TSTP Solution File: LCL806-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL806-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:53:31 EDT 2024
% Result : Unsatisfiable 1.41s 0.57s
% Output : Refutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 641
% Syntax : Number of formulae : 1154 ( 437 unt; 0 def)
% Number of atoms : 2516 ( 532 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 2400 (1038 ~;1023 |; 0 &)
% ( 339 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 27 ( 2 avg)
% Number of predicates : 364 ( 362 usr; 340 prp; 0-4 aty)
% Number of functors : 77 ( 77 usr; 35 con; 0-5 aty)
% Number of variables : 2079 (2079 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5440,plain,
$false,
inference(avatar_sat_refutation,[],[f529,f534,f539,f544,f549,f554,f559,f564,f569,f574,f579,f584,f589,f594,f599,f604,f609,f614,f619,f624,f629,f634,f639,f643,f648,f653,f657,f661,f665,f669,f673,f677,f681,f685,f689,f693,f697,f701,f705,f709,f713,f717,f722,f726,f730,f734,f738,f742,f746,f750,f754,f759,f764,f770,f774,f778,f782,f786,f790,f794,f798,f802,f806,f810,f814,f818,f822,f826,f830,f834,f847,f859,f863,f867,f872,f876,f880,f884,f888,f904,f908,f912,f916,f920,f924,f928,f932,f936,f941,f946,f950,f954,f958,f1030,f1034,f1038,f1043,f1047,f1051,f1055,f1060,f1064,f1068,f1072,f1120,f1124,f1128,f1132,f1136,f1140,f1144,f1148,f1152,f1156,f1160,f1164,f1168,f1172,f1179,f1347,f1351,f1355,f1359,f1363,f1367,f1371,f1375,f1379,f1383,f1387,f1391,f1395,f1399,f1403,f1407,f1411,f1415,f1419,f1423,f1427,f1460,f1526,f1572,f1576,f1580,f1584,f1588,f1592,f1596,f1600,f1605,f1609,f1613,f1765,f1769,f1773,f1777,f1781,f1807,f1811,f1815,f1950,f1954,f1958,f1962,f1966,f1970,f1974,f1978,f1982,f1986,f1990,f1994,f2161,f2177,f2181,f2185,f2189,f2193,f2197,f2201,f2207,f2211,f2215,f2219,f2223,f2227,f2231,f2235,f2239,f2243,f2422,f2525,f2529,f2533,f2537,f2541,f2545,f2549,f2554,f2595,f2600,f2605,f2610,f2614,f2649,f2804,f2808,f2812,f2816,f2820,f2824,f2828,f2832,f2836,f2840,f2844,f2848,f2855,f2861,f2865,f2869,f2873,f3028,f3189,f3203,f3243,f3247,f3251,f3255,f3259,f3263,f3268,f3273,f3277,f3281,f3285,f3289,f3406,f3410,f3414,f3418,f3422,f3426,f3430,f3434,f3438,f3442,f3446,f3450,f3639,f3643,f3647,f3651,f3655,f3659,f3663,f3670,f3674,f3678,f4084,f4088,f4092,f4096,f4100,f4104,f4108,f4112,f4116,f4122,f4126,f4130,f4206,f4343,f4347,f4351,f4355,f4359,f4363,f4367,f4371,f4376,f4400,f4407,f4411,f4415,f4435,f4439,f4444,f4448,f4455,f4664,f4668,f4672,f4677,f4681,f4707,f4833,f4837,f4841,f4845,f4886,f4890,f4894,f4921,f4925,f4929,f4949,f4953,f4957,f4963,f4979,f4983,f5006,f5013,f5017,f5027,f5076,f5080,f5084,f5110,f5135,f5142,f5149,f5153,f5157,f5253,f5257,f5290,f5294,f5302,f5311,f5316,f5366,f5371,f5375,f5392,f5396,f5402,f5439]) ).
fof(f5439,plain,
( ~ spl0_1
| ~ spl0_2
| spl0_22
| ~ spl0_337 ),
inference(avatar_split_clause,[],[f5397,f5390,f631,f531,f526]) ).
fof(f526,plain,
( spl0_1
<=> hBOOL(hAPP(c_InductTermi_OIT,v_xb)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f531,plain,
( spl0_2
<=> hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f631,plain,
( spl0_22
<=> hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f5390,plain,
( spl0_337
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),X0),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X0),v_xc)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f5397,plain,
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,v_xb))
| spl0_22
| ~ spl0_337 ),
inference(resolution,[],[f5391,f633]) ).
fof(f633,plain,
( ~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc)))
| spl0_22 ),
inference(avatar_component_clause,[],[f631]) ).
fof(f5391,plain,
( ! [X0] :
( hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X0),v_xc)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),X0),v_T____))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X0)) )
| ~ spl0_337 ),
inference(avatar_component_clause,[],[f5390]) ).
fof(f5402,plain,
( spl0_339
| ~ spl0_60
| ~ spl0_62
| ~ spl0_64
| ~ spl0_109
| ~ spl0_250 ),
inference(avatar_split_clause,[],[f3630,f3448,f1134,f808,f800,f792,f5400]) ).
fof(f5400,plain,
( spl0_339
<=> ! [X0,X1] : c_Nat_Ocompow(c_HOL_Oone__class_Oone(tc_nat),X0,X1,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f792,plain,
( spl0_60
<=> ! [X9] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Ozero__class_Ozero(tc_nat)) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f800,plain,
( spl0_62
<=> ! [X29,X8] : c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),X29,X8,X8) = c_Fun_Oid(X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f808,plain,
( spl0_64
<=> ! [X29,X41,X8] : c_Fun_Ocomp(X29,c_Fun_Oid(X8),X8,X41,X8) = X29 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1134,plain,
( spl0_109
<=> ! [X4,X3] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f3448,plain,
( spl0_250
<=> ! [X29,X4,X8] : c_Fun_Ocomp(X29,c_Nat_Ocompow(X4,X29,X8,X8),X8,X8,X8) = c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),X29,X8,X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f3630,plain,
( ! [X0,X1] : c_Nat_Ocompow(c_HOL_Oone__class_Oone(tc_nat),X0,X1,X1) = X0
| ~ spl0_60
| ~ spl0_62
| ~ spl0_64
| ~ spl0_109
| ~ spl0_250 ),
inference(forward_demodulation,[],[f3629,f793]) ).
fof(f793,plain,
( ! [X9] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Ozero__class_Ozero(tc_nat)) = X9
| ~ spl0_60 ),
inference(avatar_component_clause,[],[f792]) ).
fof(f3629,plain,
( ! [X0,X1] : c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1,X1) = X0
| ~ spl0_62
| ~ spl0_64
| ~ spl0_109
| ~ spl0_250 ),
inference(forward_demodulation,[],[f3628,f1135]) ).
fof(f1135,plain,
( ! [X3,X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1134]) ).
fof(f3628,plain,
( ! [X0,X1] : c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X0,X1,X1) = X0
| ~ spl0_62
| ~ spl0_64
| ~ spl0_250 ),
inference(forward_demodulation,[],[f3616,f809]) ).
fof(f809,plain,
( ! [X41,X29,X8] : c_Fun_Ocomp(X29,c_Fun_Oid(X8),X8,X41,X8) = X29
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f808]) ).
fof(f3616,plain,
( ! [X0,X1] : c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X0,X1,X1) = c_Fun_Ocomp(X0,c_Fun_Oid(X1),X1,X1,X1)
| ~ spl0_62
| ~ spl0_250 ),
inference(superposition,[],[f3449,f801]) ).
fof(f801,plain,
( ! [X29,X8] : c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),X29,X8,X8) = c_Fun_Oid(X8)
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f800]) ).
fof(f3449,plain,
( ! [X29,X8,X4] : c_Fun_Ocomp(X29,c_Nat_Ocompow(X4,X29,X8,X8),X8,X8,X8) = c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),X29,X8,X8)
| ~ spl0_250 ),
inference(avatar_component_clause,[],[f3448]) ).
fof(f5396,plain,
( spl0_338
| ~ spl0_23
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f5106,f5082,f636,f5394]) ).
fof(f5394,plain,
( spl0_338
<=> ! [X0] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X0),v_xc)),v_xa))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),X0),v_T____)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f636,plain,
( spl0_23
<=> hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f5082,plain,
( spl0_320
<=> ! [X28,X34,X13,X25,X22,X66] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X66),X25),X34))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X66),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13)),X22))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X66),X13),X34)),X28),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f5106,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X0),v_xc)),v_xa))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),X0),v_T____)) )
| ~ spl0_23
| ~ spl0_320 ),
inference(resolution,[],[f5083,f638]) ).
fof(f638,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa))
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f636]) ).
fof(f5083,plain,
( ! [X28,X34,X66,X22,X25,X13] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X66),X13),X34)),X28),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X66),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13)),X22))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X66),X25),X34)) )
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f5082]) ).
fof(f5392,plain,
( spl0_337
| ~ spl0_23
| ~ spl0_319 ),
inference(avatar_split_clause,[],[f5091,f5078,f636,f5390]) ).
fof(f5078,plain,
( spl0_319
<=> ! [X61,X60,X62,X25] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X61),X25),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X25),X60)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X61),X60),v_T____)),v_b____),X62)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f5091,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),X0),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X0),v_xc)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X0)) )
| ~ spl0_23
| ~ spl0_319 ),
inference(resolution,[],[f5079,f638]) ).
fof(f5079,plain,
( ! [X62,X60,X25,X61] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X61),X60),v_T____)),v_b____),X62))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X61),X25),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X25),X60)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X25)) )
| ~ spl0_319 ),
inference(avatar_component_clause,[],[f5078]) ).
fof(f5375,plain,
( spl0_336
| ~ spl0_23
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f3615,f3444,f636,f5373]) ).
fof(f5373,plain,
( spl0_336
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_b____),X0))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),X0),v_xa)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f3444,plain,
( spl0_249
<=> ! [X28,X38,X21,X22] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X28),X38))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X38),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f3615,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_b____),X0))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),X0),v_xa)) )
| ~ spl0_23
| ~ spl0_249 ),
inference(resolution,[],[f3445,f638]) ).
fof(f3445,plain,
( ! [X21,X28,X38,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),X22))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X28),X38))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X38),X22)) )
| ~ spl0_249 ),
inference(avatar_component_clause,[],[f3444]) ).
fof(f5371,plain,
( ~ spl0_335
| ~ spl0_101
| ~ spl0_245 ),
inference(avatar_split_clause,[],[f3553,f3428,f1057,f5368]) ).
fof(f5368,plain,
( spl0_335
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Type_Otype_Otype__size(v_T____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f1057,plain,
( spl0_101
<=> v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f3428,plain,
( spl0_245
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f3553,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) != c_Type_Otype_Otype__size(v_T____)
| ~ spl0_101
| ~ spl0_245 ),
inference(superposition,[],[f3429,f1059]) ).
fof(f1059,plain,
( v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f1057]) ).
fof(f3429,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1))
| ~ spl0_245 ),
inference(avatar_component_clause,[],[f3428]) ).
fof(f5366,plain,
spl0_334,
inference(avatar_split_clause,[],[f382,f5363]) ).
fof(f5363,plain,
( spl0_334
<=> 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),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f382,axiom,
c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_bs____,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
fof(f5316,plain,
( spl0_333
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f5312,f5309,f2612,f1134,f792,f703,f5314]) ).
fof(f5314,plain,
( spl0_333
<=> ! [X28,X13,X14,X25,X20] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13)),X20),X14) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X20,X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X20),X14)),X13)
| ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f703,plain,
( spl0_39
<=> ! [X28,X15] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X28,X15) = X28 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f2612,plain,
( spl0_205
<=> ! [X4,X28,X15] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X4,X28,X15)),X15) = c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),X28,X15) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f5309,plain,
( spl0_332
<=> ! [X28,X13,X14,X25,X20] :
( ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13)),X20),X14) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),hAPP(hAPP(c_Lambda_Olift,X20),X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X20),X14)),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f5312,plain,
( ! [X28,X14,X25,X13,X20] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13)),X20),X14) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X20,X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X20),X14)),X13)
| ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_332 ),
inference(forward_demodulation,[],[f5310,f2794]) ).
fof(f2794,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lambda_Olift,X0),X1) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X0,X1)
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205 ),
inference(forward_demodulation,[],[f2793,f793]) ).
fof(f2793,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lambda_Olift,X0),X1) = c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1)
| ~ spl0_39
| ~ spl0_109
| ~ spl0_205 ),
inference(forward_demodulation,[],[f2781,f1135]) ).
fof(f2781,plain,
( ! [X0,X1] : hAPP(hAPP(c_Lambda_Olift,X0),X1) = c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),X0,X1)
| ~ spl0_39
| ~ spl0_205 ),
inference(superposition,[],[f2613,f704]) ).
fof(f704,plain,
( ! [X28,X15] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X28,X15) = X28
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f703]) ).
fof(f2613,plain,
( ! [X28,X4,X15] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X4,X28,X15)),X15) = c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),X28,X15)
| ~ spl0_205 ),
inference(avatar_component_clause,[],[f2612]) ).
fof(f5310,plain,
( ! [X28,X14,X25,X13,X20] :
( ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13)),X20),X14) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),hAPP(hAPP(c_Lambda_Olift,X20),X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X20),X14)),X13) )
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f5309]) ).
fof(f5311,plain,
spl0_332,
inference(avatar_split_clause,[],[f473,f5309]) ).
fof(f473,plain,
! [X28,X14,X25,X13,X20] :
( ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13)),X20),X14) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),hAPP(hAPP(c_Lambda_Olift,X20),X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X20),X14)),X13) ),
inference(definition_unfolding,[],[f224,f189]) ).
fof(f189,axiom,
! [X4] : c_Suc(X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).
fof(f224,axiom,
! [X28,X14,X25,X13,X20] :
( ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),hAPP(hAPP(c_Lambda_Olift,X20),X13)),c_Suc(X14))),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X20),X14)),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13)),X20),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__subst_0) ).
fof(f5302,plain,
spl0_331,
inference(avatar_split_clause,[],[f118,f5300]) ).
fof(f5300,plain,
( spl0_331
<=> ! [X35,X34,X13,X22,X36,X27,X21] :
( ~ c_Type_Otypings(X21,X27,X36)
| c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X22,X34,X21,X35),X22,tc_Type_Otype,tc_Type_Otype) = X34
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB)),X34))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),X35,tc_Lambda_OdB,tc_Lambda_OdB)),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f118,axiom,
! [X21,X36,X27,X34,X22,X35,X13] :
( ~ c_Type_Otypings(X21,X27,X36)
| c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(X22,X34,X21,X35),X22,tc_Type_Otype,tc_Type_Otype) = X34
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB)),X34))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),X35,tc_Lambda_OdB,tc_Lambda_OdB)),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_0) ).
fof(f5294,plain,
spl0_330,
inference(avatar_split_clause,[],[f364,f5292]) ).
fof(f5292,plain,
( spl0_330
<=> ! [X28,X21,X13,X64,X63,X25,X65] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X28))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
| v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X63),X64)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X25),X63))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),X13),X63)),X28),X65)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f364,axiom,
! [X21,X28,X65,X63,X25,X13,X64] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X28))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
| v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X63),X64)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X25),X63))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),X13),X63)),X28),X65)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI1_0) ).
fof(f5290,plain,
spl0_329,
inference(avatar_split_clause,[],[f363,f5288]) ).
fof(f5288,plain,
( spl0_329
<=> ! [X28,X21,X13,X64,X63,X25,X65] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X28))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
| v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X63),X64)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X25),X64))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),X13),X64)),X28),X65)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f363,axiom,
! [X21,X28,X65,X63,X25,X13,X64] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X28))
| ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
| v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X63),X64)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X25),X64))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),X13),X64)),X28),X65)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_MI2_0) ).
fof(f5257,plain,
spl0_328,
inference(avatar_split_clause,[],[f286,f5255]) ).
fof(f5255,plain,
( spl0_328
<=> ! [X28,X13,X27,X25] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X25),X13) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X25)),X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f286,axiom,
! [X28,X27,X25,X13] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X25),X13) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X25)),X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__map_0) ).
fof(f5253,plain,
spl0_327,
inference(avatar_split_clause,[],[f268,f5251]) ).
fof(f5251,plain,
( spl0_327
<=> ! [X35,X34,X13,X22,X36,X27,X21] :
( ~ c_Type_Otypings(X21,X27,X36)
| c_Type_Otypings(X21,X35,c_Type_Osko__Type__Xvar__app__types__1__1(X22,X34,X21,X35))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB)),X34))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),X35,tc_Lambda_OdB,tc_Lambda_OdB)),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f268,axiom,
! [X21,X36,X27,X34,X35,X22,X13] :
( ~ c_Type_Otypings(X21,X27,X36)
| c_Type_Otypings(X21,X35,c_Type_Osko__Type__Xvar__app__types__1__1(X22,X34,X21,X35))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB)),X34))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),X35,tc_Lambda_OdB,tc_Lambda_OdB)),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__types_1) ).
fof(f5157,plain,
( spl0_326
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_323 ),
inference(avatar_split_clause,[],[f5145,f5140,f2612,f1134,f792,f703,f5155]) ).
fof(f5155,plain,
( spl0_326
<=> ! [X13,X14,X28,X26] :
( c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X14),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,X13)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f5140,plain,
( spl0_323
<=> ! [X13,X14,X28,X26] :
( ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X14)),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X28),X13)),hAPP(hAPP(c_Lambda_Olift,X26),X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f5145,plain,
( ! [X28,X26,X14,X13] :
( c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X14),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,X13)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_323 ),
inference(forward_demodulation,[],[f5144,f2794]) ).
fof(f5144,plain,
( ! [X28,X26,X14,X13] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X14)),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,X13)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_323 ),
inference(forward_demodulation,[],[f5143,f2794]) ).
fof(f5143,plain,
( ! [X28,X26,X14,X13] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X14)),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X28),X13)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_323 ),
inference(forward_demodulation,[],[f5141,f2794]) ).
fof(f5141,plain,
( ! [X28,X26,X14,X13] :
( ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X14)),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X28),X13)),hAPP(hAPP(c_Lambda_Olift,X26),X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat))) )
| ~ spl0_323 ),
inference(avatar_component_clause,[],[f5140]) ).
fof(f5153,plain,
( spl0_325
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_322 ),
inference(avatar_split_clause,[],[f5138,f5133,f2612,f1134,f792,f703,f5151]) ).
fof(f5151,plain,
( spl0_325
<=> ! [X13,X14,X28,X26] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,X13)),X14) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X14),X13)
| ~ c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f5133,plain,
( spl0_322
<=> ! [X13,X14,X28,X26] :
( ~ c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X14)),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X26),X13)),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f5138,plain,
( ! [X28,X26,X14,X13] :
( hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,X13)),X14) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X14),X13)
| ~ c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_322 ),
inference(forward_demodulation,[],[f5137,f2794]) ).
fof(f5137,plain,
( ! [X28,X26,X14,X13] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X14)),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,X13)),X14)
| ~ c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_322 ),
inference(forward_demodulation,[],[f5136,f2794]) ).
fof(f5136,plain,
( ! [X28,X26,X14,X13] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X14)),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,X13)),X14)
| ~ c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_322 ),
inference(forward_demodulation,[],[f5134,f2794]) ).
fof(f5134,plain,
( ! [X28,X26,X14,X13] :
( ~ c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X14)),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X26),X13)),X14) )
| ~ spl0_322 ),
inference(avatar_component_clause,[],[f5133]) ).
fof(f5149,plain,
spl0_324,
inference(avatar_split_clause,[],[f374,f5147]) ).
fof(f5147,plain,
( spl0_324
<=> ! [X13,X21,X36,X27,X25,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X25),X22))
| ~ c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),X13),X22),X27,X36)
| c_Type_Otypings(X21,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X25)),X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f374,axiom,
! [X21,X36,X27,X22,X25,X13] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X25),X22))
| ~ c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),X13),X22),X27,X36)
| c_Type_Otypings(X21,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),X25)),X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),X36) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_substs__lemma_0) ).
fof(f5142,plain,
spl0_323,
inference(avatar_split_clause,[],[f115,f5140]) ).
fof(f115,axiom,
! [X28,X26,X14,X13] :
( ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X14)),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X28),X13)),hAPP(hAPP(c_Lambda_Olift,X26),X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),c_HOL_Oone__class_Oone(tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst__lt_0) ).
fof(f5135,plain,
spl0_322,
inference(avatar_split_clause,[],[f114,f5133]) ).
fof(f114,axiom,
! [X28,X26,X14,X13] :
( ~ c_HOL_Oord__class_Oless(X14,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X14)),X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X28),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,X26),X13)),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__subst_0) ).
fof(f5110,plain,
spl0_321,
inference(avatar_split_clause,[],[f451,f5108]) ).
fof(f5108,plain,
( spl0_321
<=> ! [X8,X34,X13,X21,X22] : hAPP(hAPP(hAPP(c_Type_Oshift(X8),hAPP(hAPP(hAPP(c_Type_Oshift(X8),X21),X13),X34)),c_HOL_Ozero__class_Ozero(tc_nat)),X22) = hAPP(hAPP(hAPP(c_Type_Oshift(X8),hAPP(hAPP(hAPP(c_Type_Oshift(X8),X21),c_HOL_Ozero__class_Ozero(tc_nat)),X22)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat))),X34) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f451,plain,
! [X21,X8,X34,X22,X13] : hAPP(hAPP(hAPP(c_Type_Oshift(X8),hAPP(hAPP(hAPP(c_Type_Oshift(X8),X21),X13),X34)),c_HOL_Ozero__class_Ozero(tc_nat)),X22) = hAPP(hAPP(hAPP(c_Type_Oshift(X8),hAPP(hAPP(hAPP(c_Type_Oshift(X8),X21),c_HOL_Ozero__class_Ozero(tc_nat)),X22)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat))),X34),
inference(definition_unfolding,[],[f265,f189]) ).
fof(f265,axiom,
! [X21,X8,X34,X22,X13] : hAPP(hAPP(hAPP(c_Type_Oshift(X8),hAPP(hAPP(hAPP(c_Type_Oshift(X8),X21),X13),X34)),c_HOL_Ozero__class_Ozero(tc_nat)),X22) = hAPP(hAPP(hAPP(c_Type_Oshift(X8),hAPP(hAPP(hAPP(c_Type_Oshift(X8),X21),c_HOL_Ozero__class_Ozero(tc_nat)),X22)),c_Suc(X13)),X34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__commute_0) ).
fof(f5084,plain,
spl0_320,
inference(avatar_split_clause,[],[f380,f5082]) ).
fof(f380,axiom,
! [X28,X34,X66,X25,X22,X13] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X66),X25),X34))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X66),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X25),X13)),X22))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X66),X13),X34)),X28),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
fof(f5080,plain,
spl0_319,
inference(avatar_split_clause,[],[f353,f5078]) ).
fof(f353,axiom,
! [X62,X60,X25,X61] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X25))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X61),X25),v_T____))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),X25),X60)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X61),X60),v_T____)),v_b____),X62)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_I1_J_0) ).
fof(f5076,plain,
spl0_318,
inference(avatar_split_clause,[],[f381,f5073]) ).
fof(f5073,plain,
( spl0_318
<=> c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f381,axiom,
c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f5027,plain,
( spl0_317
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_316 ),
inference(avatar_split_clause,[],[f5021,f5015,f2612,f1134,f792,f703,f5025]) ).
fof(f5025,plain,
( spl0_317
<=> ! [X13,X28,X15] :
( c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat))) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,X15),X13)
| ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f5015,plain,
( spl0_316
<=> ! [X13,X28,X15] :
( ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X28),X15)),X13) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X28),X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f5021,plain,
( ! [X28,X15,X13] :
( c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat))) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,X15),X13)
| ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_316 ),
inference(forward_demodulation,[],[f5020,f2794]) ).
fof(f5020,plain,
( ! [X28,X15,X13] :
( c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat))) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Lambda_Olift,X28),X15),X13)
| ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_316 ),
inference(forward_demodulation,[],[f5019,f2794]) ).
fof(f5019,plain,
( ! [X28,X15,X13] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X28),X15)),X13) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_316 ),
inference(forward_demodulation,[],[f5018,f2794]) ).
fof(f5018,plain,
( ! [X28,X15,X13] :
( hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X28),X15)),X13) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),hAPP(hAPP(c_Lambda_Olift,X28),X13),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))
| ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_316 ),
inference(forward_demodulation,[],[f5016,f2794]) ).
fof(f5016,plain,
( ! [X28,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X28),X15)),X13) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X28),X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat))) )
| ~ spl0_316 ),
inference(avatar_component_clause,[],[f5015]) ).
fof(f5017,plain,
spl0_316,
inference(avatar_split_clause,[],[f472,f5015]) ).
fof(f472,plain,
! [X28,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X28),X15)),X13) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X28),X13)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat))) ),
inference(definition_unfolding,[],[f233,f189]) ).
fof(f233,axiom,
! [X28,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X28),X13)),c_Suc(X15)) = hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,X28),X15)),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__lift_0) ).
fof(f5013,plain,
spl0_315,
inference(avatar_split_clause,[],[f228,f5011]) ).
fof(f5011,plain,
( spl0_315
<=> ! [X18,X7,X31,X6,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f228,axiom,
! [X31,X18,X8,X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f5006,plain,
spl0_314,
inference(avatar_split_clause,[],[f283,f5004]) ).
fof(f5004,plain,
( spl0_314
<=> ! [X2,X0,X26] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X26),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X26),c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f283,axiom,
! [X2,X0,X26] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X26))
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0)),X26),X2,tc_Lambda_OdB,tc_Lambda_OdB)))
| ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X26),c_HOL_Ozero__class_Ozero(tc_nat)),X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).
fof(f4983,plain,
( spl0_313
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f4959,f4955,f2612,f1134,f792,f703,f4981]) ).
fof(f4981,plain,
( spl0_313
<=> ! [X13,X27,X28] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,X13),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB),X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f4955,plain,
( spl0_310
<=> ! [X13,X27,X28] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X13) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X28),X13),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f4959,plain,
( ! [X28,X27,X13] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,X13),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB),X13)
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_310 ),
inference(forward_demodulation,[],[f4958,f2794]) ).
fof(f4958,plain,
( ! [X28,X27,X13] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X13) = c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,X13),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_310 ),
inference(forward_demodulation,[],[f4956,f2794]) ).
fof(f4956,plain,
( ! [X28,X27,X13] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X13) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X28),X13),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f4955]) ).
fof(f4979,plain,
( spl0_312
| ~ spl0_243
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3991,f3653,f3420,f4977]) ).
fof(f4977,plain,
( spl0_312
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),c_Lambda_OdB_OAbs(X0)))
| v_T____ = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(v_T____,v_x,X0)),c_Type_Osko__Type__Xtyping__elims__3__2(v_T____,v_x,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f3420,plain,
( spl0_243
<=> ! [X22,X21,X28] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_Lambda_OdB_OAbs(X28)),X22))
| hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X22,X21,X28)),c_Type_Osko__Type__Xtyping__elims__3__2(X22,X21,X28)) = X22 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f3653,plain,
( spl0_255
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),X0))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),X0),v_T____)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f3991,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),c_Lambda_OdB_OAbs(X0)))
| v_T____ = hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(v_T____,v_x,X0)),c_Type_Osko__Type__Xtyping__elims__3__2(v_T____,v_x,X0)) )
| ~ spl0_243
| ~ spl0_255 ),
inference(resolution,[],[f3654,f3421]) ).
fof(f3421,plain,
( ! [X21,X28,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_Lambda_OdB_OAbs(X28)),X22))
| hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X22,X21,X28)),c_Type_Osko__Type__Xtyping__elims__3__2(X22,X21,X28)) = X22 )
| ~ spl0_243 ),
inference(avatar_component_clause,[],[f3420]) ).
fof(f3654,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),X0),v_T____))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),X0)) )
| ~ spl0_255 ),
inference(avatar_component_clause,[],[f3653]) ).
fof(f4963,plain,
spl0_311,
inference(avatar_split_clause,[],[f329,f4961]) ).
fof(f4961,plain,
( spl0_311
<=> ! [X28,X26,X34,X22,X52] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X52),X28),X22))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X52),X26),hAPP(hAPP(c_Type_Otype_OFun,X22),X34)))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X52),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f329,axiom,
! [X28,X26,X52,X34,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X52),X28),X22))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X52),X26),hAPP(hAPP(c_Type_Otype_OFun,X22),X34)))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X52),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).
fof(f4957,plain,
spl0_310,
inference(avatar_split_clause,[],[f282,f4955]) ).
fof(f282,axiom,
! [X28,X27,X13] : hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X13) = c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X28),X13),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__map_0) ).
fof(f4953,plain,
spl0_309,
inference(avatar_split_clause,[],[f141,f4951]) ).
fof(f4951,plain,
( spl0_309
<=> ! [X26,X38,X28,X37] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X26),X37))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X38))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X37),X38))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f141,axiom,
! [X38,X28,X37,X26] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X26),X37))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X38))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X37),X38))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).
fof(f4949,plain,
spl0_308,
inference(avatar_split_clause,[],[f111,f4947]) ).
fof(f4947,plain,
( spl0_308
<=> ! [X13,X21,X27,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_Lambda_OdB_OVar(X13)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X22,X21,X13,X27),X22,tc_Type_Otype,tc_Type_Otype))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f111,axiom,
! [X21,X27,X22,X13] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_Lambda_OdB_OVar(X13)),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(X22,X21,X13,X27),X22,tc_Type_Otype,tc_Type_Otype))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_0) ).
fof(f4929,plain,
spl0_307,
inference(avatar_split_clause,[],[f278,f4927]) ).
fof(f4927,plain,
( spl0_307
<=> ! [X34,X13,X21,X27,X22] :
( X22 = X34
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB)),X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f278,axiom,
! [X21,X27,X34,X22,X13] :
( X22 = X34
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB)),X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
fof(f4925,plain,
spl0_306,
inference(avatar_split_clause,[],[f266,f4923]) ).
fof(f4923,plain,
( spl0_306
<=> ! [X22,X21,X28] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_Lambda_OdB_OAbs(X28)),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(X22,X21,X28))),X28),c_Type_Osko__Type__Xtyping__elims__3__2(X22,X21,X28))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f266,axiom,
! [X21,X28,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_Lambda_OdB_OAbs(X28)),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(X22,X21,X28))),X28),c_Type_Osko__Type__Xtyping__elims__3__2(X22,X21,X28))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_1) ).
fof(f4921,plain,
( spl0_305
| ~ spl0_248
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3989,f3653,f3440,f4919]) ).
fof(f4919,plain,
( spl0_305
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| c_Type_Otypings(v_x,X1,c_Type_Osko__Type__Xvar__app__typesE__1__1(v_T____,v_x,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f3440,plain,
( spl0_248
<=> ! [X13,X21,X27,X22] :
( c_Type_Otypings(X21,X27,c_Type_Osko__Type__Xvar__app__typesE__1__1(X22,X21,X13,X27))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f3989,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X0),X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| c_Type_Otypings(v_x,X1,c_Type_Osko__Type__Xvar__app__typesE__1__1(v_T____,v_x,X0,X1)) )
| ~ spl0_248
| ~ spl0_255 ),
inference(resolution,[],[f3654,f3441]) ).
fof(f3441,plain,
( ! [X21,X27,X22,X13] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22))
| c_Type_Otypings(X21,X27,c_Type_Osko__Type__Xvar__app__typesE__1__1(X22,X21,X13,X27)) )
| ~ spl0_248 ),
inference(avatar_component_clause,[],[f3440]) ).
fof(f4894,plain,
spl0_304,
inference(avatar_split_clause,[],[f271,f4892]) ).
fof(f4892,plain,
( spl0_304
<=> ! [X28,X21,X36,X27,X22] :
( ~ c_Type_Otypings(X21,X27,X36)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),c_List_Ofoldr(c_Type_Otype_OFun,X36,X22,tc_Type_Otype,tc_Type_Otype)))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f271,axiom,
! [X21,X28,X36,X27,X22] :
( ~ c_Type_Otypings(X21,X27,X36)
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),c_List_Ofoldr(c_Type_Otype_OFun,X36,X22,tc_Type_Otype,tc_Type_Otype)))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeI_0) ).
fof(f4890,plain,
spl0_303,
inference(avatar_split_clause,[],[f64,f4888]) ).
fof(f4888,plain,
( spl0_303
<=> ! [X28,X21,X27,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X22,X21,X28,X27),X22,tc_Type_Otype,tc_Type_Otype))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f64,axiom,
! [X21,X28,X27,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(X22,X21,X28,X27),X22,tc_Type_Otype,tc_Type_Otype))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_0) ).
fof(f4886,plain,
spl0_302,
inference(avatar_split_clause,[],[f63,f4884]) ).
fof(f4884,plain,
( spl0_302
<=> ! [X28,X21,X27,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X22,X21,X28,X27),X22,tc_Type_Otype,tc_Type_Otype))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f63,axiom,
! [X21,X28,X27,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(X22,X21,X28,X27),X22,tc_Type_Otype,tc_Type_Otype))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_0) ).
fof(f4845,plain,
spl0_301,
inference(avatar_split_clause,[],[f366,f4843]) ).
fof(f4843,plain,
( spl0_301
<=> ! [X28,X34,X22,X52] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X52),c_Lambda_OdB_OAbs(X28)),hAPP(hAPP(c_Type_Otype_OFun,X22),X34)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X52),c_HOL_Ozero__class_Ozero(tc_nat)),X22)),X28),X34)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f366,axiom,
! [X28,X52,X34,X22] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X52),c_Lambda_OdB_OAbs(X28)),hAPP(hAPP(c_Type_Otype_OFun,X22),X34)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X52),c_HOL_Ozero__class_Ozero(tc_nat)),X22)),X28),X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).
fof(f4841,plain,
( spl0_300
| ~ spl0_249
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3986,f3653,f3444,f4839]) ).
fof(f4839,plain,
( spl0_300
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),X0))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X1))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),X1),v_T____)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f3986,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),X0))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X1))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),X1),v_T____)) )
| ~ spl0_249
| ~ spl0_255 ),
inference(resolution,[],[f3654,f3445]) ).
fof(f4837,plain,
spl0_299,
inference(avatar_split_clause,[],[f354,f4835]) ).
fof(f4835,plain,
( spl0_299
<=> ! [X28,X15,X25,X26] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X25)),X26),X15) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X15)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X26),X15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f354,axiom,
! [X28,X26,X15,X25] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,X28),X25)),X26),X15) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X15)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X25),X26),X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
fof(f4833,plain,
spl0_298,
inference(avatar_split_clause,[],[f267,f4831]) ).
fof(f4831,plain,
( spl0_298
<=> ! [X22,X21,X28] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_Lambda_OdB_OAbs(X28)),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(X21,X28))),X28),c_Type_Osko__Type__Xabs__typeE__1__2(X21,X28))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f267,axiom,
! [X21,X28,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_Lambda_OdB_OAbs(X28)),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(X21,X28))),X28),c_Type_Osko__Type__Xabs__typeE__1__2(X21,X28))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__typeE_0) ).
fof(f4707,plain,
( spl0_297
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_294 ),
inference(avatar_split_clause,[],[f4673,f4670,f2612,f1134,f792,f703,f4705]) ).
fof(f4705,plain,
( spl0_297
<=> ! [X28,X26,X15] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X28)),X26),X15) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f4670,plain,
( spl0_294
<=> ! [X28,X26,X15] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X28)),X26),X15) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),hAPP(hAPP(c_Lambda_Olift,X26),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f4673,plain,
( ! [X28,X26,X15] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X28)),X26),X15) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat))))
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_294 ),
inference(forward_demodulation,[],[f4671,f2794]) ).
fof(f4671,plain,
( ! [X28,X26,X15] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X28)),X26),X15) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),hAPP(hAPP(c_Lambda_Olift,X26),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat))))
| ~ spl0_294 ),
inference(avatar_component_clause,[],[f4670]) ).
fof(f4681,plain,
spl0_296,
inference(avatar_split_clause,[],[f345,f4679]) ).
fof(f4679,plain,
( spl0_296
<=> ! [X59,X58,X54,X29,X11,X8,X57,X9,X46,X41,X43] :
( hAPP(X29,hAPP(X46,X9)) != hAPP(X57,hAPP(X58,X11))
| hAPP(c_Fun_Ocomp(X29,X46,X41,X8,X43),X9) = hAPP(c_Fun_Ocomp(X57,X58,X54,X8,X59),X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f345,axiom,
! [X58,X41,X29,X46,X11,X59,X8,X57,X9,X54,X43] :
( hAPP(X29,hAPP(X46,X9)) != hAPP(X57,hAPP(X58,X11))
| hAPP(c_Fun_Ocomp(X29,X46,X41,X8,X43),X9) = hAPP(c_Fun_Ocomp(X57,X58,X54,X8,X59),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
fof(f4677,plain,
spl0_295,
inference(avatar_split_clause,[],[f279,f4675]) ).
fof(f4675,plain,
( spl0_295
<=> ! [X28,X21,X25,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X25)),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X22,X21,X28,X25)),X22))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f279,axiom,
! [X21,X28,X22,X25] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X25)),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(X22,X21,X28,X25)),X22))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_0) ).
fof(f4672,plain,
spl0_294,
inference(avatar_split_clause,[],[f263,f4670]) ).
fof(f263,axiom,
! [X28,X26,X15] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(X28)),X26),X15) = c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),hAPP(hAPP(c_Lambda_Olift,X26),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Abs_0) ).
fof(f4668,plain,
spl0_293,
inference(avatar_split_clause,[],[f256,f4666]) ).
fof(f4666,plain,
( spl0_293
<=> ! [X13,X0,X28,X26] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X0),X26))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X0),X13)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f256,axiom,
! [X28,X0,X26,X13] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X0),X26))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X0),X13)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
fof(f4664,plain,
spl0_292,
inference(avatar_split_clause,[],[f255,f4662]) ).
fof(f4662,plain,
( spl0_292
<=> ! [X13,X0,X28,X26] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X0),X26))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X28),X13)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X28),X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f255,axiom,
! [X28,X0,X26,X13] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X0),X26))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X28),X13)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X28),X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
fof(f4455,plain,
( spl0_291
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_288 ),
inference(avatar_split_clause,[],[f4440,f4437,f2612,f1134,f792,f703,f4453]) ).
fof(f4453,plain,
( spl0_291
<=> ! [X28,X34,X13,X21,X22] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),X13),X34)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,X13)),X22))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f4437,plain,
( spl0_288
<=> ! [X28,X34,X13,X21,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),X13),X34)),hAPP(hAPP(c_Lambda_Olift,X28),X13)),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f4440,plain,
( ! [X21,X28,X34,X22,X13] :
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),X13),X34)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X28,X13)),X22))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),X22)) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_288 ),
inference(forward_demodulation,[],[f4438,f2794]) ).
fof(f4438,plain,
( ! [X21,X28,X34,X22,X13] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),X13),X34)),hAPP(hAPP(c_Lambda_Olift,X28),X13)),X22)) )
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f4437]) ).
fof(f4448,plain,
spl0_290,
inference(avatar_split_clause,[],[f462,f4446]) ).
fof(f4446,plain,
( spl0_290
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X4)),c_HOL_Oone__class_Oone(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f462,plain,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X4)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition_unfolding,[],[f53,f189]) ).
fof(f53,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).
fof(f4444,plain,
spl0_289,
inference(avatar_split_clause,[],[f443,f4442]) ).
fof(f4442,plain,
( spl0_289
<=> ! [X4,X3,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X15,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X4,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f443,plain,
! [X3,X4,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X15,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X4,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f42,f189,f189]) ).
fof(f42,axiom,
! [X3,X4,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X3),X4,tc_nat),c_Suc(X15),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
fof(f4439,plain,
spl0_288,
inference(avatar_split_clause,[],[f351,f4437]) ).
fof(f351,axiom,
! [X21,X28,X34,X22,X13] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),X13),X34)),hAPP(hAPP(c_Lambda_Olift,X28),X13)),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).
fof(f4435,plain,
spl0_287,
inference(avatar_split_clause,[],[f164,f4433]) ).
fof(f4433,plain,
( spl0_287
<=> ! [X10,X9,X8,X30] :
( ~ class_OrderedGroup_Osemigroup__add(X8)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X9),X10),X30,X8,X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X9),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X8),X10,X30,X8,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f164,axiom,
! [X10,X8,X9,X30] :
( ~ class_OrderedGroup_Osemigroup__add(X8)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X9),X10),X30,X8,X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X9),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X8),X10,X30,X8,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__assoc_0) ).
fof(f4415,plain,
spl0_286,
inference(avatar_split_clause,[],[f293,f4413]) ).
fof(f4413,plain,
( spl0_286
<=> ! [X34,X13,X36,X27,X21] :
( ~ c_Type_Otypings(X21,X27,X36)
| c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),X13),X34),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),X36) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f293,axiom,
! [X21,X36,X27,X34,X13] :
( ~ c_Type_Otypings(X21,X27,X36)
| c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),X21),X13),X34),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),X13),X27,tc_Lambda_OdB,tc_Lambda_OdB),X36) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__types_0) ).
fof(f4411,plain,
spl0_285,
inference(avatar_split_clause,[],[f254,f4409]) ).
fof(f4409,plain,
( spl0_285
<=> ! [X13,X0,X28,X26] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X26))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X0),X13)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f254,axiom,
! [X28,X0,X26,X13] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X26))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X0),X13)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X28),X26),X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
fof(f4407,plain,
spl0_284,
inference(avatar_split_clause,[],[f87,f4405]) ).
fof(f4405,plain,
( spl0_284
<=> ! [X2,X0,X26] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X0),X26))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X2,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f87,axiom,
! [X2,X0,X26] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X0),X26))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
fof(f4400,plain,
( spl0_283
| ~ spl0_228
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3988,f3653,f3245,f4398]) ).
fof(f4398,plain,
( spl0_283
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| c_Type_Otypings(v_x,X1,c_Type_Osko__Type__Xlist__app__typeE__1__1(v_T____,v_x,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f3245,plain,
( spl0_228
<=> ! [X28,X21,X27,X22] :
( c_Type_Otypings(X21,X27,c_Type_Osko__Type__Xlist__app__typeE__1__1(X22,X21,X28,X27))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f3988,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| c_Type_Otypings(v_x,X1,c_Type_Osko__Type__Xlist__app__typeE__1__1(v_T____,v_x,X0,X1)) )
| ~ spl0_228
| ~ spl0_255 ),
inference(resolution,[],[f3654,f3246]) ).
fof(f3246,plain,
( ! [X21,X28,X27,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22))
| c_Type_Otypings(X21,X27,c_Type_Osko__Type__Xlist__app__typeE__1__1(X22,X21,X28,X27)) )
| ~ spl0_228 ),
inference(avatar_component_clause,[],[f3245]) ).
fof(f4376,plain,
spl0_282,
inference(avatar_split_clause,[],[f450,f4373]) ).
fof(f4373,plain,
( spl0_282
<=> hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f450,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
inference(definition_unfolding,[],[f274,f151]) ).
fof(f151,axiom,
v_n____ = v_i____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_True_0) ).
fof(f274,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_headT_0) ).
fof(f4371,plain,
spl0_281,
inference(avatar_split_clause,[],[f202,f4369]) ).
fof(f4369,plain,
( spl0_281
<=> ! [X18,X31,X6,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X18)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f202,axiom,
! [X31,X18,X8,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X18)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f4367,plain,
spl0_280,
inference(avatar_split_clause,[],[f201,f4365]) ).
fof(f4365,plain,
( spl0_280
<=> ! [X31,X7,X6,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7)),X31) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31)),X7) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f201,axiom,
! [X31,X8,X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7)),X31) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31)),X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f4363,plain,
spl0_279,
inference(avatar_split_clause,[],[f199,f4361]) ).
fof(f4361,plain,
( spl0_279
<=> ! [X31,X7,X6,X8] :
( ~ class_OrderedGroup_Oab__semigroup__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7)),X31) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f199,axiom,
! [X31,X8,X6,X7] :
( ~ class_OrderedGroup_Oab__semigroup__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7)),X31) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f4359,plain,
( spl0_278
| ~ spl0_229
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3987,f3653,f3249,f4357]) ).
fof(f4357,plain,
( spl0_278
<=> ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| c_Type_Otypings(v_x,X1,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T____,v_x,X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f3249,plain,
( spl0_229
<=> ! [X28,X21,X27,X22] :
( c_Type_Otypings(X21,X27,c_Type_Osko__Type__Xlist__app__typeD__1__1(X22,X21,X28,X27))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f3987,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)))
| c_Type_Otypings(v_x,X1,c_Type_Osko__Type__Xlist__app__typeD__1__1(v_T____,v_x,X0,X1)) )
| ~ spl0_229
| ~ spl0_255 ),
inference(resolution,[],[f3654,f3250]) ).
fof(f3250,plain,
( ! [X21,X28,X27,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22))
| c_Type_Otypings(X21,X27,c_Type_Osko__Type__Xlist__app__typeD__1__1(X22,X21,X28,X27)) )
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f3249]) ).
fof(f4355,plain,
spl0_277,
inference(avatar_split_clause,[],[f198,f4353]) ).
fof(f4353,plain,
( spl0_277
<=> ! [X31,X7,X6,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X31)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f198,axiom,
! [X31,X8,X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X31)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f4351,plain,
spl0_276,
inference(avatar_split_clause,[],[f197,f4349]) ).
fof(f4349,plain,
( spl0_276
<=> ! [X31,X7,X6,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7)),X31) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f197,axiom,
! [X31,X8,X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7)),X31) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f4347,plain,
spl0_275,
inference(avatar_split_clause,[],[f193,f4345]) ).
fof(f4345,plain,
( spl0_275
<=> ! [X40,X10,X9,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X10),X40)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X9),X10)),X40) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f193,axiom,
! [X40,X10,X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X10),X40)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X9),X10)),X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).
fof(f4343,plain,
spl0_274,
inference(avatar_split_clause,[],[f186,f4341]) ).
fof(f4341,plain,
( spl0_274
<=> ! [X3,X4,X29,X8] : c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),X29,X8,X8) = c_Fun_Ocomp(c_Nat_Ocompow(X3,X29,X8,X8),c_Nat_Ocompow(X4,X29,X8,X8),X8,X8,X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f186,axiom,
! [X3,X29,X8,X4] : c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),X29,X8,X8) = c_Fun_Ocomp(c_Nat_Ocompow(X3,X29,X8,X8),c_Nat_Ocompow(X4,X29,X8,X8),X8,X8,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funpow__add_0) ).
fof(f4206,plain,
( spl0_273
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_269 ),
inference(avatar_split_clause,[],[f4118,f4114,f2612,f1134,f792,f703,f4204]) ).
fof(f4204,plain,
( spl0_273
<=> ! [X13,X0,X26] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X0,X13)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,X13)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X0),X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f4114,plain,
( spl0_269
<=> ! [X13,X0,X26] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X0),X26))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X0),X13)),hAPP(hAPP(c_Lambda_Olift,X26),X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f4118,plain,
( ! [X0,X26,X13] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X0,X13)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,X13)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X0),X26)) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_269 ),
inference(forward_demodulation,[],[f4117,f2794]) ).
fof(f4117,plain,
( ! [X0,X26,X13] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X0),X13)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,X13)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X0),X26)) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_269 ),
inference(forward_demodulation,[],[f4115,f2794]) ).
fof(f4115,plain,
( ! [X0,X26,X13] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X0),X26))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X0),X13)),hAPP(hAPP(c_Lambda_Olift,X26),X13))) )
| ~ spl0_269 ),
inference(avatar_component_clause,[],[f4114]) ).
fof(f4130,plain,
spl0_272,
inference(avatar_split_clause,[],[f497,f4128]) ).
fof(f4128,plain,
( spl0_272
<=> ! [X24,X23] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X23),X24),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X23,tc_Type_Otype)),c_Nat_Osize__class_Osize(X24,tc_Type_Otype))),c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f497,plain,
! [X24,X23] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X23),X24),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X23,tc_Type_Otype)),c_Nat_Osize__class_Osize(X24,tc_Type_Otype))),c_HOL_Oone__class_Oone(tc_nat)),
inference(forward_demodulation,[],[f496,f238]) ).
fof(f238,axiom,
! [X9] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Ozero__class_Ozero(tc_nat)) = X9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).
fof(f496,plain,
! [X24,X23] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X23),X24),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X23,tc_Type_Otype)),c_Nat_Osize__class_Osize(X24,tc_Type_Otype))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(forward_demodulation,[],[f448,f167]) ).
fof(f167,axiom,
! [X3,X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X3) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f448,plain,
! [X24,X23] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X23),X24),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X23,tc_Type_Otype)),c_Nat_Osize__class_Osize(X24,tc_Type_Otype))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
inference(definition_unfolding,[],[f55,f189]) ).
fof(f55,axiom,
! [X24,X23] : c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,X23),X24),tc_Type_Otype) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(X23,tc_Type_Otype)),c_Nat_Osize__class_Osize(X24,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osize_I4_J_0) ).
fof(f4126,plain,
spl0_271,
inference(avatar_split_clause,[],[f371,f4124]) ).
fof(f4124,plain,
( spl0_271
<=> ! [X13,X0,X28,X26] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X26))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X28),X13)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X28),X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f371,axiom,
! [X28,X0,X26,X13] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X26))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),X28),X13)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X28),X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
fof(f4122,plain,
spl0_270,
inference(avatar_split_clause,[],[f344,f4120]) ).
fof(f4120,plain,
( spl0_270
<=> ! [X31,X41,X18,X54,X6,X7,X8,X43,X20] :
( hAPP(X6,hAPP(X7,X20)) = hAPP(X31,hAPP(X18,X20))
| c_Fun_Ocomp(X6,X7,X43,X41,X8) != c_Fun_Ocomp(X31,X18,X54,X41,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f344,axiom,
! [X31,X41,X18,X8,X6,X54,X7,X43,X20] :
( hAPP(X6,hAPP(X7,X20)) = hAPP(X31,hAPP(X18,X20))
| c_Fun_Ocomp(X6,X7,X43,X41,X8) != c_Fun_Ocomp(X31,X18,X54,X41,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
fof(f4116,plain,
spl0_269,
inference(avatar_split_clause,[],[f270,f4114]) ).
fof(f270,axiom,
! [X0,X26,X13] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X0),X26))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,X0),X13)),hAPP(hAPP(c_Lambda_Olift,X26),X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).
fof(f4112,plain,
( spl0_268
| ~ spl0_138
| ~ spl0_255 ),
inference(avatar_split_clause,[],[f3990,f3653,f1417,f4110]) ).
fof(f4110,plain,
( spl0_268
<=> ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),c_Lambda_OdB_OVar(X0)))
| v_T____ = hAPP(v_x,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f1417,plain,
( spl0_138
<=> ! [X22,X21,X13] :
( hAPP(X21,X13) = X22
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_Lambda_OdB_OVar(X13)),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f3990,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),c_Lambda_OdB_OVar(X0)))
| v_T____ = hAPP(v_x,X0) )
| ~ spl0_138
| ~ spl0_255 ),
inference(resolution,[],[f3654,f1418]) ).
fof(f1418,plain,
( ! [X21,X22,X13] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_Lambda_OdB_OVar(X13)),X22))
| hAPP(X21,X13) = X22 )
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1417]) ).
fof(f4108,plain,
spl0_267,
inference(avatar_split_clause,[],[f264,f4106]) ).
fof(f4106,plain,
( spl0_267
<=> ! [X28,X38,X21,X22] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X38))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X38),X22)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f264,axiom,
! [X38,X28,X21,X22] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X38))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X38),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
fof(f4104,plain,
spl0_266,
inference(avatar_split_clause,[],[f261,f4102]) ).
fof(f4102,plain,
( spl0_266
<=> ! [X28,X21,X25,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X25)),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X25),c_Type_Osko__Type__Xtyping__elims__2__1(X22,X21,X28,X25))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f261,axiom,
! [X21,X28,X22,X25] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X25)),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X25),c_Type_Osko__Type__Xtyping__elims__2__1(X22,X21,X28,X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I2_J_1) ).
fof(f4100,plain,
spl0_265,
inference(avatar_split_clause,[],[f183,f4098]) ).
fof(f4098,plain,
( spl0_265
<=> ! [X10,X40,X0,X9,X8] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X9),X10))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X10),X40))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X9),X40)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f183,axiom,
! [X40,X10,X0,X8,X9] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X9),X10))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X10),X40))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X9),X40)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
fof(f4096,plain,
spl0_264,
inference(avatar_split_clause,[],[f143,f4094]) ).
fof(f4094,plain,
( spl0_264
<=> ! [X38,X28,X26] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X38))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X38))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f143,axiom,
! [X38,X28,X26] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X28),X38))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X38))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
fof(f4092,plain,
spl0_263,
inference(avatar_split_clause,[],[f142,f4090]) ).
fof(f4090,plain,
( spl0_263
<=> ! [X37,X28,X26] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X26),X37))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X37),X28))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f142,axiom,
! [X28,X37,X26] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X26),X37))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),hAPP(hAPP(c_Lambda_OdB_OApp,X37),X28))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
fof(f4088,plain,
spl0_262,
inference(avatar_split_clause,[],[f78,f4086]) ).
fof(f4086,plain,
( spl0_262
<=> ! [X18,X7,X31,X6,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8)
| ~ c_HOL_Oord__class_Oless(X31,X18,X8)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X18),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f78,axiom,
! [X31,X18,X8,X6,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8)
| ~ c_HOL_Oord__class_Oless(X31,X18,X8)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X18),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f4084,plain,
spl0_261,
inference(avatar_split_clause,[],[f56,f4082]) ).
fof(f4082,plain,
( spl0_261
<=> ! [X20,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X20))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X4,X1,X20),tc_Lambda_OdB,tc_Lambda_OdB) = X20 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f56,axiom,
! [X1,X4,X20] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X20))
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X4,X1,X20),tc_Lambda_OdB,tc_Lambda_OdB) = X20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
fof(f3678,plain,
spl0_260,
inference(avatar_split_clause,[],[f479,f3676]) ).
fof(f3676,plain,
( spl0_260
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)) = X4
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f479,plain,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)) = X4
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X4,tc_nat) ),
inference(definition_unfolding,[],[f216,f189,f189]) ).
fof(f216,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_Suc(X3) = X4
| c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
fof(f3674,plain,
spl0_259,
inference(avatar_split_clause,[],[f346,f3672]) ).
fof(f3672,plain,
( spl0_259
<=> ! [X41,X54,X53,X8,X29,X43,X46] : c_Fun_Ofcomp(c_Fun_Ofcomp(X29,X46,X8,X54,X43),X53,X8,X43,X41) = c_Fun_Ofcomp(X29,c_Fun_Ofcomp(X46,X53,X54,X43,X41),X8,X54,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f346,axiom,
! [X41,X29,X46,X8,X54,X53,X43] : c_Fun_Ofcomp(c_Fun_Ofcomp(X29,X46,X8,X54,X43),X53,X8,X43,X41) = c_Fun_Ofcomp(X29,c_Fun_Ofcomp(X46,X53,X54,X43,X41),X8,X54,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__assoc_0) ).
fof(f3670,plain,
spl0_258,
inference(avatar_split_clause,[],[f333,f3668]) ).
fof(f3668,plain,
( spl0_258
<=> ! [X41,X43,X54,X53,X29,X8,X46] : c_Fun_Ocomp(X29,c_Fun_Ocomp(X46,X53,X54,X43,X8),X43,X41,X8) = c_Fun_Ocomp(c_Fun_Ocomp(X29,X46,X43,X41,X54),X53,X54,X41,X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f333,axiom,
! [X41,X29,X46,X54,X8,X53,X43] : c_Fun_Ocomp(X29,c_Fun_Ocomp(X46,X53,X54,X43,X8),X43,X41,X8) = c_Fun_Ocomp(c_Fun_Ocomp(X29,X46,X43,X41,X54),X53,X54,X41,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
fof(f3663,plain,
spl0_257,
inference(avatar_split_clause,[],[f307,f3661]) ).
fof(f3661,plain,
( spl0_257
<=> ! [X28,X26,X15] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),X15) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X26),X15)),hAPP(hAPP(c_Lambda_Olift,X28),X15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f307,axiom,
! [X28,X26,X15] : hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28)),X15) = hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,X26),X15)),hAPP(hAPP(c_Lambda_Olift,X28),X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
fof(f3659,plain,
spl0_256,
inference(avatar_split_clause,[],[f296,f3657]) ).
fof(f3657,plain,
( spl0_256
<=> ! [X31,X43,X41,X20,X6,X8,X7] :
( hAPP(X6,hAPP(X7,X20)) = hAPP(X31,X20)
| c_Fun_Ocomp(X6,X7,X43,X41,X8) != c_Fun_Ocomp(c_Fun_Oid(X41),X31,X41,X41,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f296,axiom,
! [X31,X41,X8,X6,X7,X43,X20] :
( hAPP(X6,hAPP(X7,X20)) = hAPP(X31,X20)
| c_Fun_Ocomp(X6,X7,X43,X41,X8) != c_Fun_Ocomp(c_Fun_Oid(X41),X31,X41,X41,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).
fof(f3655,plain,
( spl0_255
| ~ spl0_2
| ~ spl0_249 ),
inference(avatar_split_clause,[],[f3606,f3444,f531,f3653]) ).
fof(f3606,plain,
( ! [X0] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,v_xb),X0))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),X0),v_T____)) )
| ~ spl0_2
| ~ spl0_249 ),
inference(resolution,[],[f3445,f533]) ).
fof(f533,plain,
( hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f3651,plain,
spl0_254,
inference(avatar_split_clause,[],[f215,f3649]) ).
fof(f3649,plain,
( spl0_254
<=> ! [X6,X8,X33] :
( ~ class_OrderedGroup_Omonoid__add(X8)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X8),X6,X33,X8,X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X8),X33,c_HOL_Ozero__class_Ozero(X8),X8,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f215,axiom,
! [X8,X6,X33] :
( ~ class_OrderedGroup_Omonoid__add(X8)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X8),X6,X33,X8,X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X8),X33,c_HOL_Ozero__class_Ozero(X8),X8,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1__lemma_0) ).
fof(f3647,plain,
spl0_253,
inference(avatar_split_clause,[],[f196,f3645]) ).
fof(f3645,plain,
( spl0_253
<=> ! [X4,X3,X15] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f196,axiom,
! [X3,X4,X15] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)),X15) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
fof(f3643,plain,
spl0_252,
inference(avatar_split_clause,[],[f195,f3641]) ).
fof(f3641,plain,
( spl0_252
<=> ! [X9,X40,X10] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X40)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X40)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f195,axiom,
! [X40,X10,X9] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),X40)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X10),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X40)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
fof(f3639,plain,
spl0_251,
inference(avatar_split_clause,[],[f70,f3637]) ).
fof(f3637,plain,
( spl0_251
<=> ! [X9,X8,X30] :
( ~ class_OrderedGroup_Omonoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X9),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X8),c_HOL_Ozero__class_Ozero(X8),X30,X8,X8)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X8),X9,X30,X8,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f70,axiom,
! [X8,X9,X30] :
( ~ class_OrderedGroup_Omonoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X9),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X8),c_HOL_Ozero__class_Ozero(X8),X30,X8,X8)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X8),X9,X30,X8,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__absorb0_0) ).
fof(f3450,plain,
spl0_250,
inference(avatar_split_clause,[],[f442,f3448]) ).
fof(f442,plain,
! [X29,X8,X4] : c_Fun_Ocomp(X29,c_Nat_Ocompow(X4,X29,X8,X8),X8,X8,X8) = c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),X29,X8,X8),
inference(definition_unfolding,[],[f66,f189]) ).
fof(f66,axiom,
! [X29,X8,X4] : c_Nat_Ocompow(c_Suc(X4),X29,X8,X8) = c_Fun_Ocomp(X29,c_Nat_Ocompow(X4,X29,X8,X8),X8,X8,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funpow_Osimps_I2_J_0) ).
fof(f3446,plain,
spl0_249,
inference(avatar_split_clause,[],[f355,f3444]) ).
fof(f355,axiom,
! [X38,X28,X21,X22] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X28),X38))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X28),X22))
| hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),X38),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
fof(f3442,plain,
spl0_248,
inference(avatar_split_clause,[],[f269,f3440]) ).
fof(f269,axiom,
! [X21,X27,X22,X13] :
( c_Type_Otypings(X21,X27,c_Type_Osko__Type__Xvar__app__typesE__1__1(X22,X21,X13,X27))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X13),X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__typesE_1) ).
fof(f3438,plain,
spl0_247,
inference(avatar_split_clause,[],[f144,f3436]) ).
fof(f3436,plain,
( spl0_247
<=> ! [X2,X0,X26] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X26))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X2,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f144,axiom,
! [X2,X0,X26] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X26))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X2,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
fof(f3434,plain,
spl0_246,
inference(avatar_split_clause,[],[f128,f3432]) ).
fof(f3432,plain,
( spl0_246
<=> ! [X6,X8,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X7,X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f128,axiom,
! [X8,X6,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X7,X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f3430,plain,
( spl0_245
| ~ spl0_78
| ~ spl0_238 ),
inference(avatar_split_clause,[],[f3315,f3287,f882,f3428]) ).
fof(f882,plain,
( spl0_78
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f3287,plain,
( spl0_238
<=> ! [X24,X23] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X23),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X23)),c_Type_Otype_Otype__size(X24))),c_HOL_Oone__class_Oone(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f3315,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X0),X1))
| ~ spl0_78
| ~ spl0_238 ),
inference(superposition,[],[f883,f3288]) ).
fof(f3288,plain,
( ! [X24,X23] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X23),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X23)),c_Type_Otype_Otype__size(X24))),c_HOL_Oone__class_Oone(tc_nat))
| ~ spl0_238 ),
inference(avatar_component_clause,[],[f3287]) ).
fof(f883,plain,
( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat))
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f882]) ).
fof(f3426,plain,
spl0_244,
inference(avatar_split_clause,[],[f122,f3424]) ).
fof(f3424,plain,
( spl0_244
<=> ! [X6,X8,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7),c_HOL_Ozero__class_Ozero(X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f122,axiom,
! [X8,X6,X7] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X8)
| ~ c_HOL_Oord__class_Oless(X6,c_HOL_Ozero__class_Ozero(X8),X8)
| ~ c_HOL_Oord__class_Oless(X7,c_HOL_Ozero__class_Ozero(X8),X8)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7),c_HOL_Ozero__class_Ozero(X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f3422,plain,
spl0_243,
inference(avatar_split_clause,[],[f117,f3420]) ).
fof(f117,axiom,
! [X21,X28,X22] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_Lambda_OdB_OAbs(X28)),X22))
| hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(X22,X21,X28)),c_Type_Osko__Type__Xtyping__elims__3__2(X22,X21,X28)) = X22 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I3_J_0) ).
fof(f3418,plain,
spl0_242,
inference(avatar_split_clause,[],[f110,f3416]) ).
fof(f3416,plain,
( spl0_242
<=> ! [X31,X0,X6,X8,X7] :
( ~ hBOOL(hAPP(hAPP(X0,X7),X31))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X6),X7))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X6),X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f110,axiom,
! [X31,X0,X8,X6,X7] :
( ~ hBOOL(hAPP(hAPP(X0,X7),X31))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X6),X7))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X6),X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
fof(f3414,plain,
spl0_241,
inference(avatar_split_clause,[],[f109,f3412]) ).
fof(f3412,plain,
( spl0_241
<=> ! [X31,X0,X6,X8,X7] :
( ~ hBOOL(hAPP(hAPP(X0,X6),X7))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X7),X31))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X6),X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f109,axiom,
! [X31,X0,X8,X6,X7] :
( ~ hBOOL(hAPP(hAPP(X0,X6),X7))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X7),X31))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X6),X31)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
fof(f3410,plain,
spl0_240,
inference(avatar_split_clause,[],[f79,f3408]) ).
fof(f3408,plain,
( spl0_240
<=> ! [X17,X13,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X17,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X17),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f79,axiom,
! [X14,X17,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X15,X17,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X17),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
fof(f3406,plain,
spl0_239,
inference(avatar_split_clause,[],[f50,f3404]) ).
fof(f3404,plain,
( spl0_239
<=> ! [X8,X13,X21,X14,X22] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X8),X21),X13),X22),X14) = hAPP(X21,c_HOL_Ominus__class_Ominus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f50,axiom,
! [X21,X8,X14,X22,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X8),X21),X13),X22),X14) = hAPP(X21,c_HOL_Ominus__class_Ominus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__lt_0) ).
fof(f3289,plain,
spl0_238,
inference(avatar_split_clause,[],[f495,f3287]) ).
fof(f495,plain,
! [X24,X23] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X23),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X23)),c_Type_Otype_Otype__size(X24))),c_HOL_Oone__class_Oone(tc_nat)),
inference(forward_demodulation,[],[f494,f238]) ).
fof(f494,plain,
! [X24,X23] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X23),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X23)),c_Type_Otype_Otype__size(X24))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(forward_demodulation,[],[f447,f167]) ).
fof(f447,plain,
! [X24,X23] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X23),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X23)),c_Type_Otype_Otype__size(X24))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))),
inference(definition_unfolding,[],[f54,f189]) ).
fof(f54,axiom,
! [X24,X23] : c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,X23),X24)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(X23)),c_Type_Otype_Otype__size(X24))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osize_I2_J_0) ).
fof(f3285,plain,
spl0_237,
inference(avatar_split_clause,[],[f453,f3283]) ).
fof(f3283,plain,
( spl0_237
<=> ! [X4,X13,X16,X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X16,X4,hAPP(X16,X13),X8) = c_Nat_Osemiring__1__class_Oof__nat__aux(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),X13,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f453,plain,
! [X8,X16,X4,X13] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X16,X4,hAPP(X16,X13),X8) = c_Nat_Osemiring__1__class_Oof__nat__aux(X16,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),X13,X8) ),
inference(definition_unfolding,[],[f30,f189]) ).
fof(f30,axiom,
! [X8,X16,X4,X13] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X16,c_Suc(X4),X13,X8) = c_Nat_Osemiring__1__class_Oof__nat__aux(X16,X4,hAPP(X16,X13),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__aux_Osimps_I2_J_0) ).
fof(f3281,plain,
spl0_236,
inference(avatar_split_clause,[],[f452,f3279]) ).
fof(f3279,plain,
( spl0_236
<=> ! [X8,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_HOL_Oone__class_Oone(X8)),c_Nat_Osemiring__1__class_Oof__nat(X3,X8)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f452,plain,
! [X3,X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_HOL_Oone__class_Oone(X8)),c_Nat_Osemiring__1__class_Oof__nat(X3,X8)) = c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),X8) ),
inference(definition_unfolding,[],[f212,f189]) ).
fof(f212,axiom,
! [X3,X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat(c_Suc(X3),X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_HOL_Oone__class_Oone(X8)),c_Nat_Osemiring__1__class_Oof__nat(X3,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).
fof(f3277,plain,
( spl0_235
| ~ spl0_38
| ~ spl0_43
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1681,f1574,f720,f699,f3275]) ).
fof(f3275,plain,
( spl0_235
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f699,plain,
( spl0_38
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f720,plain,
( spl0_43
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1574,plain,
( spl0_144
<=> ! [X13,X14,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X13,X14,tc_nat),X15,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X13,X15,tc_nat),X14,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1681,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat)
| ~ spl0_38
| ~ spl0_43
| ~ spl0_144 ),
inference(forward_demodulation,[],[f1652,f721]) ).
fof(f721,plain,
( ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ spl0_43 ),
inference(avatar_component_clause,[],[f720]) ).
fof(f1652,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ spl0_38
| ~ spl0_144 ),
inference(superposition,[],[f1575,f700]) ).
fof(f700,plain,
( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f699]) ).
fof(f1575,plain,
( ! [X14,X15,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X13,X14,tc_nat),X15,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X13,X15,tc_nat),X14,tc_nat)
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1574]) ).
fof(f3273,plain,
spl0_234,
inference(avatar_split_clause,[],[f446,f3270]) ).
fof(f3270,plain,
( spl0_234
<=> hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f446,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
inference(definition_unfolding,[],[f260,f151]) ).
fof(f260,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nT_0) ).
fof(f3268,plain,
spl0_233,
inference(avatar_split_clause,[],[f445,f3265]) ).
fof(f3265,plain,
( spl0_233
<=> hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f445,plain,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)),
inference(definition_unfolding,[],[f65,f151]) ).
fof(f65,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I2_J_0) ).
fof(f3263,plain,
spl0_232,
inference(avatar_split_clause,[],[f166,f3261]) ).
fof(f3261,plain,
( spl0_232
<=> ! [X17,X4,X3,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X17,tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f166,axiom,
! [X3,X4,X17,X15] :
( ~ c_HOL_Oord__class_Oless(X15,X17,tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X17) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
fof(f3259,plain,
spl0_231,
inference(avatar_split_clause,[],[f105,f3257]) ).
fof(f3257,plain,
( spl0_231
<=> ! [X4,X8,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_Nat_Osemiring__1__class_Oof__nat(X3,X8)),c_Nat_Osemiring__1__class_Oof__nat(X4,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f105,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),X8) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_Nat_Osemiring__1__class_Oof__nat(X3,X8)),c_Nat_Osemiring__1__class_Oof__nat(X4,X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
fof(f3255,plain,
spl0_230,
inference(avatar_split_clause,[],[f62,f3253]) ).
fof(f3253,plain,
( spl0_230
<=> ! [X4,X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat(X4,X8) = c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(X8,X8,X8),c_HOL_Oplus__class_Oplus(X8)),c_HOL_Oone__class_Oone(X8)),X4,c_HOL_Ozero__class_Ozero(X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f62,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat(X4,X8) = c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(X8,X8,X8),c_HOL_Oplus__class_Oplus(X8)),c_HOL_Oone__class_Oone(X8)),X4,c_HOL_Ozero__class_Ozero(X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_semiring__1__class_Oof__nat__code_0) ).
fof(f3251,plain,
spl0_229,
inference(avatar_split_clause,[],[f60,f3249]) ).
fof(f60,axiom,
! [X21,X28,X27,X22] :
( c_Type_Otypings(X21,X27,c_Type_Osko__Type__Xlist__app__typeD__1__1(X22,X21,X28,X27))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeD_1) ).
fof(f3247,plain,
spl0_228,
inference(avatar_split_clause,[],[f59,f3245]) ).
fof(f59,axiom,
! [X21,X28,X27,X22] :
( c_Type_Otypings(X21,X27,c_Type_Osko__Type__Xlist__app__typeE__1__1(X22,X21,X28,X27))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_List_Ofoldl(c_Lambda_OdB_OApp,X28,X27,tc_Lambda_OdB,tc_Lambda_OdB)),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_list__app__typeE_1) ).
fof(f3243,plain,
spl0_227,
inference(avatar_split_clause,[],[f1,f3241]) ).
fof(f3241,plain,
( spl0_227
<=> ! [X2,X0,X1] :
( ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB)
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X2,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f1,axiom,
! [X2,X0,X1] :
( ~ c_ListOrder_Ostep1(c_Lambda_Obeta,X1,X2,tc_Lambda_OdB)
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X1,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X2,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
fof(f3203,plain,
( spl0_226
| ~ spl0_61
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1565,f1425,f796,f3201]) ).
fof(f3201,plain,
( spl0_226
<=> ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f796,plain,
( spl0_61
<=> ! [X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X4) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1425,plain,
( spl0_140
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1565,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat) )
| ~ spl0_61
| ~ spl0_140 ),
inference(superposition,[],[f1426,f797]) ).
fof(f797,plain,
( ! [X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X4) = X4
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f796]) ).
fof(f1426,plain,
( ! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1425]) ).
fof(f3189,plain,
( spl0_225
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f2857,f2853,f2612,f1134,f792,f703,f3187]) ).
fof(f3187,plain,
( spl0_225
<=> ! [X13,X0,X26] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X0,X13)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,X13)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X26)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f2853,plain,
( spl0_219
<=> ! [X13,X0,X26] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X26))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X0),X13)),hAPP(hAPP(c_Lambda_Olift,X26),X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f2857,plain,
( ! [X0,X26,X13] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X0,X13)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,X13)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X26)) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_219 ),
inference(forward_demodulation,[],[f2856,f2794]) ).
fof(f2856,plain,
( ! [X0,X26,X13] :
( hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X0),X13)),c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),X26,X13)))
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X26)) )
| ~ spl0_39
| ~ spl0_60
| ~ spl0_109
| ~ spl0_205
| ~ spl0_219 ),
inference(forward_demodulation,[],[f2854,f2794]) ).
fof(f2854,plain,
( ! [X0,X26,X13] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X26))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X0),X13)),hAPP(hAPP(c_Lambda_Olift,X26),X13))) )
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f2853]) ).
fof(f3028,plain,
( spl0_224
| ~ spl0_101
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1530,f1413,f1057,f3026]) ).
fof(f3026,plain,
( spl0_224
<=> ! [X0,X1] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X0),X1)
| v_T_H_H____ = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1413,plain,
( spl0_137
<=> ! [X24,X55,X56,X23] :
( X23 = X55
| hAPP(hAPP(c_Type_Otype_OFun,X23),X24) != hAPP(hAPP(c_Type_Otype_OFun,X55),X56) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1530,plain,
( ! [X0,X1] :
( v_T____ != hAPP(hAPP(c_Type_Otype_OFun,X0),X1)
| v_T_H_H____ = X0 )
| ~ spl0_101
| ~ spl0_137 ),
inference(superposition,[],[f1414,f1059]) ).
fof(f1414,plain,
( ! [X56,X55,X24,X23] :
( hAPP(hAPP(c_Type_Otype_OFun,X23),X24) != hAPP(hAPP(c_Type_Otype_OFun,X55),X56)
| X23 = X55 )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1413]) ).
fof(f2873,plain,
spl0_223,
inference(avatar_split_clause,[],[f466,f2871]) ).
fof(f2871,plain,
( spl0_223
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f466,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f249,f189,f189]) ).
fof(f249,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
fof(f2869,plain,
spl0_222,
inference(avatar_split_clause,[],[f297,f2867]) ).
fof(f2867,plain,
( spl0_222
<=> ! [X41,X29,X46,X8,X33,X43] : c_List_Omap(X29,c_List_Omap(X46,X33,X43,X41),X41,X8) = c_List_Omap(c_Fun_Ocomp(X29,X46,X41,X8,X43),X33,X43,X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f297,axiom,
! [X41,X29,X46,X8,X43,X33] : c_List_Omap(X29,c_List_Omap(X46,X33,X43,X41),X41,X8) = c_List_Omap(c_Fun_Ocomp(X29,X46,X41,X8,X43),X33,X43,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__map_0) ).
fof(f2865,plain,
spl0_221,
inference(avatar_split_clause,[],[f295,f2863]) ).
fof(f2863,plain,
( spl0_221
<=> ! [X25,X28,X26] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X26),X28))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X25),X26)),hAPP(hAPP(c_Lambda_OdB_OApp,X25),X28))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f295,axiom,
! [X28,X26,X25] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X26),X28))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X25),X26)),hAPP(hAPP(c_Lambda_OdB_OApp,X25),X28))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
fof(f2861,plain,
spl0_220,
inference(avatar_split_clause,[],[f294,f2859]) ).
fof(f2859,plain,
( spl0_220
<=> ! [X25,X28,X26] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X26),X28))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X25)),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X25))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f294,axiom,
! [X28,X26,X25] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X26),X28))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X25)),hAPP(hAPP(c_Lambda_OdB_OApp,X28),X25))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
fof(f2855,plain,
spl0_219,
inference(avatar_split_clause,[],[f291,f2853]) ).
fof(f291,axiom,
! [X0,X26,X13] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X0),X26))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,X0),X13)),hAPP(hAPP(c_Lambda_Olift,X26),X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
fof(f2848,plain,
spl0_218,
inference(avatar_split_clause,[],[f285,f2846]) ).
fof(f2846,plain,
( spl0_218
<=> ! [X27] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X27,tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),X27,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f285,axiom,
! [X27] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X27,tc_Lambda_OdB)
| c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),X27,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lifts__IT_0) ).
fof(f2844,plain,
spl0_217,
inference(avatar_split_clause,[],[f229,f2842]) ).
fof(f2842,plain,
( spl0_217
<=> ! [X15,X4,X28,X26] : c_Lambda_Oliftn(X4,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28),X15) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X4,X26,X15)),c_Lambda_Oliftn(X4,X28,X15)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f229,axiom,
! [X28,X26,X4,X15] : c_Lambda_Oliftn(X4,hAPP(hAPP(c_Lambda_OdB_OApp,X26),X28),X15) = hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(X4,X26,X15)),c_Lambda_Oliftn(X4,X28,X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
fof(f2840,plain,
spl0_216,
inference(avatar_split_clause,[],[f138,f2838]) ).
fof(f2838,plain,
( spl0_216
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f138,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
fof(f2836,plain,
spl0_215,
inference(avatar_split_clause,[],[f130,f2834]) ).
fof(f2834,plain,
( spl0_215
<=> ! [X31,X7,X6,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| ~ c_HOL_Oord__class_Oless(X7,X31,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f130,axiom,
! [X31,X8,X6,X7] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| ~ c_HOL_Oord__class_Oless(X7,X31,X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),X6,X8)
| c_HOL_Oord__class_Oless(X7,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f2832,plain,
spl0_214,
inference(avatar_split_clause,[],[f98,f2830]) ).
fof(f2830,plain,
( spl0_214
<=> ! [X31,X7,X6,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| c_HOL_Oord__class_Oless(X6,X7,X8)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X7),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f98,axiom,
! [X31,X8,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| c_HOL_Oord__class_Oless(X6,X7,X8)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X7),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f2828,plain,
spl0_213,
inference(avatar_split_clause,[],[f97,f2826]) ).
fof(f2826,plain,
( spl0_213
<=> ! [X31,X7,X6,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X7),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f97,axiom,
! [X31,X8,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X7),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f2824,plain,
spl0_212,
inference(avatar_split_clause,[],[f96,f2822]) ).
fof(f2822,plain,
( spl0_212
<=> ! [X31,X7,X6,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X7),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f96,axiom,
! [X31,X8,X6,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X6),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X7),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f2820,plain,
spl0_211,
inference(avatar_split_clause,[],[f95,f2818]) ).
fof(f2818,plain,
( spl0_211
<=> ! [X31,X7,X6,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| c_HOL_Oord__class_Oless(X6,X7,X8)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X31),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f95,axiom,
! [X31,X8,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| c_HOL_Oord__class_Oless(X6,X7,X8)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X31),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f2816,plain,
spl0_210,
inference(avatar_split_clause,[],[f94,f2814]) ).
fof(f2814,plain,
( spl0_210
<=> ! [X31,X7,X6,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X31),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f94,axiom,
! [X31,X8,X6,X7] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X31),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f2812,plain,
spl0_209,
inference(avatar_split_clause,[],[f93,f2810]) ).
fof(f2810,plain,
( spl0_209
<=> ! [X31,X7,X6,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X31),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f93,axiom,
! [X31,X8,X6,X7] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X31),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f2808,plain,
( spl0_208
| ~ spl0_29
| ~ spl0_198 ),
inference(avatar_split_clause,[],[f2742,f2543,f663,f2806]) ).
fof(f2806,plain,
( spl0_208
<=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X2) != hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f663,plain,
( spl0_29
<=> ! [X48,X39] : c_Lambda_OdB_OVar(X39) != c_Lambda_OdB_OAbs(X48) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f2543,plain,
( spl0_198
<=> ! [X26,X15] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X26)),X15) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f2742,plain,
( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X2) != hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X0)),X1)
| ~ spl0_29
| ~ spl0_198 ),
inference(superposition,[],[f664,f2544]) ).
fof(f2544,plain,
( ! [X26,X15] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X26)),X15) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat))))
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f2543]) ).
fof(f664,plain,
( ! [X39,X48] : c_Lambda_OdB_OVar(X39) != c_Lambda_OdB_OAbs(X48)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f663]) ).
fof(f2804,plain,
spl0_207,
inference(avatar_split_clause,[],[f44,f2802]) ).
fof(f2802,plain,
( spl0_207
<=> ! [X20,X1,X4] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X1,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X4,X1,X20),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X20)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f44,axiom,
! [X1,X4,X20] :
( c_ListOrder_Ostep1(c_Lambda_Obeta,X1,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(X4,X1,X20),tc_Lambda_OdB)
| ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB)),X20)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
fof(f2649,plain,
( spl0_206
| ~ spl0_78
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1200,f1134,f882,f2647]) ).
fof(f2647,plain,
( spl0_206
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1200,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0)
| ~ spl0_78
| ~ spl0_109 ),
inference(superposition,[],[f883,f1135]) ).
fof(f2614,plain,
spl0_205,
inference(avatar_split_clause,[],[f437,f2612]) ).
fof(f437,plain,
! [X28,X4,X15] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X4,X28,X15)),X15) = c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),X28,X15),
inference(definition_unfolding,[],[f159,f189]) ).
fof(f159,axiom,
! [X28,X4,X15] : c_Lambda_Oliftn(c_Suc(X4),X28,X15) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(X4,X28,X15)),X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
fof(f2610,plain,
spl0_204,
inference(avatar_split_clause,[],[f383,f2607]) ).
fof(f2607,plain,
( spl0_204
<=> hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__CHAINED__1(v_T____,v_b____,v_e____,v_i____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f383,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__CHAINED__1(v_T____,v_b____,v_e____,v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_1) ).
fof(f2605,plain,
spl0_203,
inference(avatar_split_clause,[],[f373,f2602]) ).
fof(f2602,plain,
( spl0_203
<=> hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__1__1(v_T____,v_b____,v_e____,v_i____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f373,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__1__1(v_T____,v_b____,v_e____,v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_I1_J_1) ).
fof(f2600,plain,
spl0_202,
inference(avatar_split_clause,[],[f369,f2597]) ).
fof(f2597,plain,
( spl0_202
<=> hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_b____,v_e____,v_i____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f369,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_b____,v_e____,v_i____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Cons_Ohyps_I1_J_1) ).
fof(f2595,plain,
spl0_201,
inference(avatar_split_clause,[],[f209,f2593]) ).
fof(f2593,plain,
( spl0_201
<=> ! [X4,X9,X29,X8] : hAPP(X29,hAPP(c_Nat_Ocompow(X4,X29,X8,X8),X9)) = hAPP(c_Nat_Ocompow(X4,X29,X8,X8),hAPP(X29,X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f209,axiom,
! [X29,X8,X9,X4] : hAPP(X29,hAPP(c_Nat_Ocompow(X4,X29,X8,X8),X9)) = hAPP(c_Nat_Ocompow(X4,X29,X8,X8),hAPP(X29,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funpow__swap1_0) ).
fof(f2554,plain,
( spl0_200
| ~ spl0_28
| ~ spl0_165
| ~ spl0_199 ),
inference(avatar_split_clause,[],[f2550,f2547,f1960,f659,f2552]) ).
fof(f2552,plain,
( spl0_200
<=> ! [X13,X15] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X13)),X15) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_OdB_OVar(X13),c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X13,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f659,plain,
( spl0_28
<=> ! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1960,plain,
( spl0_165
<=> ! [X13,X4,X15] :
( c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X13),X15) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f2547,plain,
( spl0_199
<=> ! [X13,X15] :
( c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X13)),X15) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f2550,plain,
( ! [X15,X13] :
( hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X13)),X15) = c_Lambda_Oliftn(c_HOL_Oone__class_Oone(tc_nat),c_Lambda_OdB_OVar(X13),c_HOL_Ozero__class_Ozero(tc_nat))
| c_HOL_Oord__class_Oless(X13,X15,tc_nat) )
| ~ spl0_28
| ~ spl0_165
| ~ spl0_199 ),
inference(forward_demodulation,[],[f2548,f2078]) ).
fof(f2078,plain,
( ! [X0,X1] : c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X1),X0)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_28
| ~ spl0_165 ),
inference(resolution,[],[f1961,f660]) ).
fof(f660,plain,
( ! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f1961,plain,
( ! [X4,X15,X13] :
( c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X13),X15) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X4)) )
| ~ spl0_165 ),
inference(avatar_component_clause,[],[f1960]) ).
fof(f2548,plain,
( ! [X15,X13] :
( c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X13)),X15) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat))) )
| ~ spl0_199 ),
inference(avatar_component_clause,[],[f2547]) ).
fof(f2549,plain,
spl0_199,
inference(avatar_split_clause,[],[f116,f2547]) ).
fof(f116,axiom,
! [X15,X13] :
( c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X13)),X15) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_1) ).
fof(f2545,plain,
spl0_198,
inference(avatar_split_clause,[],[f108,f2543]) ).
fof(f108,axiom,
! [X26,X15] : hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(X26)),X15) = c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,X26),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I3_J_0) ).
fof(f2541,plain,
( spl0_197
| ~ spl0_79
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1199,f1134,f886,f2539]) ).
fof(f2539,plain,
( spl0_197
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f886,plain,
( spl0_79
<=> ! [X9] : c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1199,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0),tc_nat)
| ~ spl0_79
| ~ spl0_109 ),
inference(superposition,[],[f887,f1135]) ).
fof(f887,plain,
( ! [X9] : c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f886]) ).
fof(f2537,plain,
spl0_196,
inference(avatar_split_clause,[],[f85,f2535]) ).
fof(f2535,plain,
( spl0_196
<=> ! [X8,X33] :
( ~ class_OrderedGroup_Omonoid__add(X8)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X8),c_HOL_Ozero__class_Ozero(X8),X33,X8,X8) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X8),X33,c_HOL_Ozero__class_Ozero(X8),X8,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f85,axiom,
! [X8,X33] :
( ~ class_OrderedGroup_Omonoid__add(X8)
| c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X8),c_HOL_Ozero__class_Ozero(X8),X33,X8,X8) = c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X8),X33,c_HOL_Ozero__class_Ozero(X8),X8,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__foldr1_0) ).
fof(f2533,plain,
spl0_195,
inference(avatar_split_clause,[],[f57,f2531]) ).
fof(f2531,plain,
( spl0_195
<=> ! [X13,X25,X14] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X14)),X25),X13) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f57,axiom,
! [X14,X25,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X14)),X25),X13) = c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X14,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__gt_0) ).
fof(f2529,plain,
spl0_194,
inference(avatar_split_clause,[],[f37,f2527]) ).
fof(f2527,plain,
( spl0_194
<=> ! [X4,X3,X15] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X4),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f37,axiom,
! [X3,X4,X15] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X4),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
fof(f2525,plain,
spl0_193,
inference(avatar_split_clause,[],[f36,f2523]) ).
fof(f2523,plain,
( spl0_193
<=> ! [X4,X3,X15] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X15),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f36,axiom,
! [X3,X4,X15] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X15),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
fof(f2422,plain,
( spl0_192
| ~ spl0_31
| ~ spl0_92 ),
inference(avatar_split_clause,[],[f1018,f952,f671,f2420]) ).
fof(f2420,plain,
( spl0_192
<=> ! [X0,X1] : hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,c_Fun_Oid(X0)),c_Lambda_OdB_OVar(X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f671,plain,
( spl0_31
<=> ! [X9,X8] : hAPP(c_Fun_Oid(X8),X9) = X9 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f952,plain,
( spl0_92
<=> ! [X9,X52] : hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X52),c_Lambda_OdB_OVar(X9)),hAPP(X52,X9))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1018,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,c_Fun_Oid(X0)),c_Lambda_OdB_OVar(X1)),X1))
| ~ spl0_31
| ~ spl0_92 ),
inference(superposition,[],[f953,f672]) ).
fof(f672,plain,
( ! [X8,X9] : hAPP(c_Fun_Oid(X8),X9) = X9
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f671]) ).
fof(f953,plain,
( ! [X9,X52] : hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X52),c_Lambda_OdB_OVar(X9)),hAPP(X52,X9)))
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f952]) ).
fof(f2243,plain,
spl0_191,
inference(avatar_split_clause,[],[f503,f2241]) ).
fof(f2241,plain,
( spl0_191
<=> ! [X4] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f503,plain,
! [X4] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(forward_demodulation,[],[f468,f167]) ).
fof(f468,plain,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X4 ),
inference(definition_unfolding,[],[f51,f189]) ).
fof(f51,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Suc(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).
fof(f2239,plain,
spl0_190,
inference(avatar_split_clause,[],[f478,f2237]) ).
fof(f2237,plain,
( spl0_190
<=> ! [X13,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X15,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f478,plain,
! [X14,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X15,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),X15,tc_nat) ),
inference(definition_unfolding,[],[f84,f189]) ).
fof(f84,axiom,
! [X14,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X15,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X13),X15,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
fof(f2235,plain,
spl0_189,
inference(avatar_split_clause,[],[f359,f2233]) ).
fof(f2233,plain,
( spl0_189
<=> ! [X8,X13,X21,X14,X22] :
( ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X8),X21),X13),X22),X14) = hAPP(X21,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f359,axiom,
! [X21,X8,X14,X22,X13] :
( ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X8),X21),X13),X22),X14) = hAPP(X21,X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__gt_0) ).
fof(f2231,plain,
spl0_188,
inference(avatar_split_clause,[],[f318,f2229]) ).
fof(f2229,plain,
( spl0_188
<=> ! [X28,X26] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26)),X28)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X28),c_HOL_Ozero__class_Ozero(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f318,axiom,
! [X28,X26] : hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26)),X28)),hAPP(hAPP(hAPP(c_Lambda_Osubst,X26),X28),c_HOL_Ozero__class_Ozero(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
fof(f2227,plain,
spl0_187,
inference(avatar_split_clause,[],[f306,f2225]) ).
fof(f2225,plain,
( spl0_187
<=> ! [X13,X26,X15] :
( X13 = X15
| c_HOL_Oord__class_Oless(X15,X13,tc_nat)
| c_Lambda_OdB_OVar(X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X13)),X26),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f306,axiom,
! [X26,X15,X13] :
( X13 = X15
| c_HOL_Oord__class_Oless(X15,X13,tc_nat)
| c_Lambda_OdB_OVar(X13) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X13)),X26),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).
fof(f2223,plain,
spl0_186,
inference(avatar_split_clause,[],[f259,f2221]) ).
fof(f2221,plain,
( spl0_186
<=> ! [X4,X3,X2,X1] :
( X3 = X4
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f259,axiom,
! [X2,X3,X1,X4] :
( X3 = X4
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
fof(f2219,plain,
spl0_185,
inference(avatar_split_clause,[],[f258,f2217]) ).
fof(f2217,plain,
( spl0_185
<=> ! [X2,X1,X3,X4] :
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f258,axiom,
! [X2,X3,X1,X4] :
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X3),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
fof(f2215,plain,
spl0_184,
inference(avatar_split_clause,[],[f223,f2213]) ).
fof(f2213,plain,
( spl0_184
<=> ! [X31,X7,X6,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X8)
| X7 = X31
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X6) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f223,axiom,
! [X31,X8,X6,X7] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X8)
| X7 = X31
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X31),X6) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f2211,plain,
spl0_183,
inference(avatar_split_clause,[],[f222,f2209]) ).
fof(f2209,plain,
( spl0_183
<=> ! [X31,X7,X6,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X8)
| X7 = X31
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f222,axiom,
! [X31,X8,X6,X7] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X8)
| X7 = X31
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f2207,plain,
spl0_182,
inference(avatar_split_clause,[],[f221,f2205]) ).
fof(f2205,plain,
( spl0_182
<=> ! [X31,X7,X6,X8] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X8)
| X7 = X31
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f221,axiom,
! [X31,X8,X6,X7] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X8)
| X7 = X31
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X31) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f2201,plain,
spl0_181,
inference(avatar_split_clause,[],[f150,f2199]) ).
fof(f2199,plain,
( spl0_181
<=> ! [X37,X26] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X26),X37))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X26)),c_Lambda_OdB_OAbs(X37))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f150,axiom,
! [X37,X26] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),X26),X37))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(X26)),c_Lambda_OdB_OAbs(X37))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
fof(f2197,plain,
spl0_180,
inference(avatar_split_clause,[],[f147,f2195]) ).
fof(f2195,plain,
( spl0_180
<=> ! [X26,X0,X2,X1] :
( X0 = X26
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26),X2,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f147,axiom,
! [X2,X0,X1,X26] :
( X0 = X26
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
fof(f2193,plain,
spl0_179,
inference(avatar_split_clause,[],[f146,f2191]) ).
fof(f2191,plain,
( spl0_179
<=> ! [X2,X0,X1,X26] :
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26),X2,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f146,axiom,
! [X2,X0,X1,X26] :
( X1 = X2
| c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0),X1,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
fof(f2189,plain,
spl0_178,
inference(avatar_split_clause,[],[f101,f2187]) ).
fof(f2187,plain,
( spl0_178
<=> ! [X4,X3,X15] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f101,axiom,
! [X3,X4,X15] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
fof(f2185,plain,
spl0_177,
inference(avatar_split_clause,[],[f100,f2183]) ).
fof(f2183,plain,
( spl0_177
<=> ! [X4,X3,X15] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f100,axiom,
! [X3,X4,X15] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X3),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
fof(f2181,plain,
spl0_176,
inference(avatar_split_clause,[],[f99,f2179]) ).
fof(f2179,plain,
( spl0_176
<=> ! [X13,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X15),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f99,axiom,
! [X14,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X15),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X15),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
fof(f2177,plain,
spl0_175,
inference(avatar_split_clause,[],[f24,f2175]) ).
fof(f2175,plain,
( spl0_175
<=> ! [X4,X17,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X17,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,X4,tc_nat),c_HOL_Ominus__class_Ominus(X17,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f24,axiom,
! [X3,X4,X17] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X17,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X17,X4,tc_nat),c_HOL_Ominus__class_Ominus(X17,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
fof(f2161,plain,
( spl0_174
| ~ spl0_29
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2116,f1964,f663,f2159]) ).
fof(f2159,plain,
( spl0_174
<=> ! [X2,X0,X1,X3] : c_Lambda_OdB_OVar(X3) != c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1964,plain,
( spl0_166
<=> ! [X4,X26,X15] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OAbs(X26),X15) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X4,X26,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f2116,plain,
( ! [X2,X3,X0,X1] : c_Lambda_OdB_OVar(X3) != c_Lambda_Oliftn(X0,c_Lambda_OdB_OAbs(X1),X2)
| ~ spl0_29
| ~ spl0_166 ),
inference(superposition,[],[f664,f1965]) ).
fof(f1965,plain,
( ! [X26,X4,X15] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OAbs(X26),X15) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X4,X26,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat))))
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1964]) ).
fof(f1994,plain,
spl0_173,
inference(avatar_split_clause,[],[f521,f1992]) ).
fof(f1992,plain,
( spl0_173
<=> ! [X4,X3] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
| c_HOL_Oone__class_Oone(tc_nat) = X4
| c_HOL_Oone__class_Oone(tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f521,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
| c_HOL_Oone__class_Oone(tc_nat) = X4
| c_HOL_Oone__class_Oone(tc_nat) = X3 ),
inference(forward_demodulation,[],[f520,f239]) ).
fof(f239,axiom,
! [X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),X4) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f520,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) = X4
| c_HOL_Oone__class_Oone(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f519,f239]) ).
fof(f519,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f486,f239]) ).
fof(f486,plain,
! [X3,X4] :
( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition_unfolding,[],[f68,f189,f189,f189]) ).
fof(f68,axiom,
! [X3,X4] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).
fof(f1990,plain,
spl0_172,
inference(avatar_split_clause,[],[f516,f1988]) ).
fof(f1988,plain,
( spl0_172
<=> ! [X4,X3] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
| c_HOL_Oone__class_Oone(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f516,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
| c_HOL_Oone__class_Oone(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ),
inference(forward_demodulation,[],[f515,f239]) ).
fof(f515,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f484,f239]) ).
fof(f484,plain,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition_unfolding,[],[f226,f189,f189]) ).
fof(f226,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).
fof(f1986,plain,
( spl0_171
| ~ spl0_110
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1536,f1421,f1138,f1984]) ).
fof(f1984,plain,
( spl0_171
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f1138,plain,
( spl0_110
<=> ! [X13,X3,X14] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X14),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1421,plain,
( spl0_139
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1536,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oone__class_Oone(tc_nat),tc_nat) )
| ~ spl0_110
| ~ spl0_139 ),
inference(resolution,[],[f1422,f1139]) ).
fof(f1139,plain,
( ! [X3,X14,X13] :
( c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X14),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1138]) ).
fof(f1422,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1421]) ).
fof(f1982,plain,
spl0_170,
inference(avatar_split_clause,[],[f512,f1980]) ).
fof(f1980,plain,
( spl0_170
<=> ! [X4,X3] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
| c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f512,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
| c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 ),
inference(forward_demodulation,[],[f511,f239]) ).
fof(f511,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(forward_demodulation,[],[f482,f239]) ).
fof(f482,plain,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition_unfolding,[],[f211,f189,f189]) ).
fof(f211,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).
fof(f1978,plain,
spl0_169,
inference(avatar_split_clause,[],[f509,f1976]) ).
fof(f1976,plain,
( spl0_169
<=> ! [X4,X3] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f509,plain,
! [X3,X4] :
( c_HOL_Oone__class_Oone(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4)
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 ),
inference(forward_demodulation,[],[f480,f239]) ).
fof(f480,plain,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(definition_unfolding,[],[f107,f189]) ).
fof(f107,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).
fof(f1974,plain,
spl0_168,
inference(avatar_split_clause,[],[f474,f1972]) ).
fof(f1972,plain,
( spl0_168
<=> ! [X4,X3] :
( X3 = X4
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f474,plain,
! [X3,X4] :
( X3 = X4
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f74,f189]) ).
fof(f74,axiom,
! [X3,X4] :
( X3 = X4
| c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
fof(f1970,plain,
spl0_167,
inference(avatar_split_clause,[],[f153,f1968]) ).
fof(f1968,plain,
( spl0_167
<=> ! [X6,X8,X33] :
( ~ class_OrderedGroup_Oab__semigroup__add(X8)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X8),X33,X6,X8,X8) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X8),X6,X33,X8,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f153,axiom,
! [X8,X6,X33] :
( ~ class_OrderedGroup_Oab__semigroup__add(X8)
| c_List_Ofoldr(c_HOL_Oplus__class_Oplus(X8),X33,X6,X8,X8) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(X8),X6,X33,X8,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldr__conv__foldl_0) ).
fof(f1966,plain,
spl0_166,
inference(avatar_split_clause,[],[f77,f1964]) ).
fof(f77,axiom,
! [X26,X4,X15] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OAbs(X26),X15) = c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X4,X26,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X15),c_HOL_Oone__class_Oone(tc_nat)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I3_J_0) ).
fof(f1962,plain,
spl0_165,
inference(avatar_split_clause,[],[f76,f1960]) ).
fof(f76,axiom,
! [X4,X15,X13] :
( c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X13),X15) = c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
fof(f1958,plain,
spl0_164,
inference(avatar_split_clause,[],[f32,f1956]) ).
fof(f1956,plain,
( spl0_164
<=> ! [X13,X14,X15] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X13,X14,tc_nat),X15,tc_nat) = c_HOL_Ominus__class_Ominus(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X15),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f32,axiom,
! [X14,X15,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X13,X14,tc_nat),X15,tc_nat) = c_HOL_Ominus__class_Ominus(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X15),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
fof(f1954,plain,
spl0_163,
inference(avatar_split_clause,[],[f14,f1952]) ).
fof(f1952,plain,
( spl0_163
<=> ! [X4,X3] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X4,X3,tc_nat)
| c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f14,axiom,
! [X3,X4] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X4,X3,tc_nat)
| c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
fof(f1950,plain,
spl0_162,
inference(avatar_split_clause,[],[f2,f1948]) ).
fof(f1948,plain,
( spl0_162
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f2,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).
fof(f1815,plain,
spl0_161,
inference(avatar_split_clause,[],[f505,f1813]) ).
fof(f1813,plain,
( spl0_161
<=> ! [X13,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X13,tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f505,plain,
! [X4,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X13,tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
inference(forward_demodulation,[],[f470,f436]) ).
fof(f436,plain,
! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat) = c_HOL_Ominus__class_Ominus(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f43,f189]) ).
fof(f43,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(X3,c_Suc(X4),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,c_HOL_Oone__class_Oone(tc_nat),tc_nat),X4,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).
fof(f470,plain,
! [X4,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),X4,tc_nat) ),
inference(definition_unfolding,[],[f48,f189]) ).
fof(f48,axiom,
! [X4,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X4,c_Suc(X13),tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
fof(f1811,plain,
spl0_160,
inference(avatar_split_clause,[],[f299,f1809]) ).
fof(f1809,plain,
( spl0_160
<=> ! [X42,X43,X41,X47,X5,X8] : hAPP(hAPP(hAPP(c_COMBC(X41,X43,X8),X5),X42),X47) = hAPP(hAPP(X5,X47),X42) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f299,axiom,
! [X41,X47,X8,X5,X42,X43] : hAPP(hAPP(hAPP(c_COMBC(X41,X43,X8),X5),X42),X47) = hAPP(hAPP(X5,X47),X42),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
fof(f1807,plain,
spl0_159,
inference(avatar_split_clause,[],[f225,f1805]) ).
fof(f1805,plain,
( spl0_159
<=> ! [X0,X27,X26] :
( X0 = X26
| c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X27,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X27,tc_Lambda_OdB,tc_Lambda_OdB) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f225,axiom,
! [X0,X26,X27] :
( X0 = X26
| c_List_Ofoldl(c_Lambda_OdB_OApp,X0,X27,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X27,tc_Lambda_OdB,tc_Lambda_OdB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
fof(f1781,plain,
spl0_158,
inference(avatar_split_clause,[],[f218,f1779]) ).
fof(f1779,plain,
( spl0_158
<=> ! [X4,X3,X15] :
( X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f218,axiom,
! [X3,X4,X15] :
( X3 = X4
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X15) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
fof(f1777,plain,
spl0_157,
inference(avatar_split_clause,[],[f217,f1775]) ).
fof(f1775,plain,
( spl0_157
<=> ! [X9,X40,X10] :
( X10 = X40
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X40) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f217,axiom,
! [X40,X10,X9] :
( X10 = X40
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X40) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
fof(f1773,plain,
spl0_156,
inference(avatar_split_clause,[],[f12,f1771]) ).
fof(f1771,plain,
( spl0_156
<=> ! [X13,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ominus__class_Ominus(X14,X15,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X15),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f12,axiom,
! [X14,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,c_HOL_Ominus__class_Ominus(X14,X15,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X15),X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
fof(f1769,plain,
spl0_155,
inference(avatar_split_clause,[],[f11,f1767]) ).
fof(f1767,plain,
( spl0_155
<=> ! [X13,X14,X15] :
( c_HOL_Oord__class_Oless(X13,c_HOL_Ominus__class_Ominus(X14,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X15),X14,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f11,axiom,
! [X14,X15,X13] :
( c_HOL_Oord__class_Oless(X13,c_HOL_Ominus__class_Ominus(X14,X15,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X15),X14,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
fof(f1765,plain,
spl0_154,
inference(avatar_split_clause,[],[f5,f1763]) ).
fof(f1763,plain,
( spl0_154
<=> ! [X6,X5,X7] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| hBOOL(hAPP(X5,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X5,c_HOL_Ominus__class_Ominus(X6,X7,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f5,axiom,
! [X6,X7,X5] :
( ~ c_HOL_Oord__class_Oless(X6,X7,tc_nat)
| hBOOL(hAPP(X5,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ hBOOL(hAPP(X5,c_HOL_Ominus__class_Ominus(X6,X7,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).
fof(f1613,plain,
spl0_153,
inference(avatar_split_clause,[],[f489,f1611]) ).
fof(f1611,plain,
( spl0_153
<=> ! [X13,X3] : c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X13)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f489,plain,
! [X3,X13] : c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X13)),tc_nat),
inference(forward_demodulation,[],[f428,f426]) ).
fof(f426,plain,
! [X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),
inference(definition_unfolding,[],[f188,f189]) ).
fof(f188,axiom,
! [X4] : c_Suc(X4) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).
fof(f428,plain,
! [X3,X13] : c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X13)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f177,f189]) ).
fof(f177,axiom,
! [X3,X13] : c_HOL_Oord__class_Oless(X13,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X13)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
fof(f1609,plain,
spl0_152,
inference(avatar_split_clause,[],[f488,f1607]) ).
fof(f1607,plain,
( spl0_152
<=> ! [X9,X3] : c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X9)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f488,plain,
! [X3,X9] : c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X9)),tc_nat),
inference(forward_demodulation,[],[f427,f426]) ).
fof(f427,plain,
! [X3,X9] : c_HOL_Oord__class_Oless(X3,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X9)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f176,f189]) ).
fof(f176,axiom,
! [X3,X9] : c_HOL_Oord__class_Oless(X3,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X9)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
fof(f1605,plain,
spl0_151,
inference(avatar_split_clause,[],[f360,f1602]) ).
fof(f1602,plain,
( spl0_151
<=> hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_T_H_H____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f360,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_T_H_H____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_argT_0) ).
fof(f1600,plain,
spl0_150,
inference(avatar_split_clause,[],[f357,f1598]) ).
fof(f1598,plain,
( spl0_150
<=> ! [X13,X0,X14] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),c_Lambda_OdB_OVar(X13)),X14))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f357,axiom,
! [X0,X14,X13] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,X0),c_Lambda_OdB_OVar(X13)),X14))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
fof(f1596,plain,
spl0_149,
inference(avatar_split_clause,[],[f335,f1594]) ).
fof(f1594,plain,
( spl0_149
<=> ! [X13,X25,X14] :
( ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| c_Lambda_OdB_OVar(X14) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X14)),X25),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f335,axiom,
! [X14,X25,X13] :
( ~ c_HOL_Oord__class_Oless(X14,X13,tc_nat)
| c_Lambda_OdB_OVar(X14) = hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X14)),X25),X13) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).
fof(f1592,plain,
( spl0_148
| ~ spl0_111
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1535,f1421,f1142,f1590]) ).
fof(f1590,plain,
( spl0_148
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1142,plain,
( spl0_111
<=> ! [X13,X3,X14] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1535,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_111
| ~ spl0_139 ),
inference(resolution,[],[f1422,f1143]) ).
fof(f1143,plain,
( ! [X3,X14,X13] :
( c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat) )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1142]) ).
fof(f1588,plain,
spl0_147,
inference(avatar_split_clause,[],[f276,f1586]) ).
fof(f1586,plain,
( spl0_147
<=> ! [X2,X0,X27,X4] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X27,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0),X2,tc_Lambda_OdB,tc_Lambda_OdB) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f276,axiom,
! [X2,X0,X27,X4] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X27,tc_Lambda_OdB,tc_Lambda_OdB) != c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X0),X2,tc_Lambda_OdB,tc_Lambda_OdB),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
fof(f1584,plain,
spl0_146,
inference(avatar_split_clause,[],[f168,f1582]) ).
fof(f1582,plain,
( spl0_146
<=> ! [X6,X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f168,axiom,
! [X8,X6,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),X7) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X7),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f1580,plain,
spl0_145,
inference(avatar_split_clause,[],[f165,f1578]) ).
fof(f1578,plain,
( spl0_145
<=> ! [X9,X8,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X9),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X10),X9) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f165,axiom,
! [X10,X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X9),X10) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X10),X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
fof(f1576,plain,
spl0_144,
inference(avatar_split_clause,[],[f41,f1574]) ).
fof(f41,axiom,
! [X14,X15,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X13,X14,tc_nat),X15,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X13,X15,tc_nat),X14,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
fof(f1572,plain,
spl0_143,
inference(avatar_split_clause,[],[f8,f1570]) ).
fof(f1570,plain,
( spl0_143
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f8,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Ominus__class_Ominus(X3,X4,tc_nat)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
fof(f1526,plain,
( spl0_142
| ~ spl0_69
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1201,f1134,f828,f1524]) ).
fof(f1524,plain,
( spl0_142
<=> ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) != X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f828,plain,
( spl0_69
<=> ! [X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)) != X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1201,plain,
( ! [X0] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),X0) != X0
| ~ spl0_69
| ~ spl0_109 ),
inference(superposition,[],[f829,f1135]) ).
fof(f829,plain,
( ! [X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)) != X4
| ~ spl0_69 ),
inference(avatar_component_clause,[],[f828]) ).
fof(f1460,plain,
( spl0_141
| ~ spl0_38
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f969,f902,f699,f1458]) ).
fof(f1458,plain,
( spl0_141
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f902,plain,
( spl0_80
<=> ! [X4,X14,X15] :
( ~ c_HOL_Oord__class_Oless(X14,X15,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X4,tc_nat),X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f969,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_38
| ~ spl0_80 ),
inference(superposition,[],[f903,f700]) ).
fof(f903,plain,
( ! [X14,X4,X15] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X4,tc_nat),X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(X14,X15,tc_nat) )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f902]) ).
fof(f1427,plain,
spl0_140,
inference(avatar_split_clause,[],[f464,f1425]) ).
fof(f464,plain,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f232,f189]) ).
fof(f232,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
fof(f1423,plain,
spl0_139,
inference(avatar_split_clause,[],[f456,f1421]) ).
fof(f456,plain,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f231,f189]) ).
fof(f231,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
fof(f1419,plain,
spl0_138,
inference(avatar_split_clause,[],[f368,f1417]) ).
fof(f368,axiom,
! [X21,X22,X13] :
( hAPP(X21,X13) = X22
| ~ hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X21),c_Lambda_OdB_OVar(X13)),X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
fof(f1415,plain,
spl0_137,
inference(avatar_split_clause,[],[f339,f1413]) ).
fof(f339,axiom,
! [X56,X55,X24,X23] :
( X23 = X55
| hAPP(hAPP(c_Type_Otype_OFun,X23),X24) != hAPP(hAPP(c_Type_Otype_OFun,X55),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
fof(f1411,plain,
spl0_136,
inference(avatar_split_clause,[],[f338,f1409]) ).
fof(f1409,plain,
( spl0_136
<=> ! [X24,X55,X56,X23] :
( X24 = X56
| hAPP(hAPP(c_Type_Otype_OFun,X23),X24) != hAPP(hAPP(c_Type_Otype_OFun,X55),X56) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f338,axiom,
! [X56,X55,X24,X23] :
( X24 = X56
| hAPP(hAPP(c_Type_Otype_OFun,X23),X24) != hAPP(hAPP(c_Type_Otype_OFun,X55),X56) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
fof(f1407,plain,
spl0_135,
inference(avatar_split_clause,[],[f331,f1405]) ).
fof(f1405,plain,
( spl0_135
<=> ! [X41,X43,X9,X46,X29,X8] : hAPP(c_Fun_Ofcomp(X29,X46,X41,X43,X8),X9) = hAPP(X46,hAPP(X29,X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f331,axiom,
! [X41,X29,X46,X8,X9,X43] : hAPP(c_Fun_Ofcomp(X29,X46,X41,X43,X8),X9) = hAPP(X46,hAPP(X29,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__apply_0) ).
fof(f1403,plain,
spl0_134,
inference(avatar_split_clause,[],[f328,f1401]) ).
fof(f1401,plain,
( spl0_134
<=> ! [X44,X51,X50,X45] :
( X44 = X50
| hAPP(hAPP(c_Lambda_OdB_OApp,X44),X45) != hAPP(hAPP(c_Lambda_OdB_OApp,X50),X51) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f328,axiom,
! [X50,X51,X44,X45] :
( X44 = X50
| hAPP(hAPP(c_Lambda_OdB_OApp,X44),X45) != hAPP(hAPP(c_Lambda_OdB_OApp,X50),X51) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
fof(f1399,plain,
spl0_133,
inference(avatar_split_clause,[],[f327,f1397]) ).
fof(f1397,plain,
( spl0_133
<=> ! [X45,X50,X44,X51] :
( X45 = X51
| hAPP(hAPP(c_Lambda_OdB_OApp,X44),X45) != hAPP(hAPP(c_Lambda_OdB_OApp,X50),X51) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f327,axiom,
! [X50,X51,X44,X45] :
( X45 = X51
| hAPP(hAPP(c_Lambda_OdB_OApp,X44),X45) != hAPP(hAPP(c_Lambda_OdB_OApp,X50),X51) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
fof(f1395,plain,
spl0_132,
inference(avatar_split_clause,[],[f309,f1393]) ).
fof(f1393,plain,
( spl0_132
<=> ! [X41,X20,X8,X6,X43,X7] : hAPP(X6,hAPP(X7,X20)) = hAPP(c_Fun_Ocomp(X6,X7,X43,X41,X8),X20) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f309,axiom,
! [X41,X8,X6,X7,X43,X20] : hAPP(X6,hAPP(X7,X20)) = hAPP(c_Fun_Ocomp(X6,X7,X43,X41,X8),X20),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
fof(f1391,plain,
spl0_131,
inference(avatar_split_clause,[],[f303,f1389]) ).
fof(f1389,plain,
( spl0_131
<=> ! [X40,X10,X9,X8] :
( ~ class_Orderings_Opreorder(X8)
| ~ c_HOL_Oord__class_Oless(X9,X10,X8)
| ~ c_HOL_Oord__class_Oless(X10,X40,X8)
| c_HOL_Oord__class_Oless(X9,X40,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f303,axiom,
! [X40,X10,X8,X9] :
( ~ class_Orderings_Opreorder(X8)
| ~ c_HOL_Oord__class_Oless(X9,X10,X8)
| ~ c_HOL_Oord__class_Oless(X10,X40,X8)
| c_HOL_Oord__class_Oless(X9,X40,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f1387,plain,
spl0_130,
inference(avatar_split_clause,[],[f302,f1385]) ).
fof(f1385,plain,
( spl0_130
<=> ! [X40,X10,X9,X8] :
( ~ class_Orderings_Oorder(X8)
| ~ c_HOL_Oord__class_Oless(X10,X9,X8)
| ~ c_HOL_Oord__class_Oless(X40,X10,X8)
| c_HOL_Oord__class_Oless(X40,X9,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f302,axiom,
! [X40,X10,X8,X9] :
( ~ class_Orderings_Oorder(X8)
| ~ c_HOL_Oord__class_Oless(X10,X9,X8)
| ~ c_HOL_Oord__class_Oless(X40,X10,X8)
| c_HOL_Oord__class_Oless(X40,X9,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f1383,plain,
spl0_129,
inference(avatar_split_clause,[],[f289,f1381]) ).
fof(f1381,plain,
( spl0_129
<=> ! [X28,X26] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X26),X28))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X26)),c_Lambda_OdB_OAbs(X28))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f289,axiom,
! [X28,X26] :
( ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,X26),X28))
| hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(X26)),c_Lambda_OdB_OAbs(X28))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
fof(f1379,plain,
spl0_128,
inference(avatar_split_clause,[],[f281,f1377]) ).
fof(f1377,plain,
( spl0_128
<=> ! [X4,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_Nat_Osemiring__1__class_Oof__nat(X4,X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f281,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_Nat_Osemiring__1__class_Oof__nat(X4,X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
fof(f1375,plain,
spl0_127,
inference(avatar_split_clause,[],[f280,f1373]) ).
fof(f1373,plain,
( spl0_127
<=> ! [X4,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_Nat_Osemiring__1__class_Oof__nat(X4,X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f280,axiom,
! [X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_Nat_Osemiring__1__class_Oof__nat(X4,X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
fof(f1371,plain,
spl0_126,
inference(avatar_split_clause,[],[f275,f1369]) ).
fof(f1369,plain,
( spl0_126
<=> ! [X2,X28,X4,X26] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) != hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26)),X28) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f275,axiom,
! [X2,X28,X26,X4] : c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X2,tc_Lambda_OdB,tc_Lambda_OdB) != hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(X26)),X28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
fof(f1367,plain,
( spl0_125
| ~ spl0_14
| ~ spl0_72 ),
inference(avatar_split_clause,[],[f889,f857,f591,f1365]) ).
fof(f1365,plain,
( spl0_125
<=> ! [X0,X1] : c_Nat_Osemiring__1__class_Oof__nat__aux(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f591,plain,
( spl0_14
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f857,plain,
( spl0_72
<=> ! [X13,X16,X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X16,c_HOL_Ozero__class_Ozero(tc_nat),X13,X8) = X13 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f889,plain,
( ! [X0,X1] : c_Nat_Osemiring__1__class_Oof__nat__aux(X0,c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) = X1
| ~ spl0_14
| ~ spl0_72 ),
inference(resolution,[],[f858,f593]) ).
fof(f593,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f591]) ).
fof(f858,plain,
( ! [X8,X16,X13] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X16,c_HOL_Ozero__class_Ozero(tc_nat),X13,X8) = X13 )
| ~ spl0_72 ),
inference(avatar_component_clause,[],[f857]) ).
fof(f1363,plain,
spl0_124,
inference(avatar_split_clause,[],[f234,f1361]) ).
fof(f1361,plain,
( spl0_124
<=> ! [X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_HOL_Oone__class_Oone(X8)),c_HOL_Oone__class_Oone(X8)),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f234,axiom,
! [X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_HOL_Oone__class_Oone(X8)),c_HOL_Oone__class_Oone(X8)),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).
fof(f1359,plain,
spl0_123,
inference(avatar_split_clause,[],[f133,f1357]) ).
fof(f1357,plain,
( spl0_123
<=> ! [X4,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X8),c_Nat_Osemiring__1__class_Oof__nat(X4,X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f133,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X8),c_Nat_Osemiring__1__class_Oof__nat(X4,X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
fof(f1355,plain,
spl0_122,
inference(avatar_split_clause,[],[f132,f1353]) ).
fof(f1353,plain,
( spl0_122
<=> ! [X4,X8,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X8),c_Nat_Osemiring__1__class_Oof__nat(X4,X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f132,axiom,
! [X3,X8,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X8),c_Nat_Osemiring__1__class_Oof__nat(X4,X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
fof(f1351,plain,
spl0_121,
inference(avatar_split_clause,[],[f113,f1349]) ).
fof(f1349,plain,
( spl0_121
<=> ! [X4,X1] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f113,axiom,
! [X1,X4] :
( ~ c_List_Olistsp(c_InductTermi_OIT,X1,tc_Lambda_OdB)
| hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(X4),X1,tc_Lambda_OdB,tc_Lambda_OdB))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
fof(f1347,plain,
spl0_120,
inference(avatar_split_clause,[],[f67,f1345]) ).
fof(f1345,plain,
( spl0_120
<=> ! [X10,X0,X9,X8] :
( ~ hBOOL(hAPP(hAPP(X0,X9),X10))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X9),X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f67,axiom,
! [X10,X0,X8,X9] :
( ~ hBOOL(hAPP(hAPP(X0,X9),X10))
| hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X9),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
fof(f1179,plain,
spl0_119,
inference(avatar_split_clause,[],[f425,f1177]) ).
fof(f1177,plain,
( spl0_119
<=> ! [X4,X3] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f425,plain,
! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f29,f189]) ).
fof(f29,axiom,
! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_Suc(X3),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).
fof(f1172,plain,
spl0_118,
inference(avatar_split_clause,[],[f379,f1170]) ).
fof(f1170,plain,
( spl0_118
<=> ! [X28,X26,X15] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X28),X15)),X26),X15) = X28 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f379,axiom,
! [X28,X26,X15] : hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,X28),X15)),X26),X15) = X28,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
fof(f1168,plain,
spl0_117,
inference(avatar_split_clause,[],[f326,f1166]) ).
fof(f1166,plain,
( spl0_117
<=> ! [X9,X8,X10] :
( ~ class_Orderings_Olinorder(X8)
| X9 = X10
| c_HOL_Oord__class_Oless(X10,X9,X8)
| c_HOL_Oord__class_Oless(X9,X10,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f326,axiom,
! [X10,X8,X9] :
( ~ class_Orderings_Olinorder(X8)
| X9 = X10
| c_HOL_Oord__class_Oless(X10,X9,X8)
| c_HOL_Oord__class_Oless(X9,X10,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
fof(f1164,plain,
spl0_116,
inference(avatar_split_clause,[],[f292,f1162]) ).
fof(f1162,plain,
( spl0_116
<=> ! [X13,X15] :
( ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_Lambda_OdB_OVar(X13) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X13)),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f292,axiom,
! [X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_Lambda_OdB_OVar(X13) = hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(X13)),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
fof(f1160,plain,
spl0_115,
inference(avatar_split_clause,[],[f290,f1158]) ).
fof(f1158,plain,
( spl0_115
<=> ! [X13,X28] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X28))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X28),c_Lambda_OdB_OVar(X13)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f290,axiom,
! [X28,X13] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X28))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,X28),c_Lambda_OdB_OVar(X13)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
fof(f1156,plain,
spl0_114,
inference(avatar_split_clause,[],[f257,f1154]) ).
fof(f1154,plain,
( spl0_114
<=> ! [X2,X3,X26] :
( c_Lambda_OdB_OVar(X3) = X26
| c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f257,axiom,
! [X2,X3,X26] :
( c_Lambda_OdB_OVar(X3) = X26
| c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OVar(X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
fof(f1152,plain,
spl0_113,
inference(avatar_split_clause,[],[f253,f1150]) ).
fof(f1150,plain,
( spl0_113
<=> ! [X41,X31,X29,X43] : hAPP(c_Fun_Ocomp(c_COMBK(X31,X41,X43),X29,X43,X41,t_a),v_x) = X31 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f253,axiom,
! [X31,X41,X29,X43] : hAPP(c_Fun_Ocomp(c_COMBK(X31,X41,X43),X29,X43,X41,t_a),v_x) = X31,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_K__record__comp_0) ).
fof(f1148,plain,
spl0_112,
inference(avatar_split_clause,[],[f173,f1146]) ).
fof(f1146,plain,
( spl0_112
<=> ! [X13,X14,X15] :
( c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X14),X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f173,axiom,
! [X14,X15,X13] :
( c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X14),X15,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
fof(f1144,plain,
spl0_111,
inference(avatar_split_clause,[],[f172,f1142]) ).
fof(f172,axiom,
! [X3,X14,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X3),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).
fof(f1140,plain,
spl0_110,
inference(avatar_split_clause,[],[f171,f1138]) ).
fof(f171,axiom,
! [X3,X14,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X14,tc_nat)
| c_HOL_Oord__class_Oless(X13,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X14),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
fof(f1136,plain,
spl0_109,
inference(avatar_split_clause,[],[f167,f1134]) ).
fof(f1132,plain,
( spl0_108
| ~ spl0_24
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f959,f902,f641,f1130]) ).
fof(f1130,plain,
( spl0_108
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f641,plain,
( spl0_24
<=> ! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f959,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_24
| ~ spl0_80 ),
inference(resolution,[],[f903,f642]) ).
fof(f642,plain,
( ! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f641]) ).
fof(f1128,plain,
spl0_107,
inference(avatar_split_clause,[],[f158,f1126]) ).
fof(f1126,plain,
( spl0_107
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f158,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f1124,plain,
spl0_106,
inference(avatar_split_clause,[],[f157,f1122]) ).
fof(f1122,plain,
( spl0_106
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f157,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f1120,plain,
spl0_105,
inference(avatar_split_clause,[],[f148,f1118]) ).
fof(f1118,plain,
( spl0_105
<=> ! [X2,X0,X26] :
( c_Lambda_OdB_OAbs(X0) = X26
| c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f148,axiom,
! [X2,X0,X26] :
( c_Lambda_OdB_OAbs(X0) = X26
| c_List_Ofoldl(c_Lambda_OdB_OApp,X26,X2,tc_Lambda_OdB,tc_Lambda_OdB) != c_Lambda_OdB_OAbs(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
fof(f1072,plain,
spl0_104,
inference(avatar_split_clause,[],[f365,f1070]) ).
fof(f1070,plain,
( spl0_104
<=> ! [X22,X9,X21,X8] : hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X8),X21),X9),X22),X9) = X22 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f365,axiom,
! [X21,X8,X9,X22] : hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(X8),X21),X9),X22),X9) = X22,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
fof(f1068,plain,
spl0_103,
inference(avatar_split_clause,[],[f362,f1066]) ).
fof(f1066,plain,
( spl0_103
<=> ! [X13,X28] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X28))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X28),X13))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f362,axiom,
! [X28,X13] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X28))
| hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,X28),X13))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
fof(f1064,plain,
spl0_102,
inference(avatar_split_clause,[],[f251,f1062]) ).
fof(f1062,plain,
( spl0_102
<=> ! [X13,X4,X15] :
( ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_Lambda_OdB_OVar(X13) = c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X13),X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f251,axiom,
! [X4,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X15,tc_nat)
| c_Lambda_OdB_OVar(X13) = c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X13),X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
fof(f1060,plain,
spl0_101,
inference(avatar_split_clause,[],[f214,f1057]) ).
fof(f214,axiom,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_T_0) ).
fof(f1055,plain,
spl0_100,
inference(avatar_split_clause,[],[f163,f1053]) ).
fof(f1053,plain,
( spl0_100
<=> ! [X4,X8,X3] :
( ~ class_Nat_Osemiring__char__0(X8)
| X3 = X4
| c_Nat_Osemiring__1__class_Oof__nat(X4,X8) != c_Nat_Osemiring__1__class_Oof__nat(X3,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f163,axiom,
! [X3,X8,X4] :
( ~ class_Nat_Osemiring__char__0(X8)
| X3 = X4
| c_Nat_Osemiring__1__class_Oof__nat(X4,X8) != c_Nat_Osemiring__1__class_Oof__nat(X3,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
fof(f1051,plain,
spl0_99,
inference(avatar_split_clause,[],[f160,f1049]) ).
fof(f1049,plain,
( spl0_99
<=> ! [X6,X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X6) != X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f160,axiom,
! [X6,X9] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X6
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),X6) != X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).
fof(f1047,plain,
spl0_98,
inference(avatar_split_clause,[],[f86,f1045]) ).
fof(f1045,plain,
( spl0_98
<=> ! [X6,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),c_HOL_Oone__class_Oone(X8)),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f86,axiom,
! [X8,X6] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(X6,hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),c_HOL_Oone__class_Oone(X8)),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).
fof(f1043,plain,
( spl0_97
| ~ spl0_14
| ~ spl0_58 ),
inference(avatar_split_clause,[],[f836,f784,f591,f1040]) ).
fof(f1040,plain,
( spl0_97
<=> c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f784,plain,
( spl0_58
<=> ! [X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_HOL_Oone__class_Oone(X8) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f836,plain,
( c_HOL_Oone__class_Oone(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_58 ),
inference(resolution,[],[f785,f593]) ).
fof(f785,plain,
( ! [X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_HOL_Oone__class_Oone(X8) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X8) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f784]) ).
fof(f1038,plain,
spl0_96,
inference(avatar_split_clause,[],[f31,f1036]) ).
fof(f1036,plain,
( spl0_96
<=> ! [X4,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X3),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f31,axiom,
! [X3,X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X3),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
fof(f1034,plain,
spl0_95,
inference(avatar_split_clause,[],[f4,f1032]) ).
fof(f1032,plain,
( spl0_95
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f4,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).
fof(f1030,plain,
spl0_94,
inference(avatar_split_clause,[],[f3,f1028]) ).
fof(f1028,plain,
( spl0_94
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f3,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).
fof(f958,plain,
spl0_93,
inference(avatar_split_clause,[],[f421,f956]) ).
fof(f956,plain,
( spl0_93
<=> ! [X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f421,plain,
! [X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f137,f189]) ).
fof(f137,axiom,
! [X4] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X4),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
fof(f954,plain,
spl0_92,
inference(avatar_split_clause,[],[f375,f952]) ).
fof(f375,axiom,
! [X9,X52] : hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,X52),c_Lambda_OdB_OVar(X9)),hAPP(X52,X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
fof(f950,plain,
spl0_91,
inference(avatar_split_clause,[],[f321,f948]) ).
fof(f948,plain,
( spl0_91
<=> ! [X4,X3] :
( X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f321,axiom,
! [X3,X4] :
( X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
fof(f946,plain,
spl0_90,
inference(avatar_split_clause,[],[f277,f943]) ).
fof(f943,plain,
( spl0_90
<=> c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____),v_as____,v_Ts____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f277,axiom,
c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____),v_as____,v_Ts____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_argsT_0) ).
fof(f941,plain,
( spl0_89
| ~ spl0_61
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f900,f886,f796,f938]) ).
fof(f938,plain,
( spl0_89
<=> c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f900,plain,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| ~ spl0_61
| ~ spl0_79 ),
inference(superposition,[],[f887,f797]) ).
fof(f936,plain,
spl0_88,
inference(avatar_split_clause,[],[f246,f934]) ).
fof(f934,plain,
( spl0_88
<=> ! [X6,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_HOL_Ozero__class_Ozero(X8)),X6) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f246,axiom,
! [X8,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_HOL_Ozero__class_Ozero(X8)),X6) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).
fof(f932,plain,
spl0_87,
inference(avatar_split_clause,[],[f245,f930]) ).
fof(f930,plain,
( spl0_87
<=> ! [X6,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),c_HOL_Ozero__class_Ozero(X8)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f245,axiom,
! [X8,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),c_HOL_Ozero__class_Ozero(X8)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f928,plain,
spl0_86,
inference(avatar_split_clause,[],[f244,f926]) ).
fof(f926,plain,
( spl0_86
<=> ! [X6,X8] :
( ~ class_OrderedGroup_Omonoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),c_HOL_Ozero__class_Ozero(X8)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f244,axiom,
! [X8,X6] :
( ~ class_OrderedGroup_Omonoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),c_HOL_Ozero__class_Ozero(X8)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f924,plain,
spl0_85,
inference(avatar_split_clause,[],[f243,f922]) ).
fof(f922,plain,
( spl0_85
<=> ! [X6,X8] :
( ~ class_OrderedGroup_Omonoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_HOL_Ozero__class_Ozero(X8)),X6) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f243,axiom,
! [X8,X6] :
( ~ class_OrderedGroup_Omonoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_HOL_Ozero__class_Ozero(X8)),X6) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f920,plain,
spl0_84,
inference(avatar_split_clause,[],[f242,f918]) ).
fof(f918,plain,
( spl0_84
<=> ! [X6,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),c_HOL_Ozero__class_Ozero(X8)) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f242,axiom,
! [X8,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),X6),c_HOL_Ozero__class_Ozero(X8)) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f916,plain,
spl0_83,
inference(avatar_split_clause,[],[f237,f914]) ).
fof(f914,plain,
( spl0_83
<=> ! [X6,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_HOL_Ozero__class_Ozero(X8)),X6) = X6 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f237,axiom,
! [X8,X6] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| hAPP(hAPP(c_HOL_Oplus__class_Oplus(X8),c_HOL_Ozero__class_Ozero(X8)),X6) = X6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f912,plain,
spl0_82,
inference(avatar_split_clause,[],[f46,f910]) ).
fof(f910,plain,
( spl0_82
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X3),X4,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f46,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),X3),X4,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f908,plain,
spl0_81,
inference(avatar_split_clause,[],[f45,f906]) ).
fof(f906,plain,
( spl0_81
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),X4,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f45,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),X4),X4,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
fof(f904,plain,
spl0_80,
inference(avatar_split_clause,[],[f15,f902]) ).
fof(f15,axiom,
! [X14,X4,X15] :
( ~ c_HOL_Oord__class_Oless(X14,X15,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X4,tc_nat),X15,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
fof(f888,plain,
spl0_79,
inference(avatar_split_clause,[],[f418,f886]) ).
fof(f418,plain,
! [X9] : c_HOL_Oord__class_Oless(X9,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X9),c_HOL_Oone__class_Oone(tc_nat)),tc_nat),
inference(definition_unfolding,[],[f83,f189]) ).
fof(f83,axiom,
! [X9] : c_HOL_Oord__class_Oless(X9,c_Suc(X9),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
fof(f884,plain,
spl0_78,
inference(avatar_split_clause,[],[f414,f882]) ).
fof(f414,plain,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X3),c_HOL_Oone__class_Oone(tc_nat)),
inference(definition_unfolding,[],[f81,f189]) ).
fof(f81,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
fof(f880,plain,
spl0_77,
inference(avatar_split_clause,[],[f356,f878]) ).
fof(f878,plain,
( spl0_77
<=> ! [X25,X15] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X15)),X25),X15) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f356,axiom,
! [X15,X25] : hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(X15)),X25),X15) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
fof(f876,plain,
spl0_76,
inference(avatar_split_clause,[],[f349,f874]) ).
fof(f874,plain,
( spl0_76
<=> ! [X9,X8,X10] :
( ~ class_Orderings_Opreorder(X8)
| ~ c_HOL_Oord__class_Oless(X9,X10,X8)
| ~ c_HOL_Oord__class_Oless(X10,X9,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f349,axiom,
! [X10,X8,X9] :
( ~ class_Orderings_Opreorder(X8)
| ~ c_HOL_Oord__class_Oless(X9,X10,X8)
| ~ c_HOL_Oord__class_Oless(X10,X9,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
fof(f872,plain,
( ~ spl0_75
| ~ spl0_61
| ~ spl0_69 ),
inference(avatar_split_clause,[],[f853,f828,f796,f869]) ).
fof(f869,plain,
( spl0_75
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oone__class_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f853,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oone__class_Oone(tc_nat)
| ~ spl0_61
| ~ spl0_69 ),
inference(superposition,[],[f829,f797]) ).
fof(f867,plain,
spl0_74,
inference(avatar_split_clause,[],[f348,f865]) ).
fof(f865,plain,
( spl0_74
<=> ! [X9,X8,X10] :
( ~ class_Orderings_Olinorder(X8)
| ~ c_HOL_Oord__class_Oless(X10,X9,X8)
| ~ c_HOL_Oord__class_Oless(X9,X10,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f348,axiom,
! [X10,X8,X9] :
( ~ class_Orderings_Olinorder(X8)
| ~ c_HOL_Oord__class_Oless(X10,X9,X8)
| ~ c_HOL_Oord__class_Oless(X9,X10,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f863,plain,
spl0_73,
inference(avatar_split_clause,[],[f347,f861]) ).
fof(f861,plain,
( spl0_73
<=> ! [X6,X8,X7] :
( ~ class_Orderings_Oorder(X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f347,axiom,
! [X8,X6,X7] :
( ~ class_Orderings_Oorder(X8)
| ~ c_HOL_Oord__class_Oless(X7,X6,X8)
| ~ c_HOL_Oord__class_Oless(X6,X7,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f859,plain,
spl0_72,
inference(avatar_split_clause,[],[f13,f857]) ).
fof(f13,axiom,
! [X8,X16,X13] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_Nat_Osemiring__1__class_Oof__nat__aux(X16,c_HOL_Ozero__class_Ozero(tc_nat),X13,X8) = X13 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__aux_Osimps_I1_J_0) ).
fof(f847,plain,
( spl0_71
| ~ spl0_14
| ~ spl0_57 ),
inference(avatar_split_clause,[],[f835,f780,f591,f844]) ).
fof(f844,plain,
( spl0_71
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f780,plain,
( spl0_57
<=> ! [X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_HOL_Ozero__class_Ozero(X8) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f835,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_14
| ~ spl0_57 ),
inference(resolution,[],[f781,f593]) ).
fof(f781,plain,
( ! [X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_HOL_Ozero__class_Ozero(X8) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X8) )
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f780]) ).
fof(f834,plain,
spl0_70,
inference(avatar_split_clause,[],[f500,f832]) ).
fof(f832,plain,
( spl0_70
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f500,plain,
! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_HOL_Oone__class_Oone(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ),
inference(forward_demodulation,[],[f499,f238]) ).
fof(f499,plain,
! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 ),
inference(forward_demodulation,[],[f461,f167]) ).
fof(f461,plain,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ c_HOL_Oord__class_Oless(X4,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),tc_nat) ),
inference(definition_unfolding,[],[f139,f189]) ).
fof(f139,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
fof(f830,plain,
spl0_69,
inference(avatar_split_clause,[],[f412,f828]) ).
fof(f412,plain,
! [X4] : hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X4),c_HOL_Oone__class_Oone(tc_nat)) != X4,
inference(definition_unfolding,[],[f91,f189]) ).
fof(f91,axiom,
! [X4] : c_Suc(X4) != X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
fof(f826,plain,
spl0_68,
inference(avatar_split_clause,[],[f376,f824]) ).
fof(f824,plain,
( spl0_68
<=> ! [X0] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f376,axiom,
! [X0] :
( ~ hBOOL(hAPP(c_InductTermi_OIT,X0))
| hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
fof(f822,plain,
spl0_67,
inference(avatar_split_clause,[],[f337,f820]) ).
fof(f820,plain,
( spl0_67
<=> ! [X41,X8,X46] : c_Fun_Ofcomp(c_Fun_Oid(X8),X46,X8,X8,X41) = X46 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f337,axiom,
! [X41,X46,X8] : c_Fun_Ofcomp(c_Fun_Oid(X8),X46,X8,X8,X41) = X46,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__fcomp_0) ).
fof(f818,plain,
spl0_66,
inference(avatar_split_clause,[],[f336,f816]) ).
fof(f816,plain,
( spl0_66
<=> ! [X29,X41,X8] : c_Fun_Ofcomp(X29,c_Fun_Oid(X41),X8,X41,X41) = X29 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f336,axiom,
! [X41,X29,X8] : c_Fun_Ofcomp(X29,c_Fun_Oid(X41),X8,X41,X41) = X29,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__id_0) ).
fof(f814,plain,
spl0_65,
inference(avatar_split_clause,[],[f332,f812]) ).
fof(f812,plain,
( spl0_65
<=> ! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f332,axiom,
! [X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
fof(f810,plain,
spl0_64,
inference(avatar_split_clause,[],[f305,f808]) ).
fof(f305,axiom,
! [X41,X29,X8] : c_Fun_Ocomp(X29,c_Fun_Oid(X8),X8,X41,X8) = X29,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__id_0) ).
fof(f806,plain,
spl0_63,
inference(avatar_split_clause,[],[f304,f804]) ).
fof(f804,plain,
( spl0_63
<=> ! [X41,X8,X46] : c_Fun_Ocomp(c_Fun_Oid(X41),X46,X41,X41,X8) = X46 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f304,axiom,
! [X41,X46,X8] : c_Fun_Ocomp(c_Fun_Oid(X41),X46,X41,X41,X8) = X46,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__o_0) ).
fof(f802,plain,
spl0_62,
inference(avatar_split_clause,[],[f262,f800]) ).
fof(f262,axiom,
! [X29,X8] : c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),X29,X8,X8) = c_Fun_Oid(X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funpow_Osimps_I1_J_0) ).
fof(f798,plain,
spl0_61,
inference(avatar_split_clause,[],[f239,f796]) ).
fof(f794,plain,
spl0_60,
inference(avatar_split_clause,[],[f238,f792]) ).
fof(f790,plain,
spl0_59,
inference(avatar_split_clause,[],[f235,f788]) ).
fof(f788,plain,
( spl0_59
<=> ! [X0,X8] : c_Transitive__Closure_Ortranclp(X0,X8) = c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X0,X8),X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f235,axiom,
! [X0,X8] : c_Transitive__Closure_Ortranclp(X0,X8) = c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(X0,X8),X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
fof(f786,plain,
spl0_58,
inference(avatar_split_clause,[],[f207,f784]) ).
fof(f207,axiom,
! [X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_HOL_Oone__class_Oone(X8) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).
fof(f782,plain,
spl0_57,
inference(avatar_split_clause,[],[f131,f780]) ).
fof(f131,axiom,
! [X8] :
( ~ class_Ring__and__Field_Osemiring__1(X8)
| c_HOL_Ozero__class_Ozero(X8) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
fof(f778,plain,
spl0_56,
inference(avatar_split_clause,[],[f121,f776]) ).
fof(f776,plain,
( spl0_56
<=> ! [X8,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X8),c_HOL_Ozero__class_Ozero(X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f121,axiom,
! [X3,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X8),c_HOL_Ozero__class_Ozero(X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
fof(f774,plain,
spl0_55,
inference(avatar_split_clause,[],[f90,f772]) ).
fof(f772,plain,
( spl0_55
<=> ! [X13,X14] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X13),X13,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f90,axiom,
! [X14,X13] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X14),X13),X13,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f770,plain,
spl0_54,
inference(avatar_split_clause,[],[f89,f768]) ).
fof(f768,plain,
( spl0_54
<=> ! [X13,X14] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X14),X13,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f89,axiom,
! [X14,X13] : ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),X13),X14),X13,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f764,plain,
spl0_53,
inference(avatar_split_clause,[],[f370,f761]) ).
fof(f761,plain,
( spl0_53
<=> hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f370,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I4_J_0) ).
fof(f759,plain,
spl0_52,
inference(avatar_split_clause,[],[f352,f756]) ).
fof(f756,plain,
( spl0_52
<=> hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f352,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uT_0) ).
fof(f754,plain,
spl0_51,
inference(avatar_split_clause,[],[f342,f752]) ).
fof(f752,plain,
( spl0_51
<=> ! [X50,X48,X51] : c_Lambda_OdB_OAbs(X48) != hAPP(hAPP(c_Lambda_OdB_OApp,X50),X51) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f342,axiom,
! [X50,X51,X48] : c_Lambda_OdB_OAbs(X48) != hAPP(hAPP(c_Lambda_OdB_OApp,X50),X51),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
fof(f750,plain,
spl0_50,
inference(avatar_split_clause,[],[f341,f748]) ).
fof(f748,plain,
( spl0_50
<=> ! [X32,X39] :
( X32 = X39
| c_Lambda_OdB_OVar(X39) != c_Lambda_OdB_OVar(X32) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f341,axiom,
! [X39,X32] :
( X32 = X39
| c_Lambda_OdB_OVar(X39) != c_Lambda_OdB_OVar(X32) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
fof(f746,plain,
spl0_49,
inference(avatar_split_clause,[],[f311,f744]) ).
fof(f744,plain,
( spl0_49
<=> ! [X48,X49] :
( X48 = X49
| c_Lambda_OdB_OAbs(X48) != c_Lambda_OdB_OAbs(X49) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f311,axiom,
! [X48,X49] :
( X48 = X49
| c_Lambda_OdB_OAbs(X48) != c_Lambda_OdB_OAbs(X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
fof(f742,plain,
spl0_48,
inference(avatar_split_clause,[],[f287,f740]) ).
fof(f740,plain,
( spl0_48
<=> ! [X45,X44,X39] : hAPP(hAPP(c_Lambda_OdB_OApp,X44),X45) != c_Lambda_OdB_OVar(X39) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f287,axiom,
! [X39,X44,X45] : hAPP(hAPP(c_Lambda_OdB_OApp,X44),X45) != c_Lambda_OdB_OVar(X39),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
fof(f738,plain,
spl0_47,
inference(avatar_split_clause,[],[f205,f736]) ).
fof(f736,plain,
( spl0_47
<=> ! [X41,X42,X5,X8] : hAPP(c_COMBK(X5,X8,X41),X42) = X5 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f205,axiom,
! [X41,X8,X5,X42] : hAPP(c_COMBK(X5,X8,X41),X42) = X5,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
fof(f734,plain,
spl0_46,
inference(avatar_split_clause,[],[f184,f732]) ).
fof(f732,plain,
( spl0_46
<=> ! [X9,X0,X8] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X9),X9)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f184,axiom,
! [X0,X8,X9] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X8),X9),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
fof(f730,plain,
spl0_45,
inference(avatar_split_clause,[],[f129,f728]) ).
fof(f728,plain,
( spl0_45
<=> ! [X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_HOL_Oone__class_Oone(X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f129,axiom,
! [X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X8),c_HOL_Oone__class_Oone(X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).
fof(f726,plain,
spl0_44,
inference(avatar_split_clause,[],[f127,f724]) ).
fof(f724,plain,
( spl0_44
<=> ! [X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X8),c_HOL_Ozero__class_Ozero(X8),X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f127,axiom,
! [X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X8)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(X8),c_HOL_Ozero__class_Ozero(X8),X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).
fof(f722,plain,
spl0_43,
inference(avatar_split_clause,[],[f35,f720]) ).
fof(f35,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).
fof(f717,plain,
spl0_42,
inference(avatar_split_clause,[],[f411,f715]) ).
fof(f715,plain,
( spl0_42
<=> ! [X70,X69,X8] :
( X69 = X70
| ~ c_fequal(X69,X70,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f411,axiom,
! [X70,X8,X69] :
( X69 = X70
| ~ c_fequal(X69,X70,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
fof(f713,plain,
spl0_41,
inference(avatar_split_clause,[],[f330,f711]) ).
fof(f711,plain,
( spl0_41
<=> ! [X13,X28] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X13)),X28)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f330,axiom,
! [X28,X13] : ~ hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(X13)),X28)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
fof(f709,plain,
spl0_40,
inference(avatar_split_clause,[],[f208,f707]) ).
fof(f707,plain,
( spl0_40
<=> ! [X8] :
( ~ class_Ring__and__Field_Ozero__neq__one(X8)
| c_HOL_Ozero__class_Ozero(X8) != c_HOL_Oone__class_Oone(X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f208,axiom,
! [X8] :
( ~ class_Ring__and__Field_Ozero__neq__one(X8)
| c_HOL_Ozero__class_Ozero(X8) != c_HOL_Oone__class_Oone(X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).
fof(f705,plain,
spl0_39,
inference(avatar_split_clause,[],[f88,f703]) ).
fof(f88,axiom,
! [X28,X15] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X28,X15) = X28,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).
fof(f701,plain,
spl0_38,
inference(avatar_split_clause,[],[f18,f699]) ).
fof(f18,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).
fof(f697,plain,
spl0_37,
inference(avatar_split_clause,[],[f17,f695]) ).
fof(f695,plain,
( spl0_37
<=> ! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f17,axiom,
! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).
fof(f693,plain,
spl0_36,
inference(avatar_split_clause,[],[f390,f691]) ).
fof(f691,plain,
( spl0_36
<=> ! [X67,X68] :
( ~ class_Orderings_Oorder(X68)
| class_Orderings_Oorder(tc_fun(X67,X68)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f390,axiom,
! [X68,X67] :
( ~ class_Orderings_Oorder(X68)
| class_Orderings_Oorder(tc_fun(X67,X68)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
fof(f689,plain,
spl0_35,
inference(avatar_split_clause,[],[f389,f687]) ).
fof(f687,plain,
( spl0_35
<=> ! [X67,X68] :
( ~ class_Orderings_Opreorder(X68)
| class_Orderings_Opreorder(tc_fun(X67,X68)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f389,axiom,
! [X68,X67] :
( ~ class_Orderings_Opreorder(X68)
| class_Orderings_Opreorder(tc_fun(X67,X68)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
fof(f685,plain,
spl0_34,
inference(avatar_split_clause,[],[f317,f683]) ).
fof(f683,plain,
( spl0_34
<=> ! [X9,X8] :
( ~ class_Orderings_Opreorder(X8)
| ~ c_HOL_Oord__class_Oless(X9,X9,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f317,axiom,
! [X8,X9] :
( ~ class_Orderings_Opreorder(X8)
| ~ c_HOL_Oord__class_Oless(X9,X9,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f681,plain,
spl0_33,
inference(avatar_split_clause,[],[f316,f679]) ).
fof(f679,plain,
( spl0_33
<=> ! [X9,X8] :
( ~ class_Orderings_Olinorder(X8)
| ~ c_HOL_Oord__class_Oless(X9,X9,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f316,axiom,
! [X8,X9] :
( ~ class_Orderings_Olinorder(X8)
| ~ c_HOL_Oord__class_Oless(X9,X9,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f677,plain,
spl0_32,
inference(avatar_split_clause,[],[f315,f675]) ).
fof(f675,plain,
( spl0_32
<=> ! [X9,X8] :
( ~ class_Orderings_Oorder(X8)
| ~ c_HOL_Oord__class_Oless(X9,X9,X8) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f315,axiom,
! [X8,X9] :
( ~ class_Orderings_Oorder(X8)
| ~ c_HOL_Oord__class_Oless(X9,X9,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f673,plain,
spl0_31,
inference(avatar_split_clause,[],[f288,f671]) ).
fof(f288,axiom,
! [X8,X9] : hAPP(c_Fun_Oid(X8),X9) = X9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).
fof(f669,plain,
spl0_30,
inference(avatar_split_clause,[],[f367,f667]) ).
fof(f667,plain,
( spl0_30
<=> ! [X4] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X4))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f367,axiom,
! [X4] : hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(X4))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
fof(f665,plain,
spl0_29,
inference(avatar_split_clause,[],[f310,f663]) ).
fof(f310,axiom,
! [X39,X48] : c_Lambda_OdB_OVar(X39) != c_Lambda_OdB_OAbs(X48),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
fof(f661,plain,
spl0_28,
inference(avatar_split_clause,[],[f301,f659]) ).
fof(f301,axiom,
! [X3] : ~ c_HOL_Oord__class_Oless(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
fof(f657,plain,
spl0_27,
inference(avatar_split_clause,[],[f410,f655]) ).
fof(f655,plain,
( spl0_27
<=> ! [X9,X8] : c_fequal(X9,X9,X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f410,axiom,
! [X8,X9] : c_fequal(X9,X9,X8),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
fof(f653,plain,
spl0_26,
inference(avatar_split_clause,[],[f378,f650]) ).
fof(f650,plain,
( spl0_26
<=> hBOOL(hAPP(c_InductTermi_OIT,v_u____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f378,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_u____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_uIT_0) ).
fof(f648,plain,
spl0_25,
inference(avatar_split_clause,[],[f372,f645]) ).
fof(f645,plain,
( spl0_25
<=> hBOOL(hAPP(c_InductTermi_OIT,v_ua______)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f372,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_ua______)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var_I3_J_0) ).
fof(f643,plain,
spl0_24,
inference(avatar_split_clause,[],[f313,f641]) ).
fof(f313,axiom,
! [X9] : ~ c_HOL_Oord__class_Oless(X9,X9,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
fof(f639,plain,
spl0_23,
inference(avatar_split_clause,[],[f385,f636]) ).
fof(f385,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f634,plain,
~ spl0_22,
inference(avatar_split_clause,[],[f388,f631]) ).
fof(f388,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f629,plain,
spl0_21,
inference(avatar_split_clause,[],[f409,f626]) ).
fof(f626,plain,
( spl0_21
<=> class_Orderings_Oorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f409,axiom,
class_Orderings_Oorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
fof(f624,plain,
spl0_20,
inference(avatar_split_clause,[],[f408,f621]) ).
fof(f621,plain,
( spl0_20
<=> class_Orderings_Opreorder(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f408,axiom,
class_Orderings_Opreorder(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
fof(f619,plain,
spl0_19,
inference(avatar_split_clause,[],[f407,f616]) ).
fof(f616,plain,
( spl0_19
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f407,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f614,plain,
spl0_18,
inference(avatar_split_clause,[],[f406,f611]) ).
fof(f611,plain,
( spl0_18
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f406,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f609,plain,
spl0_17,
inference(avatar_split_clause,[],[f405,f606]) ).
fof(f606,plain,
( spl0_17
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f405,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f604,plain,
spl0_16,
inference(avatar_split_clause,[],[f404,f601]) ).
fof(f601,plain,
( spl0_16
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f404,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f599,plain,
spl0_15,
inference(avatar_split_clause,[],[f403,f596]) ).
fof(f596,plain,
( spl0_15
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f403,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f594,plain,
spl0_14,
inference(avatar_split_clause,[],[f402,f591]) ).
fof(f402,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f589,plain,
spl0_13,
inference(avatar_split_clause,[],[f401,f586]) ).
fof(f586,plain,
( spl0_13
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f401,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Osemigroup__add) ).
fof(f584,plain,
spl0_12,
inference(avatar_split_clause,[],[f400,f581]) ).
fof(f581,plain,
( spl0_12
<=> class_Ring__and__Field_Ozero__neq__one(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f400,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).
fof(f579,plain,
spl0_11,
inference(avatar_split_clause,[],[f399,f576]) ).
fof(f576,plain,
( spl0_11
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f399,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f574,plain,
spl0_10,
inference(avatar_split_clause,[],[f398,f571]) ).
fof(f571,plain,
( spl0_10
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f398,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f569,plain,
spl0_9,
inference(avatar_split_clause,[],[f397,f566]) ).
fof(f566,plain,
( spl0_9
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f397,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).
fof(f564,plain,
spl0_8,
inference(avatar_split_clause,[],[f396,f561]) ).
fof(f561,plain,
( spl0_8
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f396,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f559,plain,
spl0_7,
inference(avatar_split_clause,[],[f395,f556]) ).
fof(f556,plain,
( spl0_7
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f395,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f554,plain,
spl0_6,
inference(avatar_split_clause,[],[f394,f551]) ).
fof(f551,plain,
( spl0_6
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f394,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f549,plain,
spl0_5,
inference(avatar_split_clause,[],[f393,f546]) ).
fof(f546,plain,
( spl0_5
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f393,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f544,plain,
spl0_4,
inference(avatar_split_clause,[],[f392,f541]) ).
fof(f541,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f392,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).
fof(f539,plain,
spl0_3,
inference(avatar_split_clause,[],[f391,f536]) ).
fof(f536,plain,
( spl0_3
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f391,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).
fof(f534,plain,
spl0_2,
inference(avatar_split_clause,[],[f387,f531]) ).
fof(f387,axiom,
hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f529,plain,
spl0_1,
inference(avatar_split_clause,[],[f386,f526]) ).
fof(f386,axiom,
hBOOL(hAPP(c_InductTermi_OIT,v_xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LCL806-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n015.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri May 3 14:11:21 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % (4183)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.38 % (4188)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.19/0.38 % (4186)WARNING: value z3 for option sas not known
% 0.19/0.38 % (4184)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.19/0.39 % (4185)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.39 % (4186)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.19/0.39 % (4187)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.39 % (4190)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.19/0.39 % (4189)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.19/0.51 TRYING [1]
% 0.19/0.52 TRYING [2]
% 0.19/0.56 % (4188)First to succeed.
% 1.41/0.57 % (4188)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4183"
% 1.41/0.57 % (4188)Refutation found. Thanks to Tanya!
% 1.41/0.57 % SZS status Unsatisfiable for theBenchmark
% 1.41/0.57 % SZS output start Proof for theBenchmark
% See solution above
% 1.41/0.58 % (4188)------------------------------
% 1.41/0.58 % (4188)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 1.41/0.58 % (4188)Termination reason: Refutation
% 1.41/0.58
% 1.41/0.58 % (4188)Memory used [KB]: 4166
% 1.41/0.58 % (4188)Time elapsed: 0.189 s
% 1.41/0.58 % (4188)Instructions burned: 475 (million)
% 1.41/0.58 % (4183)Success in time 0.22 s
%------------------------------------------------------------------------------