nat__Transfer_Ois__nat(X0)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ),
inference(rectify,[],[f2914]) ).
fof(f2914,axiom,
! [X20] :
( c_Nat__Transfer_Ois__nat(X20)
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31598,plain,
spl625_600,
inference(avatar_split_clause,[],[f25940,f31596]) ).
fof(f25940,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),X0))
| c_Nat__Transfer_Ois__nat(X0) ),
inference(forward_demodulation,[],[f17547,f17021]) ).
fof(f17547,plain,
! [X0] :
( c_Nat__Transfer_Ois__nat(X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ),
inference(cnf_transformation,[],[f14574]) ).
fof(f31594,plain,
spl625_599,
inference(avatar_split_clause,[],[f25816,f31592]) ).
fof(f31592,plain,
( spl625_599
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Int_OPls)
| ~ class_Rings_Oring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_599])]) ).
fof(f25816,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Int_OPls)
| ~ class_Rings_Oring__1(X0) ),
inference(forward_demodulation,[],[f17430,f17021]) ).
fof(f17430,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Rings_Oring__1(X0) ),
inference(cnf_transformation,[],[f10356]) ).
fof(f10356,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ class_Rings_Oring__1(X0) ),
inference(ennf_transformation,[],[f5520]) ).
fof(f5520,plain,
! [X0] :
( class_Rings_Oring__1(X0)
=> c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Oring__1__class_Oof__int(X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rectify,[],[f2804]) ).
fof(f2804,axiom,
! [X23] :
( class_Rings_Oring__1(X23)
=> c_Groups_Ozero__class_Ozero(X23) = hAPP(c_Int_Oring__1__class_Oof__int(X23),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31590,plain,
spl625_598,
inference(avatar_split_clause,[],[f25673,f31588]) ).
fof(f31588,plain,
( spl625_598
<=> ! [X0] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_598])]) ).
fof(f25673,plain,
! [X0] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(forward_demodulation,[],[f25672,f25523]) ).
fof(f25672,plain,
! [X0] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))) = X0,
inference(forward_demodulation,[],[f17300,f17032]) ).
fof(f17300,plain,
! [X0] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X0,
inference(cnf_transformation,[],[f5403]) ).
fof(f5403,plain,
! [X0] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X0,
inference(rectify,[],[f2163]) ).
fof(f2163,axiom,
! [X93] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),X93),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = X93,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31586,plain,
spl625_597,
inference(avatar_split_clause,[],[f25649,f31584]) ).
fof(f31584,plain,
( spl625_597
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_597])]) ).
fof(f25649,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f17257,f17032]) ).
fof(f17257,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f5360]) ).
fof(f5360,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f1496]) ).
fof(f1496,axiom,
! [X88] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X88) = X88,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31582,plain,
( ~ spl625_25
| ~ spl625_596
| ~ spl625_274
| ~ spl625_430 ),
inference(avatar_split_clause,[],[f31181,f30866,f30138,f31579,f28929]) ).
fof(f28929,plain,
( spl625_25
<=> class_Int_Onumber__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_25])]) ).
fof(f31579,plain,
( spl625_596
<=> c_Int_Oiszero(tc_Int_Oint,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_596])]) ).
fof(f30138,plain,
( spl625_274
<=> ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_274])]) ).
fof(f30866,plain,
( spl625_430
<=> ! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_430])]) ).
fof(f31181,plain,
( ~ c_Int_Oiszero(tc_Int_Oint,c_Int_OMin)
| ~ class_Int_Onumber__ring(tc_Int_Oint)
| ~ spl625_274
| ~ spl625_430 ),
inference(superposition,[],[f30867,f30139]) ).
fof(f30139,plain,
( ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = X0
| ~ spl625_274 ),
inference(avatar_component_clause,[],[f30138]) ).
fof(f30867,plain,
( ! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) )
| ~ spl625_430 ),
inference(avatar_component_clause,[],[f30866]) ).
fof(f31577,plain,
spl625_595,
inference(avatar_split_clause,[],[f25647,f31575]) ).
fof(f31575,plain,
( spl625_595
<=> ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_595])]) ).
fof(f25647,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0) = X0,
inference(forward_demodulation,[],[f17253,f17032]) ).
fof(f17253,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f5356]) ).
fof(f5356,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f2090]) ).
fof(f2090,axiom,
! [X88] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X88) = X88,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31573,plain,
spl625_594,
inference(avatar_split_clause,[],[f25646,f31571]) ).
fof(f31571,plain,
( spl625_594
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_594])]) ).
fof(f25646,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17252,f17032]) ).
fof(f17252,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f5355]) ).
fof(f5355,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f1495]) ).
fof(f1495,axiom,
! [X93] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),X93),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X93,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31569,plain,
spl625_593,
inference(avatar_split_clause,[],[f25644,f31567]) ).
fof(f31567,plain,
( spl625_593
<=> ! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_593])]) ).
fof(f25644,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17248,f17032]) ).
fof(f17248,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f5351]) ).
fof(f5351,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f1500]) ).
fof(f1500,axiom,
! [X93] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X93),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X93,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31565,plain,
spl625_592,
inference(avatar_split_clause,[],[f25643,f31563]) ).
fof(f31563,plain,
( spl625_592
<=> ! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_592])]) ).
fof(f25643,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f17247,f17032]) ).
fof(f17247,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f5350]) ).
fof(f5350,plain,
! [X0] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(rectify,[],[f2089]) ).
fof(f2089,axiom,
! [X88] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),X88),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X88,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31561,plain,
spl625_591,
inference(avatar_split_clause,[],[f25641,f31559]) ).
fof(f31559,plain,
( spl625_591
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_591])]) ).
fof(f25641,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0),
inference(forward_demodulation,[],[f17234,f17032]) ).
fof(f17234,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0),
inference(cnf_transformation,[],[f5337]) ).
fof(f5337,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X0),X0),
inference(rectify,[],[f1501]) ).
fof(f1501,axiom,
! [X93] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),X93),X93),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31557,plain,
spl625_590,
inference(avatar_split_clause,[],[f25640,f31555]) ).
fof(f31555,plain,
( spl625_590
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_590])]) ).
fof(f25640,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),c_List_Olist_ONil(X0)),
inference(forward_demodulation,[],[f17233,f17032]) ).
fof(f17233,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5336]) ).
fof(f5336,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X0)),c_List_Olist_ONil(X0)),
inference(rectify,[],[f3946]) ).
fof(f3946,axiom,
! [X23] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(X23)),c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31553,plain,
spl625_589,
inference(avatar_split_clause,[],[f25639,f31551]) ).
fof(f31551,plain,
( spl625_589
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X0)),c_Option_Ooption_ONone(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_589])]) ).
fof(f25639,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X0)),c_Option_Ooption_ONone(X0)),
inference(forward_demodulation,[],[f17232,f17032]) ).
fof(f17232,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X0)),c_Option_Ooption_ONone(X0)),
inference(cnf_transformation,[],[f5335]) ).
fof(f5335,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X0)),c_Option_Ooption_ONone(X0)),
inference(rectify,[],[f1879]) ).
fof(f1879,axiom,
! [X23] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(X23)),c_Option_Ooption_ONone(X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31548,plain,
spl625_588,
inference(avatar_split_clause,[],[f25536,f31545]) ).
fof(f31545,plain,
( spl625_588
<=> c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_588])]) ).
fof(f25536,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin)))),
inference(forward_demodulation,[],[f25535,f25522]) ).
fof(f25535,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OMin)))),
inference(forward_demodulation,[],[f24008,f17019]) ).
fof(f24008,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OPls)),c_Int_OMin)))),
inference(definition_unfolding,[],[f17067,f23983]) ).
fof(f17067,plain,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(cnf_transformation,[],[f2917]) ).
fof(f2917,axiom,
c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31543,plain,
spl625_587,
inference(avatar_split_clause,[],[f25312,f31541]) ).
fof(f31541,plain,
( spl625_587
<=> ! [X2,X1,X3] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_587])]) ).
fof(f25312,plain,
! [X2,X3,X1] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X2)),
inference(equality_resolution,[],[f22317]) ).
fof(f22317,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
| X0 != X2 ),
inference(cnf_transformation,[],[f16134]) ).
fof(f16134,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
| ( ~ hBOOL(hAPP(X1,X0))
& X0 != X2 ) )
& ( hBOOL(hAPP(X1,X0))
| X0 = X2
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0)) ) ),
inference(flattening,[],[f16133]) ).
fof(f16133,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
| ( ~ hBOOL(hAPP(X1,X0))
& X0 != X2 ) )
& ( hBOOL(hAPP(X1,X0))
| X0 = X2
| ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0)) ) ),
inference(nnf_transformation,[],[f9079]) ).
fof(f9079,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X3),X2),X1),X0))
<=> ( hBOOL(hAPP(X1,X0))
| X0 = X2 ) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X20,X19,X34,X4] :
( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(X4),X34),X19),X20))
<=> ( hBOOL(hAPP(X19,X20))
| X20 = X34 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31539,plain,
spl625_586,
inference(avatar_split_clause,[],[f25199,f31537]) ).
fof(f31537,plain,
( spl625_586
<=> ! [X2,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_586])]) ).
fof(f25199,plain,
! [X2,X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X1)),
inference(equality_resolution,[],[f21103]) ).
fof(f21103,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0)) ),
inference(cnf_transformation,[],[f15746]) ).
fof(f15746,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0))
| X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0)) )
& ( ( X0 != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0)) ) ),
inference(flattening,[],[f15745]) ).
fof(f15745,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0))
| X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0)) )
& ( ( X0 != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0)) ) ),
inference(nnf_transformation,[],[f8150]) ).
fof(f8150,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X2,tc_HOL_Obool)),X1),X0))
<=> ( X0 != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool)),X1),X0)) ) ),
inference(rectify,[],[f579]) ).
fof(f579,axiom,
! [X21,X19,X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),X19),X21))
<=> ( X19 != X21
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X19),X21)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31535,plain,
( spl625_585
| spl625_233
| ~ spl625_403 ),
inference(avatar_split_clause,[],[f30770,f30728,f29955,f31532]) ).
fof(f31532,plain,
( spl625_585
<=> sP10(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_585])]) ).
fof(f29955,plain,
( spl625_233
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_233])]) ).
fof(f30728,plain,
( spl625_403
<=> ! [X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_403])]) ).
fof(f30770,plain,
( sP10(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))
| spl625_233
| ~ spl625_403 ),
inference(resolution,[],[f30729,f29957]) ).
fof(f29957,plain,
( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| spl625_233 ),
inference(avatar_component_clause,[],[f29955]) ).
fof(f30729,plain,
( ! [X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X1,X1) )
| ~ spl625_403 ),
inference(avatar_component_clause,[],[f30728]) ).
fof(f31530,plain,
spl625_584,
inference(avatar_split_clause,[],[f25198,f31528]) ).
fof(f31528,plain,
( spl625_584
<=> ! [X2,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_584])]) ).
fof(f25198,plain,
! [X2,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X1))),
inference(equality_resolution,[],[f21101]) ).
fof(f21101,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
| X0 != X1 ),
inference(cnf_transformation,[],[f15744]) ).
fof(f15744,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
| X0 != X1 )
& ( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0))) ) ),
inference(nnf_transformation,[],[f8149]) ).
fof(f8149,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
<=> X0 = X1 ),
inference(rectify,[],[f253]) ).
fof(f253,axiom,
! [X34,X20,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),X20),hAPP(c_fequal,X34)))
<=> X20 = X34 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31526,plain,
spl625_583,
inference(avatar_split_clause,[],[f25109,f31524]) ).
fof(f31524,plain,
( spl625_583
<=> ! [X2,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_583])]) ).
fof(f25109,plain,
! [X2,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f20332]) ).
fof(f20332,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),X1))
| X0 != X1
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f15328]) ).
fof(f15328,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0)) )
| X0 != X1 ) )
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f15327]) ).
fof(f15327,plain,
! [X0,X1,X2] :
( ( ( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0)) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0)) )
| X0 != X1 ) )
| ~ class_Orderings_Oorder(X2) ),
inference(nnf_transformation,[],[f12040]) ).
fof(f12040,plain,
! [X0,X1,X2] :
( ( X0 = X1
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0)) ) )
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f7730]) ).
fof(f7730,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( X0 = X1
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),X0)) ) ) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X34,X20,X4] :
( class_Orderings_Oorder(X4)
=> ( X20 = X34
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X34),X20))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X20),X34)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31522,plain,
spl625_582,
inference(avatar_split_clause,[],[f25105,f31520]) ).
fof(f31520,plain,
( spl625_582
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_582])]) ).
fof(f25105,plain,
! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Oorder(X2) ),
inference(equality_resolution,[],[f20316]) ).
fof(f20316,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| ~ class_Orderings_Oorder(X2) ),
inference(cnf_transformation,[],[f12013]) ).
fof(f12013,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| ~ class_Orderings_Oorder(X2) ),
inference(flattening,[],[f12012]) ).
fof(f12012,plain,
! [X0,X1,X2] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| ~ class_Orderings_Oorder(X2) ),
inference(ennf_transformation,[],[f7716]) ).
fof(f7716,plain,
! [X0,X1,X2] :
( class_Orderings_Oorder(X2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
=> X0 != X1 ) ),
inference(rectify,[],[f517]) ).
fof(f517,axiom,
! [X29,X22,X23] :
( class_Orderings_Oorder(X23)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23),X22),X29))
=> X22 != X29 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31518,plain,
spl625_581,
inference(avatar_split_clause,[],[f25096,f31516]) ).
fof(f31516,plain,
( spl625_581
<=> ! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_581])]) ).
fof(f25096,plain,
! [X2,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(equality_resolution,[],[f20171]) ).
fof(f20171,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f15275]) ).
fof(f15275,plain,
! [X0,X1,X2] :
( ( ( X0 != X1
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| X0 = X1 ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(flattening,[],[f15274]) ).
fof(f15274,plain,
! [X0,X1,X2] :
( ( ( X0 != X1
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0)) ) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0))
| X0 = X1 ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(nnf_transformation,[],[f11864]) ).
fof(f11864,plain,
! [X0,X1,X2] :
( ( X0 != X1
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0)) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7614]) ).
fof(f7614,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( X0 != X1
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X0),X1))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X2),X1),X0)) ) ) ),
inference(rectify,[],[f526]) ).
fof(f526,axiom,
! [X34,X20,X4] :
( class_Orderings_Olinorder(X4)
=> ( X20 != X34
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X34),X20))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X20),X34)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31514,plain,
spl625_580,
inference(avatar_split_clause,[],[f24919,f31512]) ).
fof(f31512,plain,
( spl625_580
<=> ! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_580])]) ).
fof(f24919,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,c_Groups_Ozero__class_Ozero(X1))
| ~ class_Rings_Olinordered__idom(X1) ),
inference(equality_resolution,[],[f18323]) ).
fof(f18323,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0
| ~ class_Rings_Olinordered__idom(X1) ),
inference(cnf_transformation,[],[f14697]) ).
fof(f14697,plain,
! [X0,X1] :
( ( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| c_Groups_Ozero__class_Ozero(X1) != c_Groups_Osgn__class_Osgn(X1,X0) ) )
| ~ class_Rings_Olinordered__idom(X1) ),
inference(nnf_transformation,[],[f10623]) ).
fof(f10623,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Rings_Olinordered__idom(X1) ),
inference(ennf_transformation,[],[f6253]) ).
fof(f6253,plain,
! [X0,X1] :
( class_Rings_Olinordered__idom(X1)
=> ( c_Groups_Ozero__class_Ozero(X1) = c_Groups_Osgn__class_Osgn(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f3225]) ).
fof(f3225,axiom,
! [X6,X4] :
( class_Rings_Olinordered__idom(X4)
=> ( c_Groups_Ozero__class_Ozero(X4) = c_Groups_Osgn__class_Osgn(X4,X6)
<=> c_Groups_Ozero__class_Ozero(X4) = X6 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31510,plain,
spl625_579,
inference(avatar_split_clause,[],[f24142,f31508]) ).
fof(f31508,plain,
( spl625_579
<=> ! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_579])]) ).
fof(f24142,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X1),c_Wellfounded_Oless__than),X0)),
inference(definition_unfolding,[],[f17703,f17211]) ).
fof(f17211,plain,
! [X0] : c_Wellfounded_Omeasure(X0) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0),c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f5314]) ).
fof(f5314,plain,
! [X0] : c_Wellfounded_Omeasure(X0) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X0),c_Wellfounded_Oless__than),
inference(rectify,[],[f3088]) ).
fof(f3088,axiom,
! [X4] : c_Wellfounded_Omeasure(X4) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,X4),c_Wellfounded_Oless__than),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17703,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X0)),
inference(cnf_transformation,[],[f5719]) ).
fof(f5719,plain,
! [X0,X1] : c_Wellfounded_Owf(X1,hAPP(c_Wellfounded_Omeasure(X1),X0)),
inference(rectify,[],[f3348]) ).
fof(f3348,axiom,
! [X1,X4] : c_Wellfounded_Owf(X4,hAPP(c_Wellfounded_Omeasure(X4),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31506,plain,
spl625_578,
inference(avatar_split_clause,[],[f24140,f31504]) ).
fof(f31504,plain,
( spl625_578
<=> ! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_578])]) ).
fof(f24140,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))),
inference(definition_unfolding,[],[f17694,f17790]) ).
fof(f17790,plain,
! [X0,X1] : c_List_Oupt(X1,X0) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0)),
inference(cnf_transformation,[],[f5806]) ).
fof(f5806,plain,
! [X0,X1] : c_List_Oupt(X1,X0) = c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0)),
inference(rectify,[],[f4006]) ).
fof(f4006,axiom,
! [X78,X123] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X123),X78)) = c_List_Oupt(X123,X78),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17694,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X0)),
inference(cnf_transformation,[],[f5710]) ).
fof(f5710,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X1,X0)),
inference(rectify,[],[f4270]) ).
fof(f4270,axiom,
! [X113,X114] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(X114,X113)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31502,plain,
spl625_577,
inference(avatar_split_clause,[],[f24032,f31500]) ).
fof(f31500,plain,
( spl625_577
<=> ! [X0] : c_Int_OPls != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_577])]) ).
fof(f24032,plain,
! [X0] : c_Int_OPls != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin),
inference(definition_unfolding,[],[f17151,f23983]) ).
fof(f17151,plain,
! [X0] : c_Int_OPls != c_Int_OBit1(X0),
inference(cnf_transformation,[],[f5254]) ).
fof(f5254,plain,
! [X0] : c_Int_OPls != c_Int_OBit1(X0),
inference(rectify,[],[f2569]) ).
fof(f2569,axiom,
! [X124] : c_Int_OPls != c_Int_OBit1(X124),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31498,plain,
spl625_576,
inference(avatar_split_clause,[],[f24001,f31495]) ).
fof(f31495,plain,
( spl625_576
<=> c_Int_OMin = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OMin)),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_576])]) ).
fof(f24001,plain,
c_Int_OMin = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(c_Int_OMin)),c_Int_OMin),
inference(definition_unfolding,[],[f17017,f23983]) ).
fof(f17017,plain,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
inference(cnf_transformation,[],[f2782]) ).
fof(f2782,axiom,
c_Int_OMin = c_Int_OBit1(c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31493,plain,
spl625_575,
inference(avatar_split_clause,[],[f23427,f31491]) ).
fof(f31491,plain,
( spl625_575
<=> ! [X2,X4,X0,X5,X3,X1] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OCond(X5,X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_575])]) ).
fof(f23427,plain,
! [X2,X3,X0,X1,X4,X5] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OCond(X5,X4,X3),
inference(cnf_transformation,[],[f9741]) ).
fof(f9741,plain,
! [X0,X1,X2,X3,X4,X5] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OCond(X5,X4,X3),
inference(rectify,[],[f166]) ).
fof(f166,axiom,
! [X13,X53,X70,X55,X56,X51] : c_Com_Ocom_OLocal(X70,X53,X13) != c_Com_Ocom_OCond(X51,X56,X55),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31489,plain,
( ~ spl625_574
| ~ spl625_319
| ~ spl625_395 ),
inference(avatar_split_clause,[],[f30759,f30689,f30322,f31486]) ).
fof(f31486,plain,
( spl625_574
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_574])]) ).
fof(f30322,plain,
( spl625_319
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_319])]) ).
fof(f30689,plain,
( spl625_395
<=> c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_395])]) ).
fof(f30759,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_HOL_Obool_Obool__size(c_fTrue)
| ~ spl625_319
| ~ spl625_395 ),
inference(superposition,[],[f30323,f30691]) ).
fof(f30691,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))
| ~ spl625_395 ),
inference(avatar_component_clause,[],[f30689]) ).
fof(f30323,plain,
( ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0)
| ~ spl625_319 ),
inference(avatar_component_clause,[],[f30322]) ).
fof(f31484,plain,
spl625_573,
inference(avatar_split_clause,[],[f22308,f31482]) ).
fof(f31482,plain,
( spl625_573
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP(X2,X3))
| ~ sP57(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_573])]) ).
fof(f22308,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X2,X3))
| ~ sP57(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16130]) ).
fof(f16130,plain,
! [X0,X1,X2,X3] :
( ( sP57(X0,X1,X2,X3)
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X4),X0))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X4)) )
| ~ hBOOL(hAPP(X2,X3)) )
& ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),sK462(X0,X1,X2,X3)),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),sK462(X0,X1,X2,X3)))
& hBOOL(hAPP(X2,X3)) )
| ~ sP57(X0,X1,X2,X3) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK462])],[f16128,f16129]) ).
fof(f16129,plain,
! [X0,X1,X2,X3] :
( ? [X5] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X5),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X5)) )
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),sK462(X0,X1,X2,X3)),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),sK462(X0,X1,X2,X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f16128,plain,
! [X0,X1,X2,X3] :
( ( sP57(X0,X1,X2,X3)
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X4),X0))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X4)) )
| ~ hBOOL(hAPP(X2,X3)) )
& ( ( ? [X5] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X5),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X5)) )
& hBOOL(hAPP(X2,X3)) )
| ~ sP57(X0,X1,X2,X3) ) ),
inference(rectify,[],[f16127]) ).
fof(f16127,plain,
! [X0,X2,X3,X1] :
( ( sP57(X0,X2,X3,X1)
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
| ~ hBOOL(hAPP(X3,X1)) )
& ( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) )
| ~ sP57(X0,X2,X3,X1) ) ),
inference(flattening,[],[f16126]) ).
fof(f16126,plain,
! [X0,X2,X3,X1] :
( ( sP57(X0,X2,X3,X1)
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
| ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
| ~ hBOOL(hAPP(X3,X1)) )
& ( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) )
| ~ sP57(X0,X2,X3,X1) ) ),
inference(nnf_transformation,[],[f14500]) ).
fof(f14500,plain,
! [X0,X2,X3,X1] :
( sP57(X0,X2,X3,X1)
<=> ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP57])]) ).
fof(f31480,plain,
spl625_572,
inference(avatar_split_clause,[],[f22062,f31478]) ).
fof(f31478,plain,
( spl625_572
<=> ! [X2,X0,X1,X3] :
( hBOOL(hAPP(X2,X3))
| ~ sP53(X0,X1,X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_572])]) ).
fof(f22062,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X2,X3))
| ~ sP53(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f16008]) ).
fof(f16008,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),sK416(X0,X1,X2,X3)),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),sK416(X0,X1,X2,X3)))
& hBOOL(hAPP(X2,X3)) )
| ~ sP53(X0,X1,X2,X3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK416])],[f16006,f16007]) ).
fof(f16007,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X4)) )
=> ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),sK416(X0,X1,X2,X3)),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),sK416(X0,X1,X2,X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f16006,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X2,X1)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X1),X3),X4)) )
& hBOOL(hAPP(X2,X3)) )
| ~ sP53(X0,X1,X2,X3) ),
inference(rectify,[],[f16005]) ).
fof(f16005,plain,
! [X0,X2,X3,X1] :
( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) )
| ~ sP53(X0,X2,X3,X1) ),
inference(nnf_transformation,[],[f14492]) ).
fof(f14492,plain,
! [X0,X2,X3,X1] :
( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(X3,X2)),X4),X0))
& hBOOL(hAPP(hAPP(c_Natural_Oevalc(X2),X1),X4)) )
& hBOOL(hAPP(X3,X1)) )
| ~ sP53(X0,X2,X3,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP53])]) ).
fof(f31476,plain,
spl625_571,
inference(avatar_split_clause,[],[f21286,f31474]) ).
fof(f31474,plain,
( spl625_571
<=> ! [X2,X0,X1,X3] : c_Option_Ooption_Ooption__rec(X3,X2,X1,X0,c_Option_Ooption_ONone(X2)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_571])]) ).
fof(f21286,plain,
! [X2,X3,X0,X1] : c_Option_Ooption_Ooption__rec(X3,X2,X1,X0,c_Option_Ooption_ONone(X2)) = X1,
inference(cnf_transformation,[],[f8225]) ).
fof(f8225,plain,
! [X0,X1,X2,X3] : c_Option_Ooption_Ooption__rec(X3,X2,X1,X0,c_Option_Ooption_ONone(X2)) = X1,
inference(rectify,[],[f4906]) ).
fof(f4906,axiom,
! [X67,X25,X24,X4] : c_Option_Ooption_Ooption__rec(X4,X24,X25,X67,c_Option_Ooption_ONone(X24)) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31472,plain,
spl625_570,
inference(avatar_split_clause,[],[f21285,f31470]) ).
fof(f31470,plain,
( spl625_570
<=> ! [X2,X0,X1,X3] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_570])]) ).
fof(f21285,plain,
! [X2,X3,X0,X1] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1,
inference(cnf_transformation,[],[f8224]) ).
fof(f8224,plain,
! [X0,X1,X2,X3] : hAPP(hAPP(c_COMBK(X3,X2),X1),X0) = X1,
inference(rectify,[],[f5222]) ).
fof(f5222,axiom,
! [X326,X325,X4,X23] : hAPP(hAPP(c_COMBK(X23,X4),X325),X326) = X325,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31468,plain,
spl625_569,
inference(avatar_split_clause,[],[f20873,f31466]) ).
fof(f31466,plain,
( spl625_569
<=> ! [X2,X0,X1] :
( X1 = X2
| ~ c_List_Olist__all2(X0,X0,c_fequal,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_569])]) ).
fof(f20873,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ c_List_Olist__all2(X0,X0,c_fequal,X2,X1) ),
inference(cnf_transformation,[],[f15555]) ).
fof(f15555,plain,
! [X0,X1,X2] :
( ( X1 = X2
| ~ c_List_Olist__all2(X0,X0,c_fequal,X2,X1) )
& ( c_List_Olist__all2(X0,X0,c_fequal,X2,X1)
| X1 != X2 ) ),
inference(nnf_transformation,[],[f8096]) ).
fof(f8096,plain,
! [X0,X1,X2] :
( X1 = X2
<=> c_List_Olist__all2(X0,X0,c_fequal,X2,X1) ),
inference(rectify,[],[f4513]) ).
fof(f4513,axiom,
! [X4,X259,X258] :
( X258 = X259
<=> c_List_Olist__all2(X4,X4,c_fequal,X258,X259) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31464,plain,
spl625_568,
inference(avatar_split_clause,[],[f20497,f31462]) ).
fof(f31462,plain,
( spl625_568
<=> ! [X2,X0,X1] :
( sP23(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_568])]) ).
fof(f20497,plain,
! [X2,X0,X1] :
( sP23(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(cnf_transformation,[],[f14442]) ).
fof(f14442,plain,
! [X0,X1,X2] :
( sP23(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(definition_folding,[],[f12192,f14441,f14440]) ).
fof(f14440,plain,
! [X0,X1,X2] :
( sP22(X0,X1,X2)
<=> ? [X3] :
( ! [X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP22])]) ).
fof(f14441,plain,
! [X2,X1,X0] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> sP22(X0,X1,X2) )
| ~ sP23(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP23])]) ).
fof(f12192,plain,
! [X0,X1,X2] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> ? [X3] :
( ! [X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(flattening,[],[f12191]) ).
fof(f12191,plain,
! [X0,X1,X2] :
( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> ? [X3] :
( ! [X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(ennf_transformation,[],[f7845]) ).
fof(f7845,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
=> ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> ? [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
=> ( X3 != X4
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4) ) )
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) ) ),
inference(rectify,[],[f1653]) ).
fof(f1653,axiom,
! [X1,X19,X4] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X19))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X19) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ? [X2] :
( ! [X118] :
( hBOOL(hAPP(hAPP(c_member(X4),X118),X19))
=> ( X2 != X118
=> hAPP(X1,X118) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& hAPP(X1,X2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& hBOOL(hAPP(hAPP(c_member(X4),X2),X19)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31460,plain,
spl625_567,
inference(avatar_split_clause,[],[f20488,f31458]) ).
fof(f31458,plain,
( spl625_567
<=> ! [X2,X0,X1] :
( sP21(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_567])]) ).
fof(f20488,plain,
! [X2,X0,X1] :
( sP21(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(cnf_transformation,[],[f14439]) ).
fof(f14439,plain,
! [X0,X1,X2] :
( sP21(X2,X1,X0)
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(definition_folding,[],[f12190,f14438,f14437]) ).
fof(f14437,plain,
! [X0,X1,X2] :
( sP20(X0,X1,X2)
<=> ? [X3] :
( ! [X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP20])]) ).
fof(f14438,plain,
! [X2,X1,X0] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> sP20(X0,X1,X2) )
| ~ sP21(X2,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP21])]) ).
fof(f12190,plain,
! [X0,X1,X2] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> ? [X3] :
( ! [X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(flattening,[],[f12189]) ).
fof(f12189,plain,
! [X0,X1,X2] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> ? [X3] :
( ! [X4] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4)
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1)) )
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) )
| ~ hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1)) ),
inference(ennf_transformation,[],[f7844]) ).
fof(f7844,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X2),X1))
=> ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X2,tc_Nat_Onat),X0),X1)
<=> ? [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
=> ( X3 != X4
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(X0,X4) ) )
& c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(X0,X3)
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) ) ) ),
inference(rectify,[],[f1655]) ).
fof(f1655,axiom,
! [X1,X19,X4] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X19))
=> ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(X4,tc_Nat_Onat),X1),X19) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ? [X2] :
( ! [X118] :
( hBOOL(hAPP(hAPP(c_member(X4),X118),X19))
=> ( X2 != X118
=> hAPP(X1,X118) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& hAPP(X1,X2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& hBOOL(hAPP(hAPP(c_member(X4),X2),X19)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31456,plain,
spl625_566,
inference(avatar_split_clause,[],[f20370,f31454]) ).
fof(f31454,plain,
( spl625_566
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_566])]) ).
fof(f20370,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(cnf_transformation,[],[f12059]) ).
fof(f12059,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Equiv__Relations_Oequivp(X2,X1) ),
inference(ennf_transformation,[],[f7749]) ).
fof(f7749,plain,
! [X0,X1,X2] :
( c_Equiv__Relations_Oequivp(X2,X1)
=> hBOOL(hAPP(hAPP(X1,X0),X0)) ),
inference(rectify,[],[f1254]) ).
fof(f1254,axiom,
! [X20,X42,X4] :
( c_Equiv__Relations_Oequivp(X4,X42)
=> hBOOL(hAPP(hAPP(X42,X20),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31452,plain,
spl625_565,
inference(avatar_split_clause,[],[f20369,f31450]) ).
fof(f31450,plain,
( spl625_565
<=> ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_565])]) ).
fof(f20369,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ),
inference(cnf_transformation,[],[f12058]) ).
fof(f12058,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(X1,X0),X0))
| ~ c_Predicate_Oreflp(X2,X1) ),
inference(ennf_transformation,[],[f7748]) ).
fof(f7748,plain,
! [X0,X1,X2] :
( c_Predicate_Oreflp(X2,X1)
=> hBOOL(hAPP(hAPP(X1,X0),X0)) ),
inference(rectify,[],[f3529]) ).
fof(f3529,axiom,
! [X20,X60,X4] :
( c_Predicate_Oreflp(X4,X60)
=> hBOOL(hAPP(hAPP(X60,X20),X20)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31448,plain,
spl625_564,
inference(avatar_split_clause,[],[f19385,f31446]) ).
fof(f31446,plain,
( spl625_564
<=> ! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_564])]) ).
fof(f19385,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2),
inference(cnf_transformation,[],[f6920]) ).
fof(f6920,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Olist_OCons(X2),X1),X0) != c_List_Olist_ONil(X2),
inference(rectify,[],[f3962]) ).
fof(f3962,axiom,
! [X283,X149,X23] : c_List_Olist_ONil(X23) != hAPP(hAPP(c_List_Olist_OCons(X23),X149),X283),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31444,plain,
( spl625_563
| ~ spl625_255
| ~ spl625_347 ),
inference(avatar_split_clause,[],[f30732,f30485,f30051,f31441]) ).
fof(f31441,plain,
( spl625_563
<=> sP5(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_563])]) ).
fof(f30485,plain,
( spl625_347
<=> 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,[spl625_347])]) ).
fof(f30732,plain,
( sP5(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl625_255
| ~ spl625_347 ),
inference(superposition,[],[f30052,f30487]) ).
fof(f30487,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl625_347 ),
inference(avatar_component_clause,[],[f30485]) ).
fof(f31439,plain,
spl625_562,
inference(avatar_split_clause,[],[f19027,f31437]) ).
fof(f31437,plain,
( spl625_562
<=> ! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP7(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_562])]) ).
fof(f19027,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP7(X1,X0) ),
inference(cnf_transformation,[],[f14933]) ).
fof(f14933,plain,
! [X0,X1] :
( ( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
| ~ sP7(X1,X0) )
& ( sP7(X1,X0)
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ) ),
inference(nnf_transformation,[],[f14416]) ).
fof(f14416,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
<=> sP7(X1,X0) ),
inference(definition_folding,[],[f11274,f14415]) ).
fof(f11274,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
<=> ( ( hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ! [X2] :
( hBOOL(hAPP(X1,X2))
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) != X0 ) ) ),
inference(ennf_transformation,[],[f6774]) ).
fof(f6774,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X2] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X2) = X0
=> hBOOL(hAPP(X1,X2)) ) ) ),
inference(rectify,[],[f2499]) ).
fof(f2499,axiom,
! [X147,X5] :
( hBOOL(hAPP(X5,hAPP(c_Int_Onat,X147)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X147),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
=> hBOOL(hAPP(X5,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
& ! [X94] :
( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X94) = X147
=> hBOOL(hAPP(X5,X94)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31435,plain,
spl625_561,
inference(avatar_split_clause,[],[f19026,f31433]) ).
fof(f19026,plain,
! [X0,X1] :
( sP7(X1,X0)
| ~ hBOOL(hAPP(X1,hAPP(c_Int_Onat,X0))) ),
inference(cnf_transformation,[],[f14933]) ).
fof(f31431,plain,
spl625_560,
inference(avatar_split_clause,[],[f18952,f31429]) ).
fof(f31429,plain,
( spl625_560
<=> ! [X0,X1,X3] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_560])]) ).
fof(f18952,plain,
! [X3,X0,X1] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ),
inference(cnf_transformation,[],[f14869]) ).
fof(f14869,plain,
! [X0,X1] :
( ( c_Wellfounded_OwfP(X1,X0)
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK162(X0,X1))) )
& ( ! [X3] : hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK162])],[f14867,f14868]) ).
fof(f14868,plain,
! [X0,X1] :
( ? [X2] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2))
=> ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK162(X0,X1))) ),
introduced(choice_axiom,[]) ).
fof(f14867,plain,
! [X0,X1] :
( ( c_Wellfounded_OwfP(X1,X0)
| ? [X2] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) )
& ( ! [X3] : hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
inference(rectify,[],[f14866]) ).
fof(f14866,plain,
! [X0,X1] :
( ( c_Wellfounded_OwfP(X1,X0)
| ? [X2] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) )
& ( ! [X2] : hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2))
| ~ c_Wellfounded_OwfP(X1,X0) ) ),
inference(nnf_transformation,[],[f6752]) ).
fof(f6752,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,X0)
<=> ! [X2] : hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) ),
inference(rectify,[],[f3566]) ).
fof(f3566,axiom,
! [X60,X4] :
( c_Wellfounded_OwfP(X4,X60)
<=> ! [X48] : hBOOL(hAPP(c_Wellfounded_Oaccp(X4,X60),X48)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31427,plain,
spl625_559,
inference(avatar_split_clause,[],[f18610,f31425]) ).
fof(f31425,plain,
( spl625_559
<=> ! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_559])]) ).
fof(f18610,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10910]) ).
fof(f10910,plain,
! [X0,X1] :
( c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0))
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6486]) ).
fof(f6486,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_OwfP(X1,c_FunDef_Oin__rel(X1,X1,X0)) ),
inference(rectify,[],[f3573]) ).
fof(f3573,axiom,
! [X42,X4] :
( c_Wellfounded_Owf(X4,X42)
=> c_Wellfounded_OwfP(X4,c_FunDef_Oin__rel(X4,X4,X42)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31423,plain,
spl625_558,
inference(avatar_split_clause,[],[f18602,f31421]) ).
fof(f31421,plain,
( spl625_558
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X0),X0))
| ~ class_HOL_Oequal(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_558])]) ).
fof(f18602,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X0),X0))
| ~ class_HOL_Oequal(X1) ),
inference(cnf_transformation,[],[f10901]) ).
fof(f10901,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X0),X0))
| ~ class_HOL_Oequal(X1) ),
inference(ennf_transformation,[],[f6478]) ).
fof(f6478,plain,
! [X0,X1] :
( class_HOL_Oequal(X1)
=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X1),X0),X0)) ),
inference(rectify,[],[f4945]) ).
fof(f4945,axiom,
! [X22,X23] :
( class_HOL_Oequal(X23)
=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(X23),X22),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31419,plain,
spl625_557,
inference(avatar_split_clause,[],[f18597,f31417]) ).
fof(f31417,plain,
( spl625_557
<=> ! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_557])]) ).
fof(f18597,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(cnf_transformation,[],[f10892]) ).
fof(f10892,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(flattening,[],[f10891]) ).
fof(f10891,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(ennf_transformation,[],[f6473]) ).
fof(f6473,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X1)
=> ( c_Nat__Transfer_Ois__nat(X0)
=> c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X1,X0)) ) ),
inference(rectify,[],[f2909]) ).
fof(f2909,axiom,
! [X29,X22] :
( c_Nat__Transfer_Ois__nat(X22)
=> ( c_Nat__Transfer_Ois__nat(X29)
=> c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,X22,X29)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31415,plain,
spl625_556,
inference(avatar_split_clause,[],[f18593,f31413]) ).
fof(f31413,plain,
( spl625_556
<=> ! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_556])]) ).
fof(f18593,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(cnf_transformation,[],[f10886]) ).
fof(f10886,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0))
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(ennf_transformation,[],[f6470]) ).
fof(f6470,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X1)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X1),X0)) ),
inference(rectify,[],[f2912]) ).
fof(f2912,axiom,
! [X88,X22] :
( c_Nat__Transfer_Ois__nat(X22)
=> c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),X22),X88)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31411,plain,
spl625_555,
inference(avatar_split_clause,[],[f18551,f31409]) ).
fof(f31409,plain,
( spl625_555
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_555])]) ).
fof(f18551,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10850]) ).
fof(f10850,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6443]) ).
fof(f6443,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X0),X0)) ),
inference(rectify,[],[f14]) ).
fof(f14,axiom,
! [X22,X23] :
( class_Orderings_Opreorder(X23)
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X23),X22),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31407,plain,
spl625_554,
inference(avatar_split_clause,[],[f18550,f31405]) ).
fof(f31405,plain,
( spl625_554
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_554])]) ).
fof(f18550,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10849]) ).
fof(f10849,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6442]) ).
fof(f6442,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X1),X0),X0)) ),
inference(rectify,[],[f527]) ).
fof(f527,axiom,
! [X22,X23] :
( class_Orderings_Opreorder(X23)
=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X23),X22),X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31403,plain,
spl625_553,
inference(avatar_split_clause,[],[f18519,f31401]) ).
fof(f31401,plain,
( spl625_553
<=> ! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_553])]) ).
fof(f18519,plain,
! [X0,X1] :
( c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP0(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f14730]) ).
fof(f14730,plain,
! [X0,X1] :
( ( ( c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP0(X1,X0) )
& ( sP0(X1,X0)
| ~ c_List_Olinorder__class_Osorted(X1,X0) ) )
| ~ sP1(X0,X1) ),
inference(nnf_transformation,[],[f14403]) ).
fof(f14403,plain,
! [X0,X1] :
( ( c_List_Olinorder__class_Osorted(X1,X0)
<=> sP0(X1,X0) )
| ~ sP1(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f31399,plain,
( spl625_552
| ~ spl625_256
| ~ spl625_347 ),
inference(avatar_split_clause,[],[f30731,f30485,f30055,f31396]) ).
fof(f31396,plain,
( spl625_552
<=> sP6(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_552])]) ).
fof(f30731,plain,
( sP6(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ spl625_256
| ~ spl625_347 ),
inference(superposition,[],[f30056,f30487]) ).
fof(f31394,plain,
spl625_551,
inference(avatar_split_clause,[],[f18518,f31392]) ).
fof(f31392,plain,
( spl625_551
<=> ! [X0,X1] :
( sP0(X1,X0)
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP1(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_551])]) ).
fof(f18518,plain,
! [X0,X1] :
( sP0(X1,X0)
| ~ c_List_Olinorder__class_Osorted(X1,X0)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f14730]) ).
fof(f31390,plain,
spl625_550,
inference(avatar_split_clause,[],[f18456,f31388]) ).
fof(f31388,plain,
( spl625_550
<=> ! [X0,X1] :
( c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_550])]) ).
fof(f18456,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f10750]) ).
fof(f10750,plain,
! [X0,X1] :
( c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f6367]) ).
fof(f6367,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Divides_Odiv__class_Omod(X1,X0,c_Groups_Ozero__class_Ozero(X1)) = X0 ),
inference(rectify,[],[f2105]) ).
fof(f2105,axiom,
! [X32,X23] :
( class_Divides_Osemiring__div(X23)
=> c_Divides_Odiv__class_Omod(X23,X32,c_Groups_Ozero__class_Ozero(X23)) = X32 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31386,plain,
spl625_549,
inference(avatar_split_clause,[],[f18455,f31384]) ).
fof(f31384,plain,
( spl625_549
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0)
| ~ class_Divides_Osemiring__div(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_549])]) ).
fof(f18455,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(cnf_transformation,[],[f10749]) ).
fof(f10749,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0)
| ~ class_Divides_Osemiring__div(X1) ),
inference(ennf_transformation,[],[f6366]) ).
fof(f6366,plain,
! [X0,X1] :
( class_Divides_Osemiring__div(X1)
=> c_Groups_Ozero__class_Ozero(X1) = c_Divides_Odiv__class_Omod(X1,X0,X0) ),
inference(rectify,[],[f2104]) ).
fof(f2104,axiom,
! [X32,X23] :
( class_Divides_Osemiring__div(X23)
=> c_Groups_Ozero__class_Ozero(X23) = c_Divides_Odiv__class_Omod(X23,X32,X32) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31382,plain,
spl625_548,
inference(avatar_split_clause,[],[f18442,f31380]) ).
fof(f31380,plain,
( spl625_548
<=> ! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Int_Oiszero(X1,X0)
| ~ class_Rings_Osemiring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_548])]) ).
fof(f18442,plain,
! [X0,X1] :
( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Int_Oiszero(X1,X0)
| ~ class_Rings_Osemiring__1(X1) ),
inference(cnf_transformation,[],[f14716]) ).
fof(f14716,plain,
! [X0,X1] :
( ( ( c_Int_Oiszero(X1,X0)
| c_Groups_Ozero__class_Ozero(X1) != X0 )
& ( c_Groups_Ozero__class_Ozero(X1) = X0
| ~ c_Int_Oiszero(X1,X0) ) )
| ~ class_Rings_Osemiring__1(X1) ),
inference(nnf_transformation,[],[f10737]) ).
fof(f10737,plain,
! [X0,X1] :
( ( c_Int_Oiszero(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 )
| ~ class_Rings_Osemiring__1(X1) ),
inference(ennf_transformation,[],[f6354]) ).
fof(f6354,plain,
! [X0,X1] :
( class_Rings_Osemiring__1(X1)
=> ( c_Int_Oiszero(X1,X0)
<=> c_Groups_Ozero__class_Ozero(X1) = X0 ) ),
inference(rectify,[],[f2667]) ).
fof(f2667,axiom,
! [X116,X4] :
( class_Rings_Osemiring__1(X4)
=> ( c_Int_Oiszero(X4,X116)
<=> c_Groups_Ozero__class_Ozero(X4) = X116 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31378,plain,
spl625_547,
inference(avatar_split_clause,[],[f18199,f31376]) ).
fof(f31376,plain,
( spl625_547
<=> ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_547])]) ).
fof(f18199,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ),
inference(cnf_transformation,[],[f6158]) ).
fof(f6158,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ),
inference(rectify,[],[f5226]) ).
fof(f5226,axiom,
! [X34,X20] :
( X20 = X34
| ~ hBOOL(hAPP(hAPP(c_fequal,X20),X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31374,plain,
spl625_546,
inference(avatar_split_clause,[],[f17765,f31372]) ).
fof(f31372,plain,
( spl625_546
<=> ! [X0,X1] : c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_546])]) ).
fof(f17765,plain,
! [X0,X1] : c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X0)),
inference(cnf_transformation,[],[f5781]) ).
fof(f5781,plain,
! [X0,X1] : c_Relation_Orefl__on(X1,c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X1,X0)),
inference(rectify,[],[f4706]) ).
fof(f4706,axiom,
! [X60,X4] : c_Relation_Orefl__on(X4,c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(X4,X60)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31370,plain,
spl625_545,
inference(avatar_split_clause,[],[f17764,f31368]) ).
fof(f31368,plain,
( spl625_545
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_545])]) ).
fof(f17764,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X0)),
inference(cnf_transformation,[],[f5780]) ).
fof(f5780,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool)),X0),X0)),
inference(rectify,[],[f44]) ).
fof(f44,axiom,
! [X19,X4] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool)),X19),X19)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31366,plain,
spl625_544,
inference(avatar_split_clause,[],[f17763,f31364]) ).
fof(f31364,plain,
( spl625_544
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_544])]) ).
fof(f17763,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))),
inference(cnf_transformation,[],[f5779]) ).
fof(f5779,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X1),X0))),
inference(rectify,[],[f1885]) ).
fof(f1885,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,X153),X152))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31362,plain,
spl625_543,
inference(avatar_split_clause,[],[f17762,f31360]) ).
fof(f31360,plain,
( spl625_543
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_543])]) ).
fof(f17762,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X0))),
inference(cnf_transformation,[],[f5778]) ).
fof(f5778,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X1),X0))),
inference(rectify,[],[f1939]) ).
fof(f1939,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,X153),X152))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31358,plain,
spl625_542,
inference(avatar_split_clause,[],[f17761,f31356]) ).
fof(f31356,plain,
( spl625_542
<=> ! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_542])]) ).
fof(f17761,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(cnf_transformation,[],[f5777]) ).
fof(f5777,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(rectify,[],[f259]) ).
fof(f259,axiom,
! [X76,X4] : hAPP(c_Set_Oimage(X4,X4,c_COMBI(X4)),X76) = X76,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31354,plain,
( spl625_541
| ~ spl625_239
| ~ spl625_305 ),
inference(avatar_split_clause,[],[f30401,f30262,f29986,f31351]) ).
fof(f31351,plain,
( spl625_541
<=> sP4(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_541])]) ).
fof(f29986,plain,
( spl625_239
<=> c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_239])]) ).
fof(f30262,plain,
( spl625_305
<=> ! [X0,X1] :
( sP4(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_305])]) ).
fof(f30401,plain,
( sP4(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl625_239
| ~ spl625_305 ),
inference(resolution,[],[f30263,f29988]) ).
fof(f29988,plain,
( c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl625_239 ),
inference(avatar_component_clause,[],[f29986]) ).
fof(f30263,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,X0)
| sP4(X1,X0) )
| ~ spl625_305 ),
inference(avatar_component_clause,[],[f30262]) ).
fof(f31349,plain,
spl625_540,
inference(avatar_split_clause,[],[f17760,f31347]) ).
fof(f31347,plain,
( spl625_540
<=> ! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_540])]) ).
fof(f17760,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(cnf_transformation,[],[f5776]) ).
fof(f5776,plain,
! [X0,X1] : hAPP(c_Set_Oimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(rectify,[],[f3476]) ).
fof(f3476,axiom,
! [X76,X4] : hAPP(c_Set_Oimage(X4,X4,c_Fun_Oid(X4)),X76) = X76,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31345,plain,
spl625_539,
inference(avatar_split_clause,[],[f17758,f31343]) ).
fof(f31343,plain,
( spl625_539
<=> ! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_539])]) ).
fof(f17758,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(cnf_transformation,[],[f5774]) ).
fof(f5774,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_COMBI(X1)),X0) = X0,
inference(rectify,[],[f1258]) ).
fof(f1258,axiom,
! [X76,X4] : hAPP(c_Set_Ovimage(X4,X4,c_COMBI(X4)),X76) = X76,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31341,plain,
spl625_538,
inference(avatar_split_clause,[],[f17757,f31339]) ).
fof(f31339,plain,
( spl625_538
<=> ! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_538])]) ).
fof(f17757,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(cnf_transformation,[],[f5773]) ).
fof(f5773,plain,
! [X0,X1] : hAPP(c_Set_Ovimage(X1,X1,c_Fun_Oid(X1)),X0) = X0,
inference(rectify,[],[f3482]) ).
fof(f3482,axiom,
! [X19,X4] : hAPP(c_Set_Ovimage(X4,X4,c_Fun_Oid(X4)),X19) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31337,plain,
spl625_537,
inference(avatar_split_clause,[],[f17754,f31335]) ).
fof(f31335,plain,
( spl625_537
<=> ! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_537])]) ).
fof(f17754,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0,
inference(cnf_transformation,[],[f5770]) ).
fof(f5770,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),c_List_Olist_ONil(X1)),X0) = X0,
inference(rectify,[],[f4072]) ).
fof(f4072,axiom,
! [X266,X23] : hAPP(hAPP(c_List_Oappend(X23),c_List_Olist_ONil(X23)),X266) = X266,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31333,plain,
spl625_536,
inference(avatar_split_clause,[],[f17753,f31331]) ).
fof(f31331,plain,
( spl625_536
<=> ! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_536])]) ).
fof(f17753,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0,
inference(cnf_transformation,[],[f5769]) ).
fof(f5769,plain,
! [X0,X1] : hAPP(hAPP(c_List_Oappend(X1),X0),c_List_Olist_ONil(X1)) = X0,
inference(rectify,[],[f4070]) ).
fof(f4070,axiom,
! [X263,X23] : hAPP(hAPP(c_List_Oappend(X23),X263),c_List_Olist_ONil(X23)) = X263,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31329,plain,
spl625_535,
inference(avatar_split_clause,[],[f17752,f31327]) ).
fof(f31327,plain,
( spl625_535
<=> ! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_535])]) ).
fof(f17752,plain,
! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0,
inference(cnf_transformation,[],[f5768]) ).
fof(f5768,plain,
! [X0,X1] : hAPP(c_List_Orev(X1),hAPP(c_List_Orev(X1),X0)) = X0,
inference(rectify,[],[f4311]) ).
fof(f4311,axiom,
! [X263,X23] : hAPP(c_List_Orev(X23),hAPP(c_List_Orev(X23),X263)) = X263,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31325,plain,
spl625_534,
inference(avatar_split_clause,[],[f17751,f31323]) ).
fof(f31323,plain,
( spl625_534
<=> ! [X0,X1] : hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_534])]) ).
fof(f17751,plain,
! [X0,X1] : hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X0)) = X0,
inference(cnf_transformation,[],[f5767]) ).
fof(f5767,plain,
! [X0,X1] : hAPP(c_Option_Othe(X1),hAPP(c_Option_Ooption_OSome(X1),X0)) = X0,
inference(rectify,[],[f3638]) ).
fof(f3638,axiom,
! [X22,X23] : hAPP(c_Option_Othe(X23),hAPP(c_Option_Ooption_OSome(X23),X22)) = X22,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31321,plain,
spl625_533,
inference(avatar_split_clause,[],[f17748,f31319]) ).
fof(f31319,plain,
( spl625_533
<=> ! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_533])]) ).
fof(f17748,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(cnf_transformation,[],[f5764]) ).
fof(f5764,plain,
! [X0,X1] : c_Transitive__Closure_Ortrancl(X1,X0) = c_Transitive__Closure_Ortrancl(X1,c_Transitive__Closure_Ortrancl(X1,X0)),
inference(rectify,[],[f4707]) ).
fof(f4707,axiom,
! [X60,X4] : c_Transitive__Closure_Ortrancl(X4,X60) = c_Transitive__Closure_Ortrancl(X4,c_Transitive__Closure_Ortrancl(X4,X60)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31317,plain,
spl625_532,
inference(avatar_split_clause,[],[f17746,f31315]) ).
fof(f31315,plain,
( spl625_532
<=> ! [X0,X1] : c_List_Oremdups(X1,X0) = c_List_Oremdups(X1,c_List_Oremdups(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_532])]) ).
fof(f17746,plain,
! [X0,X1] : c_List_Oremdups(X1,X0) = c_List_Oremdups(X1,c_List_Oremdups(X1,X0)),
inference(cnf_transformation,[],[f5762]) ).
fof(f5762,plain,
! [X0,X1] : c_List_Oremdups(X1,X0) = c_List_Oremdups(X1,c_List_Oremdups(X1,X0)),
inference(rectify,[],[f4207]) ).
fof(f4207,axiom,
! [X263,X23] : c_List_Oremdups(X23,X263) = c_List_Oremdups(X23,c_List_Oremdups(X23,X263)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31313,plain,
spl625_531,
inference(avatar_split_clause,[],[f17745,f31311]) ).
fof(f31311,plain,
( spl625_531
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_531])]) ).
fof(f17745,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5761]) ).
fof(f5761,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Ofilter(X1,X0),c_List_Olist_ONil(X1)),
inference(rectify,[],[f3939]) ).
fof(f3939,axiom,
! [X5,X4] : c_List_Olist_ONil(X4) = hAPP(c_List_Ofilter(X4,X5),c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31309,plain,
( spl625_530
| ~ spl625_239
| ~ spl625_304 ),
inference(avatar_split_clause,[],[f30398,f30258,f29986,f31306]) ).
fof(f31306,plain,
( spl625_530
<=> c_Wellfounded_Oacyclic(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_530])]) ).
fof(f30258,plain,
( spl625_304
<=> ! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_304])]) ).
fof(f30398,plain,
( c_Wellfounded_Oacyclic(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less)
| ~ spl625_239
| ~ spl625_304 ),
inference(resolution,[],[f30259,f29988]) ).
fof(f30259,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Owf(X1,X0)
| c_Wellfounded_Oacyclic(X1,X0) )
| ~ spl625_304 ),
inference(avatar_component_clause,[],[f30258]) ).
fof(f31304,plain,
spl625_529,
inference(avatar_split_clause,[],[f17541,f31302]) ).
fof(f31302,plain,
( spl625_529
<=> ! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Lattices_Osemilattice__inf__class_Oinf(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__inf(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_529])]) ).
fof(f17541,plain,
! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Lattices_Osemilattice__inf__class_Oinf(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__inf(X0) ),
inference(cnf_transformation,[],[f10467]) ).
fof(f10467,plain,
! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Lattices_Osemilattice__inf__class_Oinf(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__inf(X0) ),
inference(flattening,[],[f10466]) ).
fof(f10466,plain,
! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Lattices_Osemilattice__inf__class_Oinf(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__inf(X0) ),
inference(ennf_transformation,[],[f5626]) ).
fof(f5626,plain,
! [X0] :
( ( class_Orderings_Olinorder(X0)
& class_Lattices_Osemilattice__inf(X0) )
=> c_Orderings_Oord__class_Omin(X0) = c_Lattices_Osemilattice__inf__class_Oinf(X0) ),
inference(rectify,[],[f1452]) ).
fof(f1452,axiom,
! [X4] :
( ( class_Orderings_Olinorder(X4)
& class_Lattices_Osemilattice__inf(X4) )
=> c_Lattices_Osemilattice__inf__class_Oinf(X4) = c_Orderings_Oord__class_Omin(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31300,plain,
spl625_528,
inference(avatar_split_clause,[],[f17540,f31298]) ).
fof(f31298,plain,
( spl625_528
<=> ! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Lattices_Osemilattice__sup__class_Osup(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_528])]) ).
fof(f17540,plain,
! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Lattices_Osemilattice__sup__class_Osup(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) ),
inference(cnf_transformation,[],[f10465]) ).
fof(f10465,plain,
! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Lattices_Osemilattice__sup__class_Osup(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) ),
inference(flattening,[],[f10464]) ).
fof(f10464,plain,
! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Lattices_Osemilattice__sup__class_Osup(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ class_Lattices_Osemilattice__sup(X0) ),
inference(ennf_transformation,[],[f5625]) ).
fof(f5625,plain,
! [X0] :
( ( class_Orderings_Olinorder(X0)
& class_Lattices_Osemilattice__sup(X0) )
=> c_Orderings_Oord__class_Omax(X0) = c_Lattices_Osemilattice__sup__class_Osup(X0) ),
inference(rectify,[],[f2153]) ).
fof(f2153,axiom,
! [X4] :
( ( class_Orderings_Olinorder(X4)
& class_Lattices_Osemilattice__sup(X4) )
=> c_Lattices_Osemilattice__sup__class_Osup(X4) = c_Orderings_Oord__class_Omax(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31296,plain,
spl625_527,
inference(avatar_split_clause,[],[f17483,f31294]) ).
fof(f31294,plain,
( spl625_527
<=> ! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Orderings_Oord_Omin(X0,c_Orderings_Oord__class_Oless__eq(X0))
| ~ class_Orderings_Oord(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_527])]) ).
fof(f17483,plain,
! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Orderings_Oord_Omin(X0,c_Orderings_Oord__class_Oless__eq(X0))
| ~ class_Orderings_Oord(X0) ),
inference(cnf_transformation,[],[f10409]) ).
fof(f10409,plain,
! [X0] :
( c_Orderings_Oord__class_Omin(X0) = c_Orderings_Oord_Omin(X0,c_Orderings_Oord__class_Oless__eq(X0))
| ~ class_Orderings_Oord(X0) ),
inference(ennf_transformation,[],[f5573]) ).
fof(f5573,plain,
! [X0] :
( class_Orderings_Oord(X0)
=> c_Orderings_Oord__class_Omin(X0) = c_Orderings_Oord_Omin(X0,c_Orderings_Oord__class_Oless__eq(X0)) ),
inference(rectify,[],[f1693]) ).
fof(f1693,axiom,
! [X4] :
( class_Orderings_Oord(X4)
=> c_Orderings_Oord__class_Omin(X4) = c_Orderings_Oord_Omin(X4,c_Orderings_Oord__class_Oless__eq(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31292,plain,
spl625_526,
inference(avatar_split_clause,[],[f17482,f31290]) ).
fof(f31290,plain,
( spl625_526
<=> ! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Orderings_Oord_Omax(X0,c_Orderings_Oord__class_Oless__eq(X0))
| ~ class_Orderings_Oord(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_526])]) ).
fof(f17482,plain,
! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Orderings_Oord_Omax(X0,c_Orderings_Oord__class_Oless__eq(X0))
| ~ class_Orderings_Oord(X0) ),
inference(cnf_transformation,[],[f10408]) ).
fof(f10408,plain,
! [X0] :
( c_Orderings_Oord__class_Omax(X0) = c_Orderings_Oord_Omax(X0,c_Orderings_Oord__class_Oless__eq(X0))
| ~ class_Orderings_Oord(X0) ),
inference(ennf_transformation,[],[f5572]) ).
fof(f5572,plain,
! [X0] :
( class_Orderings_Oord(X0)
=> c_Orderings_Oord__class_Omax(X0) = c_Orderings_Oord_Omax(X0,c_Orderings_Oord__class_Oless__eq(X0)) ),
inference(rectify,[],[f2199]) ).
fof(f2199,axiom,
! [X4] :
( class_Orderings_Oord(X4)
=> c_Orderings_Oord__class_Omax(X4) = c_Orderings_Oord_Omax(X4,c_Orderings_Oord__class_Oless__eq(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31288,plain,
spl625_525,
inference(avatar_split_clause,[],[f17438,f31286]) ).
fof(f31286,plain,
( spl625_525
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls)
| ~ class_Int_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_525])]) ).
fof(f17438,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls)
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f10364]) ).
fof(f10364,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls)
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f5528]) ).
fof(f5528,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> c_Groups_Ozero__class_Ozero(X0) = hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls) ),
inference(rectify,[],[f2571]) ).
fof(f2571,axiom,
! [X23] :
( class_Int_Onumber__ring(X23)
=> c_Groups_Ozero__class_Ozero(X23) = hAPP(c_Int_Onumber__class_Onumber__of(X23),c_Int_OPls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31284,plain,
spl625_524,
inference(avatar_split_clause,[],[f17426,f31282]) ).
fof(f31282,plain,
( spl625_524
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Osgn__if(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_524])]) ).
fof(f17426,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Osgn__if(X0) ),
inference(cnf_transformation,[],[f10352]) ).
fof(f10352,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Groups_Osgn__if(X0) ),
inference(ennf_transformation,[],[f5516]) ).
fof(f5516,plain,
! [X0] :
( class_Groups_Osgn__if(X0)
=> c_Groups_Ozero__class_Ozero(X0) = c_Groups_Osgn__class_Osgn(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f3224]) ).
fof(f3224,axiom,
! [X23] :
( class_Groups_Osgn__if(X23)
=> c_Groups_Ozero__class_Ozero(X23) = c_Groups_Osgn__class_Osgn(X23,c_Groups_Ozero__class_Ozero(X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31280,plain,
spl625_523,
inference(avatar_split_clause,[],[f17258,f31278]) ).
fof(f31278,plain,
( spl625_523
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_523])]) ).
fof(f17258,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))),
inference(cnf_transformation,[],[f5361]) ).
fof(f5361,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),hAPP(c_Nat_OSuc,X0))),
inference(rectify,[],[f1229]) ).
fof(f1229,axiom,
! [X88] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),hAPP(c_Nat_OSuc,X88))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31276,plain,
spl625_522,
inference(avatar_split_clause,[],[f17255,f31274]) ).
fof(f31274,plain,
( spl625_522
<=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_522])]) ).
fof(f17255,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(cnf_transformation,[],[f5358]) ).
fof(f5358,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X0) = X0,
inference(rectify,[],[f1324]) ).
fof(f1324,axiom,
! [X88] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),X88) = X88,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31272,plain,
spl625_521,
inference(avatar_split_clause,[],[f17254,f31270]) ).
fof(f31270,plain,
( spl625_521
<=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_521])]) ).
fof(f17254,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
inference(cnf_transformation,[],[f5357]) ).
fof(f5357,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X0) = X0,
inference(rectify,[],[f1793]) ).
fof(f1793,axiom,
! [X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),X30) = X30,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31268,plain,
spl625_520,
inference(avatar_split_clause,[],[f17250,f31266]) ).
fof(f31266,plain,
( spl625_520
<=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_520])]) ).
fof(f17250,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(cnf_transformation,[],[f5353]) ).
fof(f5353,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X0,
inference(rectify,[],[f1326]) ).
fof(f1326,axiom,
! [X88] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X88),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = X88,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31264,plain,
( spl625_519
| ~ spl625_208
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30388,f30166,f29841,f31262]) ).
fof(f31262,plain,
( spl625_519
<=> ! [X0] : c_fequal = c_HOL_Oequal__class_Oequal(tc_Lazy__Sequence_Olazy__sequence(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_519])]) ).
fof(f29841,plain,
( spl625_208
<=> ! [X0] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_208])]) ).
fof(f30388,plain,
( ! [X0] : c_fequal = c_HOL_Oequal__class_Oequal(tc_Lazy__Sequence_Olazy__sequence(X0))
| ~ spl625_208
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29842]) ).
fof(f29842,plain,
( ! [X0] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X0))
| ~ spl625_208 ),
inference(avatar_component_clause,[],[f29841]) ).
fof(f31260,plain,
spl625_518,
inference(avatar_split_clause,[],[f17249,f31258]) ).
fof(f31258,plain,
( spl625_518
<=> ! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_518])]) ).
fof(f17249,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f5352]) ).
fof(f5352,plain,
! [X0] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X0),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X0,
inference(rectify,[],[f1794]) ).
fof(f1794,axiom,
! [X30] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),X30),c_Groups_Oone__class_Oone(tc_Int_Oint)) = X30,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31256,plain,
spl625_517,
inference(avatar_split_clause,[],[f17246,f31254]) ).
fof(f17246,plain,
! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = X0,
inference(cnf_transformation,[],[f5349]) ).
fof(f5349,plain,
! [X0] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X0)) = X0,
inference(rectify,[],[f1814]) ).
fof(f1814,axiom,
! [X30] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),X30)) = X30,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31252,plain,
spl625_516,
inference(avatar_split_clause,[],[f17245,f31250]) ).
fof(f31250,plain,
( spl625_516
<=> ! [X0] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_516])]) ).
fof(f17245,plain,
! [X0] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)) = X0,
inference(cnf_transformation,[],[f5348]) ).
fof(f5348,plain,
! [X0] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0)) = X0,
inference(rectify,[],[f1711]) ).
fof(f1711,axiom,
! [X152] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X152)) = X152,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31248,plain,
spl625_515,
inference(avatar_split_clause,[],[f17243,f31246]) ).
fof(f17243,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Option_Oset(X0,c_Option_Ooption_ONone(X0)),
inference(cnf_transformation,[],[f5346]) ).
fof(f5346,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = c_Option_Oset(X0,c_Option_Ooption_ONone(X0)),
inference(rectify,[],[f847]) ).
fof(f847,axiom,
! [X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) = c_Option_Oset(X4,c_Option_Ooption_ONone(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31244,plain,
spl625_514,
inference(avatar_split_clause,[],[f17242,f31242]) ).
fof(f31242,plain,
( spl625_514
<=> ! [X0] : c_List_Olist_ONil(tc_List_Olist(X0)) = c_List_Otranspose(X0,c_List_Olist_ONil(tc_List_Olist(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_514])]) ).
fof(f17242,plain,
! [X0] : c_List_Olist_ONil(tc_List_Olist(X0)) = c_List_Otranspose(X0,c_List_Olist_ONil(tc_List_Olist(X0))),
inference(cnf_transformation,[],[f5345]) ).
fof(f5345,plain,
! [X0] : c_List_Olist_ONil(tc_List_Olist(X0)) = c_List_Otranspose(X0,c_List_Olist_ONil(tc_List_Olist(X0))),
inference(rectify,[],[f3941]) ).
fof(f3941,axiom,
! [X23] : c_List_Olist_ONil(tc_List_Olist(X23)) = c_List_Otranspose(X23,c_List_Olist_ONil(tc_List_Olist(X23))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31240,plain,
spl625_513,
inference(avatar_split_clause,[],[f17241,f31238]) ).
fof(f31238,plain,
( spl625_513
<=> ! [X0] : c_Int_OBit0(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_513])]) ).
fof(f17241,plain,
! [X0] : c_Int_OBit0(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0),
inference(cnf_transformation,[],[f5344]) ).
fof(f5344,plain,
! [X0] : c_Int_OBit0(X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),X0),
inference(rectify,[],[f2658]) ).
fof(f2658,axiom,
! [X112] : c_Int_OBit0(X112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X112),X112),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31235,plain,
spl625_512,
inference(avatar_split_clause,[],[f17231,f31233]) ).
fof(f31233,plain,
( spl625_512
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_512])]) ).
fof(f17231,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X0)),
inference(cnf_transformation,[],[f5334]) ).
fof(f5334,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X0)),X0)),
inference(rectify,[],[f1305]) ).
fof(f1305,axiom,
! [X88] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,X88)),X88)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31231,plain,
spl625_511,
inference(avatar_split_clause,[],[f17230,f31229]) ).
fof(f31229,plain,
( spl625_511
<=> ! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_511])]) ).
fof(f17230,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),
inference(cnf_transformation,[],[f5333]) ).
fof(f5333,plain,
! [X0] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != c_Orderings_Otop__class_Otop(tc_fun(X0,tc_HOL_Obool)),
inference(rectify,[],[f1058]) ).
fof(f1058,axiom,
! [X4] : c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)) != c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31227,plain,
spl625_510,
inference(avatar_split_clause,[],[f17098,f31224]) ).
fof(f31224,plain,
( spl625_510
<=> 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,[spl625_510])]) ).
fof(f17098,plain,
c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(cnf_transformation,[],[f4635]) ).
fof(f4635,axiom,
c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31222,plain,
spl625_509,
inference(avatar_split_clause,[],[f17097,f31219]) ).
fof(f31219,plain,
( spl625_509
<=> 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,[spl625_509])]) ).
fof(f17097,plain,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
inference(cnf_transformation,[],[f1743]) ).
fof(f1743,axiom,
c_Fun_Oinj__on(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31217,plain,
( spl625_508
| ~ spl625_211
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30385,f30166,f29853,f31215]) ).
fof(f31215,plain,
( spl625_508
<=> ! [X0] : c_fequal = c_HOL_Oequal__class_Oequal(tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_508])]) ).
fof(f29853,plain,
( spl625_211
<=> ! [X0] : class_HOL_Oequal(tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_211])]) ).
fof(f30385,plain,
( ! [X0] : c_fequal = c_HOL_Oequal__class_Oequal(tc_List_Olist(X0))
| ~ spl625_211
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29854]) ).
fof(f29854,plain,
( ! [X0] : class_HOL_Oequal(tc_List_Olist(X0))
| ~ spl625_211 ),
inference(avatar_component_clause,[],[f29853]) ).
fof(f31208,plain,
( spl625_507
| ~ spl625_210
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30379,f30166,f29849,f31206]) ).
fof(f31206,plain,
( spl625_507
<=> ! [X0] : c_fequal = c_HOL_Oequal__class_Oequal(tc_Option_Ooption(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_507])]) ).
fof(f29849,plain,
( spl625_210
<=> ! [X0] : class_HOL_Oequal(tc_Option_Ooption(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_210])]) ).
fof(f30379,plain,
( ! [X0] : c_fequal = c_HOL_Oequal__class_Oequal(tc_Option_Ooption(X0))
| ~ spl625_210
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29850]) ).
fof(f29850,plain,
( ! [X0] : class_HOL_Oequal(tc_Option_Ooption(X0))
| ~ spl625_210 ),
inference(avatar_component_clause,[],[f29849]) ).
fof(f31204,plain,
( spl625_506
| ~ spl625_209
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30374,f30166,f29845,f31202]) ).
fof(f31202,plain,
( spl625_506
<=> ! [X0] : c_fequal = c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_506])]) ).
fof(f29845,plain,
( spl625_209
<=> ! [X0] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_209])]) ).
fof(f30374,plain,
( ! [X0] : c_fequal = c_HOL_Oequal__class_Oequal(tc_Hoare__Mirabelle_Otriple(X0))
| ~ spl625_209
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29846]) ).
fof(f29846,plain,
( ! [X0] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X0))
| ~ spl625_209 ),
inference(avatar_component_clause,[],[f29845]) ).
fof(f31189,plain,
( ~ spl625_505
| ~ spl625_384
| spl625_410 ),
inference(avatar_split_clause,[],[f31167,f30778,f30643,f31186]) ).
fof(f31186,plain,
( spl625_505
<=> class_Finite__Set_Ofinite(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_505])]) ).
fof(f30778,plain,
( spl625_410
<=> 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,[spl625_410])]) ).
fof(f31167,plain,
( ~ class_Finite__Set_Ofinite(tc_Nat_Onat)
| ~ spl625_384
| spl625_410 ),
inference(resolution,[],[f30780,f30644]) ).
fof(f30780,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
| spl625_410 ),
inference(avatar_component_clause,[],[f30778]) ).
fof(f31178,plain,
( ~ spl625_504
| ~ spl625_384
| spl625_409 ),
inference(avatar_split_clause,[],[f31166,f30773,f30643,f31175]) ).
fof(f31175,plain,
( spl625_504
<=> class_Finite__Set_Ofinite(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_504])]) ).
fof(f30773,plain,
( spl625_409
<=> 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,[spl625_409])]) ).
fof(f31166,plain,
( ~ class_Finite__Set_Ofinite(tc_Int_Oint)
| ~ spl625_384
| spl625_409 ),
inference(resolution,[],[f30775,f30644]) ).
fof(f30775,plain,
( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool))))
| spl625_409 ),
inference(avatar_component_clause,[],[f30773]) ).
fof(f31165,plain,
spl625_503,
inference(avatar_split_clause,[],[f28071,f31163]) ).
fof(f31163,plain,
( spl625_503
<=> ! [X2,X1] :
( ~ sP41(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,c_Int_OPls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_503])]) ).
fof(f28071,plain,
! [X2,X1] :
( ~ sP41(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,c_Int_OPls)) ),
inference(forward_demodulation,[],[f28070,f17021]) ).
fof(f28070,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,c_Int_OPls))
| ~ sP41(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(forward_demodulation,[],[f25189,f17021]) ).
fof(f25189,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| ~ sP41(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(equality_resolution,[],[f21048]) ).
fof(f21048,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ sP41(X0,X1,X2) ),
inference(cnf_transformation,[],[f15705]) ).
fof(f15705,plain,
! [X0,X1,X2] :
( ( sP41(X0,X1,X2)
| ~ sP40(X2,X1,X0)
| ~ sP39(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP40(X2,X1,X0)
& sP39(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP41(X0,X1,X2) ) ),
inference(flattening,[],[f15704]) ).
fof(f15704,plain,
! [X0,X1,X2] :
( ( sP41(X0,X1,X2)
| ~ sP40(X2,X1,X0)
| ~ sP39(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP40(X2,X1,X0)
& sP39(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP41(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14470]) ).
fof(f14470,plain,
! [X0,X1,X2] :
( sP41(X0,X1,X2)
<=> ( sP40(X2,X1,X0)
& sP39(X2,X1,X0)
& ( hBOOL(hAPP(X2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP41])]) ).
fof(f31161,plain,
spl625_502,
inference(avatar_split_clause,[],[f28045,f31159]) ).
fof(f31159,plain,
( spl625_502
<=> ! [X2,X1] :
( ~ sP36(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_502])]) ).
fof(f28045,plain,
! [X2,X1] :
( ~ sP36(c_Int_OPls,X1,X2)
| hBOOL(hAPP(X2,X1)) ),
inference(forward_demodulation,[],[f25163,f17021]) ).
fof(f25163,plain,
! [X2,X1] :
( hBOOL(hAPP(X2,X1))
| ~ sP36(c_Groups_Ozero__class_Ozero(tc_Int_Oint),X1,X2) ),
inference(equality_resolution,[],[f20970]) ).
fof(f20970,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
| ~ sP36(X0,X1,X2) ),
inference(cnf_transformation,[],[f15652]) ).
fof(f15652,plain,
! [X0,X1,X2] :
( ( sP36(X0,X1,X2)
| ~ sP35(X2,X1,X0)
| ~ sP34(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP35(X2,X1,X0)
& sP34(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP36(X0,X1,X2) ) ),
inference(flattening,[],[f15651]) ).
fof(f15651,plain,
! [X0,X1,X2] :
( ( sP36(X0,X1,X2)
| ~ sP35(X2,X1,X0)
| ~ sP34(X2,X1,X0)
| ( ~ hBOOL(hAPP(X2,X1))
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) )
& ( ( sP35(X2,X1,X0)
& sP34(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
| ~ sP36(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f14462]) ).
fof(f14462,plain,
! [X0,X1,X2] :
( sP36(X0,X1,X2)
<=> ( sP35(X2,X1,X0)
& sP34(X2,X1,X0)
& ( hBOOL(hAPP(X2,X1))
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP36])]) ).
fof(f31157,plain,
spl625_501,
inference(avatar_split_clause,[],[f27408,f31155]) ).
fof(f31155,plain,
( spl625_501
<=> ! [X2,X0,X1] : c_Nat_Onat_Onat__case(X2,X1,X0,c_HOL_Obool_Obool__size(c_fTrue)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_501])]) ).
fof(f27408,plain,
! [X2,X0,X1] : c_Nat_Onat_Onat__case(X2,X1,X0,c_HOL_Obool_Obool__size(c_fTrue)) = X1,
inference(forward_demodulation,[],[f19383,f17032]) ).
fof(f19383,plain,
! [X2,X0,X1] : c_Nat_Onat_Onat__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(cnf_transformation,[],[f6918]) ).
fof(f6918,plain,
! [X0,X1,X2] : c_Nat_Onat_Onat__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1,
inference(rectify,[],[f2893]) ).
fof(f2893,axiom,
! [X67,X25,X4] : c_Nat_Onat_Onat__case(X4,X25,X67,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31153,plain,
spl625_500,
inference(avatar_split_clause,[],[f26057,f31151]) ).
fof(f31151,plain,
( spl625_500
<=> ! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_Option_Ooption_Ooption__size(X1,X0,c_Option_Ooption_ONone(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_500])]) ).
fof(f26057,plain,
! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_Option_Ooption_Ooption__size(X1,X0,c_Option_Ooption_ONone(X1)),
inference(forward_demodulation,[],[f17724,f17032]) ).
fof(f17724,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Option_Ooption_Ooption__size(X1,X0,c_Option_Ooption_ONone(X1)),
inference(cnf_transformation,[],[f5740]) ).
fof(f5740,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Option_Ooption_Ooption__size(X1,X0,c_Option_Ooption_ONone(X1)),
inference(rectify,[],[f1770]) ).
fof(f1770,axiom,
! [X143,X4] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Option_Ooption_Ooption__size(X4,X143,c_Option_Ooption_ONone(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31149,plain,
spl625_499,
inference(avatar_split_clause,[],[f25753,f31147]) ).
fof(f31147,plain,
( spl625_499
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_499])]) ).
fof(f25753,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Int_OPls),
inference(forward_demodulation,[],[f17397,f17021]) ).
fof(f17397,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f5500]) ).
fof(f5500,plain,
! [X0] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(rectify,[],[f2181]) ).
fof(f2181,axiom,
! [X32] :
( c_Divides_Odiv__class_Omod(tc_Int_Oint,X32,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X32
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),X32),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31145,plain,
spl625_498,
inference(avatar_split_clause,[],[f25669,f31143]) ).
fof(f31143,plain,
( spl625_498
<=> ! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),X0) = hAPP(c_Int_Onat,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_498])]) ).
fof(f31141,plain,
spl625_497,
inference(avatar_split_clause,[],[f25659,f31139]) ).
fof(f31139,plain,
( spl625_497
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_497])]) ).
fof(f25659,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f25658,f25523]) ).
fof(f25658,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f17267,f17032]) ).
fof(f17267,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f5370]) ).
fof(f5370,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rectify,[],[f2258]) ).
fof(f2258,axiom,
! [X93] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,X93,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31137,plain,
spl625_496,
inference(avatar_split_clause,[],[f25650,f31135]) ).
fof(f31135,plain,
( spl625_496
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OPls),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_496])]) ).
fof(f25650,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Int_OPls),X0),
inference(forward_demodulation,[],[f17260,f17021]) ).
fof(f17260,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0),
inference(cnf_transformation,[],[f5363]) ).
fof(f5363,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0),
inference(rectify,[],[f2013]) ).
fof(f2013,axiom,
! [X33] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31133,plain,
spl625_495,
inference(avatar_split_clause,[],[f25637,f31131]) ).
fof(f31131,plain,
( spl625_495
<=> ! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_495])]) ).
fof(f25637,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),X0)),
inference(forward_demodulation,[],[f17224,f17032]) ).
fof(f17224,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),
inference(cnf_transformation,[],[f5327]) ).
fof(f5327,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X0)),
inference(rectify,[],[f1497]) ).
fof(f1497,axiom,
! [X88] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X88)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31129,plain,
spl625_494,
inference(avatar_split_clause,[],[f25634,f31127]) ).
fof(f31127,plain,
( spl625_494
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_494])]) ).
fof(f25634,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X0)),
inference(forward_demodulation,[],[f17210,f17032]) ).
fof(f17210,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X0)),
inference(cnf_transformation,[],[f5313]) ).
fof(f5313,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X0)),
inference(rectify,[],[f1700]) ).
fof(f1700,axiom,
! [X191] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OLoc(X191)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31125,plain,
spl625_493,
inference(avatar_split_clause,[],[f25633,f31123]) ).
fof(f31123,plain,
( spl625_493
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_493])]) ).
fof(f25633,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X0)),
inference(forward_demodulation,[],[f17209,f17032]) ).
fof(f17209,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X0)),
inference(cnf_transformation,[],[f5312]) ).
fof(f5312,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X0)),
inference(rectify,[],[f1695]) ).
fof(f1695,axiom,
! [X111] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname),c_Com_Ovname_OGlb(X111)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31121,plain,
spl625_492,
inference(avatar_split_clause,[],[f25629,f31119]) ).
fof(f31119,plain,
( spl625_492
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_492])]) ).
fof(f25629,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f17202,f17032]) ).
fof(f17202,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(cnf_transformation,[],[f5305]) ).
fof(f5305,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(rectify,[],[f1416]) ).
fof(f1416,axiom,
! [X88] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31117,plain,
spl625_491,
inference(avatar_split_clause,[],[f25561,f31114]) ).
fof(f31114,plain,
( spl625_491
<=> 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,[spl625_491])]) ).
fof(f25561,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f17095,f17021]) ).
fof(f17095,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f1865]) ).
fof(f1865,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31112,plain,
spl625_490,
inference(avatar_split_clause,[],[f25560,f31109]) ).
fof(f31109,plain,
( spl625_490
<=> 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,[spl625_490])]) ).
fof(f25560,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(forward_demodulation,[],[f17094,f17021]) ).
fof(f17094,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f1825]) ).
fof(f1825,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31107,plain,
spl625_489,
inference(avatar_split_clause,[],[f25550,f31104]) ).
fof(f31104,plain,
( spl625_489
<=> hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_489])]) ).
fof(f25550,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17087,f17032]) ).
fof(f17087,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(cnf_transformation,[],[f3046]) ).
fof(f3046,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31102,plain,
spl625_488,
inference(avatar_split_clause,[],[f25306,f31100]) ).
fof(f31100,plain,
( spl625_488
<=> ! [X2,X1,X3] : c_List_Olist__all2(X3,X2,X1,c_List_Olist_ONil(X3),c_List_Olist_ONil(X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_488])]) ).
fof(f25306,plain,
! [X2,X3,X1] : c_List_Olist__all2(X3,X2,X1,c_List_Olist_ONil(X3),c_List_Olist_ONil(X2)),
inference(equality_resolution,[],[f22299]) ).
fof(f22299,plain,
! [X2,X3,X0,X1] :
( c_List_Olist__all2(X3,X2,X1,X0,c_List_Olist_ONil(X2))
| c_List_Olist_ONil(X3) != X0 ),
inference(cnf_transformation,[],[f16118]) ).
fof(f16118,plain,
! [X0,X1,X2,X3] :
( ( c_List_Olist__all2(X3,X2,X1,X0,c_List_Olist_ONil(X2))
| c_List_Olist_ONil(X3) != X0 )
& ( c_List_Olist_ONil(X3) = X0
| ~ c_List_Olist__all2(X3,X2,X1,X0,c_List_Olist_ONil(X2)) ) ),
inference(nnf_transformation,[],[f9074]) ).
fof(f9074,plain,
! [X0,X1,X2,X3] :
( c_List_Olist__all2(X3,X2,X1,X0,c_List_Olist_ONil(X2))
<=> c_List_Olist_ONil(X3) = X0 ),
inference(rectify,[],[f4511]) ).
fof(f4511,axiom,
! [X258,X5,X24,X4] :
( c_List_Olist__all2(X4,X24,X5,X258,c_List_Olist_ONil(X24))
<=> c_List_Olist_ONil(X4) = X258 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31098,plain,
spl625_487,
inference(avatar_split_clause,[],[f25299,f31096]) ).
fof(f31096,plain,
( spl625_487
<=> ! [X2,X1,X3] : ~ c_Wellfounded_Omax__extp(X3,X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_487])]) ).
fof(f25299,plain,
! [X2,X3,X1] : ~ c_Wellfounded_Omax__extp(X3,X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))),
inference(equality_resolution,[],[f22271]) ).
fof(f22271,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) != X0
| ~ c_Wellfounded_Omax__extp(X3,X2,X1,X0) ),
inference(cnf_transformation,[],[f16091]) ).
fof(f31094,plain,
spl625_486,
inference(avatar_split_clause,[],[f24977,f31092]) ).
fof(f31092,plain,
( spl625_486
<=> ! [X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_486])]) ).
fof(f24977,plain,
! [X1] : c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),c_List_Olist_ONil(X1)),
inference(equality_resolution,[],[f19039]) ).
fof(f19039,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),X0)
| c_List_Olist_ONil(X1) != X0 ),
inference(cnf_transformation,[],[f14948]) ).
fof(f14948,plain,
! [X0,X1] :
( ( c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),X0)
| c_List_Olist_ONil(X1) != X0 )
& ( c_List_Olist_ONil(X1) = X0
| c_List_Olist_ONil(X1) != hAPP(c_List_Orotate1(X1),X0) ) ),
inference(nnf_transformation,[],[f6780]) ).
fof(f6780,plain,
! [X0,X1] :
( c_List_Olist_ONil(X1) = hAPP(c_List_Orotate1(X1),X0)
<=> c_List_Olist_ONil(X1) = X0 ),
inference(rectify,[],[f4107]) ).
fof(f4107,axiom,
! [X258,X4] :
( c_List_Olist_ONil(X4) = hAPP(c_List_Orotate1(X4),X258)
<=> c_List_Olist_ONil(X4) = X258 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31090,plain,
spl625_485,
inference(avatar_split_clause,[],[f24002,f31087]) ).
fof(f31087,plain,
( spl625_485
<=> c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_485])]) ).
fof(f24002,plain,
c_Int_OPls = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OMin),
inference(definition_unfolding,[],[f17018,f17237]) ).
fof(f17018,plain,
c_Int_OPls = c_Int_Osucc(c_Int_OMin),
inference(cnf_transformation,[],[f2813]) ).
fof(f2813,axiom,
c_Int_OPls = c_Int_Osucc(c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31085,plain,
spl625_484,
inference(avatar_split_clause,[],[f22931,f31083]) ).
fof(f31083,plain,
( spl625_484
<=> ! [X2,X4,X0,X3,X1] :
( sP68(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_484])]) ).
fof(f22931,plain,
! [X2,X3,X0,X1,X4] :
( sP68(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ),
inference(cnf_transformation,[],[f14520]) ).
fof(f14520,plain,
! [X0,X1,X2,X3,X4] :
( sP68(X3,X2,X4,X1,X0)
| ~ class_Orderings_Oorder(X4) ),
inference(definition_folding,[],[f13711,f14519,f14518]) ).
fof(f14518,plain,
! [X0,X1,X4,X2,X3] :
( sP67(X0,X1,X4,X2,X3)
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X1),X0))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X2),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X1),X3)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X1),X3)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X3),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP67])]) ).
fof(f14519,plain,
! [X3,X2,X4,X1,X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X3,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X1,X0)))
<=> sP67(X0,X1,X4,X2,X3) )
| ~ sP68(X3,X2,X4,X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP68])]) ).
fof(f13711,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X3,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X1,X0)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X1),X0))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X2),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X1),X3)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X1),X3)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X3),X2)) ) ) )
| ~ class_Orderings_Oorder(X4) ),
inference(ennf_transformation,[],[f9460]) ).
fof(f9460,plain,
! [X0,X1,X2,X3,X4] :
( class_Orderings_Oorder(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X3,X2)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X1,X0)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X1),X0))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X2),X0))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X1),X3)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X1),X3)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X3),X2)) ) ) ) ),
inference(rectify,[],[f3133]) ).
fof(f3133,axiom,
! [X35,X36,X26,X6,X4] :
( class_Orderings_Oorder(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(X4,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X6,X26)),c_SetInterval_Oord__class_OatLeastAtMost(X4,X36,X35)))
<=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X36),X35))
& ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X35))
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),X6)) )
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),X35))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X36),X6)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),X26)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31081,plain,
spl625_483,
inference(avatar_split_clause,[],[f22586,f31079]) ).
fof(f31079,plain,
( spl625_483
<=> ! [X2,X4,X0,X3,X1] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_483])]) ).
fof(f22586,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3),
inference(cnf_transformation,[],[f9172]) ).
fof(f9172,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3),
inference(rectify,[],[f158]) ).
fof(f158,axiom,
! [X57,X58,X53,X10,X51] : c_Com_Ocom_OWhile(X51,X10) != c_Com_Ocom_OCond(X53,X58,X57),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31077,plain,
spl625_482,
inference(avatar_split_clause,[],[f22584,f31075]) ).
fof(f31075,plain,
( spl625_482
<=> ! [X2,X4,X0,X3,X1] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_482])]) ).
fof(f22584,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3),
inference(cnf_transformation,[],[f9170]) ).
fof(f9170,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OWhile(X4,X3),
inference(rectify,[],[f103]) ).
fof(f103,axiom,
! [X13,X53,X70,X10,X51] : c_Com_Ocom_OWhile(X51,X10) != c_Com_Ocom_OLocal(X70,X53,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31073,plain,
spl625_481,
inference(avatar_split_clause,[],[f22582,f31071]) ).
fof(f31071,plain,
( spl625_481
<=> ! [X4,X0,X3,X2,X1] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OCond(X4,X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_481])]) ).
fof(f22582,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OCond(X4,X3,X2),
inference(cnf_transformation,[],[f9168]) ).
fof(f9168,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OCond(X4,X3,X2),
inference(rectify,[],[f162]) ).
fof(f162,axiom,
! [X53,X54,X55,X56,X51] : c_Com_Ocom_OAss(X54,X53) != c_Com_Ocom_OCond(X51,X56,X55),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31069,plain,
spl625_480,
inference(avatar_split_clause,[],[f22580,f31067]) ).
fof(f31067,plain,
( spl625_480
<=> ! [X2,X4,X0,X3,X1] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OAss(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_480])]) ).
fof(f22580,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OAss(X4,X3),
inference(cnf_transformation,[],[f9166]) ).
fof(f9166,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OLocal(X2,X1,X0) != c_Com_Ocom_OAss(X4,X3),
inference(rectify,[],[f105]) ).
fof(f105,axiom,
! [X10,X51,X69,X53,X54] : c_Com_Ocom_OAss(X54,X53) != c_Com_Ocom_OLocal(X69,X51,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31065,plain,
spl625_479,
inference(avatar_split_clause,[],[f22578,f31063]) ).
fof(f31063,plain,
( spl625_479
<=> ! [X2,X4,X0,X3,X1] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OSemi(X4,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_479])]) ).
fof(f22578,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OSemi(X4,X3),
inference(cnf_transformation,[],[f9164]) ).
fof(f9164,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OCond(X2,X1,X0) != c_Com_Ocom_OSemi(X4,X3),
inference(rectify,[],[f163]) ).
fof(f163,axiom,
! [X55,X56,X51,X57,X58] : c_Com_Ocom_OSemi(X58,X57) != c_Com_Ocom_OCond(X51,X56,X55),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31061,plain,
spl625_478,
inference(avatar_split_clause,[],[f22576,f31059]) ).
fof(f31059,plain,
( spl625_478
<=> ! [X4,X0,X3,X2,X1] : c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OLocal(X4,X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_478])]) ).
fof(f22576,plain,
! [X2,X3,X0,X1,X4] : c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OLocal(X4,X3,X2),
inference(cnf_transformation,[],[f9162]) ).
fof(f9162,plain,
! [X0,X1,X2,X3,X4] : c_Com_Ocom_OSemi(X1,X0) != c_Com_Ocom_OLocal(X4,X3,X2),
inference(rectify,[],[f106]) ).
fof(f106,axiom,
! [X55,X56,X13,X53,X70] : c_Com_Ocom_OSemi(X56,X55) != c_Com_Ocom_OLocal(X70,X53,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31057,plain,
spl625_477,
inference(avatar_split_clause,[],[f21050,f31055]) ).
fof(f31055,plain,
( spl625_477
<=> ! [X2,X0,X1] :
( sP40(X2,X1,X0)
| ~ sP41(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_477])]) ).
fof(f21050,plain,
! [X2,X0,X1] :
( sP40(X2,X1,X0)
| ~ sP41(X0,X1,X2) ),
inference(cnf_transformation,[],[f15705]) ).
fof(f31053,plain,
spl625_476,
inference(avatar_split_clause,[],[f21049,f31051]) ).
fof(f31051,plain,
( spl625_476
<=> ! [X2,X0,X1] :
( sP39(X2,X1,X0)
| ~ sP41(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_476])]) ).
fof(f21049,plain,
! [X2,X0,X1] :
( sP39(X2,X1,X0)
| ~ sP41(X0,X1,X2) ),
inference(cnf_transformation,[],[f15705]) ).
fof(f31049,plain,
spl625_475,
inference(avatar_split_clause,[],[f20972,f31047]) ).
fof(f31047,plain,
( spl625_475
<=> ! [X2,X0,X1] :
( sP35(X2,X1,X0)
| ~ sP36(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_475])]) ).
fof(f20972,plain,
! [X2,X0,X1] :
( sP35(X2,X1,X0)
| ~ sP36(X0,X1,X2) ),
inference(cnf_transformation,[],[f15652]) ).
fof(f31045,plain,
spl625_474,
inference(avatar_split_clause,[],[f20971,f31043]) ).
fof(f31043,plain,
( spl625_474
<=> ! [X2,X0,X1] :
( sP34(X2,X1,X0)
| ~ sP36(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_474])]) ).
fof(f20971,plain,
! [X2,X0,X1] :
( sP34(X2,X1,X0)
| ~ sP36(X0,X1,X2) ),
inference(cnf_transformation,[],[f15652]) ).
fof(f31041,plain,
spl625_473,
inference(avatar_split_clause,[],[f20929,f31039]) ).
fof(f31039,plain,
( spl625_473
<=> ! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP31(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_473])]) ).
fof(f20929,plain,
! [X2,X0,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP31(X0,X2,X1) ),
inference(cnf_transformation,[],[f15615]) ).
fof(f15615,plain,
! [X0,X1,X2] :
( ( c_Relation_Orefl__on(X2,X1,X0)
| ~ sP31(X0,X2,X1) )
& ( sP31(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14456]) ).
fof(f14456,plain,
! [X0,X1,X2] :
( c_Relation_Orefl__on(X2,X1,X0)
<=> sP31(X0,X2,X1) ),
inference(definition_folding,[],[f12543,f14455]) ).
fof(f14455,plain,
! [X0,X2,X1] :
( sP31(X0,X2,X1)
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X3)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) )
& ! [X4] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X2),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1)))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X4),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP31])]) ).
fof(f12543,plain,
! [X0,X1,X2] :
( c_Relation_Orefl__on(X2,X1,X0)
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X3)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) )
& ! [X4] :
( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X2),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1)))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1))),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X4),X0)) ) ) ),
inference(ennf_transformation,[],[f8112]) ).
fof(f8112,plain,
! [X0,X1,X2] :
( c_Relation_Orefl__on(X2,X1,X0)
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X3)),X0)) )
& ! [X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),X4),X0))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X2,X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X2,tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X2),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X2)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X2),c_fconj),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1)))),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1))),X4)) ) ) ),
inference(rectify,[],[f3586]) ).
fof(f3586,axiom,
! [X60,X19,X4] :
( c_Relation_Orefl__on(X4,X19,X60)
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),X19))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X2),X2)),X60)) )
& ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),X2),X60))
=> hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(X4,X4,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(X4,tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X4),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,X4)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),X4),c_fconj),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X19)))),hAPP(hAPP(c_COMBC(X4,tc_fun(X4,tc_HOL_Obool),tc_HOL_Obool),c_member(X4)),X19))),X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31037,plain,
spl625_472,
inference(avatar_split_clause,[],[f20928,f31035]) ).
fof(f31035,plain,
( spl625_472
<=> ! [X2,X0,X1] :
( sP31(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_472])]) ).
fof(f20928,plain,
! [X2,X0,X1] :
( sP31(X0,X2,X1)
| ~ c_Relation_Orefl__on(X2,X1,X0) ),
inference(cnf_transformation,[],[f15615]) ).
fof(f31033,plain,
spl625_471,
inference(avatar_split_clause,[],[f20892,f31031]) ).
fof(f31031,plain,
( spl625_471
<=> ! [X2,X0,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| ~ sP30(X1,X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_471])]) ).
fof(f20892,plain,
! [X2,X0,X1] :
( c_List_Olist__ex1(X2,X1,X0)
| ~ sP30(X1,X0,X2) ),
inference(cnf_transformation,[],[f15573]) ).
fof(f15573,plain,
! [X0,X1,X2] :
( ( c_List_Olist__ex1(X2,X1,X0)
| ~ sP30(X1,X0,X2) )
& ( sP30(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14454]) ).
fof(f14454,plain,
! [X0,X1,X2] :
( c_List_Olist__ex1(X2,X1,X0)
<=> sP30(X1,X0,X2) ),
inference(definition_folding,[],[f12535,f14453]) ).
fof(f14453,plain,
! [X1,X0,X2] :
( sP30(X1,X0,X2)
<=> ? [X3] :
( ! [X4] :
( X3 = X4
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
& hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP30])]) ).
fof(f12535,plain,
! [X0,X1,X2] :
( c_List_Olist__ex1(X2,X1,X0)
<=> ? [X3] :
( ! [X4] :
( X3 = X4
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
& hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
inference(flattening,[],[f12534]) ).
fof(f12534,plain,
! [X0,X1,X2] :
( c_List_Olist__ex1(X2,X1,X0)
<=> ? [X3] :
( ! [X4] :
( X3 = X4
| ~ hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
& hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
inference(ennf_transformation,[],[f8103]) ).
fof(f8103,plain,
! [X0,X1,X2] :
( c_List_Olist__ex1(X2,X1,X0)
<=> ? [X3] :
( ! [X4] :
( ( hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
=> X3 = X4 )
& hBOOL(hAPP(X1,X3))
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X0))) ) ),
inference(rectify,[],[f4933]) ).
fof(f4933,axiom,
! [X258,X5,X4] :
( c_List_Olist__ex1(X4,X5,X258)
<=> ? [X2] :
( ! [X115] :
( ( hBOOL(hAPP(X5,X115))
& hBOOL(hAPP(hAPP(c_member(X4),X115),hAPP(c_List_Oset(X4),X258))) )
=> X2 = X115 )
& hBOOL(hAPP(X5,X2))
& hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X258))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31029,plain,
spl625_470,
inference(avatar_split_clause,[],[f20891,f31027]) ).
fof(f31027,plain,
( spl625_470
<=> ! [X2,X0,X1] :
( sP30(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_470])]) ).
fof(f20891,plain,
! [X2,X0,X1] :
( sP30(X1,X0,X2)
| ~ c_List_Olist__ex1(X2,X1,X0) ),
inference(cnf_transformation,[],[f15573]) ).
fof(f31025,plain,
spl625_469,
inference(avatar_split_clause,[],[f20503,f31023]) ).
fof(f31023,plain,
( spl625_469
<=> ! [X2,X0,X1] :
( X0 = X2
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_469])]) ).
fof(f20503,plain,
! [X2,X0,X1] :
( X0 = X2
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X2,X1,X0) ),
inference(cnf_transformation,[],[f12195]) ).
fof(f12195,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,X2,X1,X0) ),
inference(ennf_transformation,[],[f7848]) ).
fof(f7848,plain,
! [X0,X1,X2] :
( c_Natural_Oevaln(c_Com_Ocom_OSKIP,X2,X1,X0)
=> X0 = X2 ),
inference(rectify,[],[f132]) ).
fof(f132,axiom,
! [X91,X88,X92] :
( c_Natural_Oevaln(c_Com_Ocom_OSKIP,X92,X88,X91)
=> X91 = X92 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31021,plain,
spl625_468,
inference(avatar_split_clause,[],[f19384,f31019]) ).
fof(f31019,plain,
( spl625_468
<=> ! [X2,X0,X1] : c_Fun_Oinj__on(X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_468])]) ).
fof(f19384,plain,
! [X2,X0,X1] : c_Fun_Oinj__on(X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(cnf_transformation,[],[f6919]) ).
fof(f6919,plain,
! [X0,X1,X2] : c_Fun_Oinj__on(X2,X1,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),
inference(rectify,[],[f601]) ).
fof(f601,axiom,
! [X1,X24,X4] : c_Fun_Oinj__on(X4,X24,X1,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31017,plain,
spl625_467,
inference(avatar_split_clause,[],[f19382,f31015]) ).
fof(f31015,plain,
( spl625_467
<=> ! [X2,X0,X1] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_467])]) ).
fof(f19382,plain,
! [X2,X0,X1] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X1,
inference(cnf_transformation,[],[f6917]) ).
fof(f6917,plain,
! [X0,X1,X2] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X2,X1,X0,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X1,
inference(rectify,[],[f3296]) ).
fof(f3296,axiom,
! [X67,X25,X4] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(X4,X25,X67,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = X25,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31013,plain,
spl625_466,
inference(avatar_split_clause,[],[f19380,f31011]) ).
fof(f31011,plain,
( spl625_466
<=> ! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2) != X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_466])]) ).
fof(f19380,plain,
! [X2,X0,X1] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2) != X2,
inference(cnf_transformation,[],[f6915]) ).
fof(f6915,plain,
! [X0,X1,X2] : hAPP(hAPP(c_List_Olist_OCons(X1),X0),X2) != X2,
inference(rectify,[],[f3623]) ).
fof(f3623,axiom,
! [X22,X23,X263] : hAPP(hAPP(c_List_Olist_OCons(X23),X22),X263) != X263,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31009,plain,
spl625_465,
inference(avatar_split_clause,[],[f18994,f31007]) ).
fof(f31007,plain,
( spl625_465
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
| ~ sP6(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_465])]) ).
fof(f18994,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
| ~ sP6(X0,X1) ),
inference(cnf_transformation,[],[f14903]) ).
fof(f14903,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onat,X1) = X0
| ~ sP6(X0,X1) )
& ( sP6(X0,X1)
| hAPP(c_Int_Onat,X1) != X0 ) ),
inference(nnf_transformation,[],[f14414]) ).
fof(f14414,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
<=> sP6(X0,X1) ),
inference(definition_folding,[],[f11269,f14413]) ).
fof(f14413,plain,
! [X0,X1] :
( sP6(X0,X1)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f11269,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) ) ),
inference(ennf_transformation,[],[f6764]) ).
fof(f6764,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X1) = X0
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1 ) ) ),
inference(rectify,[],[f2497]) ).
fof(f2497,axiom,
! [X123,X180] :
( hAPP(c_Int_Onat,X180) = X123
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X180))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X123 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X180))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X123) = X180 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31005,plain,
spl625_464,
inference(avatar_split_clause,[],[f18986,f31003]) ).
fof(f31003,plain,
( spl625_464
<=> ! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| ~ sP5(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_464])]) ).
fof(f18986,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
| ~ sP5(X1,X0) ),
inference(cnf_transformation,[],[f14900]) ).
fof(f14900,plain,
! [X0,X1] :
( ( hAPP(c_Int_Onat,X0) = X1
| ~ sP5(X1,X0) )
& ( sP5(X1,X0)
| hAPP(c_Int_Onat,X0) != X1 ) ),
inference(nnf_transformation,[],[f14412]) ).
fof(f14412,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
<=> sP5(X1,X0) ),
inference(definition_folding,[],[f11268,f14411]) ).
fof(f14411,plain,
! [X1,X0] :
( sP5(X1,X0)
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f11268,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
<=> ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) ) ),
inference(ennf_transformation,[],[f6763]) ).
fof(f6763,plain,
! [X0,X1] :
( hAPP(c_Int_Onat,X0) = X1
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) = X0 ) ) ),
inference(rectify,[],[f2496]) ).
fof(f2496,axiom,
! [X180,X123] :
( hAPP(c_Int_Onat,X180) = X123
<=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X180))
=> c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X123 )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X180))
=> hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X123) = X180 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f31001,plain,
spl625_463,
inference(avatar_split_clause,[],[f18975,f30999]) ).
fof(f30999,plain,
( spl625_463
<=> ! [X0,X1] :
( X0 = X1
| c_Int_OBit0(X0) != c_Int_OBit0(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_463])]) ).
fof(f18975,plain,
! [X0,X1] :
( X0 = X1
| c_Int_OBit0(X0) != c_Int_OBit0(X1) ),
inference(cnf_transformation,[],[f14895]) ).
fof(f14895,plain,
! [X0,X1] :
( ( c_Int_OBit0(X0) = c_Int_OBit0(X1)
| X0 != X1 )
& ( X0 = X1
| c_Int_OBit0(X0) != c_Int_OBit0(X1) ) ),
inference(nnf_transformation,[],[f6761]) ).
fof(f6761,plain,
! [X0,X1] :
( c_Int_OBit0(X0) = c_Int_OBit0(X1)
<=> X0 = X1 ),
inference(rectify,[],[f2659]) ).
fof(f2659,axiom,
! [X153,X59] :
( c_Int_OBit0(X59) = c_Int_OBit0(X153)
<=> X59 = X153 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30997,plain,
spl625_462,
inference(avatar_split_clause,[],[f18973,f30995]) ).
fof(f30995,plain,
( spl625_462
<=> ! [X0,X1] :
( X0 = X1
| c_Com_Ovname_OLoc(X0) != c_Com_Ovname_OLoc(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_462])]) ).
fof(f18973,plain,
! [X0,X1] :
( X0 = X1
| c_Com_Ovname_OLoc(X0) != c_Com_Ovname_OLoc(X1) ),
inference(cnf_transformation,[],[f14894]) ).
fof(f14894,plain,
! [X0,X1] :
( ( c_Com_Ovname_OLoc(X0) = c_Com_Ovname_OLoc(X1)
| X0 != X1 )
& ( X0 = X1
| c_Com_Ovname_OLoc(X0) != c_Com_Ovname_OLoc(X1) ) ),
inference(nnf_transformation,[],[f6760]) ).
fof(f6760,plain,
! [X0,X1] :
( c_Com_Ovname_OLoc(X0) = c_Com_Ovname_OLoc(X1)
<=> X0 = X1 ),
inference(rectify,[],[f94]) ).
fof(f94,axiom,
! [X69,X70] :
( c_Com_Ovname_OLoc(X70) = c_Com_Ovname_OLoc(X69)
<=> X69 = X70 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30993,plain,
spl625_461,
inference(avatar_split_clause,[],[f18969,f30991]) ).
fof(f30991,plain,
( spl625_461
<=> ! [X0,X1] :
( X0 = X1
| c_Com_Ovname_OGlb(X0) != c_Com_Ovname_OGlb(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_461])]) ).
fof(f18969,plain,
! [X0,X1] :
( X0 = X1
| c_Com_Ovname_OGlb(X0) != c_Com_Ovname_OGlb(X1) ),
inference(cnf_transformation,[],[f14892]) ).
fof(f14892,plain,
! [X0,X1] :
( ( c_Com_Ovname_OGlb(X0) = c_Com_Ovname_OGlb(X1)
| X0 != X1 )
& ( X0 = X1
| c_Com_Ovname_OGlb(X0) != c_Com_Ovname_OGlb(X1) ) ),
inference(nnf_transformation,[],[f6758]) ).
fof(f6758,plain,
! [X0,X1] :
( c_Com_Ovname_OGlb(X0) = c_Com_Ovname_OGlb(X1)
<=> X0 = X1 ),
inference(rectify,[],[f188]) ).
fof(f188,axiom,
! [X109,X103] :
( c_Com_Ovname_OGlb(X103) = c_Com_Ovname_OGlb(X109)
<=> X103 = X109 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30989,plain,
spl625_460,
inference(avatar_split_clause,[],[f18912,f30987]) ).
fof(f30987,plain,
( spl625_460
<=> ! [X0,X1] :
( class_HOL_Oequal(tc_fun(X1,X0))
| ~ class_HOL_Oequal(X0)
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_460])]) ).
fof(f18912,plain,
! [X0,X1] :
( class_HOL_Oequal(tc_fun(X1,X0))
| ~ class_HOL_Oequal(X0)
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f11251]) ).
fof(f11251,plain,
! [X0,X1] :
( class_HOL_Oequal(tc_fun(X1,X0))
| ~ class_HOL_Oequal(X0)
| ~ class_Enum_Oenum(X1) ),
inference(flattening,[],[f11250]) ).
fof(f11250,plain,
! [X0,X1] :
( class_HOL_Oequal(tc_fun(X1,X0))
| ~ class_HOL_Oequal(X0)
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6730]) ).
fof(f6730,plain,
! [X0,X1] :
( ( class_HOL_Oequal(X0)
& class_Enum_Oenum(X1) )
=> class_HOL_Oequal(tc_fun(X1,X0)) ),
inference(rectify,[],[f5006]) ).
fof(f5006,axiom,
! [X324,X323] :
( ( class_HOL_Oequal(X324)
& class_Enum_Oenum(X323) )
=> class_HOL_Oequal(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30985,plain,
spl625_459,
inference(avatar_split_clause,[],[f18908,f30983]) ).
fof(f30983,plain,
( spl625_459
<=> ! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_459])]) ).
fof(f18908,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f11243]) ).
fof(f11243,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(flattening,[],[f11242]) ).
fof(f11242,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_fun(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6726]) ).
fof(f6726,plain,
! [X0,X1] :
( ( class_Enum_Oenum(X0)
& class_Enum_Oenum(X1) )
=> class_Enum_Oenum(tc_fun(X1,X0)) ),
inference(rectify,[],[f5007]) ).
fof(f5007,axiom,
! [X324,X323] :
( ( class_Enum_Oenum(X324)
& class_Enum_Oenum(X323) )
=> class_Enum_Oenum(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30981,plain,
spl625_458,
inference(avatar_split_clause,[],[f18907,f30979]) ).
fof(f30979,plain,
( spl625_458
<=> ! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_458])]) ).
fof(f18907,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f11241]) ).
fof(f11241,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(flattening,[],[f11240]) ).
fof(f11240,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_prod(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6725]) ).
fof(f6725,plain,
! [X0,X1] :
( ( class_Enum_Oenum(X0)
& class_Enum_Oenum(X1) )
=> class_Enum_Oenum(tc_prod(X1,X0)) ),
inference(rectify,[],[f5166]) ).
fof(f5166,axiom,
! [X324,X323] :
( ( class_Enum_Oenum(X324)
& class_Enum_Oenum(X323) )
=> class_Enum_Oenum(tc_prod(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30977,plain,
spl625_457,
inference(avatar_split_clause,[],[f18906,f30975]) ).
fof(f30975,plain,
( spl625_457
<=> ! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_457])]) ).
fof(f18906,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(cnf_transformation,[],[f11239]) ).
fof(f11239,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(flattening,[],[f11238]) ).
fof(f11238,plain,
! [X0,X1] :
( class_Enum_Oenum(tc_sum(X1,X0))
| ~ class_Enum_Oenum(X0)
| ~ class_Enum_Oenum(X1) ),
inference(ennf_transformation,[],[f6724]) ).
fof(f6724,plain,
! [X0,X1] :
( ( class_Enum_Oenum(X0)
& class_Enum_Oenum(X1) )
=> class_Enum_Oenum(tc_sum(X1,X0)) ),
inference(rectify,[],[f5157]) ).
fof(f5157,axiom,
! [X324,X323] :
( ( class_Enum_Oenum(X324)
& class_Enum_Oenum(X323) )
=> class_Enum_Oenum(tc_sum(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30973,plain,
spl625_456,
inference(avatar_split_clause,[],[f18905,f30971]) ).
fof(f30971,plain,
( spl625_456
<=> ! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_456])]) ).
fof(f18905,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11237]) ).
fof(f11237,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11236]) ).
fof(f11236,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_fun(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6723]) ).
fof(f6723,plain,
! [X0,X1] :
( ( class_Finite__Set_Ofinite(X0)
& class_Finite__Set_Ofinite(X1) )
=> class_Finite__Set_Ofinite(tc_fun(X1,X0)) ),
inference(rectify,[],[f4998]) ).
fof(f4998,axiom,
! [X324,X323] :
( ( class_Finite__Set_Ofinite(X324)
& class_Finite__Set_Ofinite(X323) )
=> class_Finite__Set_Ofinite(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30969,plain,
spl625_455,
inference(avatar_split_clause,[],[f18904,f30967]) ).
fof(f30967,plain,
( spl625_455
<=> ! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_455])]) ).
fof(f18904,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11235]) ).
fof(f11235,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11234]) ).
fof(f11234,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_prod(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6722]) ).
fof(f6722,plain,
! [X0,X1] :
( ( class_Finite__Set_Ofinite(X0)
& class_Finite__Set_Ofinite(X1) )
=> class_Finite__Set_Ofinite(tc_prod(X1,X0)) ),
inference(rectify,[],[f5163]) ).
fof(f5163,axiom,
! [X324,X323] :
( ( class_Finite__Set_Ofinite(X324)
& class_Finite__Set_Ofinite(X323) )
=> class_Finite__Set_Ofinite(tc_prod(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30965,plain,
spl625_454,
inference(avatar_split_clause,[],[f18903,f30963]) ).
fof(f30963,plain,
( spl625_454
<=> ! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_454])]) ).
fof(f18903,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f11233]) ).
fof(f11233,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(flattening,[],[f11232]) ).
fof(f11232,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(tc_sum(X1,X0))
| ~ class_Finite__Set_Ofinite(X0)
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6721]) ).
fof(f6721,plain,
! [X0,X1] :
( ( class_Finite__Set_Ofinite(X0)
& class_Finite__Set_Ofinite(X1) )
=> class_Finite__Set_Ofinite(tc_sum(X1,X0)) ),
inference(rectify,[],[f5155]) ).
fof(f5155,axiom,
! [X324,X323] :
( ( class_Finite__Set_Ofinite(X324)
& class_Finite__Set_Ofinite(X323) )
=> class_Finite__Set_Ofinite(tc_sum(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30961,plain,
spl625_453,
inference(avatar_split_clause,[],[f18898,f30959]) ).
fof(f30959,plain,
( spl625_453
<=> ! [X0,X1] :
( class_Smallcheck_Osmall(tc_prod(X1,X0))
| ~ class_Smallcheck_Osmall(X0)
| ~ class_Smallcheck_Osmall(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_453])]) ).
fof(f18898,plain,
! [X0,X1] :
( class_Smallcheck_Osmall(tc_prod(X1,X0))
| ~ class_Smallcheck_Osmall(X0)
| ~ class_Smallcheck_Osmall(X1) ),
inference(cnf_transformation,[],[f11225]) ).
fof(f11225,plain,
! [X0,X1] :
( class_Smallcheck_Osmall(tc_prod(X1,X0))
| ~ class_Smallcheck_Osmall(X0)
| ~ class_Smallcheck_Osmall(X1) ),
inference(flattening,[],[f11224]) ).
fof(f11224,plain,
! [X0,X1] :
( class_Smallcheck_Osmall(tc_prod(X1,X0))
| ~ class_Smallcheck_Osmall(X0)
| ~ class_Smallcheck_Osmall(X1) ),
inference(ennf_transformation,[],[f6717]) ).
fof(f6717,plain,
! [X0,X1] :
( ( class_Smallcheck_Osmall(X0)
& class_Smallcheck_Osmall(X1) )
=> class_Smallcheck_Osmall(tc_prod(X1,X0)) ),
inference(rectify,[],[f5164]) ).
fof(f5164,axiom,
! [X324,X323] :
( ( class_Smallcheck_Osmall(X324)
& class_Smallcheck_Osmall(X323) )
=> class_Smallcheck_Osmall(tc_prod(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30957,plain,
spl625_452,
inference(avatar_split_clause,[],[f18596,f30955]) ).
fof(f30955,plain,
( spl625_452
<=> ! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_452])]) ).
fof(f18596,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(cnf_transformation,[],[f10890]) ).
fof(f10890,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(flattening,[],[f10889]) ).
fof(f10889,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X0)
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(ennf_transformation,[],[f6472]) ).
fof(f6472,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X1)
=> ( c_Nat__Transfer_Ois__nat(X0)
=> c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X1,X0)) ) ),
inference(rectify,[],[f2913]) ).
fof(f2913,axiom,
! [X29,X22] :
( c_Nat__Transfer_Ois__nat(X22)
=> ( c_Nat__Transfer_Ois__nat(X29)
=> c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(X22,X29)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30953,plain,
spl625_451,
inference(avatar_split_clause,[],[f18262,f30951]) ).
fof(f30951,plain,
( spl625_451
<=> ! [X0,X1] :
( c_Fun_Oinj__on(X1,X1,c_Groups_Ouminus__class_Ouminus(X1),X0)
| ~ class_Groups_Oordered__ab__group__add(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_451])]) ).
fof(f18262,plain,
! [X0,X1] :
( c_Fun_Oinj__on(X1,X1,c_Groups_Ouminus__class_Ouminus(X1),X0)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(cnf_transformation,[],[f10566]) ).
fof(f10566,plain,
! [X0,X1] :
( c_Fun_Oinj__on(X1,X1,c_Groups_Ouminus__class_Ouminus(X1),X0)
| ~ class_Groups_Oordered__ab__group__add(X1) ),
inference(ennf_transformation,[],[f6205]) ).
fof(f6205,plain,
! [X0,X1] :
( class_Groups_Oordered__ab__group__add(X1)
=> c_Fun_Oinj__on(X1,X1,c_Groups_Ouminus__class_Ouminus(X1),X0) ),
inference(rectify,[],[f709]) ).
fof(f709,axiom,
! [X19,X4] :
( class_Groups_Oordered__ab__group__add(X4)
=> c_Fun_Oinj__on(X4,X4,c_Groups_Ouminus__class_Ouminus(X4),X19) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30949,plain,
spl625_450,
inference(avatar_split_clause,[],[f18198,f30947]) ).
fof(f30947,plain,
( spl625_450
<=> ! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_450])]) ).
fof(f18198,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(cnf_transformation,[],[f6157]) ).
fof(f6157,plain,
! [X0,X1] :
( hBOOL(X1)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(rectify,[],[f5233]) ).
fof(f5233,axiom,
! [X37,X5] :
( hBOOL(X5)
| ~ hBOOL(hAPP(hAPP(c_fconj,X5),X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30945,plain,
spl625_449,
inference(avatar_split_clause,[],[f18197,f30943]) ).
fof(f30943,plain,
( spl625_449
<=> ! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_449])]) ).
fof(f18197,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(cnf_transformation,[],[f6156]) ).
fof(f6156,plain,
! [X0,X1] :
( hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_fconj,X1),X0)) ),
inference(rectify,[],[f5234]) ).
fof(f5234,axiom,
! [X37,X5] :
( hBOOL(X37)
| ~ hBOOL(hAPP(hAPP(c_fconj,X5),X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30941,plain,
spl625_448,
inference(avatar_split_clause,[],[f18193,f30939]) ).
fof(f30939,plain,
( spl625_448
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_448])]) ).
fof(f18193,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ),
inference(cnf_transformation,[],[f6152]) ).
fof(f6152,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X1),X0))
| hBOOL(X1) ),
inference(rectify,[],[f5238]) ).
fof(f5238,axiom,
! [X37,X5] :
( hBOOL(hAPP(hAPP(c_fimplies,X5),X37))
| hBOOL(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30937,plain,
spl625_447,
inference(avatar_split_clause,[],[f18192,f30935]) ).
fof(f30935,plain,
( spl625_447
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_447])]) ).
fof(f18192,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6151]) ).
fof(f6151,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fimplies,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5239]) ).
fof(f5239,axiom,
! [X5,X37] :
( hBOOL(hAPP(hAPP(c_fimplies,X5),X37))
| ~ hBOOL(X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30933,plain,
spl625_446,
inference(avatar_split_clause,[],[f18191,f30931]) ).
fof(f30931,plain,
( spl625_446
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_446])]) ).
fof(f18191,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6150]) ).
fof(f6150,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X0),X1))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5236]) ).
fof(f5236,axiom,
! [X5,X37] :
( hBOOL(hAPP(hAPP(c_fdisj,X5),X37))
| ~ hBOOL(X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30929,plain,
spl625_445,
inference(avatar_split_clause,[],[f18190,f30927]) ).
fof(f30927,plain,
( spl625_445
<=> ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_445])]) ).
fof(f18190,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(cnf_transformation,[],[f6149]) ).
fof(f6149,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fdisj,X1),X0))
| ~ hBOOL(X1) ),
inference(rectify,[],[f5235]) ).
fof(f5235,axiom,
! [X37,X5] :
( hBOOL(hAPP(hAPP(c_fdisj,X5),X37))
| ~ hBOOL(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30925,plain,
spl625_444,
inference(avatar_split_clause,[],[f17740,f30923]) ).
fof(f30923,plain,
( spl625_444
<=> ! [X0,X1] : c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_444])]) ).
fof(f17740,plain,
! [X0,X1] : c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X0),
inference(cnf_transformation,[],[f5756]) ).
fof(f5756,plain,
! [X0,X1] : c_Fun_Oinj__on(tc_List_Olist(X1),tc_List_Olist(X1),c_List_Orev(X1),X0),
inference(rectify,[],[f4300]) ).
fof(f4300,axiom,
! [X19,X4] : c_Fun_Oinj__on(tc_List_Olist(X4),tc_List_Olist(X4),c_List_Orev(X4),X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30921,plain,
spl625_443,
inference(avatar_split_clause,[],[f17738,f30919]) ).
fof(f30919,plain,
( spl625_443
<=> ! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_443])]) ).
fof(f17738,plain,
! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))),
inference(cnf_transformation,[],[f5754]) ).
fof(f5754,plain,
! [X0,X1] : c_Hoare__Mirabelle_Ohoare__derivs(X1,X0,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X1),tc_HOL_Obool))),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X3,X4] : c_Hoare__Mirabelle_Ohoare__derivs(X4,X3,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(X4),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30917,plain,
spl625_442,
inference(avatar_split_clause,[],[f17736,f30915]) ).
fof(f30915,plain,
( spl625_442
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_442])]) ).
fof(f17736,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X0))),
inference(cnf_transformation,[],[f5752]) ).
fof(f5752,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(X1),hAPP(c_List_Oset(X1),X0))),
inference(rectify,[],[f3615]) ).
fof(f3615,axiom,
! [X258,X4] : hBOOL(hAPP(c_Finite__Set_Ofinite(X4),hAPP(c_List_Oset(X4),X258))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30913,plain,
spl625_441,
inference(avatar_split_clause,[],[f17735,f30911]) ).
fof(f30911,plain,
( spl625_441
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_441])]) ).
fof(f17735,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0))),
inference(cnf_transformation,[],[f5751]) ).
fof(f5751,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f3110]) ).
fof(f3110,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,X153,X152))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30909,plain,
spl625_440,
inference(avatar_split_clause,[],[f17734,f30907]) ).
fof(f30907,plain,
( spl625_440
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_440])]) ).
fof(f17734,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0))),
inference(cnf_transformation,[],[f5750]) ).
fof(f5750,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f2419]) ).
fof(f2419,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,X153,X152))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30905,plain,
spl625_439,
inference(avatar_split_clause,[],[f17733,f30903]) ).
fof(f30903,plain,
( spl625_439
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_439])]) ).
fof(f17733,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0))),
inference(cnf_transformation,[],[f5749]) ).
fof(f5749,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X1,X0))),
inference(rectify,[],[f2011]) ).
fof(f2011,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,X153,X152))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30901,plain,
spl625_438,
inference(avatar_split_clause,[],[f17732,f30899]) ).
fof(f30899,plain,
( spl625_438
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_438])]) ).
fof(f17732,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))),
inference(cnf_transformation,[],[f5748]) ).
fof(f5748,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f3154]) ).
fof(f3154,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X153,X152))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30897,plain,
spl625_437,
inference(avatar_split_clause,[],[f17731,f30895]) ).
fof(f30895,plain,
( spl625_437
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_437])]) ).
fof(f17731,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0))),
inference(cnf_transformation,[],[f5747]) ).
fof(f5747,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f2420]) ).
fof(f2420,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,X153,X152))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30893,plain,
spl625_436,
inference(avatar_split_clause,[],[f17730,f30891]) ).
fof(f30891,plain,
( spl625_436
<=> ! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_436])]) ).
fof(f17730,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X0))),
inference(cnf_transformation,[],[f5746]) ).
fof(f5746,plain,
! [X0,X1] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X1,X0))),
inference(rectify,[],[f2012]) ).
fof(f2012,axiom,
! [X152,X153] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,X153,X152))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30889,plain,
spl625_435,
inference(avatar_split_clause,[],[f17729,f30887]) ).
fof(f30887,plain,
( spl625_435
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_435])]) ).
fof(f17729,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5745]) ).
fof(f5745,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_OtakeWhile(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4337]) ).
fof(f4337,axiom,
! [X5,X4] : c_List_Olist_ONil(X4) = c_List_OtakeWhile(X4,X5,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30885,plain,
spl625_434,
inference(avatar_split_clause,[],[f17728,f30883]) ).
fof(f30883,plain,
( spl625_434
<=> ! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_434])]) ).
fof(f17728,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5744]) ).
fof(f5744,plain,
! [X0,X1] : c_List_Olist_ONil(X1) = c_List_Oremove1(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f3978]) ).
fof(f3978,axiom,
! [X22,X23] : c_List_Olist_ONil(X23) = c_List_Oremove1(X23,X22,c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30881,plain,
spl625_433,
inference(avatar_split_clause,[],[f17487,f30879]) ).
fof(f30879,plain,
( spl625_433
<=> ! [X0] :
( hBOOL(hAPP(c_List_Odistinct(X0),c_Enum_Oenum__class_Oenum(X0)))
| ~ class_Enum_Oenum(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_433])]) ).
fof(f17487,plain,
! [X0] :
( hBOOL(hAPP(c_List_Odistinct(X0),c_Enum_Oenum__class_Oenum(X0)))
| ~ class_Enum_Oenum(X0) ),
inference(cnf_transformation,[],[f10413]) ).
fof(f10413,plain,
! [X0] :
( hBOOL(hAPP(c_List_Odistinct(X0),c_Enum_Oenum__class_Oenum(X0)))
| ~ class_Enum_Oenum(X0) ),
inference(ennf_transformation,[],[f5577]) ).
fof(f5577,plain,
! [X0] :
( class_Enum_Oenum(X0)
=> hBOOL(hAPP(c_List_Odistinct(X0),c_Enum_Oenum__class_Oenum(X0))) ),
inference(rectify,[],[f3728]) ).
fof(f3728,axiom,
! [X23] :
( class_Enum_Oenum(X23)
=> hBOOL(hAPP(c_List_Odistinct(X23),c_Enum_Oenum__class_Oenum(X23))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30877,plain,
spl625_432,
inference(avatar_split_clause,[],[f17436,f30875]) ).
fof(f17436,plain,
! [X0] :
( c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f10362]) ).
fof(f10362,plain,
! [X0] :
( c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls))
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f5526]) ).
fof(f5526,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OPls)) ),
inference(rectify,[],[f2698]) ).
fof(f2698,axiom,
! [X23] :
( class_Int_Onumber__ring(X23)
=> c_Int_Oiszero(X23,hAPP(c_Int_Onumber__class_Onumber__of(X23),c_Int_OPls)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30873,plain,
( spl625_431
| ~ spl625_193
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30387,f30166,f29769,f30870]) ).
fof(f30870,plain,
( spl625_431
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_431])]) ).
fof(f29769,plain,
( spl625_193
<=> class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_193])]) ).
fof(f30387,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Code__Numeral_Ocode__numeral)
| ~ spl625_193
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29771]) ).
fof(f29771,plain,
( class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral)
| ~ spl625_193 ),
inference(avatar_component_clause,[],[f29769]) ).
fof(f30868,plain,
spl625_430,
inference(avatar_split_clause,[],[f17435,f30866]) ).
fof(f17435,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) ),
inference(cnf_transformation,[],[f10361]) ).
fof(f10361,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin))
| ~ class_Int_Onumber__ring(X0) ),
inference(ennf_transformation,[],[f5525]) ).
fof(f5525,plain,
! [X0] :
( class_Int_Onumber__ring(X0)
=> ~ c_Int_Oiszero(X0,hAPP(c_Int_Onumber__class_Onumber__of(X0),c_Int_OMin)) ),
inference(rectify,[],[f2809]) ).
fof(f2809,axiom,
! [X23] :
( class_Int_Onumber__ring(X23)
=> ~ c_Int_Oiszero(X23,hAPP(c_Int_Onumber__class_Onumber__of(X23),c_Int_OMin)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30864,plain,
spl625_429,
inference(avatar_split_clause,[],[f17228,f30862]) ).
fof(f30862,plain,
( spl625_429
<=> ! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_429])]) ).
fof(f17228,plain,
! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(cnf_transformation,[],[f5331]) ).
fof(f5331,plain,
! [X0] : c_Wellfounded_Owf(X0,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool))),
inference(rectify,[],[f3345]) ).
fof(f3345,axiom,
! [X4] : c_Wellfounded_Owf(X4,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X4,X4),tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30860,plain,
spl625_428,
inference(avatar_split_clause,[],[f17226,f30858]) ).
fof(f30858,plain,
( spl625_428
<=> ! [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,[spl625_428])]) ).
fof(f17226,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5329]) ).
fof(f5329,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(X0),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(rectify,[],[f704]) ).
fof(f704,axiom,
! [X4] : hBOOL(hAPP(c_Finite__Set_Ofinite(X4),c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30856,plain,
spl625_427,
inference(avatar_split_clause,[],[f17223,f30854]) ).
fof(f30854,plain,
( spl625_427
<=> ! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_427])]) ).
fof(f17223,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0))),
inference(cnf_transformation,[],[f5326]) ).
fof(f5326,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X0))),
inference(rectify,[],[f1707]) ).
fof(f1707,axiom,
! [X59] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),X59))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30852,plain,
spl625_426,
inference(avatar_split_clause,[],[f17222,f30850]) ).
fof(f30850,plain,
( spl625_426
<=> ! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_426])]) ).
fof(f17222,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0))),
inference(cnf_transformation,[],[f5325]) ).
fof(f5325,plain,
! [X0] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X0))),
inference(rectify,[],[f3182]) ).
fof(f3182,axiom,
! [X59] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),X59))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30848,plain,
spl625_425,
inference(avatar_split_clause,[],[f17221,f30846]) ).
fof(f30846,plain,
( spl625_425
<=> ! [X0] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_425])]) ).
fof(f17221,plain,
! [X0] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X0)),
inference(cnf_transformation,[],[f5324]) ).
fof(f5324,plain,
! [X0] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X0)),
inference(rectify,[],[f2588]) ).
fof(f2588,axiom,
! [X28] : c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),X28)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30844,plain,
spl625_424,
inference(avatar_split_clause,[],[f17220,f30842]) ).
fof(f30842,plain,
( spl625_424
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_424])]) ).
fof(f17220,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(cnf_transformation,[],[f5323]) ).
fof(f5323,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(rectify,[],[f2567]) ).
fof(f2567,axiom,
! [X112] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),X112),c_Int_OPls) = X112,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30840,plain,
spl625_423,
inference(avatar_split_clause,[],[f17219,f30838]) ).
fof(f30838,plain,
( spl625_423
<=> ! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_423])]) ).
fof(f17219,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(cnf_transformation,[],[f5322]) ).
fof(f5322,plain,
! [X0] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X0),c_Int_OPls) = X0,
inference(rectify,[],[f2561]) ).
fof(f2561,axiom,
! [X112] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),X112),c_Int_OPls) = X112,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30836,plain,
spl625_422,
inference(avatar_split_clause,[],[f17218,f30834]) ).
fof(f30834,plain,
( spl625_422
<=> ! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_422])]) ).
fof(f17218,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0,
inference(cnf_transformation,[],[f5321]) ).
fof(f5321,plain,
! [X0] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X0) = X0,
inference(rectify,[],[f2566]) ).
fof(f2566,axiom,
! [X112] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),X112) = X112,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30832,plain,
spl625_421,
inference(avatar_split_clause,[],[f17217,f30830]) ).
fof(f17217,plain,
! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0,
inference(cnf_transformation,[],[f5320]) ).
fof(f5320,plain,
! [X0] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) = X0,
inference(rectify,[],[f2428]) ).
fof(f2428,axiom,
! [X88] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X88)) = X88,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30828,plain,
( spl625_420
| ~ spl625_190
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30386,f30166,f29754,f30825]) ).
fof(f30825,plain,
( spl625_420
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Com_Ocom) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_420])]) ).
fof(f29754,plain,
( spl625_190
<=> class_HOL_Oequal(tc_Com_Ocom) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_190])]) ).
fof(f30386,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Com_Ocom)
| ~ spl625_190
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29756]) ).
fof(f29756,plain,
( class_HOL_Oequal(tc_Com_Ocom)
| ~ spl625_190 ),
inference(avatar_component_clause,[],[f29754]) ).
fof(f30823,plain,
spl625_419,
inference(avatar_split_clause,[],[f17214,f30821]) ).
fof(f30821,plain,
( spl625_419
<=> ! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_419])]) ).
fof(f17214,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5317]) ).
fof(f5317,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Orev(X0),c_List_Olist_ONil(X0)),
inference(rectify,[],[f4316]) ).
fof(f4316,axiom,
! [X23] : c_List_Olist_ONil(X23) = hAPP(c_List_Orev(X23),c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30819,plain,
spl625_418,
inference(avatar_split_clause,[],[f17213,f30817]) ).
fof(f30817,plain,
( spl625_418
<=> ! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_418])]) ).
fof(f17213,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5316]) ).
fof(f5316,plain,
! [X0] : c_List_Olist_ONil(X0) = hAPP(c_List_Otl(X0),c_List_Olist_ONil(X0)),
inference(rectify,[],[f4172]) ).
fof(f4172,axiom,
! [X23] : c_List_Olist_ONil(X23) = hAPP(c_List_Otl(X23),c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30815,plain,
spl625_417,
inference(avatar_split_clause,[],[f17207,f30813]) ).
fof(f30813,plain,
( spl625_417
<=> ! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_417])]) ).
fof(f17207,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0),
inference(cnf_transformation,[],[f5310]) ).
fof(f5310,plain,
! [X0] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X0),
inference(rectify,[],[f2560]) ).
fof(f2560,axiom,
! [X196] : c_Int_OPls = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),X196),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30810,plain,
( spl625_416
| ~ spl625_408
| ~ spl625_415 ),
inference(avatar_split_clause,[],[f30806,f30803,f30762,f30808]) ).
fof(f30808,plain,
( spl625_416
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OBit0(X0)),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_416])]) ).
fof(f30762,plain,
( spl625_408
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_408])]) ).
fof(f30803,plain,
( spl625_415
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_415])]) ).
fof(f30806,plain,
( ! [X0] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OBit0(X0)),c_Int_OMin))
| ~ spl625_408
| ~ spl625_415 ),
inference(forward_demodulation,[],[f30804,f30764]) ).
fof(f30764,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Int_Oint)
| ~ spl625_408 ),
inference(avatar_component_clause,[],[f30762]) ).
fof(f30804,plain,
( ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin))
| ~ spl625_415 ),
inference(avatar_component_clause,[],[f30803]) ).
fof(f30805,plain,
spl625_415,
inference(avatar_split_clause,[],[f17205,f30803]) ).
fof(f17205,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin)),
inference(cnf_transformation,[],[f5308]) ).
fof(f5308,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X0)),c_Int_OMin)),
inference(rectify,[],[f4953]) ).
fof(f4953,axiom,
! [X318] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(X318)),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30800,plain,
( spl625_414
| ~ spl625_408
| ~ spl625_413 ),
inference(avatar_split_clause,[],[f30796,f30793,f30762,f30798]) ).
fof(f30798,plain,
( spl625_414
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OMin),c_Int_OBit0(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_414])]) ).
fof(f30793,plain,
( spl625_413
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_413])]) ).
fof(f30796,plain,
( ! [X0] : ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OMin),c_Int_OBit0(X0)))
| ~ spl625_408
| ~ spl625_413 ),
inference(forward_demodulation,[],[f30794,f30764]) ).
fof(f30794,plain,
( ! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X0)))
| ~ spl625_413 ),
inference(avatar_component_clause,[],[f30793]) ).
fof(f30795,plain,
spl625_413,
inference(avatar_split_clause,[],[f17200,f30793]) ).
fof(f17200,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X0))),
inference(cnf_transformation,[],[f5303]) ).
fof(f5303,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X0))),
inference(rectify,[],[f4952]) ).
fof(f4952,axiom,
! [X317] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(X317))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30791,plain,
spl625_412,
inference(avatar_split_clause,[],[f17081,f30788]) ).
fof(f30788,plain,
( spl625_412
<=> 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,[spl625_412])]) ).
fof(f17081,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1847]) ).
fof(f1847,axiom,
c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30786,plain,
( spl625_411
| ~ spl625_191
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30384,f30166,f29759,f30783]) ).
fof(f30783,plain,
( spl625_411
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Code__Evaluation_Oterm) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_411])]) ).
fof(f29759,plain,
( spl625_191
<=> class_HOL_Oequal(tc_Code__Evaluation_Oterm) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_191])]) ).
fof(f30384,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Code__Evaluation_Oterm)
| ~ spl625_191
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29761]) ).
fof(f29761,plain,
( class_HOL_Oequal(tc_Code__Evaluation_Oterm)
| ~ spl625_191 ),
inference(avatar_component_clause,[],[f29759]) ).
fof(f30781,plain,
~ spl625_410,
inference(avatar_split_clause,[],[f17077,f30778]) ).
fof(f17077,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f1088]) ).
fof(f1088,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30776,plain,
~ spl625_409,
inference(avatar_split_clause,[],[f17076,f30773]) ).
fof(f17076,plain,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
inference(cnf_transformation,[],[f1873]) ).
fof(f1873,axiom,
~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30765,plain,
( spl625_408
| ~ spl625_194
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30383,f30166,f29774,f30762]) ).
fof(f29774,plain,
( spl625_194
<=> class_HOL_Oequal(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_194])]) ).
fof(f30383,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Int_Oint)
| ~ spl625_194
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29776]) ).
fof(f29776,plain,
( class_HOL_Oequal(tc_Int_Oint)
| ~ spl625_194 ),
inference(avatar_component_clause,[],[f29774]) ).
fof(f30758,plain,
( spl625_407
| ~ spl625_188
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30382,f30166,f29744,f30755]) ).
fof(f30755,plain,
( spl625_407
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_407])]) ).
fof(f29744,plain,
( spl625_188
<=> class_HOL_Oequal(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_188])]) ).
fof(f30382,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Product__Type_Ounit)
| ~ spl625_188
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29746]) ).
fof(f29746,plain,
( class_HOL_Oequal(tc_Product__Type_Ounit)
| ~ spl625_188 ),
inference(avatar_component_clause,[],[f29744]) ).
fof(f30752,plain,
( spl625_406
| ~ spl625_189
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30378,f30166,f29749,f30749]) ).
fof(f30749,plain,
( spl625_406
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Com_Ovname) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_406])]) ).
fof(f29749,plain,
( spl625_189
<=> class_HOL_Oequal(tc_Com_Ovname) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_189])]) ).
fof(f30378,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Com_Ovname)
| ~ spl625_189
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29751]) ).
fof(f29751,plain,
( class_HOL_Oequal(tc_Com_Ovname)
| ~ spl625_189 ),
inference(avatar_component_clause,[],[f29749]) ).
fof(f30743,plain,
( spl625_405
| ~ spl625_195
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30377,f30166,f29779,f30740]) ).
fof(f30740,plain,
( spl625_405
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_405])]) ).
fof(f29779,plain,
( spl625_195
<=> class_HOL_Oequal(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_195])]) ).
fof(f30377,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Nat_Onat)
| ~ spl625_195
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29781]) ).
fof(f29781,plain,
( class_HOL_Oequal(tc_Nat_Onat)
| ~ spl625_195 ),
inference(avatar_component_clause,[],[f29779]) ).
fof(f30737,plain,
( spl625_404
| ~ spl625_192
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30376,f30166,f29764,f30734]) ).
fof(f30734,plain,
( spl625_404
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_Com_Ostate) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_404])]) ).
fof(f29764,plain,
( spl625_192
<=> class_HOL_Oequal(tc_Com_Ostate) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_192])]) ).
fof(f30376,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_Com_Ostate)
| ~ spl625_192
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29766]) ).
fof(f29766,plain,
( class_HOL_Oequal(tc_Com_Ostate)
| ~ spl625_192 ),
inference(avatar_component_clause,[],[f29764]) ).
fof(f30730,plain,
spl625_403,
inference(avatar_split_clause,[],[f27176,f30728]) ).
fof(f27176,plain,
! [X1] :
( hBOOL(hAPP(c_Nat__Numeral_Oneg,X1))
| sP10(X1,X1) ),
inference(forward_demodulation,[],[f25012,f17178]) ).
fof(f25012,plain,
! [X1] :
( sP10(X1,X1)
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(equality_resolution,[],[f19162]) ).
fof(f19162,plain,
! [X0,X1] :
( sP10(X0,X1)
| X0 != X1
| hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1))) ),
inference(cnf_transformation,[],[f15032]) ).
fof(f30726,plain,
spl625_402,
inference(avatar_split_clause,[],[f26056,f30724]) ).
fof(f30724,plain,
( spl625_402
<=> ! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_402])]) ).
fof(f26056,plain,
! [X0,X1] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X1,X0)),
inference(forward_demodulation,[],[f17710,f17032]) ).
fof(f17710,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X1,X0)),
inference(cnf_transformation,[],[f5726]) ).
fof(f5726,plain,
! [X0,X1] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X1,X0)),
inference(rectify,[],[f1772]) ).
fof(f1772,axiom,
! [X53,X54] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(X54,X53)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30722,plain,
spl625_401,
inference(avatar_split_clause,[],[f25553,f30719]) ).
fof(f30719,plain,
( spl625_401
<=> c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_401])]) ).
fof(f25553,plain,
c_Int_OPls = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25552,f17032]) ).
fof(f25552,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Int_OPls,
inference(forward_demodulation,[],[f17089,f17021]) ).
fof(f17089,plain,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f1727]) ).
fof(f1727,axiom,
hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30717,plain,
spl625_400,
inference(avatar_split_clause,[],[f25533,f30714]) ).
fof(f30714,plain,
( spl625_400
<=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_400])]) ).
fof(f25533,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17064,f17032]) ).
fof(f17064,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
inference(cnf_transformation,[],[f2576]) ).
fof(f2576,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30712,plain,
spl625_399,
inference(avatar_split_clause,[],[f25532,f30709]) ).
fof(f30709,plain,
( spl625_399
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_399])]) ).
fof(f25532,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
inference(forward_demodulation,[],[f17063,f17032]) ).
fof(f17063,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
inference(cnf_transformation,[],[f4971]) ).
fof(f4971,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30707,plain,
spl625_398,
inference(avatar_split_clause,[],[f25531,f30704]) ).
fof(f30704,plain,
( spl625_398
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_398])]) ).
fof(f25531,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
inference(forward_demodulation,[],[f17062,f17032]) ).
fof(f17062,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
inference(cnf_transformation,[],[f4970]) ).
fof(f4970,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30702,plain,
spl625_397,
inference(avatar_split_clause,[],[f25530,f30699]) ).
fof(f30699,plain,
( spl625_397
<=> hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_397])]) ).
fof(f25530,plain,
hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17061,f17032]) ).
fof(f17061,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP),
inference(cnf_transformation,[],[f2056]) ).
fof(f2056,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30697,plain,
spl625_396,
inference(avatar_split_clause,[],[f25524,f30694]) ).
fof(f30694,plain,
( spl625_396
<=> c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_396])]) ).
fof(f30692,plain,
spl625_395,
inference(avatar_split_clause,[],[f25523,f30689]) ).
fof(f30686,plain,
spl625_394,
inference(avatar_split_clause,[],[f25482,f30684]) ).
fof(f30684,plain,
( spl625_394
<=> ! [X3,X4,X5,X1] : sP89(X5,X1,X4,X3,X4,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_394])]) ).
fof(f25482,plain,
! [X3,X1,X4,X5] : sP89(X5,X1,X4,X3,X4,X5),
inference(equality_resolution,[],[f25481]) ).
fof(f25481,plain,
! [X2,X3,X1,X4,X5] :
( sP89(X5,X1,X2,X3,X4,X5)
| X2 != X4 ),
inference(equality_resolution,[],[f23919]) ).
fof(f23919,plain,
! [X2,X3,X0,X1,X4,X5] :
( sP89(X0,X1,X2,X3,X4,X5)
| X0 != X5
| X2 != X4 ),
inference(cnf_transformation,[],[f16793]) ).
fof(f30682,plain,
spl625_393,
inference(avatar_split_clause,[],[f24986,f30680]) ).
fof(f30680,plain,
( spl625_393
<=> ! [X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_393])]) ).
fof(f24986,plain,
! [X1] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X1)),
inference(equality_resolution,[],[f19069]) ).
fof(f19069,plain,
! [X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ),
inference(cnf_transformation,[],[f14967]) ).
fof(f14967,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) )
& ( ( X0 != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ) ),
inference(flattening,[],[f14966]) ).
fof(f14966,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| X0 = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) )
& ( ( X0 != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) )
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0)) ) ),
inference(nnf_transformation,[],[f6794]) ).
fof(f6794,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
<=> ( X0 != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),X0)) ) ),
inference(rectify,[],[f1809]) ).
fof(f1809,axiom,
! [X180,X116] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X116),X180))
<=> ( X116 != X180
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X116),X180)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30678,plain,
spl625_392,
inference(avatar_split_clause,[],[f21553,f30676]) ).
fof(f30676,plain,
( spl625_392
<=> ! [X0,X3,X2,X1] :
( sP51(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_392])]) ).
fof(f21553,plain,
! [X2,X3,X0,X1] :
( sP51(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f14489]) ).
fof(f14489,plain,
! [X0,X1,X2,X3] :
( sP51(X2,X3,X0,X1)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f12622,f14488,f14487]) ).
fof(f14487,plain,
! [X1,X0,X3,X2] :
( sP50(X1,X0,X3,X2)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),c_Groups_Ozero__class_Ozero(X3))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X2)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP50])]) ).
fof(f14488,plain,
! [X2,X3,X0,X1] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
<=> sP50(X1,X0,X3,X2) )
| ~ sP51(X2,X3,X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP51])]) ).
fof(f12622,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),c_Groups_Ozero__class_Ozero(X3))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X2)) ) ) )
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(ennf_transformation,[],[f8489]) ).
fof(f8489,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),c_Groups_Ozero__class_Ozero(X3))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X2)) ) ) ) ),
inference(rectify,[],[f1547]) ).
fof(f1547,axiom,
! [X26,X6,X36,X4] :
( class_Rings_Olinordered__ring__strict(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X36),X6)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X36),X26)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X6))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30674,plain,
spl625_391,
inference(avatar_split_clause,[],[f21544,f30672]) ).
fof(f30672,plain,
( spl625_391
<=> ! [X0,X3,X2,X1] :
( sP49(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_391])]) ).
fof(f21544,plain,
! [X2,X3,X0,X1] :
( sP49(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(cnf_transformation,[],[f14486]) ).
fof(f14486,plain,
! [X0,X1,X2,X3] :
( sP49(X1,X3,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(definition_folding,[],[f12621,f14485,f14484]) ).
fof(f14484,plain,
! [X2,X0,X3,X1] :
( sP48(X2,X0,X3,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP48])]) ).
fof(f14485,plain,
! [X1,X3,X0,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
<=> sP48(X2,X0,X3,X1) )
| ~ sP49(X1,X3,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP49])]) ).
fof(f12621,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) )
| ~ class_Rings_Olinordered__ring__strict(X3) ),
inference(ennf_transformation,[],[f8488]) ).
fof(f8488,plain,
! [X0,X1,X2,X3] :
( class_Rings_Olinordered__ring__strict(X3)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X2),X1)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X3),X0),X1)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X0),X2))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X1),c_Groups_Ozero__class_Ozero(X3))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),X2),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X3),c_Groups_Ozero__class_Ozero(X3)),X1)) ) ) ) ),
inference(rectify,[],[f1546]) ).
fof(f1546,axiom,
! [X26,X36,X6,X4] :
( class_Rings_Olinordered__ring__strict(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X26),X36)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X26),X6))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X36),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),X6),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(X4),c_Groups_Ozero__class_Ozero(X4)),X36)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30670,plain,
spl625_390,
inference(avatar_split_clause,[],[f21283,f30668]) ).
fof(f30668,plain,
( spl625_390
<=> ! [X2,X0,X1,X3] : c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_390])]) ).
fof(f21283,plain,
! [X2,X3,X0,X1] : c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OSemi(X3,X2),
inference(cnf_transformation,[],[f8222]) ).
fof(f8222,plain,
! [X0,X1,X2,X3] : c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OSemi(X3,X2),
inference(rectify,[],[f76]) ).
fof(f76,axiom,
! [X10,X51,X57,X58] : c_Com_Ocom_OWhile(X51,X10) != c_Com_Ocom_OSemi(X58,X57),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30666,plain,
spl625_389,
inference(avatar_split_clause,[],[f21281,f30664]) ).
fof(f30664,plain,
( spl625_389
<=> ! [X2,X0,X1,X3] : c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OAss(X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_389])]) ).
fof(f21281,plain,
! [X2,X3,X0,X1] : c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OAss(X3,X2),
inference(cnf_transformation,[],[f8220]) ).
fof(f8220,plain,
! [X0,X1,X2,X3] : c_Com_Ocom_OWhile(X1,X0) != c_Com_Ocom_OAss(X3,X2),
inference(rectify,[],[f78]) ).
fof(f78,axiom,
! [X10,X51,X53,X54] : c_Com_Ocom_OAss(X54,X53) != c_Com_Ocom_OWhile(X51,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30662,plain,
spl625_388,
inference(avatar_split_clause,[],[f21279,f30660]) ).
fof(f30660,plain,
( spl625_388
<=> ! [X2,X0,X1,X3] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OSemi(X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_388])]) ).
fof(f21279,plain,
! [X2,X3,X0,X1] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OSemi(X3,X2),
inference(cnf_transformation,[],[f8218]) ).
fof(f8218,plain,
! [X0,X1,X2,X3] : c_Com_Ocom_OAss(X1,X0) != c_Com_Ocom_OSemi(X3,X2),
inference(rectify,[],[f71]) ).
fof(f71,axiom,
! [X53,X54,X55,X56] : c_Com_Ocom_OSemi(X56,X55) != c_Com_Ocom_OAss(X54,X53),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30658,plain,
spl625_387,
inference(avatar_split_clause,[],[f20186,f30656]) ).
fof(f30656,plain,
( spl625_387
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X1)
| ~ sP18(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_387])]) ).
fof(f20186,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X1)
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f15289]) ).
fof(f15289,plain,
! [X0,X1,X2] :
( ( sP18(X0,X1,X2)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK218(X0,X1,X2)),sK219(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK219(X0,X1,X2)),hAPP(c_List_Oset(X0),X1)))
& hBOOL(hAPP(hAPP(c_member(X0),sK218(X0,X1,X2)),hAPP(c_List_Oset(X0),X2))) )
| ~ c_List_Olinorder__class_Osorted(X0,X1)
| ~ c_List_Olinorder__class_Osorted(X0,X2) )
& ( ( ! [X5] :
( ! [X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X6),hAPP(c_List_Oset(X0),X1))) )
| ~ hBOOL(hAPP(hAPP(c_member(X0),X5),hAPP(c_List_Oset(X0),X2))) )
& c_List_Olinorder__class_Osorted(X0,X1)
& c_List_Olinorder__class_Osorted(X0,X2) )
| ~ sP18(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK218,sK219])],[f15286,f15288,f15287]) ).
fof(f15287,plain,
! [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X1))) )
& hBOOL(hAPP(hAPP(c_member(X0),X3),hAPP(c_List_Oset(X0),X2))) )
=> ( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK218(X0,X1,X2)),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X1))) )
& hBOOL(hAPP(hAPP(c_member(X0),sK218(X0,X1,X2)),hAPP(c_List_Oset(X0),X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f15288,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK218(X0,X1,X2)),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X1))) )
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK218(X0,X1,X2)),sK219(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X0),sK219(X0,X1,X2)),hAPP(c_List_Oset(X0),X1))) ) ),
introduced(choice_axiom,[]) ).
fof(f15286,plain,
! [X0,X1,X2] :
( ( sP18(X0,X1,X2)
| ? [X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X1))) )
& hBOOL(hAPP(hAPP(c_member(X0),X3),hAPP(c_List_Oset(X0),X2))) )
| ~ c_List_Olinorder__class_Osorted(X0,X1)
| ~ c_List_Olinorder__class_Osorted(X0,X2) )
& ( ( ! [X5] :
( ! [X6] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X5),X6))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X6),hAPP(c_List_Oset(X0),X1))) )
| ~ hBOOL(hAPP(hAPP(c_member(X0),X5),hAPP(c_List_Oset(X0),X2))) )
& c_List_Olinorder__class_Osorted(X0,X1)
& c_List_Olinorder__class_Osorted(X0,X2) )
| ~ sP18(X0,X1,X2) ) ),
inference(rectify,[],[f15285]) ).
fof(f15285,plain,
! [X2,X0,X1] :
( ( sP18(X2,X0,X1)
| ? [X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
| ~ c_List_Olinorder__class_Osorted(X2,X0)
| ~ c_List_Olinorder__class_Osorted(X2,X1) )
& ( ( ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
& c_List_Olinorder__class_Osorted(X2,X0)
& c_List_Olinorder__class_Osorted(X2,X1) )
| ~ sP18(X2,X0,X1) ) ),
inference(flattening,[],[f15284]) ).
fof(f15284,plain,
! [X2,X0,X1] :
( ( sP18(X2,X0,X1)
| ? [X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
& hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
| ~ c_List_Olinorder__class_Osorted(X2,X0)
| ~ c_List_Olinorder__class_Osorted(X2,X1) )
& ( ( ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
& c_List_Olinorder__class_Osorted(X2,X0)
& c_List_Olinorder__class_Osorted(X2,X1) )
| ~ sP18(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f14434]) ).
fof(f14434,plain,
! [X2,X0,X1] :
( sP18(X2,X0,X1)
<=> ( ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
& c_List_Olinorder__class_Osorted(X2,X0)
& c_List_Olinorder__class_Osorted(X2,X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f30654,plain,
spl625_386,
inference(avatar_split_clause,[],[f20185,f30652]) ).
fof(f30652,plain,
( spl625_386
<=> ! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X2)
| ~ sP18(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_386])]) ).
fof(f20185,plain,
! [X2,X0,X1] :
( c_List_Olinorder__class_Osorted(X0,X2)
| ~ sP18(X0,X1,X2) ),
inference(cnf_transformation,[],[f15289]) ).
fof(f30650,plain,
spl625_385,
inference(avatar_split_clause,[],[f18592,f30648]) ).
fof(f30648,plain,
( spl625_385
<=> ! [X0,X1] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_385])]) ).
fof(f18592,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(cnf_transformation,[],[f10885]) ).
fof(f10885,plain,
! [X0,X1] :
( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0))
| ~ c_Nat__Transfer_Ois__nat(X1) ),
inference(ennf_transformation,[],[f6469]) ).
fof(f6469,plain,
! [X0,X1] :
( c_Nat__Transfer_Ois__nat(X1)
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X1,X0)) ),
inference(rectify,[],[f3155]) ).
fof(f3155,axiom,
! [X34,X20] :
( c_Nat__Transfer_Ois__nat(X20)
=> c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,X20,X34)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30645,plain,
spl625_384,
inference(avatar_split_clause,[],[f18559,f30643]) ).
fof(f18559,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(cnf_transformation,[],[f10857]) ).
fof(f10857,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0))
| ~ class_Finite__Set_Ofinite(X1) ),
inference(ennf_transformation,[],[f6450]) ).
fof(f6450,plain,
! [X0,X1] :
( class_Finite__Set_Ofinite(X1)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X1),X0)) ),
inference(rectify,[],[f714]) ).
fof(f714,axiom,
! [X19,X4] :
( class_Finite__Set_Ofinite(X4)
=> hBOOL(hAPP(c_Finite__Set_Ofinite(X4),X19)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30641,plain,
spl625_383,
inference(avatar_split_clause,[],[f17723,f30639]) ).
fof(f30639,plain,
( spl625_383
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_383])]) ).
fof(f17723,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X0),
inference(cnf_transformation,[],[f5739]) ).
fof(f5739,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,tc_Option_Ooption(X1),c_Option_Ooption_OSome(X1),X0),
inference(rectify,[],[f797]) ).
fof(f797,axiom,
! [X19,X4] : c_Fun_Oinj__on(X4,tc_Option_Ooption(X4),c_Option_Ooption_OSome(X4),X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30637,plain,
spl625_382,
inference(avatar_split_clause,[],[f17721,f30635]) ).
fof(f30635,plain,
( spl625_382
<=> ! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_382])]) ).
fof(f17721,plain,
! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5737]) ).
fof(f5737,plain,
! [X0,X1] : c_List_Olistrelp(X1,X0,c_List_Olist_ONil(X1),c_List_Olist_ONil(X1)),
inference(rectify,[],[f3970]) ).
fof(f3970,axiom,
! [X60,X4] : c_List_Olistrelp(X4,X60,c_List_Olist_ONil(X4),c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30633,plain,
spl625_381,
inference(avatar_split_clause,[],[f17720,f30631]) ).
fof(f30631,plain,
( spl625_381
<=> ! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_381])]) ).
fof(f17720,plain,
! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(cnf_transformation,[],[f5736]) ).
fof(f5736,plain,
! [X0,X1] : c_Relation_Ototal__on(X1,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),X0),
inference(rectify,[],[f4788]) ).
fof(f4788,axiom,
! [X60,X4] : c_Relation_Ototal__on(X4,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X60),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30629,plain,
spl625_380,
inference(avatar_split_clause,[],[f17718,f30627]) ).
fof(f30627,plain,
( spl625_380
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Olistsp(X1,X0),c_List_Olist_ONil(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_380])]) ).
fof(f17718,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Olistsp(X1,X0),c_List_Olist_ONil(X1))),
inference(cnf_transformation,[],[f5734]) ).
fof(f5734,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Olistsp(X1,X0),c_List_Olist_ONil(X1))),
inference(rectify,[],[f4468]) ).
fof(f4468,axiom,
! [X19,X4] : hBOOL(hAPP(c_List_Olistsp(X4,X19),c_List_Olist_ONil(X4))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30625,plain,
spl625_379,
inference(avatar_split_clause,[],[f17717,f30623]) ).
fof(f30623,plain,
( spl625_379
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_379])]) ).
fof(f17717,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X0))),
inference(cnf_transformation,[],[f5733]) ).
fof(f5733,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(X1),c_List_Oremdups(X1,X0))),
inference(rectify,[],[f4194]) ).
fof(f4194,axiom,
! [X263,X23] : hBOOL(hAPP(c_List_Odistinct(X23),c_List_Oremdups(X23,X263))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30621,plain,
spl625_378,
inference(avatar_split_clause,[],[f17716,f30619]) ).
fof(f17716,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)),
inference(cnf_transformation,[],[f5732]) ).
fof(f5732,plain,
! [X0,X1] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X1,tc_HOL_Obool)),X0)),
inference(rectify,[],[f1191]) ).
fof(f1191,axiom,
! [X20,X4] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(X4,tc_HOL_Obool)),X20)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30617,plain,
spl625_377,
inference(avatar_split_clause,[],[f17714,f30615]) ).
fof(f30615,plain,
( spl625_377
<=> ! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_377])]) ).
fof(f17714,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))),
inference(cnf_transformation,[],[f5730]) ).
fof(f5730,plain,
! [X0,X1] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X1,X0))),
inference(rectify,[],[f3687]) ).
fof(f3687,axiom,
! [X113,X114] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(X114,X113))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30613,plain,
spl625_376,
inference(avatar_split_clause,[],[f17713,f30611]) ).
fof(f30611,plain,
( spl625_376
<=> ! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_376])]) ).
fof(f17713,plain,
! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0,
inference(cnf_transformation,[],[f5729]) ).
fof(f5729,plain,
! [X0,X1] : c_HOL_OThe(X1,hAPP(c_fequal,X0)) = X0,
inference(rectify,[],[f113]) ).
fof(f113,axiom,
! [X20,X4] : c_HOL_OThe(X4,hAPP(c_fequal,X20)) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30609,plain,
spl625_375,
inference(avatar_split_clause,[],[f17712,f30607]) ).
fof(f30607,plain,
( spl625_375
<=> ! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_375])]) ).
fof(f17712,plain,
! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0,
inference(cnf_transformation,[],[f5728]) ).
fof(f5728,plain,
! [X0,X1] : c_Hilbert__Choice_OEps(X1,hAPP(c_fequal,X0)) = X0,
inference(rectify,[],[f3882]) ).
fof(f3882,axiom,
! [X20,X4] : c_Hilbert__Choice_OEps(X4,hAPP(c_fequal,X20)) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30605,plain,
( spl625_374
| ~ spl625_329 ),
inference(avatar_split_clause,[],[f30415,f30363,f30602]) ).
fof(f30602,plain,
( spl625_374
<=> sP10(c_Int_OPls,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_374])]) ).
fof(f30363,plain,
( spl625_329
<=> ! [X1] :
( c_Int_OPls != X1
| sP10(X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_329])]) ).
fof(f30415,plain,
( sP10(c_Int_OPls,c_Int_OPls)
| ~ spl625_329 ),
inference(equality_resolution,[],[f30364]) ).
fof(f30364,plain,
( ! [X1] :
( c_Int_OPls != X1
| sP10(X1,X1) )
| ~ spl625_329 ),
inference(avatar_component_clause,[],[f30363]) ).
fof(f30600,plain,
spl625_373,
inference(avatar_split_clause,[],[f17708,f30598]) ).
fof(f30598,plain,
( spl625_373
<=> ! [X0,X1] : hAPP(c_Option_Ooption_OSome(X1),X0) != c_Option_Ooption_ONone(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_373])]) ).
fof(f17708,plain,
! [X0,X1] : hAPP(c_Option_Ooption_OSome(X1),X0) != c_Option_Ooption_ONone(X1),
inference(cnf_transformation,[],[f5724]) ).
fof(f5724,plain,
! [X0,X1] : hAPP(c_Option_Ooption_OSome(X1),X0) != c_Option_Ooption_ONone(X1),
inference(rectify,[],[f833]) ).
fof(f833,axiom,
! [X149,X23] : hAPP(c_Option_Ooption_OSome(X23),X149) != c_Option_Ooption_ONone(X23),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30596,plain,
spl625_372,
inference(avatar_split_clause,[],[f17552,f30594]) ).
fof(f30594,plain,
( spl625_372
<=> ! [X0] :
( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_372])]) ).
fof(f17552,plain,
! [X0] :
( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) ),
inference(cnf_transformation,[],[f14577]) ).
fof(f14577,plain,
! [X0] :
( ( c_Int_OPls = c_Int_OBit0(X0)
| c_Int_OPls != X0 )
& ( c_Int_OPls = X0
| c_Int_OPls != c_Int_OBit0(X0) ) ),
inference(nnf_transformation,[],[f5632]) ).
fof(f5632,plain,
! [X0] :
( c_Int_OPls = c_Int_OBit0(X0)
<=> c_Int_OPls = X0 ),
inference(rectify,[],[f2651]) ).
fof(f2651,axiom,
! [X153] :
( c_Int_OPls = c_Int_OBit0(X153)
<=> c_Int_OPls = X153 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30592,plain,
spl625_371,
inference(avatar_split_clause,[],[f17542,f30590]) ).
fof(f30590,plain,
( spl625_371
<=> ! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_371])]) ).
fof(f17542,plain,
! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ),
inference(cnf_transformation,[],[f10468]) ).
fof(f10468,plain,
! [X0] :
( c_List_Onat__list(X0)
| ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ),
inference(ennf_transformation,[],[f10152]) ).
fof(f10152,plain,
! [X0] :
( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0))
=> c_List_Onat__list(X0) ),
inference(unused_predicate_definition_removal,[],[f5627]) ).
fof(f5627,plain,
! [X0] :
( c_List_Onat__list(X0)
<=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X0)) ),
inference(rectify,[],[f3693]) ).
fof(f3693,axiom,
! [X153] :
( c_List_Onat__list(X153)
<=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),X153)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30588,plain,
spl625_370,
inference(avatar_split_clause,[],[f17481,f30586]) ).
fof(f30586,plain,
( spl625_370
<=> ! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__inf__class_Oinf(X0))
| ~ class_Lattices_Osemilattice__inf(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_370])]) ).
fof(f17481,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__inf__class_Oinf(X0))
| ~ class_Lattices_Osemilattice__inf(X0) ),
inference(cnf_transformation,[],[f10407]) ).
fof(f10407,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__inf__class_Oinf(X0))
| ~ class_Lattices_Osemilattice__inf(X0) ),
inference(ennf_transformation,[],[f5571]) ).
fof(f5571,plain,
! [X0] :
( class_Lattices_Osemilattice__inf(X0)
=> c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__inf__class_Oinf(X0)) ),
inference(rectify,[],[f671]) ).
fof(f671,axiom,
! [X4] :
( class_Lattices_Osemilattice__inf(X4)
=> c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Lattices_Osemilattice__inf__class_Oinf(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30584,plain,
spl625_369,
inference(avatar_split_clause,[],[f17480,f30582]) ).
fof(f30582,plain,
( spl625_369
<=> ! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__sup__class_Osup(X0))
| ~ class_Lattices_Osemilattice__sup(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_369])]) ).
fof(f17480,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__sup__class_Osup(X0))
| ~ class_Lattices_Osemilattice__sup(X0) ),
inference(cnf_transformation,[],[f10406]) ).
fof(f10406,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__sup__class_Osup(X0))
| ~ class_Lattices_Osemilattice__sup(X0) ),
inference(ennf_transformation,[],[f5570]) ).
fof(f5570,plain,
! [X0] :
( class_Lattices_Osemilattice__sup(X0)
=> c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Lattices_Osemilattice__sup__class_Osup(X0)) ),
inference(rectify,[],[f670]) ).
fof(f670,axiom,
! [X4] :
( class_Lattices_Osemilattice__sup(X4)
=> c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Lattices_Osemilattice__sup__class_Osup(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30580,plain,
spl625_368,
inference(avatar_split_clause,[],[f17475,f30578]) ).
fof(f30578,plain,
( spl625_368
<=> ! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_368])]) ).
fof(f17475,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10401]) ).
fof(f10401,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5565]) ).
fof(f5565,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omin(X0)) ),
inference(rectify,[],[f1513]) ).
fof(f1513,axiom,
! [X4] :
( class_Orderings_Olinorder(X4)
=> c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Orderings_Oord__class_Omin(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30576,plain,
spl625_367,
inference(avatar_split_clause,[],[f17474,f30574]) ).
fof(f30574,plain,
( spl625_367
<=> ! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_367])]) ).
fof(f17474,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10400]) ).
fof(f10400,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5564]) ).
fof(f5564,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_Finite__Set_Ofun__left__comm__idem(X0,X0,c_Orderings_Oord__class_Omax(X0)) ),
inference(rectify,[],[f2156]) ).
fof(f2156,axiom,
! [X4] :
( class_Orderings_Olinorder(X4)
=> c_Finite__Set_Ofun__left__comm__idem(X4,X4,c_Orderings_Oord__class_Omax(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30572,plain,
spl625_366,
inference(avatar_split_clause,[],[f17456,f30570]) ).
fof(f30570,plain,
( spl625_366
<=> ! [X0] :
( c_Finite__Set_Ofun__left__comm(X0,X0,c_Groups_Otimes__class_Otimes(X0))
| ~ class_Groups_Oab__semigroup__mult(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_366])]) ).
fof(f17456,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm(X0,X0,c_Groups_Otimes__class_Otimes(X0))
| ~ class_Groups_Oab__semigroup__mult(X0) ),
inference(cnf_transformation,[],[f10382]) ).
fof(f10382,plain,
! [X0] :
( c_Finite__Set_Ofun__left__comm(X0,X0,c_Groups_Otimes__class_Otimes(X0))
| ~ class_Groups_Oab__semigroup__mult(X0) ),
inference(ennf_transformation,[],[f5546]) ).
fof(f5546,plain,
! [X0] :
( class_Groups_Oab__semigroup__mult(X0)
=> c_Finite__Set_Ofun__left__comm(X0,X0,c_Groups_Otimes__class_Otimes(X0)) ),
inference(rectify,[],[f4884]) ).
fof(f4884,axiom,
! [X4] :
( class_Groups_Oab__semigroup__mult(X4)
=> c_Finite__Set_Ofun__left__comm(X4,X4,c_Groups_Otimes__class_Otimes(X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30568,plain,
spl625_365,
inference(avatar_split_clause,[],[f17453,f30566]) ).
fof(f30566,plain,
( spl625_365
<=> ! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_365])]) ).
fof(f17453,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(cnf_transformation,[],[f10379]) ).
fof(f10379,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0)
| ~ class_Rings_Ozero__neq__one(X0) ),
inference(ennf_transformation,[],[f5543]) ).
fof(f5543,plain,
! [X0] :
( class_Rings_Ozero__neq__one(X0)
=> c_Groups_Ozero__class_Ozero(X0) != c_Groups_Oone__class_Oone(X0) ),
inference(rectify,[],[f1475]) ).
fof(f1475,axiom,
! [X23] :
( class_Rings_Ozero__neq__one(X23)
=> c_Groups_Oone__class_Oone(X23) != c_Groups_Ozero__class_Ozero(X23) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30564,plain,
spl625_364,
inference(avatar_split_clause,[],[f17199,f30562]) ).
fof(f30562,plain,
( spl625_364
<=> ! [X0] : c_Finite__Set_Ofun__left__comm__idem(X0,tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_364])]) ).
fof(f17199,plain,
! [X0] : c_Finite__Set_Ofun__left__comm__idem(X0,tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0)),
inference(cnf_transformation,[],[f5302]) ).
fof(f5302,plain,
! [X0] : c_Finite__Set_Ofun__left__comm__idem(X0,tc_fun(X0,tc_HOL_Obool),c_Set_Oinsert(X0)),
inference(rectify,[],[f669]) ).
fof(f669,axiom,
! [X4] : c_Finite__Set_Ofun__left__comm__idem(X4,tc_fun(X4,tc_HOL_Obool),c_Set_Oinsert(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30560,plain,
spl625_363,
inference(avatar_split_clause,[],[f17198,f30558]) ).
fof(f17198,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f5301]) ).
fof(f5301,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f191]) ).
fof(f191,axiom,
! [X88] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),X88),X88)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30556,plain,
spl625_362,
inference(avatar_split_clause,[],[f17197,f30554]) ).
fof(f17197,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)),
inference(cnf_transformation,[],[f5300]) ).
fof(f5300,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),X0)),
inference(rectify,[],[f1813]) ).
fof(f1813,axiom,
! [X196] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X196),X196)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30552,plain,
spl625_361,
inference(avatar_split_clause,[],[f17195,f30550]) ).
fof(f17195,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X0),X0)),
inference(cnf_transformation,[],[f5298]) ).
fof(f5298,plain,
! [X0] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X0),X0)),
inference(rectify,[],[f157]) ).
fof(f157,axiom,
! [X32] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),X32),X32)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30547,plain,
spl625_360,
inference(avatar_split_clause,[],[f17194,f30545]) ).
fof(f30545,plain,
( spl625_360
<=> ! [X0] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_360])]) ).
fof(f17194,plain,
! [X0] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X0),X0)),
inference(cnf_transformation,[],[f5297]) ).
fof(f5297,plain,
! [X0] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X0),X0)),
inference(rectify,[],[f4974]) ).
fof(f4974,axiom,
! [X112] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),X112),X112)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30543,plain,
spl625_359,
inference(avatar_split_clause,[],[f17192,f30541]) ).
fof(f30541,plain,
( spl625_359
<=> ! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_359])]) ).
fof(f17192,plain,
! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0,
inference(cnf_transformation,[],[f5295]) ).
fof(f5295,plain,
! [X0] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X0)) = X0,
inference(rectify,[],[f4637]) ).
fof(f4637,axiom,
! [X112] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,X112)) = X112,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30539,plain,
spl625_358,
inference(avatar_split_clause,[],[f17191,f30537]) ).
fof(f30537,plain,
( spl625_358
<=> ! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_358])]) ).
fof(f17191,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0,
inference(cnf_transformation,[],[f5294]) ).
fof(f5294,plain,
! [X0] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X0)) = X0,
inference(rectify,[],[f4636]) ).
fof(f4636,axiom,
! [X88] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,X88)) = X88,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30535,plain,
spl625_357,
inference(avatar_split_clause,[],[f17190,f30533]) ).
fof(f30533,plain,
( spl625_357
<=> ! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_357])]) ).
fof(f17190,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0,
inference(cnf_transformation,[],[f5293]) ).
fof(f5293,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X0)) = X0,
inference(rectify,[],[f3094]) ).
fof(f3094,axiom,
! [X20] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,X20)) = X20,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30531,plain,
spl625_356,
inference(avatar_split_clause,[],[f17186,f30529]) ).
fof(f30529,plain,
( spl625_356
<=> ! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(X0,c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_356])]) ).
fof(f17186,plain,
! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(X0,c_List_Olist_ONil(X0)),
inference(cnf_transformation,[],[f5289]) ).
fof(f5289,plain,
! [X0] : c_List_Olist_ONil(X0) = c_List_Oremdups(X0,c_List_Olist_ONil(X0)),
inference(rectify,[],[f4212]) ).
fof(f4212,axiom,
! [X23] : c_List_Olist_ONil(X23) = c_List_Oremdups(X23,c_List_Olist_ONil(X23)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30527,plain,
spl625_355,
inference(avatar_split_clause,[],[f17182,f30525]) ).
fof(f30525,plain,
( spl625_355
<=> ! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_355])]) ).
fof(f17182,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(cnf_transformation,[],[f5285]) ).
fof(f5285,plain,
! [X0] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X0),X0)),
inference(rectify,[],[f657]) ).
fof(f657,axiom,
! [X88] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X88),X88)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30523,plain,
spl625_354,
inference(avatar_split_clause,[],[f17181,f30521]) ).
fof(f30521,plain,
( spl625_354
<=> ! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_354])]) ).
fof(f17181,plain,
! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(cnf_transformation,[],[f5284]) ).
fof(f5284,plain,
! [X0] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0))),
inference(rectify,[],[f2538]) ).
fof(f2538,axiom,
! [X88] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X88))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30519,plain,
spl625_353,
inference(avatar_split_clause,[],[f17074,f30516]) ).
fof(f17074,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f2790]) ).
fof(f2790,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30514,plain,
spl625_352,
inference(avatar_split_clause,[],[f17072,f30511]) ).
fof(f17072,plain,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f2795]) ).
fof(f2795,axiom,
hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30509,plain,
( spl625_351
| ~ spl625_274
| ~ spl625_350 ),
inference(avatar_split_clause,[],[f30504,f30500,f30138,f30506]) ).
fof(f30506,plain,
( spl625_351
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_351])]) ).
fof(f30500,plain,
( spl625_350
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_350])]) ).
fof(f30504,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OMin))
| ~ spl625_274
| ~ spl625_350 ),
inference(forward_demodulation,[],[f30502,f30139]) ).
fof(f30502,plain,
( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)))
| ~ spl625_350 ),
inference(avatar_component_clause,[],[f30500]) ).
fof(f30503,plain,
spl625_350,
inference(avatar_split_clause,[],[f17069,f30500]) ).
fof(f17069,plain,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
inference(cnf_transformation,[],[f2803]) ).
fof(f2803,axiom,
hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30498,plain,
spl625_349,
inference(avatar_split_clause,[],[f17066,f30495]) ).
fof(f17066,plain,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin,
inference(cnf_transformation,[],[f2801]) ).
fof(f2801,axiom,
hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30493,plain,
spl625_348,
inference(avatar_split_clause,[],[f17057,f30490]) ).
fof(f17057,plain,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
inference(cnf_transformation,[],[f2856]) ).
fof(f2856,axiom,
c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30488,plain,
spl625_347,
inference(avatar_split_clause,[],[f17054,f30485]) ).
fof(f17054,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f2450]) ).
fof(f2450,axiom,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30483,plain,
spl625_346,
inference(avatar_split_clause,[],[f17053,f30480]) ).
fof(f30480,plain,
( spl625_346
<=> 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,[spl625_346])]) ).
fof(f17053,plain,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(cnf_transformation,[],[f4627]) ).
fof(f4627,axiom,
c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30478,plain,
spl625_345,
inference(avatar_split_clause,[],[f17051,f30475]) ).
fof(f30475,plain,
( spl625_345
<=> 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,[spl625_345])]) ).
fof(f17051,plain,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f3087]) ).
fof(f3087,axiom,
c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30473,plain,
( spl625_344
| ~ spl625_203
| ~ spl625_305 ),
inference(avatar_split_clause,[],[f30400,f30262,f29820,f30470]) ).
fof(f30470,plain,
( spl625_344
<=> sP4(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_344])]) ).
fof(f29820,plain,
( spl625_203
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_203])]) ).
fof(f30400,plain,
( sP4(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl625_203
| ~ spl625_305 ),
inference(resolution,[],[f30263,f29822]) ).
fof(f29822,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl625_203 ),
inference(avatar_component_clause,[],[f29820]) ).
fof(f30468,plain,
spl625_343,
inference(avatar_split_clause,[],[f17050,f30465]) ).
fof(f30465,plain,
( spl625_343
<=> 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,[spl625_343])]) ).
fof(f17050,plain,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f3078]) ).
fof(f3078,axiom,
c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30463,plain,
spl625_342,
inference(avatar_split_clause,[],[f17049,f30460]) ).
fof(f30460,plain,
( spl625_342
<=> 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,[spl625_342])]) ).
fof(f17049,plain,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f3081]) ).
fof(f3081,axiom,
c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30458,plain,
~ spl625_341,
inference(avatar_split_clause,[],[f17048,f30455]) ).
fof(f17048,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f2791]) ).
fof(f2791,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30453,plain,
~ spl625_340,
inference(avatar_split_clause,[],[f17046,f30450]) ).
fof(f30450,plain,
( spl625_340
<=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_340])]) ).
fof(f17046,plain,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f2794]) ).
fof(f2794,axiom,
~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30448,plain,
( ~ spl625_339
| ~ spl625_194
| ~ spl625_281
| spl625_338 ),
inference(avatar_split_clause,[],[f30443,f30439,f30166,f29774,f30445]) ).
fof(f30445,plain,
( spl625_339
<=> hBOOL(hAPP(hAPP(c_fequal,c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_339])]) ).
fof(f30439,plain,
( spl625_338
<=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_338])]) ).
fof(f30443,plain,
( ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OPls),c_Int_OMin))
| ~ spl625_194
| ~ spl625_281
| spl625_338 ),
inference(forward_demodulation,[],[f30441,f30383]) ).
fof(f30441,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin))
| spl625_338 ),
inference(avatar_component_clause,[],[f30439]) ).
fof(f30442,plain,
~ spl625_338,
inference(avatar_split_clause,[],[f17044,f30439]) ).
fof(f17044,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
inference(cnf_transformation,[],[f4969]) ).
fof(f4969,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30437,plain,
( ~ spl625_337
| ~ spl625_194
| ~ spl625_281
| spl625_336 ),
inference(avatar_split_clause,[],[f30432,f30428,f30166,f29774,f30434]) ).
fof(f30434,plain,
( spl625_337
<=> hBOOL(hAPP(hAPP(c_fequal,c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_337])]) ).
fof(f30428,plain,
( spl625_336
<=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_336])]) ).
fof(f30432,plain,
( ~ hBOOL(hAPP(hAPP(c_fequal,c_Int_OMin),c_Int_OPls))
| ~ spl625_194
| ~ spl625_281
| spl625_336 ),
inference(forward_demodulation,[],[f30430,f30383]) ).
fof(f30430,plain,
( ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls))
| spl625_336 ),
inference(avatar_component_clause,[],[f30428]) ).
fof(f30431,plain,
~ spl625_336,
inference(avatar_split_clause,[],[f17043,f30428]) ).
fof(f17043,plain,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
inference(cnf_transformation,[],[f4968]) ).
fof(f4968,axiom,
~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30426,plain,
( spl625_335
| ~ spl625_202
| ~ spl625_305 ),
inference(avatar_split_clause,[],[f30399,f30262,f29815,f30423]) ).
fof(f30423,plain,
( spl625_335
<=> sP4(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_335])]) ).
fof(f29815,plain,
( spl625_202
<=> c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_202])]) ).
fof(f30399,plain,
( sP4(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl625_202
| ~ spl625_305 ),
inference(resolution,[],[f30263,f29817]) ).
fof(f29817,plain,
( c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl625_202 ),
inference(avatar_component_clause,[],[f29815]) ).
fof(f30420,plain,
~ spl625_334,
inference(avatar_split_clause,[],[f17042,f30417]) ).
fof(f30417,plain,
( spl625_334
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_334])]) ).
fof(f17042,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
inference(cnf_transformation,[],[f2582]) ).
fof(f2582,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30414,plain,
( spl625_333
| ~ spl625_203
| ~ spl625_304 ),
inference(avatar_split_clause,[],[f30397,f30258,f29820,f30411]) ).
fof(f30411,plain,
( spl625_333
<=> c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Oless__than) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_333])]) ).
fof(f30397,plain,
( c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Oless__than)
| ~ spl625_203
| ~ spl625_304 ),
inference(resolution,[],[f30259,f29822]) ).
fof(f30406,plain,
( spl625_332
| ~ spl625_202
| ~ spl625_304 ),
inference(avatar_split_clause,[],[f30396,f30258,f29815,f30403]) ).
fof(f30403,plain,
( spl625_332
<=> c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Opred__nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_332])]) ).
fof(f30396,plain,
( c_Wellfounded_Oacyclic(tc_Nat_Onat,c_Wellfounded_Opred__nat)
| ~ spl625_202
| ~ spl625_304 ),
inference(resolution,[],[f30259,f29817]) ).
fof(f30395,plain,
( spl625_331
| ~ spl625_196
| ~ spl625_281 ),
inference(avatar_split_clause,[],[f30375,f30166,f29784,f30392]) ).
fof(f30392,plain,
( spl625_331
<=> c_fequal = c_HOL_Oequal__class_Oequal(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_331])]) ).
fof(f29784,plain,
( spl625_196
<=> class_HOL_Oequal(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_196])]) ).
fof(f30375,plain,
( c_fequal = c_HOL_Oequal__class_Oequal(tc_HOL_Obool)
| ~ spl625_196
| ~ spl625_281 ),
inference(resolution,[],[f30167,f29786]) ).
fof(f29786,plain,
( class_HOL_Oequal(tc_HOL_Obool)
| ~ spl625_196 ),
inference(avatar_component_clause,[],[f29784]) ).
fof(f30373,plain,
( ~ spl625_128
| spl625_330
| ~ spl625_219
| ~ spl625_279 ),
inference(avatar_split_clause,[],[f30367,f30158,f29889,f30370,f29444]) ).
fof(f29444,plain,
( spl625_128
<=> class_Rings_Osemiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_128])]) ).
fof(f30370,plain,
( spl625_330
<=> c_Int_Oiszero(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_330])]) ).
fof(f29889,plain,
( spl625_219
<=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl625_219])]) ).
fof(f30367,plain,
( c_Int_Oiszero(tc_Int_Oint,c_Int_OPls)
| ~ class_Rings_Osemiring__1(tc_Int_Oint)
| ~ spl625_219
| ~ spl625_279 ),
inference(superposition,[],[f30159,f29891]) ).
fof(f29891,plain,
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_OPls
| ~ spl625_219 ),
inference(avatar_component_clause,[],[f29889]) ).
fof(f30365,plain,
spl625_329,
inference(avatar_split_clause,[],[f27175,f30363]) ).
fof(f27175,plain,
! [X1] :
( c_Int_OPls != X1
| sP10(X1,X1) ),
inference(forward_demodulation,[],[f27174,f17021]) ).
fof(f27174,plain,
! [X1] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1
| sP10(X1,X1) ),
inference(forward_demodulation,[],[f25011,f17178]) ).
fof(f25011,plain,
! [X1] :
( sP10(X1,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X1) ),
inference(equality_resolution,[],[f19163]) ).
fof(f19163,plain,
! [X0,X1] :
( sP10(X0,X1)
| X0 != X1
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) ),
inference(cnf_transformation,[],[f15032]) ).
fof(f30361,plain,
spl625_328,
inference(avatar_split_clause,[],[f26225,f30359]) ).
fof(f30359,plain,
( spl625_328
<=> ! [X0] : c_Nitpick_Onat__gcd(X0,c_HOL_Obool_Obool__size(c_fTrue)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_328])]) ).
fof(f26225,plain,
! [X0] : c_Nitpick_Onat__gcd(X0,c_HOL_Obool_Obool__size(c_fTrue)) = X0,
inference(forward_demodulation,[],[f24890,f17032]) ).
fof(f24890,plain,
! [X0] : c_Nitpick_Onat__gcd(X0,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0,
inference(equality_resolution,[],[f18100]) ).
fof(f18100,plain,
! [X0,X1] :
( c_Nitpick_Onat__gcd(X0,X1) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f10482]) ).
fof(f10482,plain,
! [X0,X1] :
( ( c_Nitpick_Onat__gcd(X0,X1) = c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1))
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
& ( c_Nitpick_Onat__gcd(X0,X1) = X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ) ),
inference(ennf_transformation,[],[f6109]) ).
fof(f6109,plain,
! [X0,X1] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
=> c_Nitpick_Onat__gcd(X0,X1) = c_Nitpick_Onat__gcd(X1,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X0,X1)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1
=> c_Nitpick_Onat__gcd(X0,X1) = X0 ) ),
inference(rectify,[],[f3306]) ).
fof(f3306,axiom,
! [X22,X29] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X29
=> c_Nitpick_Onat__gcd(X22,X29) = c_Nitpick_Onat__gcd(X29,c_Divides_Odiv__class_Omod(tc_Nat_Onat,X22,X29)) )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X29
=> c_Nitpick_Onat__gcd(X22,X29) = X22 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30357,plain,
spl625_327,
inference(avatar_split_clause,[],[f25764,f30354]) ).
fof(f30354,plain,
( spl625_327
<=> 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,[spl625_327])]) ).
fof(f25764,plain,
c_Int_OPls = hAPP(c_Code__Numeral_Oint__of,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(forward_demodulation,[],[f24869,f17021]) ).
fof(f24869,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,[],[f17399]) ).
fof(f17399,plain,
! [X0] :
( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X0)
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X0 ),
inference(cnf_transformation,[],[f10340]) ).
fof(f10340,plain,
! [X0] :
( ( ( ( hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) )
& ( hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ) )
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X0)
| c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X0 ) ),
inference(ennf_transformation,[],[f5501]) ).
fof(f5501,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X0
=> ( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X0) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X0),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X0
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X0) ) ),
inference(rectify,[],[f2854]) ).
fof(f2854,axiom,
! [X112] :
( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != X112
=> ( ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X112,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X112),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,X112,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
=> hAPP(c_Code__Numeral_Oint__of,X112) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Code__Numeral_Oint__of,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),X112),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = X112
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Code__Numeral_Oint__of,X112) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30352,plain,
spl625_326,
inference(avatar_split_clause,[],[f25752,f30350]) ).
fof(f30350,plain,
( spl625_326
<=> ! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OPls) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_326])]) ).
fof(f25752,plain,
! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OPls) = X0,
inference(forward_demodulation,[],[f17398,f17021]) ).
fof(f17398,plain,
! [X0] : c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = X0,
inference(cnf_transformation,[],[f5500]) ).
fof(f30348,plain,
spl625_325,
inference(avatar_split_clause,[],[f25652,f30346]) ).
fof(f30346,plain,
( spl625_325
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_325])]) ).
fof(f25652,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin),
inference(forward_demodulation,[],[f25651,f17021]) ).
fof(f25651,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,c_Int_OMin),
inference(forward_demodulation,[],[f17261,f17178]) ).
fof(f17261,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
inference(cnf_transformation,[],[f5364]) ).
fof(f5364,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
inference(rectify,[],[f2827]) ).
fof(f2827,axiom,
! [X32] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X32,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30344,plain,
spl625_324,
inference(avatar_split_clause,[],[f25642,f30342]) ).
fof(f30342,plain,
( spl625_324
<=> ! [X0] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_324])]) ).
fof(f25642,plain,
! [X0] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0) = X0,
inference(forward_demodulation,[],[f17244,f17178]) ).
fof(f17244,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0),
inference(cnf_transformation,[],[f5347]) ).
fof(f5347,plain,
! [X0] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X0) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X0),
inference(rectify,[],[f2778]) ).
fof(f2778,axiom,
! [X196] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),X196) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),X196),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30340,plain,
spl625_323,
inference(avatar_split_clause,[],[f25632,f30338]) ).
fof(f30338,plain,
( spl625_323
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OPls,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_323])]) ).
fof(f25632,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Int_OPls,X0),
inference(forward_demodulation,[],[f17208,f17021]) ).
fof(f17208,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),
inference(cnf_transformation,[],[f5311]) ).
fof(f5311,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X0),
inference(rectify,[],[f2106]) ).
fof(f2106,axiom,
! [X33] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30336,plain,
spl625_322,
inference(avatar_split_clause,[],[f25628,f30334]) ).
fof(f30334,plain,
( spl625_322
<=> ! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_322])]) ).
fof(f25628,plain,
! [X0] : c_Int_OPls = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(forward_demodulation,[],[f17185,f17021]) ).
fof(f17185,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(cnf_transformation,[],[f5288]) ).
fof(f5288,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X0,X0),
inference(rectify,[],[f2103]) ).
fof(f2103,axiom,
! [X32] : c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Divides_Odiv__class_Omod(tc_Int_Oint,X32,X32),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30332,plain,
spl625_321,
inference(avatar_split_clause,[],[f25626,f30330]) ).
fof(f30330,plain,
( spl625_321
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_321])]) ).
fof(f25626,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X0)),
inference(forward_demodulation,[],[f17172,f17032]) ).
fof(f17172,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X0)),
inference(cnf_transformation,[],[f5275]) ).
fof(f5275,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X0)),
inference(rectify,[],[f1687]) ).
fof(f1687,axiom,
! [X191] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(X191)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30328,plain,
spl625_320,
inference(avatar_split_clause,[],[f25625,f30326]) ).
fof(f30326,plain,
( spl625_320
<=> ! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_320])]) ).
fof(f25625,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X0)),
inference(forward_demodulation,[],[f17171,f17032]) ).
fof(f17171,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X0)),
inference(cnf_transformation,[],[f5274]) ).
fof(f5274,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X0)),
inference(rectify,[],[f1684]) ).
fof(f1684,axiom,
! [X111] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(X111)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30324,plain,
spl625_319,
inference(avatar_split_clause,[],[f25619,f30322]) ).
fof(f25619,plain,
! [X0] : c_HOL_Obool_Obool__size(c_fTrue) != hAPP(c_Nat_OSuc,X0),
inference(forward_demodulation,[],[f17165,f17032]) ).
fof(f17165,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X0),
inference(cnf_transformation,[],[f5268]) ).
fof(f5268,plain,
! [X0] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X0),
inference(rectify,[],[f1483]) ).
fof(f1483,axiom,
! [X185] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,X185),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30320,plain,
~ spl625_318,
inference(avatar_split_clause,[],[f25557,f30317]) ).
fof(f30317,plain,
( spl625_318
<=> c_Int_OPls = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_318])]) ).
fof(f25557,plain,
c_Int_OPls != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
inference(forward_demodulation,[],[f17092,f25525]) ).
fof(f25525,plain,
c_Int_OPls = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(forward_demodulation,[],[f17058,f17021]) ).
fof(f17058,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
inference(cnf_transformation,[],[f2578]) ).
fof(f2578,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f17092,plain,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
inference(cnf_transformation,[],[f2800]) ).
fof(f2800,axiom,
hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30315,plain,
spl625_317,
inference(avatar_split_clause,[],[f25527,f30312]) ).
fof(f30312,plain,
( spl625_317
<=> c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_317])]) ).
fof(f25527,plain,
c_HOL_Obool_Obool__size(c_fTrue) = hAPP(c_Int_Onat,c_Int_OPls),
inference(forward_demodulation,[],[f25526,f17032]) ).
fof(f25526,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Int_OPls),
inference(forward_demodulation,[],[f17059,f17021]) ).
fof(f17059,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f2443]) ).
fof(f2443,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30310,plain,
spl625_316,
inference(avatar_split_clause,[],[f25521,f30307]) ).
fof(f30307,plain,
( spl625_316
<=> c_HOL_Obool_Obool__size(c_fTrue) = c_Nat_Onat_Onat__size(c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_316])]) ).
fof(f25521,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_Nat_Onat_Onat__size(c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f17041,f17032]) ).
fof(f17041,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(cnf_transformation,[],[f1836]) ).
fof(f1836,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30305,plain,
spl625_315,
inference(avatar_split_clause,[],[f25520,f30302]) ).
fof(f30302,plain,
( spl625_315
<=> c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_315])]) ).
fof(f25520,plain,
c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17040,f17032]) ).
fof(f17040,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
inference(cnf_transformation,[],[f2921]) ).
fof(f2921,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30300,plain,
spl625_314,
inference(avatar_split_clause,[],[f25147,f30298]) ).
fof(f30298,plain,
( spl625_314
<=> ! [X2,X0] : c_List_Olist__all2(X0,X0,c_fequal,X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_314])]) ).
fof(f25147,plain,
! [X2,X0] : c_List_Olist__all2(X0,X0,c_fequal,X2,X2),
inference(equality_resolution,[],[f20872]) ).
fof(f20872,plain,
! [X2,X0,X1] :
( c_List_Olist__all2(X0,X0,c_fequal,X2,X1)
| X1 != X2 ),
inference(cnf_transformation,[],[f15555]) ).
fof(f30296,plain,
spl625_313,
inference(avatar_split_clause,[],[f24899,f30294]) ).
fof(f24899,plain,
! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_resolution,[],[f18194]) ).
fof(f18194,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
| X0 != X1 ),
inference(cnf_transformation,[],[f6153]) ).
fof(f6153,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_fequal,X1),X0))
| X0 != X1 ),
inference(rectify,[],[f5227]) ).
fof(f5227,axiom,
! [X34,X20] :
( hBOOL(hAPP(hAPP(c_fequal,X20),X34))
| X20 != X34 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30292,plain,
spl625_312,
inference(avatar_split_clause,[],[f24883,f30290]) ).
fof(f30290,plain,
( spl625_312
<=> ! [X1] : c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_312])]) ).
fof(f24883,plain,
! [X1] : c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X1),
inference(equality_resolution,[],[f18088]) ).
fof(f18088,plain,
! [X0,X1] :
( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X0)
| X0 != X1 ),
inference(cnf_transformation,[],[f10477]) ).
fof(f10477,plain,
! [X0,X1] :
( ( c_Random_Oinc__shift(X1,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X0),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
| X0 = X1 )
& ( c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X0)
| X0 != X1 ) ),
inference(ennf_transformation,[],[f6104]) ).
fof(f6104,plain,
! [X0,X1] :
( ( X0 != X1
=> c_Random_Oinc__shift(X1,X0) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X0),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) )
& ( X0 = X1
=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X1,X0) ) ),
inference(rectify,[],[f4610]) ).
fof(f4610,axiom,
! [X112,X190] :
( ( X112 != X190
=> c_Random_Oinc__shift(X190,X112) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),X112),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) )
& ( X112 = X190
=> c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = c_Random_Oinc__shift(X190,X112) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30288,plain,
spl625_311,
inference(avatar_split_clause,[],[f20191,f30286]) ).
fof(f30286,plain,
( spl625_311
<=> ! [X2,X0,X1] :
( sP19(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_311])]) ).
fof(f20191,plain,
! [X2,X0,X1] :
( sP19(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(cnf_transformation,[],[f14436]) ).
fof(f14436,plain,
! [X0,X1,X2] :
( sP19(X1,X0,X2)
| ~ class_Orderings_Olinorder(X2) ),
inference(definition_folding,[],[f11870,f14435,f14434]) ).
fof(f14435,plain,
! [X1,X0,X2] :
( ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Oappend(X2),X1),X0))
<=> sP18(X2,X0,X1) )
| ~ sP19(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
fof(f11870,plain,
! [X0,X1,X2] :
( ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Oappend(X2),X1),X0))
<=> ( ! [X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0))) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1))) )
& c_List_Olinorder__class_Osorted(X2,X0)
& c_List_Olinorder__class_Osorted(X2,X1) ) )
| ~ class_Orderings_Olinorder(X2) ),
inference(ennf_transformation,[],[f7620]) ).
fof(f7620,plain,
! [X0,X1,X2] :
( class_Orderings_Olinorder(X2)
=> ( c_List_Olinorder__class_Osorted(X2,hAPP(hAPP(c_List_Oappend(X2),X1),X0))
<=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(c_List_Oset(X2),X1)))
=> ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X4),hAPP(c_List_Oset(X2),X0)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X3),X4)) ) )
& c_List_Olinorder__class_Osorted(X2,X0)
& c_List_Olinorder__class_Osorted(X2,X1) ) ) ),
inference(rectify,[],[f4286]) ).
fof(f4286,axiom,
! [X259,X258,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_List_Olinorder__class_Osorted(X4,hAPP(hAPP(c_List_Oappend(X4),X258),X259))
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X4),X2),hAPP(c_List_Oset(X4),X258)))
=> ! [X118] :
( hBOOL(hAPP(hAPP(c_member(X4),X118),hAPP(c_List_Oset(X4),X259)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X2),X118)) ) )
& c_List_Olinorder__class_Osorted(X4,X259)
& c_List_Olinorder__class_Osorted(X4,X258) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30284,plain,
spl625_310,
inference(avatar_split_clause,[],[f19745,f30282]) ).
fof(f30282,plain,
( spl625_310
<=> ! [X2,X0,X1] :
( sP17(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_310])]) ).
fof(f19745,plain,
! [X2,X0,X1] :
( sP17(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f14433]) ).
fof(f14433,plain,
! [X0,X1,X2] :
( sP17(X1,X2,X0)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f11330,f14432,f14431]) ).
fof(f14431,plain,
! [X0,X2,X1] :
( sP16(X0,X2,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f14432,plain,
! [X1,X2,X0] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> sP16(X0,X2,X1) )
| ~ sP17(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f11330,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(ennf_transformation,[],[f7266]) ).
fof(f7266,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)),c_Groups_Ozero__class_Ozero(X2)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ) ),
inference(rectify,[],[f1537]) ).
fof(f1537,axiom,
! [X26,X6,X4] :
( class_Rings_Olinordered__ring__strict(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X26)),c_Groups_Ozero__class_Ozero(X4)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),c_Groups_Ozero__class_Ozero(X4)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X6)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30280,plain,
spl625_309,
inference(avatar_split_clause,[],[f19736,f30278]) ).
fof(f30278,plain,
( spl625_309
<=> ! [X2,X0,X1] :
( sP15(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_309])]) ).
fof(f19736,plain,
! [X2,X0,X1] :
( sP15(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(cnf_transformation,[],[f14430]) ).
fof(f14430,plain,
! [X0,X1,X2] :
( sP15(X1,X0,X2)
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(definition_folding,[],[f11329,f14429,f14428]) ).
fof(f14428,plain,
! [X2,X0,X1] :
( sP14(X2,X0,X1)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f14429,plain,
! [X1,X0,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
<=> sP14(X2,X0,X1) )
| ~ sP15(X1,X0,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f11329,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) )
| ~ class_Rings_Olinordered__ring__strict(X2) ),
inference(ennf_transformation,[],[f7265]) ).
fof(f7265,plain,
! [X0,X1,X2] :
( class_Rings_Olinordered__ring__strict(X2)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X2),X1),X0)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X0),c_Groups_Ozero__class_Ozero(X2)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),X1),c_Groups_Ozero__class_Ozero(X2))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X2),c_Groups_Ozero__class_Ozero(X2)),X1)) ) ) ) ),
inference(rectify,[],[f1538]) ).
fof(f1538,axiom,
! [X26,X6,X4] :
( class_Rings_Olinordered__ring__strict(X4)
=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(X4),X6),X26)))
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X26),c_Groups_Ozero__class_Ozero(X4)))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X6),c_Groups_Ozero__class_Ozero(X4))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X26))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),c_Groups_Ozero__class_Ozero(X4)),X6)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30276,plain,
spl625_308,
inference(avatar_split_clause,[],[f19378,f30274]) ).
fof(f30274,plain,
( spl625_308
<=> ! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X2,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_308])]) ).
fof(f19378,plain,
! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X2,X1,X0),
inference(cnf_transformation,[],[f6913]) ).
fof(f6913,plain,
! [X0,X1,X2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X2,X1,X0),
inference(rectify,[],[f168]) ).
fof(f168,axiom,
! [X55,X56,X51] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(X51,X56,X55),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30272,plain,
spl625_307,
inference(avatar_split_clause,[],[f19376,f30270]) ).
fof(f30270,plain,
( spl625_307
<=> ! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X2,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_307])]) ).
fof(f19376,plain,
! [X2,X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X2,X1,X0),
inference(cnf_transformation,[],[f6911]) ).
fof(f6911,plain,
! [X0,X1,X2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X2,X1,X0),
inference(rectify,[],[f108]) ).
fof(f108,axiom,
! [X10,X51,X69] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(X69,X51,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30268,plain,
spl625_306,
inference(avatar_split_clause,[],[f18966,f30266]) ).
fof(f30266,plain,
( spl625_306
<=> ! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ sP4(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_306])]) ).
fof(f18966,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
| ~ sP4(X1,X0) ),
inference(cnf_transformation,[],[f14887]) ).
fof(f14887,plain,
! [X0,X1] :
( ( c_Wellfounded_Owf(X1,X0)
| ~ sP4(X1,X0) )
& ( sP4(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ) ),
inference(nnf_transformation,[],[f14410]) ).
fof(f14410,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> sP4(X1,X0) ),
inference(definition_folding,[],[f11267,f14409]) ).
fof(f14409,plain,
! [X1,X0] :
( sP4(X1,X0)
<=> ! [X2] :
( ? [X4] :
( ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X0)) )
& hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) )
| ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f11267,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> ! [X2] :
( ? [X4] :
( ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X0)) )
& hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) )
| ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) ) ),
inference(ennf_transformation,[],[f6756]) ).
fof(f6756,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
<=> ! [X2] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
=> ? [X4] :
( ! [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X5),X4)),X0))
=> ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X2)) )
& hBOOL(hAPP(hAPP(c_member(X1),X4),X2)) ) ) ),
inference(rectify,[],[f4897]) ).
fof(f4897,axiom,
! [X60,X4] :
( c_Wellfounded_Owf(X4,X60)
<=> ! [X314] :
( ? [X2] : hBOOL(hAPP(hAPP(c_member(X4),X2),X314))
=> ? [X2] :
( ! [X115] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X115),X2)),X60))
=> ~ hBOOL(hAPP(hAPP(c_member(X4),X115),X314)) )
& hBOOL(hAPP(hAPP(c_member(X4),X2),X314)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30264,plain,
spl625_305,
inference(avatar_split_clause,[],[f18965,f30262]) ).
fof(f18965,plain,
! [X0,X1] :
( sP4(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f14887]) ).
fof(f30260,plain,
spl625_304,
inference(avatar_split_clause,[],[f18606,f30258]) ).
fof(f18606,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(cnf_transformation,[],[f10906]) ).
fof(f10906,plain,
! [X0,X1] :
( c_Wellfounded_Oacyclic(X1,X0)
| ~ c_Wellfounded_Owf(X1,X0) ),
inference(ennf_transformation,[],[f6482]) ).
fof(f6482,plain,
! [X0,X1] :
( c_Wellfounded_Owf(X1,X0)
=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f3579]) ).
fof(f3579,axiom,
! [X60,X4] :
( c_Wellfounded_Owf(X4,X60)
=> c_Wellfounded_Oacyclic(X4,X60) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30256,plain,
spl625_303,
inference(avatar_split_clause,[],[f18553,f30254]) ).
fof(f30254,plain,
( spl625_303
<=> ! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_303])]) ).
fof(f18553,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(cnf_transformation,[],[f10852]) ).
fof(f10852,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f6445]) ).
fof(f6445,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> class_Orderings_Oorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f5000]) ).
fof(f5000,axiom,
! [X323,X324] :
( class_Orderings_Oorder(X324)
=> class_Orderings_Oorder(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30252,plain,
spl625_302,
inference(avatar_split_clause,[],[f18552,f30250]) ).
fof(f30250,plain,
( spl625_302
<=> ! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_302])]) ).
fof(f18552,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(cnf_transformation,[],[f10851]) ).
fof(f10851,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(ennf_transformation,[],[f6444]) ).
fof(f6444,plain,
! [X0,X1] :
( class_Orderings_Oord(X1)
=> class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(rectify,[],[f5002]) ).
fof(f5002,axiom,
! [X323,X324] :
( class_Orderings_Oord(X324)
=> class_Orderings_Oord(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30248,plain,
spl625_301,
inference(avatar_split_clause,[],[f18549,f30246]) ).
fof(f30246,plain,
( spl625_301
<=> ! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_301])]) ).
fof(f18549,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(cnf_transformation,[],[f10848]) ).
fof(f10848,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X0,X1))
| ~ class_Orderings_Opreorder(X1) ),
inference(ennf_transformation,[],[f6441]) ).
fof(f6441,plain,
! [X0,X1] :
( class_Orderings_Opreorder(X1)
=> class_Orderings_Opreorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f4997]) ).
fof(f4997,axiom,
! [X323,X324] :
( class_Orderings_Opreorder(X324)
=> class_Orderings_Opreorder(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30244,plain,
spl625_300,
inference(avatar_split_clause,[],[f18548,f30242]) ).
fof(f30242,plain,
( spl625_300
<=> ! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_300])]) ).
fof(f18548,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(cnf_transformation,[],[f10847]) ).
fof(f10847,plain,
! [X0,X1] :
( class_Groups_Ominus(tc_fun(X0,X1))
| ~ class_Groups_Ominus(X1) ),
inference(ennf_transformation,[],[f6440]) ).
fof(f6440,plain,
! [X0,X1] :
( class_Groups_Ominus(X1)
=> class_Groups_Ominus(tc_fun(X0,X1)) ),
inference(rectify,[],[f5005]) ).
fof(f5005,axiom,
! [X323,X324] :
( class_Groups_Ominus(X324)
=> class_Groups_Ominus(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30240,plain,
spl625_299,
inference(avatar_split_clause,[],[f18538,f30238]) ).
fof(f30238,plain,
( spl625_299
<=> ! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_299])]) ).
fof(f18538,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10832]) ).
fof(f10832,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6430]) ).
fof(f6430,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Olattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4999]) ).
fof(f4999,axiom,
! [X323,X324] :
( class_Lattices_Olattice(X324)
=> class_Lattices_Olattice(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30236,plain,
spl625_298,
inference(avatar_split_clause,[],[f18537,f30234]) ).
fof(f30234,plain,
( spl625_298
<=> ! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_298])]) ).
fof(f18537,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10831]) ).
fof(f10831,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6429]) ).
fof(f6429,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__inf(tc_fun(X0,X1)) ),
inference(rectify,[],[f4994]) ).
fof(f4994,axiom,
! [X323,X324] :
( class_Lattices_Olattice(X324)
=> class_Lattices_Osemilattice__inf(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30232,plain,
spl625_297,
inference(avatar_split_clause,[],[f18536,f30230]) ).
fof(f30230,plain,
( spl625_297
<=> ! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_297])]) ).
fof(f18536,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f10830]) ).
fof(f10830,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f6428]) ).
fof(f6428,plain,
! [X0,X1] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__sup(tc_fun(X0,X1)) ),
inference(rectify,[],[f4993]) ).
fof(f4993,axiom,
! [X323,X324] :
( class_Lattices_Olattice(X324)
=> class_Lattices_Osemilattice__sup(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30228,plain,
spl625_296,
inference(avatar_split_clause,[],[f18531,f30226]) ).
fof(f30226,plain,
( spl625_296
<=> ! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_296])]) ).
fof(f18531,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(cnf_transformation,[],[f10825]) ).
fof(f10825,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(ennf_transformation,[],[f6423]) ).
fof(f6423,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(X1)
=> class_Lattices_Odistrib__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4995]) ).
fof(f4995,axiom,
! [X323,X324] :
( class_Lattices_Odistrib__lattice(X324)
=> class_Lattices_Odistrib__lattice(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30224,plain,
spl625_295,
inference(avatar_split_clause,[],[f18425,f30222]) ).
fof(f30222,plain,
( spl625_295
<=> ! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_295])]) ).
fof(f18425,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(cnf_transformation,[],[f10718]) ).
fof(f10718,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(ennf_transformation,[],[f6337]) ).
fof(f6337,plain,
! [X0,X1] :
( class_Orderings_Obot(X1)
=> class_Orderings_Obot(tc_fun(X0,X1)) ),
inference(rectify,[],[f5003]) ).
fof(f5003,axiom,
! [X323,X324] :
( class_Orderings_Obot(X324)
=> class_Orderings_Obot(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30220,plain,
spl625_294,
inference(avatar_split_clause,[],[f18422,f30218]) ).
fof(f30218,plain,
( spl625_294
<=> ! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_294])]) ).
fof(f18422,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(cnf_transformation,[],[f10715]) ).
fof(f10715,plain,
! [X0,X1] :
( class_Groups_Ouminus(tc_fun(X0,X1))
| ~ class_Groups_Ouminus(X1) ),
inference(ennf_transformation,[],[f6334]) ).
fof(f6334,plain,
! [X0,X1] :
( class_Groups_Ouminus(X1)
=> class_Groups_Ouminus(tc_fun(X0,X1)) ),
inference(rectify,[],[f5004]) ).
fof(f5004,axiom,
! [X323,X324] :
( class_Groups_Ouminus(X324)
=> class_Groups_Ouminus(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30216,plain,
spl625_293,
inference(avatar_split_clause,[],[f18400,f30214]) ).
fof(f30214,plain,
( spl625_293
<=> ! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_293])]) ).
fof(f18400,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(cnf_transformation,[],[f10685]) ).
fof(f10685,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1))
| ~ class_Complete__Lattice_Ocomplete__lattice(X1) ),
inference(ennf_transformation,[],[f6314]) ).
fof(f6314,plain,
! [X0,X1] :
( class_Complete__Lattice_Ocomplete__lattice(X1)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4990]) ).
fof(f4990,axiom,
! [X323,X324] :
( class_Complete__Lattice_Ocomplete__lattice(X324)
=> class_Complete__Lattice_Ocomplete__lattice(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30212,plain,
spl625_292,
inference(avatar_split_clause,[],[f18394,f30210]) ).
fof(f30210,plain,
( spl625_292
<=> ! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_292])]) ).
fof(f18394,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(cnf_transformation,[],[f10679]) ).
fof(f10679,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(tc_fun(X0,X1))
| ~ class_Lattices_Oboolean__algebra(X1) ),
inference(ennf_transformation,[],[f6308]) ).
fof(f6308,plain,
! [X0,X1] :
( class_Lattices_Oboolean__algebra(X1)
=> class_Lattices_Oboolean__algebra(tc_fun(X0,X1)) ),
inference(rectify,[],[f4996]) ).
fof(f4996,axiom,
! [X323,X324] :
( class_Lattices_Oboolean__algebra(X324)
=> class_Lattices_Oboolean__algebra(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30208,plain,
spl625_291,
inference(avatar_split_clause,[],[f18384,f30206]) ).
fof(f30206,plain,
( spl625_291
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_291])]) ).
fof(f18384,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10669]) ).
fof(f10669,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6298]) ).
fof(f6298,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X0,X1)) ),
inference(rectify,[],[f4992]) ).
fof(f4992,axiom,
! [X323,X324] :
( class_Lattices_Obounded__lattice(X324)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30204,plain,
spl625_290,
inference(avatar_split_clause,[],[f18383,f30202]) ).
fof(f30202,plain,
( spl625_290
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_290])]) ).
fof(f18383,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10668]) ).
fof(f10668,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__top(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6297]) ).
fof(f6297,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice__top(tc_fun(X0,X1)) ),
inference(rectify,[],[f4991]) ).
fof(f4991,axiom,
! [X323,X324] :
( class_Lattices_Obounded__lattice(X324)
=> class_Lattices_Obounded__lattice__top(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30200,plain,
spl625_289,
inference(avatar_split_clause,[],[f18382,f30198]) ).
fof(f30198,plain,
( spl625_289
<=> ! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_289])]) ).
fof(f18382,plain,
! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ),
inference(cnf_transformation,[],[f10667]) ).
fof(f10667,plain,
! [X0,X1] :
( class_Orderings_Otop(tc_fun(X0,X1))
| ~ class_Orderings_Otop(X1) ),
inference(ennf_transformation,[],[f6296]) ).
fof(f6296,plain,
! [X0,X1] :
( class_Orderings_Otop(X1)
=> class_Orderings_Otop(tc_fun(X0,X1)) ),
inference(rectify,[],[f5001]) ).
fof(f5001,axiom,
! [X323,X324] :
( class_Orderings_Otop(X324)
=> class_Orderings_Otop(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30196,plain,
spl625_288,
inference(avatar_split_clause,[],[f18381,f30194]) ).
fof(f30194,plain,
( spl625_288
<=> ! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_288])]) ).
fof(f18381,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(cnf_transformation,[],[f10666]) ).
fof(f10666,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Obounded__lattice(X1) ),
inference(ennf_transformation,[],[f6295]) ).
fof(f6295,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f4989]) ).
fof(f4989,axiom,
! [X323,X324] :
( class_Lattices_Obounded__lattice(X324)
=> class_Lattices_Obounded__lattice(tc_fun(X323,X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30192,plain,
spl625_287,
inference(avatar_split_clause,[],[f17707,f30190]) ).
fof(f30190,plain,
( spl625_287
<=> ! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_287])]) ).
fof(f17707,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0),
inference(cnf_transformation,[],[f5723]) ).
fof(f5723,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_COMBI(X1),X0),
inference(rectify,[],[f605]) ).
fof(f605,axiom,
! [X19,X4] : c_Fun_Oinj__on(X4,X4,c_COMBI(X4),X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30188,plain,
spl625_286,
inference(avatar_split_clause,[],[f17706,f30186]) ).
fof(f17706,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0),
inference(cnf_transformation,[],[f5722]) ).
fof(f5722,plain,
! [X0,X1] : c_Fun_Oinj__on(X1,X1,c_Fun_Oid(X1),X0),
inference(rectify,[],[f3485]) ).
fof(f3485,axiom,
! [X19,X4] : c_Fun_Oinj__on(X4,X4,c_Fun_Oid(X4),X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30184,plain,
spl625_285,
inference(avatar_split_clause,[],[f17702,f30182]) ).
fof(f30182,plain,
( spl625_285
<=> ! [X0,X1] : hAPP(c_Set_OCollect(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_285])]) ).
fof(f30180,plain,
spl625_284,
inference(avatar_split_clause,[],[f17701,f30178]) ).
fof(f30178,plain,
( spl625_284
<=> ! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_284])]) ).
fof(f17701,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f5717]) ).
fof(f5717,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(rectify,[],[f5221]) ).
fof(f5221,axiom,
! [X325,X23] : hAPP(c_COMBI(X23),X325) = X325,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30176,plain,
spl625_283,
inference(avatar_split_clause,[],[f17699,f30174]) ).
fof(f30174,plain,
( spl625_283
<=> ! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_283])]) ).
fof(f17699,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0,
inference(cnf_transformation,[],[f5715]) ).
fof(f5715,plain,
! [X0,X1] : hAPP(c_Fun_Oid(X1),X0) = X0,
inference(rectify,[],[f3483]) ).
fof(f3483,axiom,
! [X22,X23] : hAPP(c_Fun_Oid(X23),X22) = X22,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30172,plain,
spl625_282,
inference(avatar_split_clause,[],[f17671,f30170]) ).
fof(f30170,plain,
( spl625_282
<=> ! [X0] : hAPP(c_Int_OAbs__Integ,sK108(X0)) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_282])]) ).
fof(f17671,plain,
! [X0] : hAPP(c_Int_OAbs__Integ,sK108(X0)) = X0,
inference(cnf_transformation,[],[f14664]) ).
fof(f14664,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK108(X0)),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,sK108(X0)) = X0 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK108])],[f10475,f14663]) ).
fof(f14663,plain,
! [X0] :
( ? [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,X1) = X0 )
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK108(X0)),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,sK108(X0)) = X0 ) ),
introduced(choice_axiom,[]) ).
fof(f10475,plain,
! [X0] :
? [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg))
& hAPP(c_Int_OAbs__Integ,X1) = X0 ),
inference(ennf_transformation,[],[f5688]) ).
fof(f5688,plain,
! [X0] :
~ ! [X1] :
( hAPP(c_Int_OAbs__Integ,X1) = X0
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X1),c_Int_OInteg)) ),
inference(rectify,[],[f3587]) ).
fof(f3587,axiom,
! [X20] :
~ ! [X115] :
( hAPP(c_Int_OAbs__Integ,X115) = X20
=> ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),X115),c_Int_OInteg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30168,plain,
spl625_281,
inference(avatar_split_clause,[],[f17496,f30166]) ).
fof(f17496,plain,
! [X0] :
( c_fequal = c_HOL_Oequal__class_Oequal(X0)
| ~ class_HOL_Oequal(X0) ),
inference(cnf_transformation,[],[f10421]) ).
fof(f10421,plain,
! [X0] :
( c_fequal = c_HOL_Oequal__class_Oequal(X0)
| ~ class_HOL_Oequal(X0) ),
inference(ennf_transformation,[],[f5585]) ).
fof(f5585,plain,
! [X0] :
( class_HOL_Oequal(X0)
=> c_fequal = c_HOL_Oequal__class_Oequal(X0) ),
inference(rectify,[],[f4944]) ).
fof(f4944,axiom,
! [X4] :
( class_HOL_Oequal(X4)
=> c_fequal = c_HOL_Oequal__class_Oequal(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30164,plain,
spl625_280,
inference(avatar_split_clause,[],[f17472,f30162]) ).
fof(f30162,plain,
( spl625_280
<=> ! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_280])]) ).
fof(f17472,plain,
! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(cnf_transformation,[],[f10398]) ).
fof(f10398,plain,
! [X0] :
( c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0))
| ~ class_Orderings_Olinorder(X0) ),
inference(ennf_transformation,[],[f5562]) ).
fof(f5562,plain,
! [X0] :
( class_Orderings_Olinorder(X0)
=> c_List_Olinorder__class_Osorted(X0,c_List_Olist_ONil(X0)) ),
inference(rectify,[],[f4268]) ).
fof(f4268,axiom,
! [X23] :
( class_Orderings_Olinorder(X23)
=> c_List_Olinorder__class_Osorted(X23,c_List_Olist_ONil(X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30160,plain,
spl625_279,
inference(avatar_split_clause,[],[f17460,f30158]) ).
fof(f17460,plain,
! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10386]) ).
fof(f10386,plain,
! [X0] :
( c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5550]) ).
fof(f5550,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> c_Int_Oiszero(X0,c_Groups_Ozero__class_Ozero(X0)) ),
inference(rectify,[],[f2666]) ).
fof(f2666,axiom,
! [X23] :
( class_Rings_Osemiring__1(X23)
=> c_Int_Oiszero(X23,c_Groups_Ozero__class_Ozero(X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30156,plain,
spl625_278,
inference(avatar_split_clause,[],[f17459,f30154]) ).
fof(f30154,plain,
( spl625_278
<=> ! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_278])]) ).
fof(f17459,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(cnf_transformation,[],[f10385]) ).
fof(f10385,plain,
! [X0] :
( ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0))
| ~ class_Rings_Osemiring__1(X0) ),
inference(ennf_transformation,[],[f5549]) ).
fof(f5549,plain,
! [X0] :
( class_Rings_Osemiring__1(X0)
=> ~ c_Int_Oiszero(X0,c_Groups_Oone__class_Oone(X0)) ),
inference(rectify,[],[f2668]) ).
fof(f2668,axiom,
! [X23] :
( class_Rings_Osemiring__1(X23)
=> ~ c_Int_Oiszero(X23,c_Groups_Oone__class_Oone(X23)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30152,plain,
spl625_277,
inference(avatar_split_clause,[],[f17424,f30150]) ).
fof(f30150,plain,
( spl625_277
<=> ! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_277])]) ).
fof(f17424,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ),
inference(cnf_transformation,[],[f5513]) ).
fof(f5513,plain,
! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(c_fNot,X0)) ),
inference(rectify,[],[f5230]) ).
fof(f5230,axiom,
! [X5] :
( ~ hBOOL(X5)
| ~ hBOOL(hAPP(c_fNot,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30148,plain,
spl625_276,
inference(avatar_split_clause,[],[f17423,f30146]) ).
fof(f30146,plain,
( spl625_276
<=> ! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_276])]) ).
fof(f17423,plain,
! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f5512]) ).
fof(f5512,plain,
! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ),
inference(rectify,[],[f5231]) ).
fof(f5231,axiom,
! [X5] :
( hBOOL(hAPP(c_fNot,X5))
| hBOOL(X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30144,plain,
spl625_275,
inference(avatar_split_clause,[],[f17179,f30142]) ).
fof(f30142,plain,
( spl625_275
<=> ! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_275])]) ).
fof(f17179,plain,
! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))),
inference(cnf_transformation,[],[f5282]) ).
fof(f5282,plain,
! [X0] : hBOOL(hAPP(c_List_Odistinct(X0),c_List_Olist_ONil(X0))),
inference(rectify,[],[f3972]) ).
fof(f3972,axiom,
! [X23] : hBOOL(hAPP(c_List_Odistinct(X23),c_List_Olist_ONil(X23))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30140,plain,
spl625_274,
inference(avatar_split_clause,[],[f17178,f30138]) ).
fof(f30136,plain,
spl625_273,
inference(avatar_split_clause,[],[f17177,f30134]) ).
fof(f30134,plain,
( spl625_273
<=> ! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_273])]) ).
fof(f17177,plain,
! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0,
inference(cnf_transformation,[],[f5280]) ).
fof(f5280,plain,
! [X0] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X0) = X0,
inference(rectify,[],[f1874]) ).
fof(f1874,axiom,
! [X88] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),X88) = X88,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30132,plain,
spl625_272,
inference(avatar_split_clause,[],[f17038,f30129]) ).
fof(f30129,plain,
( spl625_272
<=> c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_272])]) ).
fof(f17038,plain,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
inference(cnf_transformation,[],[f2562]) ).
fof(f2562,axiom,
c_Int_OPls = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30127,plain,
( spl625_271
| ~ spl625_238 ),
inference(avatar_split_clause,[],[f29984,f29980,f30124]) ).
fof(f30124,plain,
( spl625_271
<=> c_Nat__Transfer_Onat__set(c_Option_Oset(tc_Int_Oint,c_Option_Ooption_ONone(tc_Int_Oint))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_271])]) ).
fof(f29980,plain,
( spl625_238
<=> c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_238])]) ).
fof(f29984,plain,
( c_Nat__Transfer_Onat__set(c_Option_Oset(tc_Int_Oint,c_Option_Ooption_ONone(tc_Int_Oint)))
| ~ spl625_238 ),
inference(forward_demodulation,[],[f29982,f17243]) ).
fof(f29982,plain,
( c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)))
| ~ spl625_238 ),
inference(avatar_component_clause,[],[f29980]) ).
fof(f30122,plain,
spl625_270,
inference(avatar_split_clause,[],[f28083,f30120]) ).
fof(f30120,plain,
( spl625_270
<=> ! [X0,X1] : sP42(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_270])]) ).
fof(f28083,plain,
! [X0,X1] : sP42(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25192,f17032]) ).
fof(f25192,plain,
! [X0,X1] : sP42(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f21068]) ).
fof(f21068,plain,
! [X2,X0,X1] :
( sP42(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f15723]) ).
fof(f15723,plain,
! [X0,X1,X2] :
( ( sP42(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK360(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK360(X0,X1,X2))),sK361(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK361(X0,X1,X2)),X2))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X5))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X2)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP42(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK360,sK361])],[f15721,f15722]) ).
fof(f15722,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)) )
=> ( ~ hBOOL(hAPP(X0,sK360(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK360(X0,X1,X2))),sK361(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK361(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15721,plain,
! [X0,X1,X2] :
( ( sP42(X0,X1,X2)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X5))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X2)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP42(X0,X1,X2) ) ),
inference(rectify,[],[f15720]) ).
fof(f15720,plain,
! [X2,X1,X0] :
( ( sP42(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP42(X2,X1,X0) ) ),
inference(flattening,[],[f15719]) ).
fof(f15719,plain,
! [X2,X1,X0] :
( ( sP42(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X3))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP42(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14472]) ).
fof(f14472,plain,
! [X2,X1,X0] :
( sP42(X2,X1,X0)
<=> ( ! [X3,X4] :
( hBOOL(hAPP(X2,X3))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP42])]) ).
fof(f30118,plain,
spl625_269,
inference(avatar_split_clause,[],[f28057,f30116]) ).
fof(f30116,plain,
( spl625_269
<=> ! [X0,X1] : sP37(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_269])]) ).
fof(f28057,plain,
! [X0,X1] : sP37(X0,X1,c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25166,f17032]) ).
fof(f25166,plain,
! [X0,X1] : sP37(X0,X1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f20990]) ).
fof(f20990,plain,
! [X2,X0,X1] :
( sP37(X0,X1,X2)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ),
inference(cnf_transformation,[],[f15668]) ).
fof(f15668,plain,
! [X0,X1,X2] :
( ( sP37(X0,X1,X2)
| ( ~ hBOOL(hAPP(X0,sK351(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK350(X0,X1,X2))),sK351(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK351(X0,X1,X2)),X2))
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X2)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP37(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK350,sK351])],[f15666,f15667]) ).
fof(f15667,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)) )
=> ( ~ hBOOL(hAPP(X0,sK351(X0,X1,X2)))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),sK350(X0,X1,X2))),sK351(X0,X1,X2)) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK351(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f15666,plain,
! [X0,X1,X2] :
( ( sP37(X0,X1,X2)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X0,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X2)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X2 ) )
& ( ! [X5,X6] :
( hBOOL(hAPP(X0,X6))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X2),X5)),X6) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X6),X2)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X2
| ~ sP37(X0,X1,X2) ) ),
inference(rectify,[],[f15665]) ).
fof(f15665,plain,
! [X2,X1,X0] :
( ( sP37(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP37(X2,X1,X0) ) ),
inference(flattening,[],[f15664]) ).
fof(f15664,plain,
! [X2,X1,X0] :
( ( sP37(X2,X1,X0)
| ( ? [X3,X4] :
( ~ hBOOL(hAPP(X2,X4))
& hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) = X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0 ) )
& ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| ~ sP37(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f14464]) ).
fof(f14464,plain,
! [X2,X1,X0] :
( sP37(X2,X1,X0)
<=> ( ! [X3,X4] :
( hBOOL(hAPP(X2,X4))
| hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),X0),X3)),X4) != X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),X4),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP37])]) ).
fof(f30114,plain,
spl625_268,
inference(avatar_split_clause,[],[f27239,f30111]) ).
fof(f30111,plain,
( spl625_268
<=> sP13(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_268])]) ).
fof(f27239,plain,
sP13(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f27238,f25523]) ).
fof(f27238,plain,
sP13(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f25030,f17032]) ).
fof(f25030,plain,
sP13(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f25029]) ).
fof(f25029,plain,
! [X1] :
( sP13(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f19250]) ).
fof(f19250,plain,
! [X0,X1] :
( sP13(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f15082]) ).
fof(f15082,plain,
! [X0,X1] :
( ( sP13(X0,X1)
| ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP13(X0,X1) ) ),
inference(flattening,[],[f15081]) ).
fof(f15081,plain,
! [X0,X1] :
( ( sP13(X0,X1)
| ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP13(X0,X1) ) ),
inference(nnf_transformation,[],[f14426]) ).
fof(f14426,plain,
! [X0,X1] :
( sP13(X0,X1)
<=> ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f30109,plain,
spl625_267,
inference(avatar_split_clause,[],[f27237,f30106]) ).
fof(f30106,plain,
( spl625_267
<=> sP13(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_267])]) ).
fof(f27237,plain,
sP13(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f27236,f25523]) ).
fof(f27236,plain,
sP13(hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25028,f17032]) ).
fof(f25028,plain,
sP13(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f25027]) ).
fof(f25027,plain,
! [X1] :
( sP13(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f19251]) ).
fof(f19251,plain,
! [X0,X1] :
( sP13(X0,X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f15082]) ).
fof(f30104,plain,
spl625_266,
inference(avatar_split_clause,[],[f27219,f30101]) ).
fof(f30101,plain,
( spl625_266
<=> sP12(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_266])]) ).
fof(f27219,plain,
sP12(c_HOL_Obool_Obool__size(c_fTrue),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(forward_demodulation,[],[f27218,f25523]) ).
fof(f27218,plain,
sP12(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f25026,f17032]) ).
fof(f25026,plain,
sP12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f25025]) ).
fof(f25025,plain,
! [X1] :
( sP12(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f19242]) ).
fof(f19242,plain,
! [X0,X1] :
( sP12(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(cnf_transformation,[],[f15079]) ).
fof(f15079,plain,
! [X0,X1] :
( ( sP12(X0,X1)
| ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP12(X0,X1) ) ),
inference(flattening,[],[f15078]) ).
fof(f15078,plain,
! [X0,X1] :
( ( sP12(X0,X1)
| ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 )
& ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ) ) )
& ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 )
| ~ sP12(X0,X1) ) ),
inference(nnf_transformation,[],[f14424]) ).
fof(f14424,plain,
! [X0,X1] :
( sP12(X0,X1)
<=> ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X0
& c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X1 )
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
& hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = X1 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f30099,plain,
spl625_265,
inference(avatar_split_clause,[],[f27217,f30096]) ).
fof(f30096,plain,
( spl625_265
<=> sP12(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_265])]) ).
fof(f27217,plain,
sP12(c_Groups_Oone__class_Oone(tc_Nat_Onat),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f27216,f25523]) ).
fof(f27216,plain,
sP12(hAPP(c_Nat_OSuc,c_HOL_Obool_Obool__size(c_fTrue)),c_HOL_Obool_Obool__size(c_fTrue)),
inference(forward_demodulation,[],[f25024,f17032]) ).
fof(f25024,plain,
sP12(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(equality_resolution,[],[f25023]) ).
fof(f25023,plain,
! [X1] :
( sP12(hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(equality_resolution,[],[f19243]) ).
fof(f19243,plain,
! [X0,X1] :
( sP12(X0,X1)
| hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X0
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1 ),
inference(cnf_transformation,[],[f15079]) ).
fof(f30094,plain,
spl625_264,
inference(avatar_split_clause,[],[f25770,f30091]) ).
fof(f30091,plain,
( spl625_264
<=> c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_264])]) ).
fof(f25770,plain,
c_Int_OPls = c_Groups_Osgn__class_Osgn(tc_Int_Oint,c_Int_OPls),
inference(forward_demodulation,[],[f24870,f17021]) ).
fof(f24870,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,[],[f17402]) ).
fof(f17402,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,[],[f10341]) ).
fof(f10341,plain,
! [X0] :
( ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& ( c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) ),
inference(ennf_transformation,[],[f5502]) ).
fof(f5502,plain,
! [X0] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0))
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X0) ) ),
inference(rectify,[],[f3230]) ).
fof(f3230,axiom,
! [X114] :
( ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X114
=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X114))
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X114) )
& ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X114))
=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X114) ) ) )
& ( c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X114
=> c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Osgn__class_Osgn(tc_Int_Oint,X114) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30089,plain,
spl625_263,
inference(avatar_split_clause,[],[f25519,f30086]) ).
fof(f30086,plain,
( spl625_263
<=> c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_263])]) ).
fof(f25519,plain,
c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17035,f17032]) ).
fof(f17035,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f1419]) ).
fof(f1419,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Orderings_Obot__class_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30084,plain,
spl625_262,
inference(avatar_split_clause,[],[f25518,f30081]) ).
fof(f30081,plain,
( spl625_262
<=> c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_HOL_Obool_Obool__size(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_262])]) ).
fof(f25518,plain,
c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_HOL_Obool_Obool__size(c_fTrue),
inference(forward_demodulation,[],[f17034,f17032]) ).
fof(f17034,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP),
inference(cnf_transformation,[],[f1773]) ).
fof(f1773,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30079,plain,
spl625_261,
inference(avatar_split_clause,[],[f25517,f30076]) ).
fof(f30076,plain,
( spl625_261
<=> c_HOL_Obool_Obool__size(c_fTrue) = c_HOL_Obool_Obool__size(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_261])]) ).
fof(f25517,plain,
c_HOL_Obool_Obool__size(c_fTrue) = c_HOL_Obool_Obool__size(c_fFalse),
inference(forward_demodulation,[],[f17033,f17032]) ).
fof(f17033,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
inference(cnf_transformation,[],[f4935]) ).
fof(f4935,axiom,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_HOL_Obool_Obool__size(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30074,plain,
spl625_260,
inference(avatar_split_clause,[],[f25436,f30072]) ).
fof(f30072,plain,
( spl625_260
<=> ! [X2,X3] : sP81(X3,X2,X2,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_260])]) ).
fof(f25436,plain,
! [X2,X3] : sP81(X3,X2,X2,X3),
inference(equality_resolution,[],[f25435]) ).
fof(f25435,plain,
! [X2,X3,X1] :
( sP81(X3,X1,X2,X3)
| X1 != X2 ),
inference(equality_resolution,[],[f23418]) ).
fof(f23418,plain,
! [X2,X3,X0,X1] :
( sP81(X0,X1,X2,X3)
| X0 != X3
| X1 != X2 ),
inference(cnf_transformation,[],[f16634]) ).
fof(f16634,plain,
! [X0,X1,X2,X3] :
( ( sP81(X0,X1,X2,X3)
| ( ( X0 != X1
| X2 != X3 )
& ( X0 != X3
| X1 != X2 ) ) )
& ( ( X0 = X1
& X2 = X3 )
| ( X0 = X3
& X1 = X2 )
| ~ sP81(X0,X1,X2,X3) ) ),
inference(rectify,[],[f16633]) ).
fof(f16633,plain,
! [X2,X1,X3,X0] :
( ( sP81(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP81(X2,X1,X3,X0) ) ),
inference(flattening,[],[f16632]) ).
fof(f16632,plain,
! [X2,X1,X3,X0] :
( ( sP81(X2,X1,X3,X0)
| ( ( X1 != X2
| X0 != X3 )
& ( X0 != X2
| X1 != X3 ) ) )
& ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 )
| ~ sP81(X2,X1,X3,X0) ) ),
inference(nnf_transformation,[],[f14545]) ).
fof(f14545,plain,
! [X2,X1,X3,X0] :
( sP81(X2,X1,X3,X0)
<=> ( ( X1 = X2
& X0 = X3 )
| ( X0 = X2
& X1 = X3 ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP81])]) ).
fof(f30070,plain,
spl625_259,
inference(avatar_split_clause,[],[f25434,f30068]) ).
fof(f30068,plain,
( spl625_259
<=> ! [X1,X3] : sP81(X1,X1,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_259])]) ).
fof(f25434,plain,
! [X3,X1] : sP81(X1,X1,X3,X3),
inference(equality_resolution,[],[f25433]) ).
fof(f25433,plain,
! [X2,X3,X1] :
( sP81(X1,X1,X2,X3)
| X2 != X3 ),
inference(equality_resolution,[],[f23419]) ).
fof(f23419,plain,
! [X2,X3,X0,X1] :
( sP81(X0,X1,X2,X3)
| X0 != X1
| X2 != X3 ),
inference(cnf_transformation,[],[f16634]) ).
fof(f30066,plain,
spl625_258,
inference(avatar_split_clause,[],[f25209,f30064]) ).
fof(f30064,plain,
( spl625_258
<=> ! [X0,X1] : sP46(X0,X1,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_258])]) ).
fof(f25209,plain,
! [X0,X1] : sP46(X0,X1,c_List_Olist_ONil(X1)),
inference(equality_resolution,[],[f21150]) ).
fof(f21150,plain,
! [X2,X0,X1] :
( sP46(X0,X1,X2)
| c_List_Olist_ONil(X1) != X2 ),
inference(cnf_transformation,[],[f15790]) ).
fof(f15790,plain,
! [X0,X1,X2] :
( ( sP46(X0,X1,X2)
| ( ! [X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X0))
| hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4) != X2 )
& c_List_Olist_ONil(X1) != X2 ) )
& ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),sK375(X0,X1,X2)),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),sK374(X0,X1,X2)),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),sK374(X0,X1,X2)),sK375(X0,X1,X2)) = X2 )
| c_List_Olist_ONil(X1) = X2
| ~ sP46(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK374,sK375])],[f15788,f15789]) ).
fof(f15789,plain,
! [X0,X1,X2] :
( ? [X5,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X6),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),X5),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6) = X2 )
=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),sK375(X0,X1,X2)),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),sK374(X0,X1,X2)),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),sK374(X0,X1,X2)),sK375(X0,X1,X2)) = X2 ) ),
introduced(choice_axiom,[]) ).
fof(f15788,plain,
! [X0,X1,X2] :
( ( sP46(X0,X1,X2)
| ( ! [X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X4),c_List_Olists(X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X0))
| hAPP(hAPP(c_List_Olist_OCons(X1),X3),X4) != X2 )
& c_List_Olist_ONil(X1) != X2 ) )
& ( ? [X5,X6] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X1)),X6),c_List_Olists(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(X1),X5),X0))
& hAPP(hAPP(c_List_Olist_OCons(X1),X5),X6) = X2 )
| c_List_Olist_ONil(X1) = X2
| ~ sP46(X0,X1,X2) ) ),
inference(rectify,[],[f15787]) ).
fof(f15787,plain,
! [X0,X2,X1] :
( ( sP46(X0,X2,X1)
| ( ! [X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
| hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) != X1 )
& c_List_Olist_ONil(X2) != X1 ) )
& ( ? [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
& hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) = X1 )
| c_List_Olist_ONil(X2) = X1
| ~ sP46(X0,X2,X1) ) ),
inference(flattening,[],[f15786]) ).
fof(f15786,plain,
! [X0,X2,X1] :
( ( sP46(X0,X2,X1)
| ( ! [X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
| hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) != X1 )
& c_List_Olist_ONil(X2) != X1 ) )
& ( ? [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
& hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) = X1 )
| c_List_Olist_ONil(X2) = X1
| ~ sP46(X0,X2,X1) ) ),
inference(nnf_transformation,[],[f14480]) ).
fof(f14480,plain,
! [X0,X2,X1] :
( sP46(X0,X2,X1)
<=> ( ? [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(X2)),X4),c_List_Olists(X2,X0)))
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
& hAPP(hAPP(c_List_Olist_OCons(X2),X3),X4) = X1 )
| c_List_Olist_ONil(X2) = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP46])]) ).
fof(f30062,plain,
spl625_257,
inference(avatar_split_clause,[],[f24998,f30059]) ).
fof(f30059,plain,
( spl625_257
<=> sP8(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_257])]) ).
fof(f24998,plain,
sP8(c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(equality_resolution,[],[f24997]) ).
fof(f24997,plain,
! [X1] :
( sP8(c_Groups_Oone__class_Oone(tc_Int_Oint),X1)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ),
inference(equality_resolution,[],[f19113]) ).
fof(f19113,plain,
! [X0,X1] :
( sP8(X0,X1)
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X0
| c_Groups_Oone__class_Oone(tc_Int_Oint) != X1 ),
inference(cnf_transformation,[],[f15001]) ).
fof(f30057,plain,
spl625_256,
inference(avatar_split_clause,[],[f24966,f30055]) ).
fof(f24966,plain,
! [X1] : sP6(hAPP(c_Int_Onat,X1),X1),
inference(equality_resolution,[],[f18993]) ).
fof(f18993,plain,
! [X0,X1] :
( sP6(X0,X1)
| hAPP(c_Int_Onat,X1) != X0 ),
inference(cnf_transformation,[],[f14903]) ).
fof(f30053,plain,
spl625_255,
inference(avatar_split_clause,[],[f24961,f30051]) ).
fof(f24961,plain,
! [X0] : sP5(hAPP(c_Int_Onat,X0),X0),
inference(equality_resolution,[],[f18985]) ).
fof(f18985,plain,
! [X0,X1] :
( sP5(X1,X0)
| hAPP(c_Int_Onat,X0) != X1 ),
inference(cnf_transformation,[],[f14900]) ).
fof(f30049,plain,
spl625_254,
inference(avatar_split_clause,[],[f18526,f30047]) ).
fof(f30047,plain,
( spl625_254
<=> ! [X0,X1] :
( sP1(X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_254])]) ).
fof(f18526,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(cnf_transformation,[],[f14404]) ).
fof(f14404,plain,
! [X0,X1] :
( sP1(X0,X1)
| ~ class_Orderings_Olinorder(X1) ),
inference(definition_folding,[],[f10823,f14403,f14402]) ).
fof(f14402,plain,
! [X1,X0] :
( sP0(X1,X0)
<=> ( ? [X2,X3] :
( c_List_Olinorder__class_Osorted(X1,X2)
& ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2))) )
& hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) = X0 )
| c_List_Olist_ONil(X1) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f10823,plain,
! [X0,X1] :
( ( c_List_Olinorder__class_Osorted(X1,X0)
<=> ( ? [X2,X3] :
( c_List_Olinorder__class_Osorted(X1,X2)
& ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2))) )
& hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) = X0 )
| c_List_Olist_ONil(X1) = X0 ) )
| ~ class_Orderings_Olinorder(X1) ),
inference(ennf_transformation,[],[f6421]) ).
fof(f6421,plain,
! [X0,X1] :
( class_Orderings_Olinorder(X1)
=> ( c_List_Olinorder__class_Osorted(X1,X0)
<=> ( ? [X2,X3] :
( c_List_Olinorder__class_Osorted(X1,X2)
& ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4)) )
& hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) = X0 )
| c_List_Olist_ONil(X1) = X0 ) ) ),
inference(rectify,[],[f4507]) ).
fof(f4507,axiom,
! [X6,X4] :
( class_Orderings_Olinorder(X4)
=> ( c_List_Olinorder__class_Osorted(X4,X6)
<=> ( ? [X268,X2] :
( c_List_Olinorder__class_Osorted(X4,X268)
& ! [X118] :
( hBOOL(hAPP(hAPP(c_member(X4),X118),hAPP(c_List_Oset(X4),X268)))
=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X4),X2),X118)) )
& hAPP(hAPP(c_List_Olist_OCons(X4),X2),X268) = X6 )
| c_List_Olist_ONil(X4) = X6 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30045,plain,
spl625_253,
inference(avatar_split_clause,[],[f17697,f30043]) ).
fof(f30043,plain,
( spl625_253
<=> ! [X0,X1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_253])]) ).
fof(f17697,plain,
! [X0,X1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X0,X1),
inference(cnf_transformation,[],[f5713]) ).
fof(f5713,plain,
! [X0,X1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X1,X0,X1),
inference(rectify,[],[f133]) ).
fof(f133,axiom,
! [X88,X92] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,X92,X88,X92),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30041,plain,
spl625_252,
inference(avatar_split_clause,[],[f17696,f30039]) ).
fof(f30039,plain,
( spl625_252
<=> ! [X0,X1] : c_List_Olist__all(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_252])]) ).
fof(f17696,plain,
! [X0,X1] : c_List_Olist__all(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5712]) ).
fof(f5712,plain,
! [X0,X1] : c_List_Olist__all(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4925]) ).
fof(f4925,axiom,
! [X5,X4] : c_List_Olist__all(X4,X5,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30037,plain,
spl625_251,
inference(avatar_split_clause,[],[f17693,f30035]) ).
fof(f30035,plain,
( spl625_251
<=> ! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_251])]) ).
fof(f17693,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)),
inference(cnf_transformation,[],[f5709]) ).
fof(f5709,plain,
! [X0,X1] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X1,X0)),
inference(rectify,[],[f4271]) ).
fof(f4271,axiom,
! [X113,X114] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(X114,X113)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30033,plain,
spl625_250,
inference(avatar_split_clause,[],[f17692,f30031]) ).
fof(f30031,plain,
( spl625_250
<=> ! [X0,X1] : ~ c_List_Olist__ex(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_250])]) ).
fof(f17692,plain,
! [X0,X1] : ~ c_List_Olist__ex(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5708]) ).
fof(f5708,plain,
! [X0,X1] : ~ c_List_Olist__ex(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4605]) ).
fof(f4605,axiom,
! [X5,X4] : ~ c_List_Olist__ex(X4,X5,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30029,plain,
spl625_249,
inference(avatar_split_clause,[],[f17691,f30027]) ).
fof(f30027,plain,
( spl625_249
<=> ! [X0,X1] : ~ c_List_Olist__ex1(X1,X0,c_List_Olist_ONil(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_249])]) ).
fof(f17691,plain,
! [X0,X1] : ~ c_List_Olist__ex1(X1,X0,c_List_Olist_ONil(X1)),
inference(cnf_transformation,[],[f5707]) ).
fof(f5707,plain,
! [X0,X1] : ~ c_List_Olist__ex1(X1,X0,c_List_Olist_ONil(X1)),
inference(rectify,[],[f4931]) ).
fof(f4931,axiom,
! [X5,X4] : ~ c_List_Olist__ex1(X4,X5,c_List_Olist_ONil(X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30025,plain,
spl625_248,
inference(avatar_split_clause,[],[f17687,f30023]) ).
fof(f30023,plain,
( spl625_248
<=> ! [X0,X1] : c_Com_Ovname_OGlb(X0) != c_Com_Ovname_OLoc(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_248])]) ).
fof(f17687,plain,
! [X0,X1] : c_Com_Ovname_OGlb(X0) != c_Com_Ovname_OLoc(X1),
inference(cnf_transformation,[],[f5703]) ).
fof(f5703,plain,
! [X0,X1] : c_Com_Ovname_OGlb(X0) != c_Com_Ovname_OLoc(X1),
inference(rectify,[],[f190]) ).
fof(f190,axiom,
! [X111,X110] : c_Com_Ovname_OGlb(X111) != c_Com_Ovname_OLoc(X110),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30021,plain,
spl625_247,
inference(avatar_split_clause,[],[f17685,f30019]) ).
fof(f30019,plain,
( spl625_247
<=> ! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_247])]) ).
fof(f17685,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X0),
inference(cnf_transformation,[],[f5701]) ).
fof(f5701,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X1,X0),
inference(rectify,[],[f73]) ).
fof(f73,axiom,
! [X10,X51] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(X51,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30017,plain,
spl625_246,
inference(avatar_split_clause,[],[f17683,f30015]) ).
fof(f30015,plain,
( spl625_246
<=> ! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_246])]) ).
fof(f17683,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X0),
inference(cnf_transformation,[],[f5699]) ).
fof(f5699,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X1,X0),
inference(rectify,[],[f69]) ).
fof(f69,axiom,
! [X51,X52] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(X52,X51),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30013,plain,
spl625_245,
inference(avatar_split_clause,[],[f17681,f30011]) ).
fof(f30011,plain,
( spl625_245
<=> ! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_245])]) ).
fof(f17681,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X0),
inference(cnf_transformation,[],[f5697]) ).
fof(f5697,plain,
! [X0,X1] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X1,X0),
inference(rectify,[],[f68]) ).
fof(f68,axiom,
! [X49,X50] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(X50,X49),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30009,plain,
spl625_244,
inference(avatar_split_clause,[],[f17486,f30007]) ).
fof(f30007,plain,
( spl625_244
<=> ! [X0] :
( class_Enum_Oenum(tc_Option_Ooption(X0))
| ~ class_Enum_Oenum(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_244])]) ).
fof(f17486,plain,
! [X0] :
( class_Enum_Oenum(tc_Option_Ooption(X0))
| ~ class_Enum_Oenum(X0) ),
inference(cnf_transformation,[],[f10412]) ).
fof(f10412,plain,
! [X0] :
( class_Enum_Oenum(tc_Option_Ooption(X0))
| ~ class_Enum_Oenum(X0) ),
inference(ennf_transformation,[],[f5576]) ).
fof(f5576,plain,
! [X0] :
( class_Enum_Oenum(X0)
=> class_Enum_Oenum(tc_Option_Ooption(X0)) ),
inference(rectify,[],[f5161]) ).
fof(f5161,axiom,
! [X324] :
( class_Enum_Oenum(X324)
=> class_Enum_Oenum(tc_Option_Ooption(X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30005,plain,
spl625_243,
inference(avatar_split_clause,[],[f17484,f30003]) ).
fof(f30003,plain,
( spl625_243
<=> ! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_243])]) ).
fof(f17484,plain,
! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(cnf_transformation,[],[f10410]) ).
fof(f10410,plain,
! [X0] :
( class_Finite__Set_Ofinite(tc_Option_Ooption(X0))
| ~ class_Finite__Set_Ofinite(X0) ),
inference(ennf_transformation,[],[f5574]) ).
fof(f5574,plain,
! [X0] :
( class_Finite__Set_Ofinite(X0)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X0)) ),
inference(rectify,[],[f5159]) ).
fof(f5159,axiom,
! [X324] :
( class_Finite__Set_Ofinite(X324)
=> class_Finite__Set_Ofinite(tc_Option_Ooption(X324)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f30001,plain,
spl625_242,
inference(avatar_split_clause,[],[f17164,f29999]) ).
fof(f29999,plain,
( spl625_242
<=> ! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_242])]) ).
fof(f17164,plain,
! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0),
inference(cnf_transformation,[],[f5267]) ).
fof(f5267,plain,
! [X0] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X0),
inference(rectify,[],[f1236]) ).
fof(f1236,axiom,
! [X144] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,X144),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29997,plain,
spl625_241,
inference(avatar_split_clause,[],[f17162,f29995]) ).
fof(f29995,plain,
( spl625_241
<=> ! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_241])]) ).
fof(f17162,plain,
! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(cnf_transformation,[],[f5265]) ).
fof(f5265,plain,
! [X0] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0)),
inference(rectify,[],[f2908]) ).
fof(f2908,axiom,
! [X30] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X30)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29993,plain,
spl625_240,
inference(avatar_split_clause,[],[f17159,f29991]) ).
fof(f29991,plain,
( spl625_240
<=> ! [X0] : hAPP(c_Nat_OSuc,X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl625_240])]) ).
fof(f17159,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(cnf_transformation,[],[f5262]) ).
fof(f5262,plain,
! [X0] : hAPP(c_Nat_OSuc,X0) != X0,
inference(rectify,[],[f1262]) ).
fof(f1262,axiom,
! [X88] : hAPP(c_Nat_OSuc,X88) != X88,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29989,plain,
spl625_239,
inference(avatar_split_clause,[],[f17037,f29986]) ).
fof(f17037,plain,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
inference(cnf_transformation,[],[f3357]) ).
fof(f3357,axiom,
c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29983,plain,
spl625_238,
inference(avatar_split_clause,[],[f17036,f29980]) ).
fof(f17036,plain,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
inference(cnf_transformation,[],[f2581]) ).
fof(f2581,axiom,
c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29978,plain,
spl625_237,
inference(avatar_split_clause,[],[f17032,f29975]) ).
fof(f29973,plain,
spl625_236,
inference(avatar_split_clause,[],[f17031,f29970]) ).
fof(f29970,plain,
( spl625_236
<=> c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_236])]) ).
fof(f17031,plain,
c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),
inference(cnf_transformation,[],[f1689]) ).
fof(f1689,axiom,
c_Orderings_Oord__class_Omin(tc_Nat_Onat) = c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29968,plain,
spl625_235,
inference(avatar_split_clause,[],[f17030,f29965]) ).
fof(f29965,plain,
( spl625_235
<=> c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_235])]) ).
fof(f17030,plain,
c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),
inference(cnf_transformation,[],[f2256]) ).
fof(f2256,axiom,
c_Orderings_Oord__class_Omax(tc_Nat_Onat) = c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29963,plain,
spl625_234,
inference(avatar_split_clause,[],[f17029,f29960]) ).
fof(f17029,plain,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
inference(cnf_transformation,[],[f3477]) ).
fof(f3477,axiom,
c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29958,plain,
~ spl625_233,
inference(avatar_split_clause,[],[f17024,f29955]) ).
fof(f17024,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(cnf_transformation,[],[f2537]) ).
fof(f2537,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29953,plain,
( ~ spl625_232
| spl625_231 ),
inference(avatar_split_clause,[],[f29948,f29944,f29950]) ).
fof(f29944,plain,
( spl625_231
<=> c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_231])]) ).
fof(f29948,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(c_fequal,c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)))
| spl625_231 ),
inference(forward_demodulation,[],[f29946,f26086]) ).
fof(f29946,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool))))
| spl625_231 ),
inference(avatar_component_clause,[],[f29944]) ).
fof(f29947,plain,
~ spl625_231,
inference(avatar_split_clause,[],[f16810,f29944]) ).
fof(f16810,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(cnf_transformation,[],[f5244]) ).
fof(f5244,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(flattening,[],[f5243]) ).
fof(f5243,negated_conjecture,
~ c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
inference(negated_conjecture,[],[f5242]) ).
fof(f5242,conjecture,
c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_Ga,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_a)),c_Hoare__Mirabelle_Otriple_Otriple(t_a,v_P,c_Com_Ocom_OSKIP,v_P)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29941,plain,
spl625_230,
inference(avatar_split_clause,[],[f27087,f29938]) ).
fof(f29938,plain,
( spl625_230
<=> sP6(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_230])]) ).
fof(f27087,plain,
sP6(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls),
inference(forward_demodulation,[],[f27086,f25553]) ).
fof(f27086,plain,
sP6(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f24963,f17032]) ).
fof(f24963,plain,
sP6(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f24962]) ).
fof(f24962,plain,
! [X1] :
( sP6(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f18992]) ).
fof(f18992,plain,
! [X0,X1] :
( sP6(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1 ),
inference(cnf_transformation,[],[f14902]) ).
fof(f14902,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
& ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
| ~ sP6(X0,X1) ) ),
inference(flattening,[],[f14901]) ).
fof(f14901,plain,
! [X0,X1] :
( ( sP6(X0,X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
& ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
| ~ sP6(X0,X1) ) ),
inference(nnf_transformation,[],[f14413]) ).
fof(f29936,plain,
spl625_229,
inference(avatar_split_clause,[],[f27079,f29933]) ).
fof(f29933,plain,
( spl625_229
<=> sP5(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_229])]) ).
fof(f27079,plain,
sP5(c_HOL_Obool_Obool__size(c_fTrue),c_Int_OPls),
inference(forward_demodulation,[],[f27078,f25553]) ).
fof(f27078,plain,
sP5(c_HOL_Obool_Obool__size(c_fTrue),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_HOL_Obool_Obool__size(c_fTrue))),
inference(forward_demodulation,[],[f24958,f17032]) ).
fof(f24958,plain,
sP5(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
inference(equality_resolution,[],[f24957]) ).
fof(f24957,plain,
! [X1] :
( sP5(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),X1)
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != X1 ),
inference(equality_resolution,[],[f18984]) ).
fof(f18984,plain,
! [X0,X1] :
( sP5(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
| hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1 ),
inference(cnf_transformation,[],[f14899]) ).
fof(f14899,plain,
! [X0,X1] :
( ( sP5(X0,X1)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X0
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) != X1
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
& ( ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = X0
| hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X0) = X1
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) ) )
| ~ sP5(X0,X1) ) ),
inference(rectify,[],[f14898]) ).
fof(f14898,plain,
! [X1,X0] :
( ( sP5(X1,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
| ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != X0
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
& ( ( ( 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)) ) )
| ~ sP5(X1,X0) ) ),
inference(flattening,[],[f14897]) ).
fof(f14897,plain,
! [X1,X0] :
( ( sP5(X1,X0)
| ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != X1
& ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
| ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),X1) != X0
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) ) )
& ( ( ( 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)) ) )
| ~ sP5(X1,X0) ) ),
inference(nnf_transformation,[],[f14411]) ).
fof(f29931,plain,
~ spl625_228,
inference(avatar_split_clause,[],[f25516,f29928]) ).
fof(f29928,plain,
( spl625_228
<=> hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_228])]) ).
fof(f25516,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Int_OPls)),
inference(forward_demodulation,[],[f17025,f17021]) ).
fof(f17025,plain,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
inference(cnf_transformation,[],[f2535]) ).
fof(f2535,axiom,
~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29926,plain,
~ spl625_227,
inference(avatar_split_clause,[],[f25515,f29923]) ).
fof(f29923,plain,
( spl625_227
<=> c_Groups_Oone__class_Oone(tc_Int_Oint) = c_Int_OPls ),
introduced(avatar_definition,[new_symbols(naming,[spl625_227])]) ).
fof(f25515,plain,
c_Groups_Oone__class_Oone(tc_Int_Oint) != c_Int_OPls,
inference(forward_demodulation,[],[f17023,f17021]) ).
fof(f17023,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f1824]) ).
fof(f1824,axiom,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29921,plain,
spl625_226,
inference(avatar_split_clause,[],[f24929,f29919]) ).
fof(f29919,plain,
( spl625_226
<=> ! [X0] : sP0(X0,c_List_Olist_ONil(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_226])]) ).
fof(f24929,plain,
! [X0] : sP0(X0,c_List_Olist_ONil(X0)),
inference(equality_resolution,[],[f18523]) ).
fof(f18523,plain,
! [X0,X1] :
( sP0(X0,X1)
| c_List_Olist_ONil(X0) != X1 ),
inference(cnf_transformation,[],[f14736]) ).
fof(f14736,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ! [X2,X3] :
( ~ c_List_Olinorder__class_Osorted(X0,X2)
| ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X3),sK124(X0,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X0),sK124(X0,X2,X3)),hAPP(c_List_Oset(X0),X2))) )
| hAPP(hAPP(c_List_Olist_OCons(X0),X3),X2) != X1 )
& c_List_Olist_ONil(X0) != X1 ) )
& ( ( c_List_Olinorder__class_Osorted(X0,sK125(X0,X1))
& ! [X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK126(X0,X1)),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X7),hAPP(c_List_Oset(X0),sK125(X0,X1)))) )
& hAPP(hAPP(c_List_Olist_OCons(X0),sK126(X0,X1)),sK125(X0,X1)) = X1 )
| c_List_Olist_ONil(X0) = X1
| ~ sP0(X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK124,sK125,sK126])],[f14733,f14735,f14734]) ).
fof(f14734,plain,
! [X0,X2,X3] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X2))) )
=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X3),sK124(X0,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X0),sK124(X0,X2,X3)),hAPP(c_List_Oset(X0),X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f14735,plain,
! [X0,X1] :
( ? [X5,X6] :
( c_List_Olinorder__class_Osorted(X0,X5)
& ! [X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X6),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X7),hAPP(c_List_Oset(X0),X5))) )
& hAPP(hAPP(c_List_Olist_OCons(X0),X6),X5) = X1 )
=> ( c_List_Olinorder__class_Osorted(X0,sK125(X0,X1))
& ! [X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),sK126(X0,X1)),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X7),hAPP(c_List_Oset(X0),sK125(X0,X1)))) )
& hAPP(hAPP(c_List_Olist_OCons(X0),sK126(X0,X1)),sK125(X0,X1)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f14733,plain,
! [X0,X1] :
( ( sP0(X0,X1)
| ( ! [X2,X3] :
( ~ c_List_Olinorder__class_Osorted(X0,X2)
| ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X0),X4),hAPP(c_List_Oset(X0),X2))) )
| hAPP(hAPP(c_List_Olist_OCons(X0),X3),X2) != X1 )
& c_List_Olist_ONil(X0) != X1 ) )
& ( ? [X5,X6] :
( c_List_Olinorder__class_Osorted(X0,X5)
& ! [X7] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X0),X6),X7))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X7),hAPP(c_List_Oset(X0),X5))) )
& hAPP(hAPP(c_List_Olist_OCons(X0),X6),X5) = X1 )
| c_List_Olist_ONil(X0) = X1
| ~ sP0(X0,X1) ) ),
inference(rectify,[],[f14732]) ).
fof(f14732,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ! [X2,X3] :
( ~ c_List_Olinorder__class_Osorted(X1,X2)
| ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2))) )
| hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) != X0 )
& c_List_Olist_ONil(X1) != X0 ) )
& ( ? [X2,X3] :
( c_List_Olinorder__class_Osorted(X1,X2)
& ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2))) )
& hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) = X0 )
| c_List_Olist_ONil(X1) = X0
| ~ sP0(X1,X0) ) ),
inference(flattening,[],[f14731]) ).
fof(f14731,plain,
! [X1,X0] :
( ( sP0(X1,X0)
| ( ! [X2,X3] :
( ~ c_List_Olinorder__class_Osorted(X1,X2)
| ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
& hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2))) )
| hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) != X0 )
& c_List_Olist_ONil(X1) != X0 ) )
& ( ? [X2,X3] :
( c_List_Olinorder__class_Osorted(X1,X2)
& ! [X4] :
( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(X1),X3),X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),hAPP(c_List_Oset(X1),X2))) )
& hAPP(hAPP(c_List_Olist_OCons(X1),X3),X2) = X0 )
| c_List_Olist_ONil(X1) = X0
| ~ sP0(X1,X0) ) ),
inference(nnf_transformation,[],[f14402]) ).
fof(f29917,plain,
spl625_225,
inference(avatar_split_clause,[],[f17680,f29915]) ).
fof(f17680,plain,
! [X0,X1] : class_HOL_Oequal(tc_prod(X1,X0)),
inference(cnf_transformation,[],[f5696]) ).
fof(f5696,plain,
! [X0,X1] : class_HOL_Oequal(tc_prod(X1,X0)),
inference(rectify,[],[f5165]) ).
fof(f5165,axiom,
! [X324,X323] : class_HOL_Oequal(tc_prod(X323,X324)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29913,plain,
spl625_224,
inference(avatar_split_clause,[],[f17679,f29911]) ).
fof(f17679,plain,
! [X0,X1] : class_HOL_Oequal(tc_sum(X1,X0)),
inference(cnf_transformation,[],[f5695]) ).
fof(f5695,plain,
! [X0,X1] : class_HOL_Oequal(tc_sum(X1,X0)),
inference(rectify,[],[f5156]) ).
fof(f5156,axiom,
! [X324,X323] : class_HOL_Oequal(tc_sum(X323,X324)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29909,plain,
spl625_223,
inference(avatar_split_clause,[],[f17678,f29907]) ).
fof(f29907,plain,
( spl625_223
<=> ! [X0,X1] : class_Nat_Osize(tc_prod(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_223])]) ).
fof(f17678,plain,
! [X0,X1] : class_Nat_Osize(tc_prod(X1,X0)),
inference(cnf_transformation,[],[f5694]) ).
fof(f5694,plain,
! [X0,X1] : class_Nat_Osize(tc_prod(X1,X0)),
inference(rectify,[],[f5167]) ).
fof(f5167,axiom,
! [X324,X323] : class_Nat_Osize(tc_prod(X323,X324)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29905,plain,
spl625_222,
inference(avatar_split_clause,[],[f17677,f29903]) ).
fof(f29903,plain,
( spl625_222
<=> ! [X0,X1] : class_Nat_Osize(tc_sum(X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_222])]) ).
fof(f17677,plain,
! [X0,X1] : class_Nat_Osize(tc_sum(X1,X0)),
inference(cnf_transformation,[],[f5693]) ).
fof(f5693,plain,
! [X0,X1] : class_Nat_Osize(tc_sum(X1,X0)),
inference(rectify,[],[f5158]) ).
fof(f5158,axiom,
! [X324,X323] : class_Nat_Osize(tc_sum(X323,X324)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29901,plain,
spl625_221,
inference(avatar_split_clause,[],[f17152,f29899]) ).
fof(f29899,plain,
( spl625_221
<=> ! [X0] : c_Int_OMin != c_Int_OBit0(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_221])]) ).
fof(f17152,plain,
! [X0] : c_Int_OMin != c_Int_OBit0(X0),
inference(cnf_transformation,[],[f5255]) ).
fof(f5255,plain,
! [X0] : c_Int_OMin != c_Int_OBit0(X0),
inference(rectify,[],[f2787]) ).
fof(f2787,axiom,
! [X112] : c_Int_OBit0(X112) != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29897,plain,
spl625_220,
inference(avatar_split_clause,[],[f17022,f29894]) ).
fof(f29894,plain,
( spl625_220
<=> c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_220])]) ).
fof(f17022,plain,
c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
inference(cnf_transformation,[],[f1268]) ).
fof(f1268,axiom,
c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29892,plain,
spl625_219,
inference(avatar_split_clause,[],[f17021,f29889]) ).
fof(f29887,plain,
spl625_218,
inference(avatar_split_clause,[],[f17020,f29884]) ).
fof(f29884,plain,
( spl625_218
<=> c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_Osubtract__code__numeral ),
introduced(avatar_definition,[new_symbols(naming,[spl625_218])]) ).
fof(f29882,plain,
spl625_217,
inference(avatar_split_clause,[],[f17019,f29879]) ).
fof(f29879,plain,
( spl625_217
<=> c_Int_OPls = c_Int_OBit0(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_217])]) ).
fof(f29877,plain,
spl625_216,
inference(avatar_split_clause,[],[f17015,f29874]) ).
fof(f29874,plain,
( spl625_216
<=> c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_216])]) ).
fof(f17015,plain,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f4625]) ).
fof(f4625,axiom,
c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29872,plain,
spl625_215,
inference(avatar_split_clause,[],[f27138,f29870]) ).
fof(f29870,plain,
( spl625_215
<=> ! [X0] : sP9(X0,c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_215])]) ).
fof(f27138,plain,
! [X0] : sP9(X0,c_Int_OPls),
inference(forward_demodulation,[],[f25003,f17021]) ).
fof(f25003,plain,
! [X0] : sP9(X0,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(equality_resolution,[],[f19127]) ).
fof(f19127,plain,
! [X0,X1] :
( sP9(X0,X1)
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ),
inference(cnf_transformation,[],[f15009]) ).
fof(f15009,plain,
! [X0,X1] :
( ( sP9(X0,X1)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X1 ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X0),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X0)) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X1
| ~ sP9(X0,X1) ) ),
inference(rectify,[],[f15008]) ).
fof(f15008,plain,
! [X1,X0] :
( ( sP9(X1,X0)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ sP9(X1,X0) ) ),
inference(flattening,[],[f15007]) ).
fof(f15007,plain,
! [X1,X0] :
( ( sP9(X1,X0)
| ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
& ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
| ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
& c_Groups_Ozero__class_Ozero(tc_Int_Oint) != X0 ) )
& ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0
| ~ sP9(X1,X0) ) ),
inference(nnf_transformation,[],[f14419]) ).
fof(f14419,plain,
! [X1,X0] :
( sP9(X1,X0)
<=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X0),X1))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),X1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
| ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),X1),X0))
& hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),X1)) )
| c_Groups_Ozero__class_Ozero(tc_Int_Oint) = X0 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f29868,plain,
spl625_214,
inference(avatar_split_clause,[],[f27131,f29865]) ).
fof(f29865,plain,
( spl625_214
<=> sP8(c_Int_OMin,c_Int_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_214])]) ).
fof(f27131,plain,
sP8(c_Int_OMin,c_Int_OMin),
inference(forward_demodulation,[],[f24996,f17178]) ).
fof(f24996,plain,
sP8(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,[],[f24995]) ).
fof(f24995,plain,
! [X1] :
( sP8(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),X1)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 ),
inference(equality_resolution,[],[f19114]) ).
fof(f19114,plain,
! [X0,X1] :
( sP8(X0,X1)
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X0
| hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) != X1 ),
inference(cnf_transformation,[],[f15001]) ).
fof(f29863,plain,
spl625_213,
inference(avatar_split_clause,[],[f17674,f29861]) ).
fof(f29861,plain,
( spl625_213
<=> ! [X0,X1] : c_FunDef_Ois__measure(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_213])]) ).
fof(f17674,plain,
! [X0,X1] : c_FunDef_Ois__measure(X1,X0),
inference(cnf_transformation,[],[f5690]) ).
fof(f5690,plain,
! [X0,X1] : c_FunDef_Ois__measure(X1,X0),
inference(rectify,[],[f4941]) ).
fof(f4941,axiom,
! [X1,X4] : c_FunDef_Ois__measure(X4,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29859,plain,
spl625_212,
inference(avatar_split_clause,[],[f17150,f29857]) ).
fof(f29857,plain,
( spl625_212
<=> ! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_212])]) ).
fof(f17150,plain,
! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal),
inference(cnf_transformation,[],[f5253]) ).
fof(f5253,plain,
! [X0] : c_Equiv__Relations_Oequivp(X0,c_fequal),
inference(rectify,[],[f1252]) ).
fof(f1252,axiom,
! [X4] : c_Equiv__Relations_Oequivp(X4,c_fequal),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29855,plain,
spl625_211,
inference(avatar_split_clause,[],[f17149,f29853]) ).
fof(f17149,plain,
! [X0] : class_HOL_Oequal(tc_List_Olist(X0)),
inference(cnf_transformation,[],[f5252]) ).
fof(f5252,plain,
! [X0] : class_HOL_Oequal(tc_List_Olist(X0)),
inference(rectify,[],[f5153]) ).
fof(f5153,axiom,
! [X324] : class_HOL_Oequal(tc_List_Olist(X324)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29851,plain,
spl625_210,
inference(avatar_split_clause,[],[f17148,f29849]) ).
fof(f17148,plain,
! [X0] : class_HOL_Oequal(tc_Option_Ooption(X0)),
inference(cnf_transformation,[],[f5251]) ).
fof(f5251,plain,
! [X0] : class_HOL_Oequal(tc_Option_Ooption(X0)),
inference(rectify,[],[f5160]) ).
fof(f5160,axiom,
! [X324] : class_HOL_Oequal(tc_Option_Ooption(X324)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29847,plain,
spl625_209,
inference(avatar_split_clause,[],[f17147,f29845]) ).
fof(f17147,plain,
! [X0] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X0)),
inference(cnf_transformation,[],[f5250]) ).
fof(f5250,plain,
! [X0] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X0)),
inference(rectify,[],[f5175]) ).
fof(f5175,axiom,
! [X324] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(X324)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29843,plain,
spl625_208,
inference(avatar_split_clause,[],[f17146,f29841]) ).
fof(f17146,plain,
! [X0] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X0)),
inference(cnf_transformation,[],[f5249]) ).
fof(f5249,plain,
! [X0] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X0)),
inference(rectify,[],[f5219]) ).
fof(f5219,axiom,
! [X324] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(X324)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29839,plain,
spl625_207,
inference(avatar_split_clause,[],[f17145,f29837]) ).
fof(f29837,plain,
( spl625_207
<=> ! [X0] : class_Nat_Osize(tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_207])]) ).
fof(f17145,plain,
! [X0] : class_Nat_Osize(tc_List_Olist(X0)),
inference(cnf_transformation,[],[f5248]) ).
fof(f5248,plain,
! [X0] : class_Nat_Osize(tc_List_Olist(X0)),
inference(rectify,[],[f5154]) ).
fof(f5154,axiom,
! [X324] : class_Nat_Osize(tc_List_Olist(X324)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29835,plain,
spl625_206,
inference(avatar_split_clause,[],[f17144,f29833]) ).
fof(f29833,plain,
( spl625_206
<=> ! [X0] : class_Nat_Osize(tc_Option_Ooption(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_206])]) ).
fof(f17144,plain,
! [X0] : class_Nat_Osize(tc_Option_Ooption(X0)),
inference(cnf_transformation,[],[f5247]) ).
fof(f5247,plain,
! [X0] : class_Nat_Osize(tc_Option_Ooption(X0)),
inference(rectify,[],[f5162]) ).
fof(f5162,axiom,
! [X324] : class_Nat_Osize(tc_Option_Ooption(X324)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29831,plain,
spl625_205,
inference(avatar_split_clause,[],[f17143,f29829]) ).
fof(f29829,plain,
( spl625_205
<=> ! [X0] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_205])]) ).
fof(f17143,plain,
! [X0] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X0)),
inference(cnf_transformation,[],[f5246]) ).
fof(f5246,plain,
! [X0] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X0)),
inference(rectify,[],[f5176]) ).
fof(f5176,axiom,
! [X324] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(X324)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29827,plain,
spl625_204,
inference(avatar_split_clause,[],[f17142,f29825]) ).
fof(f29825,plain,
( spl625_204
<=> ! [X0] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_204])]) ).
fof(f17142,plain,
! [X0] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)),
inference(cnf_transformation,[],[f5245]) ).
fof(f5245,plain,
! [X0] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X0)),
inference(rectify,[],[f5220]) ).
fof(f5220,axiom,
! [X324] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(X324)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29823,plain,
spl625_203,
inference(avatar_split_clause,[],[f17014,f29820]) ).
fof(f17014,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
inference(cnf_transformation,[],[f3343]) ).
fof(f3343,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29818,plain,
spl625_202,
inference(avatar_split_clause,[],[f17013,f29815]) ).
fof(f17013,plain,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
inference(cnf_transformation,[],[f3384]) ).
fof(f3384,axiom,
c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29813,plain,
( spl625_201
| ~ spl625_200 ),
inference(avatar_split_clause,[],[f29808,f29804,f29810]) ).
fof(f29810,plain,
( spl625_201
<=> c_Nat__Transfer_Ois__nat(c_Int_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_201])]) ).
fof(f29804,plain,
( spl625_200
<=> c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_200])]) ).
fof(f29808,plain,
( c_Nat__Transfer_Ois__nat(c_Int_OPls)
| ~ spl625_200 ),
inference(forward_demodulation,[],[f29806,f17021]) ).
fof(f29806,plain,
( c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ spl625_200 ),
inference(avatar_component_clause,[],[f29804]) ).
fof(f29807,plain,
spl625_200,
inference(avatar_split_clause,[],[f17012,f29804]) ).
fof(f17012,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(cnf_transformation,[],[f2911]) ).
fof(f2911,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29802,plain,
spl625_199,
inference(avatar_split_clause,[],[f17011,f29799]) ).
fof(f29799,plain,
( spl625_199
<=> c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_199])]) ).
fof(f17011,plain,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
inference(cnf_transformation,[],[f2905]) ).
fof(f2905,axiom,
c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29797,plain,
~ spl625_198,
inference(avatar_split_clause,[],[f17009,f29794]) ).
fof(f29794,plain,
( spl625_198
<=> c_Int_OPls = c_Int_OMin ),
introduced(avatar_definition,[new_symbols(naming,[spl625_198])]) ).
fof(f17009,plain,
c_Int_OPls != c_Int_OMin,
inference(cnf_transformation,[],[f2775]) ).
fof(f2775,axiom,
c_Int_OPls != c_Int_OMin,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29792,plain,
spl625_197,
inference(avatar_split_clause,[],[f17008,f29789]) ).
fof(f29789,plain,
( spl625_197
<=> hBOOL(c_fTrue) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_197])]) ).
fof(f17008,plain,
hBOOL(c_fTrue),
inference(cnf_transformation,[],[f5229]) ).
fof(f5229,axiom,
hBOOL(c_fTrue),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29787,plain,
spl625_196,
inference(avatar_split_clause,[],[f17007,f29784]) ).
fof(f17007,plain,
class_HOL_Oequal(tc_HOL_Obool),
inference(cnf_transformation,[],[f5146]) ).
fof(f5146,axiom,
class_HOL_Oequal(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29782,plain,
spl625_195,
inference(avatar_split_clause,[],[f17006,f29779]) ).
fof(f17006,plain,
class_HOL_Oequal(tc_Nat_Onat),
inference(cnf_transformation,[],[f5128]) ).
fof(f5128,axiom,
class_HOL_Oequal(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29777,plain,
spl625_194,
inference(avatar_split_clause,[],[f17005,f29774]) ).
fof(f17005,plain,
class_HOL_Oequal(tc_Int_Oint),
inference(cnf_transformation,[],[f5080]) ).
fof(f5080,axiom,
class_HOL_Oequal(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29772,plain,
spl625_193,
inference(avatar_split_clause,[],[f17004,f29769]) ).
fof(f17004,plain,
class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5217]) ).
fof(f5217,axiom,
class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29767,plain,
spl625_192,
inference(avatar_split_clause,[],[f17003,f29764]) ).
fof(f17003,plain,
class_HOL_Oequal(tc_Com_Ostate),
inference(cnf_transformation,[],[f5149]) ).
fof(f5149,axiom,
class_HOL_Oequal(tc_Com_Ostate),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29762,plain,
spl625_191,
inference(avatar_split_clause,[],[f17002,f29759]) ).
fof(f17002,plain,
class_HOL_Oequal(tc_Code__Evaluation_Oterm),
inference(cnf_transformation,[],[f5173]) ).
fof(f5173,axiom,
class_HOL_Oequal(tc_Code__Evaluation_Oterm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29757,plain,
spl625_190,
inference(avatar_split_clause,[],[f17001,f29754]) ).
fof(f17001,plain,
class_HOL_Oequal(tc_Com_Ocom),
inference(cnf_transformation,[],[f5008]) ).
fof(f5008,axiom,
class_HOL_Oequal(tc_Com_Ocom),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29752,plain,
spl625_189,
inference(avatar_split_clause,[],[f17000,f29749]) ).
fof(f17000,plain,
class_HOL_Oequal(tc_Com_Ovname),
inference(cnf_transformation,[],[f5151]) ).
fof(f5151,axiom,
class_HOL_Oequal(tc_Com_Ovname),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29747,plain,
spl625_188,
inference(avatar_split_clause,[],[f16999,f29744]) ).
fof(f16999,plain,
class_HOL_Oequal(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5170]) ).
fof(f5170,axiom,
class_HOL_Oequal(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29742,plain,
spl625_187,
inference(avatar_split_clause,[],[f16998,f29739]) ).
fof(f29739,plain,
( spl625_187
<=> class_Nat_Osize(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_187])]) ).
fof(f16998,plain,
class_Nat_Osize(tc_HOL_Obool),
inference(cnf_transformation,[],[f5148]) ).
fof(f5148,axiom,
class_Nat_Osize(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29737,plain,
spl625_186,
inference(avatar_split_clause,[],[f16997,f29734]) ).
fof(f29734,plain,
( spl625_186
<=> class_Nat_Osize(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_186])]) ).
fof(f16997,plain,
class_Nat_Osize(tc_Nat_Onat),
inference(cnf_transformation,[],[f5129]) ).
fof(f5129,axiom,
class_Nat_Osize(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29732,plain,
spl625_185,
inference(avatar_split_clause,[],[f16996,f29729]) ).
fof(f29729,plain,
( spl625_185
<=> class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_185])]) ).
fof(f16996,plain,
class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5218]) ).
fof(f5218,axiom,
class_Nat_Osize(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29727,plain,
spl625_184,
inference(avatar_split_clause,[],[f16995,f29724]) ).
fof(f29724,plain,
( spl625_184
<=> class_Nat_Osize(tc_Com_Ostate) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_184])]) ).
fof(f16995,plain,
class_Nat_Osize(tc_Com_Ostate),
inference(cnf_transformation,[],[f5150]) ).
fof(f5150,axiom,
class_Nat_Osize(tc_Com_Ostate),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29722,plain,
spl625_183,
inference(avatar_split_clause,[],[f16994,f29719]) ).
fof(f29719,plain,
( spl625_183
<=> class_Nat_Osize(tc_Code__Evaluation_Oterm) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_183])]) ).
fof(f16994,plain,
class_Nat_Osize(tc_Code__Evaluation_Oterm),
inference(cnf_transformation,[],[f5174]) ).
fof(f5174,axiom,
class_Nat_Osize(tc_Code__Evaluation_Oterm),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29717,plain,
spl625_182,
inference(avatar_split_clause,[],[f16993,f29714]) ).
fof(f29714,plain,
( spl625_182
<=> class_Nat_Osize(tc_Com_Ocom) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_182])]) ).
fof(f16993,plain,
class_Nat_Osize(tc_Com_Ocom),
inference(cnf_transformation,[],[f5009]) ).
fof(f5009,axiom,
class_Nat_Osize(tc_Com_Ocom),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29712,plain,
spl625_181,
inference(avatar_split_clause,[],[f16992,f29709]) ).
fof(f29709,plain,
( spl625_181
<=> class_Nat_Osize(tc_Com_Ovname) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_181])]) ).
fof(f16992,plain,
class_Nat_Osize(tc_Com_Ovname),
inference(cnf_transformation,[],[f5152]) ).
fof(f5152,axiom,
class_Nat_Osize(tc_Com_Ovname),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29707,plain,
spl625_180,
inference(avatar_split_clause,[],[f16991,f29704]) ).
fof(f29704,plain,
( spl625_180
<=> class_Nat_Osize(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_180])]) ).
fof(f16991,plain,
class_Nat_Osize(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5172]) ).
fof(f5172,axiom,
class_Nat_Osize(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29702,plain,
spl625_179,
inference(avatar_split_clause,[],[f16990,f29699]) ).
fof(f29699,plain,
( spl625_179
<=> class_Enum_Oenum(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_179])]) ).
fof(f16990,plain,
class_Enum_Oenum(tc_HOL_Obool),
inference(cnf_transformation,[],[f5147]) ).
fof(f5147,axiom,
class_Enum_Oenum(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29697,plain,
spl625_178,
inference(avatar_split_clause,[],[f16989,f29694]) ).
fof(f29694,plain,
( spl625_178
<=> class_Enum_Oenum(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_178])]) ).
fof(f16989,plain,
class_Enum_Oenum(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5171]) ).
fof(f5171,axiom,
class_Enum_Oenum(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29692,plain,
spl625_177,
inference(avatar_split_clause,[],[f16988,f29689]) ).
fof(f29689,plain,
( spl625_177
<=> class_Finite__Set_Ofinite(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_177])]) ).
fof(f16988,plain,
class_Finite__Set_Ofinite(tc_HOL_Obool),
inference(cnf_transformation,[],[f5138]) ).
fof(f5138,axiom,
class_Finite__Set_Ofinite(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29687,plain,
spl625_176,
inference(avatar_split_clause,[],[f16987,f29684]) ).
fof(f29684,plain,
( spl625_176
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_176])]) ).
fof(f16987,plain,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5168]) ).
fof(f5168,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29682,plain,
spl625_175,
inference(avatar_split_clause,[],[f16986,f29679]) ).
fof(f29679,plain,
( spl625_175
<=> class_Orderings_Oorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_175])]) ).
fof(f16986,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f5140]) ).
fof(f5140,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29677,plain,
spl625_174,
inference(avatar_split_clause,[],[f16985,f29674]) ).
fof(f29674,plain,
( spl625_174
<=> class_Orderings_Oorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_174])]) ).
fof(f16985,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5119]) ).
fof(f5119,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29672,plain,
spl625_173,
inference(avatar_split_clause,[],[f16984,f29669]) ).
fof(f29669,plain,
( spl625_173
<=> class_Orderings_Oorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_173])]) ).
fof(f16984,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5064]) ).
fof(f5064,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29667,plain,
spl625_172,
inference(avatar_split_clause,[],[f16983,f29664]) ).
fof(f29664,plain,
( spl625_172
<=> class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_172])]) ).
fof(f16983,plain,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5209]) ).
fof(f5209,axiom,
class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29662,plain,
spl625_171,
inference(avatar_split_clause,[],[f16982,f29659]) ).
fof(f29659,plain,
( spl625_171
<=> class_Orderings_Oord(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_171])]) ).
fof(f16982,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f5142]) ).
fof(f5142,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29657,plain,
spl625_170,
inference(avatar_split_clause,[],[f16981,f29654]) ).
fof(f29654,plain,
( spl625_170
<=> class_Orderings_Oord(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_170])]) ).
fof(f16981,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f5121]) ).
fof(f5121,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29652,plain,
spl625_169,
inference(avatar_split_clause,[],[f16980,f29649]) ).
fof(f29649,plain,
( spl625_169
<=> class_Orderings_Oord(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_169])]) ).
fof(f16980,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(cnf_transformation,[],[f5068]) ).
fof(f5068,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29647,plain,
spl625_168,
inference(avatar_split_clause,[],[f16979,f29644]) ).
fof(f29644,plain,
( spl625_168
<=> class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_168])]) ).
fof(f16979,plain,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5211]) ).
fof(f5211,axiom,
class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29642,plain,
spl625_167,
inference(avatar_split_clause,[],[f16978,f29639]) ).
fof(f29639,plain,
( spl625_167
<=> class_Orderings_Opreorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_167])]) ).
fof(f16978,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f5137]) ).
fof(f5137,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29637,plain,
spl625_166,
inference(avatar_split_clause,[],[f16977,f29634]) ).
fof(f29634,plain,
( spl625_166
<=> class_Orderings_Opreorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_166])]) ).
fof(f16977,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5111]) ).
fof(f5111,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29632,plain,
spl625_165,
inference(avatar_split_clause,[],[f16976,f29629]) ).
fof(f29629,plain,
( spl625_165
<=> class_Orderings_Opreorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_165])]) ).
fof(f16976,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5052]) ).
fof(f5052,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29627,plain,
spl625_164,
inference(avatar_split_clause,[],[f16975,f29624]) ).
fof(f29624,plain,
( spl625_164
<=> class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_164])]) ).
fof(f16975,plain,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5202]) ).
fof(f5202,axiom,
class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29622,plain,
spl625_163,
inference(avatar_split_clause,[],[f16974,f29619]) ).
fof(f29619,plain,
( spl625_163
<=> class_Groups_Ominus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_163])]) ).
fof(f16974,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(cnf_transformation,[],[f5145]) ).
fof(f5145,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29617,plain,
spl625_162,
inference(avatar_split_clause,[],[f16973,f29614]) ).
fof(f29614,plain,
( spl625_162
<=> class_Groups_Ominus(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_162])]) ).
fof(f16973,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(cnf_transformation,[],[f5123]) ).
fof(f5123,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29612,plain,
spl625_161,
inference(avatar_split_clause,[],[f16972,f29609]) ).
fof(f29609,plain,
( spl625_161
<=> class_Groups_Ominus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_161])]) ).
fof(f16972,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(cnf_transformation,[],[f5073]) ).
fof(f5073,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29607,plain,
spl625_160,
inference(avatar_split_clause,[],[f16971,f29604]) ).
fof(f29604,plain,
( spl625_160
<=> class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_160])]) ).
fof(f16971,plain,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5212]) ).
fof(f5212,axiom,
class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29602,plain,
spl625_159,
inference(avatar_split_clause,[],[f16970,f29599]) ).
fof(f29599,plain,
( spl625_159
<=> class_Lattices_Olattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_159])]) ).
fof(f16970,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5139]) ).
fof(f5139,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29597,plain,
spl625_158,
inference(avatar_split_clause,[],[f16969,f29594]) ).
fof(f29594,plain,
( spl625_158
<=> class_Lattices_Olattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_158])]) ).
fof(f16969,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f5117]) ).
fof(f5117,axiom,
class_Lattices_Olattice(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29592,plain,
spl625_157,
inference(avatar_split_clause,[],[f16968,f29589]) ).
fof(f29589,plain,
( spl625_157
<=> class_Lattices_Olattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_157])]) ).
fof(f16968,plain,
class_Lattices_Olattice(tc_Int_Oint),
inference(cnf_transformation,[],[f5060]) ).
fof(f5060,axiom,
class_Lattices_Olattice(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29587,plain,
spl625_156,
inference(avatar_split_clause,[],[f16967,f29584]) ).
fof(f29584,plain,
( spl625_156
<=> class_Lattices_Osemilattice__inf(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_156])]) ).
fof(f16967,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(cnf_transformation,[],[f5134]) ).
fof(f5134,axiom,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29582,plain,
spl625_155,
inference(avatar_split_clause,[],[f16966,f29579]) ).
fof(f29579,plain,
( spl625_155
<=> class_Lattices_Osemilattice__inf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_155])]) ).
fof(f16966,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(cnf_transformation,[],[f5096]) ).
fof(f5096,axiom,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29577,plain,
spl625_154,
inference(avatar_split_clause,[],[f16965,f29574]) ).
fof(f29574,plain,
( spl625_154
<=> class_Lattices_Osemilattice__inf(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_154])]) ).
fof(f16965,plain,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
inference(cnf_transformation,[],[f5033]) ).
fof(f5033,axiom,
class_Lattices_Osemilattice__inf(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29572,plain,
spl625_153,
inference(avatar_split_clause,[],[f16964,f29569]) ).
fof(f29569,plain,
( spl625_153
<=> class_Lattices_Osemilattice__sup(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_153])]) ).
fof(f16964,plain,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
inference(cnf_transformation,[],[f5133]) ).
fof(f5133,axiom,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29567,plain,
spl625_152,
inference(avatar_split_clause,[],[f16963,f29564]) ).
fof(f29564,plain,
( spl625_152
<=> class_Lattices_Osemilattice__sup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_152])]) ).
fof(f16963,plain,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
inference(cnf_transformation,[],[f5095]) ).
fof(f5095,axiom,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29562,plain,
spl625_151,
inference(avatar_split_clause,[],[f16962,f29559]) ).
fof(f29559,plain,
( spl625_151
<=> class_Lattices_Osemilattice__sup(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_151])]) ).
fof(f16962,plain,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
inference(cnf_transformation,[],[f5032]) ).
fof(f5032,axiom,
class_Lattices_Osemilattice__sup(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29557,plain,
spl625_150,
inference(avatar_split_clause,[],[f16961,f29554]) ).
fof(f29554,plain,
( spl625_150
<=> class_Lattices_Odistrib__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_150])]) ).
fof(f16961,plain,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5135]) ).
fof(f5135,axiom,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29552,plain,
spl625_149,
inference(avatar_split_clause,[],[f16960,f29549]) ).
fof(f29549,plain,
( spl625_149
<=> class_Lattices_Odistrib__lattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_149])]) ).
fof(f16960,plain,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f5097]) ).
fof(f5097,axiom,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29547,plain,
spl625_148,
inference(avatar_split_clause,[],[f16959,f29544]) ).
fof(f29544,plain,
( spl625_148
<=> class_Lattices_Odistrib__lattice(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_148])]) ).
fof(f16959,plain,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
inference(cnf_transformation,[],[f5034]) ).
fof(f5034,axiom,
class_Lattices_Odistrib__lattice(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29542,plain,
spl625_147,
inference(avatar_split_clause,[],[f16958,f29539]) ).
fof(f29539,plain,
( spl625_147
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_147])]) ).
fof(f16958,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5112]) ).
fof(f5112,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29537,plain,
spl625_146,
inference(avatar_split_clause,[],[f16957,f29534]) ).
fof(f29534,plain,
( spl625_146
<=> class_Orderings_Olinorder(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_146])]) ).
fof(f16957,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(cnf_transformation,[],[f5053]) ).
fof(f5053,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29532,plain,
spl625_145,
inference(avatar_split_clause,[],[f16956,f29529]) ).
fof(f29529,plain,
( spl625_145
<=> class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_145])]) ).
fof(f16956,plain,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5203]) ).
fof(f5203,axiom,
class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29527,plain,
spl625_144,
inference(avatar_split_clause,[],[f16955,f29524]) ).
fof(f29524,plain,
( spl625_144
<=> class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_144])]) ).
fof(f16955,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5103]) ).
fof(f5103,axiom,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29522,plain,
spl625_143,
inference(avatar_split_clause,[],[f16954,f29519]) ).
fof(f29519,plain,
( spl625_143
<=> class_Groups_Ocomm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_143])]) ).
fof(f16954,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5041]) ).
fof(f5041,axiom,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29517,plain,
spl625_142,
inference(avatar_split_clause,[],[f16953,f29514]) ).
fof(f29514,plain,
( spl625_142
<=> class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_142])]) ).
fof(f16953,plain,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5195]) ).
fof(f5195,axiom,
class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29512,plain,
spl625_141,
inference(avatar_split_clause,[],[f16952,f29509]) ).
fof(f29509,plain,
( spl625_141
<=> class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_141])]) ).
fof(f16952,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5099]) ).
fof(f5099,axiom,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29507,plain,
spl625_140,
inference(avatar_split_clause,[],[f16951,f29504]) ).
fof(f29504,plain,
( spl625_140
<=> class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_140])]) ).
fof(f16951,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5036]) ).
fof(f5036,axiom,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29502,plain,
spl625_139,
inference(avatar_split_clause,[],[f16950,f29499]) ).
fof(f29499,plain,
( spl625_139
<=> class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_139])]) ).
fof(f16950,plain,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5191]) ).
fof(f5191,axiom,
class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29497,plain,
spl625_138,
inference(avatar_split_clause,[],[f16949,f29494]) ).
fof(f29494,plain,
( spl625_138
<=> class_Rings_Olinordered__semidom(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_138])]) ).
fof(f16949,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(cnf_transformation,[],[f5094]) ).
fof(f5094,axiom,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29492,plain,
spl625_137,
inference(avatar_split_clause,[],[f16948,f29489]) ).
fof(f29489,plain,
( spl625_137
<=> class_Rings_Olinordered__semidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_137])]) ).
fof(f16948,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(cnf_transformation,[],[f5031]) ).
fof(f5031,axiom,
class_Rings_Olinordered__semidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29487,plain,
spl625_136,
inference(avatar_split_clause,[],[f16947,f29484]) ).
fof(f29484,plain,
( spl625_136
<=> class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_136])]) ).
fof(f16947,plain,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5189]) ).
fof(f5189,axiom,
class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29482,plain,
spl625_135,
inference(avatar_split_clause,[],[f16946,f29479]) ).
fof(f29479,plain,
( spl625_135
<=> class_Divides_Osemiring__div(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_135])]) ).
fof(f16946,plain,
class_Divides_Osemiring__div(tc_Nat_Onat),
inference(cnf_transformation,[],[f5106]) ).
fof(f5106,axiom,
class_Divides_Osemiring__div(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29477,plain,
spl625_134,
inference(avatar_split_clause,[],[f16945,f29474]) ).
fof(f29474,plain,
( spl625_134
<=> class_Divides_Osemiring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_134])]) ).
fof(f16945,plain,
class_Divides_Osemiring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f5046]) ).
fof(f5046,axiom,
class_Divides_Osemiring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29472,plain,
spl625_133,
inference(avatar_split_clause,[],[f16944,f29469]) ).
fof(f29469,plain,
( spl625_133
<=> class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_133])]) ).
fof(f16944,plain,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5198]) ).
fof(f5198,axiom,
class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29467,plain,
spl625_132,
inference(avatar_split_clause,[],[f16943,f29464]) ).
fof(f29464,plain,
( spl625_132
<=> class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_132])]) ).
fof(f16943,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f5104]) ).
fof(f5104,axiom,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29462,plain,
spl625_131,
inference(avatar_split_clause,[],[f16942,f29459]) ).
fof(f29459,plain,
( spl625_131
<=> class_Rings_Ocomm__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_131])]) ).
fof(f16942,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5044]) ).
fof(f5044,axiom,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29457,plain,
spl625_130,
inference(avatar_split_clause,[],[f16941,f29454]) ).
fof(f29454,plain,
( spl625_130
<=> class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_130])]) ).
fof(f16941,plain,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5196]) ).
fof(f5196,axiom,
class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29452,plain,
spl625_129,
inference(avatar_split_clause,[],[f16940,f29449]) ).
fof(f16940,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(cnf_transformation,[],[f5115]) ).
fof(f5115,axiom,
class_Rings_Osemiring__1(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29447,plain,
spl625_128,
inference(avatar_split_clause,[],[f16939,f29444]) ).
fof(f16939,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5058]) ).
fof(f5058,axiom,
class_Rings_Osemiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29442,plain,
spl625_127,
inference(avatar_split_clause,[],[f16938,f29439]) ).
fof(f16938,plain,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5206]) ).
fof(f5206,axiom,
class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29437,plain,
spl625_126,
inference(avatar_split_clause,[],[f16937,f29434]) ).
fof(f29434,plain,
( spl625_126
<=> class_Int_Onumber(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_126])]) ).
fof(f16937,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(cnf_transformation,[],[f5126]) ).
fof(f5126,axiom,
class_Int_Onumber(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29432,plain,
spl625_125,
inference(avatar_split_clause,[],[f16936,f29429]) ).
fof(f29429,plain,
( spl625_125
<=> class_Int_Onumber(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_125])]) ).
fof(f16936,plain,
class_Int_Onumber(tc_Int_Oint),
inference(cnf_transformation,[],[f5078]) ).
fof(f5078,axiom,
class_Int_Onumber(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29427,plain,
spl625_124,
inference(avatar_split_clause,[],[f16935,f29424]) ).
fof(f29424,plain,
( spl625_124
<=> class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_124])]) ).
fof(f16935,plain,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5215]) ).
fof(f5215,axiom,
class_Int_Onumber(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29422,plain,
spl625_123,
inference(avatar_split_clause,[],[f16934,f29419]) ).
fof(f29419,plain,
( spl625_123
<=> class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_123])]) ).
fof(f16934,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f5086]) ).
fof(f5086,axiom,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29417,plain,
spl625_122,
inference(avatar_split_clause,[],[f16933,f29414]) ).
fof(f29414,plain,
( spl625_122
<=> class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_122])]) ).
fof(f16933,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5016]) ).
fof(f5016,axiom,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29412,plain,
spl625_121,
inference(avatar_split_clause,[],[f16932,f29409]) ).
fof(f29409,plain,
( spl625_121
<=> class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_121])]) ).
fof(f16932,plain,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5181]) ).
fof(f5181,axiom,
class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29407,plain,
spl625_120,
inference(avatar_split_clause,[],[f16931,f29404]) ).
fof(f29404,plain,
( spl625_120
<=> class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_120])]) ).
fof(f16931,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5088]) ).
fof(f5088,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29402,plain,
spl625_119,
inference(avatar_split_clause,[],[f16930,f29399]) ).
fof(f29399,plain,
( spl625_119
<=> class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_119])]) ).
fof(f16930,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5019]) ).
fof(f5019,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29397,plain,
spl625_118,
inference(avatar_split_clause,[],[f16929,f29394]) ).
fof(f29394,plain,
( spl625_118
<=> class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_118])]) ).
fof(f16929,plain,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5183]) ).
fof(f5183,axiom,
class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29392,plain,
spl625_117,
inference(avatar_split_clause,[],[f16928,f29389]) ).
fof(f29389,plain,
( spl625_117
<=> class_Groups_Omonoid__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_117])]) ).
fof(f16928,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5113]) ).
fof(f5113,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29387,plain,
spl625_116,
inference(avatar_split_clause,[],[f16927,f29384]) ).
fof(f29384,plain,
( spl625_116
<=> class_Groups_Omonoid__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_116])]) ).
fof(f16927,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5054]) ).
fof(f5054,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29382,plain,
spl625_115,
inference(avatar_split_clause,[],[f16926,f29379]) ).
fof(f29379,plain,
( spl625_115
<=> class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_115])]) ).
fof(f16926,plain,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5204]) ).
fof(f5204,axiom,
class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29377,plain,
spl625_114,
inference(avatar_split_clause,[],[f16925,f29374]) ).
fof(f29374,plain,
( spl625_114
<=> class_Groups_Omonoid__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_114])]) ).
fof(f16925,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5114]) ).
fof(f5114,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29372,plain,
spl625_113,
inference(avatar_split_clause,[],[f16924,f29369]) ).
fof(f29369,plain,
( spl625_113
<=> class_Groups_Omonoid__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_113])]) ).
fof(f16924,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5056]) ).
fof(f5056,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29367,plain,
spl625_112,
inference(avatar_split_clause,[],[f16923,f29364]) ).
fof(f29364,plain,
( spl625_112
<=> class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_112])]) ).
fof(f16923,plain,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5205]) ).
fof(f5205,axiom,
class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29362,plain,
spl625_111,
inference(avatar_split_clause,[],[f16922,f29359]) ).
fof(f29359,plain,
( spl625_111
<=> class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_111])]) ).
fof(f16922,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(cnf_transformation,[],[f5098]) ).
fof(f5098,axiom,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29357,plain,
spl625_110,
inference(avatar_split_clause,[],[f16921,f29354]) ).
fof(f29354,plain,
( spl625_110
<=> class_Groups_Oab__semigroup__mult(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_110])]) ).
fof(f16921,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(cnf_transformation,[],[f5035]) ).
fof(f5035,axiom,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29352,plain,
spl625_109,
inference(avatar_split_clause,[],[f16920,f29349]) ).
fof(f29349,plain,
( spl625_109
<=> class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_109])]) ).
fof(f16920,plain,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5190]) ).
fof(f5190,axiom,
class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29347,plain,
spl625_108,
inference(avatar_split_clause,[],[f16919,f29344]) ).
fof(f29344,plain,
( spl625_108
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_108])]) ).
fof(f16919,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(cnf_transformation,[],[f5083]) ).
fof(f5083,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29342,plain,
spl625_107,
inference(avatar_split_clause,[],[f16918,f29339]) ).
fof(f29339,plain,
( spl625_107
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_107])]) ).
fof(f16918,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(cnf_transformation,[],[f5012]) ).
fof(f5012,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29337,plain,
spl625_106,
inference(avatar_split_clause,[],[f16917,f29334]) ).
fof(f29334,plain,
( spl625_106
<=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_106])]) ).
fof(f16917,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5178]) ).
fof(f5178,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29332,plain,
spl625_105,
inference(avatar_split_clause,[],[f16916,f29329]) ).
fof(f29329,plain,
( spl625_105
<=> class_Rings_Osemiring__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_105])]) ).
fof(f16916,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f5116]) ).
fof(f5116,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29327,plain,
spl625_104,
inference(avatar_split_clause,[],[f16915,f29324]) ).
fof(f29324,plain,
( spl625_104
<=> class_Rings_Osemiring__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_104])]) ).
fof(f16915,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5059]) ).
fof(f5059,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29322,plain,
spl625_103,
inference(avatar_split_clause,[],[f16914,f29319]) ).
fof(f29319,plain,
( spl625_103
<=> class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_103])]) ).
fof(f16914,plain,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5207]) ).
fof(f5207,axiom,
class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29317,plain,
spl625_102,
inference(avatar_split_clause,[],[f16913,f29314]) ).
fof(f29314,plain,
( spl625_102
<=> class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_102])]) ).
fof(f16913,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5087]) ).
fof(f5087,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29312,plain,
spl625_101,
inference(avatar_split_clause,[],[f16912,f29309]) ).
fof(f29309,plain,
( spl625_101
<=> class_Power_Opower(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_101])]) ).
fof(f16912,plain,
class_Power_Opower(tc_Nat_Onat),
inference(cnf_transformation,[],[f5124]) ).
fof(f5124,axiom,
class_Power_Opower(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29307,plain,
spl625_100,
inference(avatar_split_clause,[],[f16911,f29304]) ).
fof(f29304,plain,
( spl625_100
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_100])]) ).
fof(f16911,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5082]) ).
fof(f5082,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29302,plain,
spl625_99,
inference(avatar_split_clause,[],[f16910,f29299]) ).
fof(f29299,plain,
( spl625_99
<=> class_Power_Opower(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_99])]) ).
fof(f16910,plain,
class_Power_Opower(tc_Int_Oint),
inference(cnf_transformation,[],[f5074]) ).
fof(f5074,axiom,
class_Power_Opower(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29297,plain,
spl625_98,
inference(avatar_split_clause,[],[f16909,f29294]) ).
fof(f29294,plain,
( spl625_98
<=> class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_98])]) ).
fof(f16909,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5017]) ).
fof(f5017,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29292,plain,
spl625_97,
inference(avatar_split_clause,[],[f16908,f29289]) ).
fof(f29289,plain,
( spl625_97
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_97])]) ).
fof(f16908,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5011]) ).
fof(f5011,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29287,plain,
spl625_96,
inference(avatar_split_clause,[],[f16907,f29284]) ).
fof(f29284,plain,
( spl625_96
<=> class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_96])]) ).
fof(f16907,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5182]) ).
fof(f5182,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29282,plain,
spl625_95,
inference(avatar_split_clause,[],[f16906,f29279]) ).
fof(f29279,plain,
( spl625_95
<=> class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_95])]) ).
fof(f16906,plain,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5213]) ).
fof(f5213,axiom,
class_Power_Opower(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29277,plain,
spl625_94,
inference(avatar_split_clause,[],[f16905,f29274]) ).
fof(f29274,plain,
( spl625_94
<=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_94])]) ).
fof(f16905,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5177]) ).
fof(f5177,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29272,plain,
spl625_93,
inference(avatar_split_clause,[],[f16904,f29269]) ).
fof(f29269,plain,
( spl625_93
<=> class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_93])]) ).
fof(f16904,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5090]) ).
fof(f5090,axiom,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29267,plain,
spl625_92,
inference(avatar_split_clause,[],[f16903,f29264]) ).
fof(f29264,plain,
( spl625_92
<=> class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_92])]) ).
fof(f16903,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5023]) ).
fof(f5023,axiom,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29262,plain,
spl625_91,
inference(avatar_split_clause,[],[f16902,f29259]) ).
fof(f29259,plain,
( spl625_91
<=> class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_91])]) ).
fof(f16902,plain,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5185]) ).
fof(f5185,axiom,
class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29257,plain,
spl625_90,
inference(avatar_split_clause,[],[f16901,f29254]) ).
fof(f29254,plain,
( spl625_90
<=> class_Orderings_Obot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_90])]) ).
fof(f16901,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(cnf_transformation,[],[f5143]) ).
fof(f5143,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29252,plain,
spl625_89,
inference(avatar_split_clause,[],[f16900,f29249]) ).
fof(f29249,plain,
( spl625_89
<=> class_Orderings_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_89])]) ).
fof(f16900,plain,
class_Orderings_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f5122]) ).
fof(f5122,axiom,
class_Orderings_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29247,plain,
spl625_88,
inference(avatar_split_clause,[],[f16899,f29244]) ).
fof(f29244,plain,
( spl625_88
<=> class_Rings_Ono__zero__divisors(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_88])]) ).
fof(f16899,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(cnf_transformation,[],[f5102]) ).
fof(f5102,axiom,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29242,plain,
spl625_87,
inference(avatar_split_clause,[],[f16898,f29239]) ).
fof(f29239,plain,
( spl625_87
<=> class_Rings_Oordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_87])]) ).
fof(f16898,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5101]) ).
fof(f5101,axiom,
class_Rings_Oordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29237,plain,
spl625_86,
inference(avatar_split_clause,[],[f16897,f29234]) ).
fof(f29234,plain,
( spl625_86
<=> class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_86])]) ).
fof(f16897,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5092]) ).
fof(f5092,axiom,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29232,plain,
spl625_85,
inference(avatar_split_clause,[],[f16896,f29229]) ).
fof(f29229,plain,
( spl625_85
<=> class_Smallcheck_Osmall(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_85])]) ).
fof(f16896,plain,
class_Smallcheck_Osmall(tc_Int_Oint),
inference(cnf_transformation,[],[f5057]) ).
fof(f5057,axiom,
class_Smallcheck_Osmall(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29227,plain,
spl625_84,
inference(avatar_split_clause,[],[f16895,f29224]) ).
fof(f29224,plain,
( spl625_84
<=> class_Rings_Oordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_84])]) ).
fof(f16895,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5038]) ).
fof(f5038,axiom,
class_Rings_Oordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29222,plain,
spl625_83,
inference(avatar_split_clause,[],[f16894,f29219]) ).
fof(f29219,plain,
( spl625_83
<=> class_Rings_Ono__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_83])]) ).
fof(f16894,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5040]) ).
fof(f5040,axiom,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29217,plain,
spl625_82,
inference(avatar_split_clause,[],[f16893,f29214]) ).
fof(f29214,plain,
( spl625_82
<=> class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_82])]) ).
fof(f16893,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5029]) ).
fof(f5029,axiom,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29212,plain,
spl625_81,
inference(avatar_split_clause,[],[f16892,f29209]) ).
fof(f29209,plain,
( spl625_81
<=> class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_81])]) ).
fof(f16892,plain,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5187]) ).
fof(f5187,axiom,
class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29207,plain,
spl625_80,
inference(avatar_split_clause,[],[f16891,f29204]) ).
fof(f29204,plain,
( spl625_80
<=> class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_80])]) ).
fof(f16891,plain,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5193]) ).
fof(f5193,axiom,
class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29202,plain,
spl625_79,
inference(avatar_split_clause,[],[f16890,f29199]) ).
fof(f29199,plain,
( spl625_79
<=> class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_79])]) ).
fof(f16890,plain,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5194]) ).
fof(f5194,axiom,
class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29197,plain,
spl625_78,
inference(avatar_split_clause,[],[f16889,f29194]) ).
fof(f29194,plain,
( spl625_78
<=> class_Smallcheck_Osmall(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_78])]) ).
fof(f16889,plain,
class_Smallcheck_Osmall(tc_Product__Type_Ounit),
inference(cnf_transformation,[],[f5169]) ).
fof(f5169,axiom,
class_Smallcheck_Osmall(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29192,plain,
spl625_77,
inference(avatar_split_clause,[],[f16888,f29189]) ).
fof(f29189,plain,
( spl625_77
<=> class_Groups_Ouminus(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_77])]) ).
fof(f16888,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(cnf_transformation,[],[f5144]) ).
fof(f5144,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29187,plain,
spl625_76,
inference(avatar_split_clause,[],[f16887,f29184]) ).
fof(f29184,plain,
( spl625_76
<=> class_Rings_Osemiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_76])]) ).
fof(f16887,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5120]) ).
fof(f5120,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29182,plain,
spl625_75,
inference(avatar_split_clause,[],[f16886,f29179]) ).
fof(f29179,plain,
( spl625_75
<=> class_Rings_Omult__zero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_75])]) ).
fof(f16886,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(cnf_transformation,[],[f5118]) ).
fof(f5118,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29177,plain,
spl625_74,
inference(avatar_split_clause,[],[f16885,f29174]) ).
fof(f29174,plain,
( spl625_74
<=> class_Rings_Ozero__neq__one(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_74])]) ).
fof(f16885,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(cnf_transformation,[],[f5110]) ).
fof(f5110,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29172,plain,
spl625_73,
inference(avatar_split_clause,[],[f16884,f29169]) ).
fof(f29169,plain,
( spl625_73
<=> class_Groups_Ouminus(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_73])]) ).
fof(f16884,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(cnf_transformation,[],[f5069]) ).
fof(f5069,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29167,plain,
spl625_72,
inference(avatar_split_clause,[],[f16883,f29164]) ).
fof(f29164,plain,
( spl625_72
<=> class_Rings_Ozero__neq__one(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_72])]) ).
fof(f16883,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(cnf_transformation,[],[f5050]) ).
fof(f5050,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29162,plain,
spl625_71,
inference(avatar_split_clause,[],[f16882,f29159]) ).
fof(f29159,plain,
( spl625_71
<=> class_Rings_Omult__zero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_71])]) ).
fof(f16882,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(cnf_transformation,[],[f5063]) ).
fof(f5063,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29157,plain,
spl625_70,
inference(avatar_split_clause,[],[f16881,f29154]) ).
fof(f29154,plain,
( spl625_70
<=> class_Rings_Osemiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_70])]) ).
fof(f16881,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5067]) ).
fof(f5067,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29152,plain,
spl625_69,
inference(avatar_split_clause,[],[f16880,f29149]) ).
fof(f29149,plain,
( spl625_69
<=> class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_69])]) ).
fof(f16880,plain,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5210]) ).
fof(f5210,axiom,
class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29147,plain,
spl625_68,
inference(avatar_split_clause,[],[f16879,f29144]) ).
fof(f29144,plain,
( spl625_68
<=> class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_68])]) ).
fof(f16879,plain,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5201]) ).
fof(f5201,axiom,
class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29142,plain,
spl625_67,
inference(avatar_split_clause,[],[f16878,f29139]) ).
fof(f29139,plain,
( spl625_67
<=> class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_67])]) ).
fof(f16878,plain,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5208]) ).
fof(f5208,axiom,
class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29137,plain,
spl625_66,
inference(avatar_split_clause,[],[f16877,f29134]) ).
fof(f29134,plain,
( spl625_66
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_66])]) ).
fof(f16877,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5085]) ).
fof(f5085,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29132,plain,
spl625_65,
inference(avatar_split_clause,[],[f16876,f29129]) ).
fof(f29129,plain,
( spl625_65
<=> class_Rings_Olinordered__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_65])]) ).
fof(f16876,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5093]) ).
fof(f5093,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29127,plain,
spl625_64,
inference(avatar_split_clause,[],[f16875,f29124]) ).
fof(f29124,plain,
( spl625_64
<=> class_Nat_Osemiring__char__0(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_64])]) ).
fof(f16875,plain,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
inference(cnf_transformation,[],[f5109]) ).
fof(f5109,axiom,
class_Nat_Osemiring__char__0(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29122,plain,
spl625_63,
inference(avatar_split_clause,[],[f16874,f29119]) ).
fof(f29119,plain,
( spl625_63
<=> class_Groups_Oab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_63])]) ).
fof(f16874,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5100]) ).
fof(f5100,axiom,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29117,plain,
spl625_62,
inference(avatar_split_clause,[],[f16873,f29114]) ).
fof(f29114,plain,
( spl625_62
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_62])]) ).
fof(f16873,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5015]) ).
fof(f5015,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29112,plain,
spl625_61,
inference(avatar_split_clause,[],[f16872,f29109]) ).
fof(f29109,plain,
( spl625_61
<=> class_Nat_Osemiring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_61])]) ).
fof(f16872,plain,
class_Nat_Osemiring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5048]) ).
fof(f5048,axiom,
class_Nat_Osemiring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29107,plain,
spl625_60,
inference(avatar_split_clause,[],[f16871,f29104]) ).
fof(f29104,plain,
( spl625_60
<=> class_Groups_Oab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_60])]) ).
fof(f16871,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5037]) ).
fof(f5037,axiom,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29102,plain,
spl625_59,
inference(avatar_split_clause,[],[f16870,f29099]) ).
fof(f29099,plain,
( spl625_59
<=> class_Rings_Olinordered__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_59])]) ).
fof(f16870,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5030]) ).
fof(f5030,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29097,plain,
spl625_58,
inference(avatar_split_clause,[],[f16869,f29094]) ).
fof(f29094,plain,
( spl625_58
<=> class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_58])]) ).
fof(f16869,plain,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5200]) ).
fof(f5200,axiom,
class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29092,plain,
spl625_57,
inference(avatar_split_clause,[],[f16868,f29089]) ).
fof(f29089,plain,
( spl625_57
<=> class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_57])]) ).
fof(f16868,plain,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5192]) ).
fof(f5192,axiom,
class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29087,plain,
spl625_56,
inference(avatar_split_clause,[],[f16867,f29084]) ).
fof(f29084,plain,
( spl625_56
<=> class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_56])]) ).
fof(f16867,plain,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5188]) ).
fof(f5188,axiom,
class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29082,plain,
spl625_55,
inference(avatar_split_clause,[],[f16866,f29079]) ).
fof(f29079,plain,
( spl625_55
<=> class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_55])]) ).
fof(f16866,plain,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5180]) ).
fof(f5180,axiom,
class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29077,plain,
spl625_54,
inference(avatar_split_clause,[],[f16865,f29074]) ).
fof(f29074,plain,
( spl625_54
<=> class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_54])]) ).
fof(f16865,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5091]) ).
fof(f5091,axiom,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29072,plain,
spl625_53,
inference(avatar_split_clause,[],[f16864,f29069]) ).
fof(f29069,plain,
( spl625_53
<=> class_Groups_Osemigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_53])]) ).
fof(f16864,plain,
class_Groups_Osemigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5105]) ).
fof(f5105,axiom,
class_Groups_Osemigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29067,plain,
spl625_52,
inference(avatar_split_clause,[],[f16863,f29064]) ).
fof(f29064,plain,
( spl625_52
<=> class_Rings_Ocomm__semiring(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_52])]) ).
fof(f16863,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(cnf_transformation,[],[f5107]) ).
fof(f5107,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29062,plain,
spl625_51,
inference(avatar_split_clause,[],[f16862,f29059]) ).
fof(f29059,plain,
( spl625_51
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_51])]) ).
fof(f16862,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(cnf_transformation,[],[f5089]) ).
fof(f5089,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29057,plain,
spl625_50,
inference(avatar_split_clause,[],[f16861,f29054]) ).
fof(f29054,plain,
( spl625_50
<=> class_Groups_Ozero(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_50])]) ).
fof(f16861,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(cnf_transformation,[],[f5125]) ).
fof(f5125,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29052,plain,
spl625_49,
inference(avatar_split_clause,[],[f16860,f29049]) ).
fof(f29049,plain,
( spl625_49
<=> class_Groups_Oone(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_49])]) ).
fof(f16860,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(cnf_transformation,[],[f5127]) ).
fof(f5127,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29047,plain,
spl625_48,
inference(avatar_split_clause,[],[f16859,f29044]) ).
fof(f29044,plain,
( spl625_48
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_48])]) ).
fof(f16859,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(cnf_transformation,[],[f5084]) ).
fof(f5084,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29042,plain,
spl625_47,
inference(avatar_split_clause,[],[f16858,f29039]) ).
fof(f29039,plain,
( spl625_47
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_47])]) ).
fof(f16858,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5021]) ).
fof(f5021,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29037,plain,
spl625_46,
inference(avatar_split_clause,[],[f16857,f29034]) ).
fof(f29034,plain,
( spl625_46
<=> class_Groups_Oone(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_46])]) ).
fof(f16857,plain,
class_Groups_Oone(tc_Int_Oint),
inference(cnf_transformation,[],[f5079]) ).
fof(f5079,axiom,
class_Groups_Oone(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29032,plain,
spl625_45,
inference(avatar_split_clause,[],[f16856,f29029]) ).
fof(f29029,plain,
( spl625_45
<=> class_Rings_Oordered__comm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_45])]) ).
fof(f16856,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5026]) ).
fof(f5026,axiom,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29027,plain,
spl625_44,
inference(avatar_split_clause,[],[f16855,f29024]) ).
fof(f29024,plain,
( spl625_44
<=> class_Rings_Ocomm__semiring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_44])]) ).
fof(f16855,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(cnf_transformation,[],[f5047]) ).
fof(f5047,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29022,plain,
spl625_43,
inference(avatar_split_clause,[],[f16854,f29019]) ).
fof(f29019,plain,
( spl625_43
<=> class_Groups_Osemigroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_43])]) ).
fof(f16854,plain,
class_Groups_Osemigroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5045]) ).
fof(f5045,axiom,
class_Groups_Osemigroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29017,plain,
spl625_42,
inference(avatar_split_clause,[],[f16853,f29014]) ).
fof(f29014,plain,
( spl625_42
<=> class_Groups_Ozero(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_42])]) ).
fof(f16853,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(cnf_transformation,[],[f5075]) ).
fof(f5075,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29012,plain,
spl625_41,
inference(avatar_split_clause,[],[f16852,f29009]) ).
fof(f29009,plain,
( spl625_41
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_41])]) ).
fof(f16852,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5013]) ).
fof(f5013,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29007,plain,
spl625_40,
inference(avatar_split_clause,[],[f16851,f29004]) ).
fof(f29004,plain,
( spl625_40
<=> class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_40])]) ).
fof(f16851,plain,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5199]) ).
fof(f5199,axiom,
class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f29002,plain,
spl625_39,
inference(avatar_split_clause,[],[f16850,f28999]) ).
fof(f28999,plain,
( spl625_39
<=> class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_39])]) ).
fof(f16850,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5184]) ).
fof(f5184,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28997,plain,
spl625_38,
inference(avatar_split_clause,[],[f16849,f28994]) ).
fof(f28994,plain,
( spl625_38
<=> class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_38])]) ).
fof(f16849,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5179]) ).
fof(f5179,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28992,plain,
spl625_37,
inference(avatar_split_clause,[],[f16848,f28989]) ).
fof(f28989,plain,
( spl625_37
<=> class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_37])]) ).
fof(f16848,plain,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5197]) ).
fof(f5197,axiom,
class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28987,plain,
spl625_36,
inference(avatar_split_clause,[],[f16847,f28984]) ).
fof(f28984,plain,
( spl625_36
<=> class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_36])]) ).
fof(f16847,plain,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5214]) ).
fof(f5214,axiom,
class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28982,plain,
spl625_35,
inference(avatar_split_clause,[],[f16846,f28979]) ).
fof(f28979,plain,
( spl625_35
<=> class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_35])]) ).
fof(f16846,plain,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5186]) ).
fof(f5186,axiom,
class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28977,plain,
spl625_34,
inference(avatar_split_clause,[],[f16845,f28974]) ).
fof(f28974,plain,
( spl625_34
<=> class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_34])]) ).
fof(f16845,plain,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
inference(cnf_transformation,[],[f5216]) ).
fof(f5216,axiom,
class_Groups_Oone(tc_Code__Numeral_Ocode__numeral),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28972,plain,
spl625_33,
inference(avatar_split_clause,[],[f16844,f28969]) ).
fof(f28969,plain,
( spl625_33
<=> class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_33])]) ).
fof(f16844,plain,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f5130]) ).
fof(f5130,axiom,
class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28967,plain,
spl625_32,
inference(avatar_split_clause,[],[f16843,f28964]) ).
fof(f28964,plain,
( spl625_32
<=> class_Lattices_Oboolean__algebra(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_32])]) ).
fof(f16843,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(cnf_transformation,[],[f5136]) ).
fof(f5136,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28962,plain,
spl625_31,
inference(avatar_split_clause,[],[f16842,f28959]) ).
fof(f28959,plain,
( spl625_31
<=> class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_31])]) ).
fof(f16842,plain,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
inference(cnf_transformation,[],[f5131]) ).
fof(f5131,axiom,
class_Lattices_Obounded__lattice__top(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28957,plain,
spl625_30,
inference(avatar_split_clause,[],[f16841,f28954]) ).
fof(f28954,plain,
( spl625_30
<=> class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_30])]) ).
fof(f16841,plain,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
inference(cnf_transformation,[],[f5132]) ).
fof(f5132,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28952,plain,
spl625_29,
inference(avatar_split_clause,[],[f16840,f28949]) ).
fof(f28949,plain,
( spl625_29
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_29])]) ).
fof(f16840,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(cnf_transformation,[],[f5081]) ).
fof(f5081,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28947,plain,
spl625_28,
inference(avatar_split_clause,[],[f16839,f28944]) ).
fof(f28944,plain,
( spl625_28
<=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_28])]) ).
fof(f16839,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(cnf_transformation,[],[f5010]) ).
fof(f5010,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28942,plain,
spl625_27,
inference(avatar_split_clause,[],[f16838,f28939]) ).
fof(f28939,plain,
( spl625_27
<=> class_Lattices_Obounded__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_27])]) ).
fof(f16838,plain,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f4988]) ).
fof(f4988,axiom,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28937,plain,
spl625_26,
inference(avatar_split_clause,[],[f16837,f28934]) ).
fof(f28934,plain,
( spl625_26
<=> class_Orderings_Otop(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_26])]) ).
fof(f16837,plain,
class_Orderings_Otop(tc_HOL_Obool),
inference(cnf_transformation,[],[f5141]) ).
fof(f5141,axiom,
class_Orderings_Otop(tc_HOL_Obool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28932,plain,
spl625_25,
inference(avatar_split_clause,[],[f16836,f28929]) ).
fof(f16836,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5066]) ).
fof(f5066,axiom,
class_Int_Onumber__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28927,plain,
spl625_24,
inference(avatar_split_clause,[],[f16835,f28924]) ).
fof(f28924,plain,
( spl625_24
<=> class_Rings_Olinordered__idom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_24])]) ).
fof(f16835,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(cnf_transformation,[],[f5043]) ).
fof(f5043,axiom,
class_Rings_Olinordered__idom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28922,plain,
spl625_23,
inference(avatar_split_clause,[],[f16834,f28919]) ).
fof(f28919,plain,
( spl625_23
<=> class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_23])]) ).
fof(f16834,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f5018]) ).
fof(f5018,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28917,plain,
spl625_22,
inference(avatar_split_clause,[],[f16833,f28914]) ).
fof(f28914,plain,
( spl625_22
<=> class_Rings_Oring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_22])]) ).
fof(f16833,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5072]) ).
fof(f5072,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28912,plain,
spl625_21,
inference(avatar_split_clause,[],[f16832,f28909]) ).
fof(f28909,plain,
( spl625_21
<=> class_Groups_Oordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_21])]) ).
fof(f16832,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5028]) ).
fof(f5028,axiom,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28907,plain,
spl625_20,
inference(avatar_split_clause,[],[f16831,f28904]) ).
fof(f28904,plain,
( spl625_20
<=> class_Groups_Ogroup__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_20])]) ).
fof(f16831,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5061]) ).
fof(f5061,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28902,plain,
spl625_19,
inference(avatar_split_clause,[],[f16830,f28899]) ).
fof(f28899,plain,
( spl625_19
<=> class_Groups_Oab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_19])]) ).
fof(f16830,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5049]) ).
fof(f5049,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28897,plain,
spl625_18,
inference(avatar_split_clause,[],[f16829,f28894]) ).
fof(f28894,plain,
( spl625_18
<=> class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_18])]) ).
fof(f16829,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(cnf_transformation,[],[f5020]) ).
fof(f5020,axiom,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28892,plain,
spl625_17,
inference(avatar_split_clause,[],[f16828,f28889]) ).
fof(f28889,plain,
( spl625_17
<=> class_Rings_Olinordered__ring__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_17])]) ).
fof(f16828,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5024]) ).
fof(f5024,axiom,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28887,plain,
spl625_16,
inference(avatar_split_clause,[],[f16827,f28884]) ).
fof(f28884,plain,
( spl625_16
<=> class_Rings_Oring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_16])]) ).
fof(f16827,plain,
class_Rings_Oring(tc_Int_Oint),
inference(cnf_transformation,[],[f5076]) ).
fof(f5076,axiom,
class_Rings_Oring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28882,plain,
spl625_15,
inference(avatar_split_clause,[],[f16826,f28879]) ).
fof(f28879,plain,
( spl625_15
<=> class_Rings_Oordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_15])]) ).
fof(f16826,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5051]) ).
fof(f5051,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28877,plain,
spl625_14,
inference(avatar_split_clause,[],[f16825,f28874]) ).
fof(f28874,plain,
( spl625_14
<=> class_Int_Oring__char__0(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_14])]) ).
fof(f16825,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(cnf_transformation,[],[f5065]) ).
fof(f5065,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28872,plain,
spl625_13,
inference(avatar_split_clause,[],[f16824,f28869]) ).
fof(f28869,plain,
( spl625_13
<=> class_Divides_Oring__div(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_13])]) ).
fof(f16824,plain,
class_Divides_Oring__div(tc_Int_Oint),
inference(cnf_transformation,[],[f5062]) ).
fof(f5062,axiom,
class_Divides_Oring__div(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28867,plain,
spl625_12,
inference(avatar_split_clause,[],[f16823,f28864]) ).
fof(f28864,plain,
( spl625_12
<=> class_Orderings_Owellorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_12])]) ).
fof(f16823,plain,
class_Orderings_Owellorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f5108]) ).
fof(f5108,axiom,
class_Orderings_Owellorder(tc_Nat_Onat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28862,plain,
spl625_11,
inference(avatar_split_clause,[],[f16822,f28859]) ).
fof(f28859,plain,
( spl625_11
<=> class_Rings_Olinordered__ring(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_11])]) ).
fof(f16822,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(cnf_transformation,[],[f5042]) ).
fof(f5042,axiom,
class_Rings_Olinordered__ring(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28857,plain,
spl625_10,
inference(avatar_split_clause,[],[f16821,f28854]) ).
fof(f28854,plain,
( spl625_10
<=> class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_10])]) ).
fof(f16821,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5022]) ).
fof(f5022,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28852,plain,
spl625_9,
inference(avatar_split_clause,[],[f16820,f28849]) ).
fof(f28849,plain,
( spl625_9
<=> class_Groups_Osgn__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_9])]) ).
fof(f16820,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(cnf_transformation,[],[f5070]) ).
fof(f5070,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28847,plain,
spl625_8,
inference(avatar_split_clause,[],[f16819,f28844]) ).
fof(f28844,plain,
( spl625_8
<=> class_Rings_Ocomm__ring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_8])]) ).
fof(f16819,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5055]) ).
fof(f5055,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28842,plain,
spl625_7,
inference(avatar_split_clause,[],[f16818,f28839]) ).
fof(f28839,plain,
( spl625_7
<=> class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_7])]) ).
fof(f16818,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(cnf_transformation,[],[f5025]) ).
fof(f5025,axiom,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28837,plain,
spl625_6,
inference(avatar_split_clause,[],[f16817,f28834]) ).
fof(f28834,plain,
( spl625_6
<=> class_Rings_Olinordered__semiring__1(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_6])]) ).
fof(f16817,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(cnf_transformation,[],[f5027]) ).
fof(f5027,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28832,plain,
spl625_5,
inference(avatar_split_clause,[],[f16816,f28829]) ).
fof(f28829,plain,
( spl625_5
<=> class_Groups_Oabs__if(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_5])]) ).
fof(f16816,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(cnf_transformation,[],[f5071]) ).
fof(f5071,axiom,
class_Groups_Oabs__if(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28827,plain,
spl625_4,
inference(avatar_split_clause,[],[f16815,f28824]) ).
fof(f28824,plain,
( spl625_4
<=> class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_4])]) ).
fof(f16815,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(cnf_transformation,[],[f5014]) ).
fof(f5014,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28822,plain,
spl625_3,
inference(avatar_split_clause,[],[f16814,f28819]) ).
fof(f28819,plain,
( spl625_3
<=> class_Rings_Oordered__ring__abs(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_3])]) ).
fof(f16814,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(cnf_transformation,[],[f5039]) ).
fof(f5039,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28817,plain,
spl625_2,
inference(avatar_split_clause,[],[f16813,f28814]) ).
fof(f28814,plain,
( spl625_2
<=> class_Rings_Oidom(tc_Int_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_2])]) ).
fof(f16813,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(cnf_transformation,[],[f5077]) ).
fof(f5077,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
fof(f28812,plain,
~ spl625_1,
inference(avatar_split_clause,[],[f16812,f28809]) ).
fof(f28809,plain,
( spl625_1
<=> hBOOL(c_fFalse) ),
introduced(avatar_definition,[new_symbols(naming,[spl625_1])]) ).
fof(f16812,plain,
~ hBOOL(c_fFalse),
inference(cnf_transformation,[],[f5228]) ).
fof(f5228,axiom,
~ hBOOL(c_fFalse),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW317+1 : TPTP v8.2.0. Released v5.2.0.
% 0.07/0.12 % Command : run_vampire %s %d SAT
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jun 19 07:23:09 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.36 This is a FOF_THM_RFO_SEQ problem
% 0.13/0.36 Running first-order model finding
% 0.13/0.36 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc_sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.53/0.73 % (29392)Running in auto input_syntax mode. Trying TPTP
% 0.53/0.73 % (29400)fmb+10_1:1_sil=256000:i=98885:tgt=full:fmbsr=1.3:fmbss=10_0 on theBenchmark for (2999ds/98885Mi)
% 0.53/0.75 % (29392)Running in auto input_syntax mode. Trying TPTP
% 0.53/0.75 % (29401)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency:i=99418_0 on theBenchmark for (2999ds/99418Mi)
% 0.53/0.75 % (29392)Running in auto input_syntax mode. Trying TPTP
% 0.53/0.75 % (29403)fmb+10_1:1_sil=256000:fmbss=23:fmbes=contour:newcnf=on:fmbsr=1.14:i=152523:nm=2:gsp=on:rp=on_0 on theBenchmark for (2999ds/152523Mi)
% 0.53/0.75 % (29392)Running in auto input_syntax mode. Trying TPTP
% 0.53/0.75 % (29404)ott+21_1:1_sil=4000:i=104:fsd=on:fd=off:newcnf=on_0 on theBenchmark for (2999ds/104Mi)
% 0.53/0.75 % (29392)Running in auto input_syntax mode. Trying TPTP
% 0.53/0.75 % (29402)fmb+10_1:1_sil=256000:fmbes=contour:i=214858:bce=on_0 on theBenchmark for (2999ds/214858Mi)
% 0.53/0.75 % (29392)Running in auto input_syntax mode. Trying TPTP
% 0.53/0.75 % (29405)ott+11_8:59_sil=16000:sp=occurrence:lsd=20:abs=on:i=146:aac=none:nm=16:fdi=10:rawr=on:nicw=on_0 on theBenchmark for (2999ds/146Mi)
% 0.53/0.75 % (29392)Running in auto input_syntax mode. Trying TPTP
% 0.53/0.75 % (29406)ott-4_1:1_sil=4000:sp=reverse_arity:lcm=predicate:newcnf=on:i=115:bce=on:fd=off:fs=off:fsr=off_0 on theBenchmark for (2999ds/115Mi)
% 0.53/0.81 % (29404)Instruction limit reached!
% 0.53/0.81 % (29404)------------------------------
% 0.53/0.81 % (29404)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.53/0.81 % (29404)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.53/0.81 % (29404)Termination reason: Time limit
% 0.53/0.81 % (29404)Termination phase: NewCNF
% 0.53/0.81
% 0.53/0.81 % (29404)Memory used [KB]: 11506
% 0.53/0.81 % (29404)Time elapsed: 0.062 s
% 0.53/0.81 % (29404)Instructions burned: 104 (million)
% 0.53/0.82 % (29406)Instruction limit reached!
% 0.53/0.82 % (29406)------------------------------
% 0.53/0.82 % (29406)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.53/0.82 % (29406)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.53/0.82 % (29406)Termination reason: Time limit
% 0.53/0.82 % (29406)Termination phase: NewCNF
% 0.53/0.82
% 0.53/0.82 % (29406)Memory used [KB]: 12214
% 0.53/0.82 % (29406)Time elapsed: 0.068 s
% 0.53/0.82 % (29406)Instructions burned: 117 (million)
% 0.53/0.83 % (29405)Instruction limit reached!
% 0.53/0.83 % (29405)------------------------------
% 0.53/0.83 % (29405)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.53/0.83 % (29405)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.53/0.83 % (29405)Termination reason: Time limit
% 0.53/0.83 % (29405)Termination phase: Preprocessing 3
% 0.53/0.83
% 0.53/0.83 % (29405)Memory used [KB]: 11896
% 0.53/0.83 % (29405)Time elapsed: 0.076 s
% 0.53/0.83 % (29405)Instructions burned: 146 (million)
% 0.53/0.85 % (29392)Running in auto input_syntax mode. Trying TPTP
% 0.53/0.85 % (29426)dis+11_1:3_bsr=unit_only:sil=2000:rp=on:newcnf=on:i=404:kws=precedence:lsd=100_0 on theBenchmark for (2998ds/404Mi)
% 0.53/0.85 % (29392)Running in auto input_syntax mode. Trying TPTP
% 0.53/0.85 % (29429)ott-21_1:1_sil=4000:sp=const_frequency:i=175:fsr=off:fs=off:av=off_0 on theBenchmark for (2998ds/175Mi)
% 0.91/0.86 % (29392)Running in auto input_syntax mode. Trying TPTP
% 0.91/0.86 % (29433)ott+33_1:1_to=lpo:sil=8000:sp=weighted_frequency:rp=on:i=270:nm=3:fsr=off:sac=on_0 on theBenchmark for (2998ds/270Mi)
% 0.91/0.91 % (29429)Instruction limit reached!
% 0.91/0.91 % (29429)------------------------------
% 0.91/0.91 % (29429)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.91/0.91 % (29429)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.91/0.91 % (29429)Termination reason: Time limit
% 0.91/0.91 % (29429)Termination phase: Preprocessing 3
% 0.91/0.91
% 0.91/0.91 % (29429)Memory used [KB]: 12530
% 0.91/0.91 % (29429)Time elapsed: 0.060 s
% 0.91/0.91 % (29429)Instructions burned: 176 (million)
% 1.00/0.94 % (29433)Instruction limit reached!
% 1.00/0.94 % (29433)------------------------------
% 1.00/0.94 % (29433)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.00/0.94 % (29433)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.00/0.94 % (29433)Termination reason: Time limit
% 1.00/0.94 % (29433)Termination phase: Property scanning
% 1.00/0.94
% 1.00/0.94 % (29433)Memory used [KB]: 14522
% 1.00/0.94 % (29433)Time elapsed: 0.085 s
% 1.00/0.94 % (29433)Instructions burned: 270 (million)
% 1.00/0.95 % (29392)Running in auto input_syntax mode. Trying TPTP
% 1.00/0.95 % (29468)ott+4_1:1_sil=2000:i=900:bd=off:fsr=off_0 on theBenchmark for (2997ds/900Mi)
% 1.00/0.97 % (29426)Instruction limit reached!
% 1.00/0.97 % (29426)------------------------------
% 1.00/0.97 % (29426)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 1.00/0.97 % (29426)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 1.00/0.97 % (29426)Termination reason: Time limit
% 1.00/0.97 % (29426)Termination phase: Property scanning
% 1.00/0.97
% 1.00/0.97 % (29426)Memory used [KB]: 15411
% 1.00/0.97 % (29426)Time elapsed: 0.120 s
% 1.00/0.97 % (29426)Instructions burned: 406 (million)
% 1.00/0.98 % (29392)Running in auto input_syntax mode. Trying TPTP
% 1.00/0.98 % (29487)fmb+10_1:1_sil=8000:fde=unused:fmbes=contour:i=7859:nm=2:fmbswr=0_0 on theBenchmark for (2997ds/7859Mi)
% 1.00/1.01 % (29392)Running in auto input_syntax mode. Trying TPTP
% 1.00/1.01 % (29501)ott+11_1:2_anc=none:sil=2000:sp=const_max:spb=units:s2a=on:i=2145:s2at=5.0:awrs=converge:awrsf=170:rawr=on:gs=on:fsr=off_0 on theBenchmark for (2997ds/2145Mi)
% 3.86/1.21 % (29468)Instruction limit reached!
% 3.86/1.21 % (29468)------------------------------
% 3.86/1.21 % (29468)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 3.86/1.21 % (29468)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 3.86/1.21 % (29468)Termination reason: Time limit
% 3.86/1.21 % (29468)Termination phase: Saturation
% 3.86/1.21
% 3.86/1.21 % (29468)Memory used [KB]: 17014
% 3.86/1.21 % (29468)Time elapsed: 0.258 s
% 3.86/1.21 % (29468)Instructions burned: 902 (million)
% 4.21/1.24 % (29392)Running in auto input_syntax mode. Trying TPTP
% 4.21/1.24 % (29586)ott-30_1:1024_sil=4000:alpa=true:newcnf=on:i=1187:bs=unit_only:ins=1:amm=off_0 on theBenchmark for (2994ds/1187Mi)
% 5.60/1.47 % (29401)First to succeed.
% 5.72/1.50 % (29401)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-29392"
% 5.72/1.50 % (29392)Running in auto input_syntax mode. Trying TPTP
% 5.72/1.50 % (29401)Refutation found. Thanks to Tanya!
% 5.72/1.50 % SZS status Theorem for theBenchmark
% 5.72/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 5.90/1.53 % (29401)------------------------------
% 5.90/1.53 % (29401)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 5.90/1.53 % (29401)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 5.90/1.53 % (29401)Termination reason: Refutation
% 5.90/1.53
% 5.90/1.53 % (29401)Memory used [KB]: 24363
% 5.90/1.53 % (29401)Time elapsed: 0.752 s
% 5.90/1.53 % (29401)Instructions burned: 2038 (million)
% 5.90/1.53 % (29401)------------------------------
% 5.90/1.53 % (29401)------------------------------
% 5.90/1.53 % (29392)Success in time 0.842 s
%------------------------------------------------------------------------------