TSTP Solution File: LCL855-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LCL855-1 : 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 : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:51:45 EDT 2024
% Result : Unsatisfiable 4.10s 0.95s
% Output : Refutation 4.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 710
% Syntax : Number of formulae : 1564 ( 322 unt; 0 def)
% Number of atoms : 3937 ( 728 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 4293 (1920 ~;1901 |; 0 &)
% ( 472 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 499 ( 497 usr; 473 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 3 con; 0-3 aty)
% Number of variables : 2530 (2530 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16554,plain,
$false,
inference(avatar_sat_refutation,[],[f398,f403,f408,f413,f418,f423,f428,f433,f438,f443,f448,f453,f458,f463,f468,f473,f478,f483,f488,f493,f498,f503,f508,f513,f518,f522,f526,f530,f534,f538,f542,f546,f550,f554,f558,f562,f566,f570,f574,f578,f582,f586,f590,f594,f598,f602,f606,f610,f614,f618,f626,f630,f634,f638,f642,f646,f650,f654,f658,f662,f666,f670,f686,f690,f694,f698,f702,f706,f710,f714,f718,f722,f726,f730,f734,f738,f742,f746,f750,f754,f758,f802,f850,f854,f858,f862,f866,f870,f874,f878,f882,f886,f890,f894,f898,f902,f906,f910,f914,f918,f922,f926,f930,f934,f938,f1028,f1032,f1036,f1040,f1044,f1048,f1052,f1056,f1060,f1064,f1068,f1072,f1084,f1088,f1092,f1185,f1276,f1280,f1284,f1288,f1293,f1297,f1301,f1305,f1309,f1313,f1317,f1321,f1438,f1444,f1448,f1452,f1456,f1460,f1464,f1468,f1472,f1476,f1480,f1487,f1492,f1652,f1764,f1768,f1772,f1776,f1780,f1784,f1788,f1792,f1796,f1800,f1804,f1808,f1812,f1816,f1820,f1824,f1828,f1832,f1836,f1840,f2249,f2253,f2257,f2261,f2265,f2269,f2273,f2277,f2281,f2285,f2289,f2293,f2297,f2301,f2305,f2865,f2904,f2908,f2912,f2916,f2920,f2924,f2928,f2932,f2936,f2940,f2944,f2948,f3306,f3310,f3314,f3318,f3322,f3326,f3330,f3334,f3338,f3342,f3346,f3350,f3354,f3358,f3362,f3366,f3370,f3374,f3378,f3382,f3386,f3390,f3428,f3515,f3564,f3568,f3572,f3576,f3580,f3584,f3588,f3592,f3596,f3600,f3604,f4061,f4065,f4069,f4073,f4196,f4200,f4204,f4208,f4212,f4216,f4220,f4224,f4228,f4232,f4236,f4240,f4455,f4459,f4463,f4467,f4583,f4620,f4624,f4632,f4744,f4764,f4819,f4823,f4827,f4831,f4835,f4839,f4843,f4847,f4851,f4855,f4859,f4863,f5256,f5260,f5264,f5268,f5272,f5288,f5292,f5296,f5300,f5304,f5308,f5312,f5316,f5320,f5324,f5328,f5332,f5336,f5782,f5786,f5790,f5794,f5798,f5802,f5806,f5810,f5814,f5818,f5822,f5826,f5830,f5834,f5838,f5842,f5846,f6113,f6386,f6391,f6395,f6399,f6403,f6407,f6411,f6415,f6419,f6423,f6427,f6431,f6459,f6463,f6467,f6471,f6475,f6479,f6483,f6487,f6491,f6495,f6501,f6505,f6509,f6513,f6517,f6521,f7627,f7803,f7807,f7811,f7815,f7819,f7823,f7827,f7839,f7843,f7847,f7851,f7855,f7859,f7863,f7867,f7871,f7875,f7879,f7883,f7887,f7891,f7895,f7899,f7903,f7907,f7911,f7915,f7919,f7929,f7933,f7937,f7941,f7945,f7949,f8095,f8731,f9425,f9437,f9441,f9445,f9449,f9453,f9457,f9461,f9465,f9469,f9473,f9477,f9481,f9485,f9489,f9493,f9497,f9501,f9505,f9509,f9513,f9517,f9529,f9533,f9537,f9541,f9545,f9595,f9599,f9603,f9607,f9611,f9615,f9619,f9623,f9627,f9631,f9635,f9901,f10603,f11412,f12297,f12357,f12361,f12365,f12369,f12373,f12377,f12381,f12385,f12389,f12393,f12397,f12401,f12405,f12409,f12413,f12417,f12421,f12425,f12429,f12433,f12437,f12441,f12445,f12449,f12453,f12457,f12461,f12465,f12470,f12474,f12479,f12483,f12487,f12491,f12495,f12499,f12503,f12564,f12568,f12572,f12576,f12580,f12584,f12588,f12592,f12596,f12600,f12604,f12608,f12612,f12616,f12620,f12677,f12681,f12685,f12689,f12693,f12697,f12701,f12705,f12709,f16553]) ).
fof(f16553,plain,
( spl0_1
| ~ spl0_59
| ~ spl0_146
| ~ spl0_465 ),
inference(avatar_split_clause,[],[f16248,f12679,f1489,f656,f395]) ).
fof(f395,plain,
( spl0_1
<=> c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f656,plain,
( spl0_59
<=> ! [X25,X12,X28] : c_Lambda_Osubst(c_Lambda_Olift(X25,X12),X28,X12) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1489,plain,
( spl0_146
<=> c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f12679,plain,
( spl0_465
<=> ! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X0),X2),X1,X0) = c_Lambda_OdB_OApp(X1,c_Lambda_Osubst(X2,X1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f16248,plain,
( c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____))
| ~ spl0_59
| ~ spl0_146
| ~ spl0_465 ),
inference(forward_demodulation,[],[f16213,f657]) ).
fof(f657,plain,
( ! [X28,X25,X12] : c_Lambda_Osubst(c_Lambda_Olift(X25,X12),X28,X12) = X25
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f656]) ).
fof(f16213,plain,
( c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,c_Lambda_Osubst(c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat)),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))))
| ~ spl0_146
| ~ spl0_465 ),
inference(superposition,[],[f1491,f12680]) ).
fof(f12680,plain,
( ! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X0),X2),X1,X0) = c_Lambda_OdB_OApp(X1,c_Lambda_Osubst(X2,X1,X0))
| ~ spl0_465 ),
inference(avatar_component_clause,[],[f12679]) ).
fof(f1491,plain,
( c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f1489]) ).
fof(f12709,plain,
( spl0_472
| ~ spl0_52
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f3988,f3602,f628,f12707]) ).
fof(f12707,plain,
( spl0_472
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f628,plain,
( spl0_52
<=> ! [X5,X3] : c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Oplus__class_Oplus(X3,X5,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f3602,plain,
( spl0_230
<=> ! [X4,X12,X3] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f3988,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat)
| ~ spl0_52
| ~ spl0_230 ),
inference(superposition,[],[f629,f3603]) ).
fof(f3603,plain,
( ! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat)
| ~ spl0_230 ),
inference(avatar_component_clause,[],[f3602]) ).
fof(f629,plain,
( ! [X3,X5] : c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Oplus__class_Oplus(X3,X5,tc_nat)),tc_nat)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f628]) ).
fof(f12705,plain,
( spl0_471
| ~ spl0_51
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f3987,f3602,f624,f12703]) ).
fof(f12703,plain,
( spl0_471
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f624,plain,
( spl0_51
<=> ! [X11,X3] : c_HOL_Oord__class_Oless(X11,c_Suc(c_HOL_Oplus__class_Oplus(X3,X11,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f3987,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat)
| ~ spl0_51
| ~ spl0_230 ),
inference(superposition,[],[f625,f3603]) ).
fof(f625,plain,
( ! [X3,X11] : c_HOL_Oord__class_Oless(X11,c_Suc(c_HOL_Oplus__class_Oplus(X3,X11,tc_nat)),tc_nat)
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f624]) ).
fof(f12701,plain,
( spl0_470
| ~ spl0_52
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f3901,f3598,f628,f12699]) ).
fof(f12699,plain,
( spl0_470
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f3598,plain,
( spl0_229
<=> ! [X4,X12,X3] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f3901,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat)),tc_nat)
| ~ spl0_52
| ~ spl0_229 ),
inference(superposition,[],[f629,f3599]) ).
fof(f3599,plain,
( ! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat)
| ~ spl0_229 ),
inference(avatar_component_clause,[],[f3598]) ).
fof(f12697,plain,
( spl0_469
| ~ spl0_51
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f3900,f3598,f624,f12695]) ).
fof(f12695,plain,
( spl0_469
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f3900,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat)),tc_nat)
| ~ spl0_51
| ~ spl0_229 ),
inference(superposition,[],[f625,f3599]) ).
fof(f12693,plain,
( spl0_468
| ~ spl0_53
| ~ spl0_223 ),
inference(avatar_split_clause,[],[f3725,f3574,f632,f12691]) ).
fof(f12691,plain,
( spl0_468
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f632,plain,
( spl0_53
<=> ! [X4,X3] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_Suc(X3),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f3574,plain,
( spl0_223
<=> ! [X4,X12,X3] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f3725,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)),tc_nat)
| ~ spl0_53
| ~ spl0_223 ),
inference(superposition,[],[f633,f3575]) ).
fof(f3575,plain,
( ! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat)
| ~ spl0_223 ),
inference(avatar_component_clause,[],[f3574]) ).
fof(f633,plain,
( ! [X3,X4] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),c_Suc(X3),tc_nat)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f12689,plain,
( spl0_467
| ~ spl0_53
| ~ spl0_222 ),
inference(avatar_split_clause,[],[f3687,f3570,f632,f12687]) ).
fof(f12687,plain,
( spl0_467
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f3570,plain,
( spl0_222
<=> ! [X4,X12,X3] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f3687,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat)),tc_nat)
| ~ spl0_53
| ~ spl0_222 ),
inference(superposition,[],[f633,f3571]) ).
fof(f3571,plain,
( ! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat)
| ~ spl0_222 ),
inference(avatar_component_clause,[],[f3570]) ).
fof(f12685,plain,
( spl0_466
| ~ spl0_49
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f3277,f2938,f612,f12683]) ).
fof(f12683,plain,
( spl0_466
<=> ! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X2,c_Lambda_OdB_OVar(X0)),X1,X0) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X2,X1,X0),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f612,plain,
( spl0_49
<=> ! [X12,X15] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X15,X12) = X15 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f2938,plain,
( spl0_193
<=> ! [X28,X15,X12,X25] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X25,X15),X28,X12) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X25,X28,X12),c_Lambda_Osubst(X15,X28,X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f3277,plain,
( ! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X2,c_Lambda_OdB_OVar(X0)),X1,X0) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X2,X1,X0),X1)
| ~ spl0_49
| ~ spl0_193 ),
inference(superposition,[],[f2939,f613]) ).
fof(f613,plain,
( ! [X15,X12] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X15,X12) = X15
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f2939,plain,
( ! [X28,X15,X25,X12] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X25,X15),X28,X12) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X25,X28,X12),c_Lambda_Osubst(X15,X28,X12))
| ~ spl0_193 ),
inference(avatar_component_clause,[],[f2938]) ).
fof(f12681,plain,
( spl0_465
| ~ spl0_49
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f3275,f2938,f612,f12679]) ).
fof(f3275,plain,
( ! [X2,X0,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(X0),X2),X1,X0) = c_Lambda_OdB_OApp(X1,c_Lambda_Osubst(X2,X1,X0))
| ~ spl0_49
| ~ spl0_193 ),
inference(superposition,[],[f2939,f613]) ).
fof(f12677,plain,
( spl0_464
| ~ spl0_53
| ~ spl0_182 ),
inference(avatar_split_clause,[],[f2835,f2303,f632,f12675]) ).
fof(f12675,plain,
( spl0_464
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),c_Suc(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f2303,plain,
( spl0_182
<=> ! [X13,X12,X11] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(X11,c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f2835,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat),c_Suc(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),tc_nat)
| ~ spl0_53
| ~ spl0_182 ),
inference(superposition,[],[f633,f2304]) ).
fof(f2304,plain,
( ! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(X11,c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),tc_nat)
| ~ spl0_182 ),
inference(avatar_component_clause,[],[f2303]) ).
fof(f12620,plain,
( spl0_463
| ~ spl0_76
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2742,f2291,f736,f12618]) ).
fof(f12618,plain,
( spl0_463
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,X1)) = X0
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f736,plain,
( spl0_76
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f2291,plain,
( spl0_179
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X3,X4)) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f2742,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,X1)) = X0
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_76
| ~ spl0_179 ),
inference(resolution,[],[f2292,f737]) ).
fof(f737,plain,
( ! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_76 ),
inference(avatar_component_clause,[],[f736]) ).
fof(f2292,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X3,X4)) = X3 )
| ~ spl0_179 ),
inference(avatar_component_clause,[],[f2291]) ).
fof(f12616,plain,
( spl0_462
| ~ spl0_80
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2741,f2291,f752,f12614]) ).
fof(f12614,plain,
( spl0_462
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,X1)) = X0
| c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f752,plain,
( spl0_80
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f2741,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,X1)) = X0
| c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_80
| ~ spl0_179 ),
inference(resolution,[],[f2292,f753]) ).
fof(f753,plain,
( ! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_80 ),
inference(avatar_component_clause,[],[f752]) ).
fof(f12612,plain,
( spl0_461
| ~ spl0_44
| ~ spl0_93
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f2723,f2287,f888,f592,f12610]) ).
fof(f12610,plain,
( spl0_461
<=> ! [X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f592,plain,
( spl0_44
<=> ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f888,plain,
( spl0_93
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X4)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f2287,plain,
( spl0_178
<=> ! [X11,X4,X12] :
( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X11),X12) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X11,X4,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f2723,plain,
( ! [X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X1)) = X1 )
| ~ spl0_44
| ~ spl0_93
| ~ spl0_178 ),
inference(forward_demodulation,[],[f2705,f593]) ).
fof(f593,plain,
( ! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f592]) ).
fof(f2705,plain,
( ! [X0,X1] :
( c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X1)) = X1 )
| ~ spl0_93
| ~ spl0_178 ),
inference(resolution,[],[f2288,f889]) ).
fof(f889,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X4)) = X4 )
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f888]) ).
fof(f2288,plain,
( ! [X11,X4,X12] :
( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X11),X12) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X11,X4,tc_nat)) )
| ~ spl0_178 ),
inference(avatar_component_clause,[],[f2287]) ).
fof(f12608,plain,
( spl0_460
| ~ spl0_44
| ~ spl0_95
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f2722,f2287,f896,f592,f12606]) ).
fof(f12606,plain,
( spl0_460
<=> ! [X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f896,plain,
( spl0_95
<=> ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X4)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f2722,plain,
( ! [X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X1)) = X1 )
| ~ spl0_44
| ~ spl0_95
| ~ spl0_178 ),
inference(forward_demodulation,[],[f2704,f593]) ).
fof(f2704,plain,
( ! [X0,X1] :
( c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat))
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X1)) = X1 )
| ~ spl0_95
| ~ spl0_178 ),
inference(resolution,[],[f2288,f897]) ).
fof(f897,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X4)) = X4 )
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f896]) ).
fof(f12604,plain,
( spl0_459
| ~ spl0_118
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f2623,f2271,f1082,f12602]) ).
fof(f12602,plain,
( spl0_459
<=> ! [X2,X0,X1,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f1082,plain,
( spl0_118
<=> ! [X13,X4,X12] :
( ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X13,X4,tc_nat),X12,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f2271,plain,
( spl0_174
<=> ! [X4,X12,X3] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f2623,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X3,tc_nat) )
| ~ spl0_118
| ~ spl0_174 ),
inference(superposition,[],[f1083,f2272]) ).
fof(f2272,plain,
( ! [X3,X4,X12] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat)
| ~ spl0_174 ),
inference(avatar_component_clause,[],[f2271]) ).
fof(f1083,plain,
( ! [X4,X12,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X13,X4,tc_nat),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat) )
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f1082]) ).
fof(f12600,plain,
( spl0_458
| ~ spl0_118
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2582,f2267,f1082,f12598]) ).
fof(f12598,plain,
( spl0_458
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f2267,plain,
( spl0_173
<=> ! [X4,X12,X3] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X12,tc_nat),c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f2582,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),X3,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X3,tc_nat) )
| ~ spl0_118
| ~ spl0_173 ),
inference(superposition,[],[f1083,f2268]) ).
fof(f2268,plain,
( ! [X3,X4,X12] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X12,tc_nat),c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat)
| ~ spl0_173 ),
inference(avatar_component_clause,[],[f2267]) ).
fof(f12596,plain,
( spl0_457
| ~ spl0_53
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f2504,f2255,f632,f12594]) ).
fof(f12594,plain,
( spl0_457
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_Suc(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f2255,plain,
( spl0_170
<=> ! [X13,X12,X11] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(X11,c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f2504,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_Suc(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),tc_nat)
| ~ spl0_53
| ~ spl0_170 ),
inference(superposition,[],[f633,f2256]) ).
fof(f2256,plain,
( ! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(X11,c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),tc_nat)
| ~ spl0_170 ),
inference(avatar_component_clause,[],[f2255]) ).
fof(f12592,plain,
( spl0_456
| ~ spl0_116
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f2447,f2251,f1066,f12590]) ).
fof(f12590,plain,
( spl0_456
<=> ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f1066,plain,
( spl0_116
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f2251,plain,
( spl0_169
<=> ! [X4,X12,X3] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f2447,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X2 )
| ~ spl0_116
| ~ spl0_169 ),
inference(superposition,[],[f1067,f2252]) ).
fof(f2252,plain,
( ! [X3,X4,X12] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat)
| ~ spl0_169 ),
inference(avatar_component_clause,[],[f2251]) ).
fof(f1067,plain,
( ! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f1066]) ).
fof(f12588,plain,
( spl0_455
| ~ spl0_112
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f2445,f2251,f1050,f12586]) ).
fof(f12586,plain,
( spl0_455
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f1050,plain,
( spl0_112
<=> ! [X13,X11,X3] :
( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oplus__class_Oplus(X3,X13,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f2445,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X2,tc_nat) )
| ~ spl0_112
| ~ spl0_169 ),
inference(superposition,[],[f1051,f2252]) ).
fof(f1051,plain,
( ! [X3,X11,X13] :
( c_HOL_Oord__class_Oless(X11,c_HOL_Oplus__class_Oplus(X3,X13,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat) )
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f1050]) ).
fof(f12584,plain,
( spl0_454
| ~ spl0_52
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f2436,f2251,f628,f12582]) ).
fof(f12582,plain,
( spl0_454
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f2436,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat)
| ~ spl0_52
| ~ spl0_169 ),
inference(superposition,[],[f629,f2252]) ).
fof(f12580,plain,
( spl0_453
| ~ spl0_45
| ~ spl0_108
| ~ spl0_301
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f7796,f6519,f5836,f1034,f596,f12578]) ).
fof(f12578,plain,
( spl0_453
<=> ! [X0] : c_Lambda_OdB_OVar(c_Suc(X0)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f596,plain,
( spl0_45
<=> ! [X3] : c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1034,plain,
( spl0_108
<=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(X3,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f5836,plain,
( spl0_301
<=> ! [X0,X1] : c_Lambda_Olift(X0,X1) = c_Lambda_Oliftn(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f6519,plain,
( spl0_332
<=> ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f7796,plain,
( ! [X0] : c_Lambda_OdB_OVar(c_Suc(X0)) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0)
| ~ spl0_45
| ~ spl0_108
| ~ spl0_301
| ~ spl0_332 ),
inference(forward_demodulation,[],[f7795,f597]) ).
fof(f597,plain,
( ! [X3] : c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f596]) ).
fof(f7795,plain,
( ! [X0] : c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0) = c_Lambda_OdB_OVar(c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))
| ~ spl0_108
| ~ spl0_301
| ~ spl0_332 ),
inference(forward_demodulation,[],[f7767,f1035]) ).
fof(f1035,plain,
( ! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat))
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f1034]) ).
fof(f7767,plain,
( ! [X0] : c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X0) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))
| ~ spl0_301
| ~ spl0_332 ),
inference(superposition,[],[f6520,f5837]) ).
fof(f5837,plain,
( ! [X0,X1] : c_Lambda_Olift(X0,X1) = c_Lambda_Oliftn(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1)
| ~ spl0_301 ),
inference(avatar_component_clause,[],[f5836]) ).
fof(f6520,plain,
( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1)
| ~ spl0_332 ),
inference(avatar_component_clause,[],[f6519]) ).
fof(f12576,plain,
( spl0_452
| ~ spl0_115
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2348,f2247,f1062,f12574]) ).
fof(f12574,plain,
( spl0_452
<=> ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f1062,plain,
( spl0_115
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f2247,plain,
( spl0_168
<=> ! [X6,X5,X7] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f2348,plain,
( ! [X2,X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_115
| ~ spl0_168 ),
inference(superposition,[],[f1063,f2248]) ).
fof(f2248,plain,
( ! [X6,X7,X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),tc_nat)
| ~ spl0_168 ),
inference(avatar_component_clause,[],[f2247]) ).
fof(f1063,plain,
( ! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X3 )
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f1062]) ).
fof(f12572,plain,
( spl0_451
| ~ spl0_111
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2346,f2247,f1046,f12570]) ).
fof(f12570,plain,
( spl0_451
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(X0,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f1046,plain,
( spl0_111
<=> ! [X11,X12,X13] :
( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X12,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f2346,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),X3,tc_nat)
| c_HOL_Oord__class_Oless(X0,X3,tc_nat) )
| ~ spl0_111
| ~ spl0_168 ),
inference(superposition,[],[f1047,f2248]) ).
fof(f1047,plain,
( ! [X11,X12,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X12,tc_nat)
| c_HOL_Oord__class_Oless(X11,X12,tc_nat) )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f1046]) ).
fof(f12568,plain,
( spl0_450
| ~ spl0_110
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2345,f2247,f1042,f12566]) ).
fof(f12566,plain,
( spl0_450
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f1042,plain,
( spl0_110
<=> ! [X6,X5,X7] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f2345,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X3,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X0,tc_nat) )
| ~ spl0_110
| ~ spl0_168 ),
inference(superposition,[],[f1043,f2248]) ).
fof(f1043,plain,
( ! [X6,X7,X5] :
( c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat) )
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f1042]) ).
fof(f12564,plain,
( spl0_449
| ~ spl0_51
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2337,f2247,f624,f12562]) ).
fof(f12562,plain,
( spl0_449
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f2337,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),tc_nat)
| ~ spl0_51
| ~ spl0_168 ),
inference(superposition,[],[f625,f2248]) ).
fof(f12503,plain,
( ~ spl0_23
| spl0_448
| ~ spl0_53
| ~ spl0_166 ),
inference(avatar_split_clause,[],[f2183,f1834,f632,f12501,f505]) ).
fof(f505,plain,
( spl0_23
<=> class_Orderings_Opreorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f12501,plain,
( spl0_448
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f1834,plain,
( spl0_166
<=> ! [X5,X0,X6,X7] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f2183,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| ~ class_Orderings_Opreorder(tc_nat)
| c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat) )
| ~ spl0_53
| ~ spl0_166 ),
inference(resolution,[],[f1835,f633]) ).
fof(f1835,plain,
( ! [X0,X6,X7,X5] :
( ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| ~ class_Orderings_Opreorder(X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) )
| ~ spl0_166 ),
inference(avatar_component_clause,[],[f1834]) ).
fof(f12499,plain,
( spl0_447
| ~ spl0_63
| ~ spl0_161 ),
inference(avatar_split_clause,[],[f2110,f1814,f684,f12497]) ).
fof(f12497,plain,
( spl0_447
<=> ! [X2,X0,X1] :
( c_HOL_Otimes__class_Otimes(c_Suc(X0),X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,c_Suc(X0),tc_nat)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f684,plain,
( spl0_63
<=> ! [X4,X3] : c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1814,plain,
( spl0_161
<=> ! [X4,X12,X3] :
( X3 = X4
| c_HOL_Otimes__class_Otimes(c_Suc(X12),X3,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X12),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f2110,plain,
( ! [X2,X0,X1] :
( c_HOL_Otimes__class_Otimes(c_Suc(X0),X2,tc_nat) != c_HOL_Otimes__class_Otimes(X1,c_Suc(X0),tc_nat)
| X1 = X2 )
| ~ spl0_63
| ~ spl0_161 ),
inference(superposition,[],[f1815,f685]) ).
fof(f685,plain,
( ! [X3,X4] : c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X3,tc_nat)
| ~ spl0_63 ),
inference(avatar_component_clause,[],[f684]) ).
fof(f1815,plain,
( ! [X3,X4,X12] :
( c_HOL_Otimes__class_Otimes(c_Suc(X12),X3,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X12),X4,tc_nat)
| X3 = X4 )
| ~ spl0_161 ),
inference(avatar_component_clause,[],[f1814]) ).
fof(f12495,plain,
( spl0_446
| ~ spl0_157
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f2077,f1810,f1798,f12493]) ).
fof(f12493,plain,
( spl0_446
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f1798,plain,
( spl0_157
<=> ! [X13,X12,X11] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),X13,tc_nat)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1810,plain,
( spl0_160
<=> ! [X4,X12,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f2077,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),X0,tc_nat),tc_nat) )
| ~ spl0_157
| ~ spl0_160 ),
inference(resolution,[],[f1811,f1799]) ).
fof(f1799,plain,
( ! [X11,X12,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),X13,tc_nat)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat) )
| ~ spl0_157 ),
inference(avatar_component_clause,[],[f1798]) ).
fof(f1811,plain,
( ! [X3,X4,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_160 ),
inference(avatar_component_clause,[],[f1810]) ).
fof(f12491,plain,
( spl0_445
| ~ spl0_64
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f2063,f1806,f688,f12489]) ).
fof(f12489,plain,
( spl0_445
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f688,plain,
( spl0_64
<=> ! [X4,X3] : c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1806,plain,
( spl0_159
<=> ! [X4,X12,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f2063,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
| ~ spl0_64
| ~ spl0_159 ),
inference(superposition,[],[f1807,f689]) ).
fof(f689,plain,
( ! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X3,tc_nat)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f688]) ).
fof(f1807,plain,
( ! [X3,X4,X12] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_159 ),
inference(avatar_component_clause,[],[f1806]) ).
fof(f12487,plain,
( spl0_444
| ~ spl0_64
| ~ spl0_159 ),
inference(avatar_split_clause,[],[f2055,f1806,f688,f12485]) ).
fof(f12485,plain,
( spl0_444
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f2055,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
| ~ spl0_64
| ~ spl0_159 ),
inference(superposition,[],[f1807,f689]) ).
fof(f12483,plain,
( spl0_443
| ~ spl0_97
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f7777,f6519,f904,f12481]) ).
fof(f12481,plain,
( spl0_443
<=> ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f904,plain,
( spl0_97
<=> ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f7777,plain,
( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0)),X2)
| ~ spl0_97
| ~ spl0_332 ),
inference(superposition,[],[f905,f6520]) ).
fof(f905,plain,
( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1)
| ~ spl0_97 ),
inference(avatar_component_clause,[],[f904]) ).
fof(f12479,plain,
( spl0_442
| ~ spl0_64
| ~ spl0_158 ),
inference(avatar_split_clause,[],[f2027,f1802,f688,f12477]) ).
fof(f12477,plain,
( spl0_442
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f1802,plain,
( spl0_158
<=> ! [X13,X12,X11] :
( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f2027,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
| ~ spl0_64
| ~ spl0_158 ),
inference(superposition,[],[f1803,f689]) ).
fof(f1803,plain,
( ! [X11,X12,X13] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat) )
| ~ spl0_158 ),
inference(avatar_component_clause,[],[f1802]) ).
fof(f12474,plain,
( spl0_441
| ~ spl0_52
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f2010,f1798,f628,f12472]) ).
fof(f12472,plain,
( spl0_441
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f2010,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),X1,tc_nat),tc_nat)
| ~ spl0_52
| ~ spl0_157 ),
inference(forward_demodulation,[],[f1997,f61]) ).
fof(f61,axiom,
! [X3,X4,X12] : c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).
fof(f1997,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)),X1,tc_nat),tc_nat)
| ~ spl0_52
| ~ spl0_157 ),
inference(resolution,[],[f1799,f629]) ).
fof(f12470,plain,
( spl0_440
| ~ spl0_64
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f2002,f1798,f688,f12468]) ).
fof(f12468,plain,
( spl0_440
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f2002,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X2,X1,tc_nat),tc_nat) )
| ~ spl0_64
| ~ spl0_157 ),
inference(superposition,[],[f1799,f689]) ).
fof(f12465,plain,
( spl0_439
| ~ spl0_51
| ~ spl0_157 ),
inference(avatar_split_clause,[],[f1996,f1798,f624,f12463]) ).
fof(f12463,plain,
( spl0_439
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f1996,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),X2,tc_nat),tc_nat)
| ~ spl0_51
| ~ spl0_157 ),
inference(resolution,[],[f1799,f625]) ).
fof(f12461,plain,
( spl0_438
| ~ spl0_75
| ~ spl0_156 ),
inference(avatar_split_clause,[],[f1978,f1794,f732,f12459]) ).
fof(f12459,plain,
( spl0_438
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f732,plain,
( spl0_75
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X4,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1794,plain,
( spl0_156
<=> ! [X13,X12,X11] :
( ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),X13,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1978,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_75
| ~ spl0_156 ),
inference(superposition,[],[f1795,f733]) ).
fof(f733,plain,
( ! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X4,tc_nat) = X3
| ~ spl0_75 ),
inference(avatar_component_clause,[],[f732]) ).
fof(f1795,plain,
( ! [X11,X12,X13] :
( ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),X13,tc_nat) )
| ~ spl0_156 ),
inference(avatar_component_clause,[],[f1794]) ).
fof(f12457,plain,
( spl0_437
| ~ spl0_63
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1925,f1786,f684,f12455]) ).
fof(f12455,plain,
( spl0_437
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f1786,plain,
( spl0_154
<=> ! [X4,X12,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1925,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
| ~ spl0_63
| ~ spl0_154 ),
inference(superposition,[],[f1787,f685]) ).
fof(f1787,plain,
( ! [X3,X4,X12] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_154 ),
inference(avatar_component_clause,[],[f1786]) ).
fof(f12453,plain,
( spl0_436
| ~ spl0_63
| ~ spl0_154 ),
inference(avatar_split_clause,[],[f1921,f1786,f684,f12451]) ).
fof(f12451,plain,
( spl0_436
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f1921,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
| ~ spl0_63
| ~ spl0_154 ),
inference(superposition,[],[f1787,f685]) ).
fof(f12449,plain,
( spl0_435
| ~ spl0_103
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1755,f1485,f928,f12447]) ).
fof(f12447,plain,
( spl0_435
<=> ! [X4,X0,X3,X2,X1] :
( c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OApp(X3,X4)
| c_Lambda_Olift(X2,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f928,plain,
( spl0_103
<=> ! [X34,X32,X31,X33] :
( X32 = X34
| c_Lambda_OdB_OApp(X31,X32) != c_Lambda_OdB_OApp(X33,X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1485,plain,
( spl0_145
<=> ! [X25,X12,X28] : c_Lambda_Olift(c_Lambda_OdB_OApp(X28,X25),X12) = c_Lambda_OdB_OApp(c_Lambda_Olift(X28,X12),c_Lambda_Olift(X25,X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1755,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OApp(X3,X4)
| c_Lambda_Olift(X2,X1) = X4 )
| ~ spl0_103
| ~ spl0_145 ),
inference(superposition,[],[f929,f1486]) ).
fof(f1486,plain,
( ! [X28,X25,X12] : c_Lambda_Olift(c_Lambda_OdB_OApp(X28,X25),X12) = c_Lambda_OdB_OApp(c_Lambda_Olift(X28,X12),c_Lambda_Olift(X25,X12))
| ~ spl0_145 ),
inference(avatar_component_clause,[],[f1485]) ).
fof(f929,plain,
( ! [X31,X34,X32,X33] :
( c_Lambda_OdB_OApp(X31,X32) != c_Lambda_OdB_OApp(X33,X34)
| X32 = X34 )
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f928]) ).
fof(f12445,plain,
( spl0_434
| ~ spl0_102
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1753,f1485,f924,f12443]) ).
fof(f12443,plain,
( spl0_434
<=> ! [X4,X0,X3,X2,X1] :
( c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OApp(X3,X4)
| c_Lambda_Olift(X0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f924,plain,
( spl0_102
<=> ! [X31,X34,X33,X32] :
( X31 = X33
| c_Lambda_OdB_OApp(X31,X32) != c_Lambda_OdB_OApp(X33,X34) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1753,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OApp(X3,X4)
| c_Lambda_Olift(X0,X1) = X3 )
| ~ spl0_102
| ~ spl0_145 ),
inference(superposition,[],[f925,f1486]) ).
fof(f925,plain,
( ! [X31,X34,X32,X33] :
( c_Lambda_OdB_OApp(X31,X32) != c_Lambda_OdB_OApp(X33,X34)
| X31 = X33 )
| ~ spl0_102 ),
inference(avatar_component_clause,[],[f924]) ).
fof(f12441,plain,
( spl0_433
| ~ spl0_98
| ~ spl0_144 ),
inference(avatar_split_clause,[],[f1732,f1478,f908,f12439]) ).
fof(f12439,plain,
( spl0_433
<=> ! [X0,X1] :
( c_Suc(X0) = c_Suc(X1)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f908,plain,
( spl0_98
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1478,plain,
( spl0_144
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_Suc(X3) = X4
| c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1732,plain,
( ! [X0,X1] :
( c_Suc(X0) = c_Suc(X1)
| ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_98
| ~ spl0_144 ),
inference(resolution,[],[f1479,f909]) ).
fof(f909,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X3),c_Suc(X4),tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_98 ),
inference(avatar_component_clause,[],[f908]) ).
fof(f1479,plain,
( ! [X3,X4] :
( c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat)
| c_Suc(X3) = X4
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_144 ),
inference(avatar_component_clause,[],[f1478]) ).
fof(f12437,plain,
( spl0_432
| ~ spl0_33
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f7770,f6519,f548,f12435]) ).
fof(f12435,plain,
( spl0_432
<=> ! [X2,X0,X1] : c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0) != c_Lambda_OdB_OAbs(X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f548,plain,
( spl0_33
<=> ! [X29,X27] : c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OAbs(X29) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f7770,plain,
( ! [X2,X0,X1] : c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0) != c_Lambda_OdB_OAbs(X2)
| ~ spl0_33
| ~ spl0_332 ),
inference(superposition,[],[f549,f6520]) ).
fof(f549,plain,
( ! [X29,X27] : c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OAbs(X29)
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f12433,plain,
( spl0_431
| ~ spl0_76
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1666,f1470,f736,f12431]) ).
fof(f12431,plain,
( spl0_431
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f1470,plain,
( spl0_142
<=> ! [X13,X12,X11] :
( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X11),X12,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1666,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X2,tc_nat) )
| ~ spl0_76
| ~ spl0_142 ),
inference(resolution,[],[f1471,f737]) ).
fof(f1471,plain,
( ! [X11,X12,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X11),X12,tc_nat) )
| ~ spl0_142 ),
inference(avatar_component_clause,[],[f1470]) ).
fof(f12429,plain,
( spl0_430
| ~ spl0_80
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1665,f1470,f752,f12427]) ).
fof(f12427,plain,
( spl0_430
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f1665,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X2),tc_nat)
| c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
| ~ spl0_80
| ~ spl0_142 ),
inference(resolution,[],[f1471,f753]) ).
fof(f12425,plain,
( spl0_429
| ~ spl0_83
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1566,f1458,f848,f12423]) ).
fof(f12423,plain,
( spl0_429
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f848,plain,
( spl0_83
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f1458,plain,
( spl0_139
<=> ! [X4,X3] : c_HOL_Otimes__class_Otimes(c_Suc(X3),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1566,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) )
| ~ spl0_83
| ~ spl0_139 ),
inference(superposition,[],[f849,f1459]) ).
fof(f1459,plain,
( ! [X3,X4] : c_HOL_Otimes__class_Otimes(c_Suc(X3),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat)
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f1458]) ).
fof(f849,plain,
( ! [X3,X4] :
( c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f848]) ).
fof(f12421,plain,
( spl0_428
| ~ spl0_83
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1533,f1454,f848,f12419]) ).
fof(f12419,plain,
( spl0_428
<=> ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f1454,plain,
( spl0_138
<=> ! [X4,X3] : c_HOL_Otimes__class_Otimes(X3,c_Suc(X4),tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1533,plain,
( ! [X0,X1] :
( c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) )
| ~ spl0_83
| ~ spl0_138 ),
inference(superposition,[],[f849,f1455]) ).
fof(f1455,plain,
( ! [X3,X4] : c_HOL_Otimes__class_Otimes(X3,c_Suc(X4),tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat)
| ~ spl0_138 ),
inference(avatar_component_clause,[],[f1454]) ).
fof(f12417,plain,
( spl0_427
| ~ spl0_78
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1419,f1319,f744,f12415]) ).
fof(f12415,plain,
( spl0_427
<=> ! [X0,X1] :
( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f744,plain,
( spl0_78
<=> ! [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_78])]) ).
fof(f1319,plain,
( spl0_133
<=> ! [X13,X11,X15] :
( ~ c_HOL_Oord__class_Oless(X13,X11,tc_nat)
| c_Lambda_OdB_OVar(X13) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X15,X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1419,plain,
( ! [X0,X1] :
( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_78
| ~ spl0_133 ),
inference(resolution,[],[f1320,f745]) ).
fof(f745,plain,
( ! [X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f744]) ).
fof(f1320,plain,
( ! [X11,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X11,tc_nat)
| c_Lambda_OdB_OVar(X13) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X15,X11) )
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f1319]) ).
fof(f12413,plain,
( spl0_426
| ~ spl0_78
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1393,f1307,f744,f12411]) ).
fof(f12411,plain,
( spl0_426
<=> ! [X0,X1] :
( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f1307,plain,
( spl0_130
<=> ! [X11,X4,X12] :
( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| c_Lambda_OdB_OVar(X11) = c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1393,plain,
( ! [X0,X1] :
( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X1)
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_78
| ~ spl0_130 ),
inference(resolution,[],[f1308,f745]) ).
fof(f1308,plain,
( ! [X11,X4,X12] :
( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| c_Lambda_OdB_OVar(X11) = c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X11),X12) )
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f1307]) ).
fof(f12409,plain,
( spl0_425
| ~ spl0_117
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1379,f1299,f1070,f12407]) ).
fof(f12407,plain,
( spl0_425
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f1070,plain,
( spl0_117
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X3),c_Suc(X4),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1299,plain,
( spl0_128
<=> ! [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_128])]) ).
fof(f1379,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat) )
| ~ spl0_117
| ~ spl0_128 ),
inference(superposition,[],[f1300,f1071]) ).
fof(f1071,plain,
( ! [X3,X4] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X3),c_Suc(X4),tc_nat)
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f1070]) ).
fof(f1300,plain,
( ! [X3,X4] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f1299]) ).
fof(f12405,plain,
( spl0_424
| ~ spl0_117
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1365,f1295,f1070,f12403]) ).
fof(f12403,plain,
( spl0_424
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f1295,plain,
( spl0_127
<=> ! [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_127])]) ).
fof(f1365,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(X0),tc_nat) )
| ~ spl0_117
| ~ spl0_127 ),
inference(superposition,[],[f1296,f1071]) ).
fof(f1296,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(X4,X3,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f1295]) ).
fof(f12401,plain,
( spl0_423
| ~ spl0_109
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1348,f1282,f1038,f12399]) ).
fof(f12399,plain,
( spl0_423
<=> ! [X2,X0,X1] :
( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)
| c_Suc(X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f1038,plain,
( spl0_109
<=> ! [X4,X3] : c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X3),X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1282,plain,
( spl0_124
<=> ! [X4,X12,X3] :
( X3 = X4
| c_HOL_Oplus__class_Oplus(X4,X12,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X12,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1348,plain,
( ! [X2,X0,X1] :
( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)
| c_Suc(X0) = X2 )
| ~ spl0_109
| ~ spl0_124 ),
inference(superposition,[],[f1283,f1039]) ).
fof(f1039,plain,
( ! [X3,X4] : c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X3),X4,tc_nat)
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f1038]) ).
fof(f1283,plain,
( ! [X3,X4,X12] :
( c_HOL_Oplus__class_Oplus(X4,X12,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X12,tc_nat)
| X3 = X4 )
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f1282]) ).
fof(f12397,plain,
( spl0_422
| ~ spl0_108
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1347,f1282,f1034,f12395]) ).
fof(f12395,plain,
( spl0_422
<=> ! [X2,X0,X1] :
( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(X2,c_Suc(X1),tc_nat)
| X0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f1347,plain,
( ! [X2,X0,X1] :
( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(X2,c_Suc(X1),tc_nat)
| X0 = X2 )
| ~ spl0_108
| ~ spl0_124 ),
inference(superposition,[],[f1283,f1035]) ).
fof(f12393,plain,
( spl0_421
| ~ spl0_45
| ~ spl0_310 ),
inference(avatar_split_clause,[],[f6763,f6405,f596,f12391]) ).
fof(f12391,plain,
( spl0_421
<=> ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f6405,plain,
( spl0_310
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f6763,plain,
( ! [X0] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(X0),tc_nat)
| ~ spl0_45
| ~ spl0_310 ),
inference(superposition,[],[f6406,f597]) ).
fof(f6406,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ spl0_310 ),
inference(avatar_component_clause,[],[f6405]) ).
fof(f12389,plain,
( spl0_420
| ~ spl0_109
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1328,f1278,f1038,f12387]) ).
fof(f12387,plain,
( spl0_420
<=> ! [X2,X0,X1] :
( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(c_Suc(X0),X2,tc_nat)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f1278,plain,
( spl0_123
<=> ! [X6,X5,X7] :
( X6 = X7
| c_HOL_Oplus__class_Oplus(X5,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1328,plain,
( ! [X2,X0,X1] :
( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(c_Suc(X0),X2,tc_nat)
| X1 = X2 )
| ~ spl0_109
| ~ spl0_123 ),
inference(superposition,[],[f1279,f1039]) ).
fof(f1279,plain,
( ! [X6,X7,X5] :
( c_HOL_Oplus__class_Oplus(X5,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat)
| X6 = X7 )
| ~ spl0_123 ),
inference(avatar_component_clause,[],[f1278]) ).
fof(f12385,plain,
( spl0_419
| ~ spl0_108
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1327,f1278,f1034,f12383]) ).
fof(f12383,plain,
( spl0_419
<=> ! [X2,X0,X1] :
( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)
| c_Suc(X1) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f1327,plain,
( ! [X2,X0,X1] :
( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)
| c_Suc(X1) = X2 )
| ~ spl0_108
| ~ spl0_123 ),
inference(superposition,[],[f1279,f1035]) ).
fof(f12381,plain,
( spl0_418
| ~ spl0_96
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1269,f1090,f900,f12379]) ).
fof(f12379,plain,
( spl0_418
<=> ! [X0,X1] :
( c_Lambda_OdB_OVar(c_Suc(X0)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_Suc(X0)),c_Suc(X1))
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f900,plain,
( spl0_96
<=> ! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1090,plain,
( spl0_120
<=> ! [X11,X12] :
( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| c_Lambda_OdB_OVar(X11) = c_Lambda_Olift(c_Lambda_OdB_OVar(X11),X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1269,plain,
( ! [X0,X1] :
( c_Lambda_OdB_OVar(c_Suc(X0)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_Suc(X0)),c_Suc(X1))
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_96
| ~ spl0_120 ),
inference(resolution,[],[f1091,f901]) ).
fof(f901,plain,
( ! [X4,X5] :
( c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat)
| ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat) )
| ~ spl0_96 ),
inference(avatar_component_clause,[],[f900]) ).
fof(f1091,plain,
( ! [X11,X12] :
( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| c_Lambda_OdB_OVar(X11) = c_Lambda_Olift(c_Lambda_OdB_OVar(X11),X12) )
| ~ spl0_120 ),
inference(avatar_component_clause,[],[f1090]) ).
fof(f12377,plain,
( spl0_417
| ~ spl0_53
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1266,f1090,f632,f12375]) ).
fof(f12375,plain,
( spl0_417
<=> ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),c_Suc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f1266,plain,
( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat)),c_Suc(X0))
| ~ spl0_53
| ~ spl0_120 ),
inference(resolution,[],[f1091,f633]) ).
fof(f12373,plain,
( spl0_416
| ~ spl0_110
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1263,f1090,f1042,f12371]) ).
fof(f12371,plain,
( spl0_416
<=> ! [X2,X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat))
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f1263,plain,
( ! [X2,X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat))
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_110
| ~ spl0_120 ),
inference(resolution,[],[f1091,f1043]) ).
fof(f12369,plain,
( spl0_415
| ~ spl0_112
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1262,f1090,f1050,f12367]) ).
fof(f12367,plain,
( spl0_415
<=> ! [X2,X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat))
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f1262,plain,
( ! [X2,X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat))
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
| ~ spl0_112
| ~ spl0_120 ),
inference(resolution,[],[f1091,f1051]) ).
fof(f12365,plain,
( spl0_414
| ~ spl0_119
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1259,f1090,f1086,f12363]) ).
fof(f12363,plain,
( spl0_414
<=> ! [X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f1086,plain,
( spl0_119
<=> ! [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_119])]) ).
fof(f1259,plain,
( ! [X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1)
| c_HOL_Oord__class_Oless(X1,X0,tc_nat)
| X0 = X1 )
| ~ spl0_119
| ~ spl0_120 ),
inference(resolution,[],[f1091,f1087]) ).
fof(f1087,plain,
( ! [X3,X4] :
( c_HOL_Oord__class_Oless(X4,X3,tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| X3 = X4 )
| ~ spl0_119 ),
inference(avatar_component_clause,[],[f1086]) ).
fof(f12361,plain,
( spl0_413
| ~ spl0_111
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f1171,f1050,f1046,f12359]) ).
fof(f12359,plain,
( spl0_413
<=> ! [X0,X3,X2,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f1171,plain,
( ! [X2,X3,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X3,X2,tc_nat),tc_nat) )
| ~ spl0_111
| ~ spl0_112 ),
inference(resolution,[],[f1051,f1047]) ).
fof(f12357,plain,
( spl0_412
| ~ spl0_110
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1152,f1046,f1042,f12355]) ).
fof(f12355,plain,
( spl0_412
<=> ! [X0,X3,X2,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f1152,plain,
( ! [X2,X3,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X3,tc_nat),X1,tc_nat) )
| ~ spl0_110
| ~ spl0_111 ),
inference(resolution,[],[f1047,f1043]) ).
fof(f12297,plain,
( spl0_411
| ~ spl0_266
| ~ spl0_280 ),
inference(avatar_split_clause,[],[f5732,f5310,f4853,f12295]) ).
fof(f12295,plain,
( spl0_411
<=> ! [X0] : c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f4853,plain,
( spl0_266
<=> ! [X0] : c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f5310,plain,
( spl0_280
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f5732,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_266
| ~ spl0_280 ),
inference(superposition,[],[f5311,f4854]) ).
fof(f4854,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat) = X0
| ~ spl0_266 ),
inference(avatar_component_clause,[],[f4853]) ).
fof(f5311,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat)
| ~ spl0_280 ),
inference(avatar_component_clause,[],[f5310]) ).
fof(f11412,plain,
( spl0_410
| ~ spl0_27
| ~ spl0_271 ),
inference(avatar_split_clause,[],[f5413,f5262,f524,f11410]) ).
fof(f11410,plain,
( spl0_410
<=> ! [X0] :
( c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f524,plain,
( spl0_27
<=> ! [X4] : c_Suc(X4) != X4 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f5262,plain,
( spl0_271
<=> ! [X0] :
( c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0)) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f5413,plain,
( ! [X0] :
( c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_27
| ~ spl0_271 ),
inference(superposition,[],[f525,f5263]) ).
fof(f5263,plain,
( ! [X0] :
( c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0)) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_271 ),
inference(avatar_component_clause,[],[f5262]) ).
fof(f525,plain,
( ! [X4] : c_Suc(X4) != X4
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f10603,plain,
( spl0_409
| ~ spl0_107
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2884,f1826,f1030,f10601]) ).
fof(f10601,plain,
( spl0_409
<=> ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f1030,plain,
( spl0_107
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1826,plain,
( spl0_164
<=> ! [X0] : c_Suc(X0) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f2884,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_107
| ~ spl0_164 ),
inference(superposition,[],[f1031,f1827]) ).
fof(f1827,plain,
( ! [X0] : c_Suc(X0) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)))
| ~ spl0_164 ),
inference(avatar_component_clause,[],[f1826]) ).
fof(f1031,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_107 ),
inference(avatar_component_clause,[],[f1030]) ).
fof(f9901,plain,
( spl0_408
| ~ spl0_107
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2207,f1782,f1030,f9899]) ).
fof(f9899,plain,
( spl0_408
<=> ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f1782,plain,
( spl0_153
<=> ! [X0] : c_Suc(X0) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f2207,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_107
| ~ spl0_153 ),
inference(superposition,[],[f1031,f1783]) ).
fof(f1783,plain,
( ! [X0] : c_Suc(X0) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)))
| ~ spl0_153 ),
inference(avatar_component_clause,[],[f1782]) ).
fof(f9635,plain,
( spl0_407
| ~ spl0_47
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f3986,f3602,f604,f9633]) ).
fof(f9633,plain,
( spl0_407
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f604,plain,
( spl0_47
<=> ! [X13,X11] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f3986,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X2,tc_nat),tc_nat)
| ~ spl0_47
| ~ spl0_230 ),
inference(superposition,[],[f605,f3603]) ).
fof(f605,plain,
( ! [X11,X13] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),X11,tc_nat)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f604]) ).
fof(f9631,plain,
( spl0_406
| ~ spl0_46
| ~ spl0_230 ),
inference(avatar_split_clause,[],[f3985,f3602,f600,f9629]) ).
fof(f9629,plain,
( spl0_406
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f600,plain,
( spl0_46
<=> ! [X13,X11] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f3985,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
| ~ spl0_46
| ~ spl0_230 ),
inference(superposition,[],[f601,f3603]) ).
fof(f601,plain,
( ! [X11,X13] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X11,tc_nat)
| ~ spl0_46 ),
inference(avatar_component_clause,[],[f600]) ).
fof(f9627,plain,
( spl0_405
| ~ spl0_47
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f3899,f3598,f604,f9625]) ).
fof(f9625,plain,
( spl0_405
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f3899,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X2,X1,tc_nat),tc_nat)
| ~ spl0_47
| ~ spl0_229 ),
inference(superposition,[],[f605,f3599]) ).
fof(f9623,plain,
( spl0_404
| ~ spl0_46
| ~ spl0_229 ),
inference(avatar_split_clause,[],[f3898,f3598,f600,f9621]) ).
fof(f9621,plain,
( spl0_404
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f3898,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
| ~ spl0_46
| ~ spl0_229 ),
inference(superposition,[],[f601,f3599]) ).
fof(f9619,plain,
( spl0_403
| ~ spl0_52
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2745,f2291,f628,f9617]) ).
fof(f9617,plain,
( spl0_403
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f2745,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))) = X0 )
| ~ spl0_52
| ~ spl0_179 ),
inference(resolution,[],[f2292,f629]) ).
fof(f9615,plain,
( spl0_402
| ~ spl0_51
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2744,f2291,f624,f9613]) ).
fof(f9613,plain,
( spl0_402
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f2744,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))) = X0 )
| ~ spl0_51
| ~ spl0_179 ),
inference(resolution,[],[f2292,f625]) ).
fof(f9611,plain,
( spl0_401
| ~ spl0_117
| ~ spl0_147 ),
inference(avatar_split_clause,[],[f1961,f1650,f1070,f9609]) ).
fof(f9609,plain,
( spl0_401
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f1650,plain,
( spl0_147
<=> ! [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_147])]) ).
fof(f1961,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_117
| ~ spl0_147 ),
inference(superposition,[],[f1651,f1071]) ).
fof(f1651,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_147 ),
inference(avatar_component_clause,[],[f1650]) ).
fof(f9607,plain,
( spl0_400
| ~ spl0_42
| ~ spl0_170 ),
inference(avatar_split_clause,[],[f2500,f2255,f584,f9605]) ).
fof(f9605,plain,
( spl0_400
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f584,plain,
( spl0_42
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f2500,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat),tc_nat)
| ~ spl0_42
| ~ spl0_170 ),
inference(superposition,[],[f2256,f585]) ).
fof(f585,plain,
( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X3,X3,tc_nat)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f584]) ).
fof(f9603,plain,
( spl0_399
| ~ spl0_46
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f2433,f2251,f600,f9601]) ).
fof(f9601,plain,
( spl0_399
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f2433,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| ~ spl0_46
| ~ spl0_169 ),
inference(superposition,[],[f601,f2252]) ).
fof(f9599,plain,
( spl0_398
| ~ spl0_84
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2344,f2247,f852,f9597]) ).
fof(f9597,plain,
( spl0_398
<=> ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f852,plain,
( spl0_84
<=> ! [X4,X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f2344,plain,
( ! [X2,X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_84
| ~ spl0_168 ),
inference(superposition,[],[f853,f2248]) ).
fof(f853,plain,
( ! [X3,X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat)
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f852]) ).
fof(f9595,plain,
( spl0_397
| ~ spl0_47
| ~ spl0_168 ),
inference(avatar_split_clause,[],[f2336,f2247,f604,f9593]) ).
fof(f9593,plain,
( spl0_397
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f2336,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat),c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)
| ~ spl0_47
| ~ spl0_168 ),
inference(superposition,[],[f605,f2248]) ).
fof(f9545,plain,
( ~ spl0_12
| spl0_396
| ~ spl0_78
| ~ spl0_163 ),
inference(avatar_split_clause,[],[f2143,f1822,f744,f9543,f450]) ).
fof(f450,plain,
( spl0_12
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f9543,plain,
( spl0_396
<=> ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f1822,plain,
( spl0_163
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| 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(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f2143,plain,
( ! [X0] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Nat_Osemiring__1__class_Oof__nat(X0,tc_nat) )
| ~ spl0_78
| ~ spl0_163 ),
inference(resolution,[],[f1823,f745]) ).
fof(f1823,plain,
( ! [X0,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_163 ),
inference(avatar_component_clause,[],[f1822]) ).
fof(f9541,plain,
( spl0_395
| ~ spl0_78
| ~ spl0_162 ),
inference(avatar_split_clause,[],[f2116,f1818,f744,f9539]) ).
fof(f9539,plain,
( spl0_395
<=> ! [X0] :
( c_Suc(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f1818,plain,
( spl0_162
<=> ! [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_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f2116,plain,
( ! [X0] :
( c_Suc(c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_78
| ~ spl0_162 ),
inference(resolution,[],[f1819,f745]) ).
fof(f1819,plain,
( ! [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_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X4 )
| ~ spl0_162 ),
inference(avatar_component_clause,[],[f1818]) ).
fof(f9537,plain,
( spl0_394
| ~ spl0_52
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1669,f1470,f628,f9535]) ).
fof(f9535,plain,
( spl0_394
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f1669,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X1,X2,tc_nat)),tc_nat) )
| ~ spl0_52
| ~ spl0_142 ),
inference(resolution,[],[f1471,f629]) ).
fof(f9533,plain,
( spl0_393
| ~ spl0_51
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1668,f1470,f624,f9531]) ).
fof(f9531,plain,
( spl0_393
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f1668,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X2,X1,tc_nat)),tc_nat) )
| ~ spl0_51
| ~ spl0_142 ),
inference(resolution,[],[f1471,f625]) ).
fof(f9529,plain,
( spl0_392
| ~ spl0_53
| ~ spl0_142 ),
inference(avatar_split_clause,[],[f1664,f1470,f632,f9527]) ).
fof(f9527,plain,
( spl0_392
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f1664,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(X1),tc_nat) )
| ~ spl0_53
| ~ spl0_142 ),
inference(resolution,[],[f1471,f633]) ).
fof(f9517,plain,
( spl0_391
| ~ spl0_54
| ~ spl0_93
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1617,f1462,f888,f636,f9515]) ).
fof(f9515,plain,
( spl0_391
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f636,plain,
( spl0_54
<=> ! [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_54])]) ).
fof(f1462,plain,
( spl0_140
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1617,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0)) = X0 )
| ~ spl0_54
| ~ spl0_93
| ~ spl0_140 ),
inference(forward_demodulation,[],[f1597,f637]) ).
fof(f637,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_54 ),
inference(avatar_component_clause,[],[f636]) ).
fof(f1597,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0)) = X0 )
| ~ spl0_93
| ~ spl0_140 ),
inference(resolution,[],[f1463,f889]) ).
fof(f1463,plain,
( ! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = X3 )
| ~ spl0_140 ),
inference(avatar_component_clause,[],[f1462]) ).
fof(f9513,plain,
( spl0_390
| ~ spl0_54
| ~ spl0_95
| ~ spl0_140 ),
inference(avatar_split_clause,[],[f1616,f1462,f896,f636,f9511]) ).
fof(f9511,plain,
( spl0_390
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f1616,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X0)) = X0 )
| ~ spl0_54
| ~ spl0_95
| ~ spl0_140 ),
inference(forward_demodulation,[],[f1596,f637]) ).
fof(f1596,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat),tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X0)) = X0 )
| ~ spl0_95
| ~ spl0_140 ),
inference(resolution,[],[f1463,f897]) ).
fof(f9509,plain,
( spl0_389
| ~ spl0_75
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1565,f1458,f732,f9507]) ).
fof(f9507,plain,
( spl0_389
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f1565,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat)
| ~ spl0_75
| ~ spl0_139 ),
inference(superposition,[],[f733,f1459]) ).
fof(f9505,plain,
( spl0_388
| ~ spl0_74
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1564,f1458,f728,f9503]) ).
fof(f9503,plain,
( spl0_388
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f728,plain,
( spl0_74
<=> ! [X4,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X4,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1564,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) = X0
| ~ spl0_74
| ~ spl0_139 ),
inference(superposition,[],[f729,f1459]) ).
fof(f729,plain,
( ! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X4,tc_nat) = X3
| ~ spl0_74 ),
inference(avatar_component_clause,[],[f728]) ).
fof(f9501,plain,
( spl0_387
| ~ spl0_63
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1553,f1458,f684,f9499]) ).
fof(f9499,plain,
( spl0_387
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f1553,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(c_Suc(X0),X1,tc_nat) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
| ~ spl0_63
| ~ spl0_139 ),
inference(superposition,[],[f1459,f685]) ).
fof(f9497,plain,
( spl0_386
| ~ spl0_75
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1532,f1454,f732,f9495]) ).
fof(f9495,plain,
( spl0_386
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f1532,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X0,tc_nat)
| ~ spl0_75
| ~ spl0_138 ),
inference(superposition,[],[f733,f1455]) ).
fof(f9493,plain,
( spl0_385
| ~ spl0_74
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1531,f1454,f728,f9491]) ).
fof(f9491,plain,
( spl0_385
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f1531,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) = X0
| ~ spl0_74
| ~ spl0_138 ),
inference(superposition,[],[f729,f1455]) ).
fof(f9489,plain,
( spl0_384
| ~ spl0_63
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1521,f1454,f684,f9487]) ).
fof(f9487,plain,
( spl0_384
<=> ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f1521,plain,
( ! [X0,X1] : c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat) = c_HOL_Oplus__class_Oplus(X0,c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
| ~ spl0_63
| ~ spl0_138 ),
inference(superposition,[],[f1455,f685]) ).
fof(f9485,plain,
( spl0_383
| ~ spl0_76
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1430,f1319,f736,f9483]) ).
fof(f9483,plain,
( spl0_383
<=> ! [X2,X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(X2))
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f1430,plain,
( ! [X2,X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(X2))
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
| ~ spl0_76
| ~ spl0_133 ),
inference(resolution,[],[f1320,f737]) ).
fof(f9481,plain,
( spl0_382
| ~ spl0_80
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1429,f1319,f752,f9479]) ).
fof(f9479,plain,
( spl0_382
<=> ! [X2,X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(X2))
| c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f1429,plain,
( ! [X2,X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(X2))
| c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
| ~ spl0_80
| ~ spl0_133 ),
inference(resolution,[],[f1320,f753]) ).
fof(f9477,plain,
( spl0_381
| ~ spl0_81
| ~ spl0_333 ),
inference(avatar_split_clause,[],[f7829,f7625,f756,f9475]) ).
fof(f9475,plain,
( spl0_381
<=> ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f756,plain,
( spl0_81
<=> ! [X28,X24] :
( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X24),X28)
| c_Lambda_Obeta(X24,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X24,X28)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f7625,plain,
( spl0_333
<=> ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f7829,plain,
( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1)),X2)
| ~ spl0_81
| ~ spl0_333 ),
inference(resolution,[],[f7626,f757]) ).
fof(f757,plain,
( ! [X28,X24] :
( c_Lambda_Obeta(X24,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X24,X28))
| ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X24),X28) )
| ~ spl0_81 ),
inference(avatar_component_clause,[],[f756]) ).
fof(f7626,plain,
( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1),X2)
| ~ spl0_333 ),
inference(avatar_component_clause,[],[f7625]) ).
fof(f9473,plain,
( spl0_380
| ~ spl0_59
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1417,f1315,f656,f9471]) ).
fof(f9471,plain,
( spl0_380
<=> ! [X0,X3,X2,X1] : c_Lambda_Oliftn(X0,X1,X2) = c_Lambda_Osubst(c_Lambda_Oliftn(c_Suc(X0),X1,X2),X3,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f1315,plain,
( spl0_132
<=> ! [X25,X12,X4] : c_Lambda_Oliftn(c_Suc(X4),X25,X12) = c_Lambda_Olift(c_Lambda_Oliftn(X4,X25,X12),X12) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1417,plain,
( ! [X2,X3,X0,X1] : c_Lambda_Oliftn(X0,X1,X2) = c_Lambda_Osubst(c_Lambda_Oliftn(c_Suc(X0),X1,X2),X3,X2)
| ~ spl0_59
| ~ spl0_132 ),
inference(superposition,[],[f657,f1316]) ).
fof(f1316,plain,
( ! [X4,X25,X12] : c_Lambda_Oliftn(c_Suc(X4),X25,X12) = c_Lambda_Olift(c_Lambda_Oliftn(X4,X25,X12),X12)
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f1315]) ).
fof(f9469,plain,
( spl0_379
| ~ spl0_76
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1404,f1307,f736,f9467]) ).
fof(f9467,plain,
( spl0_379
<=> ! [X2,X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(X2))
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f1404,plain,
( ! [X2,X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(X2))
| ~ c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
| ~ spl0_76
| ~ spl0_130 ),
inference(resolution,[],[f1308,f737]) ).
fof(f9465,plain,
( spl0_378
| ~ spl0_80
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1403,f1307,f752,f9463]) ).
fof(f9463,plain,
( spl0_378
<=> ! [X2,X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(X2))
| c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f1403,plain,
( ! [X2,X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(X2))
| c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
| ~ spl0_80
| ~ spl0_130 ),
inference(resolution,[],[f1308,f753]) ).
fof(f9461,plain,
( spl0_377
| ~ spl0_53
| ~ spl0_129 ),
inference(avatar_split_clause,[],[f1382,f1303,f632,f9459]) ).
fof(f9459,plain,
( spl0_377
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f1303,plain,
( spl0_129
<=> ! [X4,X3] :
( X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1382,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X0,tc_nat)
| c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) = X0 )
| ~ spl0_53
| ~ spl0_129 ),
inference(resolution,[],[f1304,f633]) ).
fof(f1304,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| X3 = X4 )
| ~ spl0_129 ),
inference(avatar_component_clause,[],[f1303]) ).
fof(f9457,plain,
( spl0_376
| ~ spl0_78
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1258,f1090,f744,f9455]) ).
fof(f9455,plain,
( spl0_376
<=> ! [X0] :
( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f1258,plain,
( ! [X0] :
( c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_78
| ~ spl0_120 ),
inference(resolution,[],[f1091,f745]) ).
fof(f9453,plain,
( spl0_375
| ~ spl0_47
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1232,f1086,f604,f9451]) ).
fof(f9451,plain,
( spl0_375
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f1232,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X1 )
| ~ spl0_47
| ~ spl0_119 ),
inference(resolution,[],[f1087,f605]) ).
fof(f9449,plain,
( spl0_374
| ~ spl0_46
| ~ spl0_119 ),
inference(avatar_split_clause,[],[f1231,f1086,f600,f9447]) ).
fof(f9447,plain,
( spl0_374
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f1231,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat)
| c_HOL_Oplus__class_Oplus(X0,X1,tc_nat) = X0 )
| ~ spl0_46
| ~ spl0_119 ),
inference(resolution,[],[f1087,f601]) ).
fof(f9445,plain,
( spl0_373
| ~ spl0_94
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1205,f1082,f892,f9443]) ).
fof(f9443,plain,
( spl0_373
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f892,plain,
( spl0_94
<=> ! [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) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1205,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,X1,tc_nat) )
| ~ spl0_94
| ~ spl0_118 ),
inference(resolution,[],[f1083,f893]) ).
fof(f893,plain,
( ! [X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X4 )
| ~ spl0_94 ),
inference(avatar_component_clause,[],[f892]) ).
fof(f9441,plain,
( spl0_372
| ~ spl0_108
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f1178,f1050,f1034,f9439]) ).
fof(f9439,plain,
( spl0_372
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f1178,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X1),tc_nat) )
| ~ spl0_108
| ~ spl0_112 ),
inference(superposition,[],[f1051,f1035]) ).
fof(f9437,plain,
( spl0_371
| ~ spl0_109
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1158,f1046,f1038,f9435]) ).
fof(f9435,plain,
( spl0_371
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f1158,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X0),X2,tc_nat) )
| ~ spl0_109
| ~ spl0_111 ),
inference(superposition,[],[f1047,f1039]) ).
fof(f9425,plain,
( spl0_370
| ~ spl0_109
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1144,f1042,f1038,f9423]) ).
fof(f9423,plain,
( spl0_370
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f1144,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,c_Suc(X0),tc_nat) )
| ~ spl0_109
| ~ spl0_110 ),
inference(superposition,[],[f1043,f1039]) ).
fof(f8731,plain,
( spl0_369
| ~ spl0_29
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f7769,f6519,f532,f8729]) ).
fof(f8729,plain,
( spl0_369
<=> ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f532,plain,
( spl0_29
<=> ! [X25,X11] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X11),X25) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f7769,plain,
( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0),X2)
| ~ spl0_29
| ~ spl0_332 ),
inference(superposition,[],[f533,f6520]) ).
fof(f533,plain,
( ! [X11,X25] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X11),X25)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f532]) ).
fof(f8095,plain,
( spl0_368
| ~ spl0_97
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f7291,f6469,f904,f8093]) ).
fof(f8093,plain,
( spl0_368
<=> ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f6469,plain,
( spl0_320
<=> ! [X0,X3,X2,X1] :
( c_Lambda_Obeta(X0,c_Lambda_Osubst(X3,X2,X1))
| ~ c_Lambda_Obeta(c_Lambda_Olift(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f7291,plain,
( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1),X2)
| ~ spl0_97
| ~ spl0_320 ),
inference(resolution,[],[f6470,f905]) ).
fof(f6470,plain,
( ! [X2,X3,X0,X1] :
( c_Lambda_Obeta(X0,c_Lambda_Osubst(X3,X2,X1))
| ~ c_Lambda_Obeta(c_Lambda_Olift(X0,X1),X3) )
| ~ spl0_320 ),
inference(avatar_component_clause,[],[f6469]) ).
fof(f7949,plain,
( spl0_367
| ~ spl0_54
| ~ spl0_209 ),
inference(avatar_split_clause,[],[f3477,f3356,f636,f7947]) ).
fof(f7947,plain,
( spl0_367
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f3356,plain,
( spl0_209
<=> ! [X4,X3] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f3477,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_54
| ~ spl0_209 ),
inference(trivial_inequality_removal,[],[f3469]) ).
fof(f3469,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_54
| ~ spl0_209 ),
inference(superposition,[],[f3357,f637]) ).
fof(f3357,plain,
( ! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X4,X3,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat)
| X3 = X4 )
| ~ spl0_209 ),
inference(avatar_component_clause,[],[f3356]) ).
fof(f7945,plain,
( spl0_366
| ~ spl0_32
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f2685,f2287,f544,f7943]) ).
fof(f7943,plain,
( spl0_366
<=> ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),c_HOL_Ozero__class_Ozero(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f544,plain,
( spl0_32
<=> ! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f2685,plain,
( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),c_HOL_Ozero__class_Ozero(tc_nat))
| ~ spl0_32
| ~ spl0_178 ),
inference(resolution,[],[f2288,f545]) ).
fof(f545,plain,
( ! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_32 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f7941,plain,
( spl0_365
| ~ spl0_115
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1571,f1458,f1062,f7939]) ).
fof(f7939,plain,
( spl0_365
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f1571,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_115
| ~ spl0_139 ),
inference(superposition,[],[f1063,f1459]) ).
fof(f7937,plain,
( spl0_364
| ~ spl0_111
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1569,f1458,f1046,f7935]) ).
fof(f7935,plain,
( spl0_364
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f1569,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
| ~ spl0_111
| ~ spl0_139 ),
inference(superposition,[],[f1047,f1459]) ).
fof(f7933,plain,
( spl0_363
| ~ spl0_110
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1568,f1458,f1042,f7931]) ).
fof(f7931,plain,
( spl0_363
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f1568,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
| ~ spl0_110
| ~ spl0_139 ),
inference(superposition,[],[f1043,f1459]) ).
fof(f7929,plain,
( spl0_362
| ~ spl0_51
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1562,f1458,f624,f7927]) ).
fof(f7927,plain,
( spl0_362
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f1562,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)),tc_nat)
| ~ spl0_51
| ~ spl0_139 ),
inference(superposition,[],[f625,f1459]) ).
fof(f7919,plain,
( spl0_361
| ~ spl0_115
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1538,f1454,f1062,f7917]) ).
fof(f7917,plain,
( spl0_361
<=> ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f1538,plain,
( ! [X0,X1] :
( c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_115
| ~ spl0_138 ),
inference(superposition,[],[f1063,f1455]) ).
fof(f7915,plain,
( spl0_360
| ~ spl0_111
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1536,f1454,f1046,f7913]) ).
fof(f7913,plain,
( spl0_360
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f1536,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
| ~ spl0_111
| ~ spl0_138 ),
inference(superposition,[],[f1047,f1455]) ).
fof(f7911,plain,
( spl0_359
| ~ spl0_110
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1535,f1454,f1042,f7909]) ).
fof(f7909,plain,
( spl0_359
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f1535,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
| ~ spl0_110
| ~ spl0_138 ),
inference(superposition,[],[f1043,f1455]) ).
fof(f7907,plain,
( spl0_358
| ~ spl0_51
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1529,f1454,f624,f7905]) ).
fof(f7905,plain,
( spl0_358
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f1529,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat)
| ~ spl0_51
| ~ spl0_138 ),
inference(superposition,[],[f625,f1455]) ).
fof(f7903,plain,
( spl0_357
| ~ spl0_78
| ~ spl0_137 ),
inference(avatar_split_clause,[],[f1511,f1450,f744,f7901]) ).
fof(f7901,plain,
( spl0_357
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f1450,plain,
( spl0_137
<=> ! [X4,X3] :
( 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),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1511,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X0,X1,tc_nat) )
| ~ spl0_78
| ~ spl0_137 ),
inference(resolution,[],[f1451,f745]) ).
fof(f1451,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X3,tc_nat) )
| ~ spl0_137 ),
inference(avatar_component_clause,[],[f1450]) ).
fof(f7899,plain,
( spl0_356
| ~ spl0_78
| ~ spl0_136 ),
inference(avatar_split_clause,[],[f1503,f1446,f744,f7897]) ).
fof(f7897,plain,
( spl0_356
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f1446,plain,
( spl0_136
<=> ! [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),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1503,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X1,X0,tc_nat) )
| ~ spl0_78
| ~ spl0_136 ),
inference(resolution,[],[f1447,f745]) ).
fof(f1447,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) )
| ~ spl0_136 ),
inference(avatar_component_clause,[],[f1446]) ).
fof(f7895,plain,
( spl0_355
| ~ spl0_52
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1433,f1319,f628,f7893]) ).
fof(f7893,plain,
( spl0_355
<=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f1433,plain,
( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)))
| ~ spl0_52
| ~ spl0_133 ),
inference(resolution,[],[f1320,f629]) ).
fof(f7891,plain,
( spl0_354
| ~ spl0_51
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1432,f1319,f624,f7889]) ).
fof(f7889,plain,
( spl0_354
<=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f1432,plain,
( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat)))
| ~ spl0_51
| ~ spl0_133 ),
inference(resolution,[],[f1320,f625]) ).
fof(f7887,plain,
( spl0_353
| ~ spl0_52
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1407,f1307,f628,f7885]) ).
fof(f7885,plain,
( spl0_353
<=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f1407,plain,
( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)))
| ~ spl0_52
| ~ spl0_130 ),
inference(resolution,[],[f1308,f629]) ).
fof(f7883,plain,
( spl0_352
| ~ spl0_51
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1406,f1307,f624,f7881]) ).
fof(f7881,plain,
( spl0_352
<=> ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f1406,plain,
( ! [X2,X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X2,X0,tc_nat)))
| ~ spl0_51
| ~ spl0_130 ),
inference(resolution,[],[f1308,f625]) ).
fof(f7879,plain,
( spl0_351
| ~ spl0_26
| ~ spl0_332 ),
inference(avatar_split_clause,[],[f7768,f6519,f520,f7877]) ).
fof(f7877,plain,
( spl0_351
<=> ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f520,plain,
( spl0_26
<=> ! [X4] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f7768,plain,
( ! [X0,X1] : c_InductTermi_OIT(c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),X0))
| ~ spl0_26
| ~ spl0_332 ),
inference(superposition,[],[f521,f6520]) ).
fof(f521,plain,
( ! [X4] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X4))
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f520]) ).
fof(f7875,plain,
( spl0_350
| ~ spl0_75
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1378,f1299,f732,f7873]) ).
fof(f7873,plain,
( spl0_350
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f1378,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_75
| ~ spl0_128 ),
inference(superposition,[],[f1300,f733]) ).
fof(f7871,plain,
( spl0_349
| ~ spl0_74
| ~ spl0_128 ),
inference(avatar_split_clause,[],[f1377,f1299,f728,f7869]) ).
fof(f7869,plain,
( spl0_349
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f1377,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X0,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X1,tc_nat),tc_nat) )
| ~ spl0_74
| ~ spl0_128 ),
inference(superposition,[],[f1300,f729]) ).
fof(f7867,plain,
( spl0_348
| ~ spl0_64
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1325,f1278,f688,f7865]) ).
fof(f7865,plain,
( spl0_348
<=> ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f1325,plain,
( ! [X2,X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != c_HOL_Oplus__class_Oplus(X0,X2,tc_nat)
| X1 = X2 )
| ~ spl0_64
| ~ spl0_123 ),
inference(superposition,[],[f1279,f689]) ).
fof(f7863,plain,
( spl0_347
| ~ spl0_76
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1268,f1090,f736,f7861]) ).
fof(f7861,plain,
( spl0_347
<=> ! [X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(X1))
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f1268,plain,
( ! [X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(X1))
| ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat) )
| ~ spl0_76
| ~ spl0_120 ),
inference(resolution,[],[f1091,f737]) ).
fof(f7859,plain,
( spl0_346
| ~ spl0_80
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1267,f1090,f752,f7857]) ).
fof(f7857,plain,
( spl0_346
<=> ! [X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(X1))
| c_HOL_Oord__class_Oless(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f1267,plain,
( ! [X0,X1] :
( c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(X1))
| c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_80
| ~ spl0_120 ),
inference(resolution,[],[f1091,f753]) ).
fof(f7855,plain,
( spl0_345
| ~ spl0_117
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1218,f1082,f1070,f7853]) ).
fof(f7853,plain,
( spl0_345
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X0),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f1218,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),X2,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X0),X2,tc_nat) )
| ~ spl0_117
| ~ spl0_118 ),
inference(superposition,[],[f1083,f1071]) ).
fof(f7851,plain,
( spl0_344
| ~ spl0_79
| ~ spl0_118 ),
inference(avatar_split_clause,[],[f1204,f1082,f748,f7849]) ).
fof(f7849,plain,
( spl0_344
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f748,plain,
( spl0_79
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1204,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),tc_nat) )
| ~ spl0_79
| ~ spl0_118 ),
inference(resolution,[],[f1083,f749]) ).
fof(f749,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X4,c_Suc(X3),tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_79 ),
inference(avatar_component_clause,[],[f748]) ).
fof(f7847,plain,
( spl0_343
| ~ spl0_109
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f1179,f1050,f1038,f7845]) ).
fof(f7845,plain,
( spl0_343
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f1179,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X1,tc_nat) )
| ~ spl0_109
| ~ spl0_112 ),
inference(superposition,[],[f1051,f1039]) ).
fof(f7843,plain,
( spl0_342
| ~ spl0_77
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f1172,f1050,f740,f7841]) ).
fof(f7841,plain,
( spl0_342
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f740,plain,
( spl0_77
<=> ! [X4,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1172,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
| ~ spl0_77
| ~ spl0_112 ),
inference(resolution,[],[f1051,f741]) ).
fof(f741,plain,
( ! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat) )
| ~ spl0_77 ),
inference(avatar_component_clause,[],[f740]) ).
fof(f7839,plain,
( spl0_341
| ~ spl0_108
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1157,f1046,f1034,f7837]) ).
fof(f7837,plain,
( spl0_341
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f1157,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
| ~ spl0_108
| ~ spl0_111 ),
inference(superposition,[],[f1047,f1035]) ).
fof(f7827,plain,
( spl0_340
| ~ spl0_76
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1148,f1046,f736,f7825]) ).
fof(f7825,plain,
( spl0_340
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f1148,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),X1,tc_nat) )
| ~ spl0_76
| ~ spl0_111 ),
inference(resolution,[],[f1047,f737]) ).
fof(f7823,plain,
( spl0_339
| ~ spl0_80
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1147,f1046,f752,f7821]) ).
fof(f7821,plain,
( spl0_339
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f1147,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat) )
| ~ spl0_80
| ~ spl0_111 ),
inference(resolution,[],[f1047,f753]) ).
fof(f7819,plain,
( spl0_338
| ~ spl0_108
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1143,f1042,f1034,f7817]) ).
fof(f7817,plain,
( spl0_338
<=> ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f1143,plain,
( ! [X2,X0,X1] :
( c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ c_HOL_Oord__class_Oless(X2,X0,tc_nat) )
| ~ spl0_108
| ~ spl0_110 ),
inference(superposition,[],[f1043,f1035]) ).
fof(f7815,plain,
( spl0_337
| ~ spl0_77
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1137,f1042,f740,f7813]) ).
fof(f7813,plain,
( spl0_337
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f1137,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat)
| c_HOL_Oord__class_Oless(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat) )
| ~ spl0_77
| ~ spl0_110 ),
inference(resolution,[],[f1043,f741]) ).
fof(f7811,plain,
( spl0_336
| ~ spl0_84
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1122,f1038,f852,f7809]) ).
fof(f7809,plain,
( spl0_336
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f1122,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ spl0_84
| ~ spl0_109 ),
inference(superposition,[],[f853,f1039]) ).
fof(f7807,plain,
( spl0_335
| ~ spl0_83
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1121,f1038,f848,f7805]) ).
fof(f7805,plain,
( spl0_335
<=> ! [X0,X1] :
( c_Suc(X0) != c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f1121,plain,
( ! [X0,X1] :
( c_Suc(X0) != c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_83
| ~ spl0_109 ),
inference(superposition,[],[f849,f1039]) ).
fof(f7803,plain,
( spl0_334
| ~ spl0_83
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1106,f1034,f848,f7801]) ).
fof(f7801,plain,
( spl0_334
<=> ! [X0,X1] :
( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f1106,plain,
( ! [X0,X1] :
( c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = c_Suc(X1) )
| ~ spl0_83
| ~ spl0_108 ),
inference(superposition,[],[f849,f1035]) ).
fof(f7627,plain,
( spl0_333
| ~ spl0_29
| ~ spl0_320 ),
inference(avatar_split_clause,[],[f7290,f6469,f532,f7625]) ).
fof(f7290,plain,
( ! [X2,X0,X1] : ~ c_Lambda_Obeta(c_Lambda_Olift(c_Lambda_OdB_OVar(X0),X1),X2)
| ~ spl0_29
| ~ spl0_320 ),
inference(resolution,[],[f6470,f533]) ).
fof(f6521,plain,
( spl0_332
| ~ spl0_28
| ~ spl0_178 ),
inference(avatar_split_clause,[],[f2680,f2287,f528,f6519]) ).
fof(f528,plain,
( spl0_28
<=> ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f2680,plain,
( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(X1),X1)
| ~ spl0_28
| ~ spl0_178 ),
inference(resolution,[],[f2288,f529]) ).
fof(f529,plain,
( ! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f528]) ).
fof(f6517,plain,
( spl0_331
| ~ spl0_53
| ~ spl0_174 ),
inference(avatar_split_clause,[],[f2622,f2271,f632,f6515]) ).
fof(f6515,plain,
( spl0_331
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f2622,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X1,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ spl0_53
| ~ spl0_174 ),
inference(superposition,[],[f633,f2272]) ).
fof(f6513,plain,
( spl0_330
| ~ spl0_53
| ~ spl0_173 ),
inference(avatar_split_clause,[],[f2581,f2267,f632,f6511]) ).
fof(f6511,plain,
( spl0_330
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f2581,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X2,tc_nat),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ spl0_53
| ~ spl0_173 ),
inference(superposition,[],[f633,f2268]) ).
fof(f6509,plain,
( spl0_329
| ~ spl0_51
| ~ spl0_169 ),
inference(avatar_split_clause,[],[f2435,f2251,f624,f6507]) ).
fof(f6507,plain,
( spl0_329
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f2435,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X2,c_Suc(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat)),tc_nat)
| ~ spl0_51
| ~ spl0_169 ),
inference(superposition,[],[f625,f2252]) ).
fof(f6505,plain,
( spl0_328
| ~ spl0_111
| ~ spl0_160 ),
inference(avatar_split_clause,[],[f2078,f1810,f1046,f6503]) ).
fof(f6503,plain,
( spl0_328
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f2078,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X2,X1,tc_nat),tc_nat) )
| ~ spl0_111
| ~ spl0_160 ),
inference(resolution,[],[f1811,f1047]) ).
fof(f6501,plain,
( spl0_327
| ~ spl0_84
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1567,f1458,f852,f6499]) ).
fof(f6499,plain,
( spl0_327
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f1567,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),tc_nat)
| ~ spl0_84
| ~ spl0_139 ),
inference(superposition,[],[f853,f1459]) ).
fof(f6495,plain,
( spl0_326
| ~ spl0_47
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1561,f1458,f604,f6493]) ).
fof(f6493,plain,
( spl0_326
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f1561,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),c_HOL_Otimes__class_Otimes(X1,X0,tc_nat),tc_nat)
| ~ spl0_47
| ~ spl0_139 ),
inference(superposition,[],[f605,f1459]) ).
fof(f6491,plain,
( spl0_325
| ~ spl0_84
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1534,f1454,f852,f6489]) ).
fof(f6489,plain,
( spl0_325
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f1534,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),tc_nat)
| ~ spl0_84
| ~ spl0_138 ),
inference(superposition,[],[f853,f1455]) ).
fof(f6487,plain,
( spl0_324
| ~ spl0_47
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1528,f1454,f604,f6485]) ).
fof(f6485,plain,
( spl0_324
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f1528,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),c_HOL_Otimes__class_Otimes(X0,X1,tc_nat),tc_nat)
| ~ spl0_47
| ~ spl0_138 ),
inference(superposition,[],[f605,f1455]) ).
fof(f6483,plain,
( spl0_323
| ~ spl0_38
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1427,f1319,f568,f6481]) ).
fof(f6481,plain,
( spl0_323
<=> ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0,c_Suc(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f568,plain,
( spl0_38
<=> ! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1427,plain,
( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubst(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),X0,c_Suc(X1))
| ~ spl0_38
| ~ spl0_133 ),
inference(resolution,[],[f1320,f569]) ).
fof(f569,plain,
( ! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat)
| ~ spl0_38 ),
inference(avatar_component_clause,[],[f568]) ).
fof(f6479,plain,
( spl0_322
| ~ spl0_40
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1418,f1315,f576,f6477]) ).
fof(f6477,plain,
( spl0_322
<=> ! [X2,X0,X1] :
( c_InductTermi_OIT(c_Lambda_Oliftn(c_Suc(X0),X1,X2))
| ~ c_InductTermi_OIT(c_Lambda_Oliftn(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f576,plain,
( spl0_40
<=> ! [X25,X11] :
( ~ c_InductTermi_OIT(X25)
| c_InductTermi_OIT(c_Lambda_Olift(X25,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1418,plain,
( ! [X2,X0,X1] :
( c_InductTermi_OIT(c_Lambda_Oliftn(c_Suc(X0),X1,X2))
| ~ c_InductTermi_OIT(c_Lambda_Oliftn(X0,X1,X2)) )
| ~ spl0_40
| ~ spl0_132 ),
inference(superposition,[],[f577,f1316]) ).
fof(f577,plain,
( ! [X11,X25] :
( c_InductTermi_OIT(c_Lambda_Olift(X25,X11))
| ~ c_InductTermi_OIT(X25) )
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f6475,plain,
( spl0_321
| ~ spl0_59
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1412,f1311,f656,f6473]) ).
fof(f6473,plain,
( spl0_321
<=> ! [X0,X3,X2,X1] :
( c_Lambda_Obeta(c_Lambda_Osubst(X3,X2,X1),X0)
| ~ c_Lambda_Obeta(X3,c_Lambda_Olift(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f1311,plain,
( spl0_131
<=> ! [X28,X24,X11,X25] :
( ~ c_Lambda_Obeta(X24,X28)
| c_Lambda_Obeta(c_Lambda_Osubst(X24,X25,X11),c_Lambda_Osubst(X28,X25,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1412,plain,
( ! [X2,X3,X0,X1] :
( c_Lambda_Obeta(c_Lambda_Osubst(X3,X2,X1),X0)
| ~ c_Lambda_Obeta(X3,c_Lambda_Olift(X0,X1)) )
| ~ spl0_59
| ~ spl0_131 ),
inference(superposition,[],[f1312,f657]) ).
fof(f1312,plain,
( ! [X28,X11,X24,X25] :
( c_Lambda_Obeta(c_Lambda_Osubst(X24,X25,X11),c_Lambda_Osubst(X28,X25,X11))
| ~ c_Lambda_Obeta(X24,X28) )
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f1311]) ).
fof(f6471,plain,
( spl0_320
| ~ spl0_59
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1410,f1311,f656,f6469]) ).
fof(f1410,plain,
( ! [X2,X3,X0,X1] :
( c_Lambda_Obeta(X0,c_Lambda_Osubst(X3,X2,X1))
| ~ c_Lambda_Obeta(c_Lambda_Olift(X0,X1),X3) )
| ~ spl0_59
| ~ spl0_131 ),
inference(superposition,[],[f1312,f657]) ).
fof(f6467,plain,
( spl0_319
| ~ spl0_38
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1401,f1307,f568,f6465]) ).
fof(f6465,plain,
( spl0_319
<=> ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f1401,plain,
( ! [X0,X1] : c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Oliftn(X0,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(X1))
| ~ spl0_38
| ~ spl0_130 ),
inference(resolution,[],[f1308,f569]) ).
fof(f6463,plain,
( spl0_318
| ~ spl0_78
| ~ spl0_127 ),
inference(avatar_split_clause,[],[f1356,f1295,f744,f6461]) ).
fof(f6461,plain,
( spl0_318
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f1356,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X1,X0,tc_nat) )
| ~ spl0_78
| ~ spl0_127 ),
inference(resolution,[],[f1296,f745]) ).
fof(f6459,plain,
( spl0_317
| ~ spl0_52
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1271,f1090,f628,f6457]) ).
fof(f6457,plain,
( spl0_317
<=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f1271,plain,
( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)))
| ~ spl0_52
| ~ spl0_120 ),
inference(resolution,[],[f1091,f629]) ).
fof(f6431,plain,
( spl0_316
| ~ spl0_51
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1270,f1090,f624,f6429]) ).
fof(f6429,plain,
( spl0_316
<=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f1270,plain,
( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat)))
| ~ spl0_51
| ~ spl0_120 ),
inference(resolution,[],[f1091,f625]) ).
fof(f6427,plain,
( spl0_315
| ~ spl0_64
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1155,f1046,f688,f6425]) ).
fof(f6425,plain,
( spl0_315
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f1155,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),X2,tc_nat)
| c_HOL_Oord__class_Oless(X0,X2,tc_nat) )
| ~ spl0_64
| ~ spl0_111 ),
inference(superposition,[],[f1047,f689]) ).
fof(f6423,plain,
( spl0_314
| ~ spl0_51
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1149,f1046,f624,f6421]) ).
fof(f6421,plain,
( spl0_314
<=> ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f1149,plain,
( ! [X2,X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X0,X2,tc_nat),tc_nat)),tc_nat)
| ~ spl0_51
| ~ spl0_111 ),
inference(resolution,[],[f1047,f625]) ).
fof(f6419,plain,
( spl0_313
| ~ spl0_75
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1120,f1038,f732,f6417]) ).
fof(f6417,plain,
( spl0_313
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X0),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f1120,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X0),tc_nat) = X1
| ~ spl0_75
| ~ spl0_109 ),
inference(superposition,[],[f733,f1039]) ).
fof(f6415,plain,
( spl0_312
| ~ spl0_74
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1119,f1038,f728,f6413]) ).
fof(f6413,plain,
( spl0_312
<=> ! [X0,X1] : c_Suc(X0) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f1119,plain,
( ! [X0,X1] : c_Suc(X0) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat)
| ~ spl0_74
| ~ spl0_109 ),
inference(superposition,[],[f729,f1039]) ).
fof(f6411,plain,
( spl0_311
| ~ spl0_64
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1109,f1038,f688,f6409]) ).
fof(f6409,plain,
( spl0_311
<=> ! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f1109,plain,
( ! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(X1,c_Suc(X0),tc_nat)
| ~ spl0_64
| ~ spl0_109 ),
inference(superposition,[],[f1039,f689]) ).
fof(f6407,plain,
( spl0_310
| ~ spl0_84
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1107,f1034,f852,f6405]) ).
fof(f1107,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),tc_nat)
| ~ spl0_84
| ~ spl0_108 ),
inference(superposition,[],[f853,f1035]) ).
fof(f6403,plain,
( spl0_309
| ~ spl0_75
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1105,f1034,f732,f6401]) ).
fof(f6401,plain,
( spl0_309
<=> ! [X0,X1] : c_Suc(X1) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f1105,plain,
( ! [X0,X1] : c_Suc(X1) = c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat)
| ~ spl0_75
| ~ spl0_108 ),
inference(superposition,[],[f733,f1035]) ).
fof(f6399,plain,
( spl0_308
| ~ spl0_74
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1104,f1034,f728,f6397]) ).
fof(f6397,plain,
( spl0_308
<=> ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X1),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f1104,plain,
( ! [X0,X1] : c_HOL_Ominus__class_Ominus(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X1),tc_nat) = X0
| ~ spl0_74
| ~ spl0_108 ),
inference(superposition,[],[f729,f1035]) ).
fof(f6395,plain,
( spl0_307
| ~ spl0_64
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1095,f1034,f688,f6393]) ).
fof(f6393,plain,
( spl0_307
<=> ! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X1),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f1095,plain,
( ! [X0,X1] : c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X1),X0,tc_nat)
| ~ spl0_64
| ~ spl0_108 ),
inference(superposition,[],[f1035,f689]) ).
fof(f6391,plain,
( spl0_306
| ~ spl0_94
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f4748,f3513,f892,f6388]) ).
fof(f6388,plain,
( spl0_306
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f3513,plain,
( spl0_219
<=> ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f4748,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ spl0_94
| ~ spl0_219 ),
inference(resolution,[],[f3514,f893]) ).
fof(f3514,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),c_Suc(X0),tc_nat)
| ~ spl0_219 ),
inference(avatar_component_clause,[],[f3513]) ).
fof(f6386,plain,
( spl0_305
| ~ spl0_58
| ~ spl0_99 ),
inference(avatar_split_clause,[],[f1019,f912,f652,f6384]) ).
fof(f6384,plain,
( spl0_305
<=> ! [X0,X1] :
( c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X0,c_Lambda_OdB_OAbs(X1)))
| ~ c_Lambda_Obeta(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f652,plain,
( spl0_58
<=> ! [X25,X28] :
( ~ c_Lambda_Obeta(X28,X25)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X28),c_Lambda_OdB_OAbs(X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f912,plain,
( spl0_99
<=> ! [X28,X24] :
( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X24),X28)
| c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X24,X28)) = X28 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1019,plain,
( ! [X0,X1] :
( c_Lambda_OdB_OAbs(X1) = c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X0,c_Lambda_OdB_OAbs(X1)))
| ~ c_Lambda_Obeta(X0,X1) )
| ~ spl0_58
| ~ spl0_99 ),
inference(resolution,[],[f913,f653]) ).
fof(f653,plain,
( ! [X28,X25] :
( c_Lambda_Obeta(c_Lambda_OdB_OAbs(X28),c_Lambda_OdB_OAbs(X25))
| ~ c_Lambda_Obeta(X28,X25) )
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f652]) ).
fof(f913,plain,
( ! [X28,X24] :
( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X24),X28)
| c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X24,X28)) = X28 )
| ~ spl0_99 ),
inference(avatar_component_clause,[],[f912]) ).
fof(f6113,plain,
( spl0_304
| ~ spl0_94
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f4157,f3376,f892,f6110]) ).
fof(f6110,plain,
( spl0_304
<=> c_HOL_Ozero__class_Ozero(tc_nat) = c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f3376,plain,
( spl0_214
<=> ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f4157,plain,
( c_HOL_Ozero__class_Ozero(tc_nat) = c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ spl0_94
| ~ spl0_214 ),
inference(resolution,[],[f3377,f893]) ).
fof(f3377,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),c_Suc(X0),tc_nat)
| ~ spl0_214 ),
inference(avatar_component_clause,[],[f3376]) ).
fof(f5846,plain,
( spl0_303
| ~ spl0_188
| ~ spl0_190 ),
inference(avatar_split_clause,[],[f3209,f2926,f2918,f5844]) ).
fof(f5844,plain,
( spl0_303
<=> ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f2918,plain,
( spl0_188
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f2926,plain,
( spl0_190
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f3209,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1) )
| ~ spl0_188
| ~ spl0_190 ),
inference(duplicate_literal_removal,[],[f3173]) ).
fof(f3173,plain,
( ! [X2,X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X0,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_HOL_Oord__class_Oless(X2,X2,X1)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1) )
| ~ spl0_188
| ~ spl0_190 ),
inference(resolution,[],[f2927,f2919]) ).
fof(f2919,plain,
( ! [X2,X0,X1,X8] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f2918]) ).
fof(f2927,plain,
( ! [X2,X0,X1,X8] :
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0) )
| ~ spl0_190 ),
inference(avatar_component_clause,[],[f2926]) ).
fof(f5842,plain,
( spl0_302
| ~ spl0_30
| ~ spl0_179 ),
inference(avatar_split_clause,[],[f2738,f2291,f536,f5840]) ).
fof(f5840,plain,
( spl0_302
<=> ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f536,plain,
( spl0_30
<=> ! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f2738,plain,
( ! [X0] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X0
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X0,X0)) = X0 )
| ~ spl0_30
| ~ spl0_179 ),
inference(resolution,[],[f2292,f537]) ).
fof(f537,plain,
( ! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f5838,plain,
( spl0_301
| ~ spl0_48
| ~ spl0_132 ),
inference(avatar_split_clause,[],[f1413,f1315,f608,f5836]) ).
fof(f608,plain,
( spl0_48
<=> ! [X25,X12] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X25,X12) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1413,plain,
( ! [X0,X1] : c_Lambda_Olift(X0,X1) = c_Lambda_Oliftn(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,X1)
| ~ spl0_48
| ~ spl0_132 ),
inference(superposition,[],[f1316,f609]) ).
fof(f609,plain,
( ! [X25,X12] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X25,X12) = X25
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f608]) ).
fof(f5834,plain,
( spl0_300
| ~ spl0_49
| ~ spl0_131 ),
inference(avatar_split_clause,[],[f1411,f1311,f612,f5832]) ).
fof(f5832,plain,
( spl0_300
<=> ! [X2,X0,X1] :
( c_Lambda_Obeta(c_Lambda_Osubst(X2,X1,X0),X1)
| ~ c_Lambda_Obeta(X2,c_Lambda_OdB_OVar(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f1411,plain,
( ! [X2,X0,X1] :
( c_Lambda_Obeta(c_Lambda_Osubst(X2,X1,X0),X1)
| ~ c_Lambda_Obeta(X2,c_Lambda_OdB_OVar(X0)) )
| ~ spl0_49
| ~ spl0_131 ),
inference(superposition,[],[f1312,f613]) ).
fof(f5830,plain,
( spl0_299
| ~ spl0_81
| ~ spl0_125 ),
inference(avatar_split_clause,[],[f1440,f1286,f756,f5828]) ).
fof(f5828,plain,
( spl0_299
<=> ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f1286,plain,
( spl0_125
<=> ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1440,plain,
( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)))),X1)
| ~ spl0_81
| ~ spl0_125 ),
inference(resolution,[],[f1287,f757]) ).
fof(f1287,plain,
( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))),X1)
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f1286]) ).
fof(f5826,plain,
( spl0_298
| ~ spl0_45
| ~ spl0_124 ),
inference(avatar_split_clause,[],[f1344,f1282,f596,f5824]) ).
fof(f5824,plain,
( spl0_298
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f1344,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) != X0
| X0 = X1 )
| ~ spl0_45
| ~ spl0_124 ),
inference(superposition,[],[f1283,f597]) ).
fof(f5822,plain,
( spl0_297
| ~ spl0_44
| ~ spl0_123 ),
inference(avatar_split_clause,[],[f1323,f1278,f592,f5820]) ).
fof(f5820,plain,
( spl0_297
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) != X0
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f1323,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) != X0
| X0 = X1 )
| ~ spl0_44
| ~ spl0_123 ),
inference(superposition,[],[f1279,f593]) ).
fof(f5818,plain,
( spl0_296
| ~ spl0_38
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1265,f1090,f568,f5816]) ).
fof(f5816,plain,
( spl0_296
<=> ! [X0] : c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f1265,plain,
( ! [X0] : c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Olift(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(X0))
| ~ spl0_38
| ~ spl0_120 ),
inference(resolution,[],[f1091,f569]) ).
fof(f5814,plain,
( spl0_295
| ~ spl0_47
| ~ spl0_112 ),
inference(avatar_split_clause,[],[f1170,f1050,f604,f5812]) ).
fof(f5812,plain,
( spl0_295
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f1170,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X2,tc_nat)
| ~ spl0_47
| ~ spl0_112 ),
inference(resolution,[],[f1051,f605]) ).
fof(f5810,plain,
( spl0_294
| ~ spl0_47
| ~ spl0_110 ),
inference(avatar_split_clause,[],[f1136,f1042,f604,f5808]) ).
fof(f5808,plain,
( spl0_294
<=> ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f1136,plain,
( ! [X2,X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_HOL_Oplus__class_Oplus(X1,X2,tc_nat),tc_nat),X1,tc_nat)
| ~ spl0_47
| ~ spl0_110 ),
inference(resolution,[],[f1043,f605]) ).
fof(f5806,plain,
( spl0_293
| ~ spl0_52
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1116,f1038,f628,f5804]) ).
fof(f5804,plain,
( spl0_293
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f1116,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat)
| ~ spl0_52
| ~ spl0_109 ),
inference(superposition,[],[f629,f1039]) ).
fof(f5802,plain,
( spl0_292
| ~ spl0_51
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1100,f1034,f624,f5800]) ).
fof(f5800,plain,
( spl0_292
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f1100,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_Suc(X1),c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat)
| ~ spl0_51
| ~ spl0_108 ),
inference(superposition,[],[f625,f1035]) ).
fof(f5798,plain,
( spl0_291
| ~ spl0_64
| ~ spl0_84 ),
inference(avatar_split_clause,[],[f945,f852,f688,f5796]) ).
fof(f5796,plain,
( spl0_291
<=> ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f945,plain,
( ! [X0,X1] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X0,c_HOL_Oplus__class_Oplus(X1,X0,tc_nat),tc_nat)
| ~ spl0_64
| ~ spl0_84 ),
inference(superposition,[],[f853,f689]) ).
fof(f5794,plain,
( spl0_290
| ~ spl0_64
| ~ spl0_83 ),
inference(avatar_split_clause,[],[f941,f848,f688,f5792]) ).
fof(f5792,plain,
( spl0_290
<=> ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f941,plain,
( ! [X0,X1] :
( c_HOL_Oplus__class_Oplus(X1,X0,tc_nat) != X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X1 )
| ~ spl0_64
| ~ spl0_83 ),
inference(superposition,[],[f849,f689]) ).
fof(f5790,plain,
( spl0_289
| ~ spl0_77
| ~ spl0_80 ),
inference(avatar_split_clause,[],[f843,f752,f740,f5788]) ).
fof(f5788,plain,
( spl0_289
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f843,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| c_HOL_Oord__class_Oless(X1,c_Suc(X0),tc_nat) )
| ~ spl0_77
| ~ spl0_80 ),
inference(resolution,[],[f753,f741]) ).
fof(f5786,plain,
( spl0_288
| ~ spl0_76
| ~ spl0_121 ),
inference(avatar_split_clause,[],[f1342,f1183,f736,f5784]) ).
fof(f5784,plain,
( spl0_288
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f1183,plain,
( spl0_121
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1342,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(c_Suc(X0))),X0,tc_nat)
| ~ spl0_76
| ~ spl0_121 ),
inference(resolution,[],[f1184,f737]) ).
fof(f1184,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_121 ),
inference(avatar_component_clause,[],[f1183]) ).
fof(f5782,plain,
( spl0_287
| ~ spl0_76
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f821,f740,f736,f5780]) ).
fof(f5780,plain,
( spl0_287
<=> ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f821,plain,
( ! [X0,X1] :
( c_HOL_Oord__class_Oless(X0,c_Suc(X1),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X0),X1,tc_nat) )
| ~ spl0_76
| ~ spl0_77 ),
inference(resolution,[],[f741,f737]) ).
fof(f5336,plain,
( spl0_286
| ~ spl0_41
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f3292,f2946,f580,f5334]) ).
fof(f5334,plain,
( spl0_286
<=> ! [X4,X0,X3,X2,X1] : c_Lambda_OdB_OVar(X4) != c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f580,plain,
( spl0_41
<=> ! [X34,X27,X33] : c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OApp(X33,X34) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f2946,plain,
( spl0_195
<=> ! [X28,X4,X12,X25] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OApp(X28,X25),X12) = c_Lambda_OdB_OApp(c_Lambda_Oliftn(X4,X28,X12),c_Lambda_Oliftn(X4,X25,X12)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f3292,plain,
( ! [X2,X3,X0,X1,X4] : c_Lambda_OdB_OVar(X4) != c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2)
| ~ spl0_41
| ~ spl0_195 ),
inference(superposition,[],[f581,f2947]) ).
fof(f2947,plain,
( ! [X28,X4,X25,X12] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OApp(X28,X25),X12) = c_Lambda_OdB_OApp(c_Lambda_Oliftn(X4,X28,X12),c_Lambda_Oliftn(X4,X25,X12))
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f2946]) ).
fof(f581,plain,
( ! [X27,X34,X33] : c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OApp(X33,X34)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f5332,plain,
( spl0_285
| ~ spl0_39
| ~ spl0_195 ),
inference(avatar_split_clause,[],[f3291,f2946,f572,f5330]) ).
fof(f5330,plain,
( spl0_285
<=> ! [X4,X0,X3,X2,X1] : c_Lambda_OdB_OAbs(X4) != c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f572,plain,
( spl0_39
<=> ! [X29,X32,X31] : c_Lambda_OdB_OAbs(X29) != c_Lambda_OdB_OApp(X31,X32) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f3291,plain,
( ! [X2,X3,X0,X1,X4] : c_Lambda_OdB_OAbs(X4) != c_Lambda_Oliftn(X0,c_Lambda_OdB_OApp(X1,X3),X2)
| ~ spl0_39
| ~ spl0_195 ),
inference(superposition,[],[f573,f2947]) ).
fof(f573,plain,
( ! [X31,X29,X32] : c_Lambda_OdB_OAbs(X29) != c_Lambda_OdB_OApp(X31,X32)
| ~ spl0_39 ),
inference(avatar_component_clause,[],[f572]) ).
fof(f5328,plain,
( spl0_284
| ~ spl0_263
| ~ spl0_265 ),
inference(avatar_split_clause,[],[f5152,f4849,f4841,f5326]) ).
fof(f5326,plain,
( spl0_284
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f4841,plain,
( spl0_263
<=> ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f4849,plain,
( spl0_265
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f5152,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| ~ spl0_263
| ~ spl0_265 ),
inference(superposition,[],[f4850,f4842]) ).
fof(f4842,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X0
| ~ spl0_263 ),
inference(avatar_component_clause,[],[f4841]) ).
fof(f4850,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat)
| ~ spl0_265 ),
inference(avatar_component_clause,[],[f4849]) ).
fof(f5324,plain,
( spl0_283
| ~ spl0_41
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f3280,f2938,f580,f5322]) ).
fof(f5322,plain,
( spl0_283
<=> ! [X4,X0,X3,X2,X1] : c_Lambda_OdB_OVar(X4) != c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f3280,plain,
( ! [X2,X3,X0,X1,X4] : c_Lambda_OdB_OVar(X4) != c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2)
| ~ spl0_41
| ~ spl0_193 ),
inference(superposition,[],[f581,f2939]) ).
fof(f5320,plain,
( spl0_282
| ~ spl0_39
| ~ spl0_193 ),
inference(avatar_split_clause,[],[f3279,f2938,f572,f5318]) ).
fof(f5318,plain,
( spl0_282
<=> ! [X4,X0,X3,X2,X1] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2) != c_Lambda_OdB_OAbs(X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f3279,plain,
( ! [X2,X3,X0,X1,X4] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X0,X3),X1,X2) != c_Lambda_OdB_OAbs(X4)
| ~ spl0_39
| ~ spl0_193 ),
inference(superposition,[],[f573,f2939]) ).
fof(f5316,plain,
( spl0_281
| ~ spl0_52
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1563,f1458,f628,f5314]) ).
fof(f5314,plain,
( spl0_281
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f1563,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat)),tc_nat)
| ~ spl0_52
| ~ spl0_139 ),
inference(superposition,[],[f629,f1459]) ).
fof(f5312,plain,
( spl0_280
| ~ spl0_52
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1530,f1454,f628,f5310]) ).
fof(f1530,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat)),tc_nat)
| ~ spl0_52
| ~ spl0_138 ),
inference(superposition,[],[f629,f1455]) ).
fof(f5308,plain,
( spl0_279
| ~ spl0_30
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f1426,f1319,f536,f5306]) ).
fof(f5306,plain,
( spl0_279
<=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f1426,plain,
( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X0),X1,c_Suc(X0))
| ~ spl0_30
| ~ spl0_133 ),
inference(resolution,[],[f1320,f537]) ).
fof(f5304,plain,
( spl0_278
| ~ spl0_30
| ~ spl0_130 ),
inference(avatar_split_clause,[],[f1400,f1307,f536,f5302]) ).
fof(f5302,plain,
( spl0_278
<=> ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f1400,plain,
( ! [X0,X1] : c_Lambda_OdB_OVar(X0) = c_Lambda_Oliftn(X1,c_Lambda_OdB_OVar(X0),c_Suc(X0))
| ~ spl0_30
| ~ spl0_130 ),
inference(resolution,[],[f1308,f537]) ).
fof(f5300,plain,
( spl0_277
| ~ spl0_53
| ~ spl0_117 ),
inference(avatar_split_clause,[],[f1201,f1070,f632,f5298]) ).
fof(f5298,plain,
( spl0_277
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f1201,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_53
| ~ spl0_117 ),
inference(superposition,[],[f633,f1071]) ).
fof(f5296,plain,
( spl0_276
| ~ spl0_44
| ~ spl0_111 ),
inference(avatar_split_clause,[],[f1153,f1046,f592,f5294]) ).
fof(f5294,plain,
( spl0_276
<=> ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f1153,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X1,tc_nat) )
| ~ spl0_44
| ~ spl0_111 ),
inference(superposition,[],[f1047,f593]) ).
fof(f5292,plain,
( spl0_275
| ~ spl0_46
| ~ spl0_109 ),
inference(avatar_split_clause,[],[f1113,f1038,f600,f5290]) ).
fof(f5290,plain,
( spl0_275
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f1113,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X0),tc_nat)
| ~ spl0_46
| ~ spl0_109 ),
inference(superposition,[],[f601,f1039]) ).
fof(f5288,plain,
( spl0_274
| ~ spl0_47
| ~ spl0_108 ),
inference(avatar_split_clause,[],[f1099,f1034,f604,f5286]) ).
fof(f5286,plain,
( spl0_274
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f1099,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),c_Suc(X1),tc_nat)
| ~ spl0_47
| ~ spl0_108 ),
inference(superposition,[],[f605,f1035]) ).
fof(f5272,plain,
( spl0_273
| ~ spl0_59
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1022,f920,f656,f5270]) ).
fof(f5270,plain,
( spl0_273
<=> ! [X0,X1] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(c_Lambda_Olift(X0,c_HOL_Ozero__class_Ozero(tc_nat))),X1),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f920,plain,
( spl0_101
<=> ! [X25,X28] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X28),X25),c_Lambda_Osubst(X28,X25,c_HOL_Ozero__class_Ozero(tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1022,plain,
( ! [X0,X1] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(c_Lambda_Olift(X0,c_HOL_Ozero__class_Ozero(tc_nat))),X1),X0)
| ~ spl0_59
| ~ spl0_101 ),
inference(superposition,[],[f921,f657]) ).
fof(f921,plain,
( ! [X28,X25] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X28),X25),c_Lambda_Osubst(X28,X25,c_HOL_Ozero__class_Ozero(tc_nat)))
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f920]) ).
fof(f5268,plain,
( spl0_272
| ~ spl0_78
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f997,f896,f744,f5266]) ).
fof(f5266,plain,
( spl0_272
<=> ! [X0] :
( c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X0)) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f997,plain,
( ! [X0] :
( c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X0)) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_78
| ~ spl0_95 ),
inference(resolution,[],[f897,f745]) ).
fof(f5264,plain,
( spl0_271
| ~ spl0_78
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f984,f888,f744,f5262]) ).
fof(f984,plain,
( ! [X0] :
( c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X0)) = X0
| c_HOL_Ozero__class_Ozero(tc_nat) = X0 )
| ~ spl0_78
| ~ spl0_93 ),
inference(resolution,[],[f889,f745]) ).
fof(f5260,plain,
( spl0_270
| ~ spl0_52
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f823,f740,f628,f5258]) ).
fof(f5258,plain,
( spl0_270
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f823,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat))),tc_nat)
| ~ spl0_52
| ~ spl0_77 ),
inference(forward_demodulation,[],[f820,f14]) ).
fof(f14,axiom,
! [X3,X4] : c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(X3),X4,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).
fof(f820,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat)),tc_nat)
| ~ spl0_52
| ~ spl0_77 ),
inference(resolution,[],[f741,f629]) ).
fof(f5256,plain,
( spl0_269
| ~ spl0_51
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f822,f740,f624,f5254]) ).
fof(f5254,plain,
( spl0_269
<=> ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f822,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_HOL_Oplus__class_Oplus(X1,X0,tc_nat))),tc_nat)
| ~ spl0_51
| ~ spl0_77 ),
inference(forward_demodulation,[],[f819,f13]) ).
fof(f13,axiom,
! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,c_Suc(X4),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).
fof(f819,plain,
( ! [X0,X1] : c_HOL_Oord__class_Oless(X0,c_Suc(c_HOL_Oplus__class_Oplus(X1,c_Suc(X0),tc_nat)),tc_nat)
| ~ spl0_51
| ~ spl0_77 ),
inference(resolution,[],[f741,f625]) ).
fof(f4863,plain,
( spl0_268
| ~ spl0_41
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1752,f1485,f580,f4861]) ).
fof(f4861,plain,
( spl0_268
<=> ! [X2,X0,X1,X3] : c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OVar(X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f1752,plain,
( ! [X2,X3,X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OVar(X3)
| ~ spl0_41
| ~ spl0_145 ),
inference(superposition,[],[f581,f1486]) ).
fof(f4859,plain,
( spl0_267
| ~ spl0_39
| ~ spl0_145 ),
inference(avatar_split_clause,[],[f1751,f1485,f572,f4857]) ).
fof(f4857,plain,
( spl0_267
<=> ! [X2,X0,X1,X3] : c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OAbs(X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f1751,plain,
( ! [X2,X3,X0,X1] : c_Lambda_Olift(c_Lambda_OdB_OApp(X0,X2),X1) != c_Lambda_OdB_OAbs(X3)
| ~ spl0_39
| ~ spl0_145 ),
inference(superposition,[],[f573,f1486]) ).
fof(f4855,plain,
( spl0_266
| ~ spl0_45
| ~ spl0_55
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1578,f1458,f640,f596,f4853]) ).
fof(f640,plain,
( spl0_55
<=> ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1578,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat) = X0
| ~ spl0_45
| ~ spl0_55
| ~ spl0_139 ),
inference(forward_demodulation,[],[f1551,f597]) ).
fof(f1551,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X0,tc_nat)
| ~ spl0_55
| ~ spl0_139 ),
inference(superposition,[],[f1459,f641]) ).
fof(f641,plain,
( ! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f640]) ).
fof(f4851,plain,
( spl0_265
| ~ spl0_46
| ~ spl0_139 ),
inference(avatar_split_clause,[],[f1560,f1458,f600,f4849]) ).
fof(f1560,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X1),X0,tc_nat),X0,tc_nat)
| ~ spl0_46
| ~ spl0_139 ),
inference(superposition,[],[f601,f1459]) ).
fof(f4847,plain,
( spl0_264
| ~ spl0_79
| ~ spl0_219 ),
inference(avatar_split_clause,[],[f4747,f3513,f748,f4845]) ).
fof(f4845,plain,
( spl0_264
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f4747,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),tc_nat)
| ~ spl0_79
| ~ spl0_219 ),
inference(resolution,[],[f3514,f749]) ).
fof(f4843,plain,
( spl0_263
| ~ spl0_45
| ~ spl0_56
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1546,f1454,f644,f596,f4841]) ).
fof(f644,plain,
( spl0_56
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f1546,plain,
( ! [X0] : c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = X0
| ~ spl0_45
| ~ spl0_56
| ~ spl0_138 ),
inference(forward_demodulation,[],[f1520,f597]) ).
fof(f1520,plain,
( ! [X0] : c_HOL_Oplus__class_Oplus(X0,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Otimes__class_Otimes(X0,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)
| ~ spl0_56
| ~ spl0_138 ),
inference(superposition,[],[f1455,f645]) ).
fof(f645,plain,
( ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f4839,plain,
( spl0_262
| ~ spl0_46
| ~ spl0_138 ),
inference(avatar_split_clause,[],[f1527,f1454,f600,f4837]) ).
fof(f4837,plain,
( spl0_262
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f1527,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X0,c_Suc(X1),tc_nat),X0,tc_nat)
| ~ spl0_46
| ~ spl0_138 ),
inference(superposition,[],[f601,f1455]) ).
fof(f4835,plain,
( spl0_261
| ~ spl0_30
| ~ spl0_120 ),
inference(avatar_split_clause,[],[f1264,f1090,f536,f4833]) ).
fof(f4833,plain,
( spl0_261
<=> ! [X0] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f1264,plain,
( ! [X0] : c_Lambda_OdB_OVar(X0) = c_Lambda_Olift(c_Lambda_OdB_OVar(X0),c_Suc(X0))
| ~ spl0_30
| ~ spl0_120 ),
inference(resolution,[],[f1091,f537]) ).
fof(f4831,plain,
( spl0_260
| ~ spl0_49
| ~ spl0_101 ),
inference(avatar_split_clause,[],[f1021,f920,f612,f4829]) ).
fof(f4829,plain,
( spl0_260
<=> ! [X0] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f1021,plain,
( ! [X0] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat))),X0),X0)
| ~ spl0_49
| ~ spl0_101 ),
inference(superposition,[],[f921,f613]) ).
fof(f4827,plain,
( spl0_259
| ~ spl0_76
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f834,f748,f736,f4825]) ).
fof(f4825,plain,
( spl0_259
<=> ! [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_259])]) ).
fof(f834,plain,
( ! [X0,X1] :
( ~ c_HOL_Oord__class_Oless(X0,X1,tc_nat)
| ~ c_HOL_Oord__class_Oless(X1,X0,tc_nat) )
| ~ spl0_76
| ~ spl0_79 ),
inference(resolution,[],[f749,f737]) ).
fof(f4823,plain,
( spl0_258
| ~ spl0_47
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f817,f736,f604,f4821]) ).
fof(f4821,plain,
( spl0_258
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f817,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X1,tc_nat)
| ~ spl0_47
| ~ spl0_76 ),
inference(forward_demodulation,[],[f815,f13]) ).
fof(f815,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X0,c_Suc(X1),tc_nat),X1,tc_nat)
| ~ spl0_47
| ~ spl0_76 ),
inference(resolution,[],[f737,f605]) ).
fof(f4819,plain,
( spl0_257
| ~ spl0_46
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f816,f736,f600,f4817]) ).
fof(f4817,plain,
( spl0_257
<=> ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f816,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Oplus__class_Oplus(X0,X1,tc_nat)),X0,tc_nat)
| ~ spl0_46
| ~ spl0_76 ),
inference(forward_demodulation,[],[f814,f14]) ).
fof(f814,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Suc(X0),X1,tc_nat),X0,tc_nat)
| ~ spl0_46
| ~ spl0_76 ),
inference(resolution,[],[f737,f601]) ).
fof(f4764,plain,
spl0_256,
inference(avatar_split_clause,[],[f176,f4762]) ).
fof(f4762,plain,
( spl0_256
<=> ! [X8,X9,X2,X1] :
( X1 = X2
| X8 = X9
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,tc_nat),c_HOL_Otimes__class_Otimes(X2,X9,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X9,tc_nat),c_HOL_Otimes__class_Otimes(X2,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f176,axiom,
! [X2,X1,X8,X9] :
( X1 = X2
| X8 = X9
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,tc_nat),c_HOL_Otimes__class_Otimes(X2,X9,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X9,tc_nat),c_HOL_Otimes__class_Otimes(X2,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).
fof(f4744,plain,
spl0_255,
inference(avatar_split_clause,[],[f86,f4742]) ).
fof(f4742,plain,
( spl0_255
<=> ! [X0,X8,X10,X2,X1] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X10,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X10,X0),X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X10,X0),X8,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f86,axiom,
! [X2,X10,X0,X1,X8] :
( ~ class_Ring__and__Field_Osemiring(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X10,X0),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X2,X10,X0),X8,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X10,X0),X8,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).
fof(f4632,plain,
spl0_254,
inference(avatar_split_clause,[],[f85,f4630]) ).
fof(f4630,plain,
( spl0_254
<=> ! [X11,X13,X12,X15] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X13,X15,tc_nat),X12,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X15,tc_nat),X12,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f85,axiom,
! [X11,X15,X12,X13] : c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X11,X15,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X13,X15,tc_nat),X12,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X15,tc_nat),X12,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).
fof(f4624,plain,
spl0_253,
inference(avatar_split_clause,[],[f180,f4622]) ).
fof(f4622,plain,
( spl0_253
<=> ! [X0,X21,X23,X22,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),c_HOL_Otimes__class_Otimes(X21,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f180,axiom,
! [X21,X0,X22,X23,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),c_HOL_Otimes__class_Otimes(X21,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).
fof(f4620,plain,
spl0_252,
inference(avatar_split_clause,[],[f112,f4618]) ).
fof(f4618,plain,
( spl0_252
<=> ! [X0,X8,X9,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X8,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f112,axiom,
! [X2,X0,X1,X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Oplus__class_Oplus(X8,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).
fof(f4583,plain,
spl0_251,
inference(avatar_split_clause,[],[f214,f4581]) ).
fof(f4581,plain,
( spl0_251
<=> ! [X5,X24,X9,X8] :
( X8 = X9
| c_HOL_Ozero__class_Ozero(tc_nat) = X24
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X24,X8,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X24,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f214,axiom,
! [X8,X9,X24,X5] :
( X8 = X9
| c_HOL_Ozero__class_Ozero(tc_nat) = X24
| c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X24,X8,tc_nat),tc_nat) != c_HOL_Oplus__class_Oplus(X5,c_HOL_Otimes__class_Otimes(X24,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).
fof(f4467,plain,
spl0_250,
inference(avatar_split_clause,[],[f309,f4465]) ).
fof(f4465,plain,
( spl0_250
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f309,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__mult_0) ).
fof(f4463,plain,
spl0_249,
inference(avatar_split_clause,[],[f136,f4461]) ).
fof(f4461,plain,
( spl0_249
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f136,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).
fof(f4459,plain,
spl0_248,
inference(avatar_split_clause,[],[f133,f4457]) ).
fof(f4457,plain,
( spl0_248
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f133,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).
fof(f4455,plain,
spl0_247,
inference(avatar_split_clause,[],[f129,f4453]) ).
fof(f4453,plain,
( spl0_247
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f129,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X8,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X8,X1,X0),c_HOL_Otimes__class_Otimes(X8,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).
fof(f4240,plain,
spl0_246,
inference(avatar_split_clause,[],[f256,f4238]) ).
fof(f4238,plain,
( spl0_246
<=> ! [X5,X0,X6,X7] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f256,axiom,
! [X0,X6,X7,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X5,X6,X0),c_HOL_Otimes__class_Otimes(X5,X7,X0),X0) = c_HOL_Otimes__class_Otimes(X5,c_HOL_Oplus__class_Oplus(X6,X7,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).
fof(f4236,plain,
spl0_245,
inference(avatar_split_clause,[],[f253,f4234]) ).
fof(f4234,plain,
( spl0_245
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f253,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).
fof(f4232,plain,
( spl0_244
| ~ spl0_79
| ~ spl0_214 ),
inference(avatar_split_clause,[],[f4156,f3376,f748,f4230]) ).
fof(f4230,plain,
( spl0_244
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f4156,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(X0,c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),tc_nat)
| ~ spl0_79
| ~ spl0_214 ),
inference(resolution,[],[f3377,f749]) ).
fof(f4228,plain,
spl0_243,
inference(avatar_split_clause,[],[f252,f4226]) ).
fof(f4226,plain,
( spl0_243
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f252,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X1,X8,X0),c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).
fof(f4224,plain,
spl0_242,
inference(avatar_split_clause,[],[f207,f4222]) ).
fof(f4222,plain,
( spl0_242
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f207,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).
fof(f4220,plain,
spl0_241,
inference(avatar_split_clause,[],[f206,f4218]) ).
fof(f4218,plain,
( spl0_241
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f206,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).
fof(f4216,plain,
spl0_240,
inference(avatar_split_clause,[],[f196,f4214]) ).
fof(f4214,plain,
( spl0_240
<=> ! [X0,X8,X9,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f196,axiom,
! [X2,X0,X1,X8,X9] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X8,X9,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).
fof(f4212,plain,
spl0_239,
inference(avatar_split_clause,[],[f194,f4210]) ).
fof(f4210,plain,
( spl0_239
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f194,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Oplus__class_Oplus(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).
fof(f4208,plain,
spl0_238,
inference(avatar_split_clause,[],[f167,f4206]) ).
fof(f4206,plain,
( spl0_238
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f167,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).
fof(f4204,plain,
spl0_237,
inference(avatar_split_clause,[],[f166,f4202]) ).
fof(f4202,plain,
( spl0_237
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f166,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X1,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).
fof(f4200,plain,
spl0_236,
inference(avatar_split_clause,[],[f165,f4198]) ).
fof(f4198,plain,
( spl0_236
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f165,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),c_HOL_Otimes__class_Otimes(X2,X1,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).
fof(f4196,plain,
spl0_235,
inference(avatar_split_clause,[],[f90,f4194]) ).
fof(f4194,plain,
( spl0_235
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f90,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Opordered__comm__monoid__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,c_HOL_Ozero__class_Ozero(X0),X0)
| ~ c_HOL_Oord__class_Oless(X2,c_HOL_Ozero__class_Ozero(X0),X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X2,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).
fof(f4073,plain,
spl0_234,
inference(avatar_split_clause,[],[f268,f4071]) ).
fof(f4071,plain,
( spl0_234
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f268,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).
fof(f4069,plain,
spl0_233,
inference(avatar_split_clause,[],[f267,f4067]) ).
fof(f4067,plain,
( spl0_233
<=> ! [X4,X3] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f267,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),X3,tc_nat)
| c_HOL_Oord__class_Oless(X4,c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).
fof(f4065,plain,
spl0_232,
inference(avatar_split_clause,[],[f119,f4063]) ).
fof(f4063,plain,
( spl0_232
<=> ! [X4,X12,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f119,axiom,
! [X3,X4,X12] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).
fof(f4061,plain,
spl0_231,
inference(avatar_split_clause,[],[f118,f4059]) ).
fof(f4059,plain,
( spl0_231
<=> ! [X4,X12,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f118,axiom,
! [X3,X4,X12] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).
fof(f3604,plain,
spl0_230,
inference(avatar_split_clause,[],[f255,f3602]) ).
fof(f255,axiom,
! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).
fof(f3600,plain,
spl0_229,
inference(avatar_split_clause,[],[f254,f3598]) ).
fof(f254,axiom,
! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).
fof(f3596,plain,
spl0_228,
inference(avatar_split_clause,[],[f208,f3594]) ).
fof(f3594,plain,
( spl0_228
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f208,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X2,X8,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(X0),X1,X0)
| c_HOL_Oord__class_Oless(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).
fof(f3592,plain,
( spl0_227
| ~ spl0_86
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2879,f1826,f860,f3590]) ).
fof(f3590,plain,
( spl0_227
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f860,plain,
( spl0_86
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f2879,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),tc_nat)
| ~ spl0_86
| ~ spl0_164 ),
inference(superposition,[],[f861,f1827]) ).
fof(f861,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f860]) ).
fof(f3588,plain,
spl0_226,
inference(avatar_split_clause,[],[f197,f3586]) ).
fof(f3586,plain,
( spl0_226
<=> ! [X11,X13,X14,X12] :
( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),c_HOL_Oplus__class_Oplus(X13,X14,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f197,axiom,
! [X11,X14,X12,X13] :
( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),c_HOL_Oplus__class_Oplus(X13,X14,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).
fof(f3584,plain,
spl0_225,
inference(avatar_split_clause,[],[f169,f3582]) ).
fof(f3582,plain,
( spl0_225
<=> ! [X4,X3] :
( ~ 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),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f169,axiom,
! [X3,X4] :
( ~ 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),X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).
fof(f3580,plain,
spl0_224,
inference(avatar_split_clause,[],[f163,f3578]) ).
fof(f3578,plain,
( spl0_224
<=> ! [X4,X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f163,axiom,
! [X3,X4] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).
fof(f3576,plain,
spl0_223,
inference(avatar_split_clause,[],[f95,f3574]) ).
fof(f95,axiom,
! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib_0) ).
fof(f3572,plain,
spl0_222,
inference(avatar_split_clause,[],[f94,f3570]) ).
fof(f94,axiom,
! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(X12,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib2_0) ).
fof(f3568,plain,
spl0_221,
inference(avatar_split_clause,[],[f69,f3566]) ).
fof(f3566,plain,
( spl0_221
<=> ! [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),c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f69,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),c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).
fof(f3564,plain,
spl0_220,
inference(avatar_split_clause,[],[f33,f3562]) ).
fof(f3562,plain,
( spl0_220
<=> ! [X4,X3,X14] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X4,tc_nat),c_HOL_Ominus__class_Ominus(X14,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f33,axiom,
! [X3,X14,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,X14,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X14,X4,tc_nat),c_HOL_Ominus__class_Ominus(X14,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).
fof(f3515,plain,
( spl0_219
| ~ spl0_30
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2869,f1826,f536,f3513]) ).
fof(f2869,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)),c_Suc(X0),tc_nat)
| ~ spl0_30
| ~ spl0_164 ),
inference(superposition,[],[f537,f1827]) ).
fof(f3428,plain,
( spl0_218
| ~ spl0_86
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2202,f1782,f860,f3426]) ).
fof(f3426,plain,
( spl0_218
<=> ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f2202,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),tc_nat)
| ~ spl0_86
| ~ spl0_153 ),
inference(superposition,[],[f861,f1783]) ).
fof(f3390,plain,
spl0_217,
inference(avatar_split_clause,[],[f393,f3388]) ).
fof(f3388,plain,
( spl0_217
<=> ! [X4,X12,X3] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X3),X4,tc_nat),c_Suc(X12),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f393,plain,
! [X3,X4,X12] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X3),X4,tc_nat),c_Suc(X12),tc_nat) = c_HOL_Ominus__class_Ominus(X3,c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat),
inference(forward_demodulation,[],[f109,f73]) ).
fof(f73,axiom,
! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(X11,c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).
fof(f109,axiom,
! [X3,X4,X12] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(X3),X4,tc_nat),c_Suc(X12),tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),X12,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).
fof(f3386,plain,
spl0_216,
inference(avatar_split_clause,[],[f249,f3384]) ).
fof(f3384,plain,
( spl0_216
<=> ! [X20,X0,X23,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X20,c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X20,X23,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f249,axiom,
! [X0,X22,X23,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X20,c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(X22,c_HOL_Otimes__class_Otimes(X20,X23,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).
fof(f3382,plain,
spl0_215,
inference(avatar_split_clause,[],[f248,f3380]) ).
fof(f3380,plain,
( spl0_215
<=> ! [X20,X0,X23,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X20,c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f248,axiom,
! [X0,X22,X23,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X20,c_HOL_Otimes__class_Otimes(X22,X23,X0),X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),X23,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).
fof(f3378,plain,
( spl0_214
| ~ spl0_30
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2192,f1782,f536,f3376]) ).
fof(f2192,plain,
( ! [X0] : c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)),c_Suc(X0),tc_nat)
| ~ spl0_30
| ~ spl0_153 ),
inference(superposition,[],[f537,f1783]) ).
fof(f3374,plain,
spl0_213,
inference(avatar_split_clause,[],[f246,f3372]) ).
fof(f3372,plain,
( spl0_213
<=> ! [X21,X20,X0,X22] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),X22,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),X21,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f246,axiom,
! [X21,X0,X22,X20] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X21,X0),X22,X0) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X20,X22,X0),X21,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).
fof(f3370,plain,
spl0_212,
inference(avatar_split_clause,[],[f245,f3368]) ).
fof(f3368,plain,
( spl0_212
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f245,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X0)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X1,X2,X0),X8,X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Otimes__class_Otimes(X2,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).
fof(f3366,plain,
spl0_211,
inference(avatar_split_clause,[],[f239,f3364]) ).
fof(f3364,plain,
( spl0_211
<=> ! [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_211])]) ).
fof(f239,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(f3362,plain,
spl0_210,
inference(avatar_split_clause,[],[f238,f3360]) ).
fof(f3360,plain,
( spl0_210
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X0) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f238,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X0) = c_HOL_Oplus__class_Oplus(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).
fof(f3358,plain,
spl0_209,
inference(avatar_split_clause,[],[f195,f3356]) ).
fof(f195,axiom,
! [X3,X4] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X3,X4,tc_nat)
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Ominus__class_Ominus(X4,X3,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).
fof(f3354,plain,
spl0_208,
inference(avatar_split_clause,[],[f173,f3352]) ).
fof(f3352,plain,
( spl0_208
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X0) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f173,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X0) = c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).
fof(f3350,plain,
spl0_207,
inference(avatar_split_clause,[],[f108,f3348]) ).
fof(f3348,plain,
( spl0_207
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f108,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).
fof(f3346,plain,
spl0_206,
inference(avatar_split_clause,[],[f107,f3344]) ).
fof(f3344,plain,
( spl0_206
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f107,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).
fof(f3342,plain,
spl0_205,
inference(avatar_split_clause,[],[f76,f3340]) ).
fof(f3340,plain,
( spl0_205
<=> ! [X4,X12,X3] :
( X3 = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| c_HOL_Otimes__class_Otimes(X12,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X12,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f76,axiom,
! [X3,X4,X12] :
( X3 = X4
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| c_HOL_Otimes__class_Otimes(X12,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X12,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).
fof(f3338,plain,
spl0_204,
inference(avatar_split_clause,[],[f67,f3336]) ).
fof(f3336,plain,
( spl0_204
<=> ! [X0,X8,X9,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X8,X9,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f67,axiom,
! [X0,X1,X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X8,X9,X0),X0) = c_HOL_Oplus__class_Oplus(X8,c_HOL_Oplus__class_Oplus(X1,X9,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).
fof(f3334,plain,
( spl0_203
| ~ spl0_77
| ~ spl0_107 ),
inference(avatar_split_clause,[],[f1080,f1030,f740,f3332]) ).
fof(f3332,plain,
( spl0_203
<=> ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1080,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(c_Suc(X0))),tc_nat)
| ~ spl0_77
| ~ spl0_107 ),
inference(resolution,[],[f1031,f741]) ).
fof(f3330,plain,
spl0_202,
inference(avatar_split_clause,[],[f66,f3328]) ).
fof(f3328,plain,
( spl0_202
<=> ! [X0,X8,X2,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f66,axiom,
! [X2,X0,X1,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).
fof(f3326,plain,
spl0_201,
inference(avatar_split_clause,[],[f65,f3324]) ).
fof(f3324,plain,
( spl0_201
<=> ! [X0,X8,X9,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X8,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f65,axiom,
! [X0,X1,X8,X9] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X8,X9,X0),X0) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X8,X0),X9,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).
fof(f3322,plain,
spl0_200,
inference(avatar_split_clause,[],[f64,f3320]) ).
fof(f3320,plain,
( spl0_200
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f64,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Oab__semigroup__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).
fof(f3318,plain,
spl0_199,
inference(avatar_split_clause,[],[f63,f3316]) ).
fof(f3316,plain,
( spl0_199
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f63,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) = c_HOL_Oplus__class_Oplus(X2,c_HOL_Oplus__class_Oplus(X1,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).
fof(f3314,plain,
spl0_198,
inference(avatar_split_clause,[],[f62,f3312]) ).
fof(f3312,plain,
( spl0_198
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f62,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(X1,X2,X0),X8,X0) = c_HOL_Oplus__class_Oplus(X1,c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).
fof(f3310,plain,
spl0_197,
inference(avatar_split_clause,[],[f56,f3308]) ).
fof(f3308,plain,
( spl0_197
<=> ! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f56,axiom,
! [X2,X0,X1] :
( ~ class_Ring__and__Field_Ono__zero__divisors(X0)
| c_HOL_Ozero__class_Ozero(X0) = X1
| c_HOL_Ozero__class_Ozero(X0) = X2
| c_HOL_Otimes__class_Otimes(X1,X2,X0) != c_HOL_Ozero__class_Ozero(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).
fof(f3306,plain,
spl0_196,
inference(avatar_split_clause,[],[f29,f3304]) ).
fof(f3304,plain,
( spl0_196
<=> ! [X4,X14,X12,X3] :
( ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X3,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X12,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f29,axiom,
! [X3,X14,X4,X12] :
( ~ c_HOL_Oord__class_Oless(X12,X14,tc_nat)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X3,X14,tc_nat) != c_HOL_Oplus__class_Oplus(X12,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).
fof(f2948,plain,
spl0_195,
inference(avatar_split_clause,[],[f357,f2946]) ).
fof(f357,axiom,
! [X28,X4,X25,X12] : c_Lambda_Oliftn(X4,c_Lambda_OdB_OApp(X28,X25),X12) = c_Lambda_OdB_OApp(c_Lambda_Oliftn(X4,X28,X12),c_Lambda_Oliftn(X4,X25,X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I2_J_0) ).
fof(f2944,plain,
( spl0_194
| ~ spl0_27
| ~ spl0_164 ),
inference(avatar_split_clause,[],[f2868,f1826,f524,f2942]) ).
fof(f2942,plain,
( spl0_194
<=> ! [X0] : c_Suc(X0) != c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f2868,plain,
( ! [X0] : c_Suc(X0) != c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0))
| ~ spl0_27
| ~ spl0_164 ),
inference(superposition,[],[f525,f1827]) ).
fof(f2940,plain,
spl0_193,
inference(avatar_split_clause,[],[f343,f2938]) ).
fof(f343,axiom,
! [X28,X15,X25,X12] : c_Lambda_Osubst(c_Lambda_OdB_OApp(X25,X15),X28,X12) = c_Lambda_OdB_OApp(c_Lambda_Osubst(X25,X28,X12),c_Lambda_Osubst(X15,X28,X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
fof(f2936,plain,
spl0_192,
inference(avatar_split_clause,[],[f244,f2934]) ).
fof(f2934,plain,
( spl0_192
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f244,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).
fof(f2932,plain,
spl0_191,
inference(avatar_split_clause,[],[f224,f2930]) ).
fof(f2930,plain,
( spl0_191
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f224,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).
fof(f2928,plain,
spl0_190,
inference(avatar_split_clause,[],[f223,f2926]) ).
fof(f223,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).
fof(f2924,plain,
spl0_189,
inference(avatar_split_clause,[],[f222,f2922]) ).
fof(f2922,plain,
( spl0_189
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f222,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X8,X1,X0),c_HOL_Oplus__class_Oplus(X8,X2,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).
fof(f2920,plain,
spl0_188,
inference(avatar_split_clause,[],[f221,f2918]) ).
fof(f221,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).
fof(f2916,plain,
spl0_187,
inference(avatar_split_clause,[],[f220,f2914]) ).
fof(f2914,plain,
( spl0_187
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f220,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).
fof(f2912,plain,
spl0_186,
inference(avatar_split_clause,[],[f219,f2910]) ).
fof(f2910,plain,
( spl0_186
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f219,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X1,X8,X0),c_HOL_Oplus__class_Oplus(X2,X8,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).
fof(f2908,plain,
spl0_185,
inference(avatar_split_clause,[],[f98,f2906]) ).
fof(f2906,plain,
( spl0_185
<=> ! [X4,X12,X3] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X12),X3,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X12),X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f98,axiom,
! [X3,X4,X12] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(X12),X3,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(X12),X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).
fof(f2904,plain,
spl0_184,
inference(avatar_split_clause,[],[f47,f2902]) ).
fof(f2902,plain,
( spl0_184
<=> ! [X4,X12,X3] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X12
| c_HOL_Otimes__class_Otimes(X3,X12,tc_nat) != c_HOL_Otimes__class_Otimes(X4,X12,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f47,axiom,
! [X3,X4,X12] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X12
| c_HOL_Otimes__class_Otimes(X3,X12,tc_nat) != c_HOL_Otimes__class_Otimes(X4,X12,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).
fof(f2865,plain,
spl0_183,
inference(avatar_split_clause,[],[f46,f2863]) ).
fof(f2863,plain,
( spl0_183
<=> ! [X4,X12,X3] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X12
| c_HOL_Otimes__class_Otimes(X12,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X12,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f46,axiom,
! [X3,X4,X12] :
( X3 = X4
| c_HOL_Ozero__class_Ozero(tc_nat) = X12
| c_HOL_Otimes__class_Otimes(X12,X3,tc_nat) != c_HOL_Otimes__class_Otimes(X12,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).
fof(f2305,plain,
spl0_182,
inference(avatar_split_clause,[],[f392,f2303]) ).
fof(f392,plain,
! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(X11,c_HOL_Oplus__class_Oplus(X12,X13,tc_nat),tc_nat),
inference(forward_demodulation,[],[f96,f73]) ).
fof(f96,axiom,
! [X11,X12,X13] : c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X13,tc_nat),X12,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(X11,X12,tc_nat),X13,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).
fof(f2301,plain,
spl0_181,
inference(avatar_split_clause,[],[f328,f2299]) ).
fof(f2299,plain,
( spl0_181
<=> ! [X11,X12,X28] :
( X11 = X12
| c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| c_Lambda_OdB_OVar(X11) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X11),X28,X12) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f328,axiom,
! [X28,X11,X12] :
( X11 = X12
| c_HOL_Oord__class_Oless(X12,X11,tc_nat)
| c_Lambda_OdB_OVar(X11) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X11),X28,X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var_2) ).
fof(f2297,plain,
spl0_180,
inference(avatar_split_clause,[],[f304,f2295]) ).
fof(f2295,plain,
( spl0_180
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X3,X4),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f304,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| c_HOL_Oord__class_Oless(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X3,X4),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_1) ).
fof(f2293,plain,
spl0_179,
inference(avatar_split_clause,[],[f292,f2291]) ).
fof(f292,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1(X3,X4)) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_0) ).
fof(f2289,plain,
spl0_178,
inference(avatar_split_clause,[],[f286,f2287]) ).
fof(f286,axiom,
! [X11,X4,X12] :
( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X11),X12) = c_Lambda_OdB_OVar(c_HOL_Oplus__class_Oplus(X11,X4,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_1) ).
fof(f2285,plain,
( spl0_177
| ~ spl0_27
| ~ spl0_153 ),
inference(avatar_split_clause,[],[f2191,f1782,f524,f2283]) ).
fof(f2283,plain,
( spl0_177
<=> ! [X0] : c_Suc(X0) != c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f2191,plain,
( ! [X0] : c_Suc(X0) != c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0))
| ~ spl0_27
| ~ spl0_153 ),
inference(superposition,[],[f525,f1783]) ).
fof(f2281,plain,
spl0_176,
inference(avatar_split_clause,[],[f250,f2279]) ).
fof(f2279,plain,
( spl0_176
<=> ! [X4,X12,X3] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f250,axiom,
! [X3,X4,X12] : c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),X12,tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).
fof(f2277,plain,
spl0_175,
inference(avatar_split_clause,[],[f158,f2275]) ).
fof(f2275,plain,
( spl0_175
<=> ! [X4,X3] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f158,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).
fof(f2273,plain,
spl0_174,
inference(avatar_split_clause,[],[f84,f2271]) ).
fof(f84,axiom,
! [X3,X4,X12] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).
fof(f2269,plain,
spl0_173,
inference(avatar_split_clause,[],[f83,f2267]) ).
fof(f83,axiom,
! [X3,X4,X12] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X12,tc_nat),c_HOL_Oplus__class_Oplus(X4,X12,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).
fof(f2265,plain,
spl0_172,
inference(avatar_split_clause,[],[f80,f2263]) ).
fof(f2263,plain,
( spl0_172
<=> ! [X4,X12,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f80,axiom,
! [X3,X4,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).
fof(f2261,plain,
spl0_171,
inference(avatar_split_clause,[],[f79,f2259]) ).
fof(f2259,plain,
( spl0_171
<=> ! [X4,X12,X3] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f79,axiom,
! [X3,X4,X12] :
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).
fof(f2257,plain,
spl0_170,
inference(avatar_split_clause,[],[f73,f2255]) ).
fof(f2253,plain,
spl0_169,
inference(avatar_split_clause,[],[f61,f2251]) ).
fof(f2249,plain,
spl0_168,
inference(avatar_split_clause,[],[f60,f2247]) ).
fof(f60,axiom,
! [X6,X7,X5] : c_HOL_Oplus__class_Oplus(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(X6,c_HOL_Oplus__class_Oplus(X5,X7,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).
fof(f1840,plain,
spl0_167,
inference(avatar_split_clause,[],[f306,f1838]) ).
fof(f1838,plain,
( spl0_167
<=> ! [X6,X0,X5,X7] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X6,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f306,axiom,
! [X0,X6,X7,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X7,X6,X0)
| c_HOL_Oord__class_Oless(X7,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
fof(f1836,plain,
spl0_166,
inference(avatar_split_clause,[],[f305,f1834]) ).
fof(f305,axiom,
! [X0,X6,X7,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0)
| ~ c_HOL_Oord__class_Oless(X6,X7,X0)
| c_HOL_Oord__class_Oless(X5,X7,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
fof(f1832,plain,
spl0_165,
inference(avatar_split_clause,[],[f273,f1830]) ).
fof(f1830,plain,
( spl0_165
<=> ! [X4,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ 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(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f273,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ 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(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).
fof(f1828,plain,
( spl0_164
| ~ spl0_38
| ~ spl0_95 ),
inference(avatar_split_clause,[],[f991,f896,f568,f1826]) ).
fof(f991,plain,
( ! [X0] : c_Suc(X0) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(c_Suc(X0)))
| ~ spl0_38
| ~ spl0_95 ),
inference(resolution,[],[f897,f569]) ).
fof(f1824,plain,
spl0_163,
inference(avatar_split_clause,[],[f272,f1822]) ).
fof(f272,axiom,
! [X0,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| 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(X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).
fof(f1820,plain,
spl0_162,
inference(avatar_split_clause,[],[f262,f1818]) ).
fof(f262,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_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).
fof(f1816,plain,
spl0_161,
inference(avatar_split_clause,[],[f237,f1814]) ).
fof(f237,axiom,
! [X3,X4,X12] :
( X3 = X4
| c_HOL_Otimes__class_Otimes(c_Suc(X12),X3,tc_nat) != c_HOL_Otimes__class_Otimes(c_Suc(X12),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).
fof(f1812,plain,
spl0_160,
inference(avatar_split_clause,[],[f227,f1810]) ).
fof(f227,axiom,
! [X3,X4,X12] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).
fof(f1808,plain,
spl0_159,
inference(avatar_split_clause,[],[f226,f1806]) ).
fof(f226,axiom,
! [X3,X4,X12] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X12,X3,tc_nat),c_HOL_Oplus__class_Oplus(X12,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).
fof(f1804,plain,
spl0_158,
inference(avatar_split_clause,[],[f225,f1802]) ).
fof(f225,axiom,
! [X11,X12,X13] :
( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),c_HOL_Oplus__class_Oplus(X13,X12,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).
fof(f1800,plain,
spl0_157,
inference(avatar_split_clause,[],[f218,f1798]) ).
fof(f218,axiom,
! [X11,X12,X13] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),X13,tc_nat)
| c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).
fof(f1796,plain,
spl0_156,
inference(avatar_split_clause,[],[f217,f1794]) ).
fof(f217,axiom,
! [X11,X12,X13] :
( ~ c_HOL_Oord__class_Oless(X11,c_HOL_Ominus__class_Ominus(X13,X12,tc_nat),tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X12,tc_nat),X13,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).
fof(f1792,plain,
spl0_155,
inference(avatar_split_clause,[],[f203,f1790]) ).
fof(f1790,plain,
( spl0_155
<=> ! [X4,X12,X3] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f203,axiom,
! [X3,X4,X12] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X3,X12,tc_nat),c_HOL_Otimes__class_Otimes(X4,X12,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).
fof(f1788,plain,
spl0_154,
inference(avatar_split_clause,[],[f202,f1786]) ).
fof(f202,axiom,
! [X3,X4,X12] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(X12,X3,tc_nat),c_HOL_Otimes__class_Otimes(X12,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).
fof(f1784,plain,
( spl0_153
| ~ spl0_38
| ~ spl0_93 ),
inference(avatar_split_clause,[],[f978,f888,f568,f1782]) ).
fof(f978,plain,
( ! [X0] : c_Suc(X0) = c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(c_Suc(X0)))
| ~ spl0_38
| ~ spl0_93 ),
inference(resolution,[],[f889,f569]) ).
fof(f1780,plain,
spl0_152,
inference(avatar_split_clause,[],[f201,f1778]) ).
fof(f1778,plain,
( spl0_152
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f201,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).
fof(f1776,plain,
spl0_151,
inference(avatar_split_clause,[],[f200,f1774]) ).
fof(f1774,plain,
( spl0_151
<=> ! [X4,X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f200,axiom,
! [X3,X0,X4] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_Nat_Osemiring__1__class_Oof__nat(X4,X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).
fof(f1772,plain,
spl0_150,
inference(avatar_split_clause,[],[f106,f1770]) ).
fof(f1770,plain,
( spl0_150
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X8,X1,X0) != c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f106,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X8,X1,X0) != c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).
fof(f1768,plain,
spl0_149,
inference(avatar_split_clause,[],[f105,f1766]) ).
fof(f1766,plain,
( spl0_149
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X1,X8,X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f105,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X1,X8,X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).
fof(f1764,plain,
spl0_148,
inference(avatar_split_clause,[],[f104,f1762]) ).
fof(f1762,plain,
( spl0_148
<=> ! [X0,X8,X2,X1] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X1,X8,X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f104,axiom,
! [X2,X0,X1,X8] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X0)
| X2 = X8
| c_HOL_Oplus__class_Oplus(X1,X8,X0) != c_HOL_Oplus__class_Oplus(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).
fof(f1652,plain,
( spl0_147
| ~ spl0_53
| ~ spl0_79 ),
inference(avatar_split_clause,[],[f831,f748,f632,f1650]) ).
fof(f831,plain,
( ! [X0,X1] : ~ c_HOL_Oord__class_Oless(X0,c_HOL_Ominus__class_Ominus(X0,X1,tc_nat),tc_nat)
| ~ spl0_53
| ~ spl0_79 ),
inference(resolution,[],[f749,f633]) ).
fof(f1492,plain,
spl0_146,
inference(avatar_split_clause,[],[f361,f1489]) ).
fof(f361,axiom,
c_InductTermi_OIT(c_Lambda_Osubst(c_Lambda_OdB_OApp(c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_Lambda_Olift(v_ta____,c_HOL_Ozero__class_Ozero(tc_nat))),v_s____,c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).
fof(f1487,plain,
spl0_145,
inference(avatar_split_clause,[],[f352,f1485]) ).
fof(f352,axiom,
! [X28,X25,X12] : c_Lambda_Olift(c_Lambda_OdB_OApp(X28,X25),X12) = c_Lambda_OdB_OApp(c_Lambda_Olift(X28,X12),c_Lambda_Olift(X25,X12)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
fof(f1480,plain,
spl0_144,
inference(avatar_split_clause,[],[f312,f1478]) ).
fof(f312,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(f1476,plain,
spl0_143,
inference(avatar_split_clause,[],[f284,f1474]) ).
fof(f1474,plain,
( spl0_143
<=> ! [X6,X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X6
| c_HOL_Oord__class_Oless(X5,X6,X0)
| c_HOL_Oord__class_Oless(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f284,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| X5 = X6
| c_HOL_Oord__class_Oless(X5,X6,X0)
| c_HOL_Oord__class_Oless(X6,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
fof(f1472,plain,
spl0_142,
inference(avatar_split_clause,[],[f274,f1470]) ).
fof(f274,axiom,
! [X11,X12,X13] :
( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
| ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X11),X12,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
fof(f1468,plain,
spl0_141,
inference(avatar_split_clause,[],[f261,f1466]) ).
fof(f1466,plain,
( spl0_141
<=> ! [X4,X11] :
( ~ 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(X11),tc_nat),X4,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f261,axiom,
! [X11,X4] :
( ~ 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(X11),tc_nat),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).
fof(f1464,plain,
spl0_140,
inference(avatar_split_clause,[],[f242,f1462]) ).
fof(f242,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oplus__class_Oplus(X4,c_HOL_Ominus__class_Ominus(X3,X4,tc_nat),tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).
fof(f1460,plain,
spl0_139,
inference(avatar_split_clause,[],[f171,f1458]) ).
fof(f171,axiom,
! [X3,X4] : c_HOL_Otimes__class_Otimes(c_Suc(X3),X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc_0) ).
fof(f1456,plain,
spl0_138,
inference(avatar_split_clause,[],[f170,f1454]) ).
fof(f170,axiom,
! [X3,X4] : c_HOL_Otimes__class_Otimes(X3,c_Suc(X4),tc_nat) = c_HOL_Oplus__class_Oplus(X3,c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).
fof(f1452,plain,
spl0_137,
inference(avatar_split_clause,[],[f89,f1450]) ).
fof(f89,axiom,
! [X3,X4] :
( 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),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).
fof(f1448,plain,
spl0_136,
inference(avatar_split_clause,[],[f88,f1446]) ).
fof(f88,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),c_HOL_Otimes__class_Otimes(X3,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).
fof(f1444,plain,
spl0_135,
inference(avatar_split_clause,[],[f32,f1442]) ).
fof(f1442,plain,
( spl0_135
<=> ! [X4,X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
| c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f32,axiom,
! [X3,X4] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X4
| c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).
fof(f1438,plain,
spl0_134,
inference(avatar_split_clause,[],[f31,f1436]) ).
fof(f1436,plain,
( spl0_134
<=> ! [X4,X3] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f31,axiom,
! [X3,X4] :
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = X3
| c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).
fof(f1321,plain,
spl0_133,
inference(avatar_split_clause,[],[f338,f1319]) ).
fof(f338,axiom,
! [X11,X15,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X11,tc_nat)
| c_Lambda_OdB_OVar(X13) = c_Lambda_Osubst(c_Lambda_OdB_OVar(X13),X15,X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lt_0) ).
fof(f1317,plain,
spl0_132,
inference(avatar_split_clause,[],[f330,f1315]) ).
fof(f330,axiom,
! [X4,X25,X12] : c_Lambda_Oliftn(c_Suc(X4),X25,X12) = c_Lambda_Olift(c_Lambda_Oliftn(X4,X25,X12),X12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__lift_0) ).
fof(f1313,plain,
spl0_131,
inference(avatar_split_clause,[],[f329,f1311]) ).
fof(f329,axiom,
! [X28,X11,X24,X25] :
( ~ c_Lambda_Obeta(X24,X28)
| c_Lambda_Obeta(c_Lambda_Osubst(X24,X25,X11),c_Lambda_Osubst(X28,X25,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
fof(f1309,plain,
spl0_130,
inference(avatar_split_clause,[],[f325,f1307]) ).
fof(f325,axiom,
! [X11,X4,X12] :
( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| c_Lambda_OdB_OVar(X11) = c_Lambda_Oliftn(X4,c_Lambda_OdB_OVar(X11),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn_Osimps_I1_J_0) ).
fof(f1305,plain,
spl0_129,
inference(avatar_split_clause,[],[f295,f1303]) ).
fof(f295,axiom,
! [X3,X4] :
( X3 = X4
| c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).
fof(f1301,plain,
spl0_128,
inference(avatar_split_clause,[],[f231,f1299]) ).
fof(f231,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(f1297,plain,
spl0_127,
inference(avatar_split_clause,[],[f230,f1295]) ).
fof(f230,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(f1293,plain,
spl0_126,
inference(avatar_split_clause,[],[f179,f1290]) ).
fof(f1290,plain,
( spl0_126
<=> c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f179,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).
fof(f1288,plain,
( spl0_125
| ~ spl0_81
| ~ spl0_97 ),
inference(avatar_split_clause,[],[f999,f904,f756,f1286]) ).
fof(f999,plain,
( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0))),X1)
| ~ spl0_81
| ~ spl0_97 ),
inference(resolution,[],[f905,f757]) ).
fof(f1284,plain,
spl0_124,
inference(avatar_split_clause,[],[f101,f1282]) ).
fof(f101,axiom,
! [X3,X4,X12] :
( X3 = X4
| c_HOL_Oplus__class_Oplus(X4,X12,tc_nat) != c_HOL_Oplus__class_Oplus(X3,X12,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).
fof(f1280,plain,
spl0_123,
inference(avatar_split_clause,[],[f100,f1278]) ).
fof(f100,axiom,
! [X6,X7,X5] :
( X6 = X7
| c_HOL_Oplus__class_Oplus(X5,X7,tc_nat) != c_HOL_Oplus__class_Oplus(X5,X6,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).
fof(f1276,plain,
spl0_122,
inference(avatar_split_clause,[],[f34,f1274]) ).
fof(f1274,plain,
( spl0_122
<=> ! [X4,X0,X3] :
( ~ class_Nat_Osemiring__char__0(X0)
| X3 = X4
| c_Nat_Osemiring__1__class_Oof__nat(X3,X0) != c_Nat_Osemiring__1__class_Oof__nat(X4,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f34,axiom,
! [X3,X0,X4] :
( ~ class_Nat_Osemiring__char__0(X0)
| X3 = X4
| c_Nat_Osemiring__1__class_Oof__nat(X3,X0) != c_Nat_Osemiring__1__class_Oof__nat(X4,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
fof(f1185,plain,
( spl0_121
| ~ spl0_76
| ~ spl0_86 ),
inference(avatar_split_clause,[],[f949,f860,f736,f1183]) ).
fof(f949,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_76
| ~ spl0_86 ),
inference(resolution,[],[f861,f737]) ).
fof(f1092,plain,
spl0_120,
inference(avatar_split_clause,[],[f323,f1090]) ).
fof(f323,axiom,
! [X11,X12] :
( ~ c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| c_Lambda_OdB_OVar(X11) = c_Lambda_Olift(c_Lambda_OdB_OVar(X11),X12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I1_J_0) ).
fof(f1088,plain,
spl0_119,
inference(avatar_split_clause,[],[f283,f1086]) ).
fof(f283,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(f1084,plain,
spl0_118,
inference(avatar_split_clause,[],[f192,f1082]) ).
fof(f192,axiom,
! [X4,X12,X13] :
( ~ c_HOL_Oord__class_Oless(X13,X12,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(X13,X4,tc_nat),X12,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).
fof(f1072,plain,
spl0_117,
inference(avatar_split_clause,[],[f178,f1070]) ).
fof(f178,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(X3,X4,tc_nat) = c_HOL_Ominus__class_Ominus(c_Suc(X3),c_Suc(X4),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).
fof(f1068,plain,
spl0_116,
inference(avatar_split_clause,[],[f49,f1066]) ).
fof(f49,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).
fof(f1064,plain,
spl0_115,
inference(avatar_split_clause,[],[f48,f1062]) ).
fof(f48,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X3
| c_HOL_Ozero__class_Ozero(tc_nat) != c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).
fof(f1060,plain,
spl0_114,
inference(avatar_split_clause,[],[f30,f1058]) ).
fof(f1058,plain,
( spl0_114
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f30,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X5,X6,X0) = c_HOL_Oplus__class_Oplus(X6,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).
fof(f1056,plain,
spl0_113,
inference(avatar_split_clause,[],[f27,f1054]) ).
fof(f1054,plain,
( spl0_113
<=> ! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f27,axiom,
! [X2,X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,X2,X0) = c_HOL_Oplus__class_Oplus(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).
fof(f1052,plain,
spl0_112,
inference(avatar_split_clause,[],[f25,f1050]) ).
fof(f25,axiom,
! [X3,X11,X13] :
( ~ c_HOL_Oord__class_Oless(X11,X13,tc_nat)
| c_HOL_Oord__class_Oless(X11,c_HOL_Oplus__class_Oplus(X3,X13,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).
fof(f1048,plain,
spl0_111,
inference(avatar_split_clause,[],[f23,f1046]) ).
fof(f23,axiom,
! [X11,X12,X13] :
( c_HOL_Oord__class_Oless(X11,X12,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X12,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).
fof(f1044,plain,
spl0_110,
inference(avatar_split_clause,[],[f21,f1042]) ).
fof(f21,axiom,
! [X6,X7,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X6,tc_nat)
| c_HOL_Oord__class_Oless(X5,c_HOL_Oplus__class_Oplus(X6,X7,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).
fof(f1040,plain,
spl0_109,
inference(avatar_split_clause,[],[f14,f1038]) ).
fof(f1036,plain,
spl0_108,
inference(avatar_split_clause,[],[f13,f1034]) ).
fof(f1032,plain,
( spl0_107
| ~ spl0_30
| ~ spl0_77 ),
inference(avatar_split_clause,[],[f818,f740,f536,f1030]) ).
fof(f818,plain,
( ! [X0] : c_HOL_Oord__class_Oless(X0,c_Suc(c_Suc(X0)),tc_nat)
| ~ spl0_30
| ~ spl0_77 ),
inference(resolution,[],[f741,f537]) ).
fof(f1028,plain,
spl0_106,
inference(avatar_split_clause,[],[f5,f1026]) ).
fof(f1026,plain,
( spl0_106
<=> ! [X5,X0,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X5,X6,X0) = c_HOL_Otimes__class_Otimes(X6,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f5,axiom,
! [X0,X6,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Otimes__class_Otimes(X5,X6,X0) = c_HOL_Otimes__class_Otimes(X6,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).
fof(f938,plain,
spl0_105,
inference(avatar_split_clause,[],[f356,f936]) ).
fof(f936,plain,
( spl0_105
<=> ! [X25,X28,X15] :
( ~ c_Lambda_Obeta(X28,X25)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X28,X15),c_Lambda_OdB_OApp(X25,X15)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f356,axiom,
! [X28,X15,X25] :
( ~ c_Lambda_Obeta(X28,X25)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X28,X15),c_Lambda_OdB_OApp(X25,X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
fof(f934,plain,
spl0_104,
inference(avatar_split_clause,[],[f355,f932]) ).
fof(f932,plain,
( spl0_104
<=> ! [X25,X28,X15] :
( ~ c_Lambda_Obeta(X28,X25)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X15,X28),c_Lambda_OdB_OApp(X15,X25)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f355,axiom,
! [X28,X15,X25] :
( ~ c_Lambda_Obeta(X28,X25)
| c_Lambda_Obeta(c_Lambda_OdB_OApp(X15,X28),c_Lambda_OdB_OApp(X15,X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
fof(f930,plain,
spl0_103,
inference(avatar_split_clause,[],[f347,f928]) ).
fof(f347,axiom,
! [X31,X34,X32,X33] :
( X32 = X34
| c_Lambda_OdB_OApp(X31,X32) != c_Lambda_OdB_OApp(X33,X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
fof(f926,plain,
spl0_102,
inference(avatar_split_clause,[],[f346,f924]) ).
fof(f346,axiom,
! [X31,X34,X32,X33] :
( X31 = X33
| c_Lambda_OdB_OApp(X31,X32) != c_Lambda_OdB_OApp(X33,X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
fof(f922,plain,
spl0_101,
inference(avatar_split_clause,[],[f334,f920]) ).
fof(f334,axiom,
! [X28,X25] : c_Lambda_Obeta(c_Lambda_OdB_OApp(c_Lambda_OdB_OAbs(X28),X25),c_Lambda_Osubst(X28,X25,c_HOL_Ozero__class_Ozero(tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
fof(f918,plain,
spl0_100,
inference(avatar_split_clause,[],[f322,f916]) ).
fof(f916,plain,
( spl0_100
<=> ! [X11,X28,X24] :
( ~ c_Lambda_Obeta(X24,X28)
| c_Lambda_Obeta(c_Lambda_Olift(X24,X11),c_Lambda_Olift(X28,X11)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f322,axiom,
! [X28,X11,X24] :
( ~ c_Lambda_Obeta(X24,X28)
| c_Lambda_Obeta(c_Lambda_Olift(X24,X11),c_Lambda_Olift(X28,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
fof(f914,plain,
spl0_99,
inference(avatar_split_clause,[],[f320,f912]) ).
fof(f320,axiom,
! [X28,X24] :
( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X24),X28)
| c_Lambda_OdB_OAbs(c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X24,X28)) = X28 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I2_J_0) ).
fof(f910,plain,
spl0_98,
inference(avatar_split_clause,[],[f317,f908]) ).
fof(f317,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(f906,plain,
( spl0_97
| ~ spl0_29
| ~ spl0_81 ),
inference(avatar_split_clause,[],[f846,f756,f532,f904]) ).
fof(f846,plain,
( ! [X0,X1] : ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(c_Lambda_OdB_OVar(X0)),X1)
| ~ spl0_29
| ~ spl0_81 ),
inference(resolution,[],[f757,f533]) ).
fof(f902,plain,
spl0_96,
inference(avatar_split_clause,[],[f316,f900]) ).
fof(f316,axiom,
! [X4,X5] :
( ~ c_HOL_Oord__class_Oless(X5,X4,tc_nat)
| c_HOL_Oord__class_Oless(c_Suc(X5),c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
fof(f898,plain,
spl0_95,
inference(avatar_split_clause,[],[f303,f896]) ).
fof(f303,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1(X4)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_0) ).
fof(f894,plain,
spl0_94,
inference(avatar_split_clause,[],[f302,f892]) ).
fof(f302,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(f890,plain,
spl0_93,
inference(avatar_split_clause,[],[f301,f888]) ).
fof(f301,axiom,
! [X4] :
( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat)
| c_Suc(c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1(X4)) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__implies__Suc_0) ).
fof(f886,plain,
spl0_92,
inference(avatar_split_clause,[],[f260,f884]) ).
fof(f884,plain,
( spl0_92
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f260,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
fof(f882,plain,
spl0_91,
inference(avatar_split_clause,[],[f259,f880]) ).
fof(f880,plain,
( spl0_91
<=> ! [X5,X0,X6] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f259,axiom,
! [X0,X6,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X6,X5,X0)
| ~ c_HOL_Oord__class_Oless(X5,X6,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
fof(f878,plain,
spl0_90,
inference(avatar_split_clause,[],[f257,f876]) ).
fof(f876,plain,
( spl0_90
<=> ! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f257,axiom,
! [X2,X0,X1] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X1,X2,X0)
| ~ c_HOL_Oord__class_Oless(X2,X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
fof(f874,plain,
spl0_89,
inference(avatar_split_clause,[],[f191,f872]) ).
fof(f872,plain,
( spl0_89
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f191,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).
fof(f870,plain,
spl0_88,
inference(avatar_split_clause,[],[f188,f868]) ).
fof(f868,plain,
( spl0_88
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f188,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(X0),X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).
fof(f866,plain,
spl0_87,
inference(avatar_split_clause,[],[f187,f864]) ).
fof(f864,plain,
( spl0_87
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f187,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Omult__zero(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).
fof(f862,plain,
( spl0_86
| ~ spl0_28
| ~ spl0_76 ),
inference(avatar_split_clause,[],[f810,f736,f528,f860]) ).
fof(f810,plain,
( ! [X0] : ~ c_HOL_Oord__class_Oless(c_Suc(X0),X0,tc_nat)
| ~ spl0_28
| ~ spl0_76 ),
inference(resolution,[],[f737,f529]) ).
fof(f858,plain,
spl0_85,
inference(avatar_split_clause,[],[f184,f856]) ).
fof(f856,plain,
( spl0_85
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f184,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_HOL_Otimes__class_Otimes(X1,c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).
fof(f854,plain,
spl0_84,
inference(avatar_split_clause,[],[f72,f852]) ).
fof(f72,axiom,
! [X3,X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Ominus__class_Ominus(X4,c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).
fof(f850,plain,
spl0_83,
inference(avatar_split_clause,[],[f36,f848]) ).
fof(f36,axiom,
! [X3,X4] :
( c_HOL_Ozero__class_Ozero(tc_nat) = X4
| c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) != X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).
fof(f802,plain,
( spl0_82
| ~ spl0_18
| ~ spl0_65 ),
inference(avatar_split_clause,[],[f784,f692,f480,f799]) ).
fof(f799,plain,
( spl0_82
<=> 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_82])]) ).
fof(f480,plain,
( spl0_18
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f692,plain,
( spl0_65
<=> ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f784,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_18
| ~ spl0_65 ),
inference(resolution,[],[f693,f482]) ).
fof(f482,plain,
( class_Ring__and__Field_Osemiring__1(tc_nat)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f480]) ).
fof(f693,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) )
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f692]) ).
fof(f758,plain,
spl0_81,
inference(avatar_split_clause,[],[f336,f756]) ).
fof(f336,axiom,
! [X28,X24] :
( ~ c_Lambda_Obeta(c_Lambda_OdB_OAbs(X24),X28)
| c_Lambda_Obeta(X24,c_Lambda_Osko__Lambda__Xbeta__cases__2__1(X24,X28)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I2_J_1) ).
fof(f754,plain,
spl0_80,
inference(avatar_split_clause,[],[f315,f752]) ).
fof(f315,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(f750,plain,
spl0_79,
inference(avatar_split_clause,[],[f314,f748]) ).
fof(f314,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(f746,plain,
spl0_78,
inference(avatar_split_clause,[],[f271,f744]) ).
fof(f271,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(f742,plain,
spl0_77,
inference(avatar_split_clause,[],[f264,f740]) ).
fof(f264,axiom,
! [X3,X4] :
( c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(X3),X4,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
fof(f738,plain,
spl0_76,
inference(avatar_split_clause,[],[f263,f736]) ).
fof(f263,axiom,
! [X3,X4] :
( ~ c_HOL_Oord__class_Oless(X3,X4,tc_nat)
| c_HOL_Oord__class_Oless(X3,c_Suc(X4),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
fof(f734,plain,
spl0_75,
inference(avatar_split_clause,[],[f151,f732]) ).
fof(f151,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),X4,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).
fof(f730,plain,
spl0_74,
inference(avatar_split_clause,[],[f150,f728]) ).
fof(f150,axiom,
! [X3,X4] : c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(X3,X4,tc_nat),X4,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).
fof(f726,plain,
spl0_73,
inference(avatar_split_clause,[],[f147,f724]) ).
fof(f724,plain,
( spl0_73
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f147,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).
fof(f722,plain,
( spl0_72
| ~ spl0_59
| ~ spl0_61 ),
inference(avatar_split_clause,[],[f681,f664,f656,f720]) ).
fof(f720,plain,
( spl0_72
<=> ! [X0,X1] :
( c_InductTermi_OIT(X0)
| ~ c_InductTermi_OIT(c_Lambda_Olift(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f664,plain,
( spl0_61
<=> ! [X13,X11,X24] :
( ~ c_InductTermi_OIT(X24)
| c_InductTermi_OIT(c_Lambda_Osubst(X24,c_Lambda_OdB_OVar(X11),X13)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f681,plain,
( ! [X0,X1] :
( c_InductTermi_OIT(X0)
| ~ c_InductTermi_OIT(c_Lambda_Olift(X0,X1)) )
| ~ spl0_59
| ~ spl0_61 ),
inference(superposition,[],[f665,f657]) ).
fof(f665,plain,
( ! [X11,X24,X13] :
( c_InductTermi_OIT(c_Lambda_Osubst(X24,c_Lambda_OdB_OVar(X11),X13))
| ~ c_InductTermi_OIT(X24) )
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f718,plain,
spl0_71,
inference(avatar_split_clause,[],[f146,f716]) ).
fof(f716,plain,
( spl0_71
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f146,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).
fof(f714,plain,
spl0_70,
inference(avatar_split_clause,[],[f145,f712]) ).
fof(f712,plain,
( spl0_70
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f145,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Omonoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).
fof(f710,plain,
spl0_69,
inference(avatar_split_clause,[],[f144,f708]) ).
fof(f708,plain,
( spl0_69
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f144,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(X1,c_HOL_Ozero__class_Ozero(X0),X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).
fof(f706,plain,
spl0_68,
inference(avatar_split_clause,[],[f139,f704]) ).
fof(f704,plain,
( spl0_68
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f139,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X1,X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).
fof(f702,plain,
spl0_67,
inference(avatar_split_clause,[],[f138,f700]) ).
fof(f700,plain,
( spl0_67
<=> ! [X5,X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f138,axiom,
! [X0,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X0)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(X0),X5,X0) = X5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).
fof(f698,plain,
spl0_66,
inference(avatar_split_clause,[],[f113,f696]) ).
fof(f696,plain,
( spl0_66
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f113,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(X3,X0),c_HOL_Ozero__class_Ozero(X0),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).
fof(f694,plain,
spl0_65,
inference(avatar_split_clause,[],[f87,f692]) ).
fof(f87,axiom,
! [X0] :
( ~ class_Ring__and__Field_Osemiring__1(X0)
| c_HOL_Ozero__class_Ozero(X0) = c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
fof(f690,plain,
spl0_64,
inference(avatar_split_clause,[],[f28,f688]) ).
fof(f28,axiom,
! [X3,X4] : c_HOL_Oplus__class_Oplus(X3,X4,tc_nat) = c_HOL_Oplus__class_Oplus(X4,X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).
fof(f686,plain,
spl0_63,
inference(avatar_split_clause,[],[f4,f684]) ).
fof(f4,axiom,
! [X3,X4] : c_HOL_Otimes__class_Otimes(X3,X4,tc_nat) = c_HOL_Otimes__class_Otimes(X4,X3,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).
fof(f670,plain,
spl0_62,
inference(avatar_split_clause,[],[f341,f668]) ).
fof(f668,plain,
( spl0_62
<=> ! [X27,X26] :
( X26 = X27
| c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OVar(X26) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f341,axiom,
! [X26,X27] :
( X26 = X27
| c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OVar(X26) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
fof(f666,plain,
spl0_61,
inference(avatar_split_clause,[],[f339,f664]) ).
fof(f339,axiom,
! [X11,X24,X13] :
( ~ c_InductTermi_OIT(X24)
| c_InductTermi_OIT(c_Lambda_Osubst(X24,c_Lambda_OdB_OVar(X11),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
fof(f662,plain,
spl0_60,
inference(avatar_split_clause,[],[f333,f660]) ).
fof(f660,plain,
( spl0_60
<=> ! [X29,X30] :
( X29 = X30
| c_Lambda_OdB_OAbs(X29) != c_Lambda_OdB_OAbs(X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f333,axiom,
! [X29,X30] :
( X29 = X30
| c_Lambda_OdB_OAbs(X29) != c_Lambda_OdB_OAbs(X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
fof(f658,plain,
spl0_59,
inference(avatar_split_clause,[],[f324,f656]) ).
fof(f324,axiom,
! [X28,X25,X12] : c_Lambda_Osubst(c_Lambda_Olift(X25,X12),X28,X12) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
fof(f654,plain,
spl0_58,
inference(avatar_split_clause,[],[f319,f652]) ).
fof(f319,axiom,
! [X28,X25] :
( ~ c_Lambda_Obeta(X28,X25)
| c_Lambda_Obeta(c_Lambda_OdB_OAbs(X28),c_Lambda_OdB_OAbs(X25)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
fof(f650,plain,
spl0_57,
inference(avatar_split_clause,[],[f298,f648]) ).
fof(f648,plain,
( spl0_57
<=> ! [X6,X5] :
( X5 = X6
| c_Suc(X5) != c_Suc(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f298,axiom,
! [X6,X5] :
( X5 = X6
| c_Suc(X5) != c_Suc(X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
fof(f646,plain,
spl0_56,
inference(avatar_split_clause,[],[f190,f644]) ).
fof(f190,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).
fof(f642,plain,
spl0_55,
inference(avatar_split_clause,[],[f189,f640]) ).
fof(f189,axiom,
! [X4] : c_HOL_Ozero__class_Ozero(tc_nat) = c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).
fof(f638,plain,
spl0_54,
inference(avatar_split_clause,[],[f82,f636]) ).
fof(f82,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(f634,plain,
spl0_53,
inference(avatar_split_clause,[],[f57,f632]) ).
fof(f57,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(f630,plain,
spl0_52,
inference(avatar_split_clause,[],[f20,f628]) ).
fof(f20,axiom,
! [X3,X5] : c_HOL_Oord__class_Oless(X3,c_Suc(c_HOL_Oplus__class_Oplus(X3,X5,tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).
fof(f626,plain,
spl0_51,
inference(avatar_split_clause,[],[f19,f624]) ).
fof(f19,axiom,
! [X3,X11] : c_HOL_Oord__class_Oless(X11,c_Suc(c_HOL_Oplus__class_Oplus(X3,X11,tc_nat)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).
fof(f618,plain,
spl0_50,
inference(avatar_split_clause,[],[f358,f616]) ).
fof(f616,plain,
( spl0_50
<=> ! [X25,X11] :
( ~ c_InductTermi_OIT(X25)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(X25,c_Lambda_OdB_OVar(X11))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f358,axiom,
! [X11,X25] :
( ~ c_InductTermi_OIT(X25)
| c_InductTermi_OIT(c_Lambda_OdB_OApp(X25,c_Lambda_OdB_OVar(X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
fof(f614,plain,
spl0_49,
inference(avatar_split_clause,[],[f340,f612]) ).
fof(f340,axiom,
! [X15,X12] : c_Lambda_Osubst(c_Lambda_OdB_OVar(X12),X15,X12) = X15,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
fof(f610,plain,
spl0_48,
inference(avatar_split_clause,[],[f270,f608]) ).
fof(f270,axiom,
! [X25,X12] : c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),X25,X12) = X25,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_liftn__0_0) ).
fof(f606,plain,
spl0_47,
inference(avatar_split_clause,[],[f212,f604]) ).
fof(f212,axiom,
! [X11,X13] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X13,X11,tc_nat),X11,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).
fof(f602,plain,
spl0_46,
inference(avatar_split_clause,[],[f211,f600]) ).
fof(f211,axiom,
! [X11,X13] : ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(X11,X13,tc_nat),X11,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).
fof(f598,plain,
spl0_45,
inference(avatar_split_clause,[],[f142,f596]) ).
fof(f142,axiom,
! [X3] : c_HOL_Oplus__class_Oplus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f594,plain,
spl0_44,
inference(avatar_split_clause,[],[f141,f592]) ).
fof(f141,axiom,
! [X4] : c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),X4,tc_nat) = X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).
fof(f590,plain,
spl0_43,
inference(avatar_split_clause,[],[f44,f588]) ).
fof(f588,plain,
( spl0_43
<=> ! [X3] : c_HOL_Ominus__class_Ominus(X3,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f44,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(f586,plain,
spl0_42,
inference(avatar_split_clause,[],[f43,f584]) ).
fof(f43,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(f582,plain,
spl0_41,
inference(avatar_split_clause,[],[f360,f580]) ).
fof(f360,axiom,
! [X27,X34,X33] : c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OApp(X33,X34),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
fof(f578,plain,
spl0_40,
inference(avatar_split_clause,[],[f350,f576]) ).
fof(f350,axiom,
! [X11,X25] :
( ~ c_InductTermi_OIT(X25)
| c_InductTermi_OIT(c_Lambda_Olift(X25,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
fof(f574,plain,
spl0_39,
inference(avatar_split_clause,[],[f345,f572]) ).
fof(f345,axiom,
! [X31,X29,X32] : c_Lambda_OdB_OAbs(X29) != c_Lambda_OdB_OApp(X31,X32),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
fof(f570,plain,
spl0_38,
inference(avatar_split_clause,[],[f311,f568]) ).
fof(f311,axiom,
! [X5] : c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(X5),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
fof(f566,plain,
spl0_37,
inference(avatar_split_clause,[],[f289,f564]) ).
fof(f564,plain,
( spl0_37
<=> ! [X5,X0] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f289,axiom,
! [X0,X5] :
( ~ class_Orderings_Oorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
fof(f562,plain,
spl0_36,
inference(avatar_split_clause,[],[f288,f560]) ).
fof(f560,plain,
( spl0_36
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f288,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
fof(f558,plain,
spl0_35,
inference(avatar_split_clause,[],[f287,f556]) ).
fof(f556,plain,
( spl0_35
<=> ! [X5,X0] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f287,axiom,
! [X0,X5] :
( ~ class_Orderings_Opreorder(X0)
| ~ c_HOL_Oord__class_Oless(X5,X5,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
fof(f554,plain,
spl0_34,
inference(avatar_split_clause,[],[f354,f552]) ).
fof(f552,plain,
( spl0_34
<=> ! [X24] :
( ~ c_InductTermi_OIT(X24)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X24)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f354,axiom,
! [X24] :
( ~ c_InductTermi_OIT(X24)
| c_InductTermi_OIT(c_Lambda_OdB_OAbs(X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
fof(f550,plain,
spl0_33,
inference(avatar_split_clause,[],[f342,f548]) ).
fof(f342,axiom,
! [X29,X27] : c_Lambda_OdB_OVar(X27) != c_Lambda_OdB_OAbs(X29),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
fof(f546,plain,
spl0_32,
inference(avatar_split_clause,[],[f308,f544]) ).
fof(f308,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
fof(f542,plain,
spl0_31,
inference(avatar_split_clause,[],[f299,f540]) ).
fof(f540,plain,
( spl0_31
<=> ! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f299,axiom,
! [X3] : c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
fof(f538,plain,
spl0_30,
inference(avatar_split_clause,[],[f275,f536]) ).
fof(f275,axiom,
! [X5] : c_HOL_Oord__class_Oless(X5,c_Suc(X5),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
fof(f534,plain,
spl0_29,
inference(avatar_split_clause,[],[f335,f532]) ).
fof(f335,axiom,
! [X11,X25] : ~ c_Lambda_Obeta(c_Lambda_OdB_OVar(X11),X25),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
fof(f530,plain,
spl0_28,
inference(avatar_split_clause,[],[f290,f528]) ).
fof(f290,axiom,
! [X4] : ~ c_HOL_Oord__class_Oless(X4,X4,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
fof(f526,plain,
spl0_27,
inference(avatar_split_clause,[],[f266,f524]) ).
fof(f266,axiom,
! [X4] : c_Suc(X4) != X4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
fof(f522,plain,
spl0_26,
inference(avatar_split_clause,[],[f351,f520]) ).
fof(f351,axiom,
! [X4] : c_InductTermi_OIT(c_Lambda_OdB_OVar(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
fof(f518,plain,
spl0_25,
inference(avatar_split_clause,[],[f384,f515]) ).
fof(f515,plain,
( spl0_25
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f384,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
fof(f513,plain,
spl0_24,
inference(avatar_split_clause,[],[f383,f510]) ).
fof(f510,plain,
( spl0_24
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f383,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
fof(f508,plain,
spl0_23,
inference(avatar_split_clause,[],[f382,f505]) ).
fof(f382,axiom,
class_Orderings_Opreorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
fof(f503,plain,
spl0_22,
inference(avatar_split_clause,[],[f381,f500]) ).
fof(f500,plain,
( spl0_22
<=> class_Nat_Osemiring__char__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f381,axiom,
class_Nat_Osemiring__char__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
fof(f498,plain,
spl0_21,
inference(avatar_split_clause,[],[f380,f495]) ).
fof(f495,plain,
( spl0_21
<=> class_OrderedGroup_Omonoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f380,axiom,
class_OrderedGroup_Omonoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).
fof(f493,plain,
spl0_20,
inference(avatar_split_clause,[],[f379,f490]) ).
fof(f490,plain,
( spl0_20
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f379,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).
fof(f488,plain,
spl0_19,
inference(avatar_split_clause,[],[f378,f485]) ).
fof(f485,plain,
( spl0_19
<=> class_Ring__and__Field_Omult__zero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f378,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).
fof(f483,plain,
spl0_18,
inference(avatar_split_clause,[],[f377,f480]) ).
fof(f377,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
fof(f478,plain,
spl0_17,
inference(avatar_split_clause,[],[f376,f475]) ).
fof(f475,plain,
( spl0_17
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f376,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).
fof(f473,plain,
spl0_16,
inference(avatar_split_clause,[],[f375,f470]) ).
fof(f470,plain,
( spl0_16
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f375,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).
fof(f468,plain,
spl0_15,
inference(avatar_split_clause,[],[f374,f465]) ).
fof(f465,plain,
( spl0_15
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f374,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).
fof(f463,plain,
spl0_14,
inference(avatar_split_clause,[],[f373,f460]) ).
fof(f460,plain,
( spl0_14
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f373,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).
fof(f458,plain,
spl0_13,
inference(avatar_split_clause,[],[f372,f455]) ).
fof(f455,plain,
( spl0_13
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f372,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(f453,plain,
spl0_12,
inference(avatar_split_clause,[],[f371,f450]) ).
fof(f371,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).
fof(f448,plain,
spl0_11,
inference(avatar_split_clause,[],[f370,f445]) ).
fof(f445,plain,
( spl0_11
<=> class_Ring__and__Field_Ono__zero__divisors(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f370,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).
fof(f443,plain,
spl0_10,
inference(avatar_split_clause,[],[f369,f440]) ).
fof(f440,plain,
( spl0_10
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f369,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).
fof(f438,plain,
spl0_9,
inference(avatar_split_clause,[],[f368,f435]) ).
fof(f435,plain,
( spl0_9
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f368,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).
fof(f433,plain,
spl0_8,
inference(avatar_split_clause,[],[f367,f430]) ).
fof(f430,plain,
( spl0_8
<=> class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f367,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).
fof(f428,plain,
spl0_7,
inference(avatar_split_clause,[],[f366,f425]) ).
fof(f425,plain,
( spl0_7
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f366,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).
fof(f423,plain,
spl0_6,
inference(avatar_split_clause,[],[f365,f420]) ).
fof(f420,plain,
( spl0_6
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f365,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).
fof(f418,plain,
spl0_5,
inference(avatar_split_clause,[],[f364,f415]) ).
fof(f415,plain,
( spl0_5
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f364,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(f413,plain,
spl0_4,
inference(avatar_split_clause,[],[f363,f410]) ).
fof(f410,plain,
( spl0_4
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f363,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(f408,plain,
spl0_3,
inference(avatar_split_clause,[],[f353,f405]) ).
fof(f405,plain,
( spl0_3
<=> c_InductTermi_OIT(v_ta____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f353,axiom,
c_InductTermi_OIT(v_ta____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I4_J_0) ).
fof(f403,plain,
spl0_2,
inference(avatar_split_clause,[],[f349,f400]) ).
fof(f400,plain,
( spl0_2
<=> c_InductTermi_OIT(v_s____) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f349,axiom,
c_InductTermi_OIT(v_s____),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_I2_J_0) ).
fof(f398,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f362,f395]) ).
fof(f362,axiom,
~ c_InductTermi_OIT(c_Lambda_OdB_OApp(v_s____,v_ta____)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LCL855-1 : TPTP v8.1.2. Released v4.1.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Apr 29 22:37:19 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.37 % (25150)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.40 % (25153)WARNING: value z3 for option sas not known
% 0.14/0.40 % (25151)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40 % (25152)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.40 % (25154)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.40 % (25153)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)
% 0.14/0.40 % (25155)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)
% 0.14/0.40 % (25156)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)
% 0.14/0.40 % (25157)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)
% 0.22/0.43 TRYING [1]
% 0.22/0.44 TRYING [2]
% 0.22/0.48 TRYING [3]
% 0.22/0.52 TRYING [1]
% 0.22/0.53 TRYING [2]
% 1.41/0.58 TRYING [1]
% 1.55/0.58 TRYING [2]
% 1.55/0.60 TRYING [3]
% 1.55/0.61 TRYING [4]
% 2.01/0.68 TRYING [4]
% 2.47/0.75 TRYING [3]
% 3.97/0.94 % (25155)First to succeed.
% 4.10/0.95 % (25155)Refutation found. Thanks to Tanya!
% 4.10/0.95 % SZS status Unsatisfiable for theBenchmark
% 4.10/0.95 % SZS output start Proof for theBenchmark
% See solution above
% 4.10/0.96 % (25155)------------------------------
% 4.10/0.96 % (25155)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 4.10/0.96 % (25155)Termination reason: Refutation
% 4.10/0.96
% 4.10/0.96 % (25155)Memory used [KB]: 8131
% 4.10/0.96 % (25155)Time elapsed: 0.552 s
% 4.10/0.96 % (25155)Instructions burned: 1363 (million)
% 4.10/0.96 % (25155)------------------------------
% 4.10/0.96 % (25155)------------------------------
% 4.10/0.96 % (25150)Success in time 0.588 s
%------------------------------------------------------------------------------