TSTP Solution File: SCT128+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : SCT128+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 31 18:17:54 EDT 2022
% Result : Theorem 37.29s 5.11s
% Output : Refutation 37.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 455
% Syntax : Number of formulae : 4355 ( 234 unt; 0 def)
% Number of atoms : 14324 (1593 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 17582 (7613 ~;8709 |; 557 &)
% ( 376 <=>; 326 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 263 ( 261 usr; 240 prp; 0-6 aty)
% Number of functors : 105 ( 105 usr; 18 con; 0-6 aty)
% Number of variables : 9816 (9624 !; 192 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16149,plain,
$false,
inference(avatar_smt_refutation,[],[f3102,f3107,f3113,f3118,f3123,f3128,f3133,f3138,f3143,f3148,f3153,f3158,f3165,f3170,f3175,f3181,f3186,f3191,f3196,f3201,f3206,f3211,f3216,f3221,f3226,f3232,f3237,f3244,f3257,f3264,f3271,f3278,f3286,f3293,f3300,f3309,f3335,f3344,f3373,f3381,f3393,f3440,f3448,f3453,f3461,f3632,f4021,f4140,f4217,f4218,f4225,f4226,f4227,f4379,f4386,f4390,f4429,f4437,f4441,f4445,f4477,f4483,f4543,f4544,f4545,f4546,f4547,f4548,f4549,f4550,f4551,f4552,f4553,f4554,f4555,f4556,f4557,f4558,f4559,f4560,f4561,f4562,f4563,f4564,f4565,f4566,f4567,f4568,f4569,f4570,f4571,f4572,f4573,f4574,f4575,f4576,f4577,f4578,f4579,f4587,f4591,f4728,f4732,f4733,f4734,f4769,f4805,f4806,f4807,f4808,f4809,f4810,f4811,f4812,f4813,f6110,f6113,f6118,f6124,f6130,f6139,f6147,f6166,f6168,f6197,f6200,f6209,f6217,f6223,f6226,f6232,f6239,f6256,f6267,f6270,f6271,f6302,f6305,f6308,f6309,f6314,f6326,f6332,f6335,f6353,f6370,f6378,f6379,f6381,f6392,f6401,f6407,f6413,f6418,f6424,f6425,f6444,f6446,f6466,f6473,f6486,f6502,f6509,f6510,f6521,f6530,f6540,f6560,f6563,f6567,f6577,f6578,f6595,f6603,f6607,f6616,f6634,f6639,f6640,f6643,f6648,f6651,f6656,f6657,f6663,f6666,f6673,f6695,f6699,f6708,f6725,f6731,f6738,f6757,f6758,f6769,f6774,f6778,f6782,f6786,f6796,f6803,f6806,f6809,f6815,f6835,f6845,f6869,f6879,f6885,f6891,f6892,f6907,f6908,f6919,f6923,f6924,f6942,f6943,f6948,f6953,f6966,f6969,f6975,f6984,f6992,f6996,f7006,f7014,f7017,f7030,f7036,f7043,f7044,f7055,f7074,f7078,f7082,f7093,f7107,f7115,f7117,f7121,f7128,f7133,f7140,f7141,f7147,f7151,f7172,f7181,f7186,f7192,f7198,f7204,f7213,f7215,f7222,f7225,f7241,f7246,f7253,f7258,f7259,f7274,f7281,f7288,f7289,f7299,f7302,f7303,f7307,f7313,f7336,f7342,f7347,f7350,f7353,f7354,f7357,f7359,f7365,f7370,f7373,f7378,f7380,f7382,f7389,f7390,f7395,f7408,f7411,f7412,f7417,f7427,f7434,f7442,f7455,f7464,f7472,f7479,f7485,f7494,f7504,f7512,f7519,f7531,f7539,f7541,f7563,f7568,f7571,f7579,f7594,f7602,f7603,f7611,f7614,f7621,f7633,f7638,f7645,f7646,f7650,f7657,f7664,f7667,f7669,f7670,f7680,f7686,f7700,f7711,f7717,f7723,f7729,f7730,f7740,f7745,f7753,f7769,f7784,f7808,f7820,f7830,f7836,f7848,f7855,f7870,f7876,f7877,f7882,f7886,f7891,f7892,f7894,f7898,f7900,f7906,f7910,f7911,f7913,f7914,f7917,f7925,f7942,f7947,f7954,f7955,f7959,f7963,f7988,f8001,f8006,f8010,f8024,f8028,f8032,f8033,f8034,f8037,f8040,f8073,f8078,f8108,f8109,f8112,f8116,f8119,f8124,f8131,f8140,f8141,f8142,f8145,f8154,f8162,f8165,f8171,f8180,f8187,f8189,f8208,f8212,f8225,f8227,f8237,f8242,f8259,f8276,f8279,f8286,f8290,f8295,f8297,f8300,f8315,f8317,f8325,f8330,f8338,f8343,f8345,f8356,f8361,f8364,f8373,f8376,f8377,f8381,f8394,f8401,f8402,f8403,f8404,f8407,f8415,f8419,f8423,f8428,f8431,f8434,f8444,f8463,f8465,f8466,f8471,f8475,f8477,f8497,f8504,f8509,f8519,f8526,f8529,f8533,f8535,f8539,f8551,f8557,f8563,f8564,f8585,f8586,f8595,f8609,f8613,f8614,f8615,f8619,f8627,f8639,f8645,f8658,f8664,f8668,f8676,f8677,f8679,f8684,f8696,f8707,f8712,f8719,f8726,f8738,f8742,f8758,f8770,f8771,f8783,f8784,f8787,f8791,f8792,f8806,f8808,f8810,f8812,f8814,f8815,f8817,f8819,f8820,f8822,f8823,f9408,f9412,f9416,f9420,f9424,f9428,f9432,f9436,f9440,f9444,f9448,f9452,f9456,f9460,f9464,f9468,f9472,f9476,f9480,f9484,f9488,f9492,f9496,f9500,f9504,f9508,f9512,f9791,f9796,f9797,f9798,f9799,f9800,f9801,f9802,f11055,f11060,f11062,f11068,f11074,f11079,f11083,f11088,f11103,f11107,f11114,f11116,f11122,f11145,f11151,f11184,f11203,f11211,f11246,f11260,f11281,f11282,f11289,f11296,f11299,f11307,f11312,f11315,f11318,f11323,f11331,f11337,f11344,f11351,f11354,f11361,f11366,f11387,f11391,f11402,f11422,f11425,f11426,f11437,f11441,f11448,f11455,f11458,f11462,f11476,f11482,f11488,f11490,f11493,f11499,f11511,f11517,f11530,f11531,f11537,f11540,f11553,f11554,f11556,f11561,f11565,f11569,f11577,f11578,f11582,f11586,f11593,f11599,f11621,f11645,f11651,f11654,f11664,f11672,f11693,f11696,f11706,f11707,f11708,f11718,f11724,f11732,f11738,f11745,f11751,f11758,f11759,f11765,f11775,f11776,f11787,f11802,f11824,f11830,f11831,f11839,f11840,f11848,f11857,f11864,f11878,f11887,f11891,f11897,f11905,f11908,f11909,f11915,f11916,f11917,f11927,f11936,f11941,f11942,f11944,f11953,f11959,f11977,f11978,f11979,f11992,f11997,f12004,f12009,f12014,f12015,f12037,f12038,f12042,f12051,f12060,f12061,f12065,f12068,f12078,f12083,f12084,f12090,f12092,f12095,f12096,f12111,f12118,f12123,f12126,f12132,f12135,f12137,f12143,f12150,f12152,f12166,f12170,f12174,f12182,f12193,f12204,f12212,f12213,f12220,f12229,f12231,f12235,f12244,f12268,f12278,f12285,f12293,f12302,f12303,f12317,f12323,f12333,f12345,f12359,f12375,f12376,f12379,f12382,f12393,f12396,f12397,f12401,f12415,f12419,f12430,f12433,f12441,f12445,f12449,f12451,f12452,f12483,f12493,f12495,f12509,f12541,f12547,f12553,f12558,f12560,f12561,f12572,f12580,f12585,f12602,f12613,f12626,f12632,f12638,f12663,f12672,f12675,f12679,f12687,f12703,f12712,f12720,f12726,f12731,f12734,f12760,f12772,f12776,f12788,f12792,f12796,f12798,f12803,f12809,f12814,f12819,f12823,f12828,f12831,f12834,f12841,f12858,f12859,f12862,f12864,f12868,f12871,f12872,f12883,f12889,f12903,f12917,f12933,f12939,f12945,f12946,f12947,f12950,f12957,f12959,f12976,f12990,f13000,f13012,f13022,f13040,f13053,f13058,f13065,f13080,f13093,f13096,f13097,f13102,f13113,f13116,f13130,f13132,f13135,f13148,f13153,f13161,f13169,f13187,f13191,f13193,f13197,f13199,f13206,f13210,f13215,f13219,f13226,f13234,f13258,f13261,f13273,f13278,f13285,f13292,f13297,f13301,f13302,f13319,f13327,f13332,f13335,f13343,f13370,f13371,f13377,f13384,f13391,f13399,f13406,f13409,f13415,f13448,f13451,f13464,f13469,f13471,f13472,f13474,f13475,f13477,f13483,f13484,f13485,f14320,f14422,f14427,f14435,f14439,f14454,f14455,f14456,f14572,f14655,f14659,f14666,f14673,f14975,f14979,f14983,f14987,f15524,f15591,f15595,f15599,f15762,f15764,f16063,f16067,f16096,f16101,f16102,f16103,f16131,f16132,f16141,f16146,f16147,f16148]) ).
fof(f16148,plain,
( ~ spl85_4
| ~ spl85_24
| ~ spl85_55
| ~ spl85_9
| spl85_11
| ~ spl85_54 ),
inference(avatar_split_clause,[],[f16115,f4014,f3150,f3140,f4018,f3218,f3115]) ).
fof(f3115,plain,
( spl85_4
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_4])]) ).
fof(f3218,plain,
( spl85_24
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_P____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_24])]) ).
fof(f4018,plain,
( spl85_55
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,sK4(v_Q____,v_P____,v_a____,v_b____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_55])]) ).
fof(f3140,plain,
( spl85_9
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_9])]) ).
fof(f3150,plain,
( spl85_11
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_Q____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_11])]) ).
fof(f4014,plain,
( spl85_54
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,sK4(v_Q____,v_P____,v_a____,v_b____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_54])]) ).
fof(f16115,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_Q____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,sK4(v_Q____,v_P____,v_a____,v_b____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_P____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____),c_Arrow__Order__Mirabelle_OProf))
| ~ spl85_54 ),
inference(resolution,[],[f4016,f2203]) ).
fof(f2203,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,sK4(X0,X1,X2,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X1)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X0),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,sK4(X0,X1,X2,X3)))) ),
inference(cnf_transformation,[],[f1533]) ).
fof(f1533,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,sK4(X0,X1,X2,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,sK4(X0,X1,X2,X3)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,sK4(X0,X1,X2,X3))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,sK4(X0,X1,X2,X3)))) ) )
| ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X1))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X0))) ) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X0),c_Arrow__Order__Mirabelle_OProf)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f1531,f1532]) ).
fof(f1532,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,X4))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,X4))) ) )
=> ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,sK4(X0,X1,X2,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,sK4(X0,X1,X2,X3)))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,sK4(X0,X1,X2,X3))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,sK4(X0,X1,X2,X3)))) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1531,plain,
! [X0] :
( ! [X1] :
( ! [X2,X3] :
( ? [X4] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,X4))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,X4))) ) )
| ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X1))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X0))) ) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X0),c_Arrow__Order__Mirabelle_OProf)) ),
inference(rectify,[],[f1530]) ).
fof(f1530,plain,
! [X0] :
( ! [X1] :
( ! [X3,X2] :
( ? [X4] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(X0,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(X1,X4))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(X0,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(X1,X4))) ) )
| ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(v_F,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(v_F,X1))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(v_F,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(v_F,X0))) ) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X0),c_Arrow__Order__Mirabelle_OProf)) ),
inference(nnf_transformation,[],[f1357]) ).
fof(f1357,plain,
! [X0] :
( ! [X1] :
( ! [X3,X2] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(X1,X4)))
<~> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(X0,X4))) )
| ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(v_F,X0)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(v_F,X1))) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X0),c_Arrow__Order__Mirabelle_OProf)) ),
inference(ennf_transformation,[],[f928]) ).
fof(f928,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X0),c_Arrow__Order__Mirabelle_OProf))
=> ! [X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_Arrow__Order__Mirabelle_OProf))
=> ! [X2,X3] :
( ! [X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(X0,X4)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(X1,X4))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(v_F,X0)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(v_F,X1))) ) ) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf))
=> ! [X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X4),c_Arrow__Order__Mirabelle_OProf))
=> ! [X6,X5] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X6)),hAPP(X2,X3)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X6)),hAPP(X4,X3))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X6)),hAPP(v_F,X2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X6)),hAPP(v_F,X4))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_AP_058Prof_O_AALL_AP_H_058Prof_O_AALL_Aa_Ab_O_A_IALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062P_H_Ai_092_060_094esub_062_Ab_J_J_A_N_N_062_A_Ia_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062F_AP_H_092_060_094esub_062_Ab_J_096) ).
fof(f4016,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,sK4(v_Q____,v_P____,v_a____,v_b____))))
| ~ spl85_54 ),
inference(avatar_component_clause,[],[f4014]) ).
fof(f16147,plain,
( spl85_235
| ~ spl85_55 ),
inference(avatar_split_clause,[],[f16081,f4018,f16098]) ).
fof(f16098,plain,
( spl85_235
<=> hBOOL(hAPP(hAPP(v_Q____,sK4(v_Q____,v_P____,v_a____,v_b____)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_235])]) ).
fof(f16081,plain,
( hBOOL(hAPP(hAPP(v_Q____,sK4(v_Q____,v_P____,v_a____,v_b____)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)))
| ~ spl85_55 ),
inference(resolution,[],[f4020,f2710]) ).
fof(f2710,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
| hBOOL(hAPP(X2,X0)) ),
inference(cnf_transformation,[],[f1965]) ).
fof(f1965,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
| ~ hBOOL(hAPP(X2,X0)) )
& ( hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X2)) ) ),
inference(rectify,[],[f1964]) ).
fof(f1964,plain,
! [X1,X0,X2] :
( ( hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
| ~ hBOOL(hAPP(X2,X1)) )
& ( hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) ) ),
inference(nnf_transformation,[],[f760]) ).
fof(f760,plain,
! [X1,X0,X2] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
<=> hBOOL(hAPP(X2,X1)) ),
inference(rectify,[],[f32]) ).
fof(f32,axiom,
! [X8,X14,X10] :
( hBOOL(hAPP(hAPP(c_member(X8),X14),X10))
<=> hBOOL(hAPP(X10,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
fof(f4020,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,sK4(v_Q____,v_P____,v_a____,v_b____))))
| ~ spl85_55 ),
inference(avatar_component_clause,[],[f4018]) ).
fof(f16146,plain,
( spl85_239
| ~ spl85_54 ),
inference(avatar_split_clause,[],[f16113,f4014,f16143]) ).
fof(f16143,plain,
( spl85_239
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,sK4(v_Q____,v_P____,v_a____,v_b____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_239])]) ).
fof(f16113,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,sK4(v_Q____,v_P____,v_a____,v_b____))))
| ~ spl85_54 ),
inference(resolution,[],[f4016,f2671]) ).
fof(f2671,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X0)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,X0))) ),
inference(cnf_transformation,[],[f1928]) ).
fof(f1928,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,X0))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X0))) ) ),
inference(nnf_transformation,[],[f700]) ).
fof(f700,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X0)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,X0))) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,X3)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C1_C) ).
fof(f16141,plain,
( ~ spl85_237
| ~ spl85_238
| ~ spl85_54 ),
inference(avatar_split_clause,[],[f16117,f4014,f16138,f16134]) ).
fof(f16134,plain,
( spl85_237
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P____,sK4(v_Q____,v_P____,v_a____,v_b____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_237])]) ).
fof(f16138,plain,
( spl85_238
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_P____,sK4(v_Q____,v_P____,v_a____,v_b____))),c_Arrow__Order__Mirabelle_OLin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_238])]) ).
fof(f16117,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_P____,sK4(v_Q____,v_P____,v_a____,v_b____))),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_P____,sK4(v_Q____,v_P____,v_a____,v_b____))))
| ~ spl85_54 ),
inference(resolution,[],[f4016,f2792]) ).
fof(f2792,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X0)),X1)) ),
inference(cnf_transformation,[],[f2037]) ).
fof(f2037,plain,
! [X0,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X2)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin)) ),
inference(rectify,[],[f1232]) ).
fof(f1232,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(flattening,[],[f1231]) ).
fof(f1231,plain,
! [X1,X0,X2] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(ennf_transformation,[],[f676]) ).
fof(f676,plain,
! [X1,X0,X2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X0))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),X0)) ) ),
inference(rectify,[],[f27]) ).
fof(f27,axiom,
! [X12,X24,X23] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X12),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X23)),X12))
=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X24)),X12)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
fof(f16132,plain,
( spl85_55
| ~ spl85_54 ),
inference(avatar_split_clause,[],[f16114,f4014,f4018]) ).
fof(f16114,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,sK4(v_Q____,v_P____,v_a____,v_b____))))
| ~ spl85_54 ),
inference(resolution,[],[f4016,f2449]) ).
fof(f2449,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X0)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,X0))) ),
inference(cnf_transformation,[],[f1728]) ).
fof(f1728,plain,
! [X0] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X0))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,X0))) ) ),
inference(nnf_transformation,[],[f811]) ).
fof(f811,plain,
! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,X0)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X0))) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,X3)))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096ALL_Ai_O_A_Ia_A_060_092_060_094bsub_062P_Ai_092_060_094esub_062_Ab_J_A_061_A_Ia_A_060_092_060_094bsub_062Q_Ai_092_060_094esub_062_Ab_J_096) ).
fof(f16131,plain,
( spl85_236
| ~ spl85_54 ),
inference(avatar_split_clause,[],[f16120,f4014,f16128]) ).
fof(f16128,plain,
( spl85_236
<=> hBOOL(hAPP(hAPP(v_P____,sK4(v_Q____,v_P____,v_a____,v_b____)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_236])]) ).
fof(f16120,plain,
( hBOOL(hAPP(hAPP(v_P____,sK4(v_Q____,v_P____,v_a____,v_b____)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)))
| ~ spl85_54 ),
inference(resolution,[],[f4016,f2710]) ).
fof(f16103,plain,
( ~ spl85_9
| spl85_11
| spl85_55
| spl85_54
| ~ spl85_4
| ~ spl85_24 ),
inference(avatar_split_clause,[],[f9397,f3218,f3115,f4014,f4018,f3150,f3140]) ).
fof(f9397,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,sK4(v_Q____,v_P____,v_a____,v_b____))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,sK4(v_Q____,v_P____,v_a____,v_b____))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_Q____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf))
| ~ spl85_4
| ~ spl85_24 ),
inference(resolution,[],[f3311,f3220]) ).
fof(f3220,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_P____)))
| ~ spl85_24 ),
inference(avatar_component_clause,[],[f3218]) ).
fof(f3311,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,X0)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_Q____,sK4(v_Q____,X0,X1,X2))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(X0,sK4(v_Q____,X0,X1,X2))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),hAPP(v_F,v_Q____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X0),c_Arrow__Order__Mirabelle_OProf)) )
| ~ spl85_4 ),
inference(resolution,[],[f2201,f3117]) ).
fof(f3117,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____),c_Arrow__Order__Mirabelle_OProf))
| ~ spl85_4 ),
inference(avatar_component_clause,[],[f3115]) ).
fof(f2201,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X0),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,sK4(X0,X1,X2,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X1)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,sK4(X0,X1,X2,X3))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X0))) ),
inference(cnf_transformation,[],[f1533]) ).
fof(f16102,plain,
( spl85_54
| ~ spl85_55 ),
inference(avatar_split_clause,[],[f16077,f4018,f4014]) ).
fof(f16077,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,sK4(v_Q____,v_P____,v_a____,v_b____))))
| ~ spl85_55 ),
inference(resolution,[],[f4020,f2448]) ).
fof(f2448,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,X0)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X0))) ),
inference(cnf_transformation,[],[f1728]) ).
fof(f16101,plain,
( spl85_235
| ~ spl85_55 ),
inference(avatar_split_clause,[],[f16081,f4018,f16098]) ).
fof(f16096,plain,
( ~ spl85_233
| ~ spl85_234
| ~ spl85_55 ),
inference(avatar_split_clause,[],[f16078,f4018,f16093,f16089]) ).
fof(f16089,plain,
( spl85_233
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_Q____,sK4(v_Q____,v_P____,v_a____,v_b____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_233])]) ).
fof(f16093,plain,
( spl85_234
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_Q____,sK4(v_Q____,v_P____,v_a____,v_b____))),c_Arrow__Order__Mirabelle_OLin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_234])]) ).
fof(f16078,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_Q____,sK4(v_Q____,v_P____,v_a____,v_b____))),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_Q____,sK4(v_Q____,v_P____,v_a____,v_b____))))
| ~ spl85_55 ),
inference(resolution,[],[f4020,f2792]) ).
fof(f16067,plain,
( spl85_232
| spl85_64 ),
inference(avatar_split_clause,[],[f16055,f4426,f16065]) ).
fof(f16065,plain,
( spl85_232
<=> ! [X27,X26] :
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Obelow(sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X26,X27)))
| X26 = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_232])]) ).
fof(f4426,plain,
( spl85_64
<=> c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_64])]) ).
fof(f16055,plain,
! [X26,X27] :
( c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Obelow(sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X26,X27)))
| X26 = X27 ),
inference(resolution,[],[f3489,f2323]) ).
fof(f2323,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),sK12(X0,X1)),X0))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 ),
inference(cnf_transformation,[],[f1629]) ).
fof(f1629,plain,
! [X0,X1] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| hBOOL(hAPP(hAPP(c_member(X1),sK12(X0,X1)),X0)) )
& ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X0))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12])],[f1627,f1628]) ).
fof(f1628,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(hAPP(c_member(X1),X2),X0))
=> hBOOL(hAPP(hAPP(c_member(X1),sK12(X0,X1)),X0)) ),
introduced(choice_axiom,[]) ).
fof(f1627,plain,
! [X0,X1] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0
| ? [X2] : hBOOL(hAPP(hAPP(c_member(X1),X2),X0)) )
& ( ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X0))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0 ) ),
inference(rectify,[],[f1626]) ).
fof(f1626,plain,
! [X1,X0] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1
| ? [X2] : hBOOL(hAPP(hAPP(c_member(X0),X2),X1)) )
& ( ! [X2] : ~ hBOOL(hAPP(hAPP(c_member(X0),X2),X1))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != X1 ) ),
inference(nnf_transformation,[],[f992]) ).
fof(f992,plain,
! [X1,X0] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1
<=> ! [X2] : ~ hBOOL(hAPP(hAPP(c_member(X0),X2),X1)) ),
inference(rectify,[],[f465]) ).
fof(f465,axiom,
! [X8,X10] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = X10
<=> ! [X2] : ~ hBOOL(hAPP(hAPP(c_member(X8),X2),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
fof(f3489,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Obelow(X0,X1,X2)))
| X1 = X2 ),
inference(resolution,[],[f2622,f2710]) ).
fof(f2622,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X2,X0,X1)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin))
| X0 = X1 ),
inference(cnf_transformation,[],[f1878]) ).
fof(f1878,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X2,X0,X1)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin))
| X0 = X1 ),
inference(rectify,[],[f1317]) ).
fof(f1317,plain,
! [X2,X1,X0] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X1)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2 ),
inference(flattening,[],[f1316]) ).
fof(f1316,plain,
! [X1,X0,X2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X1)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2 ),
inference(ennf_transformation,[],[f809]) ).
fof(f809,plain,
! [X1,X0,X2] :
( X1 != X2
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X1)),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(rectify,[],[f38]) ).
fof(f38,axiom,
! [X12,X13,X14] :
( X13 != X14
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X12),c_Arrow__Order__Mirabelle_OLin))
=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X12,X14,X13)),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_below__Lin) ).
fof(f16063,plain,
( spl85_231
| spl85_64 ),
inference(avatar_split_clause,[],[f16056,f4426,f16061]) ).
fof(f16061,plain,
( spl85_231
<=> ! [X29,X28] :
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Obelow(sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin),X28,X29)))
| X28 = X29 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_231])]) ).
fof(f16056,plain,
! [X28,X29] :
( c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,c_Arrow__Order__Mirabelle_Obelow(sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin),X28,X29)))
| X28 = X29 ),
inference(resolution,[],[f3489,f2929]) ).
fof(f2929,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),sK82(X0,X1)),X1))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1 ),
inference(cnf_transformation,[],[f2146]) ).
fof(f2146,plain,
! [X0,X1] :
( ( hBOOL(hAPP(hAPP(c_member(X0),sK82(X0,X1)),X1))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1 )
& ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != X1
| ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK82])],[f2144,f2145]) ).
fof(f2145,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(hAPP(c_member(X0),X2),X1))
=> hBOOL(hAPP(hAPP(c_member(X0),sK82(X0,X1)),X1)) ),
introduced(choice_axiom,[]) ).
fof(f2144,plain,
! [X0,X1] :
( ( ? [X2] : hBOOL(hAPP(hAPP(c_member(X0),X2),X1))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1 )
& ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != X1
| ! [X3] : ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X1)) ) ),
inference(rectify,[],[f2143]) ).
fof(f2143,plain,
! [X1,X0] :
( ( ? [X2] : hBOOL(hAPP(hAPP(c_member(X1),X2),X0))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) = X0 )
& ( c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0
| ! [X2] : ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X0)) ) ),
inference(nnf_transformation,[],[f747]) ).
fof(f747,plain,
! [X1,X0] :
( ? [X2] : hBOOL(hAPP(hAPP(c_member(X1),X2),X0))
<=> c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != X0 ),
inference(rectify,[],[f464]) ).
fof(f464,axiom,
! [X10,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) != X10
<=> ? [X2] : hBOOL(hAPP(hAPP(c_member(X8),X2),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
fof(f15764,plain,
( spl85_230
| ~ spl85_13
| ~ spl85_31
| ~ spl85_228 ),
inference(avatar_split_clause,[],[f15763,f15593,f3268,f3162,f15759]) ).
fof(f15759,plain,
( spl85_230
<=> c_Orderings_Obot__class_Obot(tc_HOL_Obool) = c_Orderings_Obot__class_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_230])]) ).
fof(f3162,plain,
( spl85_13
<=> class_Orderings_Obot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_13])]) ).
fof(f3268,plain,
( spl85_31
<=> class_Orderings_Obot(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_31])]) ).
fof(f15593,plain,
( spl85_228
<=> ! [X60,X59] : c_Orderings_Obot__class_Obot(tc_fun(X60,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X59,tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_228])]) ).
fof(f15763,plain,
( c_Orderings_Obot__class_Obot(tc_HOL_Obool) = c_Orderings_Obot__class_Obot(tc_Nat_Onat)
| ~ spl85_13
| ~ spl85_31
| ~ spl85_228 ),
inference(backward_demodulation,[],[f14442,f15746]) ).
fof(f15746,plain,
( ! [X65,X64] : c_Orderings_Obot__class_Obot(tc_HOL_Obool) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X64,tc_Nat_Onat)),X65)
| ~ spl85_13
| ~ spl85_228 ),
inference(superposition,[],[f14441,f15594]) ).
fof(f15594,plain,
( ! [X59,X60] : c_Orderings_Obot__class_Obot(tc_fun(X60,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X59,tc_Nat_Onat))
| ~ spl85_228 ),
inference(avatar_component_clause,[],[f15593]) ).
fof(f14441,plain,
( ! [X0,X1] : c_Orderings_Obot__class_Obot(tc_HOL_Obool) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1)
| ~ spl85_13 ),
inference(resolution,[],[f2838,f3164]) ).
fof(f3164,plain,
( class_Orderings_Obot(tc_HOL_Obool)
| ~ spl85_13 ),
inference(avatar_component_clause,[],[f3162]) ).
fof(f2838,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Obot(X0)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X0)),X2) = c_Orderings_Obot__class_Obot(X0) ),
inference(cnf_transformation,[],[f2066]) ).
fof(f2066,plain,
! [X0,X1,X2] :
( ~ class_Orderings_Obot(X0)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X1,X0)),X2) = c_Orderings_Obot__class_Obot(X0) ),
inference(rectify,[],[f1257]) ).
fof(f1257,plain,
! [X2,X0,X1] :
( ~ class_Orderings_Obot(X2)
| hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,X2)),X1) = c_Orderings_Obot__class_Obot(X2) ),
inference(ennf_transformation,[],[f952]) ).
fof(f952,plain,
! [X1,X2,X0] :
( class_Orderings_Obot(X2)
=> hAPP(c_Orderings_Obot__class_Obot(tc_fun(X0,X2)),X1) = c_Orderings_Obot__class_Obot(X2) ),
inference(rectify,[],[f467]) ).
fof(f467,axiom,
! [X16,X14,X8] :
( class_Orderings_Obot(X8)
=> c_Orderings_Obot__class_Obot(X8) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X16,X8)),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__fun__def) ).
fof(f14442,plain,
( ! [X2,X3] : c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X2,tc_Nat_Onat)),X3)
| ~ spl85_31 ),
inference(resolution,[],[f2838,f3270]) ).
fof(f3270,plain,
( class_Orderings_Obot(tc_Nat_Onat)
| ~ spl85_31 ),
inference(avatar_component_clause,[],[f3268]) ).
fof(f15762,plain,
( spl85_230
| ~ spl85_13
| ~ spl85_31
| ~ spl85_228 ),
inference(avatar_split_clause,[],[f15757,f15593,f3268,f3162,f15759]) ).
fof(f15757,plain,
( c_Orderings_Obot__class_Obot(tc_HOL_Obool) = c_Orderings_Obot__class_Obot(tc_Nat_Onat)
| ~ spl85_13
| ~ spl85_31
| ~ spl85_228 ),
inference(forward_demodulation,[],[f15755,f14441]) ).
fof(f15755,plain,
( ! [X6,X7] : c_Orderings_Obot__class_Obot(tc_Nat_Onat) = hAPP(c_Orderings_Obot__class_Obot(tc_fun(X6,tc_HOL_Obool)),X7)
| ~ spl85_31
| ~ spl85_228 ),
inference(superposition,[],[f14442,f15594]) ).
fof(f15599,plain,
( ~ spl85_216
| spl85_229
| ~ spl85_31 ),
inference(avatar_split_clause,[],[f14971,f3268,f15597,f14569]) ).
fof(f14569,plain,
( spl85_216
<=> hBOOL(c_Orderings_Obot__class_Obot(tc_Nat_Onat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_216])]) ).
fof(f15597,plain,
( spl85_229
<=> ! [X134,X133,X135,X131] : c_Predicate_ODomainP(X133,X134,c_COMBI(X135),c_Orderings_Obot__class_Obot(tc_fun(X131,tc_Nat_Onat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_229])]) ).
fof(f14971,plain,
( ! [X133,X131,X134,X135] :
( c_Predicate_ODomainP(X133,X134,c_COMBI(X135),c_Orderings_Obot__class_Obot(tc_fun(X131,tc_Nat_Onat)))
| ~ hBOOL(c_Orderings_Obot__class_Obot(tc_Nat_Onat)) )
| ~ spl85_31 ),
inference(superposition,[],[f14632,f14442]) ).
fof(f14632,plain,
! [X106,X107,X104,X105,X103] :
( ~ hBOOL(hAPP(X104,X105))
| c_Predicate_ODomainP(X106,X107,c_COMBI(X103),X104) ),
inference(superposition,[],[f2844,f2523]) ).
fof(f2523,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(cnf_transformation,[],[f1795]) ).
fof(f1795,plain,
! [X0,X1] : hAPP(c_COMBI(X1),X0) = X0,
inference(rectify,[],[f551]) ).
fof(f551,plain,
! [X1,X0] : hAPP(c_COMBI(X0),X1) = X1,
inference(rectify,[],[f524]) ).
fof(f524,axiom,
! [X8,X75] : hAPP(c_COMBI(X8),X75) = X75,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBI__1) ).
fof(f2844,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(X2,X0),X4))
| c_Predicate_ODomainP(X3,X1,X2,X0) ),
inference(cnf_transformation,[],[f2071]) ).
fof(f2071,plain,
! [X0,X1,X2,X3,X4] :
( c_Predicate_ODomainP(X3,X1,X2,X0)
| ~ hBOOL(hAPP(hAPP(X2,X0),X4)) ),
inference(rectify,[],[f1274]) ).
fof(f1274,plain,
! [X2,X1,X0,X4,X3] :
( c_Predicate_ODomainP(X4,X1,X0,X2)
| ~ hBOOL(hAPP(hAPP(X0,X2),X3)) ),
inference(ennf_transformation,[],[f716]) ).
fof(f716,plain,
! [X1,X4,X3,X2,X0] :
( hBOOL(hAPP(hAPP(X0,X2),X3))
=> c_Predicate_ODomainP(X4,X1,X0,X2) ),
inference(rectify,[],[f154]) ).
fof(f154,axiom,
! [X19,X16,X24,X23,X8] :
( hBOOL(hAPP(hAPP(X19,X24),X23))
=> c_Predicate_ODomainP(X8,X16,X19,X24) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
fof(f15595,plain,
( spl85_216
| spl85_228
| ~ spl85_31 ),
inference(avatar_split_clause,[],[f15587,f3268,f15593,f14569]) ).
fof(f15587,plain,
( ! [X59,X60] :
( c_Orderings_Obot__class_Obot(tc_fun(X60,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X59,tc_Nat_Onat))
| hBOOL(c_Orderings_Obot__class_Obot(tc_Nat_Onat)) )
| ~ spl85_31 ),
inference(superposition,[],[f4391,f14442]) ).
fof(f4391,plain,
! [X0,X1] :
( hBOOL(hAPP(X1,sK12(X1,X0)))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1 ),
inference(resolution,[],[f2323,f2710]) ).
fof(f15591,plain,
( spl85_214
| spl85_227
| ~ spl85_13 ),
inference(avatar_split_clause,[],[f15586,f3162,f15589,f14451]) ).
fof(f14451,plain,
( spl85_214
<=> hBOOL(c_Orderings_Obot__class_Obot(tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_214])]) ).
fof(f15589,plain,
( spl85_227
<=> ! [X57,X58] : c_Orderings_Obot__class_Obot(tc_fun(X58,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X57,tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_227])]) ).
fof(f15586,plain,
( ! [X58,X57] :
( c_Orderings_Obot__class_Obot(tc_fun(X58,tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(X57,tc_HOL_Obool))
| hBOOL(c_Orderings_Obot__class_Obot(tc_HOL_Obool)) )
| ~ spl85_13 ),
inference(superposition,[],[f4391,f14441]) ).
fof(f15524,plain,
( ~ spl85_46
| ~ spl85_47 ),
inference(avatar_split_clause,[],[f15523,f3442,f3437]) ).
fof(f3437,plain,
( spl85_46
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_46])]) ).
fof(f3442,plain,
( spl85_47
<=> ! [X13,X14,X15] : ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X13,X14,X15),c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),v_P____),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_47])]) ).
fof(f15523,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))))
| ~ spl85_47 ),
inference(superposition,[],[f3443,f2728]) ).
fof(f2728,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(X4,X2),hAPP(X0,X2)) = hAPP(hAPP(hAPP(c_COMBS(X1,X3,X5),X4),X0),X2),
inference(cnf_transformation,[],[f1985]) ).
fof(f1985,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(X4,X2),hAPP(X0,X2)) = hAPP(hAPP(hAPP(c_COMBS(X1,X3,X5),X4),X0),X2),
inference(rectify,[],[f752]) ).
fof(f752,plain,
! [X0,X2,X3,X1,X5,X4] : hAPP(hAPP(X5,X3),hAPP(X0,X3)) = hAPP(hAPP(hAPP(c_COMBS(X2,X1,X4),X5),X0),X3),
inference(rectify,[],[f528]) ).
fof(f528,axiom,
! [X66,X31,X16,X15,X8,X18] : hAPP(hAPP(hAPP(c_COMBS(X16,X31,X8),X18),X66),X15) = hAPP(hAPP(X18,X15),hAPP(X66,X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBS__1) ).
fof(f3443,plain,
( ! [X14,X15,X13] : ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X13,X14,X15),c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),v_P____),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)))
| ~ spl85_47 ),
inference(avatar_component_clause,[],[f3442]) ).
fof(f14987,plain,
( spl85_226
| spl85_61
| ~ spl85_15 ),
inference(avatar_split_clause,[],[f14953,f3172,f4384,f14985]) ).
fof(f14985,plain,
( spl85_226
<=> ! [X18,X17,X19] : c_Predicate_ODomainP(X17,X18,c_COMBI(X19),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_226])]) ).
fof(f4384,plain,
( spl85_61
<=> ! [X179] : ~ hBOOL(X179) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_61])]) ).
fof(f3172,plain,
( spl85_15
<=> class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_15])]) ).
fof(f14953,plain,
( ! [X18,X19,X16,X17] :
( ~ hBOOL(X16)
| c_Predicate_ODomainP(X17,X18,c_COMBI(X19),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool))) )
| ~ spl85_15 ),
inference(superposition,[],[f14632,f14332]) ).
fof(f14332,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X0) = X0
| ~ spl85_15 ),
inference(resolution,[],[f2776,f3174]) ).
fof(f3174,plain,
( class_Lattices_Obounded__lattice__bot(tc_HOL_Obool)
| ~ spl85_15 ),
inference(avatar_component_clause,[],[f3172]) ).
fof(f2776,plain,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice__bot(X1)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X0) = X0 ),
inference(cnf_transformation,[],[f1411]) ).
fof(f1411,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X0) = X0
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(ennf_transformation,[],[f614]) ).
fof(f614,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),c_Orderings_Obot__class_Obot(X1)),X0) = X0 ),
inference(rectify,[],[f433]) ).
fof(f433,axiom,
! [X49,X8] :
( class_Lattices_Obounded__lattice__bot(X8)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),c_Orderings_Obot__class_Obot(X8)),X49) = X49 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__left) ).
fof(f14983,plain,
( spl85_225
| spl85_42 ),
inference(avatar_split_clause,[],[f14945,f3379,f14981]) ).
fof(f14981,plain,
( spl85_225
<=> ! [X259,X257,X258] : c_Predicate_ODomainP(X257,X258,c_COMBI(X259),c_fNot) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_225])]) ).
fof(f3379,plain,
( spl85_42
<=> ! [X6] : hBOOL(X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_42])]) ).
fof(f14945,plain,
! [X260,X259,X258,X257] :
( hBOOL(X260)
| c_Predicate_ODomainP(X257,X258,c_COMBI(X259),c_fNot) ),
inference(resolution,[],[f14632,f2866]) ).
fof(f2866,plain,
! [X0] :
( hBOOL(hAPP(c_fNot,X0))
| hBOOL(X0) ),
inference(cnf_transformation,[],[f575]) ).
fof(f575,plain,
! [X0] :
( hBOOL(X0)
| hBOOL(hAPP(c_fNot,X0)) ),
inference(rectify,[],[f532]) ).
fof(f532,axiom,
! [X18] :
( hBOOL(X18)
| hBOOL(hAPP(c_fNot,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__2) ).
fof(f14979,plain,
( spl85_224
| spl85_61 ),
inference(avatar_split_clause,[],[f14956,f4384,f14977]) ).
fof(f14977,plain,
( spl85_224
<=> ! [X34,X32,X30,X33] : c_Predicate_ODomainP(X32,X33,c_COMBI(X34),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X30,tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_224])]) ).
fof(f14956,plain,
! [X31,X34,X32,X30,X33] :
( ~ hBOOL(X31)
| c_Predicate_ODomainP(X32,X33,c_COMBI(X34),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X30,tc_HOL_Obool)))) ),
inference(superposition,[],[f14632,f2580]) ).
fof(f2580,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),X1) = X1,
inference(cnf_transformation,[],[f894]) ).
fof(f894,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))),X1) = X1,
inference(rectify,[],[f430]) ).
fof(f430,axiom,
! [X8,X9] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))),X9) = X9,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__left) ).
fof(f14975,plain,
( spl85_223
| spl85_61 ),
inference(avatar_split_clause,[],[f14968,f4384,f14973]) ).
fof(f14973,plain,
( spl85_223
<=> ! [X116,X117,X113,X115] : c_Predicate_ODomainP(X115,X116,c_COMBI(X117),c_COMBI(X113)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_223])]) ).
fof(f14968,plain,
! [X113,X116,X117,X114,X115] :
( ~ hBOOL(X114)
| c_Predicate_ODomainP(X115,X116,c_COMBI(X117),c_COMBI(X113)) ),
inference(superposition,[],[f14632,f2523]) ).
fof(f14673,plain,
( spl85_221
| spl85_222
| ~ spl85_31 ),
inference(avatar_split_clause,[],[f14635,f3268,f14671,f14668]) ).
fof(f14668,plain,
( spl85_221
<=> ! [X125,X121,X124,X122] : c_Predicate_ODomainP(X124,X125,c_Orderings_Obot__class_Obot(tc_fun(X121,tc_Nat_Onat)),X122) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_221])]) ).
fof(f14671,plain,
( spl85_222
<=> ! [X123] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_Nat_Onat),X123)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_222])]) ).
fof(f14635,plain,
( ! [X121,X124,X125,X122,X123] :
( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_Nat_Onat),X123))
| c_Predicate_ODomainP(X124,X125,c_Orderings_Obot__class_Obot(tc_fun(X121,tc_Nat_Onat)),X122) )
| ~ spl85_31 ),
inference(superposition,[],[f2844,f14442]) ).
fof(f14666,plain,
( spl85_219
| spl85_220
| ~ spl85_13 ),
inference(avatar_split_clause,[],[f14634,f3162,f14664,f14661]) ).
fof(f14661,plain,
( spl85_219
<=> ! [X118] : ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_HOL_Obool),X118)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_219])]) ).
fof(f14664,plain,
( spl85_220
<=> ! [X116,X117,X120,X119] : c_Predicate_ODomainP(X119,X120,c_Orderings_Obot__class_Obot(tc_fun(X116,tc_HOL_Obool)),X117) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_220])]) ).
fof(f14634,plain,
( ! [X120,X118,X119,X116,X117] :
( c_Predicate_ODomainP(X119,X120,c_Orderings_Obot__class_Obot(tc_fun(X116,tc_HOL_Obool)),X117)
| ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_HOL_Obool),X118)) )
| ~ spl85_13 ),
inference(superposition,[],[f2844,f14441]) ).
fof(f14659,plain,
( spl85_61
| spl85_218 ),
inference(avatar_split_clause,[],[f14643,f14657,f4384]) ).
fof(f14657,plain,
( spl85_218
<=> ! [X25,X23,X26] : c_Predicate_ODomainP(X25,X26,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X23,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_218])]) ).
fof(f14643,plain,
! [X26,X24,X25,X23] :
( c_Predicate_ODomainP(X25,X26,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X23,tc_HOL_Obool)))
| ~ hBOOL(X24) ),
inference(superposition,[],[f2844,f2580]) ).
fof(f14655,plain,
( spl85_61
| spl85_217
| ~ spl85_15 ),
inference(avatar_split_clause,[],[f14640,f3172,f14653,f4384]) ).
fof(f14653,plain,
( spl85_217
<=> ! [X13,X14] : c_Predicate_ODomainP(X13,X14,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_217])]) ).
fof(f14640,plain,
( ! [X14,X12,X13] :
( c_Predicate_ODomainP(X13,X14,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool))
| ~ hBOOL(X12) )
| ~ spl85_15 ),
inference(superposition,[],[f2844,f14332]) ).
fof(f14572,plain,
( spl85_215
| ~ spl85_216
| ~ spl85_31 ),
inference(avatar_split_clause,[],[f14546,f3268,f14569,f14566]) ).
fof(f14566,plain,
( spl85_215
<=> ! [X12,X11,X10] : hBOOL(hAPP(hAPP(c_member(X12),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_Nat_Onat)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_215])]) ).
fof(f14546,plain,
( ! [X10,X11,X12] :
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_Nat_Onat))
| hBOOL(hAPP(hAPP(c_member(X12),X11),c_Orderings_Obot__class_Obot(tc_fun(X10,tc_Nat_Onat)))) )
| ~ spl85_31 ),
inference(superposition,[],[f2711,f14442]) ).
fof(f2711,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(X2,X0))
| hBOOL(hAPP(hAPP(c_member(X1),X0),X2)) ),
inference(cnf_transformation,[],[f1965]) ).
fof(f14456,plain,
( spl85_170
| ~ spl85_214
| ~ spl85_13 ),
inference(avatar_split_clause,[],[f14444,f3162,f14451,f11305]) ).
fof(f11305,plain,
( spl85_170
<=> ! [X2,X7] : hBOOL(hAPP(X2,X7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_170])]) ).
fof(f14444,plain,
( ! [X42,X43] :
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_HOL_Obool))
| hBOOL(hAPP(X43,X42)) )
| ~ spl85_13 ),
inference(backward_demodulation,[],[f4255,f14441]) ).
fof(f4255,plain,
! [X41,X42,X43] :
( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X41,tc_HOL_Obool)),X42))
| hBOOL(hAPP(X43,X42)) ),
inference(resolution,[],[f2244,f2260]) ).
fof(f2260,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1),
inference(cnf_transformation,[],[f990]) ).
fof(f990,plain,
! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)),X1),
inference(rectify,[],[f427]) ).
fof(f427,axiom,
! [X8,X10] : c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
fof(f2244,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(cnf_transformation,[],[f1565]) ).
fof(f1565,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(X0,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ),
inference(rectify,[],[f1332]) ).
fof(f1332,plain,
! [X1,X2,X0,X3] :
( ~ hBOOL(hAPP(X2,X3))
| hBOOL(hAPP(X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,X1) ),
inference(flattening,[],[f1331]) ).
fof(f1331,plain,
! [X0,X3,X1,X2] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X2,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,X1) ),
inference(ennf_transformation,[],[f826]) ).
fof(f826,plain,
! [X0,X3,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,X1)
=> ( hBOOL(hAPP(X2,X3))
=> hBOOL(hAPP(X1,X3)) ) ),
inference(rectify,[],[f198]) ).
fof(f198,axiom,
! [X8,X66,X18,X14] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),X18,X66)
=> ( hBOOL(hAPP(X18,X14))
=> hBOOL(hAPP(X66,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
fof(f14455,plain,
( ~ spl85_214
| ~ spl85_13
| spl85_69 ),
inference(avatar_split_clause,[],[f14446,f4474,f3162,f14451]) ).
fof(f4474,plain,
( spl85_69
<=> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool)),v_F)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_69])]) ).
fof(f14446,plain,
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_HOL_Obool))
| ~ spl85_13
| spl85_69 ),
inference(backward_demodulation,[],[f4475,f14441]) ).
fof(f4475,plain,
( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool)),v_F))
| spl85_69 ),
inference(avatar_component_clause,[],[f4474]) ).
fof(f14454,plain,
( spl85_213
| spl85_170
| ~ spl85_214
| ~ spl85_13 ),
inference(avatar_split_clause,[],[f14445,f3162,f14451,f11305,f14448]) ).
fof(f14448,plain,
( spl85_213
<=> ! [X50] : ~ class_Orderings_Obot(tc_fun(X50,tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_213])]) ).
fof(f14445,plain,
( ! [X50,X51,X52] :
( ~ hBOOL(c_Orderings_Obot__class_Obot(tc_HOL_Obool))
| hBOOL(hAPP(X52,X51))
| ~ class_Orderings_Obot(tc_fun(X50,tc_HOL_Obool)) )
| ~ spl85_13 ),
inference(backward_demodulation,[],[f4258,f14441]) ).
fof(f4258,plain,
! [X50,X51,X52] :
( ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(X50,tc_HOL_Obool)),X51))
| hBOOL(hAPP(X52,X51))
| ~ class_Orderings_Obot(tc_fun(X50,tc_HOL_Obool)) ),
inference(resolution,[],[f2244,f2683]) ).
fof(f2683,plain,
! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X0,c_Orderings_Obot__class_Obot(X0),X1)
| ~ class_Orderings_Obot(X0) ),
inference(cnf_transformation,[],[f1123]) ).
fof(f1123,plain,
! [X0,X1] :
( ~ class_Orderings_Obot(X0)
| c_Orderings_Oord__class_Oless__eq(X0,c_Orderings_Obot__class_Obot(X0),X1) ),
inference(ennf_transformation,[],[f678]) ).
fof(f678,plain,
! [X0,X1] :
( class_Orderings_Obot(X0)
=> c_Orderings_Oord__class_Oless__eq(X0,c_Orderings_Obot__class_Obot(X0),X1) ),
inference(rectify,[],[f446]) ).
fof(f446,axiom,
! [X8,X49] :
( class_Orderings_Obot(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,c_Orderings_Obot__class_Obot(X8),X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__least) ).
fof(f14439,plain,
( ~ spl85_207
| spl85_212
| ~ spl85_15 ),
inference(avatar_split_clause,[],[f14402,f3172,f14437,f14416]) ).
fof(f14416,plain,
( spl85_207
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OProf)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_207])]) ).
fof(f14437,plain,
( spl85_212
<=> ! [X41,X40,X39] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X39),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40),X41)),hAPP(v_F,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40),X41)),hAPP(v_F,X39)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40),X41)),hAPP(X39,sK4(X39,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X40,X41))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40),X41)),sK4(X39,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X40,X41))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_212])]) ).
fof(f14402,plain,
( ! [X40,X41,X39] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X39),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40),X41)),sK4(X39,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X40,X41)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40),X41)),hAPP(X39,sK4(X39,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X40,X41))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40),X41)),hAPP(v_F,X39)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X40),X41)),hAPP(v_F,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool))))) )
| ~ spl85_15 ),
inference(superposition,[],[f2203,f14332]) ).
fof(f14435,plain,
( spl85_210
| ~ spl85_211
| ~ spl85_15 ),
inference(avatar_split_clause,[],[f14406,f3172,f14432,f14429]) ).
fof(f14429,plain,
( spl85_210
<=> ! [X47] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X47,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)))),sK21(X47,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool))))),sK20(X47,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)))))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X47) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_210])]) ).
fof(f14432,plain,
( spl85_211
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool))),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_211])]) ).
fof(f14406,plain,
( ! [X47] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool))),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X47,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)))),sK21(X47,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool))))),sK20(X47,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)))))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X47) )
| ~ spl85_15 ),
inference(superposition,[],[f2454,f14332]) ).
fof(f2454,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X0,X1)),sK21(X0,X1))),hAPP(X1,sK20(X0,X1))))
| c_Arrow__Order__Mirabelle_Odictator(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(cnf_transformation,[],[f1732]) ).
fof(f1732,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X0,X1)),sK21(X0,X1))),hAPP(X1,sK20(X0,X1))))
& sK21(X0,X1) != sK22(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X0,X1)),sK21(X0,X1))),hAPP(sK20(X0,X1),X0)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X0,X1)),c_Arrow__Order__Mirabelle_OProf)) )
| c_Arrow__Order__Mirabelle_Odictator(X1,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22])],[f1111,f1731,f1730]) ).
fof(f1730,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),hAPP(X1,X2)))
& X3 != X4
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),hAPP(X2,X0))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf)) )
=> ( ? [X4,X3] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),hAPP(X1,sK20(X0,X1))))
& X3 != X4
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),hAPP(sK20(X0,X1),X0))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X0,X1)),c_Arrow__Order__Mirabelle_OProf)) ) ),
introduced(choice_axiom,[]) ).
fof(f1731,plain,
! [X0,X1] :
( ? [X4,X3] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),hAPP(X1,sK20(X0,X1))))
& X3 != X4
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),hAPP(sK20(X0,X1),X0))) )
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X0,X1)),sK21(X0,X1))),hAPP(X1,sK20(X0,X1))))
& sK21(X0,X1) != sK22(X0,X1)
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X0,X1)),sK21(X0,X1))),hAPP(sK20(X0,X1),X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f1111,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ? [X2] :
( ? [X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),hAPP(X1,X2)))
& X3 != X4
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),hAPP(X2,X0))) )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf)) )
| c_Arrow__Order__Mirabelle_Odictator(X1,X0) ),
inference(flattening,[],[f1110]) ).
fof(f1110,plain,
! [X1,X0] :
( c_Arrow__Order__Mirabelle_Odictator(X1,X0)
| ? [X2] :
( ? [X4,X3] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),hAPP(X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),hAPP(X2,X0)))
& X3 != X4 )
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(ennf_transformation,[],[f710]) ).
fof(f710,plain,
! [X1,X0] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf))
=> ! [X4,X3] :
( X3 != X4
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),hAPP(X2,X0)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),hAPP(X1,X2))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X1,X0) ) ),
inference(rectify,[],[f50]) ).
fof(f50,axiom,
! [X29,X32] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X32),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf))
=> ! [X6,X5] :
( X5 != X6
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X6)),hAPP(X2,X29)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X6)),hAPP(X32,X2))) ) ) )
=> c_Arrow__Order__Mirabelle_Odictator(X32,X29) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictatorI) ).
fof(f14427,plain,
( spl85_209
| spl85_42
| ~ spl85_15 ),
inference(avatar_split_clause,[],[f14423,f3172,f3379,f14425]) ).
fof(f14425,plain,
( spl85_209
<=> ! [X36,X37] : ~ hBOOL(hAPP(hAPP(c_Product__Type_OPair(X36,X37),sK32(X36,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X37)),sK31(X36,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X37))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_209])]) ).
fof(f14423,plain,
( ! [X38,X36,X37] :
( hBOOL(X38)
| ~ hBOOL(hAPP(hAPP(c_Product__Type_OPair(X36,X37),sK32(X36,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X37)),sK31(X36,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X37))) )
| ~ spl85_15 ),
inference(forward_demodulation,[],[f14401,f14332]) ).
fof(f14401,plain,
( ! [X38,X36,X37] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_OPair(X36,X37),sK32(X36,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X37)),sK31(X36,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X37)))
| hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X38)) )
| ~ spl85_15 ),
inference(superposition,[],[f2501,f14332]) ).
fof(f2501,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X0,X2),sK32(X0,X1,X2)),sK31(X0,X1,X2))))
| hBOOL(hAPP(X1,X3)) ),
inference(cnf_transformation,[],[f1773]) ).
fof(f1773,plain,
! [X0,X1,X2] :
( ( ! [X3] : hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X0,X2),sK32(X0,X1,X2)),sK31(X0,X1,X2)))) )
& ( ! [X6,X7] : hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X0,X2),X7),X6)))
| ~ hBOOL(hAPP(X1,sK33(X1))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31,sK32,sK33])],[f1770,f1772,f1771]) ).
fof(f1771,plain,
! [X0,X1,X2] :
( ? [X4,X5] : ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X0,X2),X5),X4)))
=> ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X0,X2),sK32(X0,X1,X2)),sK31(X0,X1,X2)))) ),
introduced(choice_axiom,[]) ).
fof(f1772,plain,
! [X1] :
( ? [X8] : ~ hBOOL(hAPP(X1,X8))
=> ~ hBOOL(hAPP(X1,sK33(X1))) ),
introduced(choice_axiom,[]) ).
fof(f1770,plain,
! [X0,X1,X2] :
( ( ! [X3] : hBOOL(hAPP(X1,X3))
| ? [X4,X5] : ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X0,X2),X5),X4))) )
& ( ! [X6,X7] : hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X0,X2),X7),X6)))
| ? [X8] : ~ hBOOL(hAPP(X1,X8)) ) ),
inference(rectify,[],[f1769]) ).
fof(f1769,plain,
! [X0,X1,X2] :
( ( ! [X3] : hBOOL(hAPP(X1,X3))
| ? [X4,X5] : ~ hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X0,X2),X5),X4))) )
& ( ! [X4,X5] : hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X0,X2),X5),X4)))
| ? [X3] : ~ hBOOL(hAPP(X1,X3)) ) ),
inference(nnf_transformation,[],[f814]) ).
fof(f814,plain,
! [X0,X1,X2] :
( ! [X3] : hBOOL(hAPP(X1,X3))
<=> ! [X4,X5] : hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X0,X2),X5),X4))) ),
inference(rectify,[],[f19]) ).
fof(f19,axiom,
! [X8,X18,X16] :
( ! [X20] : hBOOL(hAPP(X18,X20))
<=> ! [X6,X5] : hBOOL(hAPP(X18,hAPP(hAPP(c_Product__Type_OPair(X8,X16),X5),X6))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
fof(f14422,plain,
( ~ spl85_207
| spl85_208
| ~ spl85_15 ),
inference(avatar_split_clause,[],[f14403,f3172,f14420,f14416]) ).
fof(f14420,plain,
( spl85_208
<=> ! [X44,X43,X42] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X42),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X43),X44)),sK4(X42,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X43,X44)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X43),X44)),hAPP(X42,sK4(X42,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X43,X44))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X43),X44)),hAPP(v_F,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X43),X44)),hAPP(v_F,X42))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_208])]) ).
fof(f14403,plain,
( ! [X44,X42,X43] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X42),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X43),X44)),hAPP(v_F,X42)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X43),X44)),hAPP(v_F,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X43),X44)),hAPP(X42,sK4(X42,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X43,X44))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool))),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X43),X44)),sK4(X42,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)),X43,X44))) )
| ~ spl85_15 ),
inference(superposition,[],[f2202,f14332]) ).
fof(f2202,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,sK4(X0,X1,X2,X3))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X0),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,sK4(X0,X1,X2,X3)))) ),
inference(cnf_transformation,[],[f1533]) ).
fof(f14320,plain,
( spl85_61
| spl85_206
| ~ spl85_15 ),
inference(avatar_split_clause,[],[f14311,f3172,f14318,f4384]) ).
fof(f14318,plain,
( spl85_206
<=> ! [X4,X3] : c_Predicate_ORangeP(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_206])]) ).
fof(f14311,plain,
( ! [X2,X3,X4] :
( c_Predicate_ORangeP(X3,X4,c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_HOL_Obool))
| ~ hBOOL(X2) )
| ~ spl85_15 ),
inference(superposition,[],[f2173,f14253]) ).
fof(f14253,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),X0),c_Orderings_Obot__class_Obot(tc_HOL_Obool)) = X0
| ~ spl85_15 ),
inference(resolution,[],[f2644,f3174]) ).
fof(f2644,plain,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice__bot(X1)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),c_Orderings_Obot__class_Obot(X1)) = X0 ),
inference(cnf_transformation,[],[f1900]) ).
fof(f1900,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),c_Orderings_Obot__class_Obot(X1)) = X0
| ~ class_Lattices_Obounded__lattice__bot(X1) ),
inference(rectify,[],[f1203]) ).
fof(f1203,plain,
! [X1,X0] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1
| ~ class_Lattices_Obounded__lattice__bot(X0) ),
inference(ennf_transformation,[],[f997]) ).
fof(f997,plain,
! [X1,X0] :
( class_Lattices_Obounded__lattice__bot(X0)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X0),X1),c_Orderings_Obot__class_Obot(X0)) = X1 ),
inference(rectify,[],[f432]) ).
fof(f432,axiom,
! [X8,X49] :
( class_Lattices_Obounded__lattice__bot(X8)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X49),c_Orderings_Obot__class_Obot(X8)) = X49 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__right) ).
fof(f2173,plain,
! [X2,X3,X0,X1,X5] :
( ~ hBOOL(hAPP(hAPP(X3,X5),X0))
| c_Predicate_ORangeP(X2,X1,X3,X0) ),
inference(cnf_transformation,[],[f1503]) ).
fof(f1503,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(X3,sK0(X0,X3)),X0))
| ~ c_Predicate_ORangeP(X2,X1,X3,X0) )
& ( c_Predicate_ORangeP(X2,X1,X3,X0)
| ! [X5] : ~ hBOOL(hAPP(hAPP(X3,X5),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f1501,f1502]) ).
fof(f1502,plain,
! [X0,X3] :
( ? [X4] : hBOOL(hAPP(hAPP(X3,X4),X0))
=> hBOOL(hAPP(hAPP(X3,sK0(X0,X3)),X0)) ),
introduced(choice_axiom,[]) ).
fof(f1501,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] : hBOOL(hAPP(hAPP(X3,X4),X0))
| ~ c_Predicate_ORangeP(X2,X1,X3,X0) )
& ( c_Predicate_ORangeP(X2,X1,X3,X0)
| ! [X5] : ~ hBOOL(hAPP(hAPP(X3,X5),X0)) ) ),
inference(rectify,[],[f1500]) ).
fof(f1500,plain,
! [X2,X3,X1,X0] :
( ( ? [X4] : hBOOL(hAPP(hAPP(X0,X4),X2))
| ~ c_Predicate_ORangeP(X1,X3,X0,X2) )
& ( c_Predicate_ORangeP(X1,X3,X0,X2)
| ! [X4] : ~ hBOOL(hAPP(hAPP(X0,X4),X2)) ) ),
inference(nnf_transformation,[],[f692]) ).
fof(f692,plain,
! [X2,X3,X1,X0] :
( ? [X4] : hBOOL(hAPP(hAPP(X0,X4),X2))
<=> c_Predicate_ORangeP(X1,X3,X0,X2) ),
inference(rectify,[],[f172]) ).
fof(f172,axiom,
! [X19,X8,X35,X16] :
( ? [X5] : hBOOL(hAPP(hAPP(X19,X5),X35))
<=> c_Predicate_ORangeP(X8,X16,X19,X35) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
fof(f13485,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f9788,f4426,f3290,f9793]) ).
fof(f9793,plain,
( spl85_161
<=> hBOOL(hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_161])]) ).
fof(f3290,plain,
( spl85_34
<=> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,v_Q____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_34])]) ).
fof(f9788,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(superposition,[],[f9759,f2523]) ).
fof(f9759,plain,
( ! [X0] : hBOOL(hAPP(X0,hAPP(v_F,v_Q____)))
| ~ spl85_34
| ~ spl85_64 ),
inference(resolution,[],[f9735,f3292]) ).
fof(f3292,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,v_Q____)))
| ~ spl85_34 ),
inference(avatar_component_clause,[],[f3290]) ).
fof(f9735,plain,
( ! [X26,X27] :
( ~ hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,X27))
| hBOOL(hAPP(X26,X27)) )
| ~ spl85_64 ),
inference(resolution,[],[f2244,f9404]) ).
fof(f9404,plain,
( ! [X7] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin,X7)
| ~ spl85_64 ),
inference(superposition,[],[f2260,f4428]) ).
fof(f4428,plain,
( c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| ~ spl85_64 ),
inference(avatar_component_clause,[],[f4426]) ).
fof(f13484,plain,
( spl85_161
| ~ spl85_26
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f9779,f4426,f3290,f3229,f9793]) ).
fof(f3229,plain,
( spl85_26
<=> class_Lattices_Osemilattice__sup(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_26])]) ).
fof(f9779,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_26
| ~ spl85_34
| ~ spl85_64 ),
inference(superposition,[],[f9759,f3829]) ).
fof(f3829,plain,
( ! [X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),X1),X1) = X1
| ~ spl85_26 ),
inference(resolution,[],[f2555,f3231]) ).
fof(f3231,plain,
( class_Lattices_Osemilattice__sup(tc_HOL_Obool)
| ~ spl85_26 ),
inference(avatar_component_clause,[],[f3229]) ).
fof(f2555,plain,
! [X0,X1] :
( ~ class_Lattices_Osemilattice__sup(X0)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X0),X1),X1) = X1 ),
inference(cnf_transformation,[],[f1822]) ).
fof(f1822,plain,
! [X0,X1] :
( ~ class_Lattices_Osemilattice__sup(X0)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X0),X1),X1) = X1 ),
inference(rectify,[],[f1449]) ).
fof(f1449,plain,
! [X1,X0] :
( ~ class_Lattices_Osemilattice__sup(X1)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0 ),
inference(ennf_transformation,[],[f959]) ).
fof(f959,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X0),X0) = X0 ),
inference(rectify,[],[f391]) ).
fof(f391,axiom,
! [X28,X8] :
( class_Lattices_Osemilattice__sup(X8)
=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X28),X28) = X28 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oidem) ).
fof(f13483,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13482,f4426,f3290,f9793]) ).
fof(f13482,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9766,f9774]) ).
fof(f9774,plain,
( ! [X37] : hAPP(v_F,v_Q____) = X37
| ~ spl85_34
| ~ spl85_64 ),
inference(resolution,[],[f9759,f2346]) ).
fof(f2346,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X0),X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f727]) ).
fof(f727,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X0),X1))
| X0 = X1 ),
inference(rectify,[],[f529]) ).
fof(f529,axiom,
! [X14,X13] :
( ~ hBOOL(hAPP(hAPP(c_fequal,X14),X13))
| X13 = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
fof(f9766,plain,
( ! [X18,X19,X16,X17,X20] : hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X17)),hAPP(hAPP(c_Product__Type_OPair(X16,X17),X18),hAPP(v_F,v_Q____))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X16,X17),tc_HOL_Obool)),X19),X20)))
| ~ spl85_34
| ~ spl85_64 ),
inference(resolution,[],[f9759,f2225]) ).
fof(f2225,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X3,c_COMBC(X5,tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_prod(X3,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X5),tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool),X5,c_member(tc_prod(X3,X5)))),c_Product__Type_OPair(X3,X5)))),X0)),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X3,c_COMBC(X5,tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_prod(X3,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X5),tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool),X5,c_member(tc_prod(X3,X5)))),c_Product__Type_OPair(X3,X5)))),X2)),X1),X4))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X5)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X1),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X5),tc_HOL_Obool)),X0),X2))) ),
inference(cnf_transformation,[],[f1552]) ).
fof(f1552,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X3,c_COMBC(X5,tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_prod(X3,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X5),tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool),X5,c_member(tc_prod(X3,X5)))),c_Product__Type_OPair(X3,X5)))),X0)),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X3,c_COMBC(X5,tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_prod(X3,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X5),tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool),X5,c_member(tc_prod(X3,X5)))),c_Product__Type_OPair(X3,X5)))),X2)),X1),X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X5)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X1),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X5),tc_HOL_Obool)),X0),X2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X5)),hAPP(hAPP(c_Product__Type_OPair(X3,X5),X1),X4)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X3,X5),tc_HOL_Obool)),X0),X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X3,c_COMBC(X5,tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_prod(X3,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X5),tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool),X5,c_member(tc_prod(X3,X5)))),c_Product__Type_OPair(X3,X5)))),X0)),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X3,c_COMBC(X5,tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_prod(X3,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X5),tc_fun(tc_fun(tc_prod(X3,X5),tc_HOL_Obool),tc_HOL_Obool),X5,c_member(tc_prod(X3,X5)))),c_Product__Type_OPair(X3,X5)))),X2)),X1),X4)) ) ),
inference(rectify,[],[f1551]) ).
fof(f1551,plain,
! [X2,X4,X1,X0,X3,X5] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X0,c_COMBC(X5,tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_prod(X0,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X5),tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool),X5,c_member(tc_prod(X0,X5)))),c_Product__Type_OPair(X0,X5)))),X2)),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X0,c_COMBC(X5,tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_prod(X0,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X5),tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool),X5,c_member(tc_prod(X0,X5)))),c_Product__Type_OPair(X0,X5)))),X1)),X4),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X5)),hAPP(hAPP(c_Product__Type_OPair(X0,X5),X4),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X5),tc_HOL_Obool)),X2),X1))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X5)),hAPP(hAPP(c_Product__Type_OPair(X0,X5),X4),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X5),tc_HOL_Obool)),X2),X1)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X0,c_COMBC(X5,tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_prod(X0,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X5),tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool),X5,c_member(tc_prod(X0,X5)))),c_Product__Type_OPair(X0,X5)))),X2)),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X0,c_COMBC(X5,tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_prod(X0,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X5),tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool),X5,c_member(tc_prod(X0,X5)))),c_Product__Type_OPair(X0,X5)))),X1)),X4),X3)) ) ),
inference(nnf_transformation,[],[f986]) ).
fof(f986,plain,
! [X2,X4,X1,X0,X3,X5] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_fun(X5,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X0,c_COMBC(X5,tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_prod(X0,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X5),tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool),X5,c_member(tc_prod(X0,X5)))),c_Product__Type_OPair(X0,X5)))),X2)),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_fun(X5,tc_HOL_Obool)),X0,c_COMBC(X5,tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X5,tc_prod(X0,X5)),tc_fun(X5,tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X5),tc_fun(tc_fun(tc_prod(X0,X5),tc_HOL_Obool),tc_HOL_Obool),X5,c_member(tc_prod(X0,X5)))),c_Product__Type_OPair(X0,X5)))),X1)),X4),X3))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X5)),hAPP(hAPP(c_Product__Type_OPair(X0,X5),X4),X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X5),tc_HOL_Obool)),X2),X1))) ),
inference(rectify,[],[f475]) ).
fof(f475,axiom,
! [X8,X34,X15,X13,X14,X16] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X16)),hAPP(hAPP(c_Product__Type_OPair(X8,X16),X14),X13)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X8,X16),tc_HOL_Obool)),X15),X34)))
<=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_fun(X16,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X8,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X8,c_COMBC(X16,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_prod(X8,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),X8,c_COMBB(tc_prod(X8,X16),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool),X16,c_member(tc_prod(X8,X16)))),c_Product__Type_OPair(X8,X16)))),X15)),hAPP(hAPP(c_COMBC(X8,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X8,c_COMBC(X16,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_prod(X8,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),X8,c_COMBB(tc_prod(X8,X16),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool),X16,c_member(tc_prod(X8,X16)))),c_Product__Type_OPair(X8,X16)))),X34)),X14),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq2) ).
fof(f13477,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13476,f4426,f3290,f9793]) ).
fof(f13476,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9773,f9774]) ).
fof(f9773,plain,
( ! [X36,X34,X35,X33] : hBOOL(hAPP(hAPP(c_member(tc_fun(X33,X34)),X35),c_FuncSet_OPi(X33,X34,X36,c_COMBK(tc_fun(X34,tc_HOL_Obool),X33,hAPP(v_F,v_Q____)))))
| ~ spl85_34
| ~ spl85_64 ),
inference(resolution,[],[f9759,f2718]) ).
fof(f2718,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X4,sK65(X0,X1,X2,X3,X4))),X0))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3,X1)),X4),c_FuncSet_OPi(X3,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X3,X0)))) ),
inference(cnf_transformation,[],[f1973]) ).
fof(f1973,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(hAPP(c_member(X3),sK65(X0,X1,X2,X3,X4)),X2))
& ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X4,sK65(X0,X1,X2,X3,X4))),X0)) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3,X1)),X4),c_FuncSet_OPi(X3,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X3,X0)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK65])],[f1971,f1972]) ).
fof(f1972,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( hBOOL(hAPP(hAPP(c_member(X3),X5),X2))
& ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X4,X5)),X0)) )
=> ( hBOOL(hAPP(hAPP(c_member(X3),sK65(X0,X1,X2,X3,X4)),X2))
& ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X4,sK65(X0,X1,X2,X3,X4))),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1971,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( hBOOL(hAPP(hAPP(c_member(X3),X5),X2))
& ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X4,X5)),X0)) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3,X1)),X4),c_FuncSet_OPi(X3,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X3,X0)))) ),
inference(rectify,[],[f1283]) ).
fof(f1283,plain,
! [X2,X4,X0,X1,X3] :
( ? [X5] :
( hBOOL(hAPP(hAPP(c_member(X1),X5),X0))
& ~ hBOOL(hAPP(hAPP(c_member(X4),hAPP(X3,X5)),X2)) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X3),c_FuncSet_OPi(X1,X4,X0,c_COMBK(tc_fun(X4,tc_HOL_Obool),X1,X2)))) ),
inference(ennf_transformation,[],[f875]) ).
fof(f875,plain,
! [X3,X1,X4,X0,X2] :
( ! [X5] :
( hBOOL(hAPP(hAPP(c_member(X1),X5),X0))
=> hBOOL(hAPP(hAPP(c_member(X4),hAPP(X3,X5)),X2)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X3),c_FuncSet_OPi(X1,X4,X0,c_COMBK(tc_fun(X4,tc_HOL_Obool),X1,X2)))) ),
inference(rectify,[],[f77]) ).
fof(f77,axiom,
! [X10,X8,X9,X1,X16] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X10))
=> hBOOL(hAPP(hAPP(c_member(X16),hAPP(X1,X2)),X9)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X8,X16)),X1),c_FuncSet_OPi(X8,X16,X10,c_COMBK(tc_fun(X16,tc_HOL_Obool),X8,X9)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcsetI) ).
fof(f13475,plain,
( spl85_161
| ~ spl85_23
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f9778,f4426,f3290,f3213,f9793]) ).
fof(f3213,plain,
( spl85_23
<=> class_Lattices_Osemilattice__sup(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_23])]) ).
fof(f9778,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_23
| ~ spl85_34
| ~ spl85_64 ),
inference(superposition,[],[f9759,f3828]) ).
fof(f3828,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X0),X0) = X0
| ~ spl85_23 ),
inference(resolution,[],[f2555,f3215]) ).
fof(f3215,plain,
( class_Lattices_Osemilattice__sup(tc_Nat_Onat)
| ~ spl85_23 ),
inference(avatar_component_clause,[],[f3213]) ).
fof(f13474,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13473,f4426,f3290,f9793]) ).
fof(f13473,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9763,f9774]) ).
fof(f9763,plain,
( ! [X6,X7,X5] : hBOOL(hAPP(hAPP(c_member(X5),hAPP(v_F,v_Q____)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X6),X7)))
| ~ spl85_34
| ~ spl85_64 ),
inference(resolution,[],[f9759,f2764]) ).
fof(f2764,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X0)),X1))
| hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X0))) ),
inference(cnf_transformation,[],[f2017]) ).
fof(f2017,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X0))) )
& ( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X0)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X0)),X1)) ) ),
inference(rectify,[],[f2016]) ).
fof(f2016,plain,
! [X1,X3,X2,X0] :
( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X0)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1)),X3))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X0),X1))) )
& ( hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X0),X1)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X0)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1)),X3)) ) ),
inference(nnf_transformation,[],[f605]) ).
fof(f605,plain,
! [X1,X3,X2,X0] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X0)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1)),X3))
<=> hBOOL(hAPP(hAPP(c_member(X2),X3),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X0),X1))) ),
inference(rectify,[],[f355]) ).
fof(f355,axiom,
! [X15,X34,X8,X14] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X15)),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X34)),X14))
<=> hBOOL(hAPP(hAPP(c_member(X8),X14),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X15),X34))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__Un__eq) ).
fof(f13472,plain,
( spl85_42
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f9789,f4426,f3290,f3379]) ).
fof(f9789,plain,
( ! [X24] : hBOOL(X24)
| ~ spl85_34
| ~ spl85_64 ),
inference(superposition,[],[f9759,f3082]) ).
fof(f3082,plain,
! [X2,X0,X1,X4,X5] : hAPP(c_Fun_Ofun__upd(X5,X0,X1,X4,X2),X4) = X2,
inference(equality_resolution,[],[f2950]) ).
fof(f2950,plain,
! [X2,X3,X0,X1,X4,X5] :
( X3 != X4
| hAPP(c_Fun_Ofun__upd(X5,X0,X1,X4,X2),X3) = X2 ),
inference(cnf_transformation,[],[f2168]) ).
fof(f2168,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( X3 = X4
| hAPP(X1,X3) = hAPP(c_Fun_Ofun__upd(X5,X0,X1,X4,X2),X3) )
& ( X3 != X4
| hAPP(c_Fun_Ofun__upd(X5,X0,X1,X4,X2),X3) = X2 ) ),
inference(rectify,[],[f1134]) ).
fof(f1134,plain,
! [X4,X1,X0,X2,X5,X3] :
( ( X2 = X5
| hAPP(X1,X2) = hAPP(c_Fun_Ofun__upd(X3,X4,X1,X5,X0),X2) )
& ( X2 != X5
| hAPP(c_Fun_Ofun__upd(X3,X4,X1,X5,X0),X2) = X0 ) ),
inference(ennf_transformation,[],[f980]) ).
fof(f980,plain,
! [X4,X0,X5,X3,X1,X2] :
( ( X2 = X5
=> hAPP(c_Fun_Ofun__upd(X3,X4,X1,X5,X0),X2) = X0 )
& ( X2 != X5
=> hAPP(X1,X2) = hAPP(c_Fun_Ofun__upd(X3,X4,X1,X5,X0),X2) ) ),
inference(rectify,[],[f334]) ).
fof(f334,axiom,
! [X13,X1,X11,X8,X16,X14] :
( ( X11 != X14
=> hAPP(c_Fun_Ofun__upd(X8,X16,X1,X14,X13),X11) = hAPP(X1,X11) )
& ( X11 = X14
=> hAPP(c_Fun_Ofun__upd(X8,X16,X1,X14,X13),X11) = X13 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_fun__upd__apply) ).
fof(f13471,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13470,f4426,f3290,f9793]) ).
fof(f13470,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9775,f9774]) ).
fof(f9775,plain,
( ! [X40,X38,X39] : hBOOL(hAPP(hAPP(c_member(tc_prod(X38,X38)),hAPP(hAPP(c_Product__Type_OPair(X38,X38),X39),hAPP(v_F,v_Q____))),c_Transitive__Closure_Ortrancl(X38,X40)))
| ~ spl85_34
| ~ spl85_64 ),
inference(resolution,[],[f9759,f2835]) ).
fof(f2835,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1,c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X0)),X2),X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X0))) ),
inference(cnf_transformation,[],[f2063]) ).
fof(f2063,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1,c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X0)),X2),X3)) )
& ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X1,c_COMBC(X1,tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X1,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X1),tc_fun(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X1,X1)))),c_Product__Type_OPair(X1,X1)))),X0)),X2),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Transitive__Closure_Ortrancl(X1,X0))) ) ),
inference(rectify,[],[f2062]) ).
fof(f2062,plain,
! [X1,X3,X0,X2] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X0),X2)),c_Transitive__Closure_Ortrancl(X3,X1)))
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X3,c_COMBC(X3,tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_prod(X3,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X3),tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool),X3,c_member(tc_prod(X3,X3)))),c_Product__Type_OPair(X3,X3)))),X1)),X0),X2)) )
& ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X3,c_COMBC(X3,tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_prod(X3,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X3),tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool),X3,c_member(tc_prod(X3,X3)))),c_Product__Type_OPair(X3,X3)))),X1)),X0),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X0),X2)),c_Transitive__Closure_Ortrancl(X3,X1))) ) ),
inference(nnf_transformation,[],[f734]) ).
fof(f734,plain,
! [X1,X3,X0,X2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X0),X2)),c_Transitive__Closure_Ortrancl(X3,X1)))
<=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X3,c_COMBC(X3,tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_prod(X3,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X3),tc_fun(tc_fun(tc_prod(X3,X3),tc_HOL_Obool),tc_HOL_Obool),X3,c_member(tc_prod(X3,X3)))),c_Product__Type_OPair(X3,X3)))),X1)),X0),X2)) ),
inference(rectify,[],[f183]) ).
fof(f183,axiom,
! [X14,X19,X62,X8] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,hAPP(hAPP(c_COMBC(X8,tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X8,tc_fun(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_fun(X8,tc_HOL_Obool)),X8,c_COMBC(X8,tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X8,tc_prod(X8,X8)),tc_fun(X8,tc_fun(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_HOL_Obool)),X8,c_COMBB(tc_prod(X8,X8),tc_fun(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),tc_HOL_Obool),X8,c_member(tc_prod(X8,X8)))),c_Product__Type_OPair(X8,X8)))),X19)),X14),X62))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X14),X62)),c_Transitive__Closure_Ortrancl(X8,X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclp__rtrancl__eq) ).
fof(f13469,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13468,f4426,f3290,f9793]) ).
fof(f13468,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9764,f9774]) ).
fof(f9764,plain,
( ! [X10,X8,X9] : hBOOL(hAPP(hAPP(c_member(X8),hAPP(v_F,v_Q____)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X9),X10)))
| ~ spl85_34
| ~ spl85_64 ),
inference(resolution,[],[f9759,f2855]) ).
fof(f2855,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)),X0))
| hBOOL(hAPP(hAPP(c_member(X2),X0),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X1),X3))) ),
inference(cnf_transformation,[],[f2081]) ).
fof(f2081,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_member(X2),X0),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X1),X3)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)),X0)) )
& ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X0),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X1),X3))) ) ),
inference(rectify,[],[f2080]) ).
fof(f2080,plain,
! [X0,X3,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_member(X1),X0),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),X0)) )
& ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X0),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2))) ) ),
inference(nnf_transformation,[],[f956]) ).
fof(f956,plain,
! [X0,X3,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X1),X0),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X3),X2)))
<=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X3)),hAPP(hAPP(c_COMBC(X1,tc_fun(X1,tc_HOL_Obool),tc_HOL_Obool),c_member(X1)),X2)),X0)) ),
inference(rectify,[],[f105]) ).
fof(f105,axiom,
! [X14,X8,X34,X15] :
( hBOOL(hAPP(hAPP(c_member(X8),X14),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X15),X34)))
<=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X15)),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X34)),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq) ).
fof(f13464,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13463,f4426,f3290,f9793]) ).
fof(f13463,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13462]) ).
fof(f13462,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10313,f9774]) ).
fof(f10313,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2237,f9774]) ).
fof(f2237,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0))) ),
inference(cnf_transformation,[],[f1562]) ).
fof(f1562,plain,
! [X0,X1,X2,X3] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X0))
& hBOOL(hAPP(hAPP(c_member(X2),X3),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X3),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0))) ),
inference(rectify,[],[f1215]) ).
fof(f1215,plain,
! [X3,X2,X0,X1] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X3))
& hBOOL(hAPP(hAPP(c_member(X0),X1),X2)) )
| ~ hBOOL(hAPP(hAPP(c_member(X0),X1),c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X2,X3))) ),
inference(ennf_transformation,[],[f876]) ).
fof(f876,plain,
! [X1,X3,X2,X0] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X2,X3)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
=> hBOOL(hAPP(hAPP(c_member(X0),X1),X3)) ) ),
inference(rectify,[],[f481]) ).
fof(f481,axiom,
! [X8,X7,X10,X9] :
( hBOOL(hAPP(hAPP(c_member(X8),X7),c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool),X10,X9)))
=> ~ ( hBOOL(hAPP(hAPP(c_member(X8),X7),X10))
=> hBOOL(hAPP(hAPP(c_member(X8),X7),X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffE) ).
fof(f13451,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10872,f4426,f3290,f9793]) ).
fof(f10872,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2968,f9774]) ).
fof(f2968,plain,
! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X4)),c_FuncSet_Orestrict(X2,X4,hAPP(c_COMBB(X1,X4,X2,X5),X3),X0)),c_FuncSet_Oextensional(X2,X4,X0))),
inference(definition_unfolding,[],[f2716,f2272]) ).
fof(f2272,plain,
! [X2,X3,X0,X1,X4,X5] : c_FuncSet_Ocompose(X0,X4,X3,X1,X5,X2) = c_FuncSet_Orestrict(X0,X3,hAPP(c_COMBB(X4,X3,X0,X5),X2),X1),
inference(cnf_transformation,[],[f1583]) ).
fof(f1583,plain,
! [X0,X1,X2,X3,X4,X5] : c_FuncSet_Ocompose(X0,X4,X3,X1,X5,X2) = c_FuncSet_Orestrict(X0,X3,hAPP(c_COMBB(X4,X3,X0,X5),X2),X1),
inference(rectify,[],[f637]) ).
fof(f637,plain,
! [X2,X3,X0,X4,X5,X1] : c_FuncSet_Orestrict(X2,X4,hAPP(c_COMBB(X5,X4,X2,X1),X0),X3) = c_FuncSet_Ocompose(X2,X5,X4,X3,X1,X0),
inference(rectify,[],[f116]) ).
fof(f116,axiom,
! [X1,X0,X8,X10,X16,X31] : c_FuncSet_Ocompose(X8,X31,X16,X10,X0,X1) = c_FuncSet_Orestrict(X8,X16,hAPP(c_COMBB(X31,X16,X8,X0),X1),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compose__def) ).
fof(f2716,plain,
! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X4)),c_FuncSet_Ocompose(X2,X1,X4,X0,X5,X3)),c_FuncSet_Oextensional(X2,X4,X0))),
inference(cnf_transformation,[],[f1969]) ).
fof(f1969,plain,
! [X0,X1,X2,X3,X4,X5] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X4)),c_FuncSet_Ocompose(X2,X1,X4,X0,X5,X3)),c_FuncSet_Oextensional(X2,X4,X0))),
inference(rectify,[],[f906]) ).
fof(f906,plain,
! [X3,X2,X5,X1,X0,X4] : hBOOL(hAPP(hAPP(c_member(tc_fun(X5,X0)),c_FuncSet_Ocompose(X5,X2,X0,X3,X4,X1)),c_FuncSet_Oextensional(X5,X0,X3))),
inference(rectify,[],[f90]) ).
fof(f90,axiom,
! [X16,X0,X31,X10,X1,X8] : hBOOL(hAPP(hAPP(c_member(tc_fun(X8,X16)),c_FuncSet_Ocompose(X8,X31,X16,X10,X1,X0)),c_FuncSet_Oextensional(X8,X16,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_compose__extensional) ).
fof(f13448,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13447,f4426,f3290,f9793]) ).
fof(f13447,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13446]) ).
fof(f13446,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13445,f9774]) ).
fof(f13445,plain,
( ! [X31,X28,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13444]) ).
fof(f13444,plain,
( ! [X31,X28,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10635,f9774]) ).
fof(f10635,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X27,X28)),X29),c_FuncSet_OPi(X27,X28,X30,X31)))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3595,f9774]) ).
fof(f3595,plain,
! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X27,X28)),X29),c_FuncSet_OPi(X27,X28,X30,X31)))
| hBOOL(hAPP(hAPP(c_member(X27),sK72(X27,sK57(X32,c_FuncSet_OPi(X27,X28,X30,X31),tc_fun(X27,X28),X33,X34),X29,X30)),X30))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34))) ),
inference(resolution,[],[f2749,f2649]) ).
fof(f2649,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(X2),sK57(X0,X1,X2,X3,X4)),X1))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X3)),X0),c_FuncSet_OPi(X2,X3,X1,X4))) ),
inference(cnf_transformation,[],[f1909]) ).
fof(f1909,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X0,sK57(X0,X1,X2,X3,X4))),hAPP(X4,sK57(X0,X1,X2,X3,X4))))
& hBOOL(hAPP(hAPP(c_member(X2),sK57(X0,X1,X2,X3,X4)),X1)) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X3)),X0),c_FuncSet_OPi(X2,X3,X1,X4))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f1907,f1908]) ).
fof(f1908,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X0,X5)),hAPP(X4,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),X5),X1)) )
=> ( ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X0,sK57(X0,X1,X2,X3,X4))),hAPP(X4,sK57(X0,X1,X2,X3,X4))))
& hBOOL(hAPP(hAPP(c_member(X2),sK57(X0,X1,X2,X3,X4)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1907,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X0,X5)),hAPP(X4,X5)))
& hBOOL(hAPP(hAPP(c_member(X2),X5),X1)) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X3)),X0),c_FuncSet_OPi(X2,X3,X1,X4))) ),
inference(rectify,[],[f1401]) ).
fof(f1401,plain,
! [X1,X0,X4,X3,X2] :
( ? [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X1,X5)),hAPP(X2,X5)))
& hBOOL(hAPP(hAPP(c_member(X4),X5),X0)) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X3)),X1),c_FuncSet_OPi(X4,X3,X0,X2))) ),
inference(ennf_transformation,[],[f921]) ).
fof(f921,plain,
! [X2,X1,X3,X0,X4] :
( ! [X5] :
( hBOOL(hAPP(hAPP(c_member(X4),X5),X0))
=> hBOOL(hAPP(hAPP(c_member(X3),hAPP(X1,X5)),hAPP(X2,X5))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X3)),X1),c_FuncSet_OPi(X4,X3,X0,X2))) ),
inference(rectify,[],[f84]) ).
fof(f84,axiom,
! [X10,X1,X9,X16,X8] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X10))
=> hBOOL(hAPP(hAPP(c_member(X16),hAPP(X1,X2)),hAPP(X9,X2))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X8,X16)),X1),c_FuncSet_OPi(X8,X16,X10,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__I_H) ).
fof(f2749,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X2),c_FuncSet_OPi(X1,X0,X4,X5)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X3),c_FuncSet_OPi(X1,X0,X4,X5)))
| hBOOL(hAPP(hAPP(c_member(X1),sK72(X1,X2,X3,X4)),X4)) ),
inference(cnf_transformation,[],[f2007]) ).
fof(f2007,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( hAPP(X3,sK72(X1,X2,X3,X4)) != hAPP(X2,sK72(X1,X2,X3,X4))
& hBOOL(hAPP(hAPP(c_member(X1),sK72(X1,X2,X3,X4)),X4)) )
| ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X2),c_FuncSet_OPi(X1,X0,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X3),c_FuncSet_OPi(X1,X0,X4,X5))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X3),c_FuncSet_OPi(X1,X0,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X2),c_FuncSet_OPi(X1,X0,X4,X5))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72])],[f2005,f2006]) ).
fof(f2006,plain,
! [X1,X2,X3,X4] :
( ? [X6] :
( hAPP(X2,X6) != hAPP(X3,X6)
& hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) )
=> ( hAPP(X3,sK72(X1,X2,X3,X4)) != hAPP(X2,sK72(X1,X2,X3,X4))
& hBOOL(hAPP(hAPP(c_member(X1),sK72(X1,X2,X3,X4)),X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f2005,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X6] :
( hAPP(X2,X6) != hAPP(X3,X6)
& hBOOL(hAPP(hAPP(c_member(X1),X6),X4)) )
| ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X2),c_FuncSet_OPi(X1,X0,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X3),c_FuncSet_OPi(X1,X0,X4,X5))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X3),c_FuncSet_OPi(X1,X0,X4,X5)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X2),c_FuncSet_OPi(X1,X0,X4,X5))) ) ) ),
inference(rectify,[],[f2004]) ).
fof(f2004,plain,
! [X3,X4,X5,X0,X1,X2] :
( ? [X6] :
( hAPP(X5,X6) != hAPP(X0,X6)
& hBOOL(hAPP(hAPP(c_member(X4),X6),X1)) )
| ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X3)),X5),c_FuncSet_OPi(X4,X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X3)),X0),c_FuncSet_OPi(X4,X3,X1,X2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X3)),X0),c_FuncSet_OPi(X4,X3,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X3)),X5),c_FuncSet_OPi(X4,X3,X1,X2))) ) ) ),
inference(nnf_transformation,[],[f1224]) ).
fof(f1224,plain,
! [X3,X4,X5,X0,X1,X2] :
( ? [X6] :
( hAPP(X5,X6) != hAPP(X0,X6)
& hBOOL(hAPP(hAPP(c_member(X4),X6),X1)) )
| ( hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X3)),X5),c_FuncSet_OPi(X4,X3,X1,X2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X3)),X0),c_FuncSet_OPi(X4,X3,X1,X2))) ) ),
inference(ennf_transformation,[],[f845]) ).
fof(f845,plain,
! [X2,X0,X1,X4,X5,X3] :
( ! [X6] :
( hBOOL(hAPP(hAPP(c_member(X4),X6),X1))
=> hAPP(X5,X6) = hAPP(X0,X6) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X3)),X5),c_FuncSet_OPi(X4,X3,X1,X2)))
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X3)),X0),c_FuncSet_OPi(X4,X3,X1,X2))) ) ),
inference(rectify,[],[f81]) ).
fof(f81,axiom,
! [X1,X10,X9,X16,X8,X0] :
( ! [X43] :
( hBOOL(hAPP(hAPP(c_member(X8),X43),X10))
=> hAPP(X1,X43) = hAPP(X0,X43) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X8,X16)),X1),c_FuncSet_OPi(X8,X16,X10,X9)))
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(X8,X16)),X0),c_FuncSet_OPi(X8,X16,X10,X9))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__cong) ).
fof(f13415,plain,
( spl85_178
| spl85_161
| ~ spl85_34
| ~ spl85_64
| ~ spl85_75 ),
inference(avatar_split_clause,[],[f13414,f4730,f4426,f3290,f9793,f11730]) ).
fof(f11730,plain,
( spl85_178
<=> ! [X7] : c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_178])]) ).
fof(f4730,plain,
( spl85_75
<=> ! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X65,sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))),sK21(X65,sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))))),hAPP(sK20(X65,sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),X65)))
| c_Arrow__Order__Mirabelle_Odictator(sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),X65) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_75])]) ).
fof(f13414,plain,
( ! [X65] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X65) )
| ~ spl85_34
| ~ spl85_64
| ~ spl85_75 ),
inference(forward_demodulation,[],[f10791,f9774]) ).
fof(f10791,plain,
( ! [X65] :
( c_Arrow__Order__Mirabelle_Odictator(sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),X65)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64
| ~ spl85_75 ),
inference(backward_demodulation,[],[f4731,f9774]) ).
fof(f4731,plain,
( ! [X65] :
( c_Arrow__Order__Mirabelle_Odictator(sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),X65)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X65,sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))),sK21(X65,sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))))),hAPP(sK20(X65,sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),X65))) )
| ~ spl85_75 ),
inference(avatar_component_clause,[],[f4730]) ).
fof(f13409,plain,
( spl85_161
| ~ spl85_25
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10771,f4426,f3290,f3223,f9793]) ).
fof(f3223,plain,
( spl85_25
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_25])]) ).
fof(f10771,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_25
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3399,f9774]) ).
fof(f3399,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____))),hAPP(c_member(X1),c_Arrow__Order__Mirabelle_OLin)))
| ~ spl85_25 ),
inference(resolution,[],[f3288,f2711]) ).
fof(f3288,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_member(X0),c_Arrow__Order__Mirabelle_OLin),hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____))))
| ~ spl85_25 ),
inference(resolution,[],[f3225,f2711]) ).
fof(f3225,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin))
| ~ spl85_25 ),
inference(avatar_component_clause,[],[f3223]) ).
fof(f13406,plain,
( spl85_205
| spl85_80
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10985,f4426,f3290,f6164,f13403]) ).
fof(f13403,plain,
( spl85_205
<=> class_Lattices_Osemilattice__sup(hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_205])]) ).
fof(f6164,plain,
( spl85_80
<=> ! [X5] : ~ class_Lattices_Olattice(X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_80])]) ).
fof(f10985,plain,
( ! [X0] :
( ~ class_Lattices_Olattice(X0)
| class_Lattices_Osemilattice__sup(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2551,f9774]) ).
fof(f2551,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__sup(tc_fun(X1,X0))
| ~ class_Lattices_Olattice(X0) ),
inference(cnf_transformation,[],[f1819]) ).
fof(f1819,plain,
! [X0,X1] :
( ~ class_Lattices_Olattice(X0)
| class_Lattices_Osemilattice__sup(tc_fun(X1,X0)) ),
inference(rectify,[],[f1198]) ).
fof(f1198,plain,
! [X1,X0] :
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Osemilattice__sup(tc_fun(X0,X1)) ),
inference(ennf_transformation,[],[f596]) ).
fof(f596,plain,
! [X1,X0] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__sup(tc_fun(X0,X1)) ),
inference(rectify,[],[f498]) ).
fof(f498,axiom,
! [X73,X74] :
( class_Lattices_Olattice(X74)
=> class_Lattices_Osemilattice__sup(tc_fun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).
fof(f13399,plain,
( spl85_161
| spl85_84
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13398,f4426,f3290,f6422,f9793]) ).
fof(f6422,plain,
( spl85_84
<=> ! [X6,X5] : c_Arrow__Order__Mirabelle_Odictator(X6,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_84])]) ).
fof(f13398,plain,
( ! [X2,X1] :
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13397]) ).
fof(f13397,plain,
( ! [X2,X1] :
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10821,f9774]) ).
fof(f10821,plain,
( ! [X2,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK65(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2)),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3866,f9774]) ).
fof(f3866,plain,
! [X2,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK65(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2)),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X1,X2)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1) ),
inference(resolution,[],[f2451,f2719]) ).
fof(f2719,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(X3),sK65(X0,X1,X2,X3,X4)),X2))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3,X1)),X4),c_FuncSet_OPi(X3,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X3,X0)))) ),
inference(cnf_transformation,[],[f1973]) ).
fof(f2451,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X0,X1)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X1,X0) ),
inference(cnf_transformation,[],[f1732]) ).
fof(f13391,plain,
( spl85_161
| ~ spl85_4
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10796,f4426,f3290,f3115,f9793]) ).
fof(f10796,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_4
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3281,f9774]) ).
fof(f3281,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_member(X0),c_Arrow__Order__Mirabelle_OProf),hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____)))
| ~ spl85_4 ),
inference(resolution,[],[f3117,f2711]) ).
fof(f13384,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13383,f4426,f3290,f9793]) ).
fof(f13383,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13382]) ).
fof(f13382,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10075,f9774]) ).
fof(f10075,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X4),c_FuncSet_OPi(X1,X2,X0,X3))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2942,f9774]) ).
fof(f2942,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(X1),sK83(X0,X1,X2,X3,X4)),X0))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X4),c_FuncSet_OPi(X1,X2,X0,X3))) ),
inference(cnf_transformation,[],[f2160]) ).
fof(f2160,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X4),c_FuncSet_OPi(X1,X2,X0,X3)))
| ( hBOOL(hAPP(hAPP(c_member(X1),sK83(X0,X1,X2,X3,X4)),X0))
& ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X4,sK83(X0,X1,X2,X3,X4))),hAPP(X3,sK83(X0,X1,X2,X3,X4)))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK83])],[f2158,f2159]) ).
fof(f2159,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( hBOOL(hAPP(hAPP(c_member(X1),X5),X0))
& ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X4,X5)),hAPP(X3,X5))) )
=> ( hBOOL(hAPP(hAPP(c_member(X1),sK83(X0,X1,X2,X3,X4)),X0))
& ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X4,sK83(X0,X1,X2,X3,X4))),hAPP(X3,sK83(X0,X1,X2,X3,X4)))) ) ),
introduced(choice_axiom,[]) ).
fof(f2158,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X4),c_FuncSet_OPi(X1,X2,X0,X3)))
| ? [X5] :
( hBOOL(hAPP(hAPP(c_member(X1),X5),X0))
& ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X4,X5)),hAPP(X3,X5))) ) ),
inference(rectify,[],[f1478]) ).
fof(f1478,plain,
! [X3,X0,X2,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_OPi(X0,X2,X3,X1)))
| ? [X5] :
( hBOOL(hAPP(hAPP(c_member(X0),X5),X3))
& ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X4,X5)),hAPP(X1,X5))) ) ),
inference(ennf_transformation,[],[f634]) ).
fof(f634,plain,
! [X2,X3,X4,X0,X1] :
( ! [X5] :
( hBOOL(hAPP(hAPP(c_member(X0),X5),X3))
=> hBOOL(hAPP(hAPP(c_member(X2),hAPP(X4,X5)),hAPP(X1,X5))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_OPi(X0,X2,X3,X1))) ),
inference(rectify,[],[f75]) ).
fof(f75,axiom,
! [X8,X9,X16,X10,X1] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X10))
=> hBOOL(hAPP(hAPP(c_member(X16),hAPP(X1,X2)),hAPP(X9,X2))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X8,X16)),X1),c_FuncSet_OPi(X8,X16,X10,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__I) ).
fof(f13377,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13376,f4426,f3290,f9793]) ).
fof(f13376,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13375]) ).
fof(f13375,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13374,f9774]) ).
fof(f13374,plain,
( ! [X38,X39,X36,X37,X35] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,X39)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13373]) ).
fof(f13373,plain,
( ! [X38,X39,X36,X37,X35] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,X39)))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10733,f9774]) ).
fof(f10733,plain,
( ! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40))))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,X39))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3603,f9774]) ).
fof(f3603,plain,
! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,X39)))
| hBOOL(hAPP(hAPP(c_member(X35),sK72(X35,X37,sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),X38)),X38)) ),
inference(resolution,[],[f2750,f2719]) ).
fof(f2750,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X3),c_FuncSet_OPi(X1,X0,X4,X5)))
| hBOOL(hAPP(hAPP(c_member(X1),sK72(X1,X2,X3,X4)),X4))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X2),c_FuncSet_OPi(X1,X0,X4,X5))) ),
inference(cnf_transformation,[],[f2007]) ).
fof(f13371,plain,
( ~ spl85_161
| ~ spl85_34
| spl85_53
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10760,f4426,f3629,f3290,f9793]) ).
fof(f3629,plain,
( spl85_53
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,v_P____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_53])]) ).
fof(f10760,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| spl85_53
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3631,f9774]) ).
fof(f3631,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,v_P____)))
| spl85_53 ),
inference(avatar_component_clause,[],[f3629]) ).
fof(f13370,plain,
( spl85_58
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13369,f4426,f3290,f9793,f4223]) ).
fof(f4223,plain,
( spl85_58
<=> ! [X57,X58] : X57 = X58 ),
introduced(avatar_definition,[new_symbols(naming,[spl85_58])]) ).
fof(f13369,plain,
( ! [X3,X0] :
( hBOOL(hAPP(v_F,v_Q____))
| X0 = X3 )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f13368]) ).
fof(f13368,plain,
( ! [X3,X0] :
( hBOOL(hAPP(v_F,v_Q____))
| X0 = X3
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13367,f9774]) ).
fof(f13367,plain,
( ! [X2,X3,X0,X1] :
( X0 = X3
| hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != c_Set_Oinsert(X2,X1,X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13366]) ).
fof(f13366,plain,
( ! [X2,X3,X0,X1] :
( X0 = X3
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != c_Set_Oinsert(X2,X1,X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13365,f9774]) ).
fof(f13365,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| X0 = X3
| hBOOL(hAPP(hAPP(c_member(X2),X1),X3))
| hAPP(v_F,v_Q____) != c_Set_Oinsert(X2,X1,X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10347,f9774]) ).
fof(f10347,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Set_Oinsert(X2,X1,X0) != c_Set_Oinsert(X2,X1,X3)
| hBOOL(hAPP(hAPP(c_member(X2),X1),X3))
| X0 = X3 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2712,f9774]) ).
fof(f2712,plain,
! [X2,X3,X0,X1] :
( c_Set_Oinsert(X2,X1,X0) != c_Set_Oinsert(X2,X1,X3)
| hBOOL(hAPP(hAPP(c_member(X2),X1),X3))
| hBOOL(hAPP(hAPP(c_member(X2),X1),X0))
| X0 = X3 ),
inference(cnf_transformation,[],[f1967]) ).
fof(f1967,plain,
! [X0,X1,X2,X3] :
( ( ( c_Set_Oinsert(X2,X1,X0) = c_Set_Oinsert(X2,X1,X3)
| X0 != X3 )
& ( X0 = X3
| c_Set_Oinsert(X2,X1,X0) != c_Set_Oinsert(X2,X1,X3) ) )
| hBOOL(hAPP(hAPP(c_member(X2),X1),X3))
| hBOOL(hAPP(hAPP(c_member(X2),X1),X0)) ),
inference(rectify,[],[f1966]) ).
fof(f1966,plain,
! [X2,X1,X3,X0] :
( ( ( c_Set_Oinsert(X3,X1,X0) = c_Set_Oinsert(X3,X1,X2)
| X0 != X2 )
& ( X0 = X2
| c_Set_Oinsert(X3,X1,X0) != c_Set_Oinsert(X3,X1,X2) ) )
| hBOOL(hAPP(hAPP(c_member(X3),X1),X0))
| hBOOL(hAPP(hAPP(c_member(X3),X1),X2)) ),
inference(nnf_transformation,[],[f1448]) ).
fof(f1448,plain,
! [X2,X1,X3,X0] :
( ( c_Set_Oinsert(X3,X1,X0) = c_Set_Oinsert(X3,X1,X2)
<=> X0 = X2 )
| hBOOL(hAPP(hAPP(c_member(X3),X1),X0))
| hBOOL(hAPP(hAPP(c_member(X3),X1),X2)) ),
inference(flattening,[],[f1447]) ).
fof(f1447,plain,
! [X0,X1,X2,X3] :
( ( c_Set_Oinsert(X3,X1,X0) = c_Set_Oinsert(X3,X1,X2)
<=> X0 = X2 )
| hBOOL(hAPP(hAPP(c_member(X3),X1),X2))
| hBOOL(hAPP(hAPP(c_member(X3),X1),X0)) ),
inference(ennf_transformation,[],[f791]) ).
fof(f791,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(hAPP(c_member(X3),X1),X0))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X3),X1),X2))
=> ( c_Set_Oinsert(X3,X1,X0) = c_Set_Oinsert(X3,X1,X2)
<=> X0 = X2 ) ) ),
inference(rectify,[],[f300]) ).
fof(f300,axiom,
! [X10,X14,X9,X8] :
( ~ hBOOL(hAPP(hAPP(c_member(X8),X14),X10))
=> ( ~ hBOOL(hAPP(hAPP(c_member(X8),X14),X9))
=> ( X9 = X10
<=> c_Set_Oinsert(X8,X14,X10) = c_Set_Oinsert(X8,X14,X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
fof(f13343,plain,
( spl85_161
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13342,f4426,f3290,f3178,f9793]) ).
fof(f3178,plain,
( spl85_16
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_16])]) ).
fof(f13342,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13341]) ).
fof(f13341,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10829,f9774]) ).
fof(f10829,plain,
( ! [X18] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3593,f9774]) ).
fof(f3593,plain,
( ! [X18] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK72(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_F,X18,c_Arrow__Order__Mirabelle_OProf)),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
| ~ spl85_16 ),
inference(resolution,[],[f2749,f3180]) ).
fof(f3180,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ~ spl85_16 ),
inference(avatar_component_clause,[],[f3178]) ).
fof(f13335,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13334,f4426,f3290,f9793]) ).
fof(f13334,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13333]) ).
fof(f13333,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10397,f9774]) ).
fof(f10397,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X3)),c_FuncSet_Orestrict(X2,X3,X0,X1)),c_FuncSet_OPi(X2,X3,X1,c_COMBK(tc_fun(X3,tc_HOL_Obool),X2,X4))))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2567,f9774]) ).
fof(f2567,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(X2),sK45(X0,X1,X2,X3,X4)),X1))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X3)),c_FuncSet_Orestrict(X2,X3,X0,X1)),c_FuncSet_OPi(X2,X3,X1,c_COMBK(tc_fun(X3,tc_HOL_Obool),X2,X4)))) ),
inference(cnf_transformation,[],[f1833]) ).
fof(f1833,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X0,sK45(X0,X1,X2,X3,X4))),X4))
& hBOOL(hAPP(hAPP(c_member(X2),sK45(X0,X1,X2,X3,X4)),X1)) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X3)),c_FuncSet_Orestrict(X2,X3,X0,X1)),c_FuncSet_OPi(X2,X3,X1,c_COMBK(tc_fun(X3,tc_HOL_Obool),X2,X4)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f1831,f1832]) ).
fof(f1832,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X0,X5)),X4))
& hBOOL(hAPP(hAPP(c_member(X2),X5),X1)) )
=> ( ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X0,sK45(X0,X1,X2,X3,X4))),X4))
& hBOOL(hAPP(hAPP(c_member(X2),sK45(X0,X1,X2,X3,X4)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1831,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X0,X5)),X4))
& hBOOL(hAPP(hAPP(c_member(X2),X5),X1)) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X3)),c_FuncSet_Orestrict(X2,X3,X0,X1)),c_FuncSet_OPi(X2,X3,X1,c_COMBK(tc_fun(X3,tc_HOL_Obool),X2,X4)))) ),
inference(rectify,[],[f1220]) ).
fof(f1220,plain,
! [X3,X1,X4,X2,X0] :
( ? [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X5)),X0))
& hBOOL(hAPP(hAPP(c_member(X4),X5),X1)) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X2)),c_FuncSet_Orestrict(X4,X2,X3,X1)),c_FuncSet_OPi(X4,X2,X1,c_COMBK(tc_fun(X2,tc_HOL_Obool),X4,X0)))) ),
inference(ennf_transformation,[],[f903]) ).
fof(f903,plain,
! [X2,X3,X1,X0,X4] :
( ! [X5] :
( hBOOL(hAPP(hAPP(c_member(X4),X5),X1))
=> hBOOL(hAPP(hAPP(c_member(X2),hAPP(X3,X5)),X0)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X2)),c_FuncSet_Orestrict(X4,X2,X3,X1)),c_FuncSet_OPi(X4,X2,X1,c_COMBK(tc_fun(X2,tc_HOL_Obool),X4,X0)))) ),
inference(rectify,[],[f138]) ).
fof(f138,axiom,
! [X9,X10,X16,X1,X8] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X10))
=> hBOOL(hAPP(hAPP(c_member(X16),hAPP(X1,X2)),X9)) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X8,X16)),c_FuncSet_Orestrict(X8,X16,X1,X10)),c_FuncSet_OPi(X8,X16,X10,c_COMBK(tc_fun(X16,tc_HOL_Obool),X8,X9)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__in__funcset) ).
fof(f13332,plain,
( spl85_86
| spl85_58
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13331,f4426,f3290,f9793,f4223,f6471]) ).
fof(f6471,plain,
( spl85_86
<=> ! [X2,X0,X1] : ~ c_Relation_Osingle__valued(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_86])]) ).
fof(f13331,plain,
( ! [X2,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| X4 = X5
| ~ c_Relation_Osingle__valued(X0,X1,X2) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13330]) ).
fof(f13330,plain,
( ! [X2,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| X4 = X5
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ c_Relation_Osingle__valued(X0,X1,X2) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13329,f9774]) ).
fof(f13329,plain,
( ! [X2,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(v_F,v_Q____)),X2))
| ~ c_Relation_Osingle__valued(X0,X1,X2)
| ~ hBOOL(hAPP(v_F,v_Q____))
| X4 = X5 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10643,f9774]) ).
fof(f10643,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X3),X5)),X2))
| X4 = X5
| ~ c_Relation_Osingle__valued(X0,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(v_F,v_Q____)),X2)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2621,f9774]) ).
fof(f2621,plain,
! [X2,X3,X0,X1,X4,X5] :
( X4 = X5
| ~ c_Relation_Osingle__valued(X0,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X3),X5)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X3),X4)),X2)) ),
inference(cnf_transformation,[],[f1877]) ).
fof(f1877,plain,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X3),X5)),X2))
| X4 = X5 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X3),X4)),X2)) )
| ~ c_Relation_Osingle__valued(X0,X1,X2) )
& ( c_Relation_Osingle__valued(X0,X1,X2)
| ( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK50(X0,X1,X2)),sK52(X0,X1,X2))),X2))
& sK52(X0,X1,X2) != sK51(X0,X1,X2)
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK50(X0,X1,X2)),sK51(X0,X1,X2))),X2)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51,sK52])],[f1874,f1876,f1875]) ).
fof(f1875,plain,
! [X0,X1,X2] :
( ? [X6,X7] :
( ? [X8] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X6),X8)),X2))
& X7 != X8 )
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X6),X7)),X2)) )
=> ( ? [X8] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK50(X0,X1,X2)),X8)),X2))
& sK51(X0,X1,X2) != X8 )
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK50(X0,X1,X2)),sK51(X0,X1,X2))),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1876,plain,
! [X0,X1,X2] :
( ? [X8] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK50(X0,X1,X2)),X8)),X2))
& sK51(X0,X1,X2) != X8 )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK50(X0,X1,X2)),sK52(X0,X1,X2))),X2))
& sK52(X0,X1,X2) != sK51(X0,X1,X2) ) ),
introduced(choice_axiom,[]) ).
fof(f1874,plain,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X3),X5)),X2))
| X4 = X5 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X3),X4)),X2)) )
| ~ c_Relation_Osingle__valued(X0,X1,X2) )
& ( c_Relation_Osingle__valued(X0,X1,X2)
| ? [X6,X7] :
( ? [X8] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X6),X8)),X2))
& X7 != X8 )
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X6),X7)),X2)) ) ) ),
inference(rectify,[],[f1873]) ).
fof(f1873,plain,
! [X2,X1,X0] :
( ( ! [X3,X4] :
( ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X5)),X0))
| X4 = X5 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X4)),X0)) )
| ~ c_Relation_Osingle__valued(X2,X1,X0) )
& ( c_Relation_Osingle__valued(X2,X1,X0)
| ? [X3,X4] :
( ? [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X5)),X0))
& X4 != X5 )
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X4)),X0)) ) ) ),
inference(nnf_transformation,[],[f1490]) ).
fof(f1490,plain,
! [X2,X1,X0] :
( ! [X3,X4] :
( ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X5)),X0))
| X4 = X5 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X4)),X0)) )
<=> c_Relation_Osingle__valued(X2,X1,X0) ),
inference(ennf_transformation,[],[f613]) ).
fof(f613,plain,
! [X1,X0,X2] :
( c_Relation_Osingle__valued(X2,X1,X0)
<=> ! [X4,X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X4)),X0))
=> ! [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X1)),hAPP(hAPP(c_Product__Type_OPair(X2,X1),X3),X5)),X0))
=> X4 = X5 ) ) ),
inference(rectify,[],[f150]) ).
fof(f150,axiom,
! [X19,X16,X8] :
( ! [X2,X41] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X16)),hAPP(hAPP(c_Product__Type_OPair(X8,X16),X2),X41)),X19))
=> ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X16)),hAPP(hAPP(c_Product__Type_OPair(X8,X16),X2),X38)),X19))
=> X38 = X41 ) )
<=> c_Relation_Osingle__valued(X8,X16,X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__def) ).
fof(f13327,plain,
( ~ spl85_161
| spl85_204
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13323,f4426,f3290,f13325,f9793]) ).
fof(f13325,plain,
( spl85_204
<=> ! [X2,X3,X9,X0,X5,X1] :
( ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(v_F,v_Q____))
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X9,hAPP(v_F,v_Q____)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_204])]) ).
fof(f13323,plain,
( ! [X2,X3,X0,X1,X9,X5] :
( ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(v_F,v_Q____))
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X9,hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13322,f9774]) ).
fof(f13322,plain,
( ! [X2,X3,X0,X1,X9,X4,X5] :
( ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X9,hAPP(sK29(X0,X1,X2,X3,X4,X5),X9)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10280,f9774]) ).
fof(f10280,plain,
( ! [X2,X3,X0,X1,X9,X4,X5] :
( ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X9),X0)),X5))
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X9,hAPP(sK29(X0,X1,X2,X3,X4,X5),X9)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2483,f9774]) ).
fof(f2483,plain,
! [X2,X3,X0,X1,X9,X4,X5] :
( c_Recdef_Owfrec__rel(X2,X1,X5,X3,X9,hAPP(sK29(X0,X1,X2,X3,X4,X5),X9))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X9),X0)),X5))
| ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(hAPP(X3,X4),X0)) ),
inference(cnf_transformation,[],[f1758]) ).
fof(f1758,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(hAPP(X3,X4),X0))
| ! [X6] :
( hAPP(hAPP(X3,X4),X0) != hAPP(hAPP(X3,X6),X0)
| ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK28(X0,X1,X2,X3,X5,X6)),X0)),X5))
& ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,sK28(X0,X1,X2,X3,X5,X6),hAPP(X6,sK28(X0,X1,X2,X3,X5,X6))) ) ) )
& ( ( hAPP(hAPP(X3,X4),X0) = hAPP(hAPP(X3,sK29(X0,X1,X2,X3,X4,X5)),X0)
& ! [X9] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X9),X0)),X5))
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X9,hAPP(sK29(X0,X1,X2,X3,X4,X5),X9)) ) )
| ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(hAPP(X3,X4),X0)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f1755,f1757,f1756]) ).
fof(f1756,plain,
! [X0,X1,X2,X3,X5,X6] :
( ? [X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X7),X0)),X5))
& ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,X7,hAPP(X6,X7)) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK28(X0,X1,X2,X3,X5,X6)),X0)),X5))
& ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,sK28(X0,X1,X2,X3,X5,X6),hAPP(X6,sK28(X0,X1,X2,X3,X5,X6))) ) ),
introduced(choice_axiom,[]) ).
fof(f1757,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X8] :
( hAPP(hAPP(X3,X8),X0) = hAPP(hAPP(X3,X4),X0)
& ! [X9] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X9),X0)),X5))
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X9,hAPP(X8,X9)) ) )
=> ( hAPP(hAPP(X3,X4),X0) = hAPP(hAPP(X3,sK29(X0,X1,X2,X3,X4,X5)),X0)
& ! [X9] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X9),X0)),X5))
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X9,hAPP(sK29(X0,X1,X2,X3,X4,X5),X9)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1755,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(hAPP(X3,X4),X0))
| ! [X6] :
( hAPP(hAPP(X3,X4),X0) != hAPP(hAPP(X3,X6),X0)
| ? [X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X7),X0)),X5))
& ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,X7,hAPP(X6,X7)) ) ) )
& ( ? [X8] :
( hAPP(hAPP(X3,X8),X0) = hAPP(hAPP(X3,X4),X0)
& ! [X9] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X9),X0)),X5))
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X9,hAPP(X8,X9)) ) )
| ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(hAPP(X3,X4),X0)) ) ),
inference(rectify,[],[f1754]) ).
fof(f1754,plain,
! [X3,X4,X1,X0,X2,X5] :
( ( c_Recdef_Owfrec__rel(X1,X4,X5,X0,X3,hAPP(hAPP(X0,X2),X3))
| ! [X6] :
( hAPP(hAPP(X0,X2),X3) != hAPP(hAPP(X0,X6),X3)
| ? [X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X7),X3)),X5))
& ~ c_Recdef_Owfrec__rel(X1,X4,X5,X0,X7,hAPP(X6,X7)) ) ) )
& ( ? [X6] :
( hAPP(hAPP(X0,X2),X3) = hAPP(hAPP(X0,X6),X3)
& ! [X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X7),X3)),X5))
| c_Recdef_Owfrec__rel(X1,X4,X5,X0,X7,hAPP(X6,X7)) ) )
| ~ c_Recdef_Owfrec__rel(X1,X4,X5,X0,X3,hAPP(hAPP(X0,X2),X3)) ) ),
inference(nnf_transformation,[],[f1222]) ).
fof(f1222,plain,
! [X3,X4,X1,X0,X2,X5] :
( c_Recdef_Owfrec__rel(X1,X4,X5,X0,X3,hAPP(hAPP(X0,X2),X3))
<=> ? [X6] :
( hAPP(hAPP(X0,X2),X3) = hAPP(hAPP(X0,X6),X3)
& ! [X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X7),X3)),X5))
| c_Recdef_Owfrec__rel(X1,X4,X5,X0,X7,hAPP(X6,X7)) ) ) ),
inference(ennf_transformation,[],[f722]) ).
fof(f722,plain,
! [X0,X5,X4,X1,X2,X3] :
( ? [X6] :
( hAPP(hAPP(X0,X2),X3) = hAPP(hAPP(X0,X6),X3)
& ! [X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X7),X3)),X5))
=> c_Recdef_Owfrec__rel(X1,X4,X5,X0,X7,hAPP(X6,X7)) ) )
<=> c_Recdef_Owfrec__rel(X1,X4,X5,X0,X3,hAPP(hAPP(X0,X2),X3)) ),
inference(rectify,[],[f53]) ).
fof(f53,axiom,
! [X32,X8,X35,X36,X16,X15] :
( c_Recdef_Owfrec__rel(X8,X16,X15,X32,X36,hAPP(hAPP(X32,X35),X36))
<=> ? [X37] :
( ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X38),X36)),X15))
=> c_Recdef_Owfrec__rel(X8,X16,X15,X32,X38,hAPP(X37,X38)) )
& hAPP(hAPP(X32,X35),X36) = hAPP(hAPP(X32,X37),X36) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Oequations) ).
fof(f13319,plain,
( ~ spl85_161
| spl85_58
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13318,f4426,f3290,f4223,f9793]) ).
fof(f13318,plain,
( ! [X2,X0] :
( X0 = X2
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13317]) ).
fof(f13317,plain,
( ! [X2,X0] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| X0 = X2
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13316,f9774]) ).
fof(f13316,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| X0 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10041,f9774]) ).
fof(f10041,plain,
( ! [X2,X0,X1] :
( X0 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3055,f9774]) ).
fof(f3055,plain,
! [X2,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X0 = X2 ),
inference(equality_resolution,[],[f2816]) ).
fof(f2816,plain,
! [X2,X3,X0,X1,X4] :
( X3 != X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X0 = X2 ),
inference(cnf_transformation,[],[f2048]) ).
fof(f2048,plain,
! [X0,X1,X2,X3,X4] :
( ( ( ( ( X2 != X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X4)),X1)) )
& ( ( ( X2 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X1)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X0)),X1))
| X0 = X3
| X2 != X4 ) )
| X2 = X3 )
& X3 != X4 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2)))
| ( X2 = X3
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X4)),X1)) )
| ( ( ( X2 != X4
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X1)) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X0)),X1))
& X0 != X3
& X2 = X4 ) )
& X2 != X3 )
| X3 = X4 ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X0 = X2 ),
inference(rectify,[],[f2047]) ).
fof(f2047,plain,
! [X4,X2,X0,X1,X3] :
( ( ( ( ( X0 != X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X2)) )
& ( ( ( X0 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X2)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X2))
| X1 = X4
| X0 != X3 ) )
| X0 = X1 )
& X1 != X3 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2),X4),X0))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2),X4),X0)))
| ( X0 = X1
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X2)) )
| ( ( ( X0 != X3
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X2)) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X2))
& X1 != X4
& X0 = X3 ) )
& X0 != X1 )
| X1 = X3 ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin))
| X0 = X4 ),
inference(flattening,[],[f2046]) ).
fof(f2046,plain,
! [X4,X2,X0,X1,X3] :
( ( ( ( ( X0 != X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X2)) )
& ( ( ( X0 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X2)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X2))
| X1 = X4
| X0 != X3 ) )
| X0 = X1 )
& X1 != X3 )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2),X4),X0))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2),X4),X0)))
| ( X0 = X1
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X2)) )
| ( ( ( X0 != X3
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X2)) )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X2))
& X1 != X4
& X0 = X3 ) )
& X0 != X1 )
| X1 = X3 ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin))
| X0 = X4 ),
inference(nnf_transformation,[],[f1306]) ).
fof(f1306,plain,
! [X4,X2,X0,X1,X3] :
( ( ( ( X0 != X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X2)) )
& ( ( ( X0 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X2)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X2))
| X1 = X4
| X0 != X3 ) )
| X0 = X1 )
& X1 != X3 )
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2),X4),X0))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin))
| X0 = X4 ),
inference(flattening,[],[f1305]) ).
fof(f1305,plain,
! [X4,X0,X2,X1,X3] :
( ( ( ( X0 != X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X2)) )
& ( ( ( X1 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X2))
| X0 != X3 )
& ( X0 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X2)) ) )
| X0 = X1 )
& X1 != X3 )
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2),X4),X0))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin))
| X0 = X4 ),
inference(ennf_transformation,[],[f664]) ).
fof(f664,plain,
! [X4,X0,X2,X1,X3] :
( X0 != X4
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin))
=> ( ( ( X0 = X1
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X2)) )
& ( X0 != X1
=> ( ( X0 = X3
=> ( X1 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X2)) ) )
& ( X0 != X3
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X2)) ) ) )
& X1 != X3 )
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X2),X4),X0))) ) ) ),
inference(rectify,[],[f34]) ).
fof(f34,axiom,
! [X23,X14,X12,X13,X24] :
( X23 != X24
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X12),c_Arrow__Order__Mirabelle_OLin))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X13)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X12),X24),X23)))
<=> ( X13 != X14
& ( X14 != X23
=> ( ( X13 != X23
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X13)),X12)) )
& ( X13 = X23
=> ( X14 = X24
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X24)),X12)) ) ) ) )
& ( X14 = X23
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X13)),X12)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__above) ).
fof(f13302,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_35
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10761,f4426,f3297,f3290,f9793]) ).
fof(f3297,plain,
( spl85_35
<=> hBOOL(hAPP(hAPP(v_F,v_P____),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_35])]) ).
fof(f10761,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_35
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3326,f9774]) ).
fof(f3326,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_member(X0),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_P____)))
| ~ spl85_35 ),
inference(resolution,[],[f3299,f2711]) ).
fof(f3299,plain,
( hBOOL(hAPP(hAPP(v_F,v_P____),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)))
| ~ spl85_35 ),
inference(avatar_component_clause,[],[f3297]) ).
fof(f13301,plain,
( spl85_168
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13300,f4426,f3290,f9793,f11279]) ).
fof(f11279,plain,
( spl85_168
<=> ! [X38,X37,X39] : c_Predicate_ORangeP(X38,X39,hAPP(v_F,v_Q____),X37) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_168])]) ).
fof(f13300,plain,
( ! [X212,X208,X209] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Predicate_ORangeP(X208,X209,hAPP(v_F,v_Q____),X212) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10304,f9774]) ).
fof(f10304,plain,
( ! [X212,X210,X211,X208,X209] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Predicate_ORangeP(X208,X209,c_Transitive__Closure_Ortranclp(X210,X211),X212) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4344,f9774]) ).
fof(f4344,plain,
! [X212,X213,X210,X211,X208,X209] :
( ~ hBOOL(hAPP(hAPP(X211,X213),X212))
| c_Predicate_ORangeP(X208,X209,c_Transitive__Closure_Ortranclp(X210,X211),X212) ),
inference(resolution,[],[f2173,f2837]) ).
fof(f2837,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X0))
| ~ hBOOL(hAPP(hAPP(X2,X3),X0)) ),
inference(cnf_transformation,[],[f2065]) ).
fof(f2065,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X2),X3),X0))
| ~ hBOOL(hAPP(hAPP(X2,X3),X0)) ),
inference(rectify,[],[f1077]) ).
fof(f1077,plain,
! [X2,X3,X1,X0] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X1),X0),X2))
| ~ hBOOL(hAPP(hAPP(X1,X0),X2)) ),
inference(ennf_transformation,[],[f784]) ).
fof(f784,plain,
! [X0,X2,X3,X1] :
( hBOOL(hAPP(hAPP(X1,X0),X2))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X3,X1),X0),X2)) ),
inference(rectify,[],[f186]) ).
fof(f186,axiom,
! [X14,X19,X13,X8] :
( hBOOL(hAPP(hAPP(X19,X14),X13))
=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X19),X14),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__rtranclp) ).
fof(f13297,plain,
( spl85_83
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13296,f4426,f3290,f9793,f6237]) ).
fof(f6237,plain,
( spl85_83
<=> ! [X2,X0,X1,X3] : ~ c_Predicate_ORangeP(X2,X1,X3,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_83])]) ).
fof(f13296,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ c_Predicate_ORangeP(X2,X1,X3,X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9891,f9774]) ).
fof(f9891,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(v_F,v_Q____),X0))
| ~ c_Predicate_ORangeP(X2,X1,X3,X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2174,f9774]) ).
fof(f2174,plain,
! [X2,X3,X0,X1] :
( ~ c_Predicate_ORangeP(X2,X1,X3,X0)
| hBOOL(hAPP(hAPP(X3,sK0(X0,X3)),X0)) ),
inference(cnf_transformation,[],[f1503]) ).
fof(f13292,plain,
( spl85_178
| spl85_161
| ~ spl85_34
| ~ spl85_64
| ~ spl85_74 ),
inference(avatar_split_clause,[],[f13291,f4726,f4426,f3290,f9793,f11730]) ).
fof(f4726,plain,
( spl85_74
<=> ! [X66] :
( c_Arrow__Order__Mirabelle_Odictator(sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),X66)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X66,sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))),c_Arrow__Order__Mirabelle_OProf)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_74])]) ).
fof(f13291,plain,
( ! [X66] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X66) )
| ~ spl85_34
| ~ spl85_64
| ~ spl85_74 ),
inference(forward_demodulation,[],[f10827,f9774]) ).
fof(f10827,plain,
( ! [X66] :
( c_Arrow__Order__Mirabelle_Odictator(sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),X66)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64
| ~ spl85_74 ),
inference(backward_demodulation,[],[f4727,f9774]) ).
fof(f4727,plain,
( ! [X66] :
( c_Arrow__Order__Mirabelle_Odictator(sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),X66)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X66,sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))),c_Arrow__Order__Mirabelle_OProf)) )
| ~ spl85_74 ),
inference(avatar_component_clause,[],[f4726]) ).
fof(f13285,plain,
( spl85_58
| spl85_161
| ~ spl85_25
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13284,f4426,f3290,f3223,f9793,f4223]) ).
fof(f13284,plain,
( ! [X0,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| X0 = X1 )
| ~ spl85_25
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13283]) ).
fof(f13283,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_25
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13282,f9774]) ).
fof(f13282,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),hAPP(v_F,v_Q____))) )
| ~ spl85_25
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10136,f9774]) ).
fof(f10136,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),hAPP(v_F,v_Q____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),hAPP(v_F,v_Q____)))
| X0 = X1 )
| ~ spl85_25
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3633,f9774]) ).
fof(f3633,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),hAPP(v_F,v_Q____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),hAPP(v_F,v_Q____))) )
| ~ spl85_25 ),
inference(resolution,[],[f2888,f3225]) ).
fof(f2888,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),X2))
| X0 = X1 ),
inference(cnf_transformation,[],[f2110]) ).
fof(f2110,plain,
! [X0,X1,X2] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin))
| ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),X2)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),X2))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),X2)) ) ) ),
inference(rectify,[],[f2109]) ).
fof(f2109,plain,
! [X1,X2,X0] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),X0))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X0)) )
& ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),X0)) ) ) ),
inference(nnf_transformation,[],[f1482]) ).
fof(f1482,plain,
! [X1,X2,X0] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),X0))
<=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X0)) ) ),
inference(flattening,[],[f1481]) ).
fof(f1481,plain,
! [X1,X2,X0] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),X0))
<=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X0)) )
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(ennf_transformation,[],[f996]) ).
fof(f996,plain,
! [X1,X2,X0] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
=> ( X1 != X2
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),X0))
<=> ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X0)) ) ) ),
inference(rectify,[],[f28]) ).
fof(f28,axiom,
! [X12,X14,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X12),c_Arrow__Order__Mirabelle_OLin))
=> ( X13 != X14
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X13)),X12))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X13),X14)),X12)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
fof(f13278,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10736,f4426,f3371,f3290,f9793]) ).
fof(f3371,plain,
( spl85_40
<=> ! [X22,X20,X21,X23] : hBOOL(hAPP(hAPP(c_Product__Type_OPair(X20,X21),X22),X23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_40])]) ).
fof(f10736,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4244,f9774]) ).
fof(f4244,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),c_member(X0)),c_Product__Type_OPair(X2,X3)),X1))
| ~ spl85_40 ),
inference(superposition,[],[f3652,f2728]) ).
fof(f3652,plain,
( ! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(c_Product__Type_OPair(X2,X3),X4)))
| ~ spl85_40 ),
inference(resolution,[],[f3372,f2711]) ).
fof(f3372,plain,
( ! [X21,X22,X23,X20] : hBOOL(hAPP(hAPP(c_Product__Type_OPair(X20,X21),X22),X23))
| ~ spl85_40 ),
inference(avatar_component_clause,[],[f3371]) ).
fof(f13273,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13272,f4426,f3290,f9793]) ).
fof(f13272,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13271]) ).
fof(f13271,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13270,f9774]) ).
fof(f13270,plain,
( ! [X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13269]) ).
fof(f13269,plain,
( ! [X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13268,f9774]) ).
fof(f13268,plain,
( ! [X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10100,f9774]) ).
fof(f10100,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),X1)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2792,f9774]) ).
fof(f13261,plain,
( spl85_179
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13260,f4426,f3290,f9793,f11785]) ).
fof(f11785,plain,
( spl85_179
<=> ! [X2,X0,X1] :
( c_Relation_Orefl__on(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(hAPP(v_F,v_Q____),X2,hAPP(v_F,v_Q____)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_179])]) ).
fof(f13260,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ c_Orderings_Oord__class_Oless__eq(hAPP(v_F,v_Q____),X0,hAPP(v_F,v_Q____))
| c_Relation_Orefl__on(X1,X2,X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13259,f9774]) ).
fof(f13259,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| c_Relation_Orefl__on(X1,X2,X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10084,f9774]) ).
fof(f10084,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2)))
| c_Relation_Orefl__on(X1,X2,X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2230,f9774]) ).
fof(f2230,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK6(X0,X1,X2)),sK6(X0,X1,X2))),X0))
| c_Relation_Orefl__on(X1,X2,X0) ),
inference(cnf_transformation,[],[f1557]) ).
fof(f1557,plain,
! [X0,X1,X2] :
( ( c_Relation_Orefl__on(X1,X2,X0)
| ( hBOOL(hAPP(hAPP(c_member(X1),sK6(X0,X1,X2)),X2))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK6(X0,X1,X2)),sK6(X0,X1,X2))),X0)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2))) )
& ( ( ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X4)),X0)) )
& c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2))) )
| ~ c_Relation_Orefl__on(X1,X2,X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f1555,f1556]) ).
fof(f1556,plain,
! [X0,X1,X2] :
( ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X0)) )
=> ( hBOOL(hAPP(hAPP(c_member(X1),sK6(X0,X1,X2)),X2))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK6(X0,X1,X2)),sK6(X0,X1,X2))),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1555,plain,
! [X0,X1,X2] :
( ( c_Relation_Orefl__on(X1,X2,X0)
| ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X0)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2))) )
& ( ( ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X4)),X0)) )
& c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2))) )
| ~ c_Relation_Orefl__on(X1,X2,X0) ) ),
inference(rectify,[],[f1554]) ).
fof(f1554,plain,
! [X0,X2,X1] :
( ( c_Relation_Orefl__on(X2,X1,X0)
| ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X3)),X0)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Product__Type_OSigma(X2,X2,X1,c_COMBK(tc_fun(X2,tc_HOL_Obool),X2,X1))) )
& ( ( ! [X3] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X3)),X0)) )
& c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Product__Type_OSigma(X2,X2,X1,c_COMBK(tc_fun(X2,tc_HOL_Obool),X2,X1))) )
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
inference(flattening,[],[f1553]) ).
fof(f1553,plain,
! [X0,X2,X1] :
( ( c_Relation_Orefl__on(X2,X1,X0)
| ? [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X3)),X0)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Product__Type_OSigma(X2,X2,X1,c_COMBK(tc_fun(X2,tc_HOL_Obool),X2,X1))) )
& ( ( ! [X3] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X3)),X0)) )
& c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Product__Type_OSigma(X2,X2,X1,c_COMBK(tc_fun(X2,tc_HOL_Obool),X2,X1))) )
| ~ c_Relation_Orefl__on(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f1462]) ).
fof(f1462,plain,
! [X0,X2,X1] :
( c_Relation_Orefl__on(X2,X1,X0)
<=> ( ! [X3] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X3)),X0)) )
& c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Product__Type_OSigma(X2,X2,X1,c_COMBK(tc_fun(X2,tc_HOL_Obool),X2,X1))) ) ),
inference(ennf_transformation,[],[f972]) ).
fof(f972,plain,
! [X0,X2,X1] :
( ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X3),X1))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X3)),X0)) )
& c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,c_Product__Type_OSigma(X2,X2,X1,c_COMBK(tc_fun(X2,tc_HOL_Obool),X2,X1))) )
<=> c_Relation_Orefl__on(X2,X1,X0) ),
inference(rectify,[],[f323]) ).
fof(f323,axiom,
! [X19,X10,X8] :
( c_Relation_Orefl__on(X8,X10,X19)
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X10))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X2),X2)),X19)) )
& c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),X19,c_Product__Type_OSigma(X8,X8,X10,c_COMBK(tc_fun(X8,tc_HOL_Obool),X8,X10))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__def) ).
fof(f13258,plain,
( ~ spl85_203
| ~ spl85_34
| ~ spl85_64
| spl85_65 ),
inference(avatar_split_clause,[],[f13253,f4431,f4426,f3290,f13255]) ).
fof(f13255,plain,
( spl85_203
<=> hAPP(v_F,v_Q____) = c_FuncSet_OPi(hAPP(v_F,v_Q____),hAPP(v_F,v_Q____),c_Arrow__Order__Mirabelle_OProf,hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_203])]) ).
fof(f4431,plain,
( spl85_65
<=> c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_65])]) ).
fof(f13253,plain,
( hAPP(v_F,v_Q____) != c_FuncSet_OPi(hAPP(v_F,v_Q____),hAPP(v_F,v_Q____),c_Arrow__Order__Mirabelle_OProf,hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64
| spl85_65 ),
inference(forward_demodulation,[],[f13252,f9774]) ).
fof(f13252,plain,
( hAPP(v_F,v_Q____) != c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,hAPP(v_F,v_Q____)),hAPP(v_F,v_Q____),c_Arrow__Order__Mirabelle_OProf,hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64
| spl85_65 ),
inference(forward_demodulation,[],[f13251,f9774]) ).
fof(f13251,plain,
( hAPP(v_F,v_Q____) != c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(hAPP(v_F,v_Q____),tc_HOL_Obool)),tc_fun(hAPP(v_F,v_Q____),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64
| spl85_65 ),
inference(forward_demodulation,[],[f13250,f9774]) ).
fof(f13250,plain,
( hAPP(v_F,v_Q____) != c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(hAPP(v_F,v_Q____),tc_HOL_Obool)),tc_fun(hAPP(v_F,v_Q____),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(hAPP(v_F,v_Q____),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(hAPP(v_F,v_Q____),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))
| ~ spl85_34
| ~ spl85_64
| spl85_65 ),
inference(forward_demodulation,[],[f10971,f9774]) ).
fof(f10971,plain,
( c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(hAPP(v_F,v_Q____),tc_HOL_Obool)),tc_fun(hAPP(v_F,v_Q____),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(hAPP(v_F,v_Q____),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(hAPP(v_F,v_Q____),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(hAPP(v_F,v_Q____),tc_HOL_Obool)),tc_fun(hAPP(v_F,v_Q____),tc_HOL_Obool)),tc_HOL_Obool))
| ~ spl85_34
| ~ spl85_64
| spl85_65 ),
inference(backward_demodulation,[],[f4432,f9774]) ).
fof(f4432,plain,
( c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool))
| spl85_65 ),
inference(avatar_component_clause,[],[f4431]) ).
fof(f13234,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13233,f4426,f3371,f3290,f9793]) ).
fof(f13233,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13232]) ).
fof(f13232,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13231,f9774]) ).
fof(f13231,plain,
( ! [X14,X15,X13] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_Product__Type_OPair(X13,X14),X15)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10206,f9774]) ).
fof(f10206,plain,
( ! [X14,X15,X13] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),hAPP(c_Product__Type_OPair(X13,X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_Product__Type_OPair(X13,X14),X15)),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4237,f9774]) ).
fof(f4237,plain,
( ! [X16,X14,X17,X15,X13] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X16),X17)),hAPP(c_Product__Type_OPair(X13,X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_Product__Type_OPair(X13,X14),X15)),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_40 ),
inference(resolution,[],[f3652,f2792]) ).
fof(f13226,plain,
( ~ spl85_161
| spl85_58
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13225,f4426,f3290,f4223,f9793]) ).
fof(f13225,plain,
( ! [X3,X1] :
( X1 = X3
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f13224]) ).
fof(f13224,plain,
( ! [X3,X1] :
( X1 = X3
| ~ hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13223,f9774]) ).
fof(f13223,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(v_F,v_Q____) != c_Product__Type_OSigma(X0,X4,X3,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2))
| ~ hBOOL(hAPP(v_F,v_Q____))
| X1 = X3 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10341,f9774]) ).
fof(f10341,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| X1 = X3
| c_Product__Type_OSigma(X0,X4,X3,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)) != c_Product__Type_OSigma(X0,X4,X1,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2625,f9774]) ).
fof(f2625,plain,
! [X2,X3,X0,X1,X4,X5] :
( X1 = X3
| c_Product__Type_OSigma(X0,X4,X3,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)) != c_Product__Type_OSigma(X0,X4,X1,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X2)) ),
inference(cnf_transformation,[],[f1881]) ).
fof(f1881,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X4),X5),X2))
| ( ( X1 = X3
| c_Product__Type_OSigma(X0,X4,X3,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)) != c_Product__Type_OSigma(X0,X4,X1,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)) )
& ( c_Product__Type_OSigma(X0,X4,X3,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)) = c_Product__Type_OSigma(X0,X4,X1,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2))
| X1 != X3 ) ) ),
inference(rectify,[],[f1880]) ).
fof(f1880,plain,
! [X2,X1,X4,X3,X5,X0] :
( ~ hBOOL(hAPP(hAPP(c_member(X5),X0),X4))
| ( ( X1 = X3
| c_Product__Type_OSigma(X2,X5,X3,c_COMBK(tc_fun(X5,tc_HOL_Obool),X2,X4)) != c_Product__Type_OSigma(X2,X5,X1,c_COMBK(tc_fun(X5,tc_HOL_Obool),X2,X4)) )
& ( c_Product__Type_OSigma(X2,X5,X3,c_COMBK(tc_fun(X5,tc_HOL_Obool),X2,X4)) = c_Product__Type_OSigma(X2,X5,X1,c_COMBK(tc_fun(X5,tc_HOL_Obool),X2,X4))
| X1 != X3 ) ) ),
inference(nnf_transformation,[],[f1280]) ).
fof(f1280,plain,
! [X2,X1,X4,X3,X5,X0] :
( ~ hBOOL(hAPP(hAPP(c_member(X5),X0),X4))
| ( X1 = X3
<=> c_Product__Type_OSigma(X2,X5,X3,c_COMBK(tc_fun(X5,tc_HOL_Obool),X2,X4)) = c_Product__Type_OSigma(X2,X5,X1,c_COMBK(tc_fun(X5,tc_HOL_Obool),X2,X4)) ) ),
inference(ennf_transformation,[],[f794]) ).
fof(f794,plain,
! [X2,X0,X4,X1,X5,X3] :
( hBOOL(hAPP(hAPP(c_member(X5),X0),X4))
=> ( X1 = X3
<=> c_Product__Type_OSigma(X2,X5,X3,c_COMBK(tc_fun(X5,tc_HOL_Obool),X2,X4)) = c_Product__Type_OSigma(X2,X5,X1,c_COMBK(tc_fun(X5,tc_HOL_Obool),X2,X4)) ) ),
inference(rectify,[],[f303]) ).
fof(f303,axiom,
! [X14,X9,X16,X10,X47,X8] :
( hBOOL(hAPP(hAPP(c_member(X8),X14),X47))
=> ( c_Product__Type_OSigma(X16,X8,X10,c_COMBK(tc_fun(X8,tc_HOL_Obool),X16,X47)) = c_Product__Type_OSigma(X16,X8,X9,c_COMBK(tc_fun(X8,tc_HOL_Obool),X16,X47))
<=> X9 = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__eq__cancel2) ).
fof(f13219,plain,
( spl85_61
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10811,f4426,f3290,f9793,f4384]) ).
fof(f10811,plain,
( ! [X31] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(X31) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4112,f9774]) ).
fof(f4112,plain,
! [X31,X32,X30] :
( hBOOL(hAPP(hAPP(c_member(X32),c_Orderings_Obot__class_Obot(tc_fun(X30,tc_HOL_Obool))),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X30,tc_HOL_Obool)),X31)))
| ~ hBOOL(X31) ),
inference(superposition,[],[f2711,f2235]) ).
fof(f2235,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X0,
inference(cnf_transformation,[],[f892]) ).
fof(f892,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))) = X0,
inference(rectify,[],[f429]) ).
fof(f429,axiom,
! [X10,X8] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X10),c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__right) ).
fof(f13215,plain,
( spl85_107
| spl85_202
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10983,f4426,f3290,f13212,f7220]) ).
fof(f7220,plain,
( spl85_107
<=> ! [X0] : ~ class_Orderings_Oorder(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_107])]) ).
fof(f13212,plain,
( spl85_202
<=> class_Orderings_Oorder(hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_202])]) ).
fof(f10983,plain,
( ! [X0] :
( class_Orderings_Oorder(hAPP(v_F,v_Q____))
| ~ class_Orderings_Oorder(X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2423,f9774]) ).
fof(f2423,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X1,X0))
| ~ class_Orderings_Oorder(X0) ),
inference(cnf_transformation,[],[f1704]) ).
fof(f1704,plain,
! [X0,X1] :
( class_Orderings_Oorder(tc_fun(X1,X0))
| ~ class_Orderings_Oorder(X0) ),
inference(rectify,[],[f1118]) ).
fof(f1118,plain,
! [X1,X0] :
( class_Orderings_Oorder(tc_fun(X0,X1))
| ~ class_Orderings_Oorder(X1) ),
inference(ennf_transformation,[],[f917]) ).
fof(f917,plain,
! [X0,X1] :
( class_Orderings_Oorder(X1)
=> class_Orderings_Oorder(tc_fun(X0,X1)) ),
inference(rectify,[],[f503]) ).
fof(f503,axiom,
! [X73,X74] :
( class_Orderings_Oorder(X74)
=> class_Orderings_Oorder(tc_fun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(f13210,plain,
( spl85_167
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10925,f4426,f3290,f9793,f11209]) ).
fof(f11209,plain,
( spl85_167
<=> ! [X2,X0] : ~ hBOOL(hAPP(X2,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_167])]) ).
fof(f10925,plain,
( ! [X3,X0] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(X0,X3)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2404,f9774]) ).
fof(f2404,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X0),X3))
| ~ hBOOL(hAPP(X0,X3)) ),
inference(cnf_transformation,[],[f1689]) ).
fof(f1689,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(X0,X3))
| X2 = X3
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X0),X3)) )
& ( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X0),X3))
| ( ~ hBOOL(hAPP(X0,X3))
& X2 != X3 ) ) ),
inference(rectify,[],[f1688]) ).
fof(f1688,plain,
! [X0,X2,X1,X3] :
( ( hBOOL(hAPP(X0,X3))
| X1 = X3
| ~ hBOOL(hAPP(c_Set_Oinsert(X2,X1,X0),X3)) )
& ( hBOOL(hAPP(c_Set_Oinsert(X2,X1,X0),X3))
| ( ~ hBOOL(hAPP(X0,X3))
& X1 != X3 ) ) ),
inference(flattening,[],[f1687]) ).
fof(f1687,plain,
! [X0,X2,X1,X3] :
( ( hBOOL(hAPP(X0,X3))
| X1 = X3
| ~ hBOOL(hAPP(c_Set_Oinsert(X2,X1,X0),X3)) )
& ( hBOOL(hAPP(c_Set_Oinsert(X2,X1,X0),X3))
| ( ~ hBOOL(hAPP(X0,X3))
& X1 != X3 ) ) ),
inference(nnf_transformation,[],[f1012]) ).
fof(f1012,plain,
! [X0,X2,X1,X3] :
( ( hBOOL(hAPP(X0,X3))
| X1 = X3 )
<=> hBOOL(hAPP(c_Set_Oinsert(X2,X1,X0),X3)) ),
inference(rectify,[],[f296]) ).
fof(f296,axiom,
! [X10,X13,X8,X14] :
( hBOOL(hAPP(c_Set_Oinsert(X8,X13,X10),X14))
<=> ( hBOOL(hAPP(X10,X14))
| X13 = X14 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
fof(f13206,plain,
( spl85_61
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10869,f4426,f3290,f9793,f4384]) ).
fof(f10869,plain,
( ! [X1] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(X1) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3359,f9774]) ).
fof(f3359,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),c_COMBI(X0)))
| ~ hBOOL(X1) ),
inference(superposition,[],[f2711,f2523]) ).
fof(f13199,plain,
( spl85_170
| ~ spl85_184
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13198,f4426,f3290,f9793,f12006,f11305]) ).
fof(f12006,plain,
( spl85_184
<=> class_Orderings_Obot(hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_184])]) ).
fof(f13198,plain,
( ! [X51,X52] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ class_Orderings_Obot(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X52,X51)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10943,f9774]) ).
fof(f10943,plain,
( ! [X50,X51,X52] :
( hBOOL(hAPP(X52,X51))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ class_Orderings_Obot(tc_fun(X50,tc_HOL_Obool)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4258,f9774]) ).
fof(f13197,plain,
( spl85_178
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13196,f4426,f3290,f9793,f11730]) ).
fof(f13196,plain,
( ! [X15] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X15) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13195]) ).
fof(f13195,plain,
( ! [X15] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X15)
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13194,f9774]) ).
fof(f13194,plain,
( ! [X18,X16,X17,X15] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X15)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17)),X18),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),c_COMBK(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16)))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10826,f9774]) ).
fof(f10826,plain,
( ! [X18,X16,X17,X15] :
( c_Arrow__Order__Mirabelle_Odictator(sK65(X16,X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18),X15)
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17)),X18),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),c_COMBK(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16)))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3871,f9774]) ).
fof(f3871,plain,
! [X18,X16,X17,X15] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X15,sK65(X16,X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18))),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17)),X18),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),c_COMBK(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16))))
| c_Arrow__Order__Mirabelle_Odictator(sK65(X16,X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18),X15) ),
inference(resolution,[],[f2451,f2719]) ).
fof(f13193,plain,
( spl85_161
| spl85_61
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10751,f4426,f3290,f4384,f9793]) ).
fof(f10751,plain,
( ! [X28] :
( ~ hBOOL(X28)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3739,f9774]) ).
fof(f3739,plain,
! [X28,X29,X27] :
( ~ hBOOL(X28)
| hBOOL(hAPP(hAPP(c_member(X29),X28),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X27,tc_HOL_Obool)),X28))) ),
inference(superposition,[],[f2711,f2397]) ).
fof(f2397,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(cnf_transformation,[],[f686]) ).
fof(f686,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X0) = X0,
inference(rectify,[],[f97]) ).
fof(f97,axiom,
! [X10,X8] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X10),X10) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb) ).
fof(f13191,plain,
( spl85_201
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10848,f4426,f3290,f9793,f13189]) ).
fof(f13189,plain,
( spl85_201
<=> ! [X100,X101,X98,X99] : c_Predicate_ORangeP(X98,X99,c_member(X100),X101) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_201])]) ).
fof(f10848,plain,
( ! [X101,X98,X99,X100] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Predicate_ORangeP(X98,X99,c_member(X100),X101) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4319,f9774]) ).
fof(f4319,plain,
! [X101,X98,X99,X104,X102,X103,X100] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X100,X103)),X102),c_FuncSet_OPi(X100,X103,X101,X104)))
| c_Predicate_ORangeP(X98,X99,c_member(X100),X101) ),
inference(resolution,[],[f2173,f2649]) ).
fof(f13187,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10901,f4426,f3290,f9793]) ).
fof(f10901,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3292,f9774]) ).
fof(f13169,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13168,f4426,f3290,f9793]) ).
fof(f13168,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13167]) ).
fof(f13167,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10626,f9774]) ).
fof(f10626,plain,
( ! [X10,X8,X6,X9,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(X10),c_FuncSet_OPi(X5,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X5,X9))),hAPP(c_member(tc_fun(X5,X6)),X7)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3492,f9774]) ).
fof(f3492,plain,
! [X10,X8,X6,X9,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(X10),c_FuncSet_OPi(X5,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X5,X9))),hAPP(c_member(tc_fun(X5,X6)),X7)))
| hBOOL(hAPP(hAPP(c_member(X5),sK65(X9,X6,X8,X5,X7)),X8)) ),
inference(resolution,[],[f2719,f2711]) ).
fof(f13161,plain,
( spl85_58
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13160,f4426,f3290,f9793,f4223]) ).
fof(f13160,plain,
( ! [X3,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| X1 = X3 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10125,f9774]) ).
fof(f10125,plain,
( ! [X2,X3,X1] :
( X1 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Omktop(X2,X3))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3097,f9774]) ).
fof(f3097,plain,
! [X2,X3,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Omktop(X2,X3)))
| X1 = X3 ),
inference(duplicate_literal_removal,[],[f3018]) ).
fof(f3018,plain,
! [X2,X3,X1] :
( X1 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Omktop(X2,X3)))
| X1 = X3 ),
inference(equality_resolution,[],[f2472]) ).
fof(f2472,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Omktop(X2,X0)))
| X0 = X1
| X0 != X3
| X1 = X3 ),
inference(cnf_transformation,[],[f1743]) ).
fof(f1743,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Omktop(X2,X0)))
| X0 = X1
| ( X0 != X3
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X2)) )
| ( X1 = X3
& X0 = X3 ) )
& ( ( X0 != X1
& ( X0 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X2)) )
& ( X1 != X3
| X0 != X3 ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Omktop(X2,X0))) ) ),
inference(rectify,[],[f1742]) ).
fof(f1742,plain,
! [X2,X3,X0,X1] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Omktop(X0,X2)))
| X2 = X3
| ( X1 != X2
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X0)) )
| ( X1 = X3
& X1 = X2 ) )
& ( ( X2 != X3
& ( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X0)) )
& ( X1 != X3
| X1 != X2 ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Omktop(X0,X2))) ) ),
inference(flattening,[],[f1741]) ).
fof(f1741,plain,
! [X2,X3,X0,X1] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Omktop(X0,X2)))
| X2 = X3
| ( X1 != X2
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X0)) )
| ( X1 = X3
& X1 = X2 ) )
& ( ( X2 != X3
& ( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X0)) )
& ( X1 != X3
| X1 != X2 ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Omktop(X0,X2))) ) ),
inference(nnf_transformation,[],[f1141]) ).
fof(f1141,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Omktop(X0,X2)))
<=> ( X2 != X3
& ( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X0)) )
& ( X1 != X3
| X1 != X2 ) ) ),
inference(ennf_transformation,[],[f670]) ).
fof(f670,plain,
! [X1,X3,X0,X2] :
( ( X2 != X3
& ( X1 != X2
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),X0)) )
& ( X1 = X2
=> X1 != X3 ) )
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X1)),c_Arrow__Order__Mirabelle_Omktop(X0,X2))) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X12,X13,X11,X14] :
( ( X11 != X14
& ( X11 != X13
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X13)),X12)) )
& ( X11 = X13
=> X13 != X14 ) )
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X13)),c_Arrow__Order__Mirabelle_Omktop(X12,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mktop) ).
fof(f13153,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_36
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10865,f4426,f3306,f3290,f9793]) ).
fof(f3306,plain,
( spl85_36
<=> hBOOL(hAPP(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),v_F)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_36])]) ).
fof(f10865,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_36
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3535,f9774]) ).
fof(f3535,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_member(X0),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ~ spl85_36 ),
inference(resolution,[],[f3308,f2711]) ).
fof(f3308,plain,
( hBOOL(hAPP(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),v_F))
| ~ spl85_36 ),
inference(avatar_component_clause,[],[f3306]) ).
fof(f13148,plain,
( spl85_200
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13144,f4426,f3290,f9793,f13146]) ).
fof(f13146,plain,
( spl85_200
<=> ! [X2,X0,X3] : ~ c_Predicate_ORangeP(X2,X0,hAPP(v_F,v_Q____),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_200])]) ).
fof(f13144,plain,
( ! [X2,X3,X0] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ c_Predicate_ORangeP(X2,X0,hAPP(v_F,v_Q____),X3) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10475,f9774]) ).
fof(f10475,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),X3),c_Relation_ORange(X2,X0,X1)))
| ~ c_Predicate_ORangeP(X2,X0,hAPP(v_F,v_Q____),X3) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2288,f9774]) ).
fof(f2288,plain,
! [X2,X3,X0,X1] :
( ~ c_Predicate_ORangeP(X2,X0,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_fun(X0,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X0,tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_fun(X0,tc_HOL_Obool)),X2,c_COMBC(X0,tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X0,tc_prod(X2,X0)),tc_fun(X0,tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X0),tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool),X0,c_member(tc_prod(X2,X0)))),c_Product__Type_OPair(X2,X0)))),X1),X3)
| hBOOL(hAPP(hAPP(c_member(X0),X3),c_Relation_ORange(X2,X0,X1))) ),
inference(cnf_transformation,[],[f1596]) ).
fof(f1596,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_member(X0),X3),c_Relation_ORange(X2,X0,X1)))
| ~ c_Predicate_ORangeP(X2,X0,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_fun(X0,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X0,tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_fun(X0,tc_HOL_Obool)),X2,c_COMBC(X0,tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X0,tc_prod(X2,X0)),tc_fun(X0,tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X0),tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool),X0,c_member(tc_prod(X2,X0)))),c_Product__Type_OPair(X2,X0)))),X1),X3) )
& ( c_Predicate_ORangeP(X2,X0,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_fun(X0,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X0,tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_fun(X0,tc_HOL_Obool)),X2,c_COMBC(X0,tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X0,tc_prod(X2,X0)),tc_fun(X0,tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X0),tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool),X0,c_member(tc_prod(X2,X0)))),c_Product__Type_OPair(X2,X0)))),X1),X3)
| ~ hBOOL(hAPP(hAPP(c_member(X0),X3),c_Relation_ORange(X2,X0,X1))) ) ),
inference(rectify,[],[f1595]) ).
fof(f1595,plain,
! [X3,X0,X2,X1] :
( ( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Relation_ORange(X2,X3,X0)))
| ~ c_Predicate_ORangeP(X2,X3,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2,c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3,c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3)))),X0),X1) )
& ( c_Predicate_ORangeP(X2,X3,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2,c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3,c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3)))),X0),X1)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X1),c_Relation_ORange(X2,X3,X0))) ) ),
inference(nnf_transformation,[],[f769]) ).
fof(f769,plain,
! [X3,X0,X2,X1] :
( hBOOL(hAPP(hAPP(c_member(X3),X1),c_Relation_ORange(X2,X3,X0)))
<=> c_Predicate_ORangeP(X2,X3,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X2,c_COMBC(X3,tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_prod(X2,X3)),tc_fun(X3,tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X3),tc_fun(tc_fun(tc_prod(X2,X3),tc_HOL_Obool),tc_HOL_Obool),X3,c_member(tc_prod(X2,X3)))),c_Product__Type_OPair(X2,X3)))),X0),X1) ),
inference(rectify,[],[f165]) ).
fof(f165,axiom,
! [X19,X14,X8,X16] :
( hBOOL(hAPP(hAPP(c_member(X16),X14),c_Relation_ORange(X8,X16,X19)))
<=> c_Predicate_ORangeP(X8,X16,hAPP(hAPP(c_COMBC(X8,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X8,c_COMBC(X16,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_prod(X8,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),X8,c_COMBB(tc_prod(X8,X16),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool),X16,c_member(tc_prod(X8,X16)))),c_Product__Type_OPair(X8,X16)))),X19),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeP__Range__eq) ).
fof(f13135,plain,
( spl85_161
| spl85_179
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13134,f4426,f3290,f11785,f9793]) ).
fof(f13134,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(hAPP(v_F,v_Q____),X2,hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| c_Relation_Orefl__on(X0,X1,X2) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13133,f9774]) ).
fof(f13133,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,hAPP(v_F,v_Q____))
| c_Relation_Orefl__on(X0,X1,X2)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10068,f9774]) ).
fof(f10068,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,c_Product__Type_OSigma(X0,X0,X1,c_COMBK(tc_fun(X0,tc_HOL_Obool),X0,X1)))
| hBOOL(hAPP(v_F,v_Q____))
| c_Relation_Orefl__on(X0,X1,X2) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2556,f9774]) ).
fof(f2556,plain,
! [X2,X0,X1] :
( c_Relation_Orefl__on(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,c_Product__Type_OSigma(X0,X0,X1,c_COMBK(tc_fun(X0,tc_HOL_Obool),X0,X1)))
| hBOOL(hAPP(hAPP(c_member(X0),sK44(X0,X1,X2)),X1)) ),
inference(cnf_transformation,[],[f1825]) ).
fof(f1825,plain,
! [X0,X1,X2] :
( c_Relation_Orefl__on(X0,X1,X2)
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK44(X0,X1,X2)),sK44(X0,X1,X2))),X2))
& hBOOL(hAPP(hAPP(c_member(X0),sK44(X0,X1,X2)),X1)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,c_Product__Type_OSigma(X0,X0,X1,c_COMBK(tc_fun(X0,tc_HOL_Obool),X0,X1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44])],[f1823,f1824]) ).
fof(f1824,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X3),X3)),X2))
& hBOOL(hAPP(hAPP(c_member(X0),X3),X1)) )
=> ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK44(X0,X1,X2)),sK44(X0,X1,X2))),X2))
& hBOOL(hAPP(hAPP(c_member(X0),sK44(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1823,plain,
! [X0,X1,X2] :
( c_Relation_Orefl__on(X0,X1,X2)
| ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X3),X3)),X2))
& hBOOL(hAPP(hAPP(c_member(X0),X3),X1)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,c_Product__Type_OSigma(X0,X0,X1,c_COMBK(tc_fun(X0,tc_HOL_Obool),X0,X1))) ),
inference(rectify,[],[f1443]) ).
fof(f1443,plain,
! [X1,X2,X0] :
( c_Relation_Orefl__on(X1,X2,X0)
| ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X0))
& hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2))) ),
inference(flattening,[],[f1442]) ).
fof(f1442,plain,
! [X2,X0,X1] :
( c_Relation_Orefl__on(X1,X2,X0)
| ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X0))
& hBOOL(hAPP(hAPP(c_member(X1),X3),X2)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2))) ),
inference(ennf_transformation,[],[f852]) ).
fof(f852,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2)))
=> ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X1),X3),X2))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),X0)) )
=> c_Relation_Orefl__on(X1,X2,X0) ) ),
inference(rectify,[],[f324]) ).
fof(f324,axiom,
! [X19,X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),X19,c_Product__Type_OSigma(X8,X8,X10,c_COMBK(tc_fun(X8,tc_HOL_Obool),X8,X10)))
=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X10))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X2),X2)),X19)) )
=> c_Relation_Orefl__on(X8,X10,X19) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onI) ).
fof(f13132,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13131,f4426,f3290,f9793]) ).
fof(f13131,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9860,f9774]) ).
fof(f9860,plain,
( ! [X11] : hBOOL(hAPP(hAPP(v_F,v_Q____),X11))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f9785,f9774]) ).
fof(f9785,plain,
( ! [X10,X11] : hBOOL(hAPP(hAPP(X10,hAPP(v_F,v_Q____)),X11))
| ~ spl85_34
| ~ spl85_64 ),
inference(superposition,[],[f9759,f2585]) ).
fof(f2585,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(hAPP(hAPP(c_COMBC(X3,X2,X4),X1),X0),X5) = hAPP(hAPP(X1,X5),X0),
inference(cnf_transformation,[],[f1844]) ).
fof(f1844,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(hAPP(hAPP(c_COMBC(X3,X2,X4),X1),X0),X5) = hAPP(hAPP(X1,X5),X0),
inference(rectify,[],[f961]) ).
fof(f961,plain,
! [X4,X2,X1,X5,X0,X3] : hAPP(hAPP(hAPP(c_COMBC(X5,X1,X0),X2),X4),X3) = hAPP(hAPP(X2,X3),X4),
inference(rectify,[],[f527]) ).
fof(f527,axiom,
! [X8,X31,X18,X15,X66,X16] : hAPP(hAPP(hAPP(c_COMBC(X16,X31,X8),X18),X66),X15) = hAPP(hAPP(X18,X15),X66),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBC__1) ).
fof(f13130,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10037,f4426,f3290,f9793]) ).
fof(f10037,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f9772,f9774]) ).
fof(f9772,plain,
( ! [X32] : hBOOL(hAPP(hAPP(v_F,v_Q____),X32))
| ~ spl85_34
| ~ spl85_64 ),
inference(resolution,[],[f9759,f2710]) ).
fof(f13116,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13115,f4426,f3290,f9793]) ).
fof(f13115,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13114]) ).
fof(f13114,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10400,f9774]) ).
fof(f10400,plain,
( ! [X10,X8,X6,X9,X7,X5] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(X10),c_FuncSet_OPi(X5,X6,X8,X9)),hAPP(c_member(tc_fun(X5,X6)),X7))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3468,f9774]) ).
fof(f3468,plain,
! [X10,X8,X6,X9,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(X10),c_FuncSet_OPi(X5,X6,X8,X9)),hAPP(c_member(tc_fun(X5,X6)),X7)))
| hBOOL(hAPP(hAPP(c_member(X5),sK57(X7,X8,X5,X6,X9)),X8)) ),
inference(resolution,[],[f2649,f2711]) ).
fof(f13113,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13112,f4426,f3290,f9793]) ).
fof(f13112,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13111]) ).
fof(f13111,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13110,f9774]) ).
fof(f13110,plain,
( ! [X2] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_COMBI(X2)),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13109]) ).
fof(f13109,plain,
( ! [X2] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_COMBI(X2)),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10175,f9774]) ).
fof(f10175,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_COMBI(X2)))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_COMBI(X2)),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3872,f9774]) ).
fof(f3872,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_COMBI(X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_COMBI(X2)))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)) ),
inference(resolution,[],[f3359,f2792]) ).
fof(f13102,plain,
( spl85_161
| spl85_84
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13101,f4426,f3290,f6422,f9793]) ).
fof(f13101,plain,
( ! [X3,X4] :
( c_Arrow__Order__Mirabelle_Odictator(X4,X3)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13100]) ).
fof(f13100,plain,
( ! [X3,X4] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(X4,X3)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10819,f9774]) ).
fof(f10819,plain,
( ! [X3,X4] :
( c_Arrow__Order__Mirabelle_Odictator(X4,X3)
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK83(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin),X4)),c_Arrow__Order__Mirabelle_OProf)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3867,f9774]) ).
fof(f3867,plain,
! [X3,X4] :
( c_Arrow__Order__Mirabelle_Odictator(X4,X3)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK83(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin),X4)),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X3,X4)),c_Arrow__Order__Mirabelle_OProf)) ),
inference(resolution,[],[f2451,f2942]) ).
fof(f13097,plain,
( spl85_161
| ~ spl85_24
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10767,f4426,f3290,f3218,f9793]) ).
fof(f10767,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_24
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3295,f9774]) ).
fof(f3295,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_member(X0),hAPP(v_F,v_P____)),hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))))
| ~ spl85_24 ),
inference(resolution,[],[f3220,f2711]) ).
fof(f13096,plain,
( ~ spl85_161
| spl85_188
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13095,f4426,f3290,f12164,f9793]) ).
fof(f12164,plain,
( spl85_188
<=> ! [X2,X1] : hAPP(X2,X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl85_188])]) ).
fof(f13095,plain,
( ! [X36,X37] :
( hAPP(X37,X36) = X36
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10689,f9774]) ).
fof(f10689,plain,
( ! [X36,X37] :
( ~ hBOOL(hAPP(hAPP(v_F,v_Q____),X36))
| hAPP(X37,X36) = X36 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3423,f9774]) ).
fof(f3423,plain,
! [X40,X38,X39,X36,X37] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X38,X39,X40),c_fequal),X37),X36))
| hAPP(X37,X36) = X36 ),
inference(superposition,[],[f2346,f2728]) ).
fof(f13093,plain,
( spl85_161
| spl85_186
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13092,f4426,f3290,f12035,f9793]) ).
fof(f12035,plain,
( spl85_186
<=> ! [X2,X3,X0,X5,X1] : c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_186])]) ).
fof(f13092,plain,
( ! [X3,X0,X1,X4,X5] :
( c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10294,f9774]) ).
fof(f10294,plain,
( ! [X3,X0,X1,X6,X4,X5] :
( c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK48(X0,X1,X3,X4,X5,X6)),X5)),X3)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3038,f9774]) ).
fof(f3038,plain,
! [X3,X0,X1,X6,X4,X5] :
( c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,hAPP(hAPP(X1,X6),X5))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK48(X0,X1,X3,X4,X5,X6)),X5)),X3)) ),
inference(equality_resolution,[],[f2610]) ).
fof(f2610,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,X2)
| hAPP(hAPP(X1,X6),X5) != X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK48(X0,X1,X3,X4,X5,X6)),X5)),X3)) ),
inference(cnf_transformation,[],[f1867]) ).
fof(f1867,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,X2)
| ! [X6] :
( hAPP(hAPP(X1,X6),X5) != X2
| ( ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,sK48(X0,X1,X3,X4,X5,X6),hAPP(X6,sK48(X0,X1,X3,X4,X5,X6)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK48(X0,X1,X3,X4,X5,X6)),X5)),X3)) ) ) )
& ( ( hAPP(hAPP(X1,sK49(X0,X1,X2,X3,X4,X5)),X5) = X2
& ! [X9] :
( c_Recdef_Owfrec__rel(X0,X4,X3,X1,X9,hAPP(sK49(X0,X1,X2,X3,X4,X5),X9))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X9),X5)),X3)) ) )
| ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK48,sK49])],[f1864,f1866,f1865]) ).
fof(f1865,plain,
! [X0,X1,X3,X4,X5,X6] :
( ? [X7] :
( ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,X7,hAPP(X6,X7))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X7),X5)),X3)) )
=> ( ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,sK48(X0,X1,X3,X4,X5,X6),hAPP(X6,sK48(X0,X1,X3,X4,X5,X6)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK48(X0,X1,X3,X4,X5,X6)),X5)),X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f1866,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X8] :
( hAPP(hAPP(X1,X8),X5) = X2
& ! [X9] :
( c_Recdef_Owfrec__rel(X0,X4,X3,X1,X9,hAPP(X8,X9))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X9),X5)),X3)) ) )
=> ( hAPP(hAPP(X1,sK49(X0,X1,X2,X3,X4,X5)),X5) = X2
& ! [X9] :
( c_Recdef_Owfrec__rel(X0,X4,X3,X1,X9,hAPP(sK49(X0,X1,X2,X3,X4,X5),X9))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X9),X5)),X3)) ) ) ),
introduced(choice_axiom,[]) ).
fof(f1864,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,X2)
| ! [X6] :
( hAPP(hAPP(X1,X6),X5) != X2
| ? [X7] :
( ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,X7,hAPP(X6,X7))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X7),X5)),X3)) ) ) )
& ( ? [X8] :
( hAPP(hAPP(X1,X8),X5) = X2
& ! [X9] :
( c_Recdef_Owfrec__rel(X0,X4,X3,X1,X9,hAPP(X8,X9))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X9),X5)),X3)) ) )
| ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,X2) ) ),
inference(rectify,[],[f1863]) ).
fof(f1863,plain,
! [X0,X4,X5,X3,X2,X1] :
( ( c_Recdef_Owfrec__rel(X0,X2,X3,X4,X1,X5)
| ! [X6] :
( hAPP(hAPP(X4,X6),X1) != X5
| ? [X7] :
( ~ c_Recdef_Owfrec__rel(X0,X2,X3,X4,X7,hAPP(X6,X7))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X7),X1)),X3)) ) ) )
& ( ? [X6] :
( hAPP(hAPP(X4,X6),X1) = X5
& ! [X7] :
( c_Recdef_Owfrec__rel(X0,X2,X3,X4,X7,hAPP(X6,X7))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X7),X1)),X3)) ) )
| ~ c_Recdef_Owfrec__rel(X0,X2,X3,X4,X1,X5) ) ),
inference(nnf_transformation,[],[f1459]) ).
fof(f1459,plain,
! [X0,X4,X5,X3,X2,X1] :
( c_Recdef_Owfrec__rel(X0,X2,X3,X4,X1,X5)
<=> ? [X6] :
( hAPP(hAPP(X4,X6),X1) = X5
& ! [X7] :
( c_Recdef_Owfrec__rel(X0,X2,X3,X4,X7,hAPP(X6,X7))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X7),X1)),X3)) ) ) ),
inference(ennf_transformation,[],[f741]) ).
fof(f741,plain,
! [X0,X5,X1,X4,X3,X2] :
( c_Recdef_Owfrec__rel(X0,X2,X3,X4,X1,X5)
<=> ? [X6] :
( ! [X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X7),X1)),X3))
=> c_Recdef_Owfrec__rel(X0,X2,X3,X4,X7,hAPP(X6,X7)) )
& hAPP(hAPP(X4,X6),X1) = X5 ) ),
inference(rectify,[],[f79]) ).
fof(f79,axiom,
! [X8,X36,X16,X15,X32,X35] :
( c_Recdef_Owfrec__rel(X8,X16,X15,X32,X36,X35)
<=> ? [X37] :
( ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X38),X36)),X15))
=> c_Recdef_Owfrec__rel(X8,X16,X15,X32,X38,hAPP(X37,X38)) )
& hAPP(hAPP(X32,X37),X36) = X35 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Osimps) ).
fof(f13080,plain,
( spl85_161
| spl85_178
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13079,f4426,f3290,f11730,f9793]) ).
fof(f13079,plain,
( ! [X7] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X7)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13078]) ).
fof(f13078,plain,
( ! [X7] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X7)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13077,f9774]) ).
fof(f13077,plain,
( ! [X10,X8,X9,X7] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X7)
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8)),X10),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X9))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10828,f9774]) ).
fof(f10828,plain,
( ! [X10,X8,X9,X7] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(sK83(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,X9,X10),X7)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8)),X10),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X9))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3869,f9774]) ).
fof(f3869,plain,
! [X10,X8,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X7,sK83(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,X9,X10))),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8)),X10),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X9)))
| c_Arrow__Order__Mirabelle_Odictator(sK83(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,X9,X10),X7) ),
inference(resolution,[],[f2451,f2942]) ).
fof(f13065,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13064,f4426,f3290,f9793]) ).
fof(f13064,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13063]) ).
fof(f13063,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13062,f9774]) ).
fof(f13062,plain,
( ! [X21,X19,X22,X23,X20] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13061]) ).
fof(f13061,plain,
( ! [X21,X19,X22,X23,X20] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10634,f9774]) ).
fof(f10634,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3601,f9774]) ).
fof(f3601,plain,
! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23)))
| hBOOL(hAPP(hAPP(c_member(X19),sK72(X19,X21,sK83(c_FuncSet_OPi(X19,X20,X22,X23),tc_fun(X19,X20),X24,X25,X26),X22)),X22))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25))) ),
inference(resolution,[],[f2750,f2942]) ).
fof(f13058,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_47
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10793,f4426,f3442,f3290,f9793]) ).
fof(f10793,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_47
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3443,f9774]) ).
fof(f13053,plain,
( spl85_199
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13049,f4426,f3290,f9793,f13051]) ).
fof(f13051,plain,
( spl85_199
<=> ! [X6,X0,X1] : hAPP(X1,X0) = X6 ),
introduced(avatar_definition,[new_symbols(naming,[spl85_199])]) ).
fof(f13049,plain,
( ! [X0,X1,X6] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hAPP(X1,X0) = X6 )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f13048]) ).
fof(f13048,plain,
( ! [X0,X1,X6] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hAPP(X1,X0) = X6
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13047,f9774]) ).
fof(f13047,plain,
( ! [X0,X1,X6] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hAPP(X1,X0) = X6 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10042,f9774]) ).
fof(f10042,plain,
( ! [X2,X3,X0,X1,X6,X4] :
( hAPP(X1,X0) = X6
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),hAPP(hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Arrow__Order__Mirabelle_Oabove),X1),X0),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3557,f9774]) ).
fof(f3557,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X5)),hAPP(hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Arrow__Order__Mirabelle_Oabove),X1),X0),X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hAPP(X1,X0) = X6 ),
inference(superposition,[],[f3055,f2728]) ).
fof(f13040,plain,
( ~ spl85_161
| spl85_198
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f13036,f4426,f3290,f13038,f9793]) ).
fof(f13038,plain,
( spl85_198
<=> ! [X6,X2,X3] : hAPP(X2,X6) = hAPP(X3,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_198])]) ).
fof(f13036,plain,
( ! [X2,X3,X6] :
( hAPP(X2,X6) = hAPP(X3,X6)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13035,f9774]) ).
fof(f13035,plain,
( ! [X2,X3,X0,X6,X5] :
( hAPP(X2,X6) = hAPP(X3,X6)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(v_F,v_Q____)),X5)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f13034]) ).
fof(f13034,plain,
( ! [X2,X3,X0,X6,X5] :
( hAPP(X2,X6) = hAPP(X3,X6)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(v_F,v_Q____)),X5))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f13033,f9774]) ).
fof(f13033,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(v_F,v_Q____) != hAPP(hAPP(hAPP(c_Recdef_Ocut(X0,X1),X2),X5),X4)
| hAPP(X2,X6) = hAPP(X3,X6)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(v_F,v_Q____)),X5)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10421,f9774]) ).
fof(f10421,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(X2,X6) = hAPP(X3,X6)
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X0,X1),X2),X5),X4) != hAPP(hAPP(hAPP(c_Recdef_Ocut(X0,X1),X3),X5),X4)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(v_F,v_Q____)),X5)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2378,f9774]) ).
fof(f2378,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(X2,X6) = hAPP(X3,X6)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X6),X4)),X5))
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X0,X1),X2),X5),X4) != hAPP(hAPP(hAPP(c_Recdef_Ocut(X0,X1),X3),X5),X4) ),
inference(cnf_transformation,[],[f1668]) ).
fof(f1668,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ! [X6] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X6),X4)),X5))
| hAPP(X2,X6) = hAPP(X3,X6) )
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X0,X1),X2),X5),X4) != hAPP(hAPP(hAPP(c_Recdef_Ocut(X0,X1),X3),X5),X4) )
& ( hAPP(hAPP(hAPP(c_Recdef_Ocut(X0,X1),X2),X5),X4) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X0,X1),X3),X5),X4)
| ( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK17(X0,X2,X3,X4,X5)),X4)),X5))
& hAPP(X3,sK17(X0,X2,X3,X4,X5)) != hAPP(X2,sK17(X0,X2,X3,X4,X5)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f1666,f1667]) ).
fof(f1667,plain,
! [X0,X2,X3,X4,X5] :
( ? [X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X7),X4)),X5))
& hAPP(X3,X7) != hAPP(X2,X7) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK17(X0,X2,X3,X4,X5)),X4)),X5))
& hAPP(X3,sK17(X0,X2,X3,X4,X5)) != hAPP(X2,sK17(X0,X2,X3,X4,X5)) ) ),
introduced(choice_axiom,[]) ).
fof(f1666,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( ! [X6] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X6),X4)),X5))
| hAPP(X2,X6) = hAPP(X3,X6) )
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X0,X1),X2),X5),X4) != hAPP(hAPP(hAPP(c_Recdef_Ocut(X0,X1),X3),X5),X4) )
& ( hAPP(hAPP(hAPP(c_Recdef_Ocut(X0,X1),X2),X5),X4) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X0,X1),X3),X5),X4)
| ? [X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X7),X4)),X5))
& hAPP(X3,X7) != hAPP(X2,X7) ) ) ),
inference(rectify,[],[f1665]) ).
fof(f1665,plain,
! [X3,X1,X5,X0,X4,X2] :
( ( ! [X6] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X6),X4)),X2))
| hAPP(X5,X6) = hAPP(X0,X6) )
| hAPP(hAPP(hAPP(c_Recdef_Ocut(X3,X1),X0),X2),X4) != hAPP(hAPP(hAPP(c_Recdef_Ocut(X3,X1),X5),X2),X4) )
& ( hAPP(hAPP(hAPP(c_Recdef_Ocut(X3,X1),X0),X2),X4) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X3,X1),X5),X2),X4)
| ? [X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X6),X4)),X2))
& hAPP(X5,X6) != hAPP(X0,X6) ) ) ),
inference(nnf_transformation,[],[f1225]) ).
fof(f1225,plain,
! [X3,X1,X5,X0,X4,X2] :
( ! [X6] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X6),X4)),X2))
| hAPP(X5,X6) = hAPP(X0,X6) )
<=> hAPP(hAPP(hAPP(c_Recdef_Ocut(X3,X1),X0),X2),X4) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X3,X1),X5),X2),X4) ),
inference(ennf_transformation,[],[f590]) ).
fof(f590,plain,
! [X4,X1,X0,X5,X3,X2] :
( ! [X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X6),X4)),X2))
=> hAPP(X5,X6) = hAPP(X0,X6) )
<=> hAPP(hAPP(hAPP(c_Recdef_Ocut(X3,X1),X0),X2),X4) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X3,X1),X5),X2),X4) ),
inference(rectify,[],[f61]) ).
fof(f61,axiom,
! [X1,X16,X19,X8,X14,X0] :
( ! [X41] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X41),X14)),X19))
=> hAPP(X1,X41) = hAPP(X0,X41) )
<=> hAPP(hAPP(hAPP(c_Recdef_Ocut(X8,X16),X1),X19),X14) = hAPP(hAPP(hAPP(c_Recdef_Ocut(X8,X16),X0),X19),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cuts__eq) ).
fof(f13022,plain,
( spl85_80
| spl85_197
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10984,f4426,f3290,f13019,f6164]) ).
fof(f13019,plain,
( spl85_197
<=> class_Lattices_Olattice(hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_197])]) ).
fof(f10984,plain,
( ! [X1] :
( class_Lattices_Olattice(hAPP(v_F,v_Q____))
| ~ class_Lattices_Olattice(X1) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2477,f9774]) ).
fof(f2477,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f1745]) ).
fof(f1745,plain,
! [X0,X1] :
( class_Lattices_Olattice(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(rectify,[],[f1052]) ).
fof(f1052,plain,
! [X1,X0] :
( class_Lattices_Olattice(tc_fun(X1,X0))
| ~ class_Lattices_Olattice(X0) ),
inference(ennf_transformation,[],[f981]) ).
fof(f981,plain,
! [X1,X0] :
( class_Lattices_Olattice(X0)
=> class_Lattices_Olattice(tc_fun(X1,X0)) ),
inference(rectify,[],[f502]) ).
fof(f502,axiom,
! [X74,X73] :
( class_Lattices_Olattice(X74)
=> class_Lattices_Olattice(tc_fun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
fof(f13012,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_50
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10779,f4426,f3455,f3290,f9793]) ).
fof(f3455,plain,
( spl85_50
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_50])]) ).
fof(f10779,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_50
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3457,f9774]) ).
fof(f3457,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____))))
| ~ spl85_50 ),
inference(avatar_component_clause,[],[f3455]) ).
fof(f13000,plain,
( spl85_78
| spl85_161
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10787,f4426,f3290,f3178,f9793,f6145]) ).
fof(f6145,plain,
( spl85_78
<=> ! [X65] : c_Arrow__Order__Mirabelle_Odictator(v_F,X65) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_78])]) ).
fof(f10787,plain,
( ! [X0] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(v_F,X0) )
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3945,f9774]) ).
fof(f3945,plain,
( ! [X0] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X0)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X0,v_F)),sK21(X0,v_F))),hAPP(sK20(X0,v_F),X0))) )
| ~ spl85_16 ),
inference(resolution,[],[f2452,f3180]) ).
fof(f2452,plain,
! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X0,X1)),sK21(X0,X1))),hAPP(sK20(X0,X1),X0)))
| c_Arrow__Order__Mirabelle_Odictator(X1,X0) ),
inference(cnf_transformation,[],[f1732]) ).
fof(f12990,plain,
( spl85_161
| spl85_84
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12989,f4426,f3290,f6422,f9793]) ).
fof(f12989,plain,
( ! [X2,X1] :
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12988]) ).
fof(f12988,plain,
( ! [X2,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10784,f9774]) ).
fof(f10784,plain,
( ! [X2,X1] :
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK65(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2)),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3946,f9774]) ).
fof(f3946,plain,
! [X2,X1] :
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK65(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2)),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X1,X2)),sK21(X1,X2))),hAPP(sK20(X1,X2),X1))) ),
inference(resolution,[],[f2452,f2719]) ).
fof(f12976,plain,
( spl85_92
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12975,f4426,f3290,f6565]) ).
fof(f6565,plain,
( spl85_92
<=> ! [X2,X0,X1] : c_Relation_Osingle__valued(X0,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_92])]) ).
fof(f12975,plain,
( ! [X2,X0,X1] : c_Relation_Osingle__valued(X0,X1,X2)
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f12974]) ).
fof(f12974,plain,
( ! [X2,X0,X1] :
( hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____)
| c_Relation_Osingle__valued(X0,X1,X2) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11047,f9774]) ).
fof(f11047,plain,
( ! [X2,X0,X1] :
( hAPP(v_F,v_Q____) != sK52(X0,X1,X2)
| c_Relation_Osingle__valued(X0,X1,X2) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2619,f9774]) ).
fof(f2619,plain,
! [X2,X0,X1] :
( c_Relation_Osingle__valued(X0,X1,X2)
| sK52(X0,X1,X2) != sK51(X0,X1,X2) ),
inference(cnf_transformation,[],[f1877]) ).
fof(f12959,plain,
( spl85_161
| spl85_178
| ~ spl85_34
| ~ spl85_64
| ~ spl85_66 ),
inference(avatar_split_clause,[],[f12958,f4435,f4426,f3290,f11730,f9793]) ).
fof(f4435,plain,
( spl85_66
<=> ! [X66] :
( c_Arrow__Order__Mirabelle_Odictator(sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X66)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X66,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))),c_Arrow__Order__Mirabelle_OProf)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_66])]) ).
fof(f12958,plain,
( ! [X66] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X66)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64
| ~ spl85_66 ),
inference(forward_demodulation,[],[f10824,f9774]) ).
fof(f10824,plain,
( ! [X66] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X66) )
| ~ spl85_34
| ~ spl85_64
| ~ spl85_66 ),
inference(backward_demodulation,[],[f4436,f9774]) ).
fof(f4436,plain,
( ! [X66] :
( c_Arrow__Order__Mirabelle_Odictator(sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X66)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X66,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))),c_Arrow__Order__Mirabelle_OProf)) )
| ~ spl85_66 ),
inference(avatar_component_clause,[],[f4435]) ).
fof(f12957,plain,
( spl85_167
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12956,f4426,f3290,f9793,f11209]) ).
fof(f12956,plain,
( ! [X2,X0] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(X0,X2)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10584,f9774]) ).
fof(f10584,plain,
( ! [X2,X0] :
( ~ hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(hAPP(v_F,v_Q____),X2)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2894,f9774]) ).
fof(f2894,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X1),X0),X2))
| ~ hBOOL(hAPP(X0,X2)) ),
inference(cnf_transformation,[],[f2116]) ).
fof(f2116,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X1),X0),X2)) ),
inference(rectify,[],[f1180]) ).
fof(f1180,plain,
! [X3,X1,X2,X0] :
( ~ hBOOL(hAPP(X3,X2))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X3),X2)) ),
inference(ennf_transformation,[],[f935]) ).
fof(f935,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X3,X2))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X3),X2)) ),
inference(rectify,[],[f374]) ).
fof(f374,axiom,
! [X8,X10,X14,X9] :
( hBOOL(hAPP(X9,X14))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X10),X9),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I2) ).
fof(f12950,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10844,f4426,f3290,f9793]) ).
fof(f10844,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3314,f9774]) ).
fof(f3314,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_member(X0),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin))
| ~ spl85_34 ),
inference(resolution,[],[f3292,f2711]) ).
fof(f12947,plain,
( spl85_161
| spl85_78
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10823,f4426,f3290,f3178,f6145,f9793]) ).
fof(f10823,plain,
( ! [X0] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X0)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3865,f9774]) ).
fof(f3865,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X0,v_F)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(v_F,X0) )
| ~ spl85_16 ),
inference(resolution,[],[f2451,f3180]) ).
fof(f12946,plain,
( spl85_161
| ~ spl85_25
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10800,f4426,f3290,f3223,f9793]) ).
fof(f10800,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_25
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3288,f9774]) ).
fof(f12945,plain,
( ~ spl85_161
| spl85_168
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12944,f4426,f3290,f11279,f9793]) ).
fof(f12944,plain,
( ! [X31,X29,X30] :
( c_Predicate_ORangeP(X30,X31,hAPP(v_F,v_Q____),X29)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10306,f9774]) ).
fof(f10306,plain,
( ! [X31,X29,X26,X27,X24,X25,X30] :
( c_Predicate_ORangeP(X30,X31,hAPP(c_COMBC(X24,X25,X26),X27),X29)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4369,f9774]) ).
fof(f4369,plain,
! [X31,X28,X29,X26,X27,X24,X25,X30] :
( c_Predicate_ORangeP(X30,X31,hAPP(c_COMBC(X24,X25,X26),X27),X29)
| ~ hBOOL(hAPP(hAPP(X27,X29),X28)) ),
inference(superposition,[],[f2173,f2585]) ).
fof(f12939,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12938,f4426,f3290,f9793]) ).
fof(f12938,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12937]) ).
fof(f12937,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12936,f9774]) ).
fof(f12936,plain,
( ! [X40,X38,X41,X39,X36,X37,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X36,X39),X38)),X42),c_FuncSet_OPi(tc_fun(X36,X39),X38,c_FuncSet_OPi(X36,X39,X40,X41),c_COMBK(tc_fun(X38,tc_HOL_Obool),tc_fun(X36,X39),X37))))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f12935]) ).
fof(f12935,plain,
( ! [X40,X38,X41,X39,X36,X37,X42] :
( hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X36,X39),X38)),X42),c_FuncSet_OPi(tc_fun(X36,X39),X38,c_FuncSet_OPi(X36,X39,X40,X41),c_COMBK(tc_fun(X38,tc_HOL_Obool),tc_fun(X36,X39),X37))))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12934,f9774]) ).
fof(f12934,plain,
( ! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hAPP(v_F,v_Q____) != hAPP(sK65(X37,X38,c_FuncSet_OPi(X36,X39,X40,X41),tc_fun(X36,X39),X42),sK72(X36,sK65(X37,X38,c_FuncSet_OPi(X36,X39,X40,X41),tc_fun(X36,X39),X42),X35,X40))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X36,X39),X38)),X42),c_FuncSet_OPi(tc_fun(X36,X39),X38,c_FuncSet_OPi(X36,X39,X40,X41),c_COMBK(tc_fun(X38,tc_HOL_Obool),tc_fun(X36,X39),X37)))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10013,f9774]) ).
fof(f10013,plain,
( ! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X36,X39)),X35),c_FuncSet_OPi(X36,X39,X40,X41)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X36,X39),X38)),X42),c_FuncSet_OPi(tc_fun(X36,X39),X38,c_FuncSet_OPi(X36,X39,X40,X41),c_COMBK(tc_fun(X38,tc_HOL_Obool),tc_fun(X36,X39),X37))))
| hAPP(v_F,v_Q____) != hAPP(sK65(X37,X38,c_FuncSet_OPi(X36,X39,X40,X41),tc_fun(X36,X39),X42),sK72(X36,sK65(X37,X38,c_FuncSet_OPi(X36,X39,X40,X41),tc_fun(X36,X39),X42),X35,X40)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3610,f9774]) ).
fof(f3610,plain,
! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X36,X39),X38)),X42),c_FuncSet_OPi(tc_fun(X36,X39),X38,c_FuncSet_OPi(X36,X39,X40,X41),c_COMBK(tc_fun(X38,tc_HOL_Obool),tc_fun(X36,X39),X37))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X36,X39)),X35),c_FuncSet_OPi(X36,X39,X40,X41)))
| hAPP(sK65(X37,X38,c_FuncSet_OPi(X36,X39,X40,X41),tc_fun(X36,X39),X42),sK72(X36,sK65(X37,X38,c_FuncSet_OPi(X36,X39,X40,X41),tc_fun(X36,X39),X42),X35,X40)) != hAPP(X35,sK72(X36,sK65(X37,X38,c_FuncSet_OPi(X36,X39,X40,X41),tc_fun(X36,X39),X42),X35,X40)) ),
inference(resolution,[],[f2751,f2719]) ).
fof(f2751,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X2),c_FuncSet_OPi(X1,X0,X4,X5)))
| hAPP(X3,sK72(X1,X2,X3,X4)) != hAPP(X2,sK72(X1,X2,X3,X4))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X3),c_FuncSet_OPi(X1,X0,X4,X5))) ),
inference(cnf_transformation,[],[f2007]) ).
fof(f12933,plain,
( ~ spl85_161
| spl85_196
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12929,f4426,f3290,f12931,f9793]) ).
fof(f12931,plain,
( spl85_196
<=> ! [X48,X55,X54,X50,X49] : c_Predicate_ORangeP(X54,X55,X48,hAPP(X50,X49)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_196])]) ).
fof(f12929,plain,
( ! [X50,X48,X49,X54,X55] :
( c_Predicate_ORangeP(X54,X55,X48,hAPP(X50,X49))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10725,f9774]) ).
fof(f10725,plain,
( ! [X50,X48,X49,X54,X55] :
( c_Predicate_ORangeP(X54,X55,X48,hAPP(X50,X49))
| ~ hBOOL(hAPP(hAPP(v_F,v_Q____),X49)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4372,f9774]) ).
fof(f4372,plain,
! [X50,X51,X48,X49,X54,X55,X52,X53] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X51,X52,X53),X48),X50),X49))
| c_Predicate_ORangeP(X54,X55,X48,hAPP(X50,X49)) ),
inference(superposition,[],[f2173,f2728]) ).
fof(f12917,plain,
( spl85_195
| spl85_95
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12913,f4426,f3290,f6693,f12915]) ).
fof(f12915,plain,
( spl85_195
<=> ! [X1,X3] : hAPP(v_F,v_Q____) != c_Set_Oinsert(X3,X1,hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_195])]) ).
fof(f6693,plain,
( spl85_95
<=> ! [X9,X8,X10] :
( X9 = X10
| X8 = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_95])]) ).
fof(f12913,plain,
( ! [X2,X3,X0,X1,X4] :
( X0 = X4
| hAPP(v_F,v_Q____) != c_Set_Oinsert(X3,X1,hAPP(v_F,v_Q____))
| X0 = X2 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12912,f9774]) ).
fof(f12912,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(v_F,v_Q____) != c_Set_Oinsert(X3,X1,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(hAPP(v_F,v_Q____))))
| X0 = X2
| X0 = X4 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10995,f9774]) ).
fof(f10995,plain,
( ! [X2,X3,X0,X1,X4] :
( X0 = X2
| X0 = X4
| c_Set_Oinsert(X3,X1,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(hAPP(v_F,v_Q____)))) != c_Set_Oinsert(X3,X4,c_Set_Oinsert(X3,X2,c_Orderings_Obot__class_Obot(hAPP(v_F,v_Q____)))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2216,f9774]) ).
fof(f2216,plain,
! [X2,X3,X0,X1,X4] :
( X0 = X4
| c_Set_Oinsert(X3,X1,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Set_Oinsert(X3,X4,c_Set_Oinsert(X3,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| X0 = X2 ),
inference(cnf_transformation,[],[f1545]) ).
fof(f1545,plain,
! [X0,X1,X2,X3,X4] :
( ( c_Set_Oinsert(X3,X1,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) = c_Set_Oinsert(X3,X4,c_Set_Oinsert(X3,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool))))
| ( ( X0 != X2
| X1 != X4 )
& ( X1 != X2
| X0 != X4 ) ) )
& ( ( X0 = X2
& X1 = X4 )
| ( X1 = X2
& X0 = X4 )
| c_Set_Oinsert(X3,X1,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) != c_Set_Oinsert(X3,X4,c_Set_Oinsert(X3,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)))) ) ),
inference(rectify,[],[f1544]) ).
fof(f1544,plain,
! [X1,X3,X0,X2,X4] :
( ( c_Set_Oinsert(X2,X3,c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = c_Set_Oinsert(X2,X4,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
| ( ( X0 != X1
| X3 != X4 )
& ( X0 != X3
| X1 != X4 ) ) )
& ( ( X0 = X1
& X3 = X4 )
| ( X0 = X3
& X1 = X4 )
| c_Set_Oinsert(X2,X3,c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) != c_Set_Oinsert(X2,X4,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) ) ),
inference(flattening,[],[f1543]) ).
fof(f1543,plain,
! [X1,X3,X0,X2,X4] :
( ( c_Set_Oinsert(X2,X3,c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = c_Set_Oinsert(X2,X4,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
| ( ( X0 != X1
| X3 != X4 )
& ( X0 != X3
| X1 != X4 ) ) )
& ( ( X0 = X1
& X3 = X4 )
| ( X0 = X3
& X1 = X4 )
| c_Set_Oinsert(X2,X3,c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) != c_Set_Oinsert(X2,X4,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) ) ),
inference(nnf_transformation,[],[f627]) ).
fof(f627,plain,
! [X1,X3,X0,X2,X4] :
( c_Set_Oinsert(X2,X3,c_Set_Oinsert(X2,X1,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)))) = c_Set_Oinsert(X2,X4,c_Set_Oinsert(X2,X0,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))))
<=> ( ( X0 = X1
& X3 = X4 )
| ( X0 = X3
& X1 = X4 ) ) ),
inference(rectify,[],[f439]) ).
fof(f439,axiom,
! [X23,X71,X8,X7,X24] :
( ( ( X24 = X71
& X7 = X23 )
| ( X7 = X24
& X23 = X71 ) )
<=> c_Set_Oinsert(X8,X24,c_Set_Oinsert(X8,X23,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))) = c_Set_Oinsert(X8,X7,c_Set_Oinsert(X8,X71,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
fof(f12903,plain,
( ~ spl85_161
| spl85_95
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12902,f4426,f3290,f6693,f9793]) ).
fof(f12902,plain,
( ! [X6,X9,X7] :
( X7 = X9
| ~ hBOOL(hAPP(v_F,v_Q____))
| X6 = X7 )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12901]) ).
fof(f12901,plain,
( ! [X6,X9,X7] :
( X7 = X9
| ~ hBOOL(hAPP(v_F,v_Q____))
| X6 = X7
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12900,f9774]) ).
fof(f12900,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(v_F,v_Q____))
| X7 = X9
| X6 = X7 )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12899]) ).
fof(f12899,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| X7 = X9
| X6 = X7 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12898,f9774]) ).
fof(f12898,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X7)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| X7 = X9
| X6 = X7 )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12897]) ).
fof(f12897,plain,
( ! [X8,X6,X9,X7] :
( X6 = X7
| X7 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X7)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12896,f9774]) ).
fof(f12896,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),X8))
| X6 = X7
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X7)),c_Arrow__Order__Mirabelle_OLin))
| X7 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10149,f9774]) ).
fof(f10149,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X6)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X7)))
| X7 = X9
| X6 = X7
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X7)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),X8))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3708,f9774]) ).
fof(f3708,plain,
! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X7)),X8))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X6)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X7)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X7)),c_Arrow__Order__Mirabelle_OLin))
| X7 = X9
| X6 = X7 ),
inference(resolution,[],[f3094,f2792]) ).
fof(f3094,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X0))
| X1 = X4 ),
inference(duplicate_literal_removal,[],[f3003]) ).
fof(f3003,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X0))
| X2 = X4
| X1 = X4 ),
inference(equality_resolution,[],[f2365]) ).
fof(f2365,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X0))
| X1 = X3
| X3 != X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X0))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(cnf_transformation,[],[f1663]) ).
fof(f1663,plain,
! [X0,X1,X2,X3,X4] :
( ( ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X0))
| X2 != X3 )
& X1 != X3
& ( X2 = X3
| ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X0))
| X3 = X4
| X1 != X2 )
& ( X1 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X0)) ) ) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X0))
& X2 = X3 )
| X1 = X3
| ( X2 != X3
& ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X0))
& X3 != X4
& X1 = X2 )
| ( X1 != X2
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X0)) ) ) ) ) )
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(rectify,[],[f1662]) ).
fof(f1662,plain,
! [X4,X0,X2,X3,X1] :
( ( ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),X4))
| X2 != X3 )
& X0 != X3
& ( X2 = X3
| ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
| X1 = X3
| X0 != X2 )
& ( X0 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X3)),X4)) ) ) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X2,X1))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X2,X1)))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),X4))
& X2 = X3 )
| X0 = X3
| ( X2 != X3
& ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
& X1 != X3
& X0 = X2 )
| ( X0 != X2
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X3)),X4)) ) ) ) ) )
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(flattening,[],[f1661]) ).
fof(f1661,plain,
! [X4,X0,X2,X3,X1] :
( ( ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),X4))
| X2 != X3 )
& X0 != X3
& ( X2 = X3
| ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
| X1 = X3
| X0 != X2 )
& ( X0 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X3)),X4)) ) ) ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X2,X1))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X2,X1)))
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),X4))
& X2 = X3 )
| X0 = X3
| ( X2 != X3
& ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
& X1 != X3
& X0 = X2 )
| ( X0 != X2
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X3)),X4)) ) ) ) ) )
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(nnf_transformation,[],[f1381]) ).
fof(f1381,plain,
! [X4,X0,X2,X3,X1] :
( ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),X4))
| X2 != X3 )
& X0 != X3
& ( X2 = X3
| ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
| X1 = X3
| X0 != X2 )
& ( X0 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X3)),X4)) ) ) ) )
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X2,X1))) )
| X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin)) ),
inference(flattening,[],[f1380]) ).
fof(f1380,plain,
! [X3,X2,X4,X0,X1] :
( ( ( X0 != X3
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),X4))
| X2 != X3 )
& ( ( ( X0 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X3)),X4)) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
| X1 = X3
| X0 != X2 ) )
| X2 = X3 ) )
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X2,X1))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin))
| X1 = X2 ),
inference(ennf_transformation,[],[f682]) ).
fof(f682,plain,
! [X3,X2,X4,X0,X1] :
( X1 != X2
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin))
=> ( ( X0 != X3
& ( X2 = X3
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),X4)) )
& ( X2 != X3
=> ( ( X0 != X2
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X3)),X4)) )
& ( X0 = X2
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X4))
| X1 = X3 ) ) ) ) )
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X3)),c_Arrow__Order__Mirabelle_Obelow(X4,X2,X1))) ) ) ),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X14,X23,X24,X13,X12] :
( X23 != X24
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X12),c_Arrow__Order__Mirabelle_OLin))
=> ( ( ( X13 = X24
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X23)),X12)) )
& ( X13 != X24
=> ( ( X14 = X24
=> ( X13 = X23
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X13)),X12)) ) )
& ( X14 != X24
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X13)),X12)) ) ) )
& X13 != X14 )
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X13)),c_Arrow__Order__Mirabelle_Obelow(X12,X24,X23))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__below) ).
fof(f12889,plain,
( spl85_162
| spl85_161
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12888,f4426,f3371,f3290,f9793,f11077]) ).
fof(f11077,plain,
( spl85_162
<=> ! [X29,X27,X28] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X27,X28),hAPP(X27,X29)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_162])]) ).
fof(f12888,plain,
( ! [X18,X19,X20] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X18,X19),hAPP(X18,X20)) )
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10464,f9774]) ).
fof(f10464,plain,
( ! [X21,X18,X19,X24,X22,X23,X20] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X18,X19),hAPP(X18,X20))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X21,X21)),hAPP(v_F,v_Q____)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X21),X21,c_Wellfounded_Olex__prod(tc_Nat_Onat,X21,c_Wellfounded_Oless__than,hAPP(c_Product__Type_OPair(X22,X23),X24)),hAPP(hAPP(c_COMBS(X21,X21,tc_prod(tc_Nat_Onat,X21)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X21,tc_prod(tc_Nat_Onat,X21)),X21,c_Product__Type_OPair(tc_Nat_Onat,X21)),X18)),c_COMBI(X21))))) )
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4238,f9774]) ).
fof(f4238,plain,
( ! [X21,X18,X19,X24,X22,X23,X20] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X18,X19),hAPP(X18,X20))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X21,X21)),hAPP(hAPP(c_Product__Type_OPair(X21,X21),X19),X20)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X21),X21,c_Wellfounded_Olex__prod(tc_Nat_Onat,X21,c_Wellfounded_Oless__than,hAPP(c_Product__Type_OPair(X22,X23),X24)),hAPP(hAPP(c_COMBS(X21,X21,tc_prod(tc_Nat_Onat,X21)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X21,tc_prod(tc_Nat_Onat,X21)),X21,c_Product__Type_OPair(tc_Nat_Onat,X21)),X18)),c_COMBI(X21))))) )
| ~ spl85_40 ),
inference(resolution,[],[f3652,f2974]) ).
fof(f2974,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X0,X4),hAPP(X0,X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X1),X1,c_Wellfounded_Olex__prod(tc_Nat_Onat,X1,c_Wellfounded_Oless__than,X2),hAPP(hAPP(c_COMBS(X1,X1,tc_prod(tc_Nat_Onat,X1)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X1,tc_prod(tc_Nat_Onat,X1)),X1,c_Product__Type_OPair(tc_Nat_Onat,X1)),X0)),c_COMBI(X1))))) ),
inference(definition_unfolding,[],[f2918,f2597]) ).
fof(f2597,plain,
! [X2,X0,X1] : c_Wellfounded_Omlex__prod(X2,X1,X0) = c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X2),X2,c_Wellfounded_Olex__prod(tc_Nat_Onat,X2,c_Wellfounded_Oless__than,X0),hAPP(hAPP(c_COMBS(X2,X2,tc_prod(tc_Nat_Onat,X2)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X2,tc_prod(tc_Nat_Onat,X2)),X2,c_Product__Type_OPair(tc_Nat_Onat,X2)),X1)),c_COMBI(X2))),
inference(cnf_transformation,[],[f600]) ).
fof(f600,plain,
! [X0,X1,X2] : c_Wellfounded_Omlex__prod(X2,X1,X0) = c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X2),X2,c_Wellfounded_Olex__prod(tc_Nat_Onat,X2,c_Wellfounded_Oless__than,X0),hAPP(hAPP(c_COMBS(X2,X2,tc_prod(tc_Nat_Onat,X2)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X2,tc_prod(tc_Nat_Onat,X2)),X2,c_Product__Type_OPair(tc_Nat_Onat,X2)),X1)),c_COMBI(X2))),
inference(rectify,[],[f340]) ).
fof(f340,axiom,
! [X15,X1,X8] : c_Wellfounded_Omlex__prod(X8,X1,X15) = c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X8),X8,c_Wellfounded_Olex__prod(tc_Nat_Onat,X8,c_Wellfounded_Oless__than,X15),hAPP(hAPP(c_COMBS(X8,X8,tc_prod(tc_Nat_Onat,X8)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X8,tc_prod(tc_Nat_Onat,X8)),X8,c_Product__Type_OPair(tc_Nat_Onat,X8)),X1)),c_COMBI(X8))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__prod__def) ).
fof(f2918,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X0,X4),hAPP(X0,X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Wellfounded_Omlex__prod(X1,X0,X2))) ),
inference(cnf_transformation,[],[f2134]) ).
fof(f2134,plain,
! [X0,X1,X2,X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X0,X4),hAPP(X0,X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X3)),c_Wellfounded_Omlex__prod(X1,X0,X2))) ),
inference(rectify,[],[f1170]) ).
fof(f1170,plain,
! [X4,X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X0)),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X1),hAPP(X4,X0))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X0)),c_Wellfounded_Omlex__prod(X2,X4,X3))) ),
inference(flattening,[],[f1169]) ).
fof(f1169,plain,
! [X1,X4,X3,X0,X2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X0)),c_Wellfounded_Omlex__prod(X2,X4,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X0)),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X1),hAPP(X4,X0)) ),
inference(ennf_transformation,[],[f740]) ).
fof(f740,plain,
! [X1,X4,X3,X0,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X1),hAPP(X4,X0))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X0)),X3))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X0)),c_Wellfounded_Omlex__prod(X2,X4,X3))) ) ),
inference(rectify,[],[f277]) ).
fof(f277,axiom,
! [X13,X14,X8,X15,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X1,X14),hAPP(X1,X13))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X14),X13)),X15))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X14),X13)),c_Wellfounded_Omlex__prod(X8,X1,X15))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
fof(f12883,plain,
( spl85_161
| spl85_58
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10036,f4426,f3290,f4223,f9793]) ).
fof(f10036,plain,
( ! [X2,X3] :
( X2 = X3
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f9760,f9774]) ).
fof(f9760,plain,
( ! [X2,X3,X1] :
( hBOOL(hAPP(X1,sK84(X2,X3)))
| X2 = X3 )
| ~ spl85_64 ),
inference(resolution,[],[f9735,f3394]) ).
fof(f3394,plain,
! [X0,X1] :
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,sK84(X0,X1)))
| X0 = X1 ),
inference(resolution,[],[f2948,f2710]) ).
fof(f2948,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK84(X0,X1)),c_Arrow__Order__Mirabelle_OLin))
| X0 = X1 ),
inference(cnf_transformation,[],[f2167]) ).
fof(f2167,plain,
! [X0,X1] :
( X0 = X1
| ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),sK84(X0,X1)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK84(X0,X1)),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK84])],[f1252,f2166]) ).
fof(f2166,plain,
! [X0,X1] :
( ? [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),X2))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin)) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),sK84(X0,X1)))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK84(X0,X1)),c_Arrow__Order__Mirabelle_OLin)) ) ),
introduced(choice_axiom,[]) ).
fof(f1252,plain,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),X2))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(ennf_transformation,[],[f932]) ).
fof(f932,plain,
! [X0,X1] :
( X0 != X1
=> ? [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),X2))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin)) ) ),
inference(rectify,[],[f48]) ).
fof(f48,axiom,
! [X23,X24] :
( X23 != X24
=> ? [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X23)),X2))
& hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complete__Lin) ).
fof(f12872,plain,
( ~ spl85_161
| ~ spl85_34
| spl85_48
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10782,f4426,f3445,f3290,f9793]) ).
fof(f3445,plain,
( spl85_48
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_48])]) ).
fof(f10782,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| spl85_48
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3446,f9774]) ).
fof(f3446,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))))
| spl85_48 ),
inference(avatar_component_clause,[],[f3445]) ).
fof(f12871,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12870,f4426,f3290,f9793]) ).
fof(f12870,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12869]) ).
fof(f12869,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9986,f9774]) ).
fof(f9986,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_OPi(X0,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X0,X1))))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3493,f9774]) ).
fof(f3493,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X3,sK65(X1,X2,X3,X0,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_OPi(X0,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X0,X1)))) ),
inference(resolution,[],[f2719,f2710]) ).
fof(f12868,plain,
( spl85_161
| spl85_167
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12867,f4426,f3290,f11209,f9793]) ).
fof(f12867,plain,
( ! [X10,X9] :
( ~ hBOOL(hAPP(X9,X10))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10585,f9774]) ).
fof(f10585,plain,
( ! [X10,X11,X9] :
( ~ hBOOL(hAPP(X9,X10))
| hBOOL(hAPP(hAPP(c_member(X11),X10),hAPP(v_F,v_Q____))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4618,f9774]) ).
fof(f4618,plain,
! [X10,X11,X9,X12,X13] :
( ~ hBOOL(hAPP(X9,X10))
| hBOOL(hAPP(hAPP(c_member(X11),X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X9),X13))) ),
inference(resolution,[],[f2374,f2711]) ).
fof(f2374,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),X0),X3))
| ~ hBOOL(hAPP(X1,X3)) ),
inference(cnf_transformation,[],[f1664]) ).
fof(f1664,plain,
! [X0,X1,X2,X3] :
( ( ~ hBOOL(hAPP(X0,X3))
& ~ hBOOL(hAPP(X1,X3)) )
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),X0),X3)) ),
inference(rectify,[],[f1336]) ).
fof(f1336,plain,
! [X3,X1,X2,X0] :
( ( ~ hBOOL(hAPP(X3,X0))
& ~ hBOOL(hAPP(X1,X0)) )
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),X3),X0)) ),
inference(ennf_transformation,[],[f985]) ).
fof(f985,plain,
! [X1,X0,X3,X2] :
( ( ~ hBOOL(hAPP(X3,X0))
=> hBOOL(hAPP(X1,X0)) )
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X1),X3),X0)) ),
inference(rectify,[],[f341]) ).
fof(f341,axiom,
! [X14,X10,X8,X9] :
( ( ~ hBOOL(hAPP(X9,X14))
=> hBOOL(hAPP(X10,X14)) )
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X10),X9),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1CI) ).
fof(f12864,plain,
( spl85_178
| spl85_161
| ~ spl85_34
| ~ spl85_64
| ~ spl85_67 ),
inference(avatar_split_clause,[],[f12863,f4439,f4426,f3290,f9793,f11730]) ).
fof(f4439,plain,
( spl85_67
<=> ! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X65,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))),sK21(X65,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))))),hAPP(sK20(X65,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))),X65)))
| c_Arrow__Order__Mirabelle_Odictator(sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X65) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_67])]) ).
fof(f12863,plain,
( ! [X65] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X65) )
| ~ spl85_34
| ~ spl85_64
| ~ spl85_67 ),
inference(forward_demodulation,[],[f10788,f9774]) ).
fof(f10788,plain,
( ! [X65] :
( c_Arrow__Order__Mirabelle_Odictator(sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X65)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64
| ~ spl85_67 ),
inference(backward_demodulation,[],[f4440,f9774]) ).
fof(f4440,plain,
( ! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X65,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))),sK21(X65,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))))),hAPP(sK20(X65,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))),X65)))
| c_Arrow__Order__Mirabelle_Odictator(sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X65) )
| ~ spl85_67 ),
inference(avatar_component_clause,[],[f4439]) ).
fof(f12862,plain,
( spl85_161
| spl85_179
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12861,f4426,f3290,f11785,f9793]) ).
fof(f12861,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(hAPP(v_F,v_Q____),X0,hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| c_Relation_Orefl__on(X1,X2,X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12860,f9774]) ).
fof(f12860,plain,
( ! [X2,X0,X1] :
( c_Relation_Orefl__on(X1,X2,X0)
| hBOOL(hAPP(v_F,v_Q____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10395,f9774]) ).
fof(f10395,plain,
( ! [X2,X0,X1] :
( c_Relation_Orefl__on(X1,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2231,f9774]) ).
fof(f2231,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),sK6(X0,X1,X2)),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2)))
| c_Relation_Orefl__on(X1,X2,X0) ),
inference(cnf_transformation,[],[f1557]) ).
fof(f12859,plain,
( spl85_161
| ~ spl85_25
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10841,f4426,f3290,f3223,f9793]) ).
fof(f10841,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_25
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3225,f9774]) ).
fof(f12858,plain,
( spl85_161
| spl85_84
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12857,f4426,f3290,f6422,f9793]) ).
fof(f12857,plain,
( ! [X6,X5] :
( c_Arrow__Order__Mirabelle_Odictator(X6,X5)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12856]) ).
fof(f12856,plain,
( ! [X6,X5] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(X6,X5) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10785,f9774]) ).
fof(f10785,plain,
( ! [X6,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK57(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(X6,X5) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3948,f9774]) ).
fof(f3948,plain,
! [X6,X5] :
( c_Arrow__Order__Mirabelle_Odictator(X6,X5)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK57(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X5,X6)),sK21(X5,X6))),hAPP(sK20(X5,X6),X5))) ),
inference(resolution,[],[f2452,f2649]) ).
fof(f12841,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12840,f4426,f3290,f9793]) ).
fof(f12840,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f12839]) ).
fof(f12839,plain,
( hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____)
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12838,f9774]) ).
fof(f12838,plain,
( ! [X2,X3,X0,X1] :
( hAPP(v_F,v_Q____) != hAPP(X0,sK72(X1,X2,X0,X3))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12837]) ).
fof(f12837,plain,
( ! [X2,X3,X0,X1] :
( hAPP(v_F,v_Q____) != hAPP(X0,sK72(X1,X2,X0,X3))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12836,f9774]) ).
fof(f12836,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X0),c_FuncSet_OPi(X1,X4,X3,X5)))
| hAPP(v_F,v_Q____) != hAPP(X0,sK72(X1,X2,X0,X3))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10000,f9774]) ).
fof(f10000,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X1),sK83(X3,X1,X4,X5,X2)),X3))
| hAPP(v_F,v_Q____) != hAPP(X0,sK72(X1,X2,X0,X3))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X0),c_FuncSet_OPi(X1,X4,X3,X5))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3604,f9774]) ).
fof(f3604,plain,
! [X2,X3,X0,X1,X4,X5] :
( hAPP(X0,sK72(X1,X2,X0,X3)) != hAPP(X2,sK72(X1,X2,X0,X3))
| hBOOL(hAPP(hAPP(c_member(X1),sK83(X3,X1,X4,X5,X2)),X3))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X0),c_FuncSet_OPi(X1,X4,X3,X5))) ),
inference(resolution,[],[f2751,f2942]) ).
fof(f12834,plain,
( ~ spl85_161
| spl85_163
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12833,f4426,f3290,f11101,f9793]) ).
fof(f11101,plain,
( spl85_163
<=> ! [X0,X1,X3] :
( ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_163])]) ).
fof(f12833,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12832]) ).
fof(f12832,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(X2,X1)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10023,f9774]) ).
fof(f10023,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X2,X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X1),X0)),c_Transitive__Closure_Ortrancl(X4,X3)))
| ~ hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X2,X0)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2910,f9774]) ).
fof(f2910,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X1),X0)),c_Transitive__Closure_Ortrancl(X4,X3)))
| hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(X2,sK80(X1,X2,X3,X4)))
| ~ hBOOL(hAPP(X2,X1)) ),
inference(cnf_transformation,[],[f2127]) ).
fof(f2127,plain,
! [X0,X1,X2,X3,X4] :
( ~ hBOOL(hAPP(X2,X1))
| ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),sK79(X1,X2,X3,X4)),sK80(X1,X2,X3,X4))),X3))
& ~ hBOOL(hAPP(X2,sK80(X1,X2,X3,X4)))
& hBOOL(hAPP(X2,sK79(X1,X2,X3,X4)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X1),sK79(X1,X2,X3,X4))),c_Transitive__Closure_Ortrancl(X4,X3))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X1),X0)),c_Transitive__Closure_Ortrancl(X4,X3)))
| hBOOL(hAPP(X2,X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80])],[f2124,f2126,f2125]) ).
fof(f2125,plain,
! [X1,X2,X3,X4] :
( ? [X5] :
( ? [X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X5),X6)),X3))
& ~ hBOOL(hAPP(X2,X6))
& hBOOL(hAPP(X2,X5)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X1),X5)),c_Transitive__Closure_Ortrancl(X4,X3))) )
=> ( ? [X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),sK79(X1,X2,X3,X4)),X6)),X3))
& ~ hBOOL(hAPP(X2,X6))
& hBOOL(hAPP(X2,sK79(X1,X2,X3,X4))) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X1),sK79(X1,X2,X3,X4))),c_Transitive__Closure_Ortrancl(X4,X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f2126,plain,
! [X1,X2,X3,X4] :
( ? [X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),sK79(X1,X2,X3,X4)),X6)),X3))
& ~ hBOOL(hAPP(X2,X6))
& hBOOL(hAPP(X2,sK79(X1,X2,X3,X4))) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),sK79(X1,X2,X3,X4)),sK80(X1,X2,X3,X4))),X3))
& ~ hBOOL(hAPP(X2,sK80(X1,X2,X3,X4)))
& hBOOL(hAPP(X2,sK79(X1,X2,X3,X4))) ) ),
introduced(choice_axiom,[]) ).
fof(f2124,plain,
! [X0,X1,X2,X3,X4] :
( ~ hBOOL(hAPP(X2,X1))
| ? [X5] :
( ? [X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X5),X6)),X3))
& ~ hBOOL(hAPP(X2,X6))
& hBOOL(hAPP(X2,X5)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X1),X5)),c_Transitive__Closure_Ortrancl(X4,X3))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X4,X4)),hAPP(hAPP(c_Product__Type_OPair(X4,X4),X1),X0)),c_Transitive__Closure_Ortrancl(X4,X3)))
| hBOOL(hAPP(X2,X0)) ),
inference(rectify,[],[f1143]) ).
fof(f1143,plain,
! [X2,X3,X1,X4,X0] :
( ~ hBOOL(hAPP(X1,X3))
| ? [X5] :
( ? [X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X5),X6)),X4))
& ~ hBOOL(hAPP(X1,X6))
& hBOOL(hAPP(X1,X5)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X3),X5)),c_Transitive__Closure_Ortrancl(X0,X4))) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X3),X2)),c_Transitive__Closure_Ortrancl(X0,X4)))
| hBOOL(hAPP(X1,X2)) ),
inference(flattening,[],[f1142]) ).
fof(f1142,plain,
! [X3,X4,X2,X0,X1] :
( hBOOL(hAPP(X1,X2))
| ? [X5] :
( ? [X6] :
( ~ hBOOL(hAPP(X1,X6))
& hBOOL(hAPP(X1,X5))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X5),X6)),X4)) )
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X3),X5)),c_Transitive__Closure_Ortrancl(X0,X4))) )
| ~ hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X3),X2)),c_Transitive__Closure_Ortrancl(X0,X4))) ),
inference(ennf_transformation,[],[f1034]) ).
fof(f1034,plain,
! [X3,X4,X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X3),X2)),c_Transitive__Closure_Ortrancl(X0,X4)))
=> ( hBOOL(hAPP(X1,X3))
=> ( ! [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X3),X5)),c_Transitive__Closure_Ortrancl(X0,X4)))
=> ! [X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X5),X6)),X4))
=> ( hBOOL(hAPP(X1,X5))
=> hBOOL(hAPP(X1,X6)) ) ) )
=> hBOOL(hAPP(X1,X2)) ) ) ),
inference(rectify,[],[f168]) ).
fof(f168,axiom,
! [X8,X18,X23,X24,X19] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X24),X23)),c_Transitive__Closure_Ortrancl(X8,X19)))
=> ( hBOOL(hAPP(X18,X24))
=> ( ! [X41] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X24),X41)),c_Transitive__Closure_Ortrancl(X8,X19)))
=> ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X41),X38)),X19))
=> ( hBOOL(hAPP(X18,X41))
=> hBOOL(hAPP(X18,X38)) ) ) )
=> hBOOL(hAPP(X18,X23)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct) ).
fof(f12831,plain,
( spl85_161
| spl85_92
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10393,f4426,f3290,f6565,f9793]) ).
fof(f10393,plain,
( ! [X2,X0,X1] :
( c_Relation_Osingle__valued(X0,X1,X2)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2735,f9774]) ).
fof(f2735,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK69(X0,X1,X2)),sK70(X0,X1,X2))),X2))
| c_Relation_Osingle__valued(X0,X1,X2) ),
inference(cnf_transformation,[],[f1993]) ).
fof(f1993,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK69(X0,X1,X2)),sK68(X0,X1,X2))),X2))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK69(X0,X1,X2)),sK70(X0,X1,X2))),X2))
& sK70(X0,X1,X2) != sK68(X0,X1,X2) )
| c_Relation_Osingle__valued(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK68,sK69,sK70])],[f1990,f1992,f1991]) ).
fof(f1991,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X4),X3)),X2))
& ? [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X4),X5)),X2))
& X3 != X5 ) )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK69(X0,X1,X2)),sK68(X0,X1,X2))),X2))
& ? [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK69(X0,X1,X2)),X5)),X2))
& sK68(X0,X1,X2) != X5 ) ) ),
introduced(choice_axiom,[]) ).
fof(f1992,plain,
! [X0,X1,X2] :
( ? [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK69(X0,X1,X2)),X5)),X2))
& sK68(X0,X1,X2) != X5 )
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK69(X0,X1,X2)),sK70(X0,X1,X2))),X2))
& sK70(X0,X1,X2) != sK68(X0,X1,X2) ) ),
introduced(choice_axiom,[]) ).
fof(f1990,plain,
! [X0,X1,X2] :
( ? [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X4),X3)),X2))
& ? [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X4),X5)),X2))
& X3 != X5 ) )
| c_Relation_Osingle__valued(X0,X1,X2) ),
inference(rectify,[],[f1160]) ).
fof(f1160,plain,
! [X1,X2,X0] :
( ? [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X3)),X0))
& ? [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X0))
& X3 != X5 ) )
| c_Relation_Osingle__valued(X1,X2,X0) ),
inference(ennf_transformation,[],[f824]) ).
fof(f824,plain,
! [X2,X0,X1] :
( ! [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X3)),X0))
=> ! [X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X4),X5)),X0))
=> X3 = X5 ) )
=> c_Relation_Osingle__valued(X1,X2,X0) ),
inference(rectify,[],[f159]) ).
fof(f159,axiom,
! [X19,X8,X16] :
( ! [X41,X2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X16)),hAPP(hAPP(c_Product__Type_OPair(X8,X16),X2),X41)),X19))
=> ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X16)),hAPP(hAPP(c_Product__Type_OPair(X8,X16),X2),X38)),X19))
=> X38 = X41 ) )
=> c_Relation_Osingle__valued(X8,X16,X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedI) ).
fof(f12828,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10803,f4426,f3290,f9793]) ).
fof(f10803,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3684,f9774]) ).
fof(f3684,plain,
( ! [X4,X5] : hBOOL(hAPP(hAPP(c_member(X4),c_Arrow__Order__Mirabelle_OLin),hAPP(c_member(X5),hAPP(v_F,v_Q____))))
| ~ spl85_34 ),
inference(resolution,[],[f3314,f2711]) ).
fof(f12823,plain,
( spl85_178
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12822,f4426,f3290,f9793,f11730]) ).
fof(f12822,plain,
( ! [X15] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X15) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12821,f9774]) ).
fof(f12821,plain,
( ! [X18,X16,X17,X15] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(sK65(X16,X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18),X15) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12820]) ).
fof(f12820,plain,
( ! [X18,X16,X17,X15] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(sK65(X16,X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18),X15) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10790,f9774]) ).
fof(f10790,plain,
( ! [X18,X16,X17,X15] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17)),X18),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),c_COMBK(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16))))
| hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(sK65(X16,X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18),X15) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3951,f9774]) ).
fof(f3951,plain,
! [X18,X16,X17,X15] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X15,sK65(X16,X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18))),sK21(X15,sK65(X16,X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18)))),hAPP(sK20(X15,sK65(X16,X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18)),X15)))
| c_Arrow__Order__Mirabelle_Odictator(sK65(X16,X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18),X15)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17)),X18),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),c_COMBK(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16)))) ),
inference(resolution,[],[f2452,f2719]) ).
fof(f12819,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12818,f4426,f3290,f9793]) ).
fof(f12818,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12817]) ).
fof(f12817,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12816,f9774]) ).
fof(f12816,plain,
( ! [X40,X38,X41,X39,X36,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40))))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12815]) ).
fof(f12815,plain,
( ! [X40,X38,X41,X39,X36,X35,X42] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40))))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10714,f9774]) ).
fof(f10714,plain,
( ! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,X39)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40)))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3596,f9774]) ).
fof(f3596,plain,
! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,X39)))
| hBOOL(hAPP(hAPP(c_member(X35),sK72(X35,sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),X37,X38)),X38))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40)))) ),
inference(resolution,[],[f2749,f2719]) ).
fof(f12814,plain,
( ~ spl85_161
| ~ spl85_34
| spl85_49
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10781,f4426,f3450,f3290,f9793]) ).
fof(f3450,plain,
( spl85_49
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_49])]) ).
fof(f10781,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| spl85_49
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3451,f9774]) ).
fof(f3451,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))))
| spl85_49 ),
inference(avatar_component_clause,[],[f3450]) ).
fof(f12809,plain,
( ~ spl85_161
| spl85_194
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12805,f4426,f3290,f12807,f9793]) ).
fof(f12807,plain,
( spl85_194
<=> ! [X16,X17] : c_Arrow__Order__Mirabelle_Odictator(c_COMBI(X16),X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_194])]) ).
fof(f12805,plain,
( ! [X16,X17] :
( c_Arrow__Order__Mirabelle_Odictator(c_COMBI(X16),X17)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12804]) ).
fof(f12804,plain,
( ! [X16,X17] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(c_COMBI(X16),X17)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10864,f9774]) ).
fof(f10864,plain,
( ! [X16,X17] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X17,c_COMBI(X16))),sK21(X17,c_COMBI(X16)))),sK20(X17,c_COMBI(X16))))
| c_Arrow__Order__Mirabelle_Odictator(c_COMBI(X16),X17) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3967,f9774]) ).
fof(f3967,plain,
! [X16,X17] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBI(X16)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X17,c_COMBI(X16))),sK21(X17,c_COMBI(X16)))),sK20(X17,c_COMBI(X16))))
| c_Arrow__Order__Mirabelle_Odictator(c_COMBI(X16),X17) ),
inference(superposition,[],[f2454,f2523]) ).
fof(f12803,plain,
( ~ spl85_161
| spl85_170
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10920,f4426,f3290,f11305,f9793]) ).
fof(f10920,plain,
( ! [X40,X39] :
( hBOOL(hAPP(X40,X39))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4254,f9774]) ).
fof(f4254,plain,
! [X40,X38,X39] :
( ~ hBOOL(hAPP(c_Relation_OId__on(X38,c_Orderings_Obot__class_Obot(tc_fun(X38,tc_HOL_Obool))),X39))
| hBOOL(hAPP(X40,X39)) ),
inference(resolution,[],[f2244,f3239]) ).
fof(f3239,plain,
! [X2,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Relation_OId__on(X2,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X1),
inference(backward_demodulation,[],[f3041,f2210]) ).
fof(f2210,plain,
! [X0] : c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)),
inference(cnf_transformation,[],[f751]) ).
fof(f751,plain,
! [X0] : c_Relation_OId__on(X0,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X0),tc_HOL_Obool)),
inference(rectify,[],[f455]) ).
fof(f455,axiom,
! [X8] : c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X8),tc_HOL_Obool)) = c_Relation_OId__on(X8,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__empty) ).
fof(f3041,plain,
! [X2,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)),X1),
inference(equality_resolution,[],[f2630]) ).
fof(f2630,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)) != X0
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,X1) ),
inference(cnf_transformation,[],[f1885]) ).
fof(f1885,plain,
! [X0,X1,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)) != X0
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X0,X1) ),
inference(rectify,[],[f1179]) ).
fof(f1179,plain,
! [X1,X0,X2] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)) != X1
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(ennf_transformation,[],[f780]) ).
fof(f780,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X2),tc_HOL_Obool)) = X1
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X2,X2),tc_HOL_Obool),X1,X0) ),
inference(rectify,[],[f443]) ).
fof(f443,axiom,
! [X9,X10,X8] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X8),tc_HOL_Obool)) = X10
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),X10,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__by__empty) ).
fof(f12798,plain,
( ~ spl85_161
| spl85_58
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10747,f4426,f3290,f4223,f9793]) ).
fof(f10747,plain,
( ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2591,f9774]) ).
fof(f2591,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
| X0 = X1 ),
inference(cnf_transformation,[],[f1851]) ).
fof(f1851,plain,
! [X0,X1,X2] :
( ( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0))) )
& ( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
| X0 != X1 ) ),
inference(rectify,[],[f1850]) ).
fof(f1850,plain,
! [X1,X2,X0] :
( ( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(X0),X2),hAPP(c_fequal,X1))) )
& ( hBOOL(hAPP(hAPP(c_member(X0),X2),hAPP(c_fequal,X1)))
| X1 != X2 ) ),
inference(nnf_transformation,[],[f633]) ).
fof(f633,plain,
! [X1,X2,X0] :
( X1 = X2
<=> hBOOL(hAPP(hAPP(c_member(X0),X2),hAPP(c_fequal,X1))) ),
inference(rectify,[],[f59]) ).
fof(f59,axiom,
! [X8,X13,X14] :
( hBOOL(hAPP(hAPP(c_member(X8),X14),hAPP(c_fequal,X13)))
<=> X13 = X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
fof(f12796,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12795,f4426,f3290,f9793]) ).
fof(f12795,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12794]) ).
fof(f12794,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12793,f9774]) ).
fof(f12793,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X10)),X9),c_FuncSet_OPi(X6,X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X8),X11)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10241,f9774]) ).
fof(f10241,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),hAPP(v_F,v_Q____)),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X8)),sK57(X9,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X8),X6,X10,X11)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X10)),X9),c_FuncSet_OPi(X6,X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X8),X11))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3657,f9774]) ).
fof(f3657,plain,
! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X7)),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X8)),sK57(X9,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X8),X6,X10,X11)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X10)),X9),c_FuncSet_OPi(X6,X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X8),X11))) ),
inference(resolution,[],[f2854,f2649]) ).
fof(f2854,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X0),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X1),X3)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)),X0)) ),
inference(cnf_transformation,[],[f2081]) ).
fof(f12792,plain,
( spl85_161
| spl85_42
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10922,f4426,f3290,f3379,f9793]) ).
fof(f10922,plain,
( ! [X0] :
( hBOOL(X0)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2866,f9774]) ).
fof(f12788,plain,
( spl85_178
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12787,f4426,f3290,f9793,f11730]) ).
fof(f12787,plain,
( ! [X94] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X94) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12786]) ).
fof(f12786,plain,
( ! [X94] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X94)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12785,f9774]) ).
fof(f12785,plain,
( ! [X90,X91,X89,X94,X92,X93] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X94,hAPP(c_COMBB(X89,X90,X91,X92),X93))),sK21(X94,hAPP(c_COMBB(X89,X90,X91,X92),X93)))),hAPP(v_F,v_Q____)))
| ~ hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X94) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12784,f9774]) ).
fof(f12784,plain,
( ! [X90,X91,X89,X94,X92,X93] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(c_COMBB(X89,X90,X91,X92),X93),X94)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X94,hAPP(c_COMBB(X89,X90,X91,X92),X93))),sK21(X94,hAPP(c_COMBB(X89,X90,X91,X92),X93)))),hAPP(v_F,v_Q____)))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9839,f9774]) ).
fof(f9839,plain,
( ! [X90,X91,X89,X94,X92,X93] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(X89,X90,X91,X92),X93)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X94,hAPP(c_COMBB(X89,X90,X91,X92),X93))),sK21(X94,hAPP(c_COMBB(X89,X90,X91,X92),X93)))),hAPP(v_F,v_Q____)))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(c_COMBB(X89,X90,X91,X92),X93),X94) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4286,f9774]) ).
fof(f4286,plain,
! [X90,X91,X89,X94,X92,X93] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X94,hAPP(c_COMBB(X89,X90,X91,X92),X93))),sK21(X94,hAPP(c_COMBB(X89,X90,X91,X92),X93)))),hAPP(X92,hAPP(X93,sK20(X94,hAPP(c_COMBB(X89,X90,X91,X92),X93))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(X89,X90,X91,X92),X93)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(c_COMBB(X89,X90,X91,X92),X93),X94) ),
inference(superposition,[],[f2454,f2177]) ).
fof(f2177,plain,
! [X2,X3,X0,X1,X4,X5] : hAPP(X0,hAPP(X1,X3)) = hAPP(hAPP(c_COMBB(X2,X5,X4,X0),X1),X3),
inference(cnf_transformation,[],[f1508]) ).
fof(f1508,plain,
! [X0,X1,X2,X3,X4,X5] : hAPP(X0,hAPP(X1,X3)) = hAPP(hAPP(c_COMBB(X2,X5,X4,X0),X1),X3),
inference(rectify,[],[f698]) ).
fof(f698,plain,
! [X1,X2,X3,X0,X4,X5] : hAPP(X1,hAPP(X2,X0)) = hAPP(hAPP(c_COMBB(X3,X5,X4,X1),X2),X0),
inference(rectify,[],[f526]) ).
fof(f526,axiom,
! [X15,X18,X66,X16,X31,X8] : hAPP(hAPP(c_COMBB(X16,X8,X31,X18),X66),X15) = hAPP(X18,hAPP(X66,X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBB__1) ).
fof(f12776,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10847,f4426,f3290,f9793]) ).
fof(f10847,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2839,f9774]) ).
fof(f2839,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X1)),c_COMBI(X1)),c_FuncSet_OPi(X1,X1,X0,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X0)))),
inference(cnf_transformation,[],[f598]) ).
fof(f598,plain,
! [X0,X1] : hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X1)),c_COMBI(X1)),c_FuncSet_OPi(X1,X1,X0,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X0)))),
inference(rectify,[],[f65]) ).
fof(f65,axiom,
! [X10,X8] : hBOOL(hAPP(hAPP(c_member(tc_fun(X8,X8)),c_COMBI(X8)),c_FuncSet_OPi(X8,X8,X10,c_COMBK(tc_fun(X8,tc_HOL_Obool),X8,X10)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_funcset__id) ).
fof(f12772,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12771,f4426,f3290,f9793]) ).
fof(f12771,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12770]) ).
fof(f12770,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12769,f9774]) ).
fof(f12769,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_fequal,hAPP(v_F,v_Q____))),c_Arrow__Order__Mirabelle_OLin))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10135,f9774]) ).
fof(f10135,plain,
( ! [X6,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X6))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_fequal,hAPP(v_F,v_Q____))),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3621,f9774]) ).
fof(f3621,plain,
! [X6,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X6))),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X6)))) ),
inference(resolution,[],[f2792,f3035]) ).
fof(f3035,plain,
! [X2,X1] : hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X1))),
inference(equality_resolution,[],[f2590]) ).
fof(f2590,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(c_fequal,X0)))
| X0 != X1 ),
inference(cnf_transformation,[],[f1851]) ).
fof(f12760,plain,
( spl85_58
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12759,f4426,f3290,f9793,f4223]) ).
fof(f12759,plain,
( ! [X0,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| X0 = X1 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10107,f9774]) ).
fof(f10107,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),sK84(X0,X1)))
| X0 = X1 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2949,f9774]) ).
fof(f2949,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),sK84(X0,X1)))
| X0 = X1 ),
inference(cnf_transformation,[],[f2167]) ).
fof(f12734,plain,
( spl85_92
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12733,f4426,f3290,f6565]) ).
fof(f12733,plain,
( ! [X2,X0,X1] : c_Relation_Osingle__valued(X0,X1,X2)
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f12732]) ).
fof(f12732,plain,
( ! [X2,X0,X1] :
( hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____)
| c_Relation_Osingle__valued(X0,X1,X2) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11048,f9774]) ).
fof(f11048,plain,
( ! [X2,X0,X1] :
( hAPP(v_F,v_Q____) != sK70(X0,X1,X2)
| c_Relation_Osingle__valued(X0,X1,X2) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2734,f9774]) ).
fof(f2734,plain,
! [X2,X0,X1] :
( c_Relation_Osingle__valued(X0,X1,X2)
| sK70(X0,X1,X2) != sK68(X0,X1,X2) ),
inference(cnf_transformation,[],[f1993]) ).
fof(f12731,plain,
( spl85_193
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12727,f4426,f3290,f9793,f12729]) ).
fof(f12729,plain,
( spl85_193
<=> ! [X2,X1,X3] :
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_193])]) ).
fof(f12727,plain,
( ! [X2,X3,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,X3)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10184,f9774]) ).
fof(f10184,plain,
( ! [X2,X3,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,X3))
| X2 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Oless__than,sK84(X3,X2)),hAPP(hAPP(c_COMBS(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt,c_Product__Type_OPair(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),X1)),c_COMBI(tc_Arrow__Order__Mirabelle_Oalt))))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3917,f9774]) ).
fof(f3917,plain,
! [X2,X3,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X1,X2),hAPP(X1,X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Oless__than,sK84(X3,X2)),hAPP(hAPP(c_COMBS(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt,c_Product__Type_OPair(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),X1)),c_COMBI(tc_Arrow__Order__Mirabelle_Oalt)))))
| X2 = X3 ),
inference(resolution,[],[f2974,f2949]) ).
fof(f12726,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12725,f4426,f3290,f9793]) ).
fof(f12725,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12724]) ).
fof(f12724,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12723,f9774]) ).
fof(f12723,plain,
( ! [X11,X8,X6,X9] :
( hBOOL(hAPP(hAPP(c_member(X6),sK72(X6,X11,X8,X9)),X9))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12722]) ).
fof(f12722,plain,
( ! [X11,X8,X6,X9] :
( hBOOL(hAPP(hAPP(c_member(X6),sK72(X6,X11,X8,X9)),X9))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10401,f9774]) ).
fof(f10401,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X7)),X8),c_FuncSet_OPi(X6,X7,X9,X10)))
| hBOOL(hAPP(hAPP(c_member(X6),sK72(X6,X11,X8,X9)),X9))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3591,f9774]) ).
fof(f3591,plain,
! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(X6),sK72(X6,X11,X8,X9)),X9))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X7)),X8),c_FuncSet_OPi(X6,X7,X9,X10)))
| hBOOL(hAPP(hAPP(c_member(X6),sK57(X11,X9,X6,X7,X10)),X9)) ),
inference(resolution,[],[f2749,f2649]) ).
fof(f12720,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12719,f4426,f3290,f9793]) ).
fof(f12719,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12718]) ).
fof(f12718,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12717,f9774]) ).
fof(f12717,plain,
( ! [X8,X9,X12,X13] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(X8),sK57(hAPP(v_F,v_Q____),X12,X8,X9,X13)),X12)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9982,f9774]) ).
fof(f9982,plain,
( ! [X10,X11,X8,X9,X7,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_fun(X8,X9))),X10),c_FuncSet_OPi(X7,tc_fun(X8,X9),X11,c_COMBK(tc_fun(tc_fun(X8,X9),tc_HOL_Obool),X7,c_FuncSet_OPi(X8,X9,X12,X13)))))
| hBOOL(hAPP(hAPP(c_member(X8),sK57(hAPP(v_F,v_Q____),X12,X8,X9,X13)),X12)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3524,f9774]) ).
fof(f3524,plain,
! [X10,X11,X8,X9,X7,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(X8),sK57(hAPP(X10,sK65(c_FuncSet_OPi(X8,X9,X12,X13),tc_fun(X8,X9),X11,X7,X10)),X12,X8,X9,X13)),X12))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_fun(X8,X9))),X10),c_FuncSet_OPi(X7,tc_fun(X8,X9),X11,c_COMBK(tc_fun(tc_fun(X8,X9),tc_HOL_Obool),X7,c_FuncSet_OPi(X8,X9,X12,X13))))) ),
inference(resolution,[],[f2718,f2649]) ).
fof(f12712,plain,
( spl85_192
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12708,f4426,f3290,f9793,f12710]) ).
fof(f12710,plain,
( spl85_192
<=> ! [X3,X4,X9,X0,X5,X2,X1] :
( ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,X2)
| c_Recdef_Owfrec__rel(X0,X4,X3,X1,X9,hAPP(v_F,v_Q____)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_192])]) ).
fof(f12708,plain,
( ! [X2,X3,X0,X1,X9,X4,X5] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,X2)
| c_Recdef_Owfrec__rel(X0,X4,X3,X1,X9,hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12707,f9774]) ).
fof(f12707,plain,
( ! [X2,X3,X0,X1,X9,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(v_F,v_Q____)),X3))
| ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,X2)
| c_Recdef_Owfrec__rel(X0,X4,X3,X1,X9,hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10434,f9774]) ).
fof(f10434,plain,
( ! [X2,X3,X0,X1,X9,X4,X5] :
( c_Recdef_Owfrec__rel(X0,X4,X3,X1,X9,hAPP(sK49(X0,X1,X2,X3,X4,X5),X9))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(v_F,v_Q____)),X3))
| ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,X2) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2608,f9774]) ).
fof(f2608,plain,
! [X2,X3,X0,X1,X9,X4,X5] :
( c_Recdef_Owfrec__rel(X0,X4,X3,X1,X9,hAPP(sK49(X0,X1,X2,X3,X4,X5),X9))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X9),X5)),X3))
| ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,X2) ),
inference(cnf_transformation,[],[f1867]) ).
fof(f12703,plain,
( spl85_167
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12702,f4426,f3290,f9793,f11209]) ).
fof(f12702,plain,
( ! [X3,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(X1,X3)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10570,f9774]) ).
fof(f10570,plain,
( ! [X3,X1] :
( ~ hBOOL(hAPP(X1,X3))
| hBOOL(hAPP(hAPP(v_F,v_Q____),X3)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2374,f9774]) ).
fof(f12687,plain,
( spl85_92
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10390,f4426,f3290,f9793,f6565]) ).
fof(f10390,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Relation_Osingle__valued(X0,X1,X2) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2618,f9774]) ).
fof(f2618,plain,
! [X2,X0,X1] :
( c_Relation_Osingle__valued(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK50(X0,X1,X2)),sK51(X0,X1,X2))),X2)) ),
inference(cnf_transformation,[],[f1877]) ).
fof(f12679,plain,
( spl85_162
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12678,f4426,f3290,f9793,f11077]) ).
fof(f12678,plain,
( ! [X6,X4,X5] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X5),hAPP(X4,X6)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10459,f9774]) ).
fof(f10459,plain,
( ! [X8,X6,X9,X7,X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X5),hAPP(X4,X6))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(v_F,v_Q____)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X7),X7,c_Wellfounded_Olex__prod(tc_Nat_Onat,X7,c_Wellfounded_Oless__than,c_Set_Oinsert(X8,hAPP(v_F,v_Q____),X9)),hAPP(hAPP(c_COMBS(X7,X7,tc_prod(tc_Nat_Onat,X7)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X7,tc_prod(tc_Nat_Onat,X7)),X7,c_Product__Type_OPair(tc_Nat_Onat,X7)),X4)),c_COMBI(X7))))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3958,f9774]) ).
fof(f3958,plain,
! [X8,X6,X9,X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X5),X6)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X7),X7,c_Wellfounded_Olex__prod(tc_Nat_Onat,X7,c_Wellfounded_Oless__than,c_Set_Oinsert(X8,hAPP(hAPP(c_Product__Type_OPair(X7,X7),X5),X6),X9)),hAPP(hAPP(c_COMBS(X7,X7,tc_prod(tc_Nat_Onat,X7)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X7,tc_prod(tc_Nat_Onat,X7)),X7,c_Product__Type_OPair(tc_Nat_Onat,X7)),X4)),c_COMBI(X7)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X5),hAPP(X4,X6)) ),
inference(resolution,[],[f3564,f2974]) ).
fof(f3564,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),X1),c_Set_Oinsert(X2,X1,X3))),
inference(resolution,[],[f3015,f2711]) ).
fof(f3015,plain,
! [X3,X0,X1] : hBOOL(hAPP(c_Set_Oinsert(X1,X3,X0),X3)),
inference(equality_resolution,[],[f2403]) ).
fof(f2403,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(c_Set_Oinsert(X1,X2,X0),X3))
| X2 != X3 ),
inference(cnf_transformation,[],[f1689]) ).
fof(f12675,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10873,f4426,f3290,f9793]) ).
fof(f10873,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2698,f9774]) ).
fof(f2698,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X0)),c_FuncSet_Orestrict(X2,X0,X1,X3)),c_FuncSet_Oextensional(X2,X0,X3))),
inference(cnf_transformation,[],[f1954]) ).
fof(f1954,plain,
! [X0,X1,X2,X3] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X0)),c_FuncSet_Orestrict(X2,X0,X1,X3)),c_FuncSet_Oextensional(X2,X0,X3))),
inference(rectify,[],[f750]) ).
fof(f750,plain,
! [X3,X1,X2,X0] : hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X3)),c_FuncSet_Orestrict(X2,X3,X1,X0)),c_FuncSet_Oextensional(X2,X3,X0))),
inference(rectify,[],[f118]) ).
fof(f118,axiom,
! [X10,X1,X8,X16] : hBOOL(hAPP(hAPP(c_member(tc_fun(X8,X16)),c_FuncSet_Orestrict(X8,X16,X1,X10)),c_FuncSet_Oextensional(X8,X16,X10))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrict__extensional) ).
fof(f12672,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12671,f4426,f3290,f9793]) ).
fof(f12671,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12670]) ).
fof(f12670,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12669,f9774]) ).
fof(f12669,plain,
( ! [X2,X3,X0,X5] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(X0),sK72(X0,X2,X5,X3)),X3)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12668]) ).
fof(f12668,plain,
( ! [X2,X3,X0,X5] :
( hBOOL(hAPP(hAPP(c_member(X0),sK72(X0,X2,X5,X3)),X3))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10080,f9774]) ).
fof(f10080,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,X4)))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(X0),sK72(X0,X2,X5,X3)),X3)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3597,f9774]) ).
fof(f3597,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X0),sK72(X0,X2,X5,X3)),X3))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,X4)))
| hBOOL(hAPP(hAPP(c_member(X0),sK83(X3,X0,X1,X4,X5)),X3)) ),
inference(resolution,[],[f2750,f2942]) ).
fof(f12663,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12662,f4426,f3290,f9793]) ).
fof(f12662,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12661]) ).
fof(f12661,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12660,f9774]) ).
fof(f12660,plain,
( ! [X2,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(v_F,v_Q____)),X2))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10217,f9774]) ).
fof(f10217,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(v_F,v_Q____)),X2)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2525,f9774]) ).
fof(f2525,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK37(X0,X1,X2)),X0)),X2)) ),
inference(cnf_transformation,[],[f1798]) ).
fof(f1798,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(X1),sK37(X0,X1,X2)),c_Wellfounded_Oacc(X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK37(X0,X1,X2)),X0)),X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f1479,f1797]) ).
fof(f1797,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X0)),X2)) )
=> ( ~ hBOOL(hAPP(hAPP(c_member(X1),sK37(X0,X1,X2)),c_Wellfounded_Oacc(X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK37(X0,X1,X2)),X0)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1479,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
| ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X0)),X2)) ) ),
inference(ennf_transformation,[],[f566]) ).
fof(f566,plain,
! [X1,X2,X0] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
=> ~ ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X0)),X2))
=> hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2))) ) ),
inference(rectify,[],[f68]) ).
fof(f68,axiom,
! [X14,X8,X15] :
( ~ hBOOL(hAPP(hAPP(c_member(X8),X14),c_Wellfounded_Oacc(X8,X15)))
=> ~ ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X38),X14)),X15))
=> hBOOL(hAPP(hAPP(c_member(X8),X38),c_Wellfounded_Oacc(X8,X15))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__acc__down) ).
fof(f12638,plain,
( ~ spl85_161
| spl85_170
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f9859,f4426,f3290,f11305,f9793]) ).
fof(f9859,plain,
( ! [X3,X1] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2501,f9774]) ).
fof(f12632,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12631,f4426,f3290,f9793]) ).
fof(f12631,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10039,f9774]) ).
fof(f10039,plain,
( ! [X2,X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Omktop(X2,X3)))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3022,f9774]) ).
fof(f3022,plain,
! [X2,X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X3)),c_Arrow__Order__Mirabelle_Omktop(X2,X3))),
inference(equality_resolution,[],[f3021]) ).
fof(f3021,plain,
! [X2,X3,X0] :
( X0 != X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X3)),c_Arrow__Order__Mirabelle_Omktop(X2,X0))) ),
inference(equality_resolution,[],[f2466]) ).
fof(f2466,plain,
! [X2,X3,X0,X1] :
( X1 != X3
| X0 != X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Omktop(X2,X0))) ),
inference(cnf_transformation,[],[f1743]) ).
fof(f12626,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12625,f4426,f3290,f9793]) ).
fof(f12625,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12624]) ).
fof(f12624,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12623,f9774]) ).
fof(f12623,plain,
( ! [X21,X19,X22,X23,X20] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12622]) ).
fof(f12622,plain,
( ! [X21,X19,X22,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23)))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10410,f9774]) ).
fof(f10410,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3594,f9774]) ).
fof(f3594,plain,
! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25)))
| hBOOL(hAPP(hAPP(c_member(X19),sK72(X19,sK83(c_FuncSet_OPi(X19,X20,X22,X23),tc_fun(X19,X20),X24,X25,X26),X21,X22)),X22))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23))) ),
inference(resolution,[],[f2749,f2942]) ).
fof(f12613,plain,
( spl85_170
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12612,f4426,f3290,f9793,f11305]) ).
fof(f12612,plain,
( ! [X9,X4] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X4,X9)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10728,f9774]) ).
fof(f10728,plain,
( ! [X9,X4] :
( hBOOL(hAPP(X4,X9))
| ~ hBOOL(hAPP(hAPP(hAPP(v_F,v_Q____),X4),X9)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4650,f9774]) ).
fof(f4650,plain,
! [X3,X8,X6,X9,X7,X4,X5] :
( hBOOL(hAPP(X4,X9))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X6,X7,X8),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool))),X5),X4),X9)) ),
inference(superposition,[],[f2617,f2728]) ).
fof(f2617,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X3),X1))
| hBOOL(hAPP(X0,X1)) ),
inference(cnf_transformation,[],[f1872]) ).
fof(f1872,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X3),X1)) ),
inference(rectify,[],[f1101]) ).
fof(f1101,plain,
! [X1,X3,X2,X0] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X1),X0),X3)) ),
inference(ennf_transformation,[],[f995]) ).
fof(f995,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X1),X0),X3))
=> hBOOL(hAPP(X1,X3)) ),
inference(rectify,[],[f95]) ).
fof(f95,axiom,
! [X9,X10,X8,X14] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X10),X9),X14))
=> hBOOL(hAPP(X10,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D1) ).
fof(f12602,plain,
( ~ spl85_161
| ~ spl85_34
| spl85_52
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10842,f4426,f3625,f3290,f9793]) ).
fof(f3625,plain,
( spl85_52
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_P____)),c_Arrow__Order__Mirabelle_OLin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_52])]) ).
fof(f10842,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| spl85_52
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3627,f9774]) ).
fof(f3627,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_P____)),c_Arrow__Order__Mirabelle_OLin))
| spl85_52 ),
inference(avatar_component_clause,[],[f3625]) ).
fof(f12585,plain,
( spl85_178
| ~ spl85_161
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12584,f4426,f3371,f3290,f9793,f11730]) ).
fof(f12584,plain,
( ! [X12] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X12) )
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10863,f9774]) ).
fof(f10863,plain,
( ! [X10,X11,X12] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(c_Product__Type_OPair(X10,X11),X12) )
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4236,f9774]) ).
fof(f4236,plain,
( ! [X10,X11,X12] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_Product__Type_OPair(X10,X11)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| c_Arrow__Order__Mirabelle_Odictator(c_Product__Type_OPair(X10,X11),X12) )
| ~ spl85_40 ),
inference(resolution,[],[f3652,f2454]) ).
fof(f12580,plain,
( ~ spl85_161
| spl85_96
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10292,f4426,f3290,f6736,f9793]) ).
fof(f6736,plain,
( spl85_96
<=> ! [X2,X0,X1,X3] : c_Predicate_ODomainP(X3,X1,X2,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_96])]) ).
fof(f10292,plain,
( ! [X2,X3,X0,X1] :
( c_Predicate_ODomainP(X3,X1,X2,X0)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2844,f9774]) ).
fof(f12572,plain,
( spl85_168
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10977,f4426,f3371,f3290,f11279]) ).
fof(f10977,plain,
( ! [X195,X199,X196] : c_Predicate_ORangeP(X195,X196,hAPP(v_F,v_Q____),X199)
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4341,f9774]) ).
fof(f4341,plain,
( ! [X195,X198,X199,X196,X197] : c_Predicate_ORangeP(X195,X196,c_Product__Type_OPair(X197,X198),X199)
| ~ spl85_40 ),
inference(resolution,[],[f2173,f3372]) ).
fof(f12561,plain,
( spl85_161
| spl85_61
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10805,f4426,f3290,f4384,f9793]) ).
fof(f10805,plain,
( ! [X23] :
( ~ hBOOL(X23)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4085,f9774]) ).
fof(f4085,plain,
! [X28,X26,X27,X24,X25,X23] :
( ~ hBOOL(X23)
| hBOOL(hAPP(hAPP(c_member(X24),c_COMBK(X25,X26,X23)),hAPP(c_member(X27),X28))) ),
inference(resolution,[],[f3315,f2711]) ).
fof(f3315,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),X3),c_COMBK(X0,X1,X2)))
| ~ hBOOL(X2) ),
inference(superposition,[],[f2711,f2430]) ).
fof(f2430,plain,
! [X2,X3,X0,X1] : hAPP(c_COMBK(X3,X0,X2),X1) = X2,
inference(cnf_transformation,[],[f1710]) ).
fof(f1710,plain,
! [X0,X1,X2,X3] : hAPP(c_COMBK(X3,X0,X2),X1) = X2,
inference(rectify,[],[f859]) ).
fof(f859,plain,
! [X2,X3,X0,X1] : hAPP(c_COMBK(X1,X2,X0),X3) = X0,
inference(rectify,[],[f525]) ).
fof(f525,axiom,
! [X75,X8,X16,X76] : hAPP(c_COMBK(X8,X16,X75),X76) = X75,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__COMBK__1) ).
fof(f12560,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12559,f4426,f3371,f3290,f9793]) ).
fof(f12559,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10734,f9774]) ).
fof(f10734,plain,
( ! [X2] : hBOOL(hAPP(hAPP(v_F,v_Q____),X2))
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3655,f9774]) ).
fof(f3655,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),c_Product__Type_OPair(X0,X1)),X3),X2))
| ~ spl85_40 ),
inference(superposition,[],[f3372,f2728]) ).
fof(f12558,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10764,f4426,f3371,f3290,f9793]) ).
fof(f10764,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4243,f9774]) ).
fof(f4243,plain,
( ! [X50,X51,X48,X49,X52,X53] : hBOOL(hAPP(hAPP(c_member(X48),hAPP(c_Product__Type_OPair(X49,X50),X51)),hAPP(c_member(X52),X53)))
| ~ spl85_40 ),
inference(resolution,[],[f3652,f2711]) ).
fof(f12553,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12552,f4426,f3290,f9793]) ).
fof(f12552,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12551]) ).
fof(f12551,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12550,f9774]) ).
fof(f12550,plain,
( ! [X16,X14,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16))))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f12549]) ).
fof(f12549,plain,
( ! [X16,X14,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16))))
| hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12548,f9774]) ).
fof(f12548,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(X17,sK72(X12,X14,X17,X15))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16)))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10005,f9774]) ).
fof(f10005,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(X12),sK65(X16,X13,X15,X12,X17)),X15))
| hAPP(v_F,v_Q____) != hAPP(X17,sK72(X12,X14,X17,X15))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16)))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3613,f9774]) ).
fof(f3613,plain,
! [X16,X14,X17,X15,X12,X13] :
( hAPP(X14,sK72(X12,X14,X17,X15)) != hAPP(X17,sK72(X12,X14,X17,X15))
| hBOOL(hAPP(hAPP(c_member(X12),sK65(X16,X13,X15,X12,X17)),X15))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16)))) ),
inference(resolution,[],[f2752,f2719]) ).
fof(f2752,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X3),c_FuncSet_OPi(X1,X0,X4,X5)))
| hAPP(X3,sK72(X1,X2,X3,X4)) != hAPP(X2,sK72(X1,X2,X3,X4))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X0)),X2),c_FuncSet_OPi(X1,X0,X4,X5))) ),
inference(cnf_transformation,[],[f2007]) ).
fof(f12547,plain,
( ~ spl85_161
| spl85_84
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12546,f4426,f3290,f6422,f9793]) ).
fof(f12546,plain,
( ! [X0,X1] :
( c_Arrow__Order__Mirabelle_Odictator(X1,X0)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12545]) ).
fof(f12545,plain,
( ! [X0,X1] :
( c_Arrow__Order__Mirabelle_Odictator(X1,X0)
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12544,f9774]) ).
fof(f12544,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X0,X1)),sK21(X0,X1))),hAPP(v_F,v_Q____)))
| c_Arrow__Order__Mirabelle_Odictator(X1,X0)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9934,f9774]) ).
fof(f9934,plain,
( ! [X0,X1] :
( c_Arrow__Order__Mirabelle_Odictator(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X0,X1)),sK21(X0,X1))),hAPP(v_F,v_Q____))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2454,f9774]) ).
fof(f12541,plain,
( spl85_191
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12537,f4426,f3290,f9793,f12539]) ).
fof(f12539,plain,
( spl85_191
<=> ! [X65,X59,X58,X64,X66] : c_Predicate_ORangeP(X65,X66,hAPP(X58,X59),X64) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_191])]) ).
fof(f12537,plain,
( ! [X65,X58,X59,X66,X64] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Predicate_ORangeP(X65,X66,hAPP(X58,X59),X64) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10724,f9774]) ).
fof(f10724,plain,
( ! [X65,X58,X59,X66,X64] :
( ~ hBOOL(hAPP(hAPP(hAPP(v_F,v_Q____),X59),X64))
| c_Predicate_ORangeP(X65,X66,hAPP(X58,X59),X64) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4355,f9774]) ).
fof(f4355,plain,
! [X65,X58,X59,X62,X63,X66,X60,X61,X64] :
( c_Predicate_ORangeP(X65,X66,hAPP(X58,X59),X64)
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X61,X62,X63),X58),X60),X59),X64)) ),
inference(superposition,[],[f2173,f2728]) ).
fof(f12509,plain,
( ~ spl85_161
| spl85_95
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12508,f4426,f3290,f6693,f9793]) ).
fof(f12508,plain,
( ! [X6,X9,X7] :
( X7 = X9
| ~ hBOOL(hAPP(v_F,v_Q____))
| X6 = X9 )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12507]) ).
fof(f12507,plain,
( ! [X6,X9,X7] :
( X7 = X9
| ~ hBOOL(hAPP(v_F,v_Q____))
| X6 = X9
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12506,f9774]) ).
fof(f12506,plain,
( ! [X8,X6,X9,X7] :
( X6 = X9
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6)))
| X7 = X9 )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12505]) ).
fof(f12505,plain,
( ! [X8,X6,X9,X7] :
( X6 = X9
| ~ hBOOL(hAPP(v_F,v_Q____))
| X7 = X9
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12504,f9774]) ).
fof(f12504,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6)))
| ~ hBOOL(hAPP(v_F,v_Q____))
| X7 = X9 )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12503]) ).
fof(f12503,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6)))
| X6 = X9
| X7 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12502,f9774]) ).
fof(f12502,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| X7 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X7)),X8))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| X6 = X9 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10146,f9774]) ).
fof(f10146,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X7)),X8))
| X7 = X9
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3699,f9774]) ).
fof(f3699,plain,
! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X9)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X7)),X8))
| X7 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6)),c_Arrow__Order__Mirabelle_OLin))
| X6 = X9 ),
inference(resolution,[],[f3089,f2792]) ).
fof(f3089,plain,
! [X2,X3,X0,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X0))
| X2 = X4
| X2 = X3 ),
inference(duplicate_literal_removal,[],[f3006]) ).
fof(f3006,plain,
! [X2,X3,X0,X4] :
( X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| X2 = X3
| X2 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X0)) ),
inference(equality_resolution,[],[f2361]) ).
fof(f2361,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| X2 = X3
| X1 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X0))
| X1 != X2
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(cnf_transformation,[],[f1663]) ).
fof(f12495,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12494,f4426,f3290,f9793]) ).
fof(f12494,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10700,f9774]) ).
fof(f10700,plain,
( ! [X11,X12,X13] : hBOOL(hAPP(hAPP(c_member(tc_prod(X11,X12)),hAPP(hAPP(c_Product__Type_OPair(X11,X12),X13),hAPP(v_F,v_Q____))),hAPP(v_F,v_Q____)))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f9765,f9774]) ).
fof(f9765,plain,
( ! [X11,X14,X15,X12,X13] : hBOOL(hAPP(hAPP(c_member(tc_prod(X11,X12)),hAPP(hAPP(c_Product__Type_OPair(X11,X12),X13),hAPP(v_F,v_Q____))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X11,X12),tc_HOL_Obool)),X14),X15)))
| ~ spl85_34
| ~ spl85_64 ),
inference(resolution,[],[f9759,f2208]) ).
fof(f2208,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X2,c_COMBC(X4,tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4,tc_prod(X2,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X4),tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool),X4,c_member(tc_prod(X2,X4)))),c_Product__Type_OPair(X2,X4)))),X0)),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X2,c_COMBC(X4,tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4,tc_prod(X2,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X4),tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool),X4,c_member(tc_prod(X2,X4)))),c_Product__Type_OPair(X2,X4)))),X5)),X1),X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X4)),hAPP(hAPP(c_Product__Type_OPair(X2,X4),X1),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X4),tc_HOL_Obool)),X0),X5))) ),
inference(cnf_transformation,[],[f1538]) ).
fof(f1538,plain,
! [X0,X1,X2,X3,X4,X5] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X2,c_COMBC(X4,tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4,tc_prod(X2,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X4),tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool),X4,c_member(tc_prod(X2,X4)))),c_Product__Type_OPair(X2,X4)))),X0)),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X2,c_COMBC(X4,tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4,tc_prod(X2,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X4),tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool),X4,c_member(tc_prod(X2,X4)))),c_Product__Type_OPair(X2,X4)))),X5)),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X4)),hAPP(hAPP(c_Product__Type_OPair(X2,X4),X1),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X4),tc_HOL_Obool)),X0),X5))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X4)),hAPP(hAPP(c_Product__Type_OPair(X2,X4),X1),X3)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X2,X4),tc_HOL_Obool)),X0),X5)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_fun(X4,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X2,c_COMBC(X4,tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4,tc_prod(X2,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X4),tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool),X4,c_member(tc_prod(X2,X4)))),c_Product__Type_OPair(X2,X4)))),X0)),hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4,tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_fun(X4,tc_HOL_Obool)),X2,c_COMBC(X4,tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X4,tc_prod(X2,X4)),tc_fun(X4,tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X4),tc_fun(tc_fun(tc_prod(X2,X4),tc_HOL_Obool),tc_HOL_Obool),X4,c_member(tc_prod(X2,X4)))),c_Product__Type_OPair(X2,X4)))),X5)),X1),X3)) ) ),
inference(rectify,[],[f1537]) ).
fof(f1537,plain,
! [X5,X3,X1,X0,X2,X4] :
( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)),X3),X0))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X0)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X4))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X0)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X4)))
| ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)),X3),X0)) ) ),
inference(nnf_transformation,[],[f838]) ).
fof(f838,plain,
! [X5,X3,X1,X0,X2,X4] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_fun(X2,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X5)),hAPP(hAPP(c_COMBC(X1,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X1,c_COMBC(X2,tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X1,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool)),X1,c_COMBB(tc_prod(X1,X2),tc_fun(tc_fun(tc_prod(X1,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X1,X2)))),c_Product__Type_OPair(X1,X2)))),X4)),X3),X0))
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X2)),hAPP(hAPP(c_Product__Type_OPair(X1,X2),X3),X0)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X2),tc_HOL_Obool)),X5),X4))) ),
inference(rectify,[],[f115]) ).
fof(f115,axiom,
! [X13,X8,X16,X14,X34,X15] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X16)),hAPP(hAPP(c_Product__Type_OPair(X8,X16),X14),X13)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X8,X16),tc_HOL_Obool)),X15),X34)))
<=> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_fun(X16,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X8,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X8,c_COMBC(X16,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_prod(X8,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),X8,c_COMBB(tc_prod(X8,X16),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool),X16,c_member(tc_prod(X8,X16)))),c_Product__Type_OPair(X8,X16)))),X15)),hAPP(hAPP(c_COMBC(X8,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X8,c_COMBC(X16,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_prod(X8,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),X8,c_COMBB(tc_prod(X8,X16),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool),X16,c_member(tc_prod(X8,X16)))),c_Product__Type_OPair(X8,X16)))),X34)),X14),X13)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__Int__eq2) ).
fof(f12493,plain,
( ~ spl85_161
| spl85_61
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10923,f4426,f3290,f4384,f9793]) ).
fof(f10923,plain,
( ! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2777,f9774]) ).
fof(f2777,plain,
! [X0] :
( ~ hBOOL(hAPP(c_fNot,X0))
| ~ hBOOL(X0) ),
inference(cnf_transformation,[],[f671]) ).
fof(f671,plain,
! [X0] :
( ~ hBOOL(hAPP(c_fNot,X0))
| ~ hBOOL(X0) ),
inference(rectify,[],[f531]) ).
fof(f531,axiom,
! [X18] :
( ~ hBOOL(X18)
| ~ hBOOL(hAPP(c_fNot,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fNot__1) ).
fof(f12483,plain,
( spl85_161
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10772,f4426,f3290,f3178,f9793]) ).
fof(f10772,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3716,f9774]) ).
fof(f3716,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F)),hAPP(c_member(X1),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))))
| ~ spl85_16 ),
inference(resolution,[],[f3304,f2711]) ).
fof(f3304,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_member(X0),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F)))
| ~ spl85_16 ),
inference(resolution,[],[f3180,f2711]) ).
fof(f12452,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10713,f4426,f3290,f9793]) ).
fof(f10713,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3415,f9774]) ).
fof(f3415,plain,
! [X2,X3,X0,X1,X4] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_member(X0)),c_fequal),X1)),
inference(superposition,[],[f3035,f2728]) ).
fof(f12451,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10766,f4426,f3290,f9793]) ).
fof(f10766,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4090,f9774]) ).
fof(f4090,plain,
! [X10,X11,X12,X13] : hBOOL(hAPP(hAPP(c_member(X10),hAPP(c_member(X11),X12)),hAPP(c_member(X13),hAPP(c_fequal,X12)))),
inference(resolution,[],[f3324,f2711]) ).
fof(f3324,plain,
! [X2,X3,X1] : hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_fequal,X2)),hAPP(c_member(X3),X2))),
inference(resolution,[],[f3035,f2711]) ).
fof(f12449,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10854,f4426,f3371,f3290,f9793]) ).
fof(f10854,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4242,f9774]) ).
fof(f4242,plain,
( ! [X41,X46,X47,X44,X45,X42,X43] : hBOOL(hAPP(hAPP(c_member(tc_fun(X41,X42)),X43),c_FuncSet_OPi(X41,X42,X44,c_COMBK(tc_fun(X42,tc_HOL_Obool),X41,hAPP(c_Product__Type_OPair(X45,X46),X47)))))
| ~ spl85_40 ),
inference(resolution,[],[f3652,f2718]) ).
fof(f12445,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12444,f4426,f3290,f9793]) ).
fof(f12444,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12443]) ).
fof(f12443,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12442,f9774]) ).
fof(f12442,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),hAPP(v_F,v_Q____)),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X8)),sK57(X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X8),X6,X10,X11))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10236,f9774]) ).
fof(f10236,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X10)),X9),c_FuncSet_OPi(X6,X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X8),X11)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),hAPP(v_F,v_Q____)),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X8)),sK57(X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X8),X6,X10,X11))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3648,f9774]) ).
fof(f3648,plain,
! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X7)),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X8)),sK57(X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X8),X6,X10,X11)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X10)),X9),c_FuncSet_OPi(X6,X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X8),X11))) ),
inference(resolution,[],[f2765,f2649]) ).
fof(f2765,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),X3),X0)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X3)),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X0)),X1)) ),
inference(cnf_transformation,[],[f2017]) ).
fof(f12441,plain,
( spl85_161
| spl85_162
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12440,f4426,f3290,f11077,f9793]) ).
fof(f12440,plain,
( ! [X28,X29,X30] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X28,X29),hAPP(X28,X30))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10465,f9774]) ).
fof(f10465,plain,
( ! [X31,X28,X29,X30] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X28,X29),hAPP(X28,X30))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X31,X31)),hAPP(v_F,v_Q____)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X31),X31,c_Wellfounded_Olex__prod(tc_Nat_Onat,X31,c_Wellfounded_Oless__than,hAPP(v_F,v_Q____)),hAPP(hAPP(c_COMBS(X31,X31,tc_prod(tc_Nat_Onat,X31)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X31,tc_prod(tc_Nat_Onat,X31)),X31,c_Product__Type_OPair(tc_Nat_Onat,X31)),X28)),c_COMBI(X31))))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f9771,f9774]) ).
fof(f9771,plain,
( ! [X31,X28,X29,X30] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X28,X29),hAPP(X28,X30))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X31,X31)),hAPP(hAPP(c_Product__Type_OPair(X31,X31),X29),X30)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X31),X31,c_Wellfounded_Olex__prod(tc_Nat_Onat,X31,c_Wellfounded_Oless__than,hAPP(v_F,v_Q____)),hAPP(hAPP(c_COMBS(X31,X31,tc_prod(tc_Nat_Onat,X31)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X31,tc_prod(tc_Nat_Onat,X31)),X31,c_Product__Type_OPair(tc_Nat_Onat,X31)),X28)),c_COMBI(X31))))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(resolution,[],[f9759,f2974]) ).
fof(f12433,plain,
( spl85_170
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12432,f4426,f3290,f9793,f11305]) ).
fof(f12432,plain,
( ! [X2,X4] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X2,X4)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12431]) ).
fof(f12431,plain,
( ! [X2,X4] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X2,X4)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9935,f9774]) ).
fof(f9935,plain,
( ! [X2,X3,X1,X4] :
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2465,f9774]) ).
fof(f2465,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X2,sK23(X0,X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3))
| hBOOL(hAPP(X2,X4)) ),
inference(cnf_transformation,[],[f1740]) ).
fof(f1740,plain,
! [X0,X1,X2,X3] :
( ( ( ! [X4] :
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3)) )
& ! [X5] :
( hBOOL(hAPP(X2,X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X0)) ) )
| ( ~ hBOOL(hAPP(X2,sK23(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X1),sK23(X0,X1,X2,X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X3))) ) )
& ( ! [X7] :
( hBOOL(hAPP(X2,X7))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X3))) )
| ( ~ hBOOL(hAPP(X2,sK24(X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X1),sK24(X1,X2,X3)),X3)) )
| ( ~ hBOOL(hAPP(X2,sK25(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X1),sK25(X0,X1,X2)),X0)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24,sK25])],[f1736,f1739,f1738,f1737]) ).
fof(f1737,plain,
! [X0,X1,X2,X3] :
( ? [X6] :
( ~ hBOOL(hAPP(X2,X6))
& hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X3))) )
=> ( ~ hBOOL(hAPP(X2,sK23(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X1),sK23(X0,X1,X2,X3)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X3))) ) ),
introduced(choice_axiom,[]) ).
fof(f1738,plain,
! [X1,X2,X3] :
( ? [X8] :
( ~ hBOOL(hAPP(X2,X8))
& hBOOL(hAPP(hAPP(c_member(X1),X8),X3)) )
=> ( ~ hBOOL(hAPP(X2,sK24(X1,X2,X3)))
& hBOOL(hAPP(hAPP(c_member(X1),sK24(X1,X2,X3)),X3)) ) ),
introduced(choice_axiom,[]) ).
fof(f1739,plain,
! [X0,X1,X2] :
( ? [X9] :
( ~ hBOOL(hAPP(X2,X9))
& hBOOL(hAPP(hAPP(c_member(X1),X9),X0)) )
=> ( ~ hBOOL(hAPP(X2,sK25(X0,X1,X2)))
& hBOOL(hAPP(hAPP(c_member(X1),sK25(X0,X1,X2)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1736,plain,
! [X0,X1,X2,X3] :
( ( ( ! [X4] :
( hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X3)) )
& ! [X5] :
( hBOOL(hAPP(X2,X5))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X0)) ) )
| ? [X6] :
( ~ hBOOL(hAPP(X2,X6))
& hBOOL(hAPP(hAPP(c_member(X1),X6),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X3))) ) )
& ( ! [X7] :
( hBOOL(hAPP(X2,X7))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X3))) )
| ? [X8] :
( ~ hBOOL(hAPP(X2,X8))
& hBOOL(hAPP(hAPP(c_member(X1),X8),X3)) )
| ? [X9] :
( ~ hBOOL(hAPP(X2,X9))
& hBOOL(hAPP(hAPP(c_member(X1),X9),X0)) ) ) ),
inference(rectify,[],[f1735]) ).
fof(f1735,plain,
! [X2,X3,X1,X0] :
( ( ( ! [X5] :
( hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& ! [X6] :
( hBOOL(hAPP(X1,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X2)) ) )
| ? [X4] :
( ~ hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X0))) )
| ? [X5] :
( ~ hBOOL(hAPP(X1,X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ? [X6] :
( ~ hBOOL(hAPP(X1,X6))
& hBOOL(hAPP(hAPP(c_member(X3),X6),X2)) ) ) ),
inference(flattening,[],[f1734]) ).
fof(f1734,plain,
! [X2,X3,X1,X0] :
( ( ( ! [X5] :
( hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& ! [X6] :
( hBOOL(hAPP(X1,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X2)) ) )
| ? [X4] :
( ~ hBOOL(hAPP(X1,X4))
& hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X0))) ) )
& ( ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X0))) )
| ? [X5] :
( ~ hBOOL(hAPP(X1,X5))
& hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
| ? [X6] :
( ~ hBOOL(hAPP(X1,X6))
& hBOOL(hAPP(hAPP(c_member(X3),X6),X2)) ) ) ),
inference(nnf_transformation,[],[f1229]) ).
fof(f1229,plain,
! [X2,X3,X1,X0] :
( ( ! [X5] :
( hBOOL(hAPP(X1,X5))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X0)) )
& ! [X6] :
( hBOOL(hAPP(X1,X6))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X6),X2)) ) )
<=> ! [X4] :
( hBOOL(hAPP(X1,X4))
| ~ hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X0))) ) ),
inference(ennf_transformation,[],[f828]) ).
fof(f828,plain,
! [X3,X1,X2,X0] :
( ( ! [X5] :
( hBOOL(hAPP(hAPP(c_member(X3),X5),X0))
=> hBOOL(hAPP(X1,X5)) )
& ! [X6] :
( hBOOL(hAPP(hAPP(c_member(X3),X6),X2))
=> hBOOL(hAPP(X1,X6)) ) )
<=> ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X3),X4),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X0)))
=> hBOOL(hAPP(X1,X4)) ) ),
inference(rectify,[],[f367]) ).
fof(f367,axiom,
! [X9,X18,X10,X8] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X10),X9)))
=> hBOOL(hAPP(X18,X2)) )
<=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X9))
=> hBOOL(hAPP(X18,X2)) )
& ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X10))
=> hBOOL(hAPP(X18,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__Un) ).
fof(f12430,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_37
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10897,f4426,f3332,f3290,f9793]) ).
fof(f3332,plain,
( spl85_37
<=> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_37])]) ).
fof(f10897,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_37
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3334,f9774]) ).
fof(f3334,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____))
| ~ spl85_37 ),
inference(avatar_component_clause,[],[f3332]) ).
fof(f12419,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12418,f4426,f3290,f9793]) ).
fof(f12418,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12417]) ).
fof(f12417,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12416,f9774]) ).
fof(f12416,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1),X2)))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10161,f9774]) ).
fof(f10161,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(v_F,v_Q____),X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1),X2))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3817,f9774]) ).
fof(f3817,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1),X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1),X2))) ),
inference(resolution,[],[f2539,f2792]) ).
fof(f2539,plain,
! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X0))),
inference(cnf_transformation,[],[f712]) ).
fof(f712,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_member(X1),X2),c_Set_Oinsert(X1,X2,X0))),
inference(rectify,[],[f302]) ).
fof(f302,axiom,
! [X9,X8,X24] : hBOOL(hAPP(hAPP(c_member(X8),X24),c_Set_Oinsert(X8,X24,X9))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
fof(f12415,plain,
( spl85_61
| spl85_161
| ~ spl85_23
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10754,f4426,f3290,f3213,f9793,f4384]) ).
fof(f10754,plain,
( ! [X14] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(X14) )
| ~ spl85_23
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3834,f9774]) ).
fof(f3834,plain,
( ! [X14,X15] :
( hBOOL(hAPP(hAPP(c_member(X15),X14),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X14)))
| ~ hBOOL(X14) )
| ~ spl85_23 ),
inference(superposition,[],[f2711,f3828]) ).
fof(f12401,plain,
( spl85_92
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10391,f4426,f3290,f9793,f6565]) ).
fof(f10391,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Relation_Osingle__valued(X0,X1,X2) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2620,f9774]) ).
fof(f2620,plain,
! [X2,X0,X1] :
( c_Relation_Osingle__valued(X0,X1,X2)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK50(X0,X1,X2)),sK52(X0,X1,X2))),X2)) ),
inference(cnf_transformation,[],[f1877]) ).
fof(f12397,plain,
( ~ spl85_161
| spl85_11
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10759,f4426,f3290,f3150,f9793]) ).
fof(f10759,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| spl85_11
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3152,f9774]) ).
fof(f3152,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_Q____)))
| spl85_11 ),
inference(avatar_component_clause,[],[f3150]) ).
fof(f12396,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12395,f4426,f3290,f9793]) ).
fof(f12395,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12394]) ).
fof(f12394,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9963,f9774]) ).
fof(f9963,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X3)),X1),c_FuncSet_OPi(X0,X3,X2,X4))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3469,f9774]) ).
fof(f3469,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(X2,sK57(X1,X2,X0,X3,X4)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X3)),X1),c_FuncSet_OPi(X0,X3,X2,X4))) ),
inference(resolution,[],[f2649,f2710]) ).
fof(f12393,plain,
( spl85_161
| spl85_188
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12392,f4426,f3290,f12164,f9793]) ).
fof(f12392,plain,
( ! [X0,X1] :
( hAPP(X1,X0) = X0
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10684,f9774]) ).
fof(f10684,plain,
( ! [X0,X1] :
( hAPP(X1,X0) = X0
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(v_F,v_Q____),X0)),sK84(hAPP(X1,X0),X0))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3464,f9774]) ).
fof(f3464,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X1,X0) = X0
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1),X0)),sK84(hAPP(X1,X0),X0))) ),
inference(superposition,[],[f2949,f2728]) ).
fof(f12382,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10648,f4426,f3371,f3290,f9793]) ).
fof(f10648,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3372,f9774]) ).
fof(f12379,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12378,f4426,f3290,f9793]) ).
fof(f12378,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12377]) ).
fof(f12377,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10745,f9774]) ).
fof(f10745,plain,
( ! [X18,X19,X16,X17,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X16,X18)),X20),c_FuncSet_OPi(X16,X18,X17,X19)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3480,f9774]) ).
fof(f3480,plain,
! [X21,X18,X19,X16,X17,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X16,X18)),X20),c_FuncSet_OPi(X16,X18,X17,X19)))
| hBOOL(hAPP(hAPP(c_member(X21),X17),hAPP(c_member(X16),sK83(X17,X16,X18,X19,X20)))) ),
inference(resolution,[],[f2942,f2711]) ).
fof(f12376,plain,
( spl85_161
| spl85_61
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10755,f4426,f3290,f4384,f9793]) ).
fof(f10755,plain,
( ! [X24] :
( ~ hBOOL(X24)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3749,f9774]) ).
fof(f3749,plain,
! [X24,X25,X23] :
( hBOOL(hAPP(hAPP(c_member(X25),X24),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X23,tc_HOL_Obool)),X24)))
| ~ hBOOL(X24) ),
inference(superposition,[],[f2711,f2793]) ).
fof(f2793,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X1) = X1,
inference(cnf_transformation,[],[f792]) ).
fof(f792,plain,
! [X0,X1] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X1) = X1,
inference(rectify,[],[f373]) ).
fof(f373,axiom,
! [X8,X10] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X10),X10) = X10,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb) ).
fof(f12375,plain,
( spl85_61
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10757,f4426,f3290,f9793,f4384]) ).
fof(f10757,plain,
( ! [X37] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(X37) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4121,f9774]) ).
fof(f4121,plain,
! [X38,X36,X37] :
( hBOOL(hAPP(hAPP(c_member(X38),X37),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X36,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X36,tc_HOL_Obool)))))
| ~ hBOOL(X37) ),
inference(superposition,[],[f2711,f2580]) ).
fof(f12359,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_38
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10798,f4426,f3341,f3290,f9793]) ).
fof(f3341,plain,
( spl85_38
<=> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P_H____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_38])]) ).
fof(f10798,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_38
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3589,f9774]) ).
fof(f3589,plain,
( ! [X6,X7] : hBOOL(hAPP(hAPP(c_member(X6),c_Arrow__Order__Mirabelle_OProf),hAPP(c_member(X7),v_P_H____)))
| ~ spl85_38 ),
inference(resolution,[],[f3358,f2711]) ).
fof(f3358,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_member(X0),v_P_H____),c_Arrow__Order__Mirabelle_OProf))
| ~ spl85_38 ),
inference(resolution,[],[f3343,f2711]) ).
fof(f3343,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P_H____))
| ~ spl85_38 ),
inference(avatar_component_clause,[],[f3341]) ).
fof(f12345,plain,
( spl85_161
| spl85_190
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12341,f4426,f3290,f12343,f9793]) ).
fof(f12343,plain,
( spl85_190
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(hAPP(v_F,v_Q____),hAPP(v_F,v_Q____),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_190])]) ).
fof(f12341,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(hAPP(v_F,v_Q____),hAPP(v_F,v_Q____),X0)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12340,f9774]) ).
fof(f12340,plain,
( ! [X3,X0] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),hAPP(v_F,v_Q____),X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10336,f9774]) ).
fof(f10336,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2548,f9774]) ).
fof(f2548,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0)
| hBOOL(hAPP(hAPP(c_member(X3),X2),X0)) ),
inference(cnf_transformation,[],[f1817]) ).
fof(f1817,plain,
! [X0,X1,X2,X3] :
( ( ( hBOOL(hAPP(hAPP(c_member(X3),X2),X0))
& c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0)
| ~ hBOOL(hAPP(hAPP(c_member(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0) ) ),
inference(rectify,[],[f1816]) ).
fof(f1816,plain,
! [X2,X3,X0,X1] :
( ( ( hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
& c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X0,X3),X2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X0,X3),X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2) ) ),
inference(flattening,[],[f1815]) ).
fof(f1815,plain,
! [X2,X3,X0,X1] :
( ( ( hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
& c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X0,X3),X2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X0,X3),X2)
| ~ hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2) ) ),
inference(nnf_transformation,[],[f548]) ).
fof(f548,plain,
! [X2,X3,X0,X1] :
( ( hBOOL(hAPP(hAPP(c_member(X1),X0),X2))
& c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X3,X2) )
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),c_Set_Oinsert(X1,X0,X3),X2) ),
inference(rectify,[],[f305]) ).
fof(f305,axiom,
! [X14,X8,X9,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),c_Set_Oinsert(X8,X14,X10),X9)
<=> ( hBOOL(hAPP(hAPP(c_member(X8),X14),X9))
& c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),X10,X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
fof(f12333,plain,
( spl85_178
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12332,f4426,f3290,f9793,f11730]) ).
fof(f12332,plain,
( ! [X56] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X56) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12331,f9774]) ).
fof(f12331,plain,
( ! [X56,X55] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool))),X56)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12330]) ).
fof(f12330,plain,
( ! [X56,X55] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool))),X56) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10862,f9774]) ).
fof(f10862,plain,
( ! [X56,X55] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X56,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool))))),sK21(X56,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool)))))),sK20(X56,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool))))))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool))),X56)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4127,f9774]) ).
fof(f4127,plain,
! [X56,X55] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool)))),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool))),X56)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X56,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool))))),sK21(X56,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool)))))),sK20(X56,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool)))))) ),
inference(superposition,[],[f2454,f2580]) ).
fof(f12323,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12322,f4426,f3290,f9793]) ).
fof(f12322,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12321]) ).
fof(f12321,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12320,f9774]) ).
fof(f12320,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1)),hAPP(v_F,v_Q____)),sK83(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),X2),X0,X3,X4,X5))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10240,f9774]) ).
fof(f10240,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X3)),X5),c_FuncSet_OPi(X0,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),X2),X4)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1)),hAPP(v_F,v_Q____)),sK83(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),X2),X0,X3,X4,X5))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3656,f9774]) ).
fof(f3656,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X3)),X5),c_FuncSet_OPi(X0,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),X2),X4)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1)),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X2)),sK83(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),X2),X0,X3,X4,X5))) ),
inference(resolution,[],[f2854,f2942]) ).
fof(f12317,plain,
( ~ spl85_161
| spl85_170
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12316,f4426,f3290,f11305,f9793]) ).
fof(f12316,plain,
( ! [X0,X1] :
( hBOOL(hAPP(X0,X1))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10506,f9774]) ).
fof(f10506,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(v_F,v_Q____),X1))
| hBOOL(hAPP(X0,X1)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2617,f9774]) ).
fof(f12303,plain,
( spl85_168
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11037,f4426,f3290,f11279]) ).
fof(f11037,plain,
( ! [X203,X207,X204] : c_Predicate_ORangeP(X203,X204,hAPP(v_F,v_Q____),X207)
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4343,f9774]) ).
fof(f4343,plain,
! [X205,X203,X206,X207,X204] : c_Predicate_ORangeP(X203,X204,c_Transitive__Closure_Ortranclp(X205,X206),X207),
inference(resolution,[],[f2173,f3016]) ).
fof(f3016,plain,
! [X3,X0,X1] : hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X0),X3),X3)),
inference(equality_resolution,[],[f2440]) ).
fof(f2440,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X0),X3),X2))
| X2 != X3 ),
inference(cnf_transformation,[],[f1722]) ).
fof(f1722,plain,
! [X0,X1,X2,X3] :
( ( X2 = X3
| ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X0),X3),sK19(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(X0,sK19(X0,X1,X2,X3)),X2)) )
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X0),X3),X2)) )
& ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X0),X3),X2))
| ( X2 != X3
& ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X0),X3),X5))
| ~ hBOOL(hAPP(hAPP(X0,X5),X2)) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f1720,f1721]) ).
fof(f1721,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X0),X3),X4))
& hBOOL(hAPP(hAPP(X0,X4),X2)) )
=> ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X0),X3),sK19(X0,X1,X2,X3)))
& hBOOL(hAPP(hAPP(X0,sK19(X0,X1,X2,X3)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1720,plain,
! [X0,X1,X2,X3] :
( ( X2 = X3
| ? [X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X0),X3),X4))
& hBOOL(hAPP(hAPP(X0,X4),X2)) )
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X0),X3),X2)) )
& ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X0),X3),X2))
| ( X2 != X3
& ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X1,X0),X3),X5))
| ~ hBOOL(hAPP(hAPP(X0,X5),X2)) ) ) ) ),
inference(rectify,[],[f1719]) ).
fof(f1719,plain,
! [X1,X0,X3,X2] :
( ( X2 = X3
| ? [X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X1),X2),X4))
& hBOOL(hAPP(hAPP(X1,X4),X3)) )
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X1),X2),X3)) )
& ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X1),X2),X3))
| ( X2 != X3
& ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X3)) ) ) ) ),
inference(flattening,[],[f1718]) ).
fof(f1718,plain,
! [X1,X0,X3,X2] :
( ( X2 = X3
| ? [X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X1),X2),X4))
& hBOOL(hAPP(hAPP(X1,X4),X3)) )
| ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X1),X2),X3)) )
& ( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X1),X2),X3))
| ( X2 != X3
& ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X1),X2),X4))
| ~ hBOOL(hAPP(hAPP(X1,X4),X3)) ) ) ) ),
inference(nnf_transformation,[],[f827]) ).
fof(f827,plain,
! [X1,X0,X3,X2] :
( ( X2 = X3
| ? [X4] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X1),X2),X4))
& hBOOL(hAPP(hAPP(X1,X4),X3)) ) )
<=> hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X0,X1),X2),X3)) ),
inference(rectify,[],[f203]) ).
fof(f203,axiom,
! [X8,X19,X36,X67] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X19),X36),X67))
<=> ( X36 = X67
| ? [X6] :
( hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(X8,X19),X36),X6))
& hBOOL(hAPP(hAPP(X19,X6),X67)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclp_Oequations_I2_J) ).
fof(f12302,plain,
( spl85_161
| spl85_167
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12301,f4426,f3290,f11209,f9793]) ).
fof(f12301,plain,
( ! [X10,X11] :
( ~ hBOOL(hAPP(X10,X11))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10588,f9774]) ).
fof(f10588,plain,
( ! [X10,X11,X12] :
( hBOOL(hAPP(hAPP(c_member(X12),X11),hAPP(v_F,v_Q____)))
| ~ hBOOL(hAPP(X10,X11)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4676,f9774]) ).
fof(f4676,plain,
! [X10,X11,X14,X12,X13] :
( ~ hBOOL(hAPP(X10,X11))
| hBOOL(hAPP(hAPP(c_member(X12),X11),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X13,tc_HOL_Obool)),X14),X10))) ),
inference(resolution,[],[f2894,f2711]) ).
fof(f12293,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_38
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10769,f4426,f3341,f3290,f9793]) ).
fof(f10769,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_38
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3964,f9774]) ).
fof(f3964,plain,
( ! [X2,X3,X1] : hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_member(X2),v_P_H____)),hAPP(c_member(X3),c_Arrow__Order__Mirabelle_OProf)))
| ~ spl85_38 ),
inference(resolution,[],[f3589,f2711]) ).
fof(f12285,plain,
( spl85_61
| spl85_161
| ~ spl85_26
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10756,f4426,f3290,f3229,f9793,f4384]) ).
fof(f10756,plain,
( ! [X14] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(X14) )
| ~ spl85_26
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3845,f9774]) ).
fof(f3845,plain,
( ! [X14,X15] :
( hBOOL(hAPP(hAPP(c_member(X15),X14),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),X14)))
| ~ hBOOL(X14) )
| ~ spl85_26 ),
inference(superposition,[],[f2711,f3829]) ).
fof(f12278,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12277,f4426,f3290,f9793]) ).
fof(f12277,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12276]) ).
fof(f12276,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9984,f9774]) ).
fof(f9984,plain,
( ! [X3,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X4)),X3),c_FuncSet_OPi(X6,X4,X5,c_COMBK(tc_fun(X4,tc_HOL_Obool),X6,c_fNot))))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3729,f9774]) ).
fof(f3729,plain,
! [X3,X6,X4,X5] :
( hBOOL(hAPP(X3,sK65(c_fNot,X4,X5,X6,X3)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X4)),X3),c_FuncSet_OPi(X6,X4,X5,c_COMBK(tc_fun(X4,tc_HOL_Obool),X6,c_fNot)))) ),
inference(resolution,[],[f3383,f2718]) ).
fof(f3383,plain,
! [X2,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),c_fNot))
| hBOOL(X1) ),
inference(resolution,[],[f2866,f2711]) ).
fof(f12268,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12267,f4426,f3290,f9793]) ).
fof(f12267,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12266]) ).
fof(f12266,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10624,f9774]) ).
fof(f10624,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X3,X1)),X4),c_FuncSet_OPi(X3,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X3,X0))))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2719,f9774]) ).
fof(f12244,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_38
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10899,f4426,f3341,f3290,f9793]) ).
fof(f10899,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_38
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3343,f9774]) ).
fof(f12235,plain,
( ~ spl85_161
| spl85_170
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12234,f4426,f3290,f11305,f9793]) ).
fof(f12234,plain,
( ! [X2,X0] :
( hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10514,f9774]) ).
fof(f10514,plain,
( ! [X2,X0] :
( hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(hAPP(v_F,v_Q____),X2)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2833,f9774]) ).
fof(f2833,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),X0),X2))
| hBOOL(hAPP(X0,X2)) ),
inference(cnf_transformation,[],[f2061]) ).
fof(f2061,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(X0,X2))
& hBOOL(hAPP(X1,X2)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X1),X0),X2)) ),
inference(rectify,[],[f1254]) ).
fof(f1254,plain,
! [X2,X3,X1,X0] :
( ( hBOOL(hAPP(X2,X1))
& hBOOL(hAPP(X3,X1)) )
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X3),X2),X1)) ),
inference(ennf_transformation,[],[f771]) ).
fof(f771,plain,
! [X2,X3,X1,X0] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X3),X2),X1))
=> ~ ( hBOOL(hAPP(X3,X1))
=> ~ hBOOL(hAPP(X2,X1)) ) ),
inference(rectify,[],[f92]) ).
fof(f92,axiom,
! [X8,X14,X9,X10] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X10),X9),X14))
=> ~ ( hBOOL(hAPP(X10,X14))
=> ~ hBOOL(hAPP(X9,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1E) ).
fof(f12231,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10748,f4426,f3290,f9793]) ).
fof(f10748,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3035,f9774]) ).
fof(f12229,plain,
( ~ spl85_161
| spl85_95
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12228,f4426,f3290,f6693,f9793]) ).
fof(f12228,plain,
( ! [X10,X8,X9] :
( X9 = X10
| X8 = X9
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12227]) ).
fof(f12227,plain,
( ! [X10,X8,X9] :
( X8 = X9
| ~ hBOOL(hAPP(v_F,v_Q____))
| X9 = X10
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12226,f9774]) ).
fof(f12226,plain,
( ! [X10,X8,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
| X8 = X9
| ~ hBOOL(hAPP(v_F,v_Q____))
| X9 = X10 )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12225]) ).
fof(f12225,plain,
( ! [X10,X8,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| X8 = X9
| X9 = X10 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12224,f9774]) ).
fof(f12224,plain,
( ! [X10,X8,X9,X7] :
( X9 = X10
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
| X8 = X9 )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12223]) ).
fof(f12223,plain,
( ! [X10,X8,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
| X9 = X10
| X8 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12222,f9774]) ).
fof(f12222,plain,
( ! [X10,X8,X9,X7] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
| X8 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)))
| X9 = X10 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10141,f9774]) ).
fof(f10141,plain,
( ! [X10,X8,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8),X10)),X7))
| X8 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)))
| X9 = X10
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3687,f9774]) ).
fof(f3687,plain,
! [X10,X8,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8),X10)),X7))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X9),X8)),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
| X8 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)),c_Arrow__Order__Mirabelle_OLin))
| X9 = X10 ),
inference(resolution,[],[f2999,f2792]) ).
fof(f2999,plain,
! [X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X3,X4)))
| X1 = X3
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X0)) ),
inference(equality_resolution,[],[f2369]) ).
fof(f2369,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X0))
| X1 = X3
| X2 != X3
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(cnf_transformation,[],[f1663]) ).
fof(f12220,plain,
( spl85_80
| spl85_189
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10987,f4426,f3290,f12217,f6164]) ).
fof(f12217,plain,
( spl85_189
<=> class_Lattices_Osemilattice__inf(hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_189])]) ).
fof(f10987,plain,
( ! [X1] :
( class_Lattices_Osemilattice__inf(hAPP(v_F,v_Q____))
| ~ class_Lattices_Olattice(X1) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2583,f9774]) ).
fof(f2583,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(tc_fun(X0,X1))
| ~ class_Lattices_Olattice(X1) ),
inference(cnf_transformation,[],[f1132]) ).
fof(f1132,plain,
! [X0,X1] :
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Osemilattice__inf(tc_fun(X0,X1)) ),
inference(ennf_transformation,[],[f757]) ).
fof(f757,plain,
! [X1,X0] :
( class_Lattices_Olattice(X1)
=> class_Lattices_Osemilattice__inf(tc_fun(X0,X1)) ),
inference(rectify,[],[f499]) ).
fof(f499,axiom,
! [X73,X74] :
( class_Lattices_Olattice(X74)
=> class_Lattices_Osemilattice__inf(tc_fun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
fof(f12213,plain,
( spl85_168
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10906,f4426,f3290,f11279]) ).
fof(f10906,plain,
( ! [X0,X1,X6] : c_Predicate_ORangeP(X0,X1,hAPP(v_F,v_Q____),X6)
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4297,f9774]) ).
fof(f4297,plain,
! [X2,X3,X0,X1,X6,X4,X5] : c_Predicate_ORangeP(X0,X1,hAPP(c_COMBS(X2,X3,X4),c_member(X5)),X6),
inference(resolution,[],[f2173,f3415]) ).
fof(f12212,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12211,f4426,f3290,f9793]) ).
fof(f12211,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12210]) ).
fof(f12210,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10072,f9774]) ).
fof(f10072,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X1)),c_FuncSet_Orestrict(X2,X1,X3,X0)),c_FuncSet_OPi(X2,X1,X0,X4))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2727,f9774]) ).
fof(f2727,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X1)),c_FuncSet_Orestrict(X2,X1,X3,X0)),c_FuncSet_OPi(X2,X1,X0,X4)))
| hBOOL(hAPP(hAPP(c_member(X2),sK67(X0,X1,X2,X3,X4)),X0)) ),
inference(cnf_transformation,[],[f1984]) ).
fof(f1984,plain,
! [X0,X1,X2,X3,X4] :
( ( hBOOL(hAPP(hAPP(c_member(X2),sK67(X0,X1,X2,X3,X4)),X0))
& ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X3,sK67(X0,X1,X2,X3,X4))),hAPP(X4,sK67(X0,X1,X2,X3,X4)))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X1)),c_FuncSet_Orestrict(X2,X1,X3,X0)),c_FuncSet_OPi(X2,X1,X0,X4))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67])],[f1982,f1983]) ).
fof(f1983,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( hBOOL(hAPP(hAPP(c_member(X2),X5),X0))
& ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X3,X5)),hAPP(X4,X5))) )
=> ( hBOOL(hAPP(hAPP(c_member(X2),sK67(X0,X1,X2,X3,X4)),X0))
& ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X3,sK67(X0,X1,X2,X3,X4))),hAPP(X4,sK67(X0,X1,X2,X3,X4)))) ) ),
introduced(choice_axiom,[]) ).
fof(f1982,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( hBOOL(hAPP(hAPP(c_member(X2),X5),X0))
& ~ hBOOL(hAPP(hAPP(c_member(X1),hAPP(X3,X5)),hAPP(X4,X5))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X1)),c_FuncSet_Orestrict(X2,X1,X3,X0)),c_FuncSet_OPi(X2,X1,X0,X4))) ),
inference(rectify,[],[f1379]) ).
fof(f1379,plain,
! [X1,X0,X2,X3,X4] :
( ? [X5] :
( hBOOL(hAPP(hAPP(c_member(X2),X5),X1))
& ~ hBOOL(hAPP(hAPP(c_member(X0),hAPP(X3,X5)),hAPP(X4,X5))) )
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X0)),c_FuncSet_Orestrict(X2,X0,X3,X1)),c_FuncSet_OPi(X2,X0,X1,X4))) ),
inference(ennf_transformation,[],[f594]) ).
fof(f594,plain,
! [X1,X0,X4,X2,X3] :
( ! [X5] :
( hBOOL(hAPP(hAPP(c_member(X2),X5),X1))
=> hBOOL(hAPP(hAPP(c_member(X0),hAPP(X3,X5)),hAPP(X4,X5))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X0)),c_FuncSet_Orestrict(X2,X0,X3,X1)),c_FuncSet_OPi(X2,X0,X1,X4))) ),
inference(rectify,[],[f137]) ).
fof(f137,axiom,
! [X16,X10,X8,X1,X9] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X10))
=> hBOOL(hAPP(hAPP(c_member(X16),hAPP(X1,X2)),hAPP(X9,X2))) )
=> hBOOL(hAPP(hAPP(c_member(tc_fun(X8,X16)),c_FuncSet_Orestrict(X8,X16,X1,X10)),c_FuncSet_OPi(X8,X16,X10,X9))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_restrictI) ).
fof(f12204,plain,
( ~ spl85_161
| spl85_58
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12203,f4426,f3290,f4223,f9793]) ).
fof(f12203,plain,
( ! [X3,X4] :
( X3 = X4
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12202]) ).
fof(f12202,plain,
( ! [X3,X4] :
( X3 = X4
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12201,f9774]) ).
fof(f12201,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X3),c_FuncSet_Oextensional(X0,X2,X1)))
| X3 = X4 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12200,f9774]) ).
fof(f12200,plain,
( ! [X2,X3,X0,X1,X4] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_Oextensional(X0,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X3),c_FuncSet_Oextensional(X0,X2,X1))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f12199]) ).
fof(f12199,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_Oextensional(X0,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X3),c_FuncSet_Oextensional(X0,X2,X1)))
| X3 = X4 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9892,f9774]) ).
fof(f9892,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(v_F,v_Q____) != hAPP(X3,sK3(X0,X1,X3,X4))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_Oextensional(X0,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X3),c_FuncSet_Oextensional(X0,X2,X1))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2199,f9774]) ).
fof(f2199,plain,
! [X2,X3,X0,X1,X4] :
( hAPP(X3,sK3(X0,X1,X3,X4)) != hAPP(X4,sK3(X0,X1,X3,X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X3),c_FuncSet_Oextensional(X0,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_Oextensional(X0,X2,X1)))
| X3 = X4 ),
inference(cnf_transformation,[],[f1529]) ).
fof(f1529,plain,
! [X0,X1,X2,X3,X4] :
( ( hAPP(X3,sK3(X0,X1,X3,X4)) != hAPP(X4,sK3(X0,X1,X3,X4))
& hBOOL(hAPP(hAPP(c_member(X0),sK3(X0,X1,X3,X4)),X1)) )
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X3),c_FuncSet_Oextensional(X0,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_Oextensional(X0,X2,X1))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f1527,f1528]) ).
fof(f1528,plain,
! [X0,X1,X3,X4] :
( ? [X5] :
( hAPP(X3,X5) != hAPP(X4,X5)
& hBOOL(hAPP(hAPP(c_member(X0),X5),X1)) )
=> ( hAPP(X3,sK3(X0,X1,X3,X4)) != hAPP(X4,sK3(X0,X1,X3,X4))
& hBOOL(hAPP(hAPP(c_member(X0),sK3(X0,X1,X3,X4)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f1527,plain,
! [X0,X1,X2,X3,X4] :
( ? [X5] :
( hAPP(X3,X5) != hAPP(X4,X5)
& hBOOL(hAPP(hAPP(c_member(X0),X5),X1)) )
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X3),c_FuncSet_Oextensional(X0,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_Oextensional(X0,X2,X1))) ),
inference(rectify,[],[f1244]) ).
fof(f1244,plain,
! [X0,X2,X1,X3,X4] :
( ? [X5] :
( hAPP(X3,X5) != hAPP(X4,X5)
& hBOOL(hAPP(hAPP(c_member(X0),X5),X2)) )
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X3),c_FuncSet_Oextensional(X0,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X4),c_FuncSet_Oextensional(X0,X1,X2))) ),
inference(flattening,[],[f1243]) ).
fof(f1243,plain,
! [X0,X2,X1,X4,X3] :
( X3 = X4
| ? [X5] :
( hAPP(X3,X5) != hAPP(X4,X5)
& hBOOL(hAPP(hAPP(c_member(X0),X5),X2)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X4),c_FuncSet_Oextensional(X0,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X3),c_FuncSet_Oextensional(X0,X1,X2))) ),
inference(ennf_transformation,[],[f650]) ).
fof(f650,plain,
! [X0,X2,X1,X4,X3] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X3),c_FuncSet_Oextensional(X0,X1,X2)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X4),c_FuncSet_Oextensional(X0,X1,X2)))
=> ( ! [X5] :
( hBOOL(hAPP(hAPP(c_member(X0),X5),X2))
=> hAPP(X3,X5) = hAPP(X4,X5) )
=> X3 = X4 ) ) ),
inference(rectify,[],[f83]) ).
fof(f83,axiom,
! [X8,X16,X10,X1,X0] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X8,X16)),X1),c_FuncSet_Oextensional(X8,X16,X10)))
=> ( hBOOL(hAPP(hAPP(c_member(tc_fun(X8,X16)),X0),c_FuncSet_Oextensional(X8,X16,X10)))
=> ( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X10))
=> hAPP(X1,X2) = hAPP(X0,X2) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_extensionalityI) ).
fof(f12193,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12192,f4426,f3290,f9793]) ).
fof(f12192,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10207,f9774]) ).
fof(f10207,plain,
( ! [X2,X0] : hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(v_F,v_Q____)),c_Transitive__Closure_Ortrancl(X2,X0)))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2771,f9774]) ).
fof(f2771,plain,
! [X2,X0,X1] : hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X1)),c_Transitive__Closure_Ortrancl(X2,X0))),
inference(cnf_transformation,[],[f2023]) ).
fof(f2023,plain,
! [X0,X1,X2] : hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X1)),c_Transitive__Closure_Ortrancl(X2,X0))),
inference(rectify,[],[f743]) ).
fof(f743,plain,
! [X1,X2,X0] : hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X2),X2)),c_Transitive__Closure_Ortrancl(X0,X1))),
inference(rectify,[],[f107]) ).
fof(f107,axiom,
! [X8,X19,X24] : hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X24),X24)),c_Transitive__Closure_Ortrancl(X8,X19))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
fof(f12182,plain,
( spl85_186
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12181,f4426,f3290,f9793,f12035]) ).
fof(f12181,plain,
( ! [X2,X0,X1,X4,X5] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Recdef_Owfrec__rel(X0,X1,X4,X5,X2,hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10290,f9774]) ).
fof(f10290,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Recdef_Owfrec__rel(X0,X1,X4,X5,X2,hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK61(X0,X1,X2,X3,X4,X5)),X2)),X4)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2684,f9774]) ).
fof(f2684,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Recdef_Owfrec__rel(X0,X1,X4,X5,X2,hAPP(hAPP(X5,X3),X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK61(X0,X1,X2,X3,X4,X5)),X2)),X4)) ),
inference(cnf_transformation,[],[f1940]) ).
fof(f1940,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Recdef_Owfrec__rel(X0,X1,X4,X5,X2,hAPP(hAPP(X5,X3),X2))
| ( ~ c_Recdef_Owfrec__rel(X0,X1,X4,X5,sK61(X0,X1,X2,X3,X4,X5),hAPP(X3,sK61(X0,X1,X2,X3,X4,X5)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK61(X0,X1,X2,X3,X4,X5)),X2)),X4)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK61])],[f1938,f1939]) ).
fof(f1939,plain,
! [X0,X1,X2,X3,X4,X5] :
( ? [X6] :
( ~ c_Recdef_Owfrec__rel(X0,X1,X4,X5,X6,hAPP(X3,X6))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X6),X2)),X4)) )
=> ( ~ c_Recdef_Owfrec__rel(X0,X1,X4,X5,sK61(X0,X1,X2,X3,X4,X5),hAPP(X3,sK61(X0,X1,X2,X3,X4,X5)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK61(X0,X1,X2,X3,X4,X5)),X2)),X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f1938,plain,
! [X0,X1,X2,X3,X4,X5] :
( c_Recdef_Owfrec__rel(X0,X1,X4,X5,X2,hAPP(hAPP(X5,X3),X2))
| ? [X6] :
( ~ c_Recdef_Owfrec__rel(X0,X1,X4,X5,X6,hAPP(X3,X6))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X6),X2)),X4)) ) ),
inference(rectify,[],[f1071]) ).
fof(f1071,plain,
! [X2,X0,X3,X1,X4,X5] :
( c_Recdef_Owfrec__rel(X2,X0,X4,X5,X3,hAPP(hAPP(X5,X1),X3))
| ? [X6] :
( ~ c_Recdef_Owfrec__rel(X2,X0,X4,X5,X6,hAPP(X1,X6))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X6),X3)),X4)) ) ),
inference(ennf_transformation,[],[f770]) ).
fof(f770,plain,
! [X1,X0,X4,X3,X5,X2] :
( ! [X6] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X6),X3)),X4))
=> c_Recdef_Owfrec__rel(X2,X0,X4,X5,X6,hAPP(X1,X6)) )
=> c_Recdef_Owfrec__rel(X2,X0,X4,X5,X3,hAPP(hAPP(X5,X1),X3)) ),
inference(rectify,[],[f80]) ).
fof(f80,axiom,
! [X16,X0,X8,X14,X15,X32] :
( ! [X38] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X38),X14)),X15))
=> c_Recdef_Owfrec__rel(X8,X16,X15,X32,X38,hAPP(X0,X38)) )
=> c_Recdef_Owfrec__rel(X8,X16,X15,X32,X14,hAPP(hAPP(X32,X0),X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Ointros) ).
fof(f12174,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12173,f4426,f3290,f9793]) ).
fof(f12173,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12172]) ).
fof(f12172,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12171,f9774]) ).
fof(f12171,plain,
( ! [X2,X3,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_Relation_ODomain(X1,X1,X2))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10208,f9774]) ).
fof(f10208,plain,
( ! [X2,X3,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(v_F,v_Q____)),c_Transitive__Closure_Ortrancl(X1,X2)))
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_Relation_ODomain(X1,X1,X2))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2988,f9774]) ).
fof(f2988,plain,
! [X2,X3,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Relation_ODomain(X1,X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),c_Transitive__Closure_Ortrancl(X1,X2))) ),
inference(equality_resolution,[],[f2275]) ).
fof(f2275,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X0)),c_Transitive__Closure_Ortrancl(X1,X2)))
| X0 != X3
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_Relation_ODomain(X1,X1,X2))) ),
inference(cnf_transformation,[],[f1586]) ).
fof(f1586,plain,
! [X0,X1,X2,X3] :
( ( ( X0 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X0)),c_Transitive__Closure_Ortrancl(X1,X2))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X0)),c_Transitive__Closure_Ortrancl(X1,X2)))
| X0 != X3 ) )
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_Relation_ODomain(X1,X1,X2))) ),
inference(rectify,[],[f1585]) ).
fof(f1585,plain,
! [X1,X0,X3,X2] :
( ( ( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X2),X1)),c_Transitive__Closure_Ortrancl(X0,X3))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X2),X1)),c_Transitive__Closure_Ortrancl(X0,X3)))
| X1 != X2 ) )
| hBOOL(hAPP(hAPP(c_member(X0),X2),c_Relation_ODomain(X0,X0,X3))) ),
inference(nnf_transformation,[],[f1495]) ).
fof(f1495,plain,
! [X1,X0,X3,X2] :
( ( X1 = X2
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X2),X1)),c_Transitive__Closure_Ortrancl(X0,X3))) )
| hBOOL(hAPP(hAPP(c_member(X0),X2),c_Relation_ODomain(X0,X0,X3))) ),
inference(ennf_transformation,[],[f687]) ).
fof(f687,plain,
! [X2,X3,X1,X0] :
( ~ hBOOL(hAPP(hAPP(c_member(X0),X2),c_Relation_ODomain(X0,X0,X3)))
=> ( X1 = X2
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X2),X1)),c_Transitive__Closure_Ortrancl(X0,X3))) ) ),
inference(rectify,[],[f140]) ).
fof(f140,axiom,
! [X8,X13,X14,X15] :
( ~ hBOOL(hAPP(hAPP(c_member(X8),X14),c_Relation_ODomain(X8,X8,X15)))
=> ( X13 = X14
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X14),X13)),c_Transitive__Closure_Ortrancl(X8,X15))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
fof(f12170,plain,
( spl85_61
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12169,f4426,f3290,f9793,f4384]) ).
fof(f12169,plain,
( ! [X0] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12168]) ).
fof(f12168,plain,
( ! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12167,f9774]) ).
fof(f12167,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_COMBK(X1,X2,X0)))
| ~ hBOOL(X0)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10204,f9774]) ).
fof(f10204,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_COMBK(X1,X2,X0)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_COMBK(X1,X2,X0))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4081,f9774]) ).
fof(f4081,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),c_COMBK(X1,X2,X0)))
| ~ hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_COMBK(X1,X2,X0)),c_Arrow__Order__Mirabelle_OLin)) ),
inference(resolution,[],[f3315,f2792]) ).
fof(f12166,plain,
( spl85_188
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12162,f4426,f3290,f9793,f12164]) ).
fof(f12162,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hAPP(X2,X1) = X1 )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12161]) ).
fof(f12161,plain,
( ! [X2,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hAPP(X2,X1) = X1
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12160,f9774]) ).
fof(f12160,plain,
( ! [X2,X0,X1] :
( hAPP(X2,X1) = X1
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10043,f9774]) ).
fof(f10043,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),hAPP(c_Arrow__Order__Mirabelle_Oabove,X0)),X2),X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hAPP(X2,X1) = X1 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3558,f9774]) ).
fof(f3558,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(X2,X1) = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X6)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),hAPP(c_Arrow__Order__Mirabelle_Oabove,X0)),X2),X1))) ),
inference(superposition,[],[f3055,f2728]) ).
fof(f12152,plain,
( spl85_58
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12151,f4426,f3290,f9793,f4223]) ).
fof(f12151,plain,
( ! [X2,X3] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| X2 = X3 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10415,f9774]) ).
fof(f10415,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(v_F,v_Q____)),c_Relation_OId__on(X1,X0)))
| X2 = X3 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2281,f9774]) ).
fof(f2281,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Relation_OId__on(X1,X0))) ),
inference(cnf_transformation,[],[f1591]) ).
fof(f1591,plain,
! [X0,X1,X2,X3] :
( ( ( X2 = X3
& hBOOL(hAPP(hAPP(c_member(X1),X2),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Relation_OId__on(X1,X0))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X3)),c_Relation_OId__on(X1,X0)))
| X2 != X3
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),X0)) ) ),
inference(rectify,[],[f1590]) ).
fof(f1590,plain,
! [X1,X0,X3,X2] :
( ( ( X2 = X3
& hBOOL(hAPP(hAPP(c_member(X0),X3),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X3),X2)),c_Relation_OId__on(X0,X1))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X3),X2)),c_Relation_OId__on(X0,X1)))
| X2 != X3
| ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X1)) ) ),
inference(flattening,[],[f1589]) ).
fof(f1589,plain,
! [X1,X0,X3,X2] :
( ( ( X2 = X3
& hBOOL(hAPP(hAPP(c_member(X0),X3),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X3),X2)),c_Relation_OId__on(X0,X1))) )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X3),X2)),c_Relation_OId__on(X0,X1)))
| X2 != X3
| ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X1)) ) ),
inference(nnf_transformation,[],[f713]) ).
fof(f713,plain,
! [X1,X0,X3,X2] :
( ( X2 = X3
& hBOOL(hAPP(hAPP(c_member(X0),X3),X1)) )
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X3),X2)),c_Relation_OId__on(X0,X1))) ),
inference(rectify,[],[f158]) ).
fof(f158,axiom,
! [X8,X10,X13,X14] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X14),X13)),c_Relation_OId__on(X8,X10)))
<=> ( X13 = X14
& hBOOL(hAPP(hAPP(c_member(X8),X14),X10)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__iff) ).
fof(f12150,plain,
( spl85_161
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10806,f4426,f3290,f3178,f9793]) ).
fof(f10806,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3304,f9774]) ).
fof(f12143,plain,
( spl85_122
| spl85_187
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10978,f4426,f3290,f12140,f7880]) ).
fof(f7880,plain,
( spl85_122
<=> ! [X0] : ~ class_Orderings_Opreorder(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_122])]) ).
fof(f12140,plain,
( spl85_187
<=> class_Orderings_Opreorder(hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_187])]) ).
fof(f10978,plain,
( ! [X0] :
( class_Orderings_Opreorder(hAPP(v_F,v_Q____))
| ~ class_Orderings_Opreorder(X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2188,f9774]) ).
fof(f2188,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X1,X0))
| ~ class_Orderings_Opreorder(X0) ),
inference(cnf_transformation,[],[f1466]) ).
fof(f1466,plain,
! [X0,X1] :
( class_Orderings_Opreorder(tc_fun(X1,X0))
| ~ class_Orderings_Opreorder(X0) ),
inference(ennf_transformation,[],[f831]) ).
fof(f831,plain,
! [X1,X0] :
( class_Orderings_Opreorder(X0)
=> class_Orderings_Opreorder(tc_fun(X1,X0)) ),
inference(rectify,[],[f501]) ).
fof(f501,axiom,
! [X74,X73] :
( class_Orderings_Opreorder(X74)
=> class_Orderings_Opreorder(tc_fun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(f12137,plain,
( spl85_168
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12136,f4426,f3290,f9793,f11279]) ).
fof(f12136,plain,
( ! [X48,X46,X47] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Predicate_ORangeP(X47,X48,hAPP(v_F,v_Q____),X46) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10616,f9774]) ).
fof(f10616,plain,
( ! [X40,X41,X48,X46,X47,X44,X42,X43] :
( c_Predicate_ORangeP(X47,X48,hAPP(hAPP(c_COMBS(X40,X41,X42),X43),X44),X46)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4353,f9774]) ).
fof(f4353,plain,
! [X40,X41,X48,X46,X47,X44,X45,X42,X43] :
( ~ hBOOL(hAPP(hAPP(hAPP(X43,X45),hAPP(X44,X45)),X46))
| c_Predicate_ORangeP(X47,X48,hAPP(hAPP(c_COMBS(X40,X41,X42),X43),X44),X46) ),
inference(superposition,[],[f2173,f2728]) ).
fof(f12135,plain,
( spl85_161
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12134,f4426,f3290,f3178,f9793]) ).
fof(f12134,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12133]) ).
fof(f12133,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10830,f9774]) ).
fof(f10830,plain,
( ! [X18] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3600,f9774]) ).
fof(f3600,plain,
( ! [X18] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK72(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18,v_F,c_Arrow__Order__Mirabelle_OProf)),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
| ~ spl85_16 ),
inference(resolution,[],[f2750,f3180]) ).
fof(f12132,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10924,f4426,f3290,f9793]) ).
fof(f10924,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3015,f9774]) ).
fof(f12126,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12125,f4426,f3290,f9793]) ).
fof(f12125,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12124]) ).
fof(f12124,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10077,f9774]) ).
fof(f10077,plain,
( ! [X10,X8,X6,X9,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(X10),c_FuncSet_OPi(X5,X6,X8,X9)),hAPP(c_member(tc_fun(X5,X6)),X7)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3475,f9774]) ).
fof(f3475,plain,
! [X10,X8,X6,X9,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(X10),c_FuncSet_OPi(X5,X6,X8,X9)),hAPP(c_member(tc_fun(X5,X6)),X7)))
| hBOOL(hAPP(hAPP(c_member(X5),sK83(X8,X5,X6,X9,X7)),X8)) ),
inference(resolution,[],[f2942,f2711]) ).
fof(f12123,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12122,f4426,f3290,f9793]) ).
fof(f12122,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12121]) ).
fof(f12121,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12120,f9774]) ).
fof(f12120,plain,
( ! [X14,X17,X15,X12] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(X12),sK72(X12,X17,X14,X15)),X15)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12119]) ).
fof(f12119,plain,
( ! [X14,X17,X15,X12] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(X12),sK72(X12,X17,X14,X15)),X15))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10627,f9774]) ).
fof(f10627,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16))))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(X12),sK72(X12,X17,X14,X15)),X15)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3592,f9774]) ).
fof(f3592,plain,
! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(X12),sK72(X12,X17,X14,X15)),X15))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16))))
| hBOOL(hAPP(hAPP(c_member(X12),sK65(X16,X13,X15,X12,X17)),X15)) ),
inference(resolution,[],[f2749,f2719]) ).
fof(f12118,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12117,f4426,f3290,f9793]) ).
fof(f12117,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12116]) ).
fof(f12116,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12115,f9774]) ).
fof(f12115,plain,
( ! [X31,X28,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f12114]) ).
fof(f12114,plain,
( ! [X31,X28,X27,X34,X32,X30,X33] :
( hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____)
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12113,f9774]) ).
fof(f12113,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hAPP(v_F,v_Q____) != hAPP(sK57(X32,c_FuncSet_OPi(X27,X28,X30,X31),tc_fun(X27,X28),X33,X34),sK72(X27,X29,sK57(X32,c_FuncSet_OPi(X27,X28,X30,X31),tc_fun(X27,X28),X33,X34),X30))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10010,f9774]) ).
fof(f10010,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X27,X28)),X29),c_FuncSet_OPi(X27,X28,X30,X31)))
| hAPP(v_F,v_Q____) != hAPP(sK57(X32,c_FuncSet_OPi(X27,X28,X30,X31),tc_fun(X27,X28),X33,X34),sK72(X27,X29,sK57(X32,c_FuncSet_OPi(X27,X28,X30,X31),tc_fun(X27,X28),X33,X34),X30))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3616,f9774]) ).
fof(f3616,plain,
! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X27,X28)),X29),c_FuncSet_OPi(X27,X28,X30,X31)))
| hAPP(X29,sK72(X27,X29,sK57(X32,c_FuncSet_OPi(X27,X28,X30,X31),tc_fun(X27,X28),X33,X34),X30)) != hAPP(sK57(X32,c_FuncSet_OPi(X27,X28,X30,X31),tc_fun(X27,X28),X33,X34),sK72(X27,X29,sK57(X32,c_FuncSet_OPi(X27,X28,X30,X31),tc_fun(X27,X28),X33,X34),X30))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34))) ),
inference(resolution,[],[f2752,f2649]) ).
fof(f12111,plain,
( spl85_58
| spl85_58
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12110,f4426,f3290,f9793,f4223,f4223]) ).
fof(f12110,plain,
( ! [X10,X8,X9,X7] :
( hBOOL(hAPP(v_F,v_Q____))
| X9 = X10
| X7 = X8 )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12109]) ).
fof(f12109,plain,
( ! [X10,X8,X9,X7] :
( X7 = X8
| hBOOL(hAPP(v_F,v_Q____))
| X9 = X10
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12108,f9774]) ).
fof(f12108,plain,
( ! [X10,X8,X9,X7] :
( X7 = X8
| X9 = X10
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),sK84(X9,X10)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10138,f9774]) ).
fof(f10138,plain,
( ! [X10,X8,X9,X7] :
( X7 = X8
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8),X7)),sK84(X9,X10)))
| X9 = X10
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),sK84(X9,X10))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3635,f9774]) ).
fof(f3635,plain,
! [X10,X8,X9,X7] :
( X9 = X10
| X7 = X8
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X8)),sK84(X9,X10)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8),X7)),sK84(X9,X10))) ),
inference(resolution,[],[f2888,f2948]) ).
fof(f12096,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10763,f4426,f3290,f9793]) ).
fof(f10763,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4097,f9774]) ).
fof(f4097,plain,
! [X16,X14,X17,X15,X13] : hBOOL(hAPP(hAPP(c_member(X13),hAPP(c_Transitive__Closure_Ortranclp(X14,X15),X16)),hAPP(c_member(X17),X16))),
inference(resolution,[],[f3644,f2711]) ).
fof(f3644,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(c_Transitive__Closure_Ortranclp(X2,X3),X1))),
inference(resolution,[],[f3016,f2711]) ).
fof(f12095,plain,
( spl85_167
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12094,f4426,f3290,f9793,f11209]) ).
fof(f12094,plain,
( ! [X7,X12] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(X7,X12)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10732,f9774]) ).
fof(f10732,plain,
( ! [X7,X12] :
( ~ hBOOL(hAPP(X7,X12))
| hBOOL(hAPP(hAPP(hAPP(v_F,v_Q____),X7),X12)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4623,f9774]) ).
fof(f4623,plain,
! [X10,X11,X8,X6,X9,X7,X12] :
( hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X9,X10,X11),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool))),X8),X7),X12))
| ~ hBOOL(hAPP(X7,X12)) ),
inference(superposition,[],[f2374,f2728]) ).
fof(f12092,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_41
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10893,f4426,f3376,f3290,f9793]) ).
fof(f3376,plain,
( spl85_41
<=> ! [X4,X5,X3] : ~ hBOOL(hAPP(hAPP(c_Product__Type_OPair(X4,X5),sK32(X4,c_COMBI(X3),X5)),sK31(X4,c_COMBI(X3),X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_41])]) ).
fof(f10893,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_41
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3377,f9774]) ).
fof(f3377,plain,
( ! [X3,X4,X5] : ~ hBOOL(hAPP(hAPP(c_Product__Type_OPair(X4,X5),sK32(X4,c_COMBI(X3),X5)),sK31(X4,c_COMBI(X3),X5)))
| ~ spl85_41 ),
inference(avatar_component_clause,[],[f3376]) ).
fof(f12090,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12089,f4426,f3290,f9793]) ).
fof(f12089,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f12088]) ).
fof(f12088,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____)
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12087,f9774]) ).
fof(f12087,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(sK57(X29,c_FuncSet_OPi(X28,X30,X31,X32),tc_fun(X28,X30),X33,X34),sK72(X28,sK57(X29,c_FuncSet_OPi(X28,X30,X31,X32),tc_fun(X28,X30),X33,X34),X27,X31)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12086]) ).
fof(f12086,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(sK57(X29,c_FuncSet_OPi(X28,X30,X31,X32),tc_fun(X28,X30),X33,X34),sK72(X28,sK57(X29,c_FuncSet_OPi(X28,X30,X31,X32),tc_fun(X28,X30),X33,X34),X27,X31)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12085,f9774]) ).
fof(f12085,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X28,X30),X33)),X29),c_FuncSet_OPi(tc_fun(X28,X30),X33,c_FuncSet_OPi(X28,X30,X31,X32),X34)))
| hAPP(v_F,v_Q____) != hAPP(sK57(X29,c_FuncSet_OPi(X28,X30,X31,X32),tc_fun(X28,X30),X33,X34),sK72(X28,sK57(X29,c_FuncSet_OPi(X28,X30,X31,X32),tc_fun(X28,X30),X33,X34),X27,X31))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10012,f9774]) ).
fof(f10012,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X28,X30)),X27),c_FuncSet_OPi(X28,X30,X31,X32)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X28,X30),X33)),X29),c_FuncSet_OPi(tc_fun(X28,X30),X33,c_FuncSet_OPi(X28,X30,X31,X32),X34)))
| hAPP(v_F,v_Q____) != hAPP(sK57(X29,c_FuncSet_OPi(X28,X30,X31,X32),tc_fun(X28,X30),X33,X34),sK72(X28,sK57(X29,c_FuncSet_OPi(X28,X30,X31,X32),tc_fun(X28,X30),X33,X34),X27,X31)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3609,f9774]) ).
fof(f3609,plain,
! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X28,X30),X33)),X29),c_FuncSet_OPi(tc_fun(X28,X30),X33,c_FuncSet_OPi(X28,X30,X31,X32),X34)))
| hAPP(sK57(X29,c_FuncSet_OPi(X28,X30,X31,X32),tc_fun(X28,X30),X33,X34),sK72(X28,sK57(X29,c_FuncSet_OPi(X28,X30,X31,X32),tc_fun(X28,X30),X33,X34),X27,X31)) != hAPP(X27,sK72(X28,sK57(X29,c_FuncSet_OPi(X28,X30,X31,X32),tc_fun(X28,X30),X33,X34),X27,X31))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X28,X30)),X27),c_FuncSet_OPi(X28,X30,X31,X32))) ),
inference(resolution,[],[f2751,f2649]) ).
fof(f12084,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10737,f4426,f3290,f9793]) ).
fof(f10737,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4101,f9774]) ).
fof(f4101,plain,
! [X2,X3,X0,X1,X6,X4,X5] : hBOOL(hAPP(hAPP(hAPP(c_COMBS(X4,X5,X6),c_member(X0)),c_Transitive__Closure_Ortranclp(X2,X3)),X1)),
inference(superposition,[],[f3644,f2728]) ).
fof(f12083,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10753,f4426,f3290,f9793]) ).
fof(f10753,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3644,f9774]) ).
fof(f12078,plain,
( spl85_161
| spl85_58
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12077,f4426,f3290,f4223,f9793]) ).
fof(f12077,plain,
( ! [X2,X0] :
( X0 = X2
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10118,f9774]) ).
fof(f10118,plain,
( ! [X2,X3,X0] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2)))
| X0 = X2 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3084,f9774]) ).
fof(f3084,plain,
! [X2,X3,X0] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X0)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2)))
| X0 = X2 ),
inference(duplicate_literal_removal,[],[f3023]) ).
fof(f3023,plain,
! [X2,X3,X0] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X0)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2)))
| X0 = X2
| X0 = X2 ),
inference(equality_resolution,[],[f2497]) ).
fof(f2497,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2)))
| X0 = X2
| X0 = X1
| X1 != X2 ),
inference(cnf_transformation,[],[f1767]) ).
fof(f1767,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2)))
| X0 = X2
| ( X0 = X1
& X1 = X2 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),X3))
& X1 != X2 ) )
& ( ( X0 != X2
& ( X0 != X1
| X1 != X2 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),X3))
| X1 = X2 ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2))) ) ),
inference(rectify,[],[f1766]) ).
fof(f1766,plain,
! [X2,X1,X0,X3] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X0)))
| X0 = X2
| ( X1 = X2
& X0 = X1 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
& X0 != X1 ) )
& ( ( X0 != X2
& ( X1 != X2
| X0 != X1 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| X0 = X1 ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X0))) ) ),
inference(flattening,[],[f1765]) ).
fof(f1765,plain,
! [X2,X1,X0,X3] :
( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X0)))
| X0 = X2
| ( X1 = X2
& X0 = X1 )
| ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
& X0 != X1 ) )
& ( ( X0 != X2
& ( X1 != X2
| X0 != X1 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| X0 = X1 ) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X0))) ) ),
inference(nnf_transformation,[],[f1346]) ).
fof(f1346,plain,
! [X2,X1,X0,X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X0)))
<=> ( X0 != X2
& ( X1 != X2
| X0 != X1 )
& ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3))
| X0 = X1 ) ) ),
inference(ennf_transformation,[],[f711]) ).
fof(f711,plain,
! [X1,X2,X0,X3] :
( ( ( X0 = X1
=> X1 != X2 )
& X0 != X2
& ( X0 != X1
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),X3)) ) )
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X0))) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X11,X14,X13,X12] :
( ( ( X11 = X14
=> X13 != X14 )
& ( X11 != X14
=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X13)),X12)) )
& X11 != X13 )
<=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X13)),c_Arrow__Order__Mirabelle_Omkbot(X12,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mkbot) ).
fof(f12068,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10553,f4426,f3290,f9793]) ).
fof(f10553,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3016,f9774]) ).
fof(f12065,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12064,f4426,f3290,f9793]) ).
fof(f12064,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12063]) ).
fof(f12063,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12062,f9774]) ).
fof(f12062,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_fun(X1,X2))),X3),c_FuncSet_OPi(X0,tc_fun(X1,X2),X4,c_COMBK(tc_fun(tc_fun(X1,X2),tc_HOL_Obool),X0,c_FuncSet_OPi(X1,X2,X5,X6)))))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9981,f9774]) ).
fof(f9981,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X1),sK83(X5,X1,X2,X6,hAPP(v_F,v_Q____))),X5))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_fun(X1,X2))),X3),c_FuncSet_OPi(X0,tc_fun(X1,X2),X4,c_COMBK(tc_fun(tc_fun(X1,X2),tc_HOL_Obool),X0,c_FuncSet_OPi(X1,X2,X5,X6))))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3523,f9774]) ).
fof(f3523,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_fun(X1,X2))),X3),c_FuncSet_OPi(X0,tc_fun(X1,X2),X4,c_COMBK(tc_fun(tc_fun(X1,X2),tc_HOL_Obool),X0,c_FuncSet_OPi(X1,X2,X5,X6)))))
| hBOOL(hAPP(hAPP(c_member(X1),sK83(X5,X1,X2,X6,hAPP(X3,sK65(c_FuncSet_OPi(X1,X2,X5,X6),tc_fun(X1,X2),X4,X0,X3)))),X5)) ),
inference(resolution,[],[f2718,f2942]) ).
fof(f12061,plain,
( spl85_94
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10272,f4426,f3290,f9793,f6637]) ).
fof(f6637,plain,
( spl85_94
<=> ! [X2,X0,X1,X3] : c_Predicate_ORangeP(X2,X1,X3,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_94])]) ).
fof(f10272,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Predicate_ORangeP(X2,X1,X3,X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2173,f9774]) ).
fof(f12060,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12059,f4426,f3290,f9793]) ).
fof(f12059,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10112,f9774]) ).
fof(f10112,plain,
( ! [X2,X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2)))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3025,f9774]) ).
fof(f3025,plain,
! [X2,X3,X1] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2))),
inference(equality_resolution,[],[f2494]) ).
fof(f2494,plain,
! [X2,X3,X0,X1] :
( X0 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2))) ),
inference(cnf_transformation,[],[f1767]) ).
fof(f12051,plain,
( ~ spl85_161
| spl85_178
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12050,f4426,f3290,f11730,f9793]) ).
fof(f12050,plain,
( ! [X15] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X15)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12049,f9774]) ).
fof(f12049,plain,
( ! [X14,X15,X12,X13] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(c_COMBK(X12,X13,X14),X15) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f12048]) ).
fof(f12048,plain,
( ! [X14,X15,X12,X13] :
( c_Arrow__Order__Mirabelle_Odictator(c_COMBK(X12,X13,X14),X15)
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10621,f9774]) ).
fof(f10621,plain,
( ! [X14,X15,X12,X13] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(X12,X13,X14)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ~ hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(c_COMBK(X12,X13,X14),X15) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3966,f9774]) ).
fof(f3966,plain,
! [X14,X15,X12,X13] :
( c_Arrow__Order__Mirabelle_Odictator(c_COMBK(X12,X13,X14),X15)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X15,c_COMBK(X12,X13,X14))),sK21(X15,c_COMBK(X12,X13,X14)))),X14))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(X12,X13,X14)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(superposition,[],[f2454,f2430]) ).
fof(f12042,plain,
( spl85_161
| ~ spl85_24
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10758,f4426,f3290,f3218,f9793]) ).
fof(f10758,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_24
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3220,f9774]) ).
fof(f12038,plain,
( spl85_161
| ~ spl85_33
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10768,f4426,f3290,f3283,f9793]) ).
fof(f3283,plain,
( spl85_33
<=> hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_33])]) ).
fof(f10768,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_33
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3886,f9774]) ).
fof(f3886,plain,
( ! [X2,X3,X1] : hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_member(X2),v_Q____)),hAPP(c_member(X3),c_Arrow__Order__Mirabelle_OProf)))
| ~ spl85_33 ),
inference(resolution,[],[f3563,f2711]) ).
fof(f3563,plain,
( ! [X6,X7] : hBOOL(hAPP(hAPP(c_member(X6),c_Arrow__Order__Mirabelle_OProf),hAPP(c_member(X7),v_Q____)))
| ~ spl85_33 ),
inference(resolution,[],[f3312,f2711]) ).
fof(f3312,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_member(X0),v_Q____),c_Arrow__Order__Mirabelle_OProf))
| ~ spl85_33 ),
inference(resolution,[],[f3285,f2711]) ).
fof(f3285,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____))
| ~ spl85_33 ),
inference(avatar_component_clause,[],[f3283]) ).
fof(f12037,plain,
( spl85_161
| spl85_186
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f12033,f4426,f3290,f12035,f9793]) ).
fof(f12033,plain,
( ! [X2,X3,X0,X1,X5] :
( c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f12032]) ).
fof(f12032,plain,
( ! [X2,X3,X0,X1,X5] :
( c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12031,f9774]) ).
fof(f12031,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hAPP(v_F,v_Q____) != hAPP(hAPP(X3,X4),X0)
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12030,f9774]) ).
fof(f12030,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(v_F,v_Q____)),X5))
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(hAPP(X3,X4),X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f12029,f9774]) ).
fof(f12029,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(hAPP(X3,X4),X0))
| hAPP(v_F,v_Q____) != hAPP(hAPP(X3,X4),X0)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(v_F,v_Q____)),X5)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10216,f9774]) ).
fof(f10216,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(hAPP(X3,X4),X0) != hAPP(hAPP(X3,X6),X0)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(v_F,v_Q____)),X5))
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(hAPP(X3,X4),X0)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2486,f9774]) ).
fof(f2486,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(hAPP(X3,X4),X0))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK28(X0,X1,X2,X3,X5,X6)),X0)),X5))
| hAPP(hAPP(X3,X4),X0) != hAPP(hAPP(X3,X6),X0) ),
inference(cnf_transformation,[],[f1758]) ).
fof(f12015,plain,
( spl85_170
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10345,f4426,f3290,f9793,f11305]) ).
fof(f10345,plain,
( ! [X2,X0] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X2,X0)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2710,f9774]) ).
fof(f12014,plain,
( spl85_127
| spl85_185
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10981,f4426,f3290,f12011,f8134]) ).
fof(f8134,plain,
( spl85_127
<=> ! [X0] : ~ class_Lattices_Obounded__lattice(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_127])]) ).
fof(f12011,plain,
( spl85_185
<=> class_Lattices_Obounded__lattice(hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_185])]) ).
fof(f10981,plain,
( ! [X0] :
( class_Lattices_Obounded__lattice(hAPP(v_F,v_Q____))
| ~ class_Lattices_Obounded__lattice(X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2382,f9774]) ).
fof(f2382,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(tc_fun(X1,X0))
| ~ class_Lattices_Obounded__lattice(X0) ),
inference(cnf_transformation,[],[f1671]) ).
fof(f1671,plain,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| class_Lattices_Obounded__lattice(tc_fun(X1,X0)) ),
inference(rectify,[],[f1444]) ).
fof(f1444,plain,
! [X1,X0] :
( ~ class_Lattices_Obounded__lattice(X1)
| class_Lattices_Obounded__lattice(tc_fun(X0,X1)) ),
inference(ennf_transformation,[],[f913]) ).
fof(f913,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X1)
=> class_Lattices_Obounded__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f496]) ).
fof(f496,axiom,
! [X73,X74] :
( class_Lattices_Obounded__lattice(X74)
=> class_Lattices_Obounded__lattice(tc_fun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice) ).
fof(f12009,plain,
( spl85_184
| spl85_88
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10982,f4426,f3290,f6496,f12006]) ).
fof(f6496,plain,
( spl85_88
<=> ! [X1] : ~ class_Orderings_Obot(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_88])]) ).
fof(f10982,plain,
( ! [X1] :
( ~ class_Orderings_Obot(X1)
| class_Orderings_Obot(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2391,f9774]) ).
fof(f2391,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(cnf_transformation,[],[f1678]) ).
fof(f1678,plain,
! [X0,X1] :
( class_Orderings_Obot(tc_fun(X0,X1))
| ~ class_Orderings_Obot(X1) ),
inference(rectify,[],[f1328]) ).
fof(f1328,plain,
! [X1,X0] :
( class_Orderings_Obot(tc_fun(X1,X0))
| ~ class_Orderings_Obot(X0) ),
inference(ennf_transformation,[],[f901]) ).
fof(f901,plain,
! [X1,X0] :
( class_Orderings_Obot(X0)
=> class_Orderings_Obot(tc_fun(X1,X0)) ),
inference(rectify,[],[f505]) ).
fof(f505,axiom,
! [X74,X73] :
( class_Orderings_Obot(X74)
=> class_Orderings_Obot(tc_fun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
fof(f12004,plain,
( ~ spl85_183
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11999,f4426,f3290,f12001]) ).
fof(f12001,plain,
( spl85_183
<=> hAPP(v_F,v_Q____) = c_Orderings_Obot__class_Obot(hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_183])]) ).
fof(f11999,plain,
( hAPP(v_F,v_Q____) != c_Orderings_Obot__class_Obot(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11006,f9774]) ).
fof(f11006,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(hAPP(v_F,v_Q____)) != c_Set_Oinsert(X0,X1,X2)
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2646,f9774]) ).
fof(f2646,plain,
! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != c_Set_Oinsert(X0,X1,X2),
inference(cnf_transformation,[],[f1902]) ).
fof(f1902,plain,
! [X0,X1,X2] : c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != c_Set_Oinsert(X0,X1,X2),
inference(rectify,[],[f988]) ).
fof(f988,plain,
! [X1,X2,X0] : c_Set_Oinsert(X1,X2,X0) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)),
inference(rectify,[],[f437]) ).
fof(f437,axiom,
! [X10,X8,X24] : c_Set_Oinsert(X8,X24,X10) != c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__not__insert) ).
fof(f11997,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10809,f4426,f3290,f9793]) ).
fof(f10809,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3960,f9774]) ).
fof(f3960,plain,
! [X16,X14,X17,X15,X13] : hBOOL(hAPP(hAPP(c_member(X13),c_Set_Oinsert(X14,X15,X16)),hAPP(c_member(X17),X15))),
inference(resolution,[],[f3564,f2711]) ).
fof(f11992,plain,
( spl85_98
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10879,f4426,f3290,f9793,f6883]) ).
fof(f6883,plain,
( spl85_98
<=> ! [X0,X1] : c_Wellfounded_Oacyclic(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_98])]) ).
fof(f10879,plain,
( ! [X0,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Wellfounded_Oacyclic(X1,X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2722,f9774]) ).
fof(f2722,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK66(X0,X1)),sK66(X0,X1))),c_Transitive__Closure_Otrancl(X1,X0)))
| c_Wellfounded_Oacyclic(X1,X0) ),
inference(cnf_transformation,[],[f1979]) ).
fof(f1979,plain,
! [X0,X1] :
( ( ! [X2] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Otrancl(X1,X0)))
| ~ c_Wellfounded_Oacyclic(X1,X0) )
& ( c_Wellfounded_Oacyclic(X1,X0)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK66(X0,X1)),sK66(X0,X1))),c_Transitive__Closure_Otrancl(X1,X0))) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f1977,f1978]) ).
fof(f1978,plain,
! [X0,X1] :
( ? [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),c_Transitive__Closure_Otrancl(X1,X0)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK66(X0,X1)),sK66(X0,X1))),c_Transitive__Closure_Otrancl(X1,X0))) ),
introduced(choice_axiom,[]) ).
fof(f1977,plain,
! [X0,X1] :
( ( ! [X2] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Otrancl(X1,X0)))
| ~ c_Wellfounded_Oacyclic(X1,X0) )
& ( c_Wellfounded_Oacyclic(X1,X0)
| ? [X3] : hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X3)),c_Transitive__Closure_Otrancl(X1,X0))) ) ),
inference(rectify,[],[f1976]) ).
fof(f1976,plain,
! [X0,X1] :
( ( ! [X2] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Otrancl(X1,X0)))
| ~ c_Wellfounded_Oacyclic(X1,X0) )
& ( c_Wellfounded_Oacyclic(X1,X0)
| ? [X2] : hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Otrancl(X1,X0))) ) ),
inference(nnf_transformation,[],[f882]) ).
fof(f882,plain,
! [X0,X1] :
( ! [X2] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Otrancl(X1,X0)))
<=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f280]) ).
fof(f280,axiom,
! [X19,X8] :
( ! [X2] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X2),X2)),c_Transitive__Closure_Otrancl(X8,X19)))
<=> c_Wellfounded_Oacyclic(X8,X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__def) ).
fof(f11979,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10746,f4426,f3371,f3290,f9793]) ).
fof(f10746,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3652,f9774]) ).
fof(f11978,plain,
( spl85_161
| ~ spl85_33
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10898,f4426,f3290,f3283,f9793]) ).
fof(f10898,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_33
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3285,f9774]) ).
fof(f11977,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11976,f4426,f3290,f9793]) ).
fof(f11976,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11975]) ).
fof(f11975,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11974,f9774]) ).
fof(f11974,plain,
( ! [X18,X19,X16,X14,X17,X15,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X14,tc_fun(X15,X16))),X17),c_FuncSet_OPi(X14,tc_fun(X15,X16),X18,c_COMBK(tc_fun(tc_fun(X15,X16),tc_HOL_Obool),X14,c_FuncSet_OPi(X15,X16,X19,c_COMBK(tc_fun(X16,tc_HOL_Obool),X15,X20))))))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9980,f9774]) ).
fof(f9980,plain,
( ! [X18,X19,X16,X14,X17,X15,X20] :
( hBOOL(hAPP(hAPP(c_member(X15),sK65(X20,X16,X19,X15,hAPP(v_F,v_Q____))),X19))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X14,tc_fun(X15,X16))),X17),c_FuncSet_OPi(X14,tc_fun(X15,X16),X18,c_COMBK(tc_fun(tc_fun(X15,X16),tc_HOL_Obool),X14,c_FuncSet_OPi(X15,X16,X19,c_COMBK(tc_fun(X16,tc_HOL_Obool),X15,X20)))))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3525,f9774]) ).
fof(f3525,plain,
! [X18,X19,X16,X14,X17,X15,X20] :
( hBOOL(hAPP(hAPP(c_member(X15),sK65(X20,X16,X19,X15,hAPP(X17,sK65(c_FuncSet_OPi(X15,X16,X19,c_COMBK(tc_fun(X16,tc_HOL_Obool),X15,X20)),tc_fun(X15,X16),X18,X14,X17)))),X19))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X14,tc_fun(X15,X16))),X17),c_FuncSet_OPi(X14,tc_fun(X15,X16),X18,c_COMBK(tc_fun(tc_fun(X15,X16),tc_HOL_Obool),X14,c_FuncSet_OPi(X15,X16,X19,c_COMBK(tc_fun(X16,tc_HOL_Obool),X15,X20)))))) ),
inference(resolution,[],[f2718,f2719]) ).
fof(f11959,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11958,f4426,f3290,f9793]) ).
fof(f11958,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f11957]) ).
fof(f11957,plain,
( hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____)
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11956,f9774]) ).
fof(f11956,plain,
( ! [X14,X15,X12,X13] :
( hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(X12,sK72(X13,X14,X12,X15)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11955]) ).
fof(f11955,plain,
( ! [X14,X15,X12,X13] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(X12,sK72(X13,X14,X12,X15)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11954,f9774]) ).
fof(f11954,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X16)),X12),c_FuncSet_OPi(X13,X16,X15,c_COMBK(tc_fun(X16,tc_HOL_Obool),X13,X17))))
| hAPP(v_F,v_Q____) != hAPP(X12,sK72(X13,X14,X12,X15))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10002,f9774]) ).
fof(f10002,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),sK65(X17,X16,X15,X13,X14)),X15))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X16)),X12),c_FuncSet_OPi(X13,X16,X15,c_COMBK(tc_fun(X16,tc_HOL_Obool),X13,X17))))
| hAPP(v_F,v_Q____) != hAPP(X12,sK72(X13,X14,X12,X15)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3606,f9774]) ).
fof(f3606,plain,
! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X16)),X12),c_FuncSet_OPi(X13,X16,X15,c_COMBK(tc_fun(X16,tc_HOL_Obool),X13,X17))))
| hBOOL(hAPP(hAPP(c_member(X13),sK65(X17,X16,X15,X13,X14)),X15))
| hAPP(X14,sK72(X13,X14,X12,X15)) != hAPP(X12,sK72(X13,X14,X12,X15)) ),
inference(resolution,[],[f2751,f2719]) ).
fof(f11953,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11952,f4426,f3290,f9793]) ).
fof(f11952,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11951]) ).
fof(f11951,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11950,f9774]) ).
fof(f11950,plain,
( ! [X40,X38,X41,X39,X36,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40))))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f11949]) ).
fof(f11949,plain,
( ! [X40,X38,X41,X39,X36,X35,X42] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40))))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11948,f9774]) ).
fof(f11948,plain,
( ! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),sK72(X35,X37,sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),X38))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40)))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10009,f9774]) ).
fof(f10009,plain,
( ! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,X39)))
| hAPP(v_F,v_Q____) != hAPP(sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),sK72(X35,X37,sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),X38))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40)))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3617,f9774]) ).
fof(f3617,plain,
! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40))))
| hAPP(X37,sK72(X35,X37,sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),X38)) != hAPP(sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),sK72(X35,X37,sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),X38))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,X39))) ),
inference(resolution,[],[f2752,f2719]) ).
fof(f11944,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_36
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10908,f4426,f3306,f3290,f9793]) ).
fof(f10908,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_36
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3308,f9774]) ).
fof(f11942,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10762,f4426,f3290,f9793]) ).
fof(f10762,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3324,f9774]) ).
fof(f11941,plain,
( spl85_168
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11940,f4426,f3290,f9793,f11279]) ).
fof(f11940,plain,
( ! [X46,X47,X45] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Predicate_ORangeP(X46,X47,hAPP(v_F,v_Q____),X45) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9830,f9774]) ).
fof(f9830,plain,
( ! [X40,X41,X46,X47,X45,X42,X43] :
( c_Predicate_ORangeP(X46,X47,c_COMBB(X40,X41,X42,X43),X45)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4371,f9774]) ).
fof(f4371,plain,
! [X40,X41,X46,X47,X44,X45,X42,X43] :
( c_Predicate_ORangeP(X46,X47,c_COMBB(X40,X41,X42,X43),X45)
| ~ hBOOL(hAPP(X43,hAPP(X44,X45))) ),
inference(superposition,[],[f2173,f2177]) ).
fof(f11936,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11935,f4426,f3290,f9793]) ).
fof(f11935,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11934]) ).
fof(f11934,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11933,f9774]) ).
fof(f11933,plain,
( ! [X2,X0,X6] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X0)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f11932]) ).
fof(f11932,plain,
( ! [X2,X0,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X0))
| ~ hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11931,f9774]) ).
fof(f11931,plain,
( ! [X2,X0,X6] :
( hAPP(v_F,v_Q____) != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X0))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10354,f9774]) ).
fof(f10354,plain,
( ! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X0)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3044,f9774]) ).
fof(f3044,plain,
! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X0))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1)) ),
inference(equality_resolution,[],[f2679]) ).
fof(f2679,plain,
! [X2,X0,X1,X6,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1))
| X5 != X6
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X0))
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1) ),
inference(cnf_transformation,[],[f1937]) ).
fof(f1937,plain,
! [X0,X1,X2] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1)
| ( hBOOL(hAPP(hAPP(c_member(X2),sK60(X0,X1,X2)),X1))
& sK59(X0,X1,X2) = sK60(X0,X1,X2)
& hBOOL(hAPP(hAPP(c_member(X2),sK59(X0,X1,X2)),X0)) ) )
& ( ! [X5] :
( ! [X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1))
| X5 != X6 )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X0)) )
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59,sK60])],[f1934,f1936,f1935]) ).
fof(f1935,plain,
! [X0,X1,X2] :
( ? [X3] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
& X3 = X4 )
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0)) )
=> ( ? [X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
& sK59(X0,X1,X2) = X4 )
& hBOOL(hAPP(hAPP(c_member(X2),sK59(X0,X1,X2)),X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f1936,plain,
! [X0,X1,X2] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
& sK59(X0,X1,X2) = X4 )
=> ( hBOOL(hAPP(hAPP(c_member(X2),sK60(X0,X1,X2)),X1))
& sK59(X0,X1,X2) = sK60(X0,X1,X2) ) ),
introduced(choice_axiom,[]) ).
fof(f1934,plain,
! [X0,X1,X2] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1)
| ? [X3] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
& X3 = X4 )
& hBOOL(hAPP(hAPP(c_member(X2),X3),X0)) ) )
& ( ! [X5] :
( ! [X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X1))
| X5 != X6 )
| ~ hBOOL(hAPP(hAPP(c_member(X2),X5),X0)) )
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1) ) ),
inference(rectify,[],[f1933]) ).
fof(f1933,plain,
! [X0,X2,X1] :
( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
| ? [X3] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
& X3 = X4 )
& hBOOL(hAPP(hAPP(c_member(X1),X3),X0)) ) )
& ( ! [X3] :
( ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| X3 != X4 )
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X0)) )
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X2) != c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ) ),
inference(nnf_transformation,[],[f1427]) ).
fof(f1427,plain,
! [X0,X2,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
<=> ! [X3] :
( ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
| X3 != X4 )
| ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X0)) ) ),
inference(ennf_transformation,[],[f883]) ).
fof(f883,plain,
! [X1,X0,X2] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X2) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X1),X3),X0))
=> ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X1),X4),X2))
=> X3 != X4 ) ) ),
inference(rectify,[],[f459]) ).
fof(f459,axiom,
! [X10,X8,X9] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X10))
=> ! [X4] :
( hBOOL(hAPP(hAPP(c_member(X8),X4),X9))
=> X2 != X4 ) )
<=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X10),X9) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).
fof(f11927,plain,
( spl85_58
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10801,f4426,f3290,f9793,f4223]) ).
fof(f10801,plain,
( ! [X2,X3] :
( hBOOL(hAPP(v_F,v_Q____))
| X2 = X3 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3395,f9774]) ).
fof(f3395,plain,
! [X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),c_Arrow__Order__Mirabelle_OLin),hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK84(X2,X3))))
| X2 = X3 ),
inference(resolution,[],[f2948,f2711]) ).
fof(f11917,plain,
( spl85_161
| spl85_98
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10880,f4426,f3290,f6883,f9793]) ).
fof(f10880,plain,
( ! [X0,X1] :
( c_Wellfounded_Oacyclic(X0,X1)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2175,f9774]) ).
fof(f2175,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK1(X0,X1)),sK1(X0,X1))),c_Transitive__Closure_Otrancl(X0,X1)))
| c_Wellfounded_Oacyclic(X0,X1) ),
inference(cnf_transformation,[],[f1506]) ).
fof(f1506,plain,
! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK1(X0,X1)),sK1(X0,X1))),c_Transitive__Closure_Otrancl(X0,X1)))
| c_Wellfounded_Oacyclic(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f1504,f1505]) ).
fof(f1505,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X2),X2)),c_Transitive__Closure_Otrancl(X0,X1)))
=> hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK1(X0,X1)),sK1(X0,X1))),c_Transitive__Closure_Otrancl(X0,X1))) ),
introduced(choice_axiom,[]) ).
fof(f1504,plain,
! [X0,X1] :
( ? [X2] : hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),X2),X2)),c_Transitive__Closure_Otrancl(X0,X1)))
| c_Wellfounded_Oacyclic(X0,X1) ),
inference(rectify,[],[f1076]) ).
fof(f1076,plain,
! [X1,X0] :
( ? [X2] : hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Otrancl(X1,X0)))
| c_Wellfounded_Oacyclic(X1,X0) ),
inference(ennf_transformation,[],[f556]) ).
fof(f556,plain,
! [X0,X1] :
( ! [X2] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Otrancl(X1,X0)))
=> c_Wellfounded_Oacyclic(X1,X0) ),
inference(rectify,[],[f284]) ).
fof(f284,axiom,
! [X19,X8] :
( ! [X2] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X2),X2)),c_Transitive__Closure_Otrancl(X8,X19)))
=> c_Wellfounded_Oacyclic(X8,X19) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclicI) ).
fof(f11916,plain,
( spl85_161
| spl85_58
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10902,f4426,f3290,f4223,f9793]) ).
fof(f10902,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3394,f9774]) ).
fof(f11915,plain,
( spl85_127
| spl85_182
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10979,f4426,f3290,f11912,f8134]) ).
fof(f11912,plain,
( spl85_182
<=> class_Lattices_Obounded__lattice__bot(hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_182])]) ).
fof(f10979,plain,
( ! [X0] :
( class_Lattices_Obounded__lattice__bot(hAPP(v_F,v_Q____))
| ~ class_Lattices_Obounded__lattice(X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2256,f9774]) ).
fof(f2256,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice__bot(tc_fun(X1,X0))
| ~ class_Lattices_Obounded__lattice(X0) ),
inference(cnf_transformation,[],[f1394]) ).
fof(f1394,plain,
! [X0,X1] :
( ~ class_Lattices_Obounded__lattice(X0)
| class_Lattices_Obounded__lattice__bot(tc_fun(X1,X0)) ),
inference(ennf_transformation,[],[f934]) ).
fof(f934,plain,
! [X0,X1] :
( class_Lattices_Obounded__lattice(X0)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X1,X0)) ),
inference(rectify,[],[f497]) ).
fof(f497,axiom,
! [X74,X73] :
( class_Lattices_Obounded__lattice(X74)
=> class_Lattices_Obounded__lattice__bot(tc_fun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Obounded__lattice__bot) ).
fof(f11909,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f9862,f4426,f3290,f9793]) ).
fof(f9862,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f9759,f9774]) ).
fof(f11908,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11907,f4426,f3290,f9793]) ).
fof(f11907,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9861,f9774]) ).
fof(f9861,plain,
( ! [X16] : hBOOL(hAPP(hAPP(v_F,v_Q____),hAPP(X16,hAPP(v_F,v_Q____))))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f9786,f9774]) ).
fof(f9786,plain,
( ! [X16,X15] : hBOOL(hAPP(hAPP(X15,hAPP(v_F,v_Q____)),hAPP(X16,hAPP(v_F,v_Q____))))
| ~ spl85_34
| ~ spl85_64 ),
inference(superposition,[],[f9759,f2728]) ).
fof(f11905,plain,
( spl85_178
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11904,f4426,f3290,f9793,f11730]) ).
fof(f11904,plain,
( ! [X11] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X11) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11903]) ).
fof(f11903,plain,
( ! [X11] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X11)
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11902,f9774]) ).
fof(f11902,plain,
( ! [X11,X14,X12,X13] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X11)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13)),X12),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X14)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10789,f9774]) ).
fof(f10789,plain,
( ! [X11,X14,X12,X13] :
( c_Arrow__Order__Mirabelle_Odictator(sK57(X12,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,X14),X11)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13)),X12),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X14)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3950,f9774]) ).
fof(f3950,plain,
! [X11,X14,X12,X13] :
( c_Arrow__Order__Mirabelle_Odictator(sK57(X12,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,X14),X11)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13)),X12),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X14)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X11,sK57(X12,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,X14))),sK21(X11,sK57(X12,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,X14)))),hAPP(sK20(X11,sK57(X12,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,X14)),X11))) ),
inference(resolution,[],[f2452,f2649]) ).
fof(f11897,plain,
( spl85_181
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11893,f4426,f3290,f9793,f11895]) ).
fof(f11895,plain,
( spl85_181
<=> ! [X2,X0,X1] : c_Predicate_ODomainP(X2,X1,hAPP(v_F,v_Q____),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_181])]) ).
fof(f11893,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Predicate_ODomainP(X2,X1,hAPP(v_F,v_Q____),X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10478,f9774]) ).
fof(f10478,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X0),c_Relation_ODomain(X2,X1,X3)))
| c_Predicate_ODomainP(X2,X1,hAPP(v_F,v_Q____),X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2593,f9774]) ).
fof(f2593,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X0),c_Relation_ODomain(X2,X1,X3)))
| c_Predicate_ODomainP(X2,X1,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2,c_COMBC(X1,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X1),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X2,X1)))),c_Product__Type_OPair(X2,X1)))),X3),X0) ),
inference(cnf_transformation,[],[f1854]) ).
fof(f1854,plain,
! [X0,X1,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_member(X2),X0),c_Relation_ODomain(X2,X1,X3)))
| ~ c_Predicate_ODomainP(X2,X1,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2,c_COMBC(X1,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X1),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X2,X1)))),c_Product__Type_OPair(X2,X1)))),X3),X0) )
& ( c_Predicate_ODomainP(X2,X1,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2,c_COMBC(X1,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X1),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X2,X1)))),c_Product__Type_OPair(X2,X1)))),X3),X0)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X0),c_Relation_ODomain(X2,X1,X3))) ) ),
inference(rectify,[],[f1853]) ).
fof(f1853,plain,
! [X1,X0,X2,X3] :
( ( hBOOL(hAPP(hAPP(c_member(X2),X1),c_Relation_ODomain(X2,X0,X3)))
| ~ c_Predicate_ODomainP(X2,X0,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_fun(X0,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X0,tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_fun(X0,tc_HOL_Obool)),X2,c_COMBC(X0,tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X0,tc_prod(X2,X0)),tc_fun(X0,tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X0),tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool),X0,c_member(tc_prod(X2,X0)))),c_Product__Type_OPair(X2,X0)))),X3),X1) )
& ( c_Predicate_ODomainP(X2,X0,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_fun(X0,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X0,tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_fun(X0,tc_HOL_Obool)),X2,c_COMBC(X0,tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X0,tc_prod(X2,X0)),tc_fun(X0,tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X0),tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool),X0,c_member(tc_prod(X2,X0)))),c_Product__Type_OPair(X2,X0)))),X3),X1)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X1),c_Relation_ODomain(X2,X0,X3))) ) ),
inference(nnf_transformation,[],[f635]) ).
fof(f635,plain,
! [X1,X0,X2,X3] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),c_Relation_ODomain(X2,X0,X3)))
<=> c_Predicate_ODomainP(X2,X0,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_fun(X0,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X0,tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_fun(X0,tc_HOL_Obool)),X2,c_COMBC(X0,tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X0,tc_prod(X2,X0)),tc_fun(X0,tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X0),tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool),X0,c_member(tc_prod(X2,X0)))),c_Product__Type_OPair(X2,X0)))),X3),X1) ),
inference(rectify,[],[f152]) ).
fof(f152,axiom,
! [X16,X14,X8,X19] :
( hBOOL(hAPP(hAPP(c_member(X8),X14),c_Relation_ODomain(X8,X16,X19)))
<=> c_Predicate_ODomainP(X8,X16,hAPP(hAPP(c_COMBC(X8,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X8,c_COMBC(X16,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_prod(X8,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),X8,c_COMBB(tc_prod(X8,X16),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool),X16,c_member(tc_prod(X8,X16)))),c_Product__Type_OPair(X8,X16)))),X19),X14) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainP__Domain__eq) ).
fof(f11891,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11890,f4426,f3290,f9793]) ).
fof(f11890,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11889]) ).
fof(f11889,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11888,f9774]) ).
fof(f11888,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(c_Transitive__Closure_Ortranclp(X0,X1),hAPP(v_F,v_Q____)))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10205,f9774]) ).
fof(f10205,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_Transitive__Closure_Ortranclp(X0,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3))),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(c_Transitive__Closure_Ortranclp(X0,X1),hAPP(v_F,v_Q____)))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4094,f9774]) ).
fof(f4094,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(c_Transitive__Closure_Ortranclp(X0,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_Transitive__Closure_Ortranclp(X0,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3))),c_Arrow__Order__Mirabelle_OLin)) ),
inference(resolution,[],[f3644,f2792]) ).
fof(f11887,plain,
( spl85_161
| spl85_180
| ~ spl85_24
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11883,f4426,f3290,f3218,f11885,f9793]) ).
fof(f11885,plain,
( spl85_180
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X0,v_a____),hAPP(X0,v_b____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_180])]) ).
fof(f11883,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X0,v_a____),hAPP(X0,v_b____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_24
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10812,f9774]) ).
fof(f10812,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X0,v_a____),hAPP(X0,v_b____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Oless__than,hAPP(v_F,v_P____)),hAPP(hAPP(c_COMBS(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt,c_Product__Type_OPair(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),X0)),c_COMBI(tc_Arrow__Order__Mirabelle_Oalt))))) )
| ~ spl85_24
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3916,f9774]) ).
fof(f3916,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Oless__than,hAPP(v_F,v_P____)),hAPP(hAPP(c_COMBS(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt,c_Product__Type_OPair(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),X0)),c_COMBI(tc_Arrow__Order__Mirabelle_Oalt)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X0,v_a____),hAPP(X0,v_b____)) )
| ~ spl85_24 ),
inference(resolution,[],[f2974,f3220]) ).
fof(f11878,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_55
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10780,f4426,f4018,f3290,f9793]) ).
fof(f10780,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_55
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4020,f9774]) ).
fof(f11864,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10063,f4426,f3290,f9793]) ).
fof(f10063,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f9762,f9774]) ).
fof(f9762,plain,
( ! [X3,X4] : hBOOL(hAPP(hAPP(c_member(X3),hAPP(v_F,v_Q____)),X4))
| ~ spl85_34
| ~ spl85_64 ),
inference(resolution,[],[f9759,f2711]) ).
fof(f11857,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11856,f4426,f3290,f9793]) ).
fof(f11856,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10040,f9774]) ).
fof(f10040,plain,
( ! [X2,X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2)))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3027,f9774]) ).
fof(f3027,plain,
! [X2,X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X2)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2))),
inference(equality_resolution,[],[f3026]) ).
fof(f3026,plain,
! [X2,X3,X1] :
( X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X1)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2))) ),
inference(equality_resolution,[],[f2493]) ).
fof(f2493,plain,
! [X2,X3,X0,X1] :
( X0 != X1
| X1 != X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_Arrow__Order__Mirabelle_Omkbot(X3,X2))) ),
inference(cnf_transformation,[],[f1767]) ).
fof(f11848,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11847,f4426,f3290,f9793]) ).
fof(f11847,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11846]) ).
fof(f11846,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11845,f9774]) ).
fof(f11845,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,X4))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11844]) ).
fof(f11844,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,X4))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10079,f9774]) ).
fof(f10079,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X0),sK72(X0,X5,X2,X3)),X3))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,X4))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3590,f9774]) ).
fof(f3590,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,X4)))
| hBOOL(hAPP(hAPP(c_member(X0),sK72(X0,X5,X2,X3)),X3))
| hBOOL(hAPP(hAPP(c_member(X0),sK83(X3,X0,X1,X4,X5)),X3)) ),
inference(resolution,[],[f2749,f2942]) ).
fof(f11840,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_56
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10892,f4426,f4138,f3290,f9793]) ).
fof(f4138,plain,
( spl85_56
<=> ! [X41,X40,X39] : ~ hBOOL(hAPP(hAPP(c_Product__Type_OPair(X40,X41),sK32(X40,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X39,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X39,tc_HOL_Obool))),X41)),sK31(X40,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X39,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X39,tc_HOL_Obool))),X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_56])]) ).
fof(f10892,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_56
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4139,f9774]) ).
fof(f4139,plain,
( ! [X40,X41,X39] : ~ hBOOL(hAPP(hAPP(c_Product__Type_OPair(X40,X41),sK32(X40,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X39,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X39,tc_HOL_Obool))),X41)),sK31(X40,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X39,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X39,tc_HOL_Obool))),X41)))
| ~ spl85_56 ),
inference(avatar_component_clause,[],[f4138]) ).
fof(f11839,plain,
( spl85_170
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11838,f4426,f3290,f9793,f11305]) ).
fof(f11838,plain,
( ! [X2,X5] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X2,X5)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11837]) ).
fof(f11837,plain,
( ! [X2,X5] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X2,X5))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9936,f9774]) ).
fof(f9936,plain,
( ! [X2,X0,X1,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X0))
| hBOOL(hAPP(X2,X5))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2463,f9774]) ).
fof(f2463,plain,
! [X2,X3,X0,X1,X5] :
( ~ hBOOL(hAPP(X2,sK23(X0,X1,X2,X3)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X5),X0))
| hBOOL(hAPP(X2,X5)) ),
inference(cnf_transformation,[],[f1740]) ).
fof(f11831,plain,
( spl85_58
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10843,f4426,f3290,f9793,f4223]) ).
fof(f10843,plain,
( ! [X0,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| X0 = X1 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3696,f9774]) ).
fof(f3696,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),sK84(X0,X1)),c_Arrow__Order__Mirabelle_OLin))
| X0 = X1 ),
inference(resolution,[],[f3394,f2711]) ).
fof(f11830,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_35
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10794,f4426,f3297,f3290,f9793]) ).
fof(f10794,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_35
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3299,f9774]) ).
fof(f11824,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11823,f4426,f3290,f9793]) ).
fof(f11823,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11822]) ).
fof(f11822,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11821,f9774]) ).
fof(f11821,plain,
( ! [X10,X11,X6,X9,X7] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(X6),sK57(X11,X9,X6,X7,X10)),X9)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11820,f9774]) ).
fof(f11820,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X7)),X8),c_FuncSet_OPi(X6,X7,X9,X10)))
| hBOOL(hAPP(hAPP(c_member(X6),sK57(X11,X9,X6,X7,X10)),X9)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f11819]) ).
fof(f11819,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(X6),sK57(X11,X9,X6,X7,X10)),X9))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X7)),X8),c_FuncSet_OPi(X6,X7,X9,X10))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10004,f9774]) ).
fof(f10004,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hAPP(v_F,v_Q____) != hAPP(X11,sK72(X6,X8,X11,X9))
| hBOOL(hAPP(hAPP(c_member(X6),sK57(X11,X9,X6,X7,X10)),X9))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X7)),X8),c_FuncSet_OPi(X6,X7,X9,X10))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3612,f9774]) ).
fof(f3612,plain,
! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X7)),X8),c_FuncSet_OPi(X6,X7,X9,X10)))
| hAPP(X8,sK72(X6,X8,X11,X9)) != hAPP(X11,sK72(X6,X8,X11,X9))
| hBOOL(hAPP(hAPP(c_member(X6),sK57(X11,X9,X6,X7,X10)),X9)) ),
inference(resolution,[],[f2752,f2649]) ).
fof(f11802,plain,
( spl85_161
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11801,f4426,f3290,f3178,f9793]) ).
fof(f11801,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11800,f9774]) ).
fof(f11800,plain,
( ! [X18] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f11799]) ).
fof(f11799,plain,
( ! [X18] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____) )
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9997,f9774]) ).
fof(f9997,plain,
( ! [X18] :
( hAPP(v_F,v_Q____) != hAPP(v_F,sK72(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_F,X18,c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3607,f9774]) ).
fof(f3607,plain,
( ! [X18] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| hAPP(X18,sK72(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_F,X18,c_Arrow__Order__Mirabelle_OProf)) != hAPP(v_F,sK72(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_F,X18,c_Arrow__Order__Mirabelle_OProf)) )
| ~ spl85_16 ),
inference(resolution,[],[f2751,f3180]) ).
fof(f11787,plain,
( ~ spl85_161
| spl85_179
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11783,f4426,f3290,f11785,f9793]) ).
fof(f11783,plain,
( ! [X2,X0,X1] :
( c_Relation_Orefl__on(X0,X1,X2)
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ c_Orderings_Oord__class_Oless__eq(hAPP(v_F,v_Q____),X2,hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11782,f9774]) ).
fof(f11782,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,hAPP(v_F,v_Q____))
| c_Relation_Orefl__on(X0,X1,X2)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10389,f9774]) ).
fof(f10389,plain,
( ! [X2,X0,X1] :
( c_Relation_Orefl__on(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,c_Product__Type_OSigma(X0,X0,X1,c_COMBK(tc_fun(X0,tc_HOL_Obool),X0,X1)))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2557,f9774]) ).
fof(f2557,plain,
! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK44(X0,X1,X2)),sK44(X0,X1,X2))),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,c_Product__Type_OSigma(X0,X0,X1,c_COMBK(tc_fun(X0,tc_HOL_Obool),X0,X1)))
| c_Relation_Orefl__on(X0,X1,X2) ),
inference(cnf_transformation,[],[f1825]) ).
fof(f11776,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10859,f4426,f3290,f9793]) ).
fof(f10859,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3791,f9774]) ).
fof(f3791,plain,
! [X6,X7,X4,X5] : hBOOL(hAPP(hAPP(c_member(tc_fun(X4,X6)),X5),c_FuncSet_OPi(X4,X6,c_Orderings_Obot__class_Obot(tc_fun(X4,tc_HOL_Obool)),X7))),
inference(resolution,[],[f3081,f2649]) ).
fof(f3081,plain,
! [X3,X0] : ~ hBOOL(hAPP(hAPP(c_member(X0),X3),c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))),
inference(equality_resolution,[],[f2928]) ).
fof(f2928,plain,
! [X3,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != X1
| ~ hBOOL(hAPP(hAPP(c_member(X0),X3),X1)) ),
inference(cnf_transformation,[],[f2146]) ).
fof(f11775,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11774,f4426,f3290,f9793]) ).
fof(f11774,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11773]) ).
fof(f11773,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11772,f9774]) ).
fof(f11772,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10215,f9774]) ).
fof(f10215,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(v_F,v_Q____)),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2351,f9774]) ).
fof(f2351,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK16(X0,X1,X2)),X0)),X2)) ),
inference(cnf_transformation,[],[f1657]) ).
fof(f1657,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(X1),sK16(X0,X1,X2)),c_Wellfounded_Oacc(X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK16(X0,X1,X2)),X0)),X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK16])],[f1655,f1656]) ).
fof(f1656,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X0)),X2)) )
=> ( ~ hBOOL(hAPP(hAPP(c_member(X1),sK16(X0,X1,X2)),c_Wellfounded_Oacc(X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK16(X0,X1,X2)),X0)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1655,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
| ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X0)),X2)) ) ),
inference(rectify,[],[f1164]) ).
fof(f1164,plain,
! [X1,X2,X0] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),c_Wellfounded_Oacc(X2,X0)))
| ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X3),c_Wellfounded_Oacc(X2,X0)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X1)),X0)) ) ),
inference(ennf_transformation,[],[f755]) ).
fof(f755,plain,
! [X1,X0,X2] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X1)),X0))
=> hBOOL(hAPP(hAPP(c_member(X2),X3),c_Wellfounded_Oacc(X2,X0))) )
=> hBOOL(hAPP(hAPP(c_member(X2),X1),c_Wellfounded_Oacc(X2,X0))) ),
inference(rectify,[],[f69]) ).
fof(f69,axiom,
! [X19,X14,X8] :
( ! [X41] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X41),X14)),X19))
=> hBOOL(hAPP(hAPP(c_member(X8),X41),c_Wellfounded_Oacc(X8,X19))) )
=> hBOOL(hAPP(hAPP(c_member(X8),X14),c_Wellfounded_Oacc(X8,X19))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_OaccI) ).
fof(f11765,plain,
( spl85_161
| ~ spl85_33
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10797,f4426,f3290,f3283,f9793]) ).
fof(f10797,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_33
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3563,f9774]) ).
fof(f11759,plain,
( spl85_61
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10846,f4426,f3290,f9793,f4384]) ).
fof(f10846,plain,
( ! [X2] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(X2) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3315,f9774]) ).
fof(f11758,plain,
( spl85_178
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11757,f4426,f3290,f9793,f11730]) ).
fof(f11757,plain,
( ! [X11] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X11) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11756]) ).
fof(f11756,plain,
( ! [X11] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X11)
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11755,f9774]) ).
fof(f11755,plain,
( ! [X11,X14,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13)),X12),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X14)))
| hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X11) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10825,f9774]) ).
fof(f10825,plain,
( ! [X11,X14,X12,X13] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(sK57(X12,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,X14),X11)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13)),X12),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X14))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3870,f9774]) ).
fof(f3870,plain,
! [X11,X14,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X11,sK57(X12,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,X14))),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13)),X12),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X14)))
| c_Arrow__Order__Mirabelle_Odictator(sK57(X12,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,X14),X11) ),
inference(resolution,[],[f2451,f2649]) ).
fof(f11751,plain,
( spl85_58
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11750,f4426,f3290,f9793,f4223]) ).
fof(f11750,plain,
( ! [X3,X4] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| X3 = X4 )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11749]) ).
fof(f11749,plain,
( ! [X3,X4] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| X3 = X4
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11748,f9774]) ).
fof(f11748,plain,
( ! [X2,X3,X4] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11747]) ).
fof(f11747,plain,
( ! [X2,X3,X4] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4)))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11746,f9774]) ).
fof(f11746,plain,
( ! [X2,X3,X4] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4)))
| X3 = X4 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10134,f9774]) ).
fof(f10134,plain,
( ! [X2,X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4)),c_Arrow__Order__Mirabelle_OLin))
| X3 = X4 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3620,f9774]) ).
fof(f3620,plain,
! [X2,X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4)),c_Arrow__Order__Mirabelle_OLin))
| X3 = X4 ),
inference(resolution,[],[f2792,f3085]) ).
fof(f3085,plain,
! [X2,X0,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X4)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| X2 = X4 ),
inference(duplicate_literal_removal,[],[f3008]) ).
fof(f3008,plain,
! [X2,X0,X4] :
( X2 = X4
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| X2 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X4)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4))) ),
inference(equality_resolution,[],[f3007]) ).
fof(f3007,plain,
! [X2,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| X2 = X4
| X1 = X4
| X1 != X2
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(equality_resolution,[],[f2359]) ).
fof(f2359,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| X2 = X3
| X1 = X3
| X3 != X4
| X1 != X2
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(cnf_transformation,[],[f1663]) ).
fof(f11745,plain,
( spl85_178
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11744,f4426,f3290,f9793,f11730]) ).
fof(f11744,plain,
( ! [X5] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X5) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11743]) ).
fof(f11743,plain,
( ! [X5] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X5)
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11742,f9774]) ).
fof(f11742,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X5)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11741,f9774]) ).
fof(f11741,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X5,hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4))),sK21(X5,hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4)))),hAPP(hAPP(v_F,v_Q____),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9933,f9774]) ).
fof(f9933,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X5,hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4))),sK21(X5,hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4)))),hAPP(hAPP(v_F,v_Q____),X4))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3965,f9774]) ).
fof(f3965,plain,
! [X2,X3,X0,X1,X4,X5] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X5,hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4))),sK21(X5,hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4)))),hAPP(hAPP(X3,sK20(X5,hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4))),X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(superposition,[],[f2454,f2585]) ).
fof(f11738,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_37
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10795,f4426,f3332,f3290,f9793]) ).
fof(f10795,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_37
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3585,f9774]) ).
fof(f3585,plain,
( ! [X6,X7] : hBOOL(hAPP(hAPP(c_member(X6),c_Arrow__Order__Mirabelle_OProf),hAPP(c_member(X7),v_P____)))
| ~ spl85_37 ),
inference(resolution,[],[f3357,f2711]) ).
fof(f3357,plain,
( ! [X0] : hBOOL(hAPP(hAPP(c_member(X0),v_P____),c_Arrow__Order__Mirabelle_OProf))
| ~ spl85_37 ),
inference(resolution,[],[f3334,f2711]) ).
fof(f11732,plain,
( spl85_178
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11728,f4426,f3290,f9793,f11730]) ).
fof(f11728,plain,
( ! [X7] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(v_F,v_Q____),X7) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11727,f9774]) ).
fof(f11727,plain,
( ! [X10,X8,X9,X7] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(sK83(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,X9,X10),X7) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11726]) ).
fof(f11726,plain,
( ! [X10,X8,X9,X7] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(sK83(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,X9,X10),X7)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10792,f9774]) ).
fof(f10792,plain,
( ! [X10,X8,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8)),X10),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X9)))
| hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(sK83(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,X9,X10),X7) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3949,f9774]) ).
fof(f3949,plain,
! [X10,X8,X9,X7] :
( c_Arrow__Order__Mirabelle_Odictator(sK83(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,X9,X10),X7)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8)),X10),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X9)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X7,sK83(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,X9,X10))),sK21(X7,sK83(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,X9,X10)))),hAPP(sK20(X7,sK83(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,X9,X10)),X7))) ),
inference(resolution,[],[f2452,f2942]) ).
fof(f11724,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11723,f4426,f3290,f9793]) ).
fof(f11723,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f11722]) ).
fof(f11722,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____)
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11721,f9774]) ).
fof(f11721,plain,
( ! [X2,X3,X0,X5] :
( hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(X5,sK72(X0,X2,X5,X3)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11720]) ).
fof(f11720,plain,
( ! [X2,X3,X0,X5] :
( hAPP(v_F,v_Q____) != hAPP(X5,sK72(X0,X2,X5,X3))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11719,f9774]) ).
fof(f11719,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X0),sK83(X3,X0,X1,X4,X5)),X3))
| hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(X5,sK72(X0,X2,X5,X3)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10003,f9774]) ).
fof(f10003,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,X4)))
| hBOOL(hAPP(hAPP(c_member(X0),sK83(X3,X0,X1,X4,X5)),X3))
| hAPP(v_F,v_Q____) != hAPP(X5,sK72(X0,X2,X5,X3)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3611,f9774]) ).
fof(f3611,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,X4)))
| hAPP(X5,sK72(X0,X2,X5,X3)) != hAPP(X2,sK72(X0,X2,X5,X3))
| hBOOL(hAPP(hAPP(c_member(X0),sK83(X3,X0,X1,X4,X5)),X3)) ),
inference(resolution,[],[f2752,f2942]) ).
fof(f11718,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11717,f4426,f3290,f9793]) ).
fof(f11717,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11716]) ).
fof(f11716,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11715,f9774]) ).
fof(f11715,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),hAPP(v_F,v_Q____)),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X14)),sK65(X15,X16,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X13),X14),X12,X17))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10237,f9774]) ).
fof(f10237,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X16)),X17),c_FuncSet_OPi(X12,X16,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X13),X14),c_COMBK(tc_fun(X16,tc_HOL_Obool),X12,X15))))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),hAPP(v_F,v_Q____)),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X14)),sK65(X15,X16,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X13),X14),X12,X17))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3649,f9774]) ).
fof(f3649,plain,
! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X16)),X17),c_FuncSet_OPi(X12,X16,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X13),X14),c_COMBK(tc_fun(X16,tc_HOL_Obool),X12,X15))))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X13)),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X14)),sK65(X15,X16,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X13),X14),X12,X17))) ),
inference(resolution,[],[f2765,f2719]) ).
fof(f11708,plain,
( spl85_58
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10226,f4426,f3290,f9793,f4223]) ).
fof(f10226,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| X0 = X1 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2346,f9774]) ).
fof(f11707,plain,
( spl85_161
| ~ spl85_24
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10765,f4426,f3290,f3218,f9793]) ).
fof(f10765,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_24
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3466,f9774]) ).
fof(f3466,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))),hAPP(c_member(X1),hAPP(v_F,v_P____))))
| ~ spl85_24 ),
inference(resolution,[],[f3295,f2711]) ).
fof(f11706,plain,
( spl85_177
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10926,f4426,f3290,f9793,f11704]) ).
fof(f11704,plain,
( spl85_177
<=> ! [X2,X0,X3] :
( hBOOL(hAPP(X0,X3))
| X2 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_177])]) ).
fof(f10926,plain,
( ! [X2,X3,X0] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X0,X3))
| X2 = X3 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2405,f9774]) ).
fof(f2405,plain,
! [X2,X3,X0,X1] :
( X2 = X3
| ~ hBOOL(hAPP(c_Set_Oinsert(X1,X2,X0),X3))
| hBOOL(hAPP(X0,X3)) ),
inference(cnf_transformation,[],[f1689]) ).
fof(f11696,plain,
( ~ spl85_161
| spl85_168
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11695,f4426,f3290,f11279,f9793]) ).
fof(f11695,plain,
( ! [X72,X73,X74] :
( c_Predicate_ORangeP(X73,X74,hAPP(v_F,v_Q____),X72)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11694,f9774]) ).
fof(f11694,plain,
( ! [X72,X73,X68,X69,X67,X74] :
( ~ hBOOL(hAPP(c_Product__Type_OSigma(X67,X68,X69,hAPP(v_F,v_Q____)),X72))
| c_Predicate_ORangeP(X73,X74,hAPP(v_F,v_Q____),X72) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10666,f9774]) ).
fof(f10666,plain,
( ! [X72,X70,X73,X68,X69,X67,X74] :
( c_Predicate_ORangeP(X73,X74,hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X67,X68),tc_HOL_Obool)),c_Product__Type_OSigma(X67,X68,X69,X70)),X72)
| ~ hBOOL(hAPP(c_Product__Type_OSigma(X67,X68,X69,hAPP(v_F,v_Q____)),X72)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4356,f9774]) ).
fof(f4356,plain,
! [X72,X70,X73,X71,X68,X69,X67,X74] :
( c_Predicate_ORangeP(X73,X74,hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X67,X68),tc_HOL_Obool)),c_Product__Type_OSigma(X67,X68,X69,X70)),X72)
| ~ hBOOL(hAPP(c_Product__Type_OSigma(X67,X68,X69,hAPP(hAPP(c_COMBS(X67,tc_fun(X68,tc_HOL_Obool),tc_fun(X68,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X68,tc_HOL_Obool),tc_fun(tc_fun(X68,tc_HOL_Obool),tc_fun(X68,tc_HOL_Obool)),X67,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X68,tc_HOL_Obool))),X70)),X71)),X72)) ),
inference(superposition,[],[f2173,f2353]) ).
fof(f2353,plain,
! [X2,X3,X0,X1,X4] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X1),tc_HOL_Obool)),c_Product__Type_OSigma(X4,X1,X0,X2)),c_Product__Type_OSigma(X4,X1,X0,X3)) = c_Product__Type_OSigma(X4,X1,X0,hAPP(hAPP(c_COMBS(X4,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X2)),X3)),
inference(cnf_transformation,[],[f1658]) ).
fof(f1658,plain,
! [X0,X1,X2,X3,X4] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X4,X1),tc_HOL_Obool)),c_Product__Type_OSigma(X4,X1,X0,X2)),c_Product__Type_OSigma(X4,X1,X0,X3)) = c_Product__Type_OSigma(X4,X1,X0,hAPP(hAPP(c_COMBS(X4,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X4,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool))),X2)),X3)),
inference(rectify,[],[f937]) ).
fof(f937,plain,
! [X0,X3,X2,X4,X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X1,X3),tc_HOL_Obool)),c_Product__Type_OSigma(X1,X3,X0,X2)),c_Product__Type_OSigma(X1,X3,X0,X4)) = c_Product__Type_OSigma(X1,X3,X0,hAPP(hAPP(c_COMBS(X1,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X1,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool))),X2)),X4)),
inference(rectify,[],[f314]) ).
fof(f314,axiom,
! [X69,X8,X10,X16,X9] : c_Product__Type_OSigma(X8,X16,X69,hAPP(hAPP(c_COMBS(X8,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X8,c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool))),X10)),X9)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X8,X16),tc_HOL_Obool)),c_Product__Type_OSigma(X8,X16,X69,X10)),c_Product__Type_OSigma(X8,X16,X69,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Int__distrib2) ).
fof(f11693,plain,
( spl85_176
| spl85_129
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10986,f4426,f3290,f8152,f11690]) ).
fof(f11690,plain,
( spl85_176
<=> class_Lattices_Odistrib__lattice(hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_176])]) ).
fof(f8152,plain,
( spl85_129
<=> ! [X1] : ~ class_Lattices_Odistrib__lattice(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_129])]) ).
fof(f10986,plain,
( ! [X1] :
( ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2561,f9774]) ).
fof(f2561,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(cnf_transformation,[],[f1438]) ).
fof(f1438,plain,
! [X0,X1] :
( class_Lattices_Odistrib__lattice(tc_fun(X0,X1))
| ~ class_Lattices_Odistrib__lattice(X1) ),
inference(ennf_transformation,[],[f694]) ).
fof(f694,plain,
! [X1,X0] :
( class_Lattices_Odistrib__lattice(X1)
=> class_Lattices_Odistrib__lattice(tc_fun(X0,X1)) ),
inference(rectify,[],[f500]) ).
fof(f500,axiom,
! [X73,X74] :
( class_Lattices_Odistrib__lattice(X74)
=> class_Lattices_Odistrib__lattice(tc_fun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).
fof(f11672,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11671,f4426,f3290,f9793]) ).
fof(f11671,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11670]) ).
fof(f11670,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11669,f9774]) ).
fof(f11669,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10219,f9774]) ).
fof(f10219,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(v_F,v_Q____)),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2890,f9774]) ).
fof(f2890,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK78(X0,X1,X2)),X0)),X2)) ),
inference(cnf_transformation,[],[f2115]) ).
fof(f2115,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X0)),X2)) )
| ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2))) )
& ( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
| ( ~ hBOOL(hAPP(hAPP(c_member(X1),sK78(X0,X1,X2)),c_Wellfounded_Oacc(X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK78(X0,X1,X2)),X0)),X2)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK78])],[f2113,f2114]) ).
fof(f2114,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X0)),X2)) )
=> ( ~ hBOOL(hAPP(hAPP(c_member(X1),sK78(X0,X1,X2)),c_Wellfounded_Oacc(X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),sK78(X0,X1,X2)),X0)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f2113,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X0)),X2)) )
| ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2))) )
& ( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
| ? [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X4),c_Wellfounded_Oacc(X1,X2)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X4),X0)),X2)) ) ) ),
inference(rectify,[],[f2112]) ).
fof(f2112,plain,
! [X2,X1,X0] :
( ( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X0)) )
| ~ hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X0))) )
& ( hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X0)))
| ? [X3] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X0)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X0)) ) ) ),
inference(nnf_transformation,[],[f1053]) ).
fof(f1053,plain,
! [X2,X1,X0] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X0)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X0)) )
<=> hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X0))) ),
inference(ennf_transformation,[],[f945]) ).
fof(f945,plain,
! [X0,X1,X2] :
( ! [X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X3),X2)),X0))
=> hBOOL(hAPP(hAPP(c_member(X1),X3),c_Wellfounded_Oacc(X1,X0))) )
<=> hBOOL(hAPP(hAPP(c_member(X1),X2),c_Wellfounded_Oacc(X1,X0))) ),
inference(rectify,[],[f51]) ).
fof(f51,axiom,
! [X19,X8,X24] :
( hBOOL(hAPP(hAPP(c_member(X8),X24),c_Wellfounded_Oacc(X8,X19)))
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X2),X24)),X19))
=> hBOOL(hAPP(hAPP(c_member(X8),X2),c_Wellfounded_Oacc(X8,X19))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_Osimps) ).
fof(f11664,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11663,f4426,f3290,f9793]) ).
fof(f11663,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10111,f9774]) ).
fof(f10111,plain,
( ! [X2,X1] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Omktop(X2,X1)))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3020,f9774]) ).
fof(f3020,plain,
! [X2,X3,X1] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Omktop(X2,X1))),
inference(equality_resolution,[],[f2468]) ).
fof(f2468,plain,
! [X2,X3,X0,X1] :
( X0 != X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Omktop(X2,X0))) ),
inference(cnf_transformation,[],[f1743]) ).
fof(f11654,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10888,f4426,f3290,f9793]) ).
fof(f10888,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3081,f9774]) ).
fof(f11651,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11650,f4426,f3290,f9793]) ).
fof(f11650,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11649]) ).
fof(f11649,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10398,f9774]) ).
fof(f10398,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X3)),X0),c_FuncSet_OPi(X2,X3,X1,X4))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2649,f9774]) ).
fof(f11645,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11644,f4426,f3290,f9793]) ).
fof(f11644,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11643]) ).
fof(f11643,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11642,f9774]) ).
fof(f11642,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),hAPP(v_F,v_Q____)),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X14)),sK65(X15,X16,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X13),X14),X12,X17)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10242,f9774]) ).
fof(f10242,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X16)),X17),c_FuncSet_OPi(X12,X16,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X13),X14),c_COMBK(tc_fun(X16,tc_HOL_Obool),X12,X15))))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),hAPP(v_F,v_Q____)),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X14)),sK65(X15,X16,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X13),X14),X12,X17))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3658,f9774]) ).
fof(f3658,plain,
! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X16)),X17),c_FuncSet_OPi(X12,X16,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X13),X14),c_COMBK(tc_fun(X16,tc_HOL_Obool),X12,X15))))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X13)),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X14)),sK65(X15,X16,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X13),X14),X12,X17))) ),
inference(resolution,[],[f2854,f2719]) ).
fof(f11621,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11620,f4426,f3290,f9793]) ).
fof(f11620,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11619]) ).
fof(f11619,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11618,f9774]) ).
fof(f11618,plain,
( ! [X14,X17,X15,X12] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(X12),sK72(X12,X14,X17,X15)),X15)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11617]) ).
fof(f11617,plain,
( ! [X14,X17,X15,X12] :
( hBOOL(hAPP(hAPP(c_member(X12),sK72(X12,X14,X17,X15)),X15))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10628,f9774]) ).
fof(f10628,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16))))
| hBOOL(hAPP(hAPP(c_member(X12),sK72(X12,X14,X17,X15)),X15)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3599,f9774]) ).
fof(f3599,plain,
! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(X12),sK72(X12,X14,X17,X15)),X15))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16))))
| hBOOL(hAPP(hAPP(c_member(X12),sK65(X16,X13,X15,X12,X17)),X15)) ),
inference(resolution,[],[f2750,f2719]) ).
fof(f11599,plain,
( ~ spl85_161
| spl85_101
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11598,f4426,f3290,f6990,f9793]) ).
fof(f6990,plain,
( spl85_101
<=> ! [X0,X1] : ~ c_Wellfounded_Oacyclic(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_101])]) ).
fof(f11598,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X1,X0)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10210,f9774]) ).
fof(f10210,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(v_F,v_Q____)),c_Transitive__Closure_Otrancl(X1,X0))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2723,f9774]) ).
fof(f2723,plain,
! [X2,X0,X1] :
( ~ c_Wellfounded_Oacyclic(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X2)),c_Transitive__Closure_Otrancl(X1,X0))) ),
inference(cnf_transformation,[],[f1979]) ).
fof(f11593,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10053,f4426,f3290,f9793]) ).
fof(f10053,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3075,f9774]) ).
fof(f3075,plain,
! [X1] : hBOOL(hAPP(hAPP(c_fequal,X1),X1)),
inference(equality_resolution,[],[f2886]) ).
fof(f2886,plain,
! [X0,X1] :
( X0 != X1
| hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ),
inference(cnf_transformation,[],[f2108]) ).
fof(f2108,plain,
! [X0,X1] :
( X0 != X1
| hBOOL(hAPP(hAPP(c_fequal,X1),X0)) ),
inference(rectify,[],[f971]) ).
fof(f971,plain,
! [X1,X0] :
( X0 != X1
| hBOOL(hAPP(hAPP(c_fequal,X0),X1)) ),
inference(rectify,[],[f530]) ).
fof(f530,axiom,
! [X14,X13] :
( hBOOL(hAPP(hAPP(c_fequal,X14),X13))
| X13 != X14 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
fof(f11586,plain,
( ~ spl85_161
| spl85_168
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11585,f4426,f3290,f11279,f9793]) ).
fof(f11585,plain,
( ! [X38,X39,X37] :
( c_Predicate_ORangeP(X38,X39,hAPP(v_F,v_Q____),X37)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10739,f9774]) ).
fof(f10739,plain,
( ! [X38,X39,X37,X34,X35,X32,X33] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Predicate_ORangeP(X38,X39,hAPP(c_COMBS(X32,X33,X34),X35),X37) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4370,f9774]) ).
fof(f4370,plain,
! [X38,X39,X36,X37,X34,X35,X32,X33] :
( ~ hBOOL(hAPP(hAPP(X35,X37),hAPP(X36,X37)))
| c_Predicate_ORangeP(X38,X39,hAPP(c_COMBS(X32,X33,X34),X35),X37) ),
inference(superposition,[],[f2173,f2728]) ).
fof(f11582,plain,
( spl85_161
| spl85_58
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11581,f4426,f3290,f4223,f9793]) ).
fof(f11581,plain,
( ! [X2,X3] :
( X2 = X3
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10127,f9774]) ).
fof(f10127,plain,
( ! [X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),sK84(X2,X3)),hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____))))
| X2 = X3 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3463,f9774]) ).
fof(f3463,plain,
! [X2,X3,X4] :
( X2 = X3
| hBOOL(hAPP(hAPP(c_member(X4),sK84(X2,X3)),hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)))) ),
inference(resolution,[],[f2949,f2711]) ).
fof(f11578,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_37
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10831,f4426,f3332,f3290,f9793]) ).
fof(f10831,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_37
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3357,f9774]) ).
fof(f11577,plain,
( spl85_61
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10855,f4426,f3290,f9793,f4384]) ).
fof(f10855,plain,
( ! [X16] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(X16) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4084,f9774]) ).
fof(f4084,plain,
! [X21,X18,X19,X16,X17,X22,X20] :
( ~ hBOOL(X16)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X17,X18)),X19),c_FuncSet_OPi(X17,X18,X20,c_COMBK(tc_fun(X18,tc_HOL_Obool),X17,c_COMBK(X21,X22,X16))))) ),
inference(resolution,[],[f3315,f2718]) ).
fof(f11569,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11568,f4426,f3290,f9793]) ).
fof(f11568,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11567]) ).
fof(f11567,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11566,f9774]) ).
fof(f11566,plain,
( ! [X3,X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Set_Oinsert(X0,hAPP(v_F,v_Q____),X3)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10195,f9774]) ).
fof(f10195,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),c_Set_Oinsert(X0,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Set_Oinsert(X0,hAPP(v_F,v_Q____),X3)),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3957,f9774]) ).
fof(f3957,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Set_Oinsert(X0,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2),X3)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),c_Set_Oinsert(X0,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2),X3))) ),
inference(resolution,[],[f3564,f2792]) ).
fof(f11565,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11564,f4426,f3290,f9793]) ).
fof(f11564,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f11563]) ).
fof(f11563,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____)
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11562,f9774]) ).
fof(f11562,plain,
( ! [X3,X1] :
( hAPP(v_F,v_Q____) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3,X1),tc_HOL_Obool))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10623,f9774]) ).
fof(f10623,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3,X1),tc_HOL_Obool)) != c_FuncSet_OPi(X3,X1,X2,X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2637,f9774]) ).
fof(f2637,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3,X1),tc_HOL_Obool)) != c_FuncSet_OPi(X3,X1,X2,X0)
| hBOOL(hAPP(hAPP(c_member(X3),sK53(X0,X1,X2,X3)),X2)) ),
inference(cnf_transformation,[],[f1892]) ).
fof(f1892,plain,
! [X0,X1,X2,X3] :
( ( ( hBOOL(hAPP(hAPP(c_member(X3),sK53(X0,X1,X2,X3)),X2))
& hAPP(X0,sK53(X0,X1,X2,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) )
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3,X1),tc_HOL_Obool)) != c_FuncSet_OPi(X3,X1,X2,X0) )
& ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3,X1),tc_HOL_Obool)) = c_FuncSet_OPi(X3,X1,X2,X0)
| ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X2))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(X0,X5) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK53])],[f1890,f1891]) ).
fof(f1891,plain,
! [X0,X1,X2,X3] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_member(X3),X4),X2))
& hAPP(X0,X4) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) )
=> ( hBOOL(hAPP(hAPP(c_member(X3),sK53(X0,X1,X2,X3)),X2))
& hAPP(X0,sK53(X0,X1,X2,X3)) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) ) ),
introduced(choice_axiom,[]) ).
fof(f1890,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_member(X3),X4),X2))
& hAPP(X0,X4) = c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) )
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3,X1),tc_HOL_Obool)) != c_FuncSet_OPi(X3,X1,X2,X0) )
& ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3,X1),tc_HOL_Obool)) = c_FuncSet_OPi(X3,X1,X2,X0)
| ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X3),X5),X2))
| c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)) != hAPP(X0,X5) ) ) ),
inference(rectify,[],[f1889]) ).
fof(f1889,plain,
! [X0,X3,X1,X2] :
( ( ? [X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
& c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = hAPP(X0,X4) )
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,X3),tc_HOL_Obool)) != c_FuncSet_OPi(X2,X3,X1,X0) )
& ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,X3),tc_HOL_Obool)) = c_FuncSet_OPi(X2,X3,X1,X0)
| ! [X4] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
| c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) != hAPP(X0,X4) ) ) ),
inference(nnf_transformation,[],[f884]) ).
fof(f884,plain,
! [X0,X3,X1,X2] :
( ? [X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X4),X1))
& c_Orderings_Obot__class_Obot(tc_fun(X3,tc_HOL_Obool)) = hAPP(X0,X4) )
<=> c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X2,X3),tc_HOL_Obool)) = c_FuncSet_OPi(X2,X3,X1,X0) ),
inference(rectify,[],[f451]) ).
fof(f451,axiom,
! [X9,X10,X8,X16] :
( ? [X2] :
( hBOOL(hAPP(hAPP(c_member(X8),X2),X10))
& hAPP(X9,X2) = c_Orderings_Obot__class_Obot(tc_fun(X16,tc_HOL_Obool)) )
<=> c_FuncSet_OPi(X8,X16,X10,X9) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X8,X16),tc_HOL_Obool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pi__eq__empty) ).
fof(f11561,plain,
( spl85_161
| spl85_61
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10807,f4426,f3290,f4384,f9793]) ).
fof(f10807,plain,
( ! [X10] :
( ~ hBOOL(X10)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3875,f9774]) ).
fof(f3875,plain,
! [X10,X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(X11),c_COMBI(X12)),hAPP(c_member(X13),X10)))
| ~ hBOOL(X10) ),
inference(resolution,[],[f3359,f2711]) ).
fof(f11556,plain,
( spl85_161
| spl85_58
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11555,f4426,f3290,f4223,f9793]) ).
fof(f11555,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10126,f9774]) ).
fof(f10126,plain,
( ! [X0,X1] :
( hBOOL(hAPP(sK84(X0,X1),hAPP(v_F,v_Q____)))
| X0 = X1 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3462,f9774]) ).
fof(f3462,plain,
! [X0,X1] :
( hBOOL(hAPP(sK84(X0,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)))
| X0 = X1 ),
inference(resolution,[],[f2949,f2710]) ).
fof(f11554,plain,
( spl85_92
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10392,f4426,f3290,f9793,f6565]) ).
fof(f10392,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Relation_Osingle__valued(X0,X1,X2) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2736,f9774]) ).
fof(f2736,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),sK69(X0,X1,X2)),sK68(X0,X1,X2))),X2))
| c_Relation_Osingle__valued(X0,X1,X2) ),
inference(cnf_transformation,[],[f1993]) ).
fof(f11553,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11552,f4426,f3290,f9793]) ).
fof(f11552,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11551]) ).
fof(f11551,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11550,f9774]) ).
fof(f11550,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1),X0)),X5)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11549]) ).
fof(f11549,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1),X0)),X5))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11548,f9774]) ).
fof(f11548,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),X5))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1),X0)),X5)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10212,f9774]) ).
fof(f10212,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1),X0)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),X5)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3622,f9774]) ).
fof(f3622,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1),X0)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(X1,X0)),X0)),X5)) ),
inference(superposition,[],[f2792,f2728]) ).
fof(f11540,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_38
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10833,f4426,f3341,f3290,f9793]) ).
fof(f10833,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_38
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3358,f9774]) ).
fof(f11537,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11536,f4426,f3290,f9793]) ).
fof(f11536,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11535]) ).
fof(f11535,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10743,f9774]) ).
fof(f10743,plain,
( ! [X18,X19,X16,X17,X20] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X16,X18)),X20),c_FuncSet_OPi(X16,X18,X19,c_COMBK(tc_fun(X18,tc_HOL_Obool),X16,X17)))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3497,f9774]) ).
fof(f3497,plain,
! [X21,X18,X19,X16,X17,X20] :
( hBOOL(hAPP(hAPP(c_member(X21),X19),hAPP(c_member(X16),sK65(X17,X18,X19,X16,X20))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X16,X18)),X20),c_FuncSet_OPi(X16,X18,X19,c_COMBK(tc_fun(X18,tc_HOL_Obool),X16,X17)))) ),
inference(resolution,[],[f2719,f2711]) ).
fof(f11531,plain,
( ~ spl85_161
| spl85_170
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10942,f4426,f3290,f11305,f9793]) ).
fof(f10942,plain,
( ! [X42,X43] :
( hBOOL(hAPP(X43,X42))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4255,f9774]) ).
fof(f11530,plain,
( spl85_161
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11529,f4426,f3290,f3178,f9793]) ).
fof(f11529,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f11528]) ).
fof(f11528,plain,
( hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____)
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11527,f9774]) ).
fof(f11527,plain,
( ! [X18] :
( hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(v_F,sK72(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18,v_F,c_Arrow__Order__Mirabelle_OProf)) )
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9996,f9774]) ).
fof(f9996,plain,
( ! [X18] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| hAPP(v_F,v_Q____) != hAPP(v_F,sK72(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18,v_F,c_Arrow__Order__Mirabelle_OProf)) )
| ~ spl85_16
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3614,f9774]) ).
fof(f3614,plain,
( ! [X18] :
( hAPP(X18,sK72(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18,v_F,c_Arrow__Order__Mirabelle_OProf)) != hAPP(v_F,sK72(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18,v_F,c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
| ~ spl85_16 ),
inference(resolution,[],[f2752,f3180]) ).
fof(f11517,plain,
( spl85_58
| spl85_58
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11516,f4426,f3290,f9793,f4223,f4223]) ).
fof(f11516,plain,
( ! [X10,X8,X9,X7] :
( hBOOL(hAPP(v_F,v_Q____))
| X7 = X8
| X9 = X10 )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10131,f9774]) ).
fof(f10131,plain,
( ! [X10,X8,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK84(X9,X10)),X7),X8)))
| X9 = X10
| X7 = X8 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3567,f9774]) ).
fof(f3567,plain,
! [X10,X8,X9,X7] :
( X9 = X10
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X8)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK84(X9,X10)),X7),X8)))
| X7 = X8 ),
inference(resolution,[],[f3090,f2948]) ).
fof(f3090,plain,
! [X3,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X3),X4)))
| X3 = X4 ),
inference(duplicate_literal_removal,[],[f3058]) ).
fof(f3058,plain,
! [X3,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X3),X4)))
| X3 = X4
| X3 = X4
| X3 = X4 ),
inference(equality_resolution,[],[f3057]) ).
fof(f3057,plain,
! [X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X4)))
| X3 = X4
| X0 != X3
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X0 = X4 ),
inference(equality_resolution,[],[f2814]) ).
fof(f2814,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2)))
| X2 = X3
| X2 != X4
| X0 != X3
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X0 = X2 ),
inference(cnf_transformation,[],[f2048]) ).
fof(f11511,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11510,f4426,f3290,f9793]) ).
fof(f11510,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11509]) ).
fof(f11509,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11508,f9774]) ).
fof(f11508,plain,
( ! [X31,X28,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11507]) ).
fof(f11507,plain,
( ! [X31,X28,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10715,f9774]) ).
fof(f10715,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X27,X28)),X29),c_FuncSet_OPi(X27,X28,X30,X31)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3602,f9774]) ).
fof(f3602,plain,
! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X27,X28)),X29),c_FuncSet_OPi(X27,X28,X30,X31)))
| hBOOL(hAPP(hAPP(c_member(X27),sK72(X27,X29,sK57(X32,c_FuncSet_OPi(X27,X28,X30,X31),tc_fun(X27,X28),X33,X34),X30)),X30)) ),
inference(resolution,[],[f2750,f2649]) ).
fof(f11499,plain,
( spl85_161
| spl85_175
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11495,f4426,f3290,f11497,f9793]) ).
fof(f11497,plain,
( spl85_175
<=> ! [X2,X0,X3] :
( ~ hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(X3,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_175])]) ).
fof(f11495,plain,
( ! [X2,X3,X0] :
( ~ hBOOL(hAPP(X2,X0))
| hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(X3,X0)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10512,f9774]) ).
fof(f10512,plain,
( ! [X2,X3,X0] :
( ~ hBOOL(hAPP(X2,X0))
| hBOOL(hAPP(hAPP(v_F,v_Q____),X0))
| ~ hBOOL(hAPP(X3,X0)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2762,f9774]) ).
fof(f2762,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X0))
| ~ hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(X3,X0)) ),
inference(cnf_transformation,[],[f2015]) ).
fof(f2015,plain,
! [X0,X1,X2,X3] :
( ~ hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(X3,X0))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X3),X0)) ),
inference(rectify,[],[f1286]) ).
fof(f1286,plain,
! [X3,X1,X0,X2] :
( ~ hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(X2,X3))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X2),X3)) ),
inference(flattening,[],[f1285]) ).
fof(f1285,plain,
! [X0,X3,X2,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X2),X3))
| ~ hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(X0,X3)) ),
inference(ennf_transformation,[],[f549]) ).
fof(f549,plain,
! [X0,X3,X2,X1] :
( hBOOL(hAPP(X0,X3))
=> ( hBOOL(hAPP(X2,X3))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X2),X3)) ) ),
inference(rectify,[],[f91]) ).
fof(f91,axiom,
! [X10,X8,X9,X14] :
( hBOOL(hAPP(X10,X14))
=> ( hBOOL(hAPP(X9,X14))
=> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X10),X9),X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1I) ).
fof(f11493,plain,
( spl85_161
| spl85_84
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11492,f4426,f3290,f6422,f9793]) ).
fof(f11492,plain,
( ! [X6,X5] :
( c_Arrow__Order__Mirabelle_Odictator(X6,X5)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11491]) ).
fof(f11491,plain,
( ! [X6,X5] :
( c_Arrow__Order__Mirabelle_Odictator(X6,X5)
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10820,f9774]) ).
fof(f10820,plain,
( ! [X6,X5] :
( c_Arrow__Order__Mirabelle_Odictator(X6,X5)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK57(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3868,f9774]) ).
fof(f3868,plain,
! [X6,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X5,X6)),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK57(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X6,X5) ),
inference(resolution,[],[f2451,f2649]) ).
fof(f11490,plain,
( spl85_168
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11489,f4426,f3290,f9793,f11279]) ).
fof(f11489,plain,
( ! [X2,X3,X0] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Predicate_ORangeP(X2,X0,hAPP(v_F,v_Q____),X3) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10474,f9774]) ).
fof(f10474,plain,
( ! [X2,X3,X0,X1] :
( c_Predicate_ORangeP(X2,X0,hAPP(v_F,v_Q____),X3)
| ~ hBOOL(hAPP(hAPP(c_member(X0),X3),c_Relation_ORange(X2,X0,X1))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2287,f9774]) ).
fof(f2287,plain,
! [X2,X3,X0,X1] :
( c_Predicate_ORangeP(X2,X0,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_fun(X0,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X0,tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_fun(X0,tc_HOL_Obool)),X2,c_COMBC(X0,tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X0,tc_prod(X2,X0)),tc_fun(X0,tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X0),tc_fun(tc_fun(tc_prod(X2,X0),tc_HOL_Obool),tc_HOL_Obool),X0,c_member(tc_prod(X2,X0)))),c_Product__Type_OPair(X2,X0)))),X1),X3)
| ~ hBOOL(hAPP(hAPP(c_member(X0),X3),c_Relation_ORange(X2,X0,X1))) ),
inference(cnf_transformation,[],[f1596]) ).
fof(f11488,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11487,f4426,f3290,f9793]) ).
fof(f11487,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11486]) ).
fof(f11486,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11485,f9774]) ).
fof(f11485,plain,
( ! [X10,X11,X8,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),sK57(X8,X9,X7,X10,X11)),X9))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11484,f9774]) ).
fof(f11484,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X10)),X6),c_FuncSet_OPi(X7,X10,X9,X11)))
| hBOOL(hAPP(hAPP(c_member(X7),sK57(X8,X9,X7,X10,X11)),X9)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f11483]) ).
fof(f11483,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X10)),X6),c_FuncSet_OPi(X7,X10,X9,X11)))
| hBOOL(hAPP(hAPP(c_member(X7),sK57(X8,X9,X7,X10,X11)),X9))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10001,f9774]) ).
fof(f10001,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hAPP(v_F,v_Q____) != hAPP(X6,sK72(X7,X8,X6,X9))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X10)),X6),c_FuncSet_OPi(X7,X10,X9,X11)))
| hBOOL(hAPP(hAPP(c_member(X7),sK57(X8,X9,X7,X10,X11)),X9)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3605,f9774]) ).
fof(f3605,plain,
! [X10,X11,X8,X6,X9,X7] :
( hAPP(X6,sK72(X7,X8,X6,X9)) != hAPP(X8,sK72(X7,X8,X6,X9))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X10)),X6),c_FuncSet_OPi(X7,X10,X9,X11)))
| hBOOL(hAPP(hAPP(c_member(X7),sK57(X8,X9,X7,X10,X11)),X9)) ),
inference(resolution,[],[f2751,f2649]) ).
fof(f11482,plain,
( spl85_174
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11478,f4426,f3290,f9793,f11480]) ).
fof(f11480,plain,
( spl85_174
<=> ! [X2] : ~ c_Wellfounded_Oacyclic(X2,hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_174])]) ).
fof(f11478,plain,
( ! [X2] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ c_Wellfounded_Oacyclic(X2,hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11477,f9774]) ).
fof(f11477,plain,
( ! [X2,X3] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(v_F,v_Q____)),c_Transitive__Closure_Ortrancl(X2,X3)))
| ~ c_Wellfounded_Oacyclic(X2,hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10425,f9774]) ).
fof(f10425,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Oacyclic(X2,c_Set_Oinsert(tc_prod(X2,X2),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X0),X1),X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(v_F,v_Q____)),c_Transitive__Closure_Ortrancl(X2,X3))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2414,f9774]) ).
fof(f2414,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X0)),c_Transitive__Closure_Ortrancl(X2,X3)))
| ~ c_Wellfounded_Oacyclic(X2,c_Set_Oinsert(tc_prod(X2,X2),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X0),X1),X3)) ),
inference(cnf_transformation,[],[f1699]) ).
fof(f1699,plain,
! [X0,X1,X2,X3] :
( ( ( c_Wellfounded_Oacyclic(X2,X3)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X0)),c_Transitive__Closure_Ortrancl(X2,X3))) )
| ~ c_Wellfounded_Oacyclic(X2,c_Set_Oinsert(tc_prod(X2,X2),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X0),X1),X3)) )
& ( c_Wellfounded_Oacyclic(X2,c_Set_Oinsert(tc_prod(X2,X2),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X0),X1),X3))
| ~ c_Wellfounded_Oacyclic(X2,X3)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X0)),c_Transitive__Closure_Ortrancl(X2,X3))) ) ),
inference(rectify,[],[f1698]) ).
fof(f1698,plain,
! [X2,X0,X1,X3] :
( ( ( c_Wellfounded_Oacyclic(X1,X3)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X0),X2)),c_Transitive__Closure_Ortrancl(X1,X3))) )
| ~ c_Wellfounded_Oacyclic(X1,c_Set_Oinsert(tc_prod(X1,X1),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X0),X3)) )
& ( c_Wellfounded_Oacyclic(X1,c_Set_Oinsert(tc_prod(X1,X1),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X0),X3))
| ~ c_Wellfounded_Oacyclic(X1,X3)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X0),X2)),c_Transitive__Closure_Ortrancl(X1,X3))) ) ),
inference(flattening,[],[f1697]) ).
fof(f1697,plain,
! [X2,X0,X1,X3] :
( ( ( c_Wellfounded_Oacyclic(X1,X3)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X0),X2)),c_Transitive__Closure_Ortrancl(X1,X3))) )
| ~ c_Wellfounded_Oacyclic(X1,c_Set_Oinsert(tc_prod(X1,X1),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X0),X3)) )
& ( c_Wellfounded_Oacyclic(X1,c_Set_Oinsert(tc_prod(X1,X1),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X0),X3))
| ~ c_Wellfounded_Oacyclic(X1,X3)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X0),X2)),c_Transitive__Closure_Ortrancl(X1,X3))) ) ),
inference(nnf_transformation,[],[f661]) ).
fof(f661,plain,
! [X2,X0,X1,X3] :
( ( c_Wellfounded_Oacyclic(X1,X3)
& ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X0),X2)),c_Transitive__Closure_Ortrancl(X1,X3))) )
<=> c_Wellfounded_Oacyclic(X1,c_Set_Oinsert(tc_prod(X1,X1),hAPP(hAPP(c_Product__Type_OPair(X1,X1),X2),X0),X3)) ),
inference(rectify,[],[f286]) ).
fof(f286,axiom,
! [X14,X8,X13,X19] :
( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X14),X13)),c_Transitive__Closure_Ortrancl(X8,X19)))
& c_Wellfounded_Oacyclic(X8,X19) )
<=> c_Wellfounded_Oacyclic(X8,c_Set_Oinsert(tc_prod(X8,X8),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X13),X14),X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__insert) ).
fof(f11476,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11475,f4426,f3290,f9793]) ).
fof(f11475,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11474]) ).
fof(f11474,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11473,f9774]) ).
fof(f11473,plain,
( ! [X21,X19,X22,X23,X20] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11472,f9774]) ).
fof(f11472,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f11471]) ).
fof(f11471,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25)))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10008,f9774]) ).
fof(f10008,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hAPP(v_F,v_Q____) != hAPP(sK83(c_FuncSet_OPi(X19,X20,X22,X23),tc_fun(X19,X20),X24,X25,X26),sK72(X19,X21,sK83(c_FuncSet_OPi(X19,X20,X22,X23),tc_fun(X19,X20),X24,X25,X26),X22))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3615,f9774]) ).
fof(f3615,plain,
! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25)))
| hAPP(X21,sK72(X19,X21,sK83(c_FuncSet_OPi(X19,X20,X22,X23),tc_fun(X19,X20),X24,X25,X26),X22)) != hAPP(sK83(c_FuncSet_OPi(X19,X20,X22,X23),tc_fun(X19,X20),X24,X25,X26),sK72(X19,X21,sK83(c_FuncSet_OPi(X19,X20,X22,X23),tc_fun(X19,X20),X24,X25,X26),X22))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23))) ),
inference(resolution,[],[f2752,f2942]) ).
fof(f11462,plain,
( spl85_161
| spl85_61
| ~ spl85_12
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10752,f4426,f3290,f3155,f4384,f9793]) ).
fof(f3155,plain,
( spl85_12
<=> class_Lattices_Osemilattice__inf(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_12])]) ).
fof(f10752,plain,
( ! [X14] :
( ~ hBOOL(X14)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_12
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3856,f9774]) ).
fof(f3856,plain,
( ! [X14,X15] :
( ~ hBOOL(X14)
| hBOOL(hAPP(hAPP(c_member(X15),X14),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),X14))) )
| ~ spl85_12 ),
inference(superposition,[],[f2711,f3847]) ).
fof(f3847,plain,
( ! [X1] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),X1),X1) = X1
| ~ spl85_12 ),
inference(resolution,[],[f2707,f3157]) ).
fof(f3157,plain,
( class_Lattices_Osemilattice__inf(tc_HOL_Obool)
| ~ spl85_12 ),
inference(avatar_component_clause,[],[f3155]) ).
fof(f2707,plain,
! [X0,X1] :
( ~ class_Lattices_Osemilattice__inf(X0)
| hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X0),X1),X1) = X1 ),
inference(cnf_transformation,[],[f1962]) ).
fof(f1962,plain,
! [X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X0),X1),X1) = X1
| ~ class_Lattices_Osemilattice__inf(X0) ),
inference(rectify,[],[f1383]) ).
fof(f1383,plain,
! [X1,X0] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0
| ~ class_Lattices_Osemilattice__inf(X1) ),
inference(ennf_transformation,[],[f795]) ).
fof(f795,plain,
! [X0,X1] :
( class_Lattices_Osemilattice__inf(X1)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X0) = X0 ),
inference(rectify,[],[f120]) ).
fof(f120,axiom,
! [X49,X8] :
( class_Lattices_Osemilattice__inf(X8)
=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X49),X49) = X49 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__idem) ).
fof(f11458,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11457,f4426,f3290,f9793]) ).
fof(f11457,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11456]) ).
fof(f11456,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10031,f9774]) ).
fof(f10031,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_OPi(X0,X2,X1,X3)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3476,f9774]) ).
fof(f3476,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_OPi(X0,X2,X1,X3)))
| hBOOL(hAPP(X1,sK83(X1,X0,X2,X3,X4))) ),
inference(resolution,[],[f2942,f2710]) ).
fof(f11455,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11454,f4426,f3290,f9793]) ).
fof(f11454,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11453]) ).
fof(f11453,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11452,f9774]) ).
fof(f11452,plain,
( ! [X1] :
( hBOOL(hAPP(hAPP(v_F,v_Q____),X1))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10024,f9774]) ).
fof(f10024,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X2,X0),X1))
| hBOOL(hAPP(hAPP(v_F,v_Q____),X1)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2912,f9774]) ).
fof(f2912,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X2,X0),X1))
| hBOOL(hAPP(hAPP(X0,sK81(X0,X1,X2)),X1)) ),
inference(cnf_transformation,[],[f2131]) ).
fof(f2131,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X2,X0),X3))
| ~ hBOOL(hAPP(hAPP(X0,X3),X1)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2,X0),X1)) )
& ( hBOOL(hAPP(c_Wellfounded_Oaccp(X2,X0),X1))
| ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2,X0),sK81(X0,X1,X2)))
& hBOOL(hAPP(hAPP(X0,sK81(X0,X1,X2)),X1)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK81])],[f2129,f2130]) ).
fof(f2130,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2,X0),X4))
& hBOOL(hAPP(hAPP(X0,X4),X1)) )
=> ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2,X0),sK81(X0,X1,X2)))
& hBOOL(hAPP(hAPP(X0,sK81(X0,X1,X2)),X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f2129,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X2,X0),X3))
| ~ hBOOL(hAPP(hAPP(X0,X3),X1)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2,X0),X1)) )
& ( hBOOL(hAPP(c_Wellfounded_Oaccp(X2,X0),X1))
| ? [X4] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X2,X0),X4))
& hBOOL(hAPP(hAPP(X0,X4),X1)) ) ) ),
inference(rectify,[],[f2128]) ).
fof(f2128,plain,
! [X0,X2,X1] :
( ( ! [X3] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ hBOOL(hAPP(hAPP(X0,X3),X2)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) )
& ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2))
| ? [X3] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
& hBOOL(hAPP(hAPP(X0,X3),X2)) ) ) ),
inference(nnf_transformation,[],[f1259]) ).
fof(f1259,plain,
! [X0,X2,X1] :
( ! [X3] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ hBOOL(hAPP(hAPP(X0,X3),X2)) )
<=> hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) ),
inference(ennf_transformation,[],[f807]) ).
fof(f807,plain,
! [X2,X1,X0] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2))
<=> ! [X3] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3)) ) ),
inference(rectify,[],[f71]) ).
fof(f71,axiom,
! [X19,X8,X24] :
( ! [X2] :
( hBOOL(hAPP(hAPP(X19,X2),X24))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X8,X19),X2)) )
<=> hBOOL(hAPP(c_Wellfounded_Oaccp(X8,X19),X24)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Osimps) ).
fof(f11448,plain,
( ~ spl85_173
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11443,f4426,f3290,f9793,f11445]) ).
fof(f11445,plain,
( spl85_173
<=> hAPP(v_F,v_Q____) = c_Arrow__Order__Mirabelle_OLin ),
introduced(avatar_definition,[new_symbols(naming,[spl85_173])]) ).
fof(f11443,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != c_Arrow__Order__Mirabelle_OLin
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10088,f9774]) ).
fof(f10088,plain,
( ! [X2,X3] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_OLin != c_FuncSet_OPi(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool,X2,X3) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f9517,f9774]) ).
fof(f9517,plain,
( ! [X2,X3] :
( c_Arrow__Order__Mirabelle_OLin != c_FuncSet_OPi(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool,X2,X3)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),sK53(X3,tc_HOL_Obool,X2,tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),X2)) )
| ~ spl85_64 ),
inference(superposition,[],[f2637,f4428]) ).
fof(f11441,plain,
( spl85_172
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10815,f4426,f3290,f9793,f11439]) ).
fof(f11439,plain,
( spl85_172
<=> ! [X2,X0,X1] :
( hAPP(X0,X2) = hAPP(X2,X1)
| ~ c_Arrow__Order__Mirabelle_Odictator(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_172])]) ).
fof(f10815,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hAPP(X0,X2) = hAPP(X2,X1)
| ~ c_Arrow__Order__Mirabelle_Odictator(X0,X1) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2943,f9774]) ).
fof(f2943,plain,
! [X2,X0,X1] :
( ~ c_Arrow__Order__Mirabelle_Odictator(X0,X1)
| hAPP(X0,X2) = hAPP(X2,X1)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf)) ),
inference(cnf_transformation,[],[f2161]) ).
fof(f2161,plain,
! [X0,X1] :
( ! [X2] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf))
| hAPP(X0,X2) = hAPP(X2,X1) )
| ~ c_Arrow__Order__Mirabelle_Odictator(X0,X1) ),
inference(rectify,[],[f1318]) ).
fof(f1318,plain,
! [X1,X0] :
( ! [X2] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf))
| hAPP(X1,X2) = hAPP(X2,X0) )
| ~ c_Arrow__Order__Mirabelle_Odictator(X1,X0) ),
inference(ennf_transformation,[],[f1039]) ).
fof(f1039,plain,
! [X0,X1] :
( c_Arrow__Order__Mirabelle_Odictator(X1,X0)
=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf))
=> hAPP(X1,X2) = hAPP(X2,X0) ) ),
inference(unused_predicate_definition_removal,[],[f756]) ).
fof(f756,plain,
! [X0,X1] :
( ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf))
=> hAPP(X1,X2) = hAPP(X2,X0) )
<=> c_Arrow__Order__Mirabelle_Odictator(X1,X0) ),
inference(rectify,[],[f42]) ).
fof(f42,axiom,
! [X29,X32] :
( c_Arrow__Order__Mirabelle_Odictator(X32,X29)
<=> ! [X2] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X2),c_Arrow__Order__Mirabelle_OProf))
=> hAPP(X32,X2) = hAPP(X2,X29) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictator__def) ).
fof(f11437,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_37
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10770,f4426,f3332,f3290,f9793]) ).
fof(f10770,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_37
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3962,f9774]) ).
fof(f3962,plain,
( ! [X2,X3,X1] : hBOOL(hAPP(hAPP(c_member(X1),hAPP(c_member(X2),v_P____)),hAPP(c_member(X3),c_Arrow__Order__Mirabelle_OProf)))
| ~ spl85_37 ),
inference(resolution,[],[f3585,f2711]) ).
fof(f11426,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10740,f4426,f3290,f9793]) ).
fof(f10740,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4102,f9774]) ).
fof(f4102,plain,
! [X2,X3,X0,X1,X4,X5] : hBOOL(hAPP(hAPP(c_member(X0),X1),hAPP(hAPP(c_COMBS(X2,X3,X4),c_member(X5)),c_fequal))),
inference(resolution,[],[f3415,f2711]) ).
fof(f11425,plain,
( spl85_161
| spl85_84
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11424,f4426,f3290,f6422,f9793]) ).
fof(f11424,plain,
( ! [X3,X4] :
( c_Arrow__Order__Mirabelle_Odictator(X4,X3)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11423]) ).
fof(f11423,plain,
( ! [X3,X4] :
( c_Arrow__Order__Mirabelle_Odictator(X4,X3)
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10783,f9774]) ).
fof(f10783,plain,
( ! [X3,X4] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK83(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin),X4)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X4,X3) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3947,f9774]) ).
fof(f3947,plain,
! [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X3,X4)),sK21(X3,X4))),hAPP(sK20(X3,X4),X3)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK83(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin),X4)),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X4,X3) ),
inference(resolution,[],[f2452,f2942]) ).
fof(f11422,plain,
( spl85_171
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11418,f4426,f3290,f9793,f11420]) ).
fof(f11420,plain,
( spl85_171
<=> ! [X2,X3] :
( c_Wellfounded_Oacyclic(X2,hAPP(v_F,v_Q____))
| ~ c_Wellfounded_Oacyclic(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_171])]) ).
fof(f11418,plain,
( ! [X2,X3] :
( hBOOL(hAPP(v_F,v_Q____))
| c_Wellfounded_Oacyclic(X2,hAPP(v_F,v_Q____))
| ~ c_Wellfounded_Oacyclic(X2,X3) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11417,f9774]) ).
fof(f11417,plain,
( ! [X2,X3,X0,X1] :
( c_Wellfounded_Oacyclic(X2,hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X0)),c_Transitive__Closure_Ortrancl(X2,X3)))
| ~ c_Wellfounded_Oacyclic(X2,X3) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10424,f9774]) ).
fof(f10424,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Oacyclic(X2,X3)
| c_Wellfounded_Oacyclic(X2,c_Set_Oinsert(tc_prod(X2,X2),hAPP(v_F,v_Q____),X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X0)),c_Transitive__Closure_Ortrancl(X2,X3))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2413,f9774]) ).
fof(f2413,plain,
! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Oacyclic(X2,X3)
| c_Wellfounded_Oacyclic(X2,c_Set_Oinsert(tc_prod(X2,X2),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X0),X1),X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X0)),c_Transitive__Closure_Ortrancl(X2,X3))) ),
inference(cnf_transformation,[],[f1699]) ).
fof(f11402,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11401,f4426,f3290,f9793]) ).
fof(f11401,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11400]) ).
fof(f11400,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11399,f9774]) ).
fof(f11399,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11398]) ).
fof(f11398,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11397,f9774]) ).
fof(f11397,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9849,f9774]) ).
fof(f9849,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3623,f9774]) ).
fof(f3623,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1))),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1))))
| ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1))) ),
inference(superposition,[],[f2792,f2728]) ).
fof(f11391,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11390,f4426,f3290,f9793]) ).
fof(f11390,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11389]) ).
fof(f11389,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10742,f9774]) ).
fof(f10742,plain,
( ! [X18,X19,X16,X17,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X16,X19)),X17),c_FuncSet_OPi(X16,X19,X18,X20)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3473,f9774]) ).
fof(f3473,plain,
! [X21,X18,X19,X16,X17,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X16,X19)),X17),c_FuncSet_OPi(X16,X19,X18,X20)))
| hBOOL(hAPP(hAPP(c_member(X21),X18),hAPP(c_member(X16),sK57(X17,X18,X16,X19,X20)))) ),
inference(resolution,[],[f2649,f2711]) ).
fof(f11387,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11386,f4426,f3290,f9793]) ).
fof(f11386,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11385]) ).
fof(f11385,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10625,f9774]) ).
fof(f10625,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(c_FuncSet_OPi(X0,X1,X3,c_COMBK(tc_fun(X1,tc_HOL_Obool),X0,X4)),X2)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3491,f9774]) ).
fof(f3491,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(X0),sK65(X4,X1,X3,X0,X2)),X3))
| hBOOL(hAPP(c_FuncSet_OPi(X0,X1,X3,c_COMBK(tc_fun(X1,tc_HOL_Obool),X0,X4)),X2)) ),
inference(resolution,[],[f2719,f2710]) ).
fof(f11366,plain,
( ~ spl85_161
| spl85_170
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10900,f4426,f3290,f11305,f9793]) ).
fof(f10900,plain,
( ! [X26,X27] :
( hBOOL(hAPP(X26,X27))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f9735,f9774]) ).
fof(f11361,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11360,f4426,f3290,f9793]) ).
fof(f11360,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11359]) ).
fof(f11359,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10076,f9774]) ).
fof(f10076,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(c_FuncSet_OPi(X0,X1,X3,X4),X2)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3474,f9774]) ).
fof(f3474,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(X0),sK83(X3,X0,X1,X4,X2)),X3))
| hBOOL(hAPP(c_FuncSet_OPi(X0,X1,X3,X4),X2)) ),
inference(resolution,[],[f2942,f2710]) ).
fof(f11354,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10860,f4426,f3290,f9793]) ).
fof(f10860,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4087,f9774]) ).
fof(f4087,plain,
! [X2,X3,X0,X1] : hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),c_fequal),c_FuncSet_OPi(X0,X1,X2,c_member(X3)))),
inference(resolution,[],[f3324,f2650]) ).
fof(f2650,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(X3),hAPP(X0,sK57(X0,X1,X2,X3,X4))),hAPP(X4,sK57(X0,X1,X2,X3,X4))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X3)),X0),c_FuncSet_OPi(X2,X3,X1,X4))) ),
inference(cnf_transformation,[],[f1909]) ).
fof(f11351,plain,
( spl85_58
| spl85_161
| ~ spl85_25
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11350,f4426,f3290,f3223,f9793,f4223]) ).
fof(f11350,plain,
( ! [X0,X1] :
( hBOOL(hAPP(v_F,v_Q____))
| X0 = X1 )
| ~ spl85_25
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10045,f9774]) ).
fof(f10045,plain,
( ! [X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),hAPP(hAPP(v_F,v_Q____),X1)))
| X0 = X1 )
| ~ spl85_25
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3565,f9774]) ).
fof(f3565,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,hAPP(v_F,v_Q____)),X0),X1))) )
| ~ spl85_25 ),
inference(resolution,[],[f3090,f3225]) ).
fof(f11344,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_57
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10839,f4426,f4220,f3290,f9793]) ).
fof(f4220,plain,
( spl85_57
<=> ! [X56] : ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X56),c_Arrow__Order__Mirabelle_OLin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_57])]) ).
fof(f10839,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_57
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4221,f9774]) ).
fof(f4221,plain,
( ! [X56] : ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X56),c_Arrow__Order__Mirabelle_OLin))
| ~ spl85_57 ),
inference(avatar_component_clause,[],[f4220]) ).
fof(f11337,plain,
( spl85_161
| spl85_61
| ~ spl85_7
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10750,f4426,f3290,f3130,f4384,f9793]) ).
fof(f3130,plain,
( spl85_7
<=> class_Lattices_Osemilattice__inf(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_7])]) ).
fof(f10750,plain,
( ! [X14] :
( ~ hBOOL(X14)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_7
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3852,f9774]) ).
fof(f3852,plain,
( ! [X14,X15] :
( hBOOL(hAPP(hAPP(c_member(X15),X14),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X14)))
| ~ hBOOL(X14) )
| ~ spl85_7 ),
inference(superposition,[],[f2711,f3846]) ).
fof(f3846,plain,
( ! [X0] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X0),X0) = X0
| ~ spl85_7 ),
inference(resolution,[],[f2707,f3132]) ).
fof(f3132,plain,
( class_Lattices_Osemilattice__inf(tc_Nat_Onat)
| ~ spl85_7 ),
inference(avatar_component_clause,[],[f3130]) ).
fof(f11331,plain,
( spl85_161
| ~ spl85_10
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10817,f4426,f3290,f3145,f9793]) ).
fof(f3145,plain,
( spl85_10
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P_H____),c_Arrow__Order__Mirabelle_OProf)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_10])]) ).
fof(f10817,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_10
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3147,f9774]) ).
fof(f3147,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P_H____),c_Arrow__Order__Mirabelle_OProf))
| ~ spl85_10 ),
inference(avatar_component_clause,[],[f3145]) ).
fof(f11323,plain,
( spl85_42
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10808,f4426,f3290,f9793,f3379]) ).
fof(f10808,plain,
( ! [X7] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(X7) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3730,f9774]) ).
fof(f3730,plain,
! [X8,X9,X7] :
( hBOOL(X7)
| hBOOL(hAPP(hAPP(c_member(X8),c_fNot),hAPP(c_member(X9),X7))) ),
inference(resolution,[],[f3383,f2711]) ).
fof(f11318,plain,
( spl85_161
| spl85_167
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10885,f4426,f3290,f11209,f9793]) ).
fof(f10885,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4029,f9774]) ).
fof(f4029,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),c_Set_Oinsert(X3,X4,X0)))
| ~ hBOOL(hAPP(X0,X1)) ),
inference(resolution,[],[f2404,f2711]) ).
fof(f11315,plain,
( spl85_42
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10882,f4426,f3290,f9793,f3379]) ).
fof(f10882,plain,
( ! [X1] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(X1) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3383,f9774]) ).
fof(f11312,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_46
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10778,f4426,f3437,f3290,f9793]) ).
fof(f10778,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_46
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3439,f9774]) ).
fof(f3439,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))))
| ~ spl85_46 ),
inference(avatar_component_clause,[],[f3437]) ).
fof(f11307,plain,
( spl85_170
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11303,f4426,f3290,f9793,f11305]) ).
fof(f11303,plain,
( ! [X2,X7] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X2,X7)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11302]) ).
fof(f11302,plain,
( ! [X2,X7] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X2,X7))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11301,f9774]) ).
fof(f11301,plain,
( ! [X2,X0,X1,X7] :
( hBOOL(hAPP(X2,X7))
| ~ hBOOL(hAPP(X2,sK25(X0,X1,X2)))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11300]) ).
fof(f11300,plain,
( ! [X2,X0,X1,X7] :
( hBOOL(hAPP(X2,X7))
| ~ hBOOL(hAPP(X2,sK25(X0,X1,X2)))
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9938,f9774]) ).
fof(f9938,plain,
( ! [X2,X3,X0,X1,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X3)))
| ~ hBOOL(hAPP(X2,sK25(X0,X1,X2)))
| ~ hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X2,X7)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2461,f9774]) ).
fof(f2461,plain,
! [X2,X3,X0,X1,X7] :
( hBOOL(hAPP(X2,X7))
| ~ hBOOL(hAPP(X2,sK24(X1,X2,X3)))
| ~ hBOOL(hAPP(X2,sK25(X0,X1,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X1),X7),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X3))) ),
inference(cnf_transformation,[],[f1740]) ).
fof(f11299,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64
| spl85_69 ),
inference(avatar_split_clause,[],[f10945,f4474,f4426,f3290,f9793]) ).
fof(f10945,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64
| spl85_69 ),
inference(backward_demodulation,[],[f4475,f9774]) ).
fof(f11296,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11295,f4426,f3290,f9793]) ).
fof(f11295,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11294]) ).
fof(f11294,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11293,f9774]) ).
fof(f11293,plain,
( ! [X21,X19,X22,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X20,X21)),X19),c_FuncSet_OPi(X20,X21,X22,X23)))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11292,f9774]) ).
fof(f11292,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X20,X21),X24)),X26),c_FuncSet_OPi(tc_fun(X20,X21),X24,c_FuncSet_OPi(X20,X21,X22,X23),X25)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X20,X21)),X19),c_FuncSet_OPi(X20,X21,X22,X23))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f11291]) ).
fof(f11291,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X20,X21)),X19),c_FuncSet_OPi(X20,X21,X22,X23)))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X20,X21),X24)),X26),c_FuncSet_OPi(tc_fun(X20,X21),X24,c_FuncSet_OPi(X20,X21,X22,X23),X25))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10015,f9774]) ).
fof(f10015,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hAPP(v_F,v_Q____) != hAPP(sK83(c_FuncSet_OPi(X20,X21,X22,X23),tc_fun(X20,X21),X24,X25,X26),sK72(X20,sK83(c_FuncSet_OPi(X20,X21,X22,X23),tc_fun(X20,X21),X24,X25,X26),X19,X22))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X20,X21)),X19),c_FuncSet_OPi(X20,X21,X22,X23)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X20,X21),X24)),X26),c_FuncSet_OPi(tc_fun(X20,X21),X24,c_FuncSet_OPi(X20,X21,X22,X23),X25))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3608,f9774]) ).
fof(f3608,plain,
! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X20,X21),X24)),X26),c_FuncSet_OPi(tc_fun(X20,X21),X24,c_FuncSet_OPi(X20,X21,X22,X23),X25)))
| hAPP(X19,sK72(X20,sK83(c_FuncSet_OPi(X20,X21,X22,X23),tc_fun(X20,X21),X24,X25,X26),X19,X22)) != hAPP(sK83(c_FuncSet_OPi(X20,X21,X22,X23),tc_fun(X20,X21),X24,X25,X26),sK72(X20,sK83(c_FuncSet_OPi(X20,X21,X22,X23),tc_fun(X20,X21),X24,X25,X26),X19,X22))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X20,X21)),X19),c_FuncSet_OPi(X20,X21,X22,X23))) ),
inference(resolution,[],[f2751,f2942]) ).
fof(f11289,plain,
( spl85_115
| spl85_169
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10980,f4426,f3290,f11286,f7573]) ).
fof(f7573,plain,
( spl85_115
<=> ! [X1] : ~ class_Orderings_Oord(X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_115])]) ).
fof(f11286,plain,
( spl85_169
<=> class_Orderings_Oord(hAPP(v_F,v_Q____)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_169])]) ).
fof(f10980,plain,
( ! [X1] :
( class_Orderings_Oord(hAPP(v_F,v_Q____))
| ~ class_Orderings_Oord(X1) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2259,f9774]) ).
fof(f2259,plain,
! [X0,X1] :
( class_Orderings_Oord(tc_fun(X0,X1))
| ~ class_Orderings_Oord(X1) ),
inference(cnf_transformation,[],[f1326]) ).
fof(f1326,plain,
! [X0,X1] :
( ~ class_Orderings_Oord(X1)
| class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(ennf_transformation,[],[f879]) ).
fof(f879,plain,
! [X1,X0] :
( class_Orderings_Oord(X1)
=> class_Orderings_Oord(tc_fun(X0,X1)) ),
inference(rectify,[],[f504]) ).
fof(f504,axiom,
! [X73,X74] :
( class_Orderings_Oord(X74)
=> class_Orderings_Oord(tc_fun(X73,X74)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(f11282,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10886,f4426,f3290,f9793]) ).
fof(f10886,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3564,f9774]) ).
fof(f11281,plain,
( spl85_168
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11277,f4426,f3290,f9793,f11279]) ).
fof(f11277,plain,
( ! [X38,X39,X37] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Predicate_ORangeP(X38,X39,hAPP(v_F,v_Q____),X37) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11276,f9774]) ).
fof(f11276,plain,
( ! [X31,X38,X39,X37,X34,X35,X32,X33] :
( c_Predicate_ORangeP(X38,X39,hAPP(hAPP(c_COMBC(X31,X32,X33),X34),X35),X37)
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10305,f9774]) ).
fof(f10305,plain,
( ! [X31,X38,X39,X37,X34,X35,X32,X33] :
( ~ hBOOL(hAPP(hAPP(v_F,v_Q____),X37))
| c_Predicate_ORangeP(X38,X39,hAPP(hAPP(c_COMBC(X31,X32,X33),X34),X35),X37) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4352,f9774]) ).
fof(f4352,plain,
! [X31,X38,X39,X36,X37,X34,X35,X32,X33] :
( c_Predicate_ORangeP(X38,X39,hAPP(hAPP(c_COMBC(X31,X32,X33),X34),X35),X37)
| ~ hBOOL(hAPP(hAPP(hAPP(X34,X36),X35),X37)) ),
inference(superposition,[],[f2173,f2585]) ).
fof(f11260,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11259,f4426,f3290,f9793]) ).
fof(f11259,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11258]) ).
fof(f11258,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11257,f9774]) ).
fof(f11257,plain,
( ! [X11,X8,X6,X9] :
( hBOOL(hAPP(hAPP(c_member(X6),sK72(X6,X8,X11,X9)),X9))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11256]) ).
fof(f11256,plain,
( ! [X11,X8,X6,X9] :
( hBOOL(hAPP(hAPP(c_member(X6),sK72(X6,X8,X11,X9)),X9))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10402,f9774]) ).
fof(f10402,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X7)),X8),c_FuncSet_OPi(X6,X7,X9,X10)))
| hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(c_member(X6),sK72(X6,X8,X11,X9)),X9)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3598,f9774]) ).
fof(f3598,plain,
! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(X6),sK57(X11,X9,X6,X7,X10)),X9))
| hBOOL(hAPP(hAPP(c_member(X6),sK72(X6,X8,X11,X9)),X9))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X7)),X8),c_FuncSet_OPi(X6,X7,X9,X10))) ),
inference(resolution,[],[f2750,f2649]) ).
fof(f11246,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10849,f4426,f3371,f3290,f9793]) ).
fof(f10849,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_40
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4241,f9774]) ).
fof(f4241,plain,
( ! [X40,X38,X39,X36,X37,X35] : hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,c_Product__Type_OPair(X39,X40))))
| ~ spl85_40 ),
inference(resolution,[],[f3652,f2941]) ).
fof(f2941,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),hAPP(X4,sK83(X0,X1,X2,X3,X4))),hAPP(X3,sK83(X0,X1,X2,X3,X4))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X4),c_FuncSet_OPi(X1,X2,X0,X3))) ),
inference(cnf_transformation,[],[f2160]) ).
fof(f11211,plain,
( spl85_167
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10346,f4426,f3290,f9793,f11209]) ).
fof(f10346,plain,
( ! [X2,X0] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(X2,X0)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2711,f9774]) ).
fof(f11203,plain,
( spl85_161
| spl85_166
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11199,f4426,f3290,f11201,f9793]) ).
fof(f11201,plain,
( spl85_166
<=> ! [X2,X0,X1] : ~ c_Predicate_ODomainP(X2,X1,hAPP(v_F,v_Q____),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_166])]) ).
fof(f11199,plain,
( ! [X2,X0,X1] :
( ~ c_Predicate_ODomainP(X2,X1,hAPP(v_F,v_Q____),X0)
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10479,f9774]) ).
fof(f10479,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X0),c_Relation_ODomain(X2,X1,X3)))
| ~ c_Predicate_ODomainP(X2,X1,hAPP(v_F,v_Q____),X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2594,f9774]) ).
fof(f2594,plain,
! [X2,X3,X0,X1] :
( ~ c_Predicate_ODomainP(X2,X1,hAPP(hAPP(c_COMBC(X2,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X2,c_COMBC(X1,tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X2,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool)),X2,c_COMBB(tc_prod(X2,X1),tc_fun(tc_fun(tc_prod(X2,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X2,X1)))),c_Product__Type_OPair(X2,X1)))),X3),X0)
| hBOOL(hAPP(hAPP(c_member(X2),X0),c_Relation_ODomain(X2,X1,X3))) ),
inference(cnf_transformation,[],[f1854]) ).
fof(f11184,plain,
( ~ spl85_161
| spl85_58
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11183,f4426,f3290,f4223,f9793]) ).
fof(f11183,plain,
( ! [X2,X4] :
( X2 = X4
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11182]) ).
fof(f11182,plain,
( ! [X2,X4] :
( X2 = X4
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11181,f9774]) ).
fof(f11181,plain,
( ! [X2,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| X2 = X4
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10038,f9774]) ).
fof(f10038,plain,
( ! [X2,X0,X4] :
( X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2997,f9774]) ).
fof(f2997,plain,
! [X2,X3,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| X2 = X4 ),
inference(equality_resolution,[],[f2372]) ).
fof(f2372,plain,
! [X2,X3,X0,X1,X4] :
( X1 != X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin)) ),
inference(cnf_transformation,[],[f1663]) ).
fof(f11151,plain,
( spl85_165
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11147,f4426,f3290,f9793,f11149]) ).
fof(f11149,plain,
( spl85_165
<=> ! [X2,X0,X3] :
( hBOOL(hAPP(X0,X3))
| hBOOL(hAPP(X2,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_165])]) ).
fof(f11147,plain,
( ! [X2,X3,X0] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X0,X3))
| hBOOL(hAPP(X2,X3)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10563,f9774]) ).
fof(f10563,plain,
( ! [X2,X3,X0] :
( hBOOL(hAPP(X2,X3))
| hBOOL(hAPP(X0,X3))
| ~ hBOOL(hAPP(hAPP(v_F,v_Q____),X3)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2265,f9774]) ).
fof(f2265,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X2),X3))
| hBOOL(hAPP(X2,X3))
| hBOOL(hAPP(X0,X3)) ),
inference(cnf_transformation,[],[f1579]) ).
fof(f1579,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(X0,X3))
| hBOOL(hAPP(X2,X3))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X2),X3)) ),
inference(rectify,[],[f1109]) ).
fof(f1109,plain,
! [X0,X3,X1,X2] :
( hBOOL(hAPP(X0,X2))
| hBOOL(hAPP(X1,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X0),X1),X2)) ),
inference(flattening,[],[f1108]) ).
fof(f1108,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(X1,X2))
| hBOOL(hAPP(X0,X2))
| ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X0),X1),X2)) ),
inference(ennf_transformation,[],[f675]) ).
fof(f675,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X0),X1),X2))
=> ( ~ hBOOL(hAPP(X0,X2))
=> hBOOL(hAPP(X1,X2)) ) ),
inference(rectify,[],[f342]) ).
fof(f342,axiom,
! [X10,X9,X14,X8] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X10),X9),X14))
=> ( ~ hBOOL(hAPP(X10,X14))
=> hBOOL(hAPP(X9,X14)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1E) ).
fof(f11145,plain,
( ~ spl85_161
| spl85_58
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11144,f4426,f3290,f4223,f9793]) ).
fof(f11144,plain,
( ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11143]) ).
fof(f11143,plain,
( ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11142,f9774]) ).
fof(f11142,plain,
( ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK84(X0,X1)),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10133,f9774]) ).
fof(f10133,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(v_F,v_Q____)),sK84(X0,X1)))
| X0 = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK84(X0,X1)),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3619,f9774]) ).
fof(f3619,plain,
! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK84(X0,X1)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),sK84(X0,X1))) ),
inference(resolution,[],[f2792,f2949]) ).
fof(f11122,plain,
( spl85_164
| spl85_58
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11118,f4426,f3290,f4223,f11120]) ).
fof(f11120,plain,
( spl85_164
<=> ! [X1] : hAPP(v_F,v_Q____) != hAPP(hAPP(v_F,v_Q____),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_164])]) ).
fof(f11118,plain,
( ! [X3,X0,X1] :
( X0 = X3
| hAPP(v_F,v_Q____) != hAPP(hAPP(v_F,v_Q____),X1) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10646,f9774]) ).
fof(f10646,plain,
( ! [X2,X3,X0,X1,X4] :
( hAPP(v_F,v_Q____) != hAPP(hAPP(c_Product__Type_OPair(X2,X4),X3),X1)
| X0 = X3 )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2787,f9774]) ).
fof(f2787,plain,
! [X2,X3,X0,X1,X4,X5] :
( hAPP(hAPP(c_Product__Type_OPair(X2,X4),X0),X5) != hAPP(hAPP(c_Product__Type_OPair(X2,X4),X3),X1)
| X0 = X3 ),
inference(cnf_transformation,[],[f2035]) ).
fof(f2035,plain,
! [X0,X1,X2,X3,X4,X5] :
( hAPP(hAPP(c_Product__Type_OPair(X2,X4),X0),X5) != hAPP(hAPP(c_Product__Type_OPair(X2,X4),X3),X1)
| ( X1 = X5
& X0 = X3 ) ),
inference(rectify,[],[f1276]) ).
fof(f1276,plain,
! [X3,X0,X5,X1,X4,X2] :
( hAPP(hAPP(c_Product__Type_OPair(X5,X4),X1),X0) != hAPP(hAPP(c_Product__Type_OPair(X5,X4),X3),X2)
| ( X0 = X2
& X1 = X3 ) ),
inference(ennf_transformation,[],[f537]) ).
fof(f537,plain,
! [X1,X2,X4,X3,X0,X5] :
( hAPP(hAPP(c_Product__Type_OPair(X5,X4),X1),X0) = hAPP(hAPP(c_Product__Type_OPair(X5,X4),X3),X2)
=> ~ ( X1 = X3
=> X0 != X2 ) ),
inference(rectify,[],[f21]) ).
fof(f21,axiom,
! [X25,X26,X27,X28,X16,X8] :
( hAPP(hAPP(c_Product__Type_OPair(X8,X16),X28),X27) = hAPP(hAPP(c_Product__Type_OPair(X8,X16),X26),X25)
=> ~ ( X26 = X28
=> X25 != X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
fof(f11116,plain,
( spl85_161
| spl85_162
| spl85_61
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11115,f4426,f3290,f4384,f11077,f9793]) ).
fof(f11115,plain,
( ! [X8,X6,X7,X5] :
( ~ hBOOL(X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X6,X7),hAPP(X6,X8))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10462,f9774]) ).
fof(f10462,plain,
( ! [X10,X11,X8,X6,X9,X7,X5] :
( ~ hBOOL(X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X6,X7),hAPP(X6,X8))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(v_F,v_Q____)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X9),X9,c_Wellfounded_Olex__prod(tc_Nat_Onat,X9,c_Wellfounded_Oless__than,c_COMBK(X10,X11,X5)),hAPP(hAPP(c_COMBS(X9,X9,tc_prod(tc_Nat_Onat,X9)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X9,tc_prod(tc_Nat_Onat,X9)),X9,c_Product__Type_OPair(tc_Nat_Onat,X9)),X6)),c_COMBI(X9))))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4082,f9774]) ).
fof(f4082,plain,
! [X10,X11,X8,X6,X9,X7,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X6,X7),hAPP(X6,X8))
| ~ hBOOL(X5)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X7),X8)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X9),X9,c_Wellfounded_Olex__prod(tc_Nat_Onat,X9,c_Wellfounded_Oless__than,c_COMBK(X10,X11,X5)),hAPP(hAPP(c_COMBS(X9,X9,tc_prod(tc_Nat_Onat,X9)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X9,tc_prod(tc_Nat_Onat,X9)),X9,c_Product__Type_OPair(tc_Nat_Onat,X9)),X6)),c_COMBI(X9))))) ),
inference(resolution,[],[f3315,f2974]) ).
fof(f11114,plain,
( ~ spl85_161
| ~ spl85_34
| spl85_54
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10777,f4426,f4014,f3290,f9793]) ).
fof(f10777,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| spl85_54
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4015,f9774]) ).
fof(f4015,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,sK4(v_Q____,v_P____,v_a____,v_b____))))
| spl85_54 ),
inference(avatar_component_clause,[],[f4014]) ).
fof(f11107,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11106,f4426,f3290,f9793]) ).
fof(f11106,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11105]) ).
fof(f11105,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11104,f9774]) ).
fof(f11104,plain,
( ! [X2] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(v_F,v_Q____),X2)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9923,f9774]) ).
fof(f9923,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2))
| hBOOL(hAPP(hAPP(v_F,v_Q____),X2)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2337,f9774]) ).
fof(f2337,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(X0,sK14(X0,X1,X2)),X2))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) ),
inference(cnf_transformation,[],[f1645]) ).
fof(f1645,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2))
| ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK14(X0,X1,X2)))
& hBOOL(hAPP(hAPP(X0,sK14(X0,X1,X2)),X2)) ) )
& ( ! [X4] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X4))
| ~ hBOOL(hAPP(hAPP(X0,X4),X2)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK14])],[f1643,f1644]) ).
fof(f1644,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
& hBOOL(hAPP(hAPP(X0,X3),X2)) )
=> ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),sK14(X0,X1,X2)))
& hBOOL(hAPP(hAPP(X0,sK14(X0,X1,X2)),X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f1643,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2))
| ? [X3] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
& hBOOL(hAPP(hAPP(X0,X3),X2)) ) )
& ( ! [X4] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X4))
| ~ hBOOL(hAPP(hAPP(X0,X4),X2)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) ) ),
inference(rectify,[],[f1642]) ).
fof(f1642,plain,
! [X0,X1,X2] :
( ( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2))
| ? [X3] :
( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
& hBOOL(hAPP(hAPP(X0,X3),X2)) ) )
& ( ! [X3] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ hBOOL(hAPP(hAPP(X0,X3),X2)) )
| ~ hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) ) ),
inference(nnf_transformation,[],[f1082]) ).
fof(f1082,plain,
! [X0,X1,X2] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2))
<=> ! [X3] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3))
| ~ hBOOL(hAPP(hAPP(X0,X3),X2)) ) ),
inference(ennf_transformation,[],[f1028]) ).
fof(f1028,plain,
! [X1,X0,X2] :
( ! [X3] :
( hBOOL(hAPP(hAPP(X0,X3),X2))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X3)) )
<=> hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2)) ),
inference(rectify,[],[f72]) ).
fof(f72,axiom,
! [X19,X8,X24] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X8,X19),X24))
<=> ! [X2] :
( hBOOL(hAPP(hAPP(X19,X2),X24))
=> hBOOL(hAPP(c_Wellfounded_Oaccp(X8,X19),X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_accp_Oequations) ).
fof(f11103,plain,
( ~ spl85_161
| spl85_163
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11099,f4426,f3290,f11101,f9793]) ).
fof(f11099,plain,
( ! [X3,X0,X1] :
( ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11098]) ).
fof(f11098,plain,
( ! [X3,X0,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,X0))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f9949,f9774]) ).
fof(f9949,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X1,X0))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X0)),c_Transitive__Closure_Ortrancl(X2,X4)))
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2529,f9774]) ).
fof(f2529,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(X1,sK39(X0,X1,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X0)),c_Transitive__Closure_Ortrancl(X2,X4)))
| hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,X0)) ),
inference(cnf_transformation,[],[f1802]) ).
fof(f1802,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,X0))
| ( hBOOL(hAPP(X1,sK38(X0,X1,X2,X4)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK38(X0,X1,X2,X4)),X0)),c_Transitive__Closure_Ortrancl(X2,X4)))
& ~ hBOOL(hAPP(X1,sK39(X0,X1,X2,X4)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK39(X0,X1,X2,X4)),sK38(X0,X1,X2,X4))),X4)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X0)),c_Transitive__Closure_Ortrancl(X2,X4))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK38,sK39])],[f1800,f1801]) ).
fof(f1801,plain,
! [X0,X1,X2,X4] :
( ? [X5,X6] :
( hBOOL(hAPP(X1,X5))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X5),X0)),c_Transitive__Closure_Ortrancl(X2,X4)))
& ~ hBOOL(hAPP(X1,X6))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X6),X5)),X4)) )
=> ( hBOOL(hAPP(X1,sK38(X0,X1,X2,X4)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK38(X0,X1,X2,X4)),X0)),c_Transitive__Closure_Ortrancl(X2,X4)))
& ~ hBOOL(hAPP(X1,sK39(X0,X1,X2,X4)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK39(X0,X1,X2,X4)),sK38(X0,X1,X2,X4))),X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f1800,plain,
! [X0,X1,X2,X3,X4] :
( hBOOL(hAPP(X1,X3))
| ~ hBOOL(hAPP(X1,X0))
| ? [X5,X6] :
( hBOOL(hAPP(X1,X5))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X5),X0)),c_Transitive__Closure_Ortrancl(X2,X4)))
& ~ hBOOL(hAPP(X1,X6))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X6),X5)),X4)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X3),X0)),c_Transitive__Closure_Ortrancl(X2,X4))) ),
inference(rectify,[],[f1363]) ).
fof(f1363,plain,
! [X4,X2,X3,X0,X1] :
( hBOOL(hAPP(X2,X0))
| ~ hBOOL(hAPP(X2,X4))
| ? [X5,X6] :
( hBOOL(hAPP(X2,X5))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X5),X4)),c_Transitive__Closure_Ortrancl(X3,X1)))
& ~ hBOOL(hAPP(X2,X6))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X6),X5)),X1)) )
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X0),X4)),c_Transitive__Closure_Ortrancl(X3,X1))) ),
inference(flattening,[],[f1362]) ).
fof(f1362,plain,
! [X0,X1,X2,X4,X3] :
( hBOOL(hAPP(X2,X0))
| ? [X6,X5] :
( ~ hBOOL(hAPP(X2,X6))
& hBOOL(hAPP(X2,X5))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X5),X4)),c_Transitive__Closure_Ortrancl(X3,X1)))
& hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X6),X5)),X1)) )
| ~ hBOOL(hAPP(X2,X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X0),X4)),c_Transitive__Closure_Ortrancl(X3,X1))) ),
inference(ennf_transformation,[],[f583]) ).
fof(f583,plain,
! [X0,X1,X2,X4,X3] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X0),X4)),c_Transitive__Closure_Ortrancl(X3,X1)))
=> ( hBOOL(hAPP(X2,X4))
=> ( ! [X6,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X6),X5)),X1))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X3,X3)),hAPP(hAPP(c_Product__Type_OPair(X3,X3),X5),X4)),c_Transitive__Closure_Ortrancl(X3,X1)))
=> ( hBOOL(hAPP(X2,X5))
=> hBOOL(hAPP(X2,X6)) ) ) )
=> hBOOL(hAPP(X2,X0)) ) ) ),
inference(rectify,[],[f169]) ).
fof(f169,axiom,
! [X24,X19,X18,X8,X23] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X24),X23)),c_Transitive__Closure_Ortrancl(X8,X19)))
=> ( hBOOL(hAPP(X18,X23))
=> ( ! [X38,X41] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X41),X38)),X19))
=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(X8,X8)),hAPP(hAPP(c_Product__Type_OPair(X8,X8),X38),X23)),c_Transitive__Closure_Ortrancl(X8,X19)))
=> ( hBOOL(hAPP(X18,X38))
=> hBOOL(hAPP(X18,X41)) ) ) )
=> hBOOL(hAPP(X18,X24)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct) ).
fof(f11088,plain,
( spl85_162
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11087,f4426,f3290,f9793,f11077]) ).
fof(f11087,plain,
( ! [X6,X4,X5] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X5),hAPP(X4,X6)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10463,f9774]) ).
fof(f10463,plain,
( ! [X8,X6,X9,X7,X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X5),hAPP(X4,X6))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(v_F,v_Q____)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X7),X7,c_Wellfounded_Olex__prod(tc_Nat_Onat,X7,c_Wellfounded_Oless__than,hAPP(c_Transitive__Closure_Ortranclp(X8,X9),hAPP(v_F,v_Q____))),hAPP(hAPP(c_COMBS(X7,X7,tc_prod(tc_Nat_Onat,X7)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X7,tc_prod(tc_Nat_Onat,X7)),X7,c_Product__Type_OPair(tc_Nat_Onat,X7)),X4)),c_COMBI(X7))))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f4095,f9774]) ).
fof(f4095,plain,
! [X8,X6,X9,X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X5),X6)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X7),X7,c_Wellfounded_Olex__prod(tc_Nat_Onat,X7,c_Wellfounded_Oless__than,hAPP(c_Transitive__Closure_Ortranclp(X8,X9),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X5),X6))),hAPP(hAPP(c_COMBS(X7,X7,tc_prod(tc_Nat_Onat,X7)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X7,tc_prod(tc_Nat_Onat,X7)),X7,c_Product__Type_OPair(tc_Nat_Onat,X7)),X4)),c_COMBI(X7)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X5),hAPP(X4,X6)) ),
inference(resolution,[],[f3644,f2974]) ).
fof(f11083,plain,
( spl85_161
| ~ spl85_33
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10832,f4426,f3290,f3283,f9793]) ).
fof(f10832,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_33
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3312,f9774]) ).
fof(f11079,plain,
( spl85_161
| spl85_162
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11075,f4426,f3290,f11077,f9793]) ).
fof(f11075,plain,
( ! [X28,X29,X27] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X27,X28),hAPP(X27,X29))
| hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10457,f9774]) ).
fof(f10457,plain,
( ! [X28,X29,X27,X30] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X30,X30)),hAPP(v_F,v_Q____)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X30),X30,c_Wellfounded_Olex__prod(tc_Nat_Onat,X30,c_Wellfounded_Oless__than,hAPP(c_fequal,hAPP(v_F,v_Q____))),hAPP(hAPP(c_COMBS(X30,X30,tc_prod(tc_Nat_Onat,X30)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X30,tc_prod(tc_Nat_Onat,X30)),X30,c_Product__Type_OPair(tc_Nat_Onat,X30)),X27)),c_COMBI(X30)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X27,X28),hAPP(X27,X29)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3923,f9774]) ).
fof(f3923,plain,
! [X28,X29,X27,X30] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X27,X28),hAPP(X27,X29))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30,X30)),hAPP(hAPP(c_Product__Type_OPair(X30,X30),X28),X29)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X30),X30,c_Wellfounded_Olex__prod(tc_Nat_Onat,X30,c_Wellfounded_Oless__than,hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(X30,X30),X28),X29))),hAPP(hAPP(c_COMBS(X30,X30,tc_prod(tc_Nat_Onat,X30)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X30,tc_prod(tc_Nat_Onat,X30)),X30,c_Product__Type_OPair(tc_Nat_Onat,X30)),X27)),c_COMBI(X30))))) ),
inference(resolution,[],[f2974,f3035]) ).
fof(f11074,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11073,f4426,f3290,f9793]) ).
fof(f11073,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11072]) ).
fof(f11072,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11071,f9774]) ).
fof(f11071,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1)),hAPP(v_F,v_Q____)),sK83(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X2),X0,X3,X4,X5))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10235,f9774]) ).
fof(f10235,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X3)),X5),c_FuncSet_OPi(X0,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X2),X4)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1)),hAPP(v_F,v_Q____)),sK83(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X2),X0,X3,X4,X5))) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3647,f9774]) ).
fof(f3647,plain,
! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1)),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X2)),sK83(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X2),X0,X3,X4,X5)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X3)),X5),c_FuncSet_OPi(X0,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X2),X4))) ),
inference(resolution,[],[f2765,f2942]) ).
fof(f11068,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11067,f4426,f3290,f9793]) ).
fof(f11067,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(duplicate_literal_removal,[],[f11066]) ).
fof(f11066,plain,
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10399,f9774]) ).
fof(f10399,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(v_F,v_Q____))
| hBOOL(hAPP(c_FuncSet_OPi(X0,X1,X3,X4),X2)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3467,f9774]) ).
fof(f3467,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(X0),sK57(X2,X3,X0,X1,X4)),X3))
| hBOOL(hAPP(c_FuncSet_OPi(X0,X1,X3,X4),X2)) ),
inference(resolution,[],[f2649,f2710]) ).
fof(f11062,plain,
( ~ spl85_161
| spl85_58
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10884,f4426,f3290,f4223,f9793]) ).
fof(f10884,plain,
( ! [X2,X1] :
( X1 = X2
| ~ hBOOL(hAPP(v_F,v_Q____)) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2564,f9774]) ).
fof(f2564,plain,
! [X2,X0,X1] :
( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(X0),X2),c_Set_Oinsert(X0,X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))) ),
inference(cnf_transformation,[],[f1829]) ).
fof(f1829,plain,
! [X0,X1,X2] :
( ( X1 = X2
| ~ hBOOL(hAPP(hAPP(c_member(X0),X2),c_Set_Oinsert(X0,X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))) )
& ( hBOOL(hAPP(hAPP(c_member(X0),X2),c_Set_Oinsert(X0,X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))))
| X1 != X2 ) ),
inference(rectify,[],[f1828]) ).
fof(f1828,plain,
! [X1,X2,X0] :
( ( X0 = X2
| ~ hBOOL(hAPP(hAPP(c_member(X1),X0),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) )
& ( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool)))))
| X0 != X2 ) ),
inference(nnf_transformation,[],[f938]) ).
fof(f938,plain,
! [X1,X2,X0] :
( X0 = X2
<=> hBOOL(hAPP(hAPP(c_member(X1),X0),c_Set_Oinsert(X1,X2,c_Orderings_Obot__class_Obot(tc_fun(X1,tc_HOL_Obool))))) ),
inference(rectify,[],[f471]) ).
fof(f471,axiom,
! [X23,X8,X24] :
( hBOOL(hAPP(hAPP(c_member(X8),X23),c_Set_Oinsert(X8,X24,c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)))))
<=> X23 = X24 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__iff) ).
fof(f11060,plain,
( spl85_84
| ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f11059,f4426,f3290,f9793,f6422]) ).
fof(f11059,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(X1,X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(trivial_inequality_removal,[],[f11058]) ).
fof(f11058,plain,
( ! [X0,X1] :
( c_Arrow__Order__Mirabelle_Odictator(X1,X0)
| ~ hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != hAPP(v_F,v_Q____) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f11057,f9774]) ).
fof(f11057,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| hAPP(v_F,v_Q____) != sK21(X0,X1)
| c_Arrow__Order__Mirabelle_Odictator(X1,X0) )
| ~ spl85_34
| ~ spl85_64 ),
inference(forward_demodulation,[],[f10861,f9774]) ).
fof(f10861,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(v_F,v_Q____))
| c_Arrow__Order__Mirabelle_Odictator(X1,X0)
| sK21(X0,X1) != sK22(X0,X1) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f2453,f9774]) ).
fof(f2453,plain,
! [X0,X1] :
( sK21(X0,X1) != sK22(X0,X1)
| c_Arrow__Order__Mirabelle_Odictator(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) ),
inference(cnf_transformation,[],[f1732]) ).
fof(f11055,plain,
( spl85_61
| spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f10887,f4426,f3290,f9793,f4384]) ).
fof(f10887,plain,
( ! [X37] :
( hBOOL(hAPP(v_F,v_Q____))
| ~ hBOOL(X37) )
| ~ spl85_34
| ~ spl85_64 ),
inference(backward_demodulation,[],[f3956,f9774]) ).
fof(f3956,plain,
! [X38,X36,X37,X34,X35,X33] :
( hBOOL(hAPP(hAPP(c_member(X38),X36),c_Fun_Ofun__upd(X33,X34,X35,X36,X37)))
| ~ hBOOL(X37) ),
inference(superposition,[],[f2711,f3082]) ).
fof(f9802,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f9783,f4426,f3290,f9793]) ).
fof(f9783,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(superposition,[],[f9759,f2793]) ).
fof(f9801,plain,
( spl85_161
| ~ spl85_7
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f9780,f4426,f3290,f3130,f9793]) ).
fof(f9780,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_7
| ~ spl85_34
| ~ spl85_64 ),
inference(superposition,[],[f9759,f3846]) ).
fof(f9800,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f9784,f4426,f3290,f9793]) ).
fof(f9784,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(superposition,[],[f9759,f2580]) ).
fof(f9799,plain,
( spl85_42
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f9787,f4426,f3290,f3379]) ).
fof(f9787,plain,
( ! [X19] : hBOOL(X19)
| ~ spl85_34
| ~ spl85_64 ),
inference(superposition,[],[f9759,f2430]) ).
fof(f9798,plain,
( ~ spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f9777,f4426,f3290,f9793]) ).
fof(f9777,plain,
( ~ hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(resolution,[],[f9759,f2777]) ).
fof(f9797,plain,
( spl85_161
| ~ spl85_12
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f9781,f4426,f3290,f3155,f9793]) ).
fof(f9781,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_12
| ~ spl85_34
| ~ spl85_64 ),
inference(superposition,[],[f9759,f3847]) ).
fof(f9796,plain,
( spl85_161
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f9782,f4426,f3290,f9793]) ).
fof(f9782,plain,
( hBOOL(hAPP(v_F,v_Q____))
| ~ spl85_34
| ~ spl85_64 ),
inference(superposition,[],[f9759,f2397]) ).
fof(f9791,plain,
( spl85_11
| ~ spl85_34
| ~ spl85_64 ),
inference(avatar_contradiction_clause,[],[f9769]) ).
fof(f9769,plain,
( $false
| spl85_11
| ~ spl85_34
| ~ spl85_64 ),
inference(resolution,[],[f9759,f3152]) ).
fof(f9512,plain,
( spl85_64
| spl85_160 ),
inference(avatar_split_clause,[],[f4708,f9510,f4426]) ).
fof(f9510,plain,
( spl85_160
<=> ! [X48,X47,X46,X45] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X45),X46)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X47),X48)))
| X45 = X48
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X45),X47)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X45),X46)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X45 = X46
| X47 = X48 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_160])]) ).
fof(f4708,plain,
! [X48,X46,X47,X45] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X45),X46)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X47),X48)))
| X47 = X48
| X45 = X46
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X45),X46)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X45),X47)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X45 = X48
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool)) ),
inference(resolution,[],[f2929,f2812]) ).
fof(f2812,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X1))
| X3 = X4
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X0)),X1))
| X0 = X2 ),
inference(cnf_transformation,[],[f2048]) ).
fof(f9508,plain,
( spl85_159
| spl85_64 ),
inference(avatar_split_clause,[],[f4714,f4426,f9506]) ).
fof(f9506,plain,
( spl85_159
<=> ! [X64,X62,X63] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X63),X64)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X63),X64)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X63),X62)))
| X62 = X63
| X63 = X64 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_159])]) ).
fof(f4714,plain,
! [X62,X63,X64] :
( c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X63),X64)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X63 = X64
| X62 = X63
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X63),X64)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X63),X62))) ),
inference(resolution,[],[f2929,f3093]) ).
fof(f3093,plain,
! [X2,X3,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X1))
| X2 = X3
| X3 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X3),X2))) ),
inference(duplicate_literal_removal,[],[f3066]) ).
fof(f3066,plain,
! [X2,X3,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X1))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X1))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X3),X2)))
| X3 = X4 ),
inference(equality_resolution,[],[f2804]) ).
fof(f2804,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X4)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X1))
| X0 != X3
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X0 = X2 ),
inference(cnf_transformation,[],[f2048]) ).
fof(f9504,plain,
( spl85_64
| spl85_158 ),
inference(avatar_split_clause,[],[f4403,f9502,f4426]) ).
fof(f9502,plain,
( spl85_158
<=> ! [X38,X40,X39,X37] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X37),X38)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X39),X40)))
| X39 = X40
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X37),X39)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X37 = X38
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X37),X38)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X39),X38)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_158])]) ).
fof(f4403,plain,
! [X40,X38,X39,X37] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X37),X38)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X39),X40)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X39),X38)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X37),X38)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X37 = X38
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X37),X39)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| X39 = X40 ),
inference(resolution,[],[f2323,f2805]) ).
fof(f2805,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X4)),X1))
| X3 = X4
| X0 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X0)),X1)) ),
inference(cnf_transformation,[],[f2048]) ).
fof(f9500,plain,
( spl85_64
| spl85_157 ),
inference(avatar_split_clause,[],[f4411,f9498,f4426]) ).
fof(f9498,plain,
( spl85_157
<=> ! [X64,X62,X63] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X63),X64)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X63),X62)))
| X62 = X63
| X63 = X64
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X63),X64)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_157])]) ).
fof(f4411,plain,
! [X62,X63,X64] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X63),X64)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X63),X62)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X63),X64)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X63 = X64
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| X62 = X63 ),
inference(resolution,[],[f2323,f3093]) ).
fof(f9496,plain,
( spl85_64
| spl85_156 ),
inference(avatar_split_clause,[],[f4709,f9494,f4426]) ).
fof(f9494,plain,
( spl85_156
<=> ! [X50,X49] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49),X50)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X49 = X50
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50),X49)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_156])]) ).
fof(f4709,plain,
! [X50,X49] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49),X50)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50),X49)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| X49 = X50 ),
inference(resolution,[],[f2929,f2888]) ).
fof(f9492,plain,
( spl85_64
| spl85_155 ),
inference(avatar_split_clause,[],[f4408,f9490,f4426]) ).
fof(f9490,plain,
( spl85_155
<=> ! [X54,X55,X56] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X54),X55)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X55 = X56
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X56),X55)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X54),X56)))
| X54 = X56 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_155])]) ).
fof(f4408,plain,
! [X56,X54,X55] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X54),X55)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X54 = X56
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X56),X55)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X54),X56)))
| X55 = X56 ),
inference(resolution,[],[f2323,f3067]) ).
fof(f3067,plain,
! [X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X3 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X3)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X4)),X1))
| X0 = X3 ),
inference(equality_resolution,[],[f2802]) ).
fof(f2802,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X4)),X1))
| X2 != X3
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X0 = X2 ),
inference(cnf_transformation,[],[f2048]) ).
fof(f9488,plain,
( spl85_64
| spl85_154 ),
inference(avatar_split_clause,[],[f4707,f9486,f4426]) ).
fof(f9486,plain,
( spl85_154
<=> ! [X41,X42,X44,X43] :
( X43 = X44
| X42 = X44
| X41 = X44
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X43),X44)))
| X41 = X42
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_154])]) ).
fof(f4707,plain,
! [X41,X44,X42,X43] :
( X43 = X44
| X41 = X42
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X43),X44)))
| X41 = X44
| X42 = X44
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool)) ),
inference(resolution,[],[f2929,f2810]) ).
fof(f2810,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X3 = X4
| X2 = X4
| X0 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2)))
| X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X1)) ),
inference(cnf_transformation,[],[f2048]) ).
fof(f9484,plain,
( spl85_64
| spl85_153 ),
inference(avatar_split_clause,[],[f4400,f9482,f4426]) ).
fof(f9482,plain,
( spl85_153
<=> ! [X28,X27,X25,X26] :
( X25 = X28
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X26)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X25 = X27
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X28)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X26 = X27
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X28)),c_Arrow__Order__Mirabelle_Obelow(sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X27,X26))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_153])]) ).
fof(f4400,plain,
! [X28,X26,X27,X25] :
( X25 = X28
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X28)),c_Arrow__Order__Mirabelle_Obelow(sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X27,X26)))
| X26 = X27
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X28)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X25 = X27
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X26)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool)) ),
inference(resolution,[],[f2323,f2363]) ).
fof(f2363,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X0))
| X1 = X3
| X2 = X4
| X1 = X2 ),
inference(cnf_transformation,[],[f1663]) ).
fof(f9480,plain,
( spl85_64
| spl85_152 ),
inference(avatar_split_clause,[],[f4401,f9478,f4426]) ).
fof(f9478,plain,
( spl85_152
<=> ! [X31,X29,X32,X30] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X31),X29)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X29 = X32
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X31),X30)),c_Arrow__Order__Mirabelle_Obelow(sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X32,X29)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X29),X30)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X30 = X31
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X31),X30)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_152])]) ).
fof(f4401,plain,
! [X31,X29,X32,X30] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X31),X29)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X31),X30)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X30 = X31
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X29),X30)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X31),X30)),c_Arrow__Order__Mirabelle_Obelow(sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X32,X29)))
| X29 = X32 ),
inference(resolution,[],[f2323,f2367]) ).
fof(f2367,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X0))
| X2 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X4)),X0))
| X1 = X3 ),
inference(cnf_transformation,[],[f1663]) ).
fof(f9476,plain,
( spl85_64
| spl85_151 ),
inference(avatar_split_clause,[],[f4702,f9474,f4426]) ).
fof(f9474,plain,
( spl85_151
<=> ! [X24,X21,X23,X22] :
( X21 = X22
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X22)),c_Arrow__Order__Mirabelle_Obelow(sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin),X23,X24)))
| X22 = X23
| X23 = X24
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X22)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X22)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_151])]) ).
fof(f4702,plain,
! [X21,X24,X22,X23] :
( X21 = X22
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X22)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X22)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X23 = X24
| X22 = X23
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X22)),c_Arrow__Order__Mirabelle_Obelow(sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin),X23,X24)))
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool)) ),
inference(resolution,[],[f2929,f2360]) ).
fof(f2360,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| X2 = X4
| X2 = X3
| X1 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X4),X3)),X0))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X0)) ),
inference(cnf_transformation,[],[f1663]) ).
fof(f9472,plain,
( spl85_64
| spl85_150 ),
inference(avatar_split_clause,[],[f4705,f9470,f4426]) ).
fof(f9470,plain,
( spl85_150
<=> ! [X35,X33,X34,X36] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X33),X35)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X35 = X36
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X36),X35)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X36),X35)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X33),X34)))
| X33 = X34
| X34 = X35 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_150])]) ).
fof(f4705,plain,
! [X36,X34,X35,X33] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X33),X35)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| X34 = X35
| X33 = X34
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X36),X35)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X33),X34)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X36),X35)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X35 = X36 ),
inference(resolution,[],[f2929,f2803]) ).
fof(f2803,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X0 = X2
| X3 = X4
| X2 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X4)),X1))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),X1)) ),
inference(cnf_transformation,[],[f2048]) ).
fof(f9468,plain,
( spl85_64
| spl85_149 ),
inference(avatar_split_clause,[],[f4402,f9466,f4426]) ).
fof(f9466,plain,
( spl85_149
<=> ! [X35,X33,X34,X36] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X36),X35)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X33),X34)))
| X33 = X34
| X34 = X35
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X36),X35)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X33),X35)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X35 = X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_149])]) ).
fof(f4402,plain,
! [X36,X34,X35,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X36),X35)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X33),X34)))
| X35 = X36
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X33),X35)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X36),X35)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X34 = X35
| X33 = X34
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool)) ),
inference(resolution,[],[f2323,f2803]) ).
fof(f9464,plain,
( spl85_64
| spl85_148 ),
inference(avatar_split_clause,[],[f4711,f9462,f4426]) ).
fof(f9462,plain,
( spl85_148
<=> ! [X54,X55,X56] :
( X55 = X56
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X56),X55)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X54),X56)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X54),X55)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X54 = X56 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_148])]) ).
fof(f4711,plain,
! [X56,X54,X55] :
( X55 = X56
| X54 = X56
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X54),X55)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X56),X55)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X54),X56))) ),
inference(resolution,[],[f2929,f3067]) ).
fof(f9460,plain,
( spl85_147
| spl85_64 ),
inference(avatar_split_clause,[],[f4703,f4426,f9458]) ).
fof(f9458,plain,
( spl85_147
<=> ! [X28,X27,X25,X26] :
( X25 = X27
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X26)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X25 = X28
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X28)),c_Arrow__Order__Mirabelle_Obelow(sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin),X27,X26)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X28)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X26 = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_147])]) ).
fof(f4703,plain,
! [X28,X26,X27,X25] :
( c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| X25 = X27
| X26 = X27
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X28)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X28)),c_Arrow__Order__Mirabelle_Obelow(sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin),X27,X26)))
| X25 = X28
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X25),X26)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin))) ),
inference(resolution,[],[f2929,f2363]) ).
fof(f9456,plain,
( spl85_64
| spl85_146 ),
inference(avatar_split_clause,[],[f4398,f9454,f4426]) ).
fof(f9454,plain,
( spl85_146
<=> ! [X18,X20,X17,X19] :
( X17 = X18
| X19 = X20
| X18 = X19
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17),X18)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17),X18)),c_Arrow__Order__Mirabelle_Obelow(sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X19,X20)))
| X17 = X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_146])]) ).
fof(f4398,plain,
! [X18,X19,X17,X20] :
( X17 = X18
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| X17 = X19
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17),X18)),c_Arrow__Order__Mirabelle_Obelow(sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X19,X20)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17),X18)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X18 = X19
| X19 = X20 ),
inference(resolution,[],[f2323,f2356]) ).
fof(f2356,plain,
! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),X0))
| X2 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X3)),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| X2 = X4
| X1 = X3
| X1 = X2 ),
inference(cnf_transformation,[],[f1663]) ).
fof(f9452,plain,
( spl85_64
| spl85_145 ),
inference(avatar_split_clause,[],[f4706,f9450,f4426]) ).
fof(f9450,plain,
( spl85_145
<=> ! [X38,X40,X39,X37] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X37),X38)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X39),X40)))
| X39 = X40
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X37),X38)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X37),X39)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X39),X38)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X37 = X38 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_145])]) ).
fof(f4706,plain,
! [X40,X38,X39,X37] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X37),X38)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X39),X40)))
| X37 = X38
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X39),X38)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X37),X39)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X37),X38)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X39 = X40
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool)) ),
inference(resolution,[],[f2929,f2805]) ).
fof(f9448,plain,
( spl85_64
| spl85_144 ),
inference(avatar_split_clause,[],[f4713,f9446,f4426]) ).
fof(f9446,plain,
( spl85_144
<=> ! [X61,X60] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X60),X61)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X60),X61)))
| X60 = X61 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_144])]) ).
fof(f4713,plain,
! [X60,X61] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X60),X61)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X60),X61)))
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| X60 = X61 ),
inference(resolution,[],[f2929,f3090]) ).
fof(f9444,plain,
( spl85_64
| spl85_143 ),
inference(avatar_split_clause,[],[f4399,f9442,f4426]) ).
fof(f9442,plain,
( spl85_143
<=> ! [X24,X21,X23,X22] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X22)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X23 = X24
| X22 = X23
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X22)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X22)),c_Arrow__Order__Mirabelle_Obelow(sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X23,X24)))
| X21 = X22 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_143])]) ).
fof(f4399,plain,
! [X21,X24,X22,X23] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X22)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X21 = X22
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X21),X22)),c_Arrow__Order__Mirabelle_Obelow(sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X23,X24)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X24),X22)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X22 = X23
| X23 = X24
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool)) ),
inference(resolution,[],[f2323,f2360]) ).
fof(f9440,plain,
( spl85_142
| spl85_64 ),
inference(avatar_split_clause,[],[f4405,f4426,f9438]) ).
fof(f9438,plain,
( spl85_142
<=> ! [X48,X47,X46,X45] :
( X45 = X46
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X45),X47)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X47 = X48
| X45 = X48
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X45),X46)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X45),X46)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X47),X48))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_142])]) ).
fof(f4405,plain,
! [X48,X46,X47,X45] :
( c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| X45 = X46
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X45),X46)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X47),X48)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X45),X46)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X45 = X48
| X47 = X48
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X45),X47)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))) ),
inference(resolution,[],[f2323,f2812]) ).
fof(f9436,plain,
( spl85_64
| spl85_141 ),
inference(avatar_split_clause,[],[f4409,f9434,f4426]) ).
fof(f9434,plain,
( spl85_141
<=> ! [X57,X59,X58] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X59),X57)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X59),X58)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X57),X58)))
| X57 = X58
| X58 = X59 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_141])]) ).
fof(f4409,plain,
! [X58,X59,X57] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X59),X57)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X58 = X59
| X57 = X58
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X59),X58)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X57),X58)))
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool)) ),
inference(resolution,[],[f2323,f3083]) ).
fof(f3083,plain,
! [X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X0)),X1))
| X0 = X4
| X3 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X4))) ),
inference(duplicate_literal_removal,[],[f3056]) ).
fof(f3056,plain,
! [X3,X0,X1,X4] :
( X3 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X4)))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X0 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X0)),X1)) ),
inference(equality_resolution,[],[f2815]) ).
fof(f2815,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2)))
| X2 = X3
| X2 != X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X0)),X1))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X0 = X2 ),
inference(cnf_transformation,[],[f2048]) ).
fof(f9432,plain,
( spl85_64
| spl85_140 ),
inference(avatar_split_clause,[],[f4404,f9430,f4426]) ).
fof(f9430,plain,
( spl85_140
<=> ! [X41,X42,X44,X43] :
( X42 = X44
| X43 = X44
| X41 = X42
| X41 = X44
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X43),X44)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_140])]) ).
fof(f4404,plain,
! [X41,X44,X42,X43] :
( X42 = X44
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X41),X42)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X43),X44)))
| X41 = X44
| X41 = X42
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| X43 = X44 ),
inference(resolution,[],[f2323,f2810]) ).
fof(f9428,plain,
( spl85_64
| spl85_139 ),
inference(avatar_split_clause,[],[f4704,f9426,f4426]) ).
fof(f9426,plain,
( spl85_139
<=> ! [X31,X29,X32,X30] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X31),X29)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X31),X30)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X30 = X31
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X31),X30)),c_Arrow__Order__Mirabelle_Obelow(sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin),X32,X29)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X29),X30)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X29 = X32 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_139])]) ).
fof(f4704,plain,
! [X31,X29,X32,X30] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X31),X29)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X29 = X32
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X29),X30)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X31),X30)),c_Arrow__Order__Mirabelle_Obelow(sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin),X32,X29)))
| X30 = X31
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X31),X30)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin))) ),
inference(resolution,[],[f2929,f2367]) ).
fof(f9424,plain,
( spl85_64
| spl85_138 ),
inference(avatar_split_clause,[],[f4407,f9422,f4426]) ).
fof(f9422,plain,
( spl85_138
<=> ! [X52,X53,X51] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53),X52)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X51),X52)))
| X52 = X53
| X51 = X52
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53),X51)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X51),X52)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_138])]) ).
fof(f4407,plain,
! [X51,X52,X53] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53),X52)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X51),X52)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X51),X52)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53),X51)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| X51 = X52
| X52 = X53 ),
inference(resolution,[],[f2323,f3062]) ).
fof(f3062,plain,
! [X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X0 = X4
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X4)))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X4)),X1)) ),
inference(equality_resolution,[],[f2808]) ).
fof(f2808,plain,
! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X4)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X4)),X1))
| X2 != X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X0)),X1))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| X0 = X2 ),
inference(cnf_transformation,[],[f2048]) ).
fof(f9420,plain,
( spl85_137
| spl85_64 ),
inference(avatar_split_clause,[],[f4701,f4426,f9418]) ).
fof(f9418,plain,
( spl85_137
<=> ! [X18,X20,X17,X19] :
( X17 = X18
| X18 = X19
| X19 = X20
| X17 = X19
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17),X18)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17),X18)),c_Arrow__Order__Mirabelle_Obelow(sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin),X19,X20))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_137])]) ).
fof(f4701,plain,
! [X18,X19,X17,X20] :
( c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| X17 = X18
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17),X18)),c_Arrow__Order__Mirabelle_Obelow(sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin),X19,X20)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X17),X18)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X17 = X19
| X19 = X20
| X18 = X19 ),
inference(resolution,[],[f2929,f2356]) ).
fof(f9416,plain,
( spl85_64
| spl85_136 ),
inference(avatar_split_clause,[],[f4712,f9414,f4426]) ).
fof(f9414,plain,
( spl85_136
<=> ! [X57,X59,X58] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X59),X58)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X57),X58)))
| X57 = X58
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X59),X57)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X58 = X59 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_136])]) ).
fof(f4712,plain,
! [X58,X59,X57] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X59),X58)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X57),X58)))
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| X58 = X59
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X59),X57)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X57 = X58 ),
inference(resolution,[],[f2929,f3083]) ).
fof(f9412,plain,
( spl85_135
| spl85_64 ),
inference(avatar_split_clause,[],[f4710,f4426,f9410]) ).
fof(f9410,plain,
( spl85_135
<=> ! [X52,X53,X51] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X51),X52)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53),X52)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X51),X52)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53),X51)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X52 = X53
| X51 = X52 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_135])]) ).
fof(f4710,plain,
! [X51,X52,X53] :
( c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X51),X52)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| X51 = X52
| X52 = X53
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53),X51)),sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X53),X52)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK82(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OLin)),X51),X52))) ),
inference(resolution,[],[f2929,f3062]) ).
fof(f9408,plain,
( spl85_57
| ~ spl85_64 ),
inference(avatar_split_clause,[],[f9402,f4426,f4220]) ).
fof(f9402,plain,
( ! [X4] : ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X4),c_Arrow__Order__Mirabelle_OLin))
| ~ spl85_64 ),
inference(superposition,[],[f3081,f4428]) ).
fof(f8823,plain,
( spl85_42
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f4800,f4474,f3379]) ).
fof(f4800,plain,
( ! [X25] : hBOOL(X25)
| ~ spl85_69 ),
inference(superposition,[],[f4770,f3082]) ).
fof(f4770,plain,
( ! [X0] : hBOOL(hAPP(X0,v_F))
| ~ spl85_69 ),
inference(resolution,[],[f4476,f4255]) ).
fof(f4476,plain,
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool)),v_F))
| ~ spl85_69 ),
inference(avatar_component_clause,[],[f4474]) ).
fof(f8822,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8821,f4474,f4802]) ).
fof(f4802,plain,
( spl85_76
<=> hBOOL(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_76])]) ).
fof(f8821,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4777,f4784]) ).
fof(f4784,plain,
( ! [X34] : v_F = X34
| ~ spl85_69 ),
inference(resolution,[],[f4770,f2346]) ).
fof(f4777,plain,
( ! [X18,X19,X16,X17,X20] : hBOOL(hAPP(hAPP(c_member(tc_prod(X16,X17)),hAPP(hAPP(c_Product__Type_OPair(X16,X17),X18),v_F)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X16,X17),tc_HOL_Obool)),X19),X20)))
| ~ spl85_69 ),
inference(resolution,[],[f4770,f2225]) ).
fof(f8820,plain,
( spl85_103
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f4773,f4474,f7028]) ).
fof(f7028,plain,
( spl85_103
<=> ! [X54,X48,X55] : c_Predicate_ORangeP(X54,X55,X48,v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_103])]) ).
fof(f4773,plain,
( ! [X2,X3,X4] : c_Predicate_ORangeP(X2,X3,X4,v_F)
| ~ spl85_69 ),
inference(resolution,[],[f4770,f2173]) ).
fof(f8819,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8818,f4474,f4802]) ).
fof(f8818,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4772,f4784]) ).
fof(f4772,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),v_F),X1))
| ~ spl85_69 ),
inference(resolution,[],[f4770,f2711]) ).
fof(f8817,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8816,f4474,f4802]) ).
fof(f8816,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4785,f4784]) ).
fof(f4785,plain,
( ! [X36,X37,X35] : hBOOL(hAPP(hAPP(c_member(tc_prod(X35,X35)),hAPP(hAPP(c_Product__Type_OPair(X35,X35),X36),v_F)),c_Transitive__Closure_Ortrancl(X35,X37)))
| ~ spl85_69 ),
inference(resolution,[],[f4770,f2835]) ).
fof(f8815,plain,
( spl85_76
| ~ spl85_7
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f4790,f4474,f3130,f4802]) ).
fof(f4790,plain,
( hBOOL(v_F)
| ~ spl85_7
| ~ spl85_69 ),
inference(superposition,[],[f4770,f3846]) ).
fof(f8814,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8813,f4474,f4802]) ).
fof(f8813,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4797,f4784]) ).
fof(f4797,plain,
( ! [X16,X17] : hBOOL(hAPP(X16,hAPP(X17,v_F)))
| ~ spl85_69 ),
inference(superposition,[],[f4770,f2177]) ).
fof(f8812,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8811,f4474,f4802]) ).
fof(f8811,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4796,f4784]) ).
fof(f4796,plain,
( ! [X11,X12] : hBOOL(hAPP(hAPP(X11,v_F),hAPP(X12,v_F)))
| ~ spl85_69 ),
inference(superposition,[],[f4770,f2728]) ).
fof(f8810,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8809,f4474,f4802]) ).
fof(f8809,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4795,f4784]) ).
fof(f4795,plain,
( ! [X6,X7] : hBOOL(hAPP(hAPP(X6,v_F),X7))
| ~ spl85_69 ),
inference(superposition,[],[f4770,f2585]) ).
fof(f8808,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8807,f4474,f4802]) ).
fof(f8807,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4775,f4784]) ).
fof(f4775,plain,
( ! [X10,X8,X9] : hBOOL(hAPP(hAPP(c_member(X8),v_F),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X9),X10)))
| ~ spl85_69 ),
inference(resolution,[],[f4770,f2855]) ).
fof(f8806,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8805,f4474,f4802]) ).
fof(f8805,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8804]) ).
fof(f8804,plain,
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8803,f4784]) ).
fof(f8803,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_F),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4780,f4784]) ).
fof(f4780,plain,
( ! [X24,X23] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X23),X24)),v_F))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_F),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_69 ),
inference(resolution,[],[f4770,f2792]) ).
fof(f8792,plain,
( spl85_78
| spl85_76
| ~ spl85_16
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5860,f4474,f3178,f4802,f6145]) ).
fof(f5860,plain,
( ! [X0] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(v_F,X0) )
| ~ spl85_16
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3865,f4784]) ).
fof(f8791,plain,
( spl85_80
| spl85_79
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8790,f4474,f6161,f6164]) ).
fof(f6161,plain,
( spl85_79
<=> ! [X7] : c_Orderings_Oord__class_Oless__eq(v_F,v_F,X7) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_79])]) ).
fof(f8790,plain,
( ! [X6,X5] :
( c_Orderings_Oord__class_Oless__eq(v_F,v_F,X6)
| ~ class_Lattices_Olattice(X5) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5754,f4784]) ).
fof(f5754,plain,
( ! [X6,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X5),v_F,X6)
| ~ class_Lattices_Olattice(X5) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3996,f4784]) ).
fof(f3996,plain,
! [X6,X7,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,X5)),X6),X7),X6)
| ~ class_Lattices_Olattice(X5) ),
inference(resolution,[],[f2330,f2477]) ).
fof(f2330,plain,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X0)
| c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X0),X1),X2),X1) ),
inference(cnf_transformation,[],[f1636]) ).
fof(f1636,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X0),X1),X2),X1)
| ~ class_Lattices_Olattice(X0) ),
inference(rectify,[],[f1196]) ).
fof(f1196,plain,
! [X1,X0,X2] :
( c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X2),X0)
| ~ class_Lattices_Olattice(X1) ),
inference(ennf_transformation,[],[f656]) ).
fof(f656,plain,
! [X0,X2,X1] :
( class_Lattices_Olattice(X1)
=> c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X0),X2),X0) ),
inference(rectify,[],[f225]) ).
fof(f225,axiom,
! [X49,X8,X50] :
( class_Lattices_Olattice(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X49),X50),X49) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
fof(f8787,plain,
( spl85_79
| ~ spl85_22
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8786,f4474,f3208,f6161]) ).
fof(f3208,plain,
( spl85_22
<=> class_Lattices_Olattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_22])]) ).
fof(f8786,plain,
( ! [X2] : c_Orderings_Oord__class_Oless__eq(v_F,v_F,X2)
| ~ spl85_22
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5419,f4784]) ).
fof(f5419,plain,
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,v_F,X2)
| ~ spl85_22
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3995,f4784]) ).
fof(f3995,plain,
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),X2),X3),X2)
| ~ spl85_22 ),
inference(resolution,[],[f2330,f3210]) ).
fof(f3210,plain,
( class_Lattices_Olattice(tc_HOL_Obool)
| ~ spl85_22 ),
inference(avatar_component_clause,[],[f3208]) ).
fof(f8784,plain,
( spl85_128
| ~ spl85_30
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6049,f4474,f3261,f8137]) ).
fof(f8137,plain,
( spl85_128
<=> class_Lattices_Obounded__lattice(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_128])]) ).
fof(f3261,plain,
( spl85_30
<=> class_Lattices_Obounded__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_30])]) ).
fof(f6049,plain,
( class_Lattices_Obounded__lattice(v_F)
| ~ spl85_30
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3263,f4784]) ).
fof(f3263,plain,
( class_Lattices_Obounded__lattice(tc_HOL_Obool)
| ~ spl85_30 ),
inference(avatar_component_clause,[],[f3261]) ).
fof(f8783,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8782,f4474,f4802]) ).
fof(f8782,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8781]) ).
fof(f8781,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8780,f4784]) ).
fof(f8780,plain,
( ! [X2,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),v_F),X2))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5380,f4784]) ).
fof(f5380,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),v_F),X2)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2351,f4784]) ).
fof(f8771,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5925,f4474,f4802]) ).
fof(f5925,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3564,f4784]) ).
fof(f8770,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5827,f4474,f4802]) ).
fof(f5827,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3035,f4784]) ).
fof(f8758,plain,
( spl85_76
| spl85_84
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8757,f4474,f6422,f4802]) ).
fof(f8757,plain,
( ! [X2,X1] :
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8756]) ).
fof(f8756,plain,
( ! [X2,X1] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5842,f4784]) ).
fof(f5842,plain,
( ! [X2,X1] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK65(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2)),c_Arrow__Order__Mirabelle_OProf)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3946,f4784]) ).
fof(f8742,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5962,f4474,f4802]) ).
fof(f5962,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3015,f4784]) ).
fof(f8738,plain,
( spl85_76
| ~ spl85_50
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5823,f4474,f3455,f4802]) ).
fof(f5823,plain,
( hBOOL(v_F)
| ~ spl85_50
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3457,f4784]) ).
fof(f8726,plain,
( ~ spl85_76
| spl85_78
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8725,f4474,f6145,f4802]) ).
fof(f8725,plain,
( ! [X17] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X17)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8724]) ).
fof(f8724,plain,
( ! [X17] :
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(v_F,X17) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8723,f4784]) ).
fof(f8723,plain,
( ! [X16,X17] :
( ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X17,c_COMBI(X16))),sK21(X17,c_COMBI(X16)))),sK20(X17,c_COMBI(X16))))
| c_Arrow__Order__Mirabelle_Odictator(v_F,X17) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5902,f4784]) ).
fof(f5902,plain,
( ! [X16,X17] :
( c_Arrow__Order__Mirabelle_Odictator(c_COMBI(X16),X17)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X17,c_COMBI(X16))),sK21(X17,c_COMBI(X16)))),sK20(X17,c_COMBI(X16))))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3967,f4784]) ).
fof(f8719,plain,
( ~ spl85_76
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5387,f4474,f4223,f4802]) ).
fof(f5387,plain,
( ! [X0,X1] :
( X0 = X1
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2346,f4784]) ).
fof(f8712,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8711,f4474,f4802]) ).
fof(f8711,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8710]) ).
fof(f8710,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5256,f4784]) ).
fof(f5256,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X1)),c_FuncSet_Orestrict(X2,X1,X3,X0)),c_FuncSet_OPi(X2,X1,X0,X4))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2727,f4784]) ).
fof(f8707,plain,
( spl85_111
| ~ spl85_22
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6046,f4474,f3208,f7414]) ).
fof(f7414,plain,
( spl85_111
<=> class_Lattices_Olattice(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_111])]) ).
fof(f6046,plain,
( class_Lattices_Olattice(v_F)
| ~ spl85_22
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3210,f4784]) ).
fof(f8696,plain,
( spl85_76
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5879,f4474,f4223,f4802]) ).
fof(f5879,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2948,f4784]) ).
fof(f8684,plain,
( ~ spl85_76
| spl85_77
| ~ spl85_7
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8683,f4474,f3130,f6128,f4802]) ).
fof(f6128,plain,
( spl85_77
<=> ! [X48,X46,X47] : c_Predicate_ORangeP(X47,X48,v_F,X46) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_77])]) ).
fof(f8683,plain,
( ! [X10,X11,X9] :
( c_Predicate_ORangeP(X10,X11,v_F,X9)
| ~ hBOOL(v_F) )
| ~ spl85_7
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5040,f4784]) ).
fof(f5040,plain,
( ! [X10,X11,X8,X9] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X10,X11,hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X8),X9) )
| ~ spl85_7
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4347,f4784]) ).
fof(f4347,plain,
( ! [X10,X11,X8,X9] :
( ~ hBOOL(hAPP(X8,X9))
| c_Predicate_ORangeP(X10,X11,hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X8),X9) )
| ~ spl85_7 ),
inference(superposition,[],[f2173,f3846]) ).
fof(f8679,plain,
( spl85_76
| spl85_78
| ~ spl85_66
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8678,f4474,f4435,f6145,f4802]) ).
fof(f8678,plain,
( ! [X66] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X66)
| hBOOL(v_F) )
| ~ spl85_66
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5861,f4784]) ).
fof(f5861,plain,
( ! [X66] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X66) )
| ~ spl85_66
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4436,f4784]) ).
fof(f8677,plain,
( spl85_76
| ~ spl85_24
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5778,f4474,f3218,f4802]) ).
fof(f5778,plain,
( hBOOL(v_F)
| ~ spl85_24
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3220,f4784]) ).
fof(f8676,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8675,f4474,f4802]) ).
fof(f8675,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5290,f4784]) ).
fof(f5290,plain,
( ! [X2,X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Omkbot(X3,X2)))
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3025,f4784]) ).
fof(f8668,plain,
( spl85_78
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8667,f4474,f4802,f6145]) ).
fof(f8667,plain,
( ! [X11] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(v_F,X11) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8666]) ).
fof(f8666,plain,
( ! [X11] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X11)
| hBOOL(v_F)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8665,f4784]) ).
fof(f8665,plain,
( ! [X11,X14,X12,X13] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13)),X12),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X14)))
| c_Arrow__Order__Mirabelle_Odictator(v_F,X11) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5845,f4784]) ).
fof(f5845,plain,
( ! [X11,X14,X12,X13] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(sK57(X12,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,X14),X11)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13)),X12),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X14))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3950,f4784]) ).
fof(f8664,plain,
( ~ spl85_76
| spl85_77
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8663,f4474,f6128,f4802]) ).
fof(f8663,plain,
( ! [X18,X19,X20] :
( c_Predicate_ORangeP(X19,X20,v_F,X18)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5042,f4784]) ).
fof(f5042,plain,
( ! [X18,X19,X16,X17,X20] :
( c_Predicate_ORangeP(X19,X20,hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X17),X18)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4349,f4784]) ).
fof(f4349,plain,
! [X18,X19,X16,X17,X20] :
( c_Predicate_ORangeP(X19,X20,hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X16,tc_HOL_Obool)),X17),X18)
| ~ hBOOL(hAPP(X17,X18)) ),
inference(superposition,[],[f2173,f2397]) ).
fof(f8658,plain,
( ~ spl85_112
| spl85_6
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5978,f4474,f3125,f7461]) ).
fof(f7461,plain,
( spl85_112
<=> v_F = v_a_H____ ),
introduced(avatar_definition,[new_symbols(naming,[spl85_112])]) ).
fof(f3125,plain,
( spl85_6
<=> v_b_H____ = v_a_H____ ),
introduced(avatar_definition,[new_symbols(naming,[spl85_6])]) ).
fof(f5978,plain,
( v_F != v_a_H____
| spl85_6
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3127,f4784]) ).
fof(f3127,plain,
( v_b_H____ != v_a_H____
| spl85_6 ),
inference(avatar_component_clause,[],[f3125]) ).
fof(f8645,plain,
( spl85_76
| spl85_61
| ~ spl85_23
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5837,f4474,f3213,f4384,f4802]) ).
fof(f5837,plain,
( ! [X14] :
( ~ hBOOL(X14)
| hBOOL(v_F) )
| ~ spl85_23
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3834,f4784]) ).
fof(f8639,plain,
( spl85_61
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5830,f4474,f4802,f4384]) ).
fof(f5830,plain,
( ! [X28] :
( hBOOL(v_F)
| ~ hBOOL(X28) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3739,f4784]) ).
fof(f8627,plain,
( spl85_92
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5487,f4474,f4802,f6565]) ).
fof(f5487,plain,
( ! [X2,X0,X1] :
( hBOOL(v_F)
| c_Relation_Osingle__valued(X0,X1,X2) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2735,f4784]) ).
fof(f8619,plain,
( spl85_79
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8618,f4474,f6161]) ).
fof(f8618,plain,
( ! [X3] : c_Orderings_Oord__class_Oless__eq(v_F,v_F,X3)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8617,f4784]) ).
fof(f8617,plain,
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),v_F,X3)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5765,f4784]) ).
fof(f5765,plain,
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),hAPP(v_F,X3),X3)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4229,f4784]) ).
fof(f4229,plain,
! [X2,X3,X6,X7,X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),hAPP(hAPP(hAPP(c_COMBS(X5,X6,X7),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool))),X4),X3),X3),
inference(superposition,[],[f2852,f2728]) ).
fof(f2852,plain,
! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1),X0),
inference(cnf_transformation,[],[f2078]) ).
fof(f2078,plain,
! [X0,X1,X2] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1),X0),
inference(rectify,[],[f890]) ).
fof(f890,plain,
! [X0,X2,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X2),X0),
inference(rectify,[],[f233]) ).
fof(f233,axiom,
! [X10,X8,X9] : c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X10),X9),X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower1) ).
fof(f8615,plain,
( spl85_127
| spl85_110
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6059,f4474,f7367,f8134]) ).
fof(f7367,plain,
( spl85_110
<=> class_Lattices_Obounded__lattice__bot(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_110])]) ).
fof(f6059,plain,
( ! [X0] :
( class_Lattices_Obounded__lattice__bot(v_F)
| ~ class_Lattices_Obounded__lattice(X0) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2256,f4784]) ).
fof(f8614,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5901,f4474,f4802]) ).
fof(f5901,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2839,f4784]) ).
fof(f8613,plain,
( ~ spl85_82
| spl85_108
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8612,f4474,f7331,f6214]) ).
fof(f6214,plain,
( spl85_82
<=> c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_82])]) ).
fof(f7331,plain,
( spl85_108
<=> ! [X2,X1] : c_Orderings_Oord__class_Oless__eq(v_F,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_108])]) ).
fof(f8612,plain,
( ! [X2,X0] :
( c_Orderings_Oord__class_Oless__eq(v_F,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8611,f4784]) ).
fof(f8611,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_fun(X1,tc_HOL_Obool)),v_F,v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,X2,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8610,f4784]) ).
fof(f8610,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_fun(X1,tc_HOL_Obool)),v_F,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5559,f4784]) ).
fof(f5559,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3,c_COMBC(X1,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X3,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X1),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X3,X1)))),c_Product__Type_OPair(X3,X1)))),X2),v_F)
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),X2,X0) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2345,f4784]) ).
fof(f2345,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3,c_COMBC(X1,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X3,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X1),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X3,X1)))),c_Product__Type_OPair(X3,X1)))),X2),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3,c_COMBC(X1,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X3,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X1),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X3,X1)))),c_Product__Type_OPair(X3,X1)))),X0))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),X2,X0) ),
inference(cnf_transformation,[],[f1650]) ).
fof(f1650,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3,c_COMBC(X1,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X3,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X1),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X3,X1)))),c_Product__Type_OPair(X3,X1)))),X2),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3,c_COMBC(X1,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X3,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X1),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X3,X1)))),c_Product__Type_OPair(X3,X1)))),X0)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3,c_COMBC(X1,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X3,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X1),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X3,X1)))),c_Product__Type_OPair(X3,X1)))),X2),hAPP(hAPP(c_COMBC(X3,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X3,c_COMBC(X1,tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X3,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool)),X3,c_COMBB(tc_prod(X3,X1),tc_fun(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X3,X1)))),c_Product__Type_OPair(X3,X1)))),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X3,X1),tc_HOL_Obool),X2,X0) ) ),
inference(rectify,[],[f1649]) ).
fof(f1649,plain,
! [X1,X2,X3,X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X0,c_COMBC(X2,tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X0,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X2),tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X0,X2)))),c_Product__Type_OPair(X0,X2)))),X3),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X0,c_COMBC(X2,tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X0,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X2),tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X0,X2)))),c_Product__Type_OPair(X0,X2)))),X1)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X0,c_COMBC(X2,tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X0,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X2),tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X0,X2)))),c_Product__Type_OPair(X0,X2)))),X3),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X0,c_COMBC(X2,tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X0,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X2),tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X0,X2)))),c_Product__Type_OPair(X0,X2)))),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),X3,X1) ) ),
inference(nnf_transformation,[],[f582]) ).
fof(f582,plain,
! [X1,X2,X3,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),X3,X1)
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X2,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X0,c_COMBC(X2,tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X0,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X2),tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X0,X2)))),c_Product__Type_OPair(X0,X2)))),X3),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_fun(X2,tc_HOL_Obool)),X0,c_COMBC(X2,tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X2,tc_prod(X0,X2)),tc_fun(X2,tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X2),tc_fun(tc_fun(tc_prod(X0,X2),tc_HOL_Obool),tc_HOL_Obool),X2,c_member(tc_prod(X0,X2)))),c_Product__Type_OPair(X0,X2)))),X1)) ),
inference(rectify,[],[f263]) ).
fof(f263,axiom,
! [X8,X34,X16,X15] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),X15,X34)
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_fun(X16,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X8,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X8,c_COMBC(X16,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_prod(X8,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),X8,c_COMBB(tc_prod(X8,X16),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool),X16,c_member(tc_prod(X8,X16)))),c_Product__Type_OPair(X8,X16)))),X15),hAPP(hAPP(c_COMBC(X8,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X8,c_COMBC(X16,tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_prod(X8,X16)),tc_fun(X16,tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool)),X8,c_COMBB(tc_prod(X8,X16),tc_fun(tc_fun(tc_prod(X8,X16),tc_HOL_Obool),tc_HOL_Obool),X16,c_member(tc_prod(X8,X16)))),c_Product__Type_OPair(X8,X16)))),X34)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq2) ).
fof(f8609,plain,
( ~ spl85_76
| spl85_134
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8605,f4474,f8607,f4802]) ).
fof(f8607,plain,
( spl85_134
<=> ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(v_F,X1,X0)
| c_Orderings_Oord__class_Oless__eq(v_F,v_F,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_134])]) ).
fof(f8605,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(v_F,X1,X0)
| c_Orderings_Oord__class_Oless__eq(v_F,v_F,X0)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8604,f4784]) ).
fof(f8604,plain,
( ! [X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),v_F,X0)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,X1,X0)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8603,f4784]) ).
fof(f8603,plain,
( ! [X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),v_F,X0)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5451,f4784]) ).
fof(f5451,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(v_F)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2546,f4784]) ).
fof(f2546,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X3),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0) ),
inference(cnf_transformation,[],[f1817]) ).
fof(f8595,plain,
( spl85_85
| ~ spl85_3
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6089,f4474,f3110,f6441]) ).
fof(f6441,plain,
( spl85_85
<=> class_Orderings_Opreorder(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_85])]) ).
fof(f3110,plain,
( spl85_3
<=> class_Orderings_Opreorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_3])]) ).
fof(f6089,plain,
( class_Orderings_Opreorder(v_F)
| ~ spl85_3
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3112,f4784]) ).
fof(f3112,plain,
( class_Orderings_Opreorder(tc_Nat_Onat)
| ~ spl85_3 ),
inference(avatar_component_clause,[],[f3110]) ).
fof(f8586,plain,
( spl85_42
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5920,f4474,f4802,f3379]) ).
fof(f5920,plain,
( ! [X1] :
( hBOOL(v_F)
| hBOOL(X1) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3383,f4784]) ).
fof(f8585,plain,
( spl85_77
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8584,f4474,f4802,f6128]) ).
fof(f8584,plain,
( ! [X212,X208,X209] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X208,X209,v_F,X212) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8583,f4784]) ).
fof(f8583,plain,
( ! [X212,X208,X209] :
( c_Predicate_ORangeP(X208,X209,v_F,X212)
| ~ hBOOL(hAPP(v_F,X212)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5037,f4784]) ).
fof(f5037,plain,
( ! [X212,X210,X211,X208,X209] :
( c_Predicate_ORangeP(X208,X209,c_Transitive__Closure_Ortranclp(X210,X211),X212)
| ~ hBOOL(hAPP(v_F,X212)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4344,f4784]) ).
fof(f8564,plain,
( spl85_76
| ~ spl85_24
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5807,f4474,f3218,f4802]) ).
fof(f5807,plain,
( hBOOL(v_F)
| ~ spl85_24
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3295,f4784]) ).
fof(f8563,plain,
( spl85_87
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8562,f4474,f6484]) ).
fof(f6484,plain,
( spl85_87
<=> ! [X6] : c_Orderings_Oord__class_Oless__eq(v_F,X6,v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_87])]) ).
fof(f8562,plain,
( ! [X2] : c_Orderings_Oord__class_Oless__eq(v_F,X2,v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8561,f4784]) ).
fof(f8561,plain,
( ! [X2,X0] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,v_F),X2,v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6033,f4784]) ).
fof(f6033,plain,
( ! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,v_F),X2,c_Set_Oinsert(X0,X1,X2))
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2871,f4784]) ).
fof(f2871,plain,
! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,c_Set_Oinsert(X0,X1,X2)),
inference(cnf_transformation,[],[f2094]) ).
fof(f2094,plain,
! [X0,X1,X2] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,c_Set_Oinsert(X0,X1,X2)),
inference(rectify,[],[f782]) ).
fof(f782,plain,
! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,c_Set_Oinsert(X2,X0,X1)),
inference(rectify,[],[f290]) ).
fof(f290,axiom,
! [X24,X9,X8] : c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),X9,c_Set_Oinsert(X8,X24,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
fof(f8557,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8556,f4474,f4802]) ).
fof(f8556,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8555]) ).
fof(f8555,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8554,f4784]) ).
fof(f8554,plain,
( ! [X16,X14,X17,X15,X13] :
( hBOOL(hAPP(hAPP(c_member(X13),sK65(X17,X16,X15,X13,X14)),X15))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8553,f4784]) ).
fof(f8553,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X16)),X12),c_FuncSet_OPi(X13,X16,X15,c_COMBK(tc_fun(X16,tc_HOL_Obool),X13,X17))))
| hBOOL(hAPP(hAPP(c_member(X13),sK65(X17,X16,X15,X13,X14)),X15)) )
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f8552]) ).
fof(f8552,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( v_F != v_F
| hBOOL(hAPP(hAPP(c_member(X13),sK65(X17,X16,X15,X13,X14)),X15))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X16)),X12),c_FuncSet_OPi(X13,X16,X15,c_COMBK(tc_fun(X16,tc_HOL_Obool),X13,X17)))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5206,f4784]) ).
fof(f5206,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( v_F != hAPP(X12,sK72(X13,X14,X12,X15))
| hBOOL(hAPP(hAPP(c_member(X13),sK65(X17,X16,X15,X13,X14)),X15))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X13,X16)),X12),c_FuncSet_OPi(X13,X16,X15,c_COMBK(tc_fun(X16,tc_HOL_Obool),X13,X17)))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3606,f4784]) ).
fof(f8551,plain,
( spl85_131
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8550,f4474,f8371]) ).
fof(f8371,plain,
( spl85_131
<=> ! [X1] : c_Orderings_Obot__class_Obot(v_F) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl85_131])]) ).
fof(f8550,plain,
( ! [X1] : c_Orderings_Obot__class_Obot(v_F) = X1
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8549,f4784]) ).
fof(f8549,plain,
( ! [X1] : c_Orderings_Obot__class_Obot(tc_fun(v_F,tc_HOL_Obool)) = X1
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f8548]) ).
fof(f8548,plain,
( ! [X1] :
( v_F != v_F
| c_Orderings_Obot__class_Obot(tc_fun(v_F,tc_HOL_Obool)) = X1 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8547,f4784]) ).
fof(f8547,plain,
( ! [X1] :
( v_F != c_Orderings_Obot__class_Obot(v_F)
| c_Orderings_Obot__class_Obot(tc_fun(v_F,tc_HOL_Obool)) = X1 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8546,f4784]) ).
fof(f8546,plain,
( ! [X2,X1] :
( v_F != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(v_F,tc_HOL_Obool)) = X1 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5990,f4784]) ).
fof(f5990,plain,
( ! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != c_Relation_ODomain(X2,X0,X1)
| c_Orderings_Obot__class_Obot(tc_fun(v_F,tc_HOL_Obool)) = X1 )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2870,f4784]) ).
fof(f2870,plain,
! [X2,X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X0),tc_HOL_Obool)) = X1
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != c_Relation_ODomain(X2,X0,X1) ),
inference(cnf_transformation,[],[f2093]) ).
fof(f2093,plain,
! [X0,X1,X2] :
( ( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X0),tc_HOL_Obool)) = X1
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != c_Relation_ODomain(X2,X0,X1) )
& ( c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) = c_Relation_ODomain(X2,X0,X1)
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X2,X0),tc_HOL_Obool)) != X1 ) ),
inference(rectify,[],[f2092]) ).
fof(f2092,plain,
! [X1,X2,X0] :
( ( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_HOL_Obool)) = X2
| c_Relation_ODomain(X0,X1,X2) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) )
& ( c_Relation_ODomain(X0,X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_HOL_Obool)) != X2 ) ),
inference(nnf_transformation,[],[f888]) ).
fof(f888,plain,
! [X1,X2,X0] :
( c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X0,X1),tc_HOL_Obool)) = X2
<=> c_Relation_ODomain(X0,X1,X2) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) ),
inference(rectify,[],[f449]) ).
fof(f449,axiom,
! [X8,X16,X19] :
( c_Relation_ODomain(X8,X16,X19) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))
<=> c_Orderings_Obot__class_Obot(tc_fun(tc_prod(X8,X16),tc_HOL_Obool)) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).
fof(f8539,plain,
( spl85_76
| ~ spl85_16
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5784,f4474,f3178,f4802]) ).
fof(f5784,plain,
( hBOOL(v_F)
| ~ spl85_16
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3716,f4784]) ).
fof(f8535,plain,
( spl85_77
| ~ spl85_76
| ~ spl85_26
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8534,f4474,f3229,f4802,f6128]) ).
fof(f8534,plain,
( ! [X6,X7,X5] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X6,X7,v_F,X5) )
| ~ spl85_26
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5039,f4784]) ).
fof(f5039,plain,
( ! [X6,X7,X4,X5] :
( c_Predicate_ORangeP(X6,X7,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),X4),X5)
| ~ hBOOL(v_F) )
| ~ spl85_26
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4346,f4784]) ).
fof(f4346,plain,
( ! [X6,X7,X4,X5] :
( c_Predicate_ORangeP(X6,X7,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),X4),X5)
| ~ hBOOL(hAPP(X4,X5)) )
| ~ spl85_26 ),
inference(superposition,[],[f2173,f3829]) ).
fof(f8533,plain,
( spl85_132
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8532,f4474,f8392]) ).
fof(f8392,plain,
( spl85_132
<=> ! [X1,X3] :
( c_Orderings_Oord__class_Oless__eq(v_F,X3,v_F)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_132])]) ).
fof(f8532,plain,
( ! [X3,X1] :
( c_Orderings_Oord__class_Oless__eq(v_F,X3,v_F)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,X3,X1) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8531,f4784]) ).
fof(f8531,plain,
( ! [X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(v_F,X3,X1)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8530,f4784]) ).
fof(f8530,plain,
( ! [X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,v_F),X3,X1)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6021,f4784]) ).
fof(f6021,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,c_Set_Oinsert(X0,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,v_F),X3,X1) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2321,f4784]) ).
fof(f2321,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,X1)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,c_Set_Oinsert(X0,X2,X1)) ),
inference(cnf_transformation,[],[f1625]) ).
fof(f1625,plain,
! [X0,X1,X2,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,c_Set_Oinsert(X0,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,X1) ),
inference(rectify,[],[f1137]) ).
fof(f1137,plain,
! [X2,X1,X0,X3] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X3,c_Set_Oinsert(X2,X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X3,X1) ),
inference(ennf_transformation,[],[f1004]) ).
fof(f1004,plain,
! [X3,X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X3,X1)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X3,c_Set_Oinsert(X2,X0,X1)) ),
inference(rectify,[],[f291]) ).
fof(f291,axiom,
! [X23,X9,X8,X10] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),X10,X9)
=> c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),X10,c_Set_Oinsert(X8,X23,X9)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
fof(f8529,plain,
( spl85_77
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5948,f4474,f6128]) ).
fof(f5948,plain,
( ! [X0,X1,X6] : c_Predicate_ORangeP(X0,X1,v_F,X6)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4297,f4784]) ).
fof(f8526,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8525,f4474,f4802]) ).
fof(f8525,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8524]) ).
fof(f8524,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8523,f4784]) ).
fof(f8523,plain,
( ! [X10,X11,X8,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(X7),sK57(X8,X9,X7,X10,X11)),X9))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f8522]) ).
fof(f8522,plain,
( ! [X10,X11,X8,X9,X7] :
( v_F != v_F
| hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(X7),sK57(X8,X9,X7,X10,X11)),X9)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8521,f4784]) ).
fof(f8521,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( v_F != hAPP(X6,sK72(X7,X8,X6,X9))
| hBOOL(hAPP(hAPP(c_member(X7),sK57(X8,X9,X7,X10,X11)),X9))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5205,f4784]) ).
fof(f5205,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,X10)),X6),c_FuncSet_OPi(X7,X10,X9,X11)))
| hBOOL(hAPP(hAPP(c_member(X7),sK57(X8,X9,X7,X10,X11)),X9))
| v_F != hAPP(X6,sK72(X7,X8,X6,X9)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3605,f4784]) ).
fof(f8519,plain,
( ~ spl85_76
| spl85_77
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8518,f4474,f6128,f4802]) ).
fof(f8518,plain,
( ! [X106,X107,X105] :
( c_Predicate_ORangeP(X106,X107,v_F,X105)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5051,f4784]) ).
fof(f5051,plain,
( ! [X101,X106,X107,X104,X102,X105,X103,X100] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X106,X107,c_Fun_Ofun__upd(X100,X101,X102,X103,X104),X105) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4361,f4784]) ).
fof(f4361,plain,
! [X101,X106,X107,X104,X102,X105,X103,X100] :
( ~ hBOOL(hAPP(X104,X105))
| c_Predicate_ORangeP(X106,X107,c_Fun_Ofun__upd(X100,X101,X102,X103,X104),X105) ),
inference(superposition,[],[f2173,f3082]) ).
fof(f8509,plain,
( ~ spl85_76
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8508,f4474,f4223,f4802]) ).
fof(f8508,plain,
( ! [X2,X4] :
( X2 = X4
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8507]) ).
fof(f8507,plain,
( ! [X2,X4] :
( X2 = X4
| ~ hBOOL(v_F)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8506,f4784]) ).
fof(f8506,plain,
( ! [X2,X0,X4] :
( X2 = X4
| ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5235,f4784]) ).
fof(f5235,plain,
( ! [X2,X0,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X0),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X0,X2,X4)))
| X2 = X4 )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2997,f4784]) ).
fof(f8504,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8503,f4474,f4802]) ).
fof(f8503,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8502]) ).
fof(f8502,plain,
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8501,f4784]) ).
fof(f8501,plain,
( ! [X6,X5] :
( ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X6)))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5313,f4784]) ).
fof(f5313,plain,
( ! [X6,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_fequal,v_F)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X5)),hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X5),X6)))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3621,f4784]) ).
fof(f8497,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8496,f4474,f4802]) ).
fof(f8496,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8495]) ).
fof(f8495,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5234,f4784]) ).
fof(f5234,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_OPi(X0,X2,X1,X3)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3476,f4784]) ).
fof(f8477,plain,
( spl85_77
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8476,f4474,f4802,f6128]) ).
fof(f8476,plain,
( ! [X2,X3,X0] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X2,X0,v_F,X3) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5556,f4784]) ).
fof(f5556,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X0),X3),c_Relation_ORange(X2,X0,X1)))
| c_Predicate_ORangeP(X2,X0,v_F,X3) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2287,f4784]) ).
fof(f8475,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8474,f4474,f4802]) ).
fof(f8474,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8473]) ).
fof(f8473,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5175,f4784]) ).
fof(f5175,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X3)),X1),c_FuncSet_OPi(X0,X3,X2,X4))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3469,f4784]) ).
fof(f8471,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8470,f4474,f4802]) ).
fof(f8470,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8469]) ).
fof(f8469,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8468,f4784]) ).
fof(f8468,plain,
( ! [X14,X17,X15,X12] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(X12),sK72(X12,X14,X17,X15)),X15)) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8467]) ).
fof(f8467,plain,
( ! [X14,X17,X15,X12] :
( hBOOL(v_F)
| hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(X12),sK72(X12,X14,X17,X15)),X15)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5693,f4784]) ).
fof(f5693,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16))))
| hBOOL(hAPP(hAPP(c_member(X12),sK72(X12,X14,X17,X15)),X15))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3599,f4784]) ).
fof(f8466,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5240,f4474,f4802]) ).
fof(f5240,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3075,f4784]) ).
fof(f8465,plain,
( spl85_76
| ~ spl85_34
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5880,f4474,f3290,f4802]) ).
fof(f5880,plain,
( hBOOL(v_F)
| ~ spl85_34
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3314,f4784]) ).
fof(f8463,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8462,f4474,f4802]) ).
fof(f8462,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8461]) ).
fof(f8461,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5690,f4784]) ).
fof(f5690,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(v_F)
| hBOOL(hAPP(c_FuncSet_OPi(X0,X1,X3,c_COMBK(tc_fun(X1,tc_HOL_Obool),X0,X4)),X2)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3491,f4784]) ).
fof(f8444,plain,
( spl85_76
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8443,f4474,f4223,f4802]) ).
fof(f8443,plain,
( ! [X3,X1] :
( X1 = X3
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5303,f4784]) ).
fof(f5303,plain,
( ! [X2,X3,X1] :
( X1 = X3
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Omktop(X2,X3))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3097,f4784]) ).
fof(f8434,plain,
( ~ spl85_117
| spl85_65
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8433,f4474,f4431,f7618]) ).
fof(f7618,plain,
( spl85_117
<=> v_F = c_Orderings_Obot__class_Obot(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_117])]) ).
fof(f8433,plain,
( v_F != c_Orderings_Obot__class_Obot(v_F)
| spl85_65
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8432,f4784]) ).
fof(f8432,plain,
( v_F != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(v_F,v_F),tc_HOL_Obool)),tc_fun(tc_prod(v_F,v_F),tc_HOL_Obool)),tc_HOL_Obool))
| spl85_65
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5982,f4784]) ).
fof(f5982,plain,
( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(v_F,v_F),tc_HOL_Obool)),tc_fun(tc_prod(v_F,v_F),tc_HOL_Obool)),tc_HOL_Obool)) != c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(v_F,v_F),tc_HOL_Obool)),tc_fun(tc_prod(v_F,v_F),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(v_F,v_F),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(v_F,v_F),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))
| spl85_65
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4432,f4784]) ).
fof(f8431,plain,
( spl85_84
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8430,f4474,f4802,f6422]) ).
fof(f8430,plain,
( ! [X6,X5] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X6,X5) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8429]) ).
fof(f8429,plain,
( ! [X6,X5] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X6,X5)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5840,f4784]) ).
fof(f5840,plain,
( ! [X6,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK57(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X6,X5)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3948,f4784]) ).
fof(f8428,plain,
( spl85_133
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8424,f4474,f4802,f8426]) ).
fof(f8426,plain,
( spl85_133
<=> ! [X2,X0,X1] : ~ c_Predicate_ODomainP(X2,X1,v_F,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_133])]) ).
fof(f8424,plain,
( ! [X2,X0,X1] :
( hBOOL(v_F)
| ~ c_Predicate_ODomainP(X2,X1,v_F,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5561,f4784]) ).
fof(f5561,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Predicate_ODomainP(X2,X1,v_F,X0)
| hBOOL(hAPP(hAPP(c_member(X2),X0),c_Relation_ODomain(X2,X1,X3))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2594,f4784]) ).
fof(f8423,plain,
( spl85_58
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8422,f4474,f4802,f4223]) ).
fof(f8422,plain,
( ! [X3,X1] :
( ~ hBOOL(v_F)
| X1 = X3 )
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f8421]) ).
fof(f8421,plain,
( ! [X3,X1] :
( X1 = X3
| ~ hBOOL(v_F)
| v_F != v_F )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8420,f4784]) ).
fof(f8420,plain,
( ! [X2,X3,X0,X1,X4] :
( X1 = X3
| ~ hBOOL(v_F)
| v_F != c_Product__Type_OSigma(X0,X4,X3,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5457,f4784]) ).
fof(f5457,plain,
( ! [X2,X3,X0,X1,X4] :
( X1 = X3
| ~ hBOOL(v_F)
| c_Product__Type_OSigma(X0,X4,X3,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)) != c_Product__Type_OSigma(X0,X4,X1,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2625,f4784]) ).
fof(f8419,plain,
( spl85_78
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8418,f4474,f4802,f6145]) ).
fof(f8418,plain,
( ! [X56] :
( ~ hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(v_F,X56) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8417,f4784]) ).
fof(f8417,plain,
( ! [X56,X55] :
( ~ hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool))),X56) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8416]) ).
fof(f8416,plain,
( ! [X56,X55] :
( ~ hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool))),X56)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5898,f4784]) ).
fof(f5898,plain,
( ! [X56,X55] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X56,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool))))),sK21(X56,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool)))))),sK20(X56,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool))))))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X55,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X55,tc_HOL_Obool))),X56)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4127,f4784]) ).
fof(f8415,plain,
( ~ spl85_76
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8414,f4474,f4223,f4802]) ).
fof(f8414,plain,
( ! [X2,X0] :
( X0 = X2
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8413]) ).
fof(f8413,plain,
( ! [X2,X0] :
( X0 = X2
| ~ hBOOL(v_F)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8412,f4784]) ).
fof(f8412,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2)))
| X0 = X2
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5238,f4784]) ).
fof(f5238,plain,
( ! [X2,X0,X1] :
( X0 = X2
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,X1),X0),X2))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3055,f4784]) ).
fof(f8407,plain,
( spl85_87
| ~ spl85_23
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8406,f4474,f3213,f6484]) ).
fof(f8406,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(v_F,X1,v_F)
| ~ spl85_23
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8405,f4784]) ).
fof(f8405,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,v_F)
| ~ spl85_23
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5749,f4784]) ).
fof(f5749,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(v_F,X1))
| ~ spl85_23
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4039,f4784]) ).
fof(f4039,plain,
( ! [X2,X3,X1,X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X1,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat)),X2),X1))
| ~ spl85_23 ),
inference(superposition,[],[f4035,f2728]) ).
fof(f4035,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X0),X1))
| ~ spl85_23 ),
inference(resolution,[],[f2409,f3215]) ).
fof(f2409,plain,
! [X2,X0,X1] :
( ~ class_Lattices_Osemilattice__sup(X0)
| c_Orderings_Oord__class_Oless__eq(X0,X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X0),X1),X2)) ),
inference(cnf_transformation,[],[f1693]) ).
fof(f1693,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X0,X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X0),X1),X2))
| ~ class_Lattices_Osemilattice__sup(X0) ),
inference(rectify,[],[f1049]) ).
fof(f1049,plain,
! [X2,X1,X0] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X0))
| ~ class_Lattices_Osemilattice__sup(X2) ),
inference(ennf_transformation,[],[f767]) ).
fof(f767,plain,
! [X1,X0,X2] :
( class_Lattices_Osemilattice__sup(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X1),X0)) ),
inference(rectify,[],[f395]) ).
fof(f395,axiom,
! [X50,X49,X8] :
( class_Lattices_Osemilattice__sup(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,X49,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X49),X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge1) ).
fof(f8404,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5892,f4474,f4802]) ).
fof(f5892,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4783,f4784]) ).
fof(f4783,plain,
( ! [X31,X32,X30,X33] : hBOOL(hAPP(hAPP(c_member(tc_fun(X30,X31)),X32),c_FuncSet_OPi(X30,X31,X33,c_COMBK(tc_fun(X31,tc_HOL_Obool),X30,v_F))))
| ~ spl85_69 ),
inference(resolution,[],[f4770,f2718]) ).
fof(f8403,plain,
( spl85_61
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5804,f4474,f4802,f4384]) ).
fof(f5804,plain,
( ! [X23] :
( hBOOL(v_F)
| ~ hBOOL(X23) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4085,f4784]) ).
fof(f8402,plain,
( spl85_76
| ~ spl85_10
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5854,f4474,f3145,f4802]) ).
fof(f5854,plain,
( hBOOL(v_F)
| ~ spl85_10
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3147,f4784]) ).
fof(f8401,plain,
( ~ spl85_82
| spl85_108
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8400,f4474,f4802,f7331,f6214]) ).
fof(f8400,plain,
( ! [X1,X5] :
( ~ hBOOL(v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,X1,X5)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8399,f4784]) ).
fof(f8399,plain,
( ! [X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(v_F,X1,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X4),tc_HOL_Obool),v_F,v_F)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8398,f4784]) ).
fof(f8398,plain,
( ! [X2,X0,X1,X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X4),tc_HOL_Obool),c_Product__Type_OSigma(X0,X4,X1,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)),v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,X1,X5)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8397,f4784]) ).
fof(f8397,plain,
( ! [X2,X0,X1,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X4),tc_HOL_Obool),c_Product__Type_OSigma(X0,X4,X1,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)),v_F)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5454,f4784]) ).
fof(f5454,plain,
( ! [X2,X0,X1,X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X4),tc_HOL_Obool),c_Product__Type_OSigma(X0,X4,X1,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)),c_Product__Type_OSigma(X0,X4,X5,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1,X5)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2570,f4784]) ).
fof(f2570,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X4),tc_HOL_Obool),c_Product__Type_OSigma(X0,X4,X1,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)),c_Product__Type_OSigma(X0,X4,X5,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)))
| ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X2))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1,X5) ),
inference(cnf_transformation,[],[f1835]) ).
fof(f1835,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(X4),X3),X2))
| ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X4),tc_HOL_Obool),c_Product__Type_OSigma(X0,X4,X1,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)),c_Product__Type_OSigma(X0,X4,X5,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2))) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X4),tc_HOL_Obool),c_Product__Type_OSigma(X0,X4,X1,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)),c_Product__Type_OSigma(X0,X4,X5,c_COMBK(tc_fun(X4,tc_HOL_Obool),X0,X2)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1,X5) ) ) ),
inference(rectify,[],[f1834]) ).
fof(f1834,plain,
! [X0,X4,X5,X3,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
| ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X4,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),c_Product__Type_OSigma(X0,X1,X4,c_COMBK(tc_fun(X1,tc_HOL_Obool),X0,X5)),c_Product__Type_OSigma(X0,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X0,X5))) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),c_Product__Type_OSigma(X0,X1,X4,c_COMBK(tc_fun(X1,tc_HOL_Obool),X0,X5)),c_Product__Type_OSigma(X0,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X0,X5)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X4,X2) ) ) ),
inference(nnf_transformation,[],[f1226]) ).
fof(f1226,plain,
! [X0,X4,X5,X3,X1,X2] :
( ~ hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
| ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X4,X2)
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),c_Product__Type_OSigma(X0,X1,X4,c_COMBK(tc_fun(X1,tc_HOL_Obool),X0,X5)),c_Product__Type_OSigma(X0,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X0,X5))) ) ),
inference(ennf_transformation,[],[f591]) ).
fof(f591,plain,
! [X4,X3,X2,X5,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),X3),X5))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X4,X2)
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),c_Product__Type_OSigma(X0,X1,X4,c_COMBK(tc_fun(X1,tc_HOL_Obool),X0,X5)),c_Product__Type_OSigma(X0,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X0,X5))) ) ),
inference(rectify,[],[f322]) ).
fof(f322,axiom,
! [X16,X8,X9,X14,X10,X47] :
( hBOOL(hAPP(hAPP(c_member(X8),X14),X47))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X16,X8),tc_HOL_Obool),c_Product__Type_OSigma(X16,X8,X10,c_COMBK(tc_fun(X8,tc_HOL_Obool),X16,X47)),c_Product__Type_OSigma(X16,X8,X9,c_COMBK(tc_fun(X8,tc_HOL_Obool),X16,X47)))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X16,tc_HOL_Obool),X10,X9) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Times__subset__cancel2) ).
fof(f8394,plain,
( spl85_76
| spl85_132
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8390,f4474,f8392,f4802]) ).
fof(f8390,plain,
( ! [X3,X1] :
( c_Orderings_Oord__class_Oless__eq(v_F,X3,v_F)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,X3,X1)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8389,f4784]) ).
fof(f8389,plain,
( ! [X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,X1)
| hBOOL(v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,X3,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8388,f4784]) ).
fof(f8388,plain,
( ! [X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,v_F)
| hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,X1) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5435,f4784]) ).
fof(f5435,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(v_F)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,c_Set_Oinsert(X0,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,X1) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2247,f4784]) ).
fof(f2247,plain,
! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),X2),X3))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,c_Set_Oinsert(X0,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,X1) ),
inference(cnf_transformation,[],[f1568]) ).
fof(f1568,plain,
! [X0,X1,X2,X3] :
( hBOOL(hAPP(hAPP(c_member(X0),X2),X3))
| ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,c_Set_Oinsert(X0,X2,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,c_Set_Oinsert(X0,X2,X1)) ) ) ),
inference(rectify,[],[f1567]) ).
fof(f1567,plain,
! [X0,X3,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
| ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,c_Set_Oinsert(X0,X1,X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,X3) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,c_Set_Oinsert(X0,X1,X3)) ) ) ),
inference(nnf_transformation,[],[f1450]) ).
fof(f1450,plain,
! [X0,X3,X1,X2] :
( hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
| ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,c_Set_Oinsert(X0,X1,X3))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,X3) ) ),
inference(ennf_transformation,[],[f684]) ).
fof(f684,plain,
! [X1,X0,X2,X3] :
( ~ hBOOL(hAPP(hAPP(c_member(X0),X1),X2))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,c_Set_Oinsert(X0,X1,X3))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,X3) ) ),
inference(rectify,[],[f306]) ).
fof(f306,axiom,
! [X8,X14,X10,X9] :
( ~ hBOOL(hAPP(hAPP(c_member(X8),X14),X10))
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),X10,X9)
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),X10,c_Set_Oinsert(X8,X14,X9)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
fof(f8381,plain,
( spl85_87
| ~ spl85_26
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8380,f4474,f3229,f6484]) ).
fof(f8380,plain,
( ! [X2] : c_Orderings_Oord__class_Oless__eq(v_F,X2,v_F)
| ~ spl85_26
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5425,f4784]) ).
fof(f5425,plain,
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X2,v_F)
| ~ spl85_26
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4036,f4784]) ).
fof(f4036,plain,
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),X2),X3))
| ~ spl85_26 ),
inference(resolution,[],[f2409,f3231]) ).
fof(f8377,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5910,f4474,f4802]) ).
fof(f5910,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2968,f4784]) ).
fof(f8376,plain,
( spl85_76
| ~ spl85_25
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5812,f4474,f3223,f4802]) ).
fof(f5812,plain,
( hBOOL(v_F)
| ~ spl85_25
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3288,f4784]) ).
fof(f8373,plain,
( spl85_131
| ~ spl85_117
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8369,f4474,f7618,f8371]) ).
fof(f8369,plain,
( ! [X1] :
( v_F != c_Orderings_Obot__class_Obot(v_F)
| c_Orderings_Obot__class_Obot(v_F) = X1 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8368,f4784]) ).
fof(f8368,plain,
( ! [X0,X1] :
( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1
| v_F != c_Orderings_Obot__class_Obot(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5666,f4784]) ).
fof(f5666,plain,
( ! [X0,X1] :
( v_F != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1 )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2386,f4784]) ).
fof(f2386,plain,
! [X2,X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X1) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1 ),
inference(cnf_transformation,[],[f1675]) ).
fof(f1675,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X2
& c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1 )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X1) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != X2
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != X1 ) ),
inference(flattening,[],[f1674]) ).
fof(f1674,plain,
! [X0,X1,X2] :
( ( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X2
& c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1 )
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X1) != c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != X2
| c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) != X1 ) ),
inference(nnf_transformation,[],[f738]) ).
fof(f738,plain,
! [X0,X1,X2] :
( ( c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X2
& c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) = X1 )
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X1) = c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)) ),
inference(rectify,[],[f428]) ).
fof(f428,axiom,
! [X8,X9,X10] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X10),X9) = c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool))
<=> ( c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = X9
& c_Orderings_Obot__class_Obot(tc_fun(X8,tc_HOL_Obool)) = X10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty) ).
fof(f8364,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5792,f4474,f4802]) ).
fof(f5792,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3324,f4784]) ).
fof(f8361,plain,
( spl85_79
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8360,f4474,f6161]) ).
fof(f8360,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(v_F,v_F,X1)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8359,f4784]) ).
fof(f8359,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,v_F),v_F,X1)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6018,f4784]) ).
fof(f6018,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X0,v_F),c_Orderings_Obot__class_Obot(tc_fun(X0,v_F)),X1)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2260,f4784]) ).
fof(f8356,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8355,f4474,f4802]) ).
fof(f8355,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8354]) ).
fof(f8354,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8353,f4784]) ).
fof(f8353,plain,
( ! [X18,X19,X16,X14,X17,X15,X20] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X14,tc_fun(X15,X16))),X17),c_FuncSet_OPi(X14,tc_fun(X15,X16),X18,c_COMBK(tc_fun(tc_fun(X15,X16),tc_HOL_Obool),X14,c_FuncSet_OPi(X15,X16,X19,c_COMBK(tc_fun(X16,tc_HOL_Obool),X15,X20)))))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5194,f4784]) ).
fof(f5194,plain,
( ! [X18,X19,X16,X14,X17,X15,X20] :
( hBOOL(hAPP(hAPP(c_member(X15),sK65(X20,X16,X19,X15,v_F)),X19))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X14,tc_fun(X15,X16))),X17),c_FuncSet_OPi(X14,tc_fun(X15,X16),X18,c_COMBK(tc_fun(tc_fun(X15,X16),tc_HOL_Obool),X14,c_FuncSet_OPi(X15,X16,X19,c_COMBK(tc_fun(X16,tc_HOL_Obool),X15,X20)))))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3525,f4784]) ).
fof(f8345,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8344,f4474,f4802]) ).
fof(f8344,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5374,f4784]) ).
fof(f5374,plain,
( ! [X2,X0] : hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),v_F),c_Transitive__Closure_Ortrancl(X2,X0)))
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2771,f4784]) ).
fof(f8343,plain,
( spl85_93
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8342,f4474,f4802,f6593]) ).
fof(f6593,plain,
( spl85_93
<=> ! [X2,X3,X0,X5,X1] : c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_93])]) ).
fof(f8342,plain,
( ! [X3,X0,X1,X4,X5] :
( hBOOL(v_F)
| c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8341,f4784]) ).
fof(f8341,plain,
( ! [X3,X0,X1,X4,X5] :
( hBOOL(v_F)
| c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,hAPP(v_F,X5)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4911,f4784]) ).
fof(f4911,plain,
( ! [X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK48(X0,X1,X3,X4,X5,X6)),X5)),X3))
| c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,hAPP(v_F,X5)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3038,f4784]) ).
fof(f8338,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8337,f4474,f4802]) ).
fof(f8337,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8336]) ).
fof(f8336,plain,
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5433,f4784]) ).
fof(f5433,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X3),c_Groups_Ominus__class_Ominus(tc_fun(X2,tc_HOL_Obool),X1,X0)))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2237,f4784]) ).
fof(f8330,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8329,f4474,f4802]) ).
fof(f8329,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8328]) ).
fof(f8328,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8327,f4784]) ).
fof(f8327,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5382,f4784]) ).
fof(f5382,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),v_F),X2))
| hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2890,f4784]) ).
fof(f8325,plain,
( spl85_76
| ~ spl85_43
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8324,f4474,f3387,f4802]) ).
fof(f3387,plain,
( spl85_43
<=> hBOOL(sK33(c_fNot)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_43])]) ).
fof(f8324,plain,
( hBOOL(v_F)
| ~ spl85_43
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6087,f4784]) ).
fof(f6087,plain,
( hBOOL(sK33(v_F))
| ~ spl85_43
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3389,f4784]) ).
fof(f3389,plain,
( hBOOL(sK33(c_fNot))
| ~ spl85_43 ),
inference(avatar_component_clause,[],[f3387]) ).
fof(f8317,plain,
( spl85_76
| ~ spl85_40
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8316,f4474,f3371,f4802]) ).
fof(f8316,plain,
( hBOOL(v_F)
| ~ spl85_40
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5769,f4784]) ).
fof(f5769,plain,
( ! [X2] : hBOOL(hAPP(v_F,X2))
| ~ spl85_40
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3655,f4784]) ).
fof(f8315,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5626,f4474,f4802]) ).
fof(f5626,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3016,f4784]) ).
fof(f8300,plain,
( spl85_77
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8299,f4474,f4802,f6128]) ).
fof(f8299,plain,
( ! [X31,X29,X30] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X30,X31,v_F,X29) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8298,f4784]) ).
fof(f8298,plain,
( ! [X31,X28,X29,X30] :
( ~ hBOOL(hAPP(v_F,X28))
| c_Predicate_ORangeP(X30,X31,v_F,X29) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5052,f4784]) ).
fof(f5052,plain,
( ! [X31,X28,X29,X26,X27,X24,X25,X30] :
( c_Predicate_ORangeP(X30,X31,hAPP(c_COMBC(X24,X25,X26),X27),X29)
| ~ hBOOL(hAPP(v_F,X28)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4369,f4784]) ).
fof(f8297,plain,
( spl85_76
| ~ spl85_37
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5794,f4474,f3332,f4802]) ).
fof(f5794,plain,
( hBOOL(v_F)
| ~ spl85_37
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3962,f4784]) ).
fof(f8295,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8294,f4474,f4802]) ).
fof(f8294,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8293]) ).
fof(f8293,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5797,f4784]) ).
fof(f5797,plain,
( ! [X18,X19,X16,X17,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X16,X19)),X17),c_FuncSet_OPi(X16,X19,X18,X20)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3473,f4784]) ).
fof(f8290,plain,
( spl85_76
| ~ spl85_33
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5786,f4474,f3283,f4802]) ).
fof(f5786,plain,
( hBOOL(v_F)
| ~ spl85_33
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3563,f4784]) ).
fof(f8286,plain,
( spl85_76
| spl85_93
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8285,f4474,f6593,f4802]) ).
fof(f8285,plain,
( ! [X2,X0,X1,X4,X5] :
( c_Recdef_Owfrec__rel(X0,X1,X4,X5,X2,v_F)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8284,f4784]) ).
fof(f8284,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK61(X0,X1,X2,X3,X4,X5)),X2)),X4))
| c_Recdef_Owfrec__rel(X0,X1,X4,X5,X2,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4875,f4784]) ).
fof(f4875,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Recdef_Owfrec__rel(X0,X1,X4,X5,X2,hAPP(v_F,X2))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),hAPP(hAPP(c_Product__Type_OPair(X0,X0),sK61(X0,X1,X2,X3,X4,X5)),X2)),X4)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2684,f4784]) ).
fof(f8279,plain,
( spl85_92
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8278,f4474,f6565]) ).
fof(f8278,plain,
( ! [X2,X0,X1] : c_Relation_Osingle__valued(X0,X1,X2)
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f8277]) ).
fof(f8277,plain,
( ! [X2,X0,X1] :
( c_Relation_Osingle__valued(X0,X1,X2)
| v_F != v_F )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6108,f4784]) ).
fof(f6108,plain,
( ! [X2,X0,X1] :
( c_Relation_Osingle__valued(X0,X1,X2)
| v_F != sK70(X0,X1,X2) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2734,f4784]) ).
fof(f8276,plain,
( ~ spl85_76
| spl85_130
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8272,f4474,f8274,f4802]) ).
fof(f8274,plain,
( spl85_130
<=> ! [X3,X4,X9,X0,X5,X2,X1] :
( ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,X2)
| c_Recdef_Owfrec__rel(X0,X4,X3,X1,X9,v_F) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_130])]) ).
fof(f8272,plain,
( ! [X2,X3,X0,X1,X9,X4,X5] :
( ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,X2)
| c_Recdef_Owfrec__rel(X0,X4,X3,X1,X9,v_F)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8271,f4784]) ).
fof(f8271,plain,
( ! [X2,X3,X0,X1,X9,X4,X5] :
( ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,X2)
| c_Recdef_Owfrec__rel(X0,X4,X3,X1,X9,hAPP(sK49(X0,X1,X2,X3,X4,X5),X9))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5527,f4784]) ).
fof(f5527,plain,
( ! [X2,X3,X0,X1,X9,X4,X5] :
( ~ c_Recdef_Owfrec__rel(X0,X4,X3,X1,X5,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X0)),v_F),X3))
| c_Recdef_Owfrec__rel(X0,X4,X3,X1,X9,hAPP(sK49(X0,X1,X2,X3,X4,X5),X9)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2608,f4784]) ).
fof(f8259,plain,
( spl85_76
| ~ spl85_16
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8258,f4474,f3178,f4802]) ).
fof(f8258,plain,
( hBOOL(v_F)
| ~ spl85_16
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8257]) ).
fof(f8257,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_16
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5867,f4784]) ).
fof(f5867,plain,
( ! [X18] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| hBOOL(v_F) )
| ~ spl85_16
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3600,f4784]) ).
fof(f8242,plain,
( spl85_84
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8241,f4474,f4802,f6422]) ).
fof(f8241,plain,
( ! [X3,X4] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X4,X3) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8240]) ).
fof(f8240,plain,
( ! [X3,X4] :
( hBOOL(v_F)
| hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X4,X3) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5841,f4784]) ).
fof(f5841,plain,
( ! [X3,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK83(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin),X4)),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X4,X3) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3947,f4784]) ).
fof(f8237,plain,
( ~ spl85_76
| spl85_77
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8236,f4474,f6128,f4802]) ).
fof(f8236,plain,
( ! [X72,X73,X74] :
( c_Predicate_ORangeP(X73,X74,v_F,X72)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8235,f4784]) ).
fof(f8235,plain,
( ! [X72,X70,X73,X68,X69,X67,X74] :
( c_Predicate_ORangeP(X73,X74,hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X67,X68),tc_HOL_Obool)),c_Product__Type_OSigma(X67,X68,X69,X70)),X72)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5728,f4784]) ).
fof(f5728,plain,
( ! [X72,X70,X73,X68,X69,X67,X74] :
( ~ hBOOL(hAPP(c_Product__Type_OSigma(X67,X68,X69,v_F),X72))
| c_Predicate_ORangeP(X73,X74,hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X67,X68),tc_HOL_Obool)),c_Product__Type_OSigma(X67,X68,X69,X70)),X72) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4356,f4784]) ).
fof(f8227,plain,
( spl85_76
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8226,f4474,f4223,f4802]) ).
fof(f8226,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5304,f4784]) ).
fof(f5304,plain,
( ! [X0,X1] :
( hBOOL(hAPP(sK84(X0,X1),v_F))
| X0 = X1 )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3462,f4784]) ).
fof(f8225,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8224,f4474,f4802]) ).
fof(f8224,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8223]) ).
fof(f8223,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8222,f4784]) ).
fof(f8222,plain,
( ! [X31,X28,X27,X34,X32,X30,X33] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34))) )
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f8221]) ).
fof(f8221,plain,
( ! [X31,X28,X27,X34,X32,X30,X33] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34)))
| v_F != v_F )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8220,f4784]) ).
fof(f8220,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(v_F)
| v_F != hAPP(sK57(X32,c_FuncSet_OPi(X27,X28,X30,X31),tc_fun(X27,X28),X33,X34),sK72(X27,X29,sK57(X32,c_FuncSet_OPi(X27,X28,X30,X31),tc_fun(X27,X28),X33,X34),X30))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5219,f4784]) ).
fof(f5219,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X27,X28)),X29),c_FuncSet_OPi(X27,X28,X30,X31)))
| v_F != hAPP(sK57(X32,c_FuncSet_OPi(X27,X28,X30,X31),tc_fun(X27,X28),X33,X34),sK72(X27,X29,sK57(X32,c_FuncSet_OPi(X27,X28,X30,X31),tc_fun(X27,X28),X33,X34),X30))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3616,f4784]) ).
fof(f8212,plain,
( spl85_89
| ~ spl85_31
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6096,f4474,f3268,f6499]) ).
fof(f6499,plain,
( spl85_89
<=> class_Orderings_Obot(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_89])]) ).
fof(f6096,plain,
( class_Orderings_Obot(v_F)
| ~ spl85_31
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3270,f4784]) ).
fof(f8208,plain,
( spl85_76
| spl85_78
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8207,f4474,f6145,f4802]) ).
fof(f8207,plain,
( ! [X11] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X11)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8206,f4784]) ).
fof(f8206,plain,
( ! [X11,X14,X12,X13] :
( c_Arrow__Order__Mirabelle_Odictator(sK57(X12,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,X14),X11)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8205]) ).
fof(f8205,plain,
( ! [X11,X14,X12,X13] :
( c_Arrow__Order__Mirabelle_Odictator(sK57(X12,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,X14),X11)
| hBOOL(v_F)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5862,f4784]) ).
fof(f5862,plain,
( ! [X11,X14,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13)),X12),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X14)))
| hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(sK57(X12,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X13,X14),X11) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3870,f4784]) ).
fof(f8189,plain,
( ~ spl85_76
| spl85_77
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8188,f4474,f6128,f4802]) ).
fof(f8188,plain,
( ! [X98,X99,X97] :
( c_Predicate_ORangeP(X98,X99,v_F,X97)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5050,f4784]) ).
fof(f5050,plain,
( ! [X98,X99,X97,X95] :
( c_Predicate_ORangeP(X98,X99,c_COMBI(X95),X97)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4360,f4784]) ).
fof(f4360,plain,
! [X98,X99,X96,X97,X95] :
( ~ hBOOL(hAPP(X96,X97))
| c_Predicate_ORangeP(X98,X99,c_COMBI(X95),X97) ),
inference(superposition,[],[f2173,f2523]) ).
fof(f8187,plain,
( spl85_79
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8186,f4474,f6161]) ).
fof(f8186,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(v_F,v_F,X1)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8185,f4784]) ).
fof(f8185,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(v_F,tc_HOL_Obool),v_F,X1)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6003,f4784]) ).
fof(f6003,plain,
( ! [X2,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(v_F,tc_HOL_Obool),c_Relation_OId__on(X2,c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))),X1)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3239,f4784]) ).
fof(f8180,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8179,f4474,f4802]) ).
fof(f8179,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8178]) ).
fof(f8178,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8177,f4784]) ).
fof(f8177,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X16)),X17),c_FuncSet_OPi(X12,X16,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X13),X14),c_COMBK(tc_fun(X16,tc_HOL_Obool),X12,X15))))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5406,f4784]) ).
fof(f5406,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),v_F),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X14)),sK65(X15,X16,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X13),X14),X12,X17)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X16)),X17),c_FuncSet_OPi(X12,X16,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X12,tc_HOL_Obool)),X13),X14),c_COMBK(tc_fun(X16,tc_HOL_Obool),X12,X15)))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3658,f4784]) ).
fof(f8171,plain,
( spl85_78
| ~ spl85_76
| ~ spl85_40
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8170,f4474,f3371,f4802,f6145]) ).
fof(f8170,plain,
( ! [X12] :
( ~ hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(v_F,X12) )
| ~ spl85_40
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5899,f4784]) ).
fof(f5899,plain,
( ! [X10,X11,X12] :
( ~ hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(c_Product__Type_OPair(X10,X11),X12) )
| ~ spl85_40
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4236,f4784]) ).
fof(f8165,plain,
( spl85_61
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5883,f4474,f4802,f4384]) ).
fof(f5883,plain,
( ! [X2] :
( hBOOL(v_F)
| ~ hBOOL(X2) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3315,f4784]) ).
fof(f8162,plain,
( spl85_61
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5801,f4474,f4802,f4384]) ).
fof(f5801,plain,
( ! [X10] :
( hBOOL(v_F)
| ~ hBOOL(X10) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3875,f4784]) ).
fof(f8154,plain,
( spl85_91
| spl85_129
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6066,f4474,f8152,f6557]) ).
fof(f6557,plain,
( spl85_91
<=> class_Lattices_Odistrib__lattice(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_91])]) ).
fof(f6066,plain,
( ! [X1] :
( ~ class_Lattices_Odistrib__lattice(X1)
| class_Lattices_Odistrib__lattice(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2561,f4784]) ).
fof(f8145,plain,
( spl85_105
| ~ spl85_12
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6041,f4474,f3155,f7090]) ).
fof(f7090,plain,
( spl85_105
<=> class_Lattices_Osemilattice__inf(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_105])]) ).
fof(f6041,plain,
( class_Lattices_Osemilattice__inf(v_F)
| ~ spl85_12
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3157,f4784]) ).
fof(f8142,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5974,f4474,f4802]) ).
fof(f5974,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4476,f4784]) ).
fof(f8141,plain,
( ~ spl85_76
| spl85_52
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5878,f4474,f3625,f4802]) ).
fof(f5878,plain,
( ~ hBOOL(v_F)
| spl85_52
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3627,f4784]) ).
fof(f8140,plain,
( spl85_127
| spl85_128
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6061,f4474,f8137,f8134]) ).
fof(f6061,plain,
( ! [X0] :
( class_Lattices_Obounded__lattice(v_F)
| ~ class_Lattices_Obounded__lattice(X0) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2382,f4784]) ).
fof(f8131,plain,
( spl85_76
| spl85_78
| ~ spl85_16
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5843,f4474,f3178,f6145,f4802]) ).
fof(f5843,plain,
( ! [X0] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X0)
| hBOOL(v_F) )
| ~ spl85_16
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3945,f4784]) ).
fof(f8124,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8123,f4474,f4802]) ).
fof(f8123,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8122]) ).
fof(f8122,plain,
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8121,f4784]) ).
fof(f8121,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_COMBI(X2)))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8120]) ).
fof(f8120,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_COMBI(X2)))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5345,f4784]) ).
fof(f5345,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_COMBI(X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_COMBI(X2))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3872,f4784]) ).
fof(f8119,plain,
( spl85_87
| ~ spl85_26
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8118,f4474,f3229,f6484]) ).
fof(f8118,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(v_F,X1,v_F)
| ~ spl85_26
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8117,f4784]) ).
fof(f8117,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X1,v_F)
| ~ spl85_26
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5750,f4784]) ).
fof(f5750,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X1,hAPP(v_F,X1))
| ~ spl85_26
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4061,f4784]) ).
fof(f4061,plain,
( ! [X2,X3,X1,X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X1,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool)),X2),X1))
| ~ spl85_26 ),
inference(superposition,[],[f4036,f2728]) ).
fof(f8116,plain,
( spl85_80
| spl85_106
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6065,f4474,f7195,f6164]) ).
fof(f7195,plain,
( spl85_106
<=> class_Lattices_Osemilattice__sup(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_106])]) ).
fof(f6065,plain,
( ! [X0] :
( class_Lattices_Osemilattice__sup(v_F)
| ~ class_Lattices_Olattice(X0) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2551,f4784]) ).
fof(f8112,plain,
( spl85_100
| ~ spl85_5
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6090,f4474,f3120,f6981]) ).
fof(f6981,plain,
( spl85_100
<=> class_Orderings_Oorder(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_100])]) ).
fof(f3120,plain,
( spl85_5
<=> class_Orderings_Oorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_5])]) ).
fof(f6090,plain,
( class_Orderings_Oorder(v_F)
| ~ spl85_5
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3122,f4784]) ).
fof(f3122,plain,
( class_Orderings_Oorder(tc_Nat_Onat)
| ~ spl85_5 ),
inference(avatar_component_clause,[],[f3120]) ).
fof(f8109,plain,
( ~ spl85_76
| spl85_48
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5826,f4474,f3445,f4802]) ).
fof(f5826,plain,
( ~ hBOOL(v_F)
| spl85_48
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3446,f4784]) ).
fof(f8108,plain,
( ~ spl85_76
| spl85_49
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5825,f4474,f3450,f4802]) ).
fof(f5825,plain,
( ~ hBOOL(v_F)
| spl85_49
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3451,f4784]) ).
fof(f8078,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8077,f4474,f4802]) ).
fof(f8077,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8076]) ).
fof(f8076,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5259,f4784]) ).
fof(f5259,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(v_F)
| hBOOL(hAPP(c_FuncSet_OPi(X0,X1,X3,X4),X2)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3474,f4784]) ).
fof(f8073,plain,
( spl85_76
| spl85_126
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8069,f4474,f8071,f4802]) ).
fof(f8071,plain,
( spl85_126
<=> ! [X2,X3] :
( ~ c_Wellfounded_Oacyclic(X2,X3)
| c_Wellfounded_Oacyclic(X2,v_F) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_126])]) ).
fof(f8069,plain,
( ! [X2,X3] :
( ~ c_Wellfounded_Oacyclic(X2,X3)
| hBOOL(v_F)
| c_Wellfounded_Oacyclic(X2,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8068,f4784]) ).
fof(f8068,plain,
( ! [X2,X3,X0,X1] :
( c_Wellfounded_Oacyclic(X2,v_F)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X0)),c_Transitive__Closure_Ortrancl(X2,X3)))
| ~ c_Wellfounded_Oacyclic(X2,X3) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5518,f4784]) ).
fof(f5518,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Oacyclic(X2,X3)
| c_Wellfounded_Oacyclic(X2,c_Set_Oinsert(tc_prod(X2,X2),v_F,X3))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X1),X0)),c_Transitive__Closure_Ortrancl(X2,X3))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2413,f4784]) ).
fof(f8040,plain,
( spl85_92
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8039,f4474,f6565]) ).
fof(f8039,plain,
( ! [X2,X0,X1] : c_Relation_Osingle__valued(X0,X1,X2)
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f8038]) ).
fof(f8038,plain,
( ! [X2,X0,X1] :
( v_F != v_F
| c_Relation_Osingle__valued(X0,X1,X2) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6107,f4784]) ).
fof(f6107,plain,
( ! [X2,X0,X1] :
( c_Relation_Osingle__valued(X0,X1,X2)
| v_F != sK52(X0,X1,X2) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2619,f4784]) ).
fof(f8037,plain,
( spl85_79
| ~ spl85_29
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8036,f4474,f3254,f6161]) ).
fof(f3254,plain,
( spl85_29
<=> class_Lattices_Olattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_29])]) ).
fof(f8036,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(v_F,v_F,X0)
| ~ spl85_29
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5421,f4784]) ).
fof(f5421,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,X0)
| ~ spl85_29
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3994,f4784]) ).
fof(f3994,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X0),X1),X0)
| ~ spl85_29 ),
inference(resolution,[],[f2330,f3256]) ).
fof(f3256,plain,
( class_Lattices_Olattice(tc_Nat_Onat)
| ~ spl85_29 ),
inference(avatar_component_clause,[],[f3254]) ).
fof(f8034,plain,
( spl85_111
| spl85_80
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6064,f4474,f6164,f7414]) ).
fof(f6064,plain,
( ! [X1] :
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Olattice(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2477,f4784]) ).
fof(f8033,plain,
( spl85_116
| ~ spl85_20
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6044,f4474,f3198,f7576]) ).
fof(f7576,plain,
( spl85_116
<=> class_Orderings_Oord(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_116])]) ).
fof(f3198,plain,
( spl85_20
<=> class_Orderings_Oord(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_20])]) ).
fof(f6044,plain,
( class_Orderings_Oord(v_F)
| ~ spl85_20
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3200,f4784]) ).
fof(f3200,plain,
( class_Orderings_Oord(tc_HOL_Obool)
| ~ spl85_20 ),
inference(avatar_component_clause,[],[f3198]) ).
fof(f8032,plain,
( spl85_78
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8031,f4474,f4802,f6145]) ).
fof(f8031,plain,
( ! [X7] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(v_F,X7) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8030]) ).
fof(f8030,plain,
( ! [X7] :
( hBOOL(v_F)
| hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(v_F,X7) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8029,f4784]) ).
fof(f8029,plain,
( ! [X10,X8,X9,X7] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(v_F,X7)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8)),X10),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X9))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5865,f4784]) ).
fof(f5865,plain,
( ! [X10,X8,X9,X7] :
( c_Arrow__Order__Mirabelle_Odictator(sK83(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,X9,X10),X7)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8)),X10),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X9)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3869,f4784]) ).
fof(f8028,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8027,f4474,f4802]) ).
fof(f8027,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8026]) ).
fof(f8026,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8025,f4784]) ).
fof(f8025,plain,
( ! [X2,X0,X1] :
( hBOOL(v_F)
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2,X0),X1)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5223,f4784]) ).
fof(f5223,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(v_F,X1))
| hBOOL(hAPP(c_Wellfounded_Oaccp(X2,X0),X1)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2912,f4784]) ).
fof(f8024,plain,
( spl85_84
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8023,f4474,f4802,f6422]) ).
fof(f8023,plain,
( ! [X0,X1] :
( ~ hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X1,X0) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8022]) ).
fof(f8022,plain,
( ! [X0,X1] :
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X1,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8021,f4784]) ).
fof(f8021,plain,
( ! [X0,X1] :
( ~ hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X0,X1)),sK21(X0,X1))),v_F)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5160,f4784]) ).
fof(f5160,plain,
( ! [X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X0,X1)),sK21(X0,X1))),v_F))
| c_Arrow__Order__Mirabelle_Odictator(X1,X0) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2454,f4784]) ).
fof(f8010,plain,
( ~ spl85_82
| spl85_76
| ~ spl85_24
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8009,f4474,f3218,f4802,f6214]) ).
fof(f8009,plain,
( hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| ~ spl85_24
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8008,f4784]) ).
fof(f8008,plain,
( ! [X0] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Oless__than,hAPP(v_F,v_P____)),hAPP(hAPP(c_COMBS(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt,c_Product__Type_OPair(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),X0)),c_COMBI(tc_Arrow__Order__Mirabelle_Oalt)))))
| ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F) )
| ~ spl85_24
| ~ spl85_69 ),
inference(forward_demodulation,[],[f8007,f4784]) ).
fof(f8007,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,v_F)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Oless__than,hAPP(v_F,v_P____)),hAPP(hAPP(c_COMBS(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt,c_Product__Type_OPair(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),X0)),c_COMBI(tc_Arrow__Order__Mirabelle_Oalt))))) )
| ~ spl85_24
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5107,f4784]) ).
fof(f5107,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,hAPP(X0,v_b____))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Oless__than,hAPP(v_F,v_P____)),hAPP(hAPP(c_COMBS(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt,c_Product__Type_OPair(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),X0)),c_COMBI(tc_Arrow__Order__Mirabelle_Oalt))))) )
| ~ spl85_24
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3916,f4784]) ).
fof(f8006,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f8005,f4474,f4802]) ).
fof(f8005,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f8004]) ).
fof(f8004,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5196,f4784]) ).
fof(f5196,plain,
( ! [X3,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X4)),X3),c_FuncSet_OPi(X6,X4,X5,c_COMBK(tc_fun(X4,tc_HOL_Obool),X6,c_fNot))))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3729,f4784]) ).
fof(f8001,plain,
( spl85_91
| ~ spl85_2
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6039,f4474,f3104,f6557]) ).
fof(f3104,plain,
( spl85_2
<=> class_Lattices_Odistrib__lattice(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_2])]) ).
fof(f6039,plain,
( class_Lattices_Odistrib__lattice(v_F)
| ~ spl85_2
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3106,f4784]) ).
fof(f3106,plain,
( class_Lattices_Odistrib__lattice(tc_HOL_Obool)
| ~ spl85_2 ),
inference(avatar_component_clause,[],[f3104]) ).
fof(f7988,plain,
( spl85_76
| spl85_78
| ~ spl85_69
| ~ spl85_74 ),
inference(avatar_split_clause,[],[f7987,f4726,f4474,f6145,f4802]) ).
fof(f7987,plain,
( ! [X66] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X66)
| hBOOL(v_F) )
| ~ spl85_69
| ~ spl85_74 ),
inference(forward_demodulation,[],[f5864,f4784]) ).
fof(f5864,plain,
( ! [X66] :
( c_Arrow__Order__Mirabelle_Odictator(sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),X66)
| hBOOL(v_F) )
| ~ spl85_69
| ~ spl85_74 ),
inference(backward_demodulation,[],[f4727,f4784]) ).
fof(f7963,plain,
( spl85_78
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7962,f4474,f4802,f6145]) ).
fof(f7962,plain,
( ! [X15] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(v_F,X15) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7961]) ).
fof(f7961,plain,
( ! [X15] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(v_F,X15)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7960,f4784]) ).
fof(f7960,plain,
( ! [X18,X16,X17,X15] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X15)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17)),X18),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),c_COMBK(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16))))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5863,f4784]) ).
fof(f5863,plain,
( ! [X18,X16,X17,X15] :
( c_Arrow__Order__Mirabelle_Odictator(sK65(X16,X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18),X15)
| hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17)),X18),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),c_COMBK(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16)))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3871,f4784]) ).
fof(f7959,plain,
( spl85_58
| spl85_76
| ~ spl85_25
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7958,f4474,f3223,f4802,f4223]) ).
fof(f7958,plain,
( ! [X0,X1] :
( hBOOL(v_F)
| X0 = X1 )
| ~ spl85_25
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5241,f4784]) ).
fof(f5241,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),hAPP(v_F,X1))) )
| ~ spl85_25
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3565,f4784]) ).
fof(f7955,plain,
( ~ spl85_76
| spl85_11
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5780,f4474,f3150,f4802]) ).
fof(f5780,plain,
( ~ hBOOL(v_F)
| spl85_11
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3152,f4784]) ).
fof(f7954,plain,
( ~ spl85_76
| spl85_125
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7950,f4474,f7952,f4802]) ).
fof(f7952,plain,
( spl85_125
<=> ! [X2,X3,X9,X0,X5,X1] :
( ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,v_F)
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X9,v_F) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_125])]) ).
fof(f7950,plain,
( ! [X2,X3,X0,X1,X9,X5] :
( ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,v_F)
| ~ hBOOL(v_F)
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X9,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7949,f4784]) ).
fof(f7949,plain,
( ! [X2,X3,X0,X1,X9,X4,X5] :
( ~ hBOOL(v_F)
| ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,v_F)
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X9,hAPP(sK29(X0,X1,X2,X3,X4,X5),X9)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7948,f4784]) ).
fof(f7948,plain,
( ! [X2,X3,X0,X1,X9,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X9),X0)),X5))
| ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,v_F)
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X9,hAPP(sK29(X0,X1,X2,X3,X4,X5),X9)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4848,f4784]) ).
fof(f4848,plain,
( ! [X2,X3,X0,X1,X9,X4,X5] :
( ~ c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(v_F,X0))
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X9,hAPP(sK29(X0,X1,X2,X3,X4,X5),X9))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X9),X0)),X5)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2483,f4784]) ).
fof(f7947,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7946,f4474,f4802]) ).
fof(f7946,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7945]) ).
fof(f7945,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5494,f4784]) ).
fof(f5494,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X3)),c_FuncSet_Orestrict(X2,X3,X0,X1)),c_FuncSet_OPi(X2,X3,X1,c_COMBK(tc_fun(X3,tc_HOL_Obool),X2,X4))))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2567,f4784]) ).
fof(f7942,plain,
( spl85_123
| spl85_124
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7935,f4474,f7940,f7937]) ).
fof(f7937,plain,
( spl85_123
<=> ! [X3] :
( c_Orderings_Oord__class_Oless__eq(X3,v_F,v_F)
| ~ class_Orderings_Oord(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_123])]) ).
fof(f7940,plain,
( spl85_124
<=> ! [X2,X1] : ~ c_Orderings_Oord__class_Oless__eq(v_F,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_124])]) ).
fof(f7935,plain,
( ! [X2,X3,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(v_F,X1,X2)
| c_Orderings_Oord__class_Oless__eq(X3,v_F,v_F)
| ~ class_Orderings_Oord(X3) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7934,f4784]) ).
fof(f7934,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(X3,v_F,v_F)
| ~ class_Orderings_Oord(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X3),X1,X2) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4870,f4784]) ).
fof(f4870,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Orderings_Oord__class_Oless__eq(X3,v_F,hAPP(X2,X4))
| ~ class_Orderings_Oord(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X3),X1,X2) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2648,f4784]) ).
fof(f2648,plain,
! [X2,X3,X0,X1,X4] :
( ~ class_Orderings_Oord(X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X3),X1,X2)
| c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X2,X4)) ),
inference(cnf_transformation,[],[f1906]) ).
fof(f1906,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oord(X3)
| ( ( ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X3),X1,X2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X3),X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK56(X1,X2,X3)),hAPP(X2,sK56(X1,X2,X3))) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK56])],[f1904,f1905]) ).
fof(f1905,plain,
! [X1,X2,X3] :
( ? [X5] : ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X2,X5))
=> ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK56(X1,X2,X3)),hAPP(X2,sK56(X1,X2,X3))) ),
introduced(choice_axiom,[]) ).
fof(f1904,plain,
! [X0,X1,X2,X3] :
( ~ class_Orderings_Oord(X3)
| ( ( ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X4),hAPP(X2,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X3),X1,X2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X3),X1,X2)
| ? [X5] : ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,X5),hAPP(X2,X5)) ) ) ),
inference(rectify,[],[f1903]) ).
fof(f1903,plain,
! [X0,X2,X1,X3] :
( ~ class_Orderings_Oord(X3)
| ( ( ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X2,X4),hAPP(X1,X4))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X3),X2,X1) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X3),X2,X1)
| ? [X4] : ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X2,X4),hAPP(X1,X4)) ) ) ),
inference(nnf_transformation,[],[f1414]) ).
fof(f1414,plain,
! [X0,X2,X1,X3] :
( ~ class_Orderings_Oord(X3)
| ( ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X2,X4),hAPP(X1,X4))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X3),X2,X1) ) ),
inference(ennf_transformation,[],[f776]) ).
fof(f776,plain,
! [X2,X3,X0,X1] :
( class_Orderings_Oord(X3)
=> ( ! [X4] : c_Orderings_Oord__class_Oless__eq(X3,hAPP(X2,X4),hAPP(X1,X4))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X3),X2,X1) ) ),
inference(rectify,[],[f256]) ).
fof(f256,axiom,
! [X8,X0,X1,X16] :
( class_Orderings_Oord(X16)
=> ( ! [X2] : c_Orderings_Oord__class_Oless__eq(X16,hAPP(X1,X2),hAPP(X0,X2))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X8,X16),X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
fof(f7925,plain,
( spl85_92
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5488,f4474,f4802,f6565]) ).
fof(f5488,plain,
( ! [X2,X0,X1] :
( hBOOL(v_F)
| c_Relation_Osingle__valued(X0,X1,X2) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2736,f4784]) ).
fof(f7917,plain,
( spl85_87
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7916,f4474,f6484]) ).
fof(f7916,plain,
( ! [X2] : c_Orderings_Oord__class_Oless__eq(v_F,X2,v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5672,f4784]) ).
fof(f5672,plain,
( ! [X2,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2742,f4784]) ).
fof(f2742,plain,
! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X2)),
inference(cnf_transformation,[],[f576]) ).
fof(f576,plain,
! [X0,X1,X2] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X0),X2)),
inference(rectify,[],[f409]) ).
fof(f409,axiom,
! [X10,X8,X9] : c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X10),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper2) ).
fof(f7914,plain,
( spl85_116
| ~ spl85_19
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6093,f4474,f3193,f7576]) ).
fof(f3193,plain,
( spl85_19
<=> class_Orderings_Oord(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_19])]) ).
fof(f6093,plain,
( class_Orderings_Oord(v_F)
| ~ spl85_19
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3195,f4784]) ).
fof(f3195,plain,
( class_Orderings_Oord(tc_Nat_Onat)
| ~ spl85_19 ),
inference(avatar_component_clause,[],[f3193]) ).
fof(f7913,plain,
( spl85_79
| ~ spl85_29
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7912,f4474,f3254,f6161]) ).
fof(f7912,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(v_F,v_F,X1)
| ~ spl85_29
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5422,f4784]) ).
fof(f5422,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,X1)
| ~ spl85_29
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3979,f4784]) ).
fof(f3979,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat),X0),X1),X1)
| ~ spl85_29 ),
inference(resolution,[],[f2278,f3256]) ).
fof(f2278,plain,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X0),X0) ),
inference(cnf_transformation,[],[f1588]) ).
fof(f1588,plain,
! [X0,X1,X2] :
( ~ class_Lattices_Olattice(X1)
| c_Orderings_Oord__class_Oless__eq(X1,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X1),X2),X0),X0) ),
inference(rectify,[],[f1432]) ).
fof(f1432,plain,
! [X1,X0,X2] :
( ~ class_Lattices_Olattice(X0)
| c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X0),X2),X1),X1) ),
inference(ennf_transformation,[],[f638]) ).
fof(f638,plain,
! [X1,X0,X2] :
( class_Lattices_Olattice(X0)
=> c_Orderings_Oord__class_Oless__eq(X0,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X0),X2),X1),X1) ),
inference(rectify,[],[f223]) ).
fof(f223,axiom,
! [X8,X50,X49] :
( class_Lattices_Olattice(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(X8),X49),X50),X50) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
fof(f7911,plain,
( ~ spl85_76
| spl85_54
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5821,f4474,f4014,f4802]) ).
fof(f5821,plain,
( ~ hBOOL(v_F)
| spl85_54
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4015,f4784]) ).
fof(f7910,plain,
( spl85_80
| spl85_87
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7909,f4474,f6484,f6164]) ).
fof(f7909,plain,
( ! [X6,X5] :
( c_Orderings_Oord__class_Oless__eq(v_F,X6,v_F)
| ~ class_Lattices_Olattice(X5) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5759,f4784]) ).
fof(f5759,plain,
( ! [X6,X4,X5] :
( ~ class_Lattices_Olattice(X5)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X5),X6,v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4037,f4784]) ).
fof(f4037,plain,
! [X6,X7,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X5),X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,X5)),X6),X7))
| ~ class_Lattices_Olattice(X5) ),
inference(resolution,[],[f2409,f2551]) ).
fof(f7906,plain,
( ~ spl85_76
| spl85_78
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7905,f4474,f6145,f4802]) ).
fof(f7905,plain,
( ! [X5] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X5)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7904,f4784]) ).
fof(f7904,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4),X5)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7903]) ).
fof(f7903,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4),X5)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7902,f4784]) ).
fof(f7902,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X5,hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4))),sK21(X5,hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4)))),hAPP(v_F,X4)))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4),X5) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5159,f4784]) ).
fof(f5159,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4),X5)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X5,hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4))),sK21(X5,hAPP(hAPP(c_COMBC(X0,X1,X2),X3),X4)))),hAPP(v_F,X4))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3965,f4784]) ).
fof(f7900,plain,
( spl85_58
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7899,f4474,f4802,f4223]) ).
fof(f7899,plain,
( ! [X0,X1] :
( hBOOL(v_F)
| X0 = X1 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5285,f4784]) ).
fof(f5285,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),sK84(X0,X1))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2949,f4784]) ).
fof(f7898,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7897,f4474,f4802]) ).
fof(f7897,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7896]) ).
fof(f7896,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7895,f4784]) ).
fof(f7895,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X10)),X9),c_FuncSet_OPi(X6,X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X8),X11))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5405,f4784]) ).
fof(f5405,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),v_F),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X8)),sK57(X9,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X8),X6,X10,X11)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X10)),X9),c_FuncSet_OPi(X6,X10,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X6,tc_HOL_Obool)),X7),X8),X11))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3657,f4784]) ).
fof(f7894,plain,
( spl85_76
| spl85_42
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5960,f4474,f3379,f4802]) ).
fof(f5960,plain,
( ! [X0] :
( hBOOL(X0)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2866,f4784]) ).
fof(f7892,plain,
( spl85_76
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5881,f4474,f4223,f4802]) ).
fof(f5881,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3696,f4784]) ).
fof(f7891,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5897,f4474,f4802]) ).
fof(f5897,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3791,f4784]) ).
fof(f7886,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7885,f4474,f4802]) ).
fof(f7885,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7884]) ).
fof(f7884,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7883,f4784]) ).
fof(f7883,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1)),v_F),sK83(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),X2),X0,X3,X4,X5)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5404,f4784]) ).
fof(f5404,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X3)),X5),c_FuncSet_OPi(X0,X3,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),X2),X4)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1)),v_F),sK83(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),X2),X0,X3,X4,X5))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3656,f4784]) ).
fof(f7882,plain,
( spl85_85
| spl85_122
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6058,f4474,f7880,f6441]) ).
fof(f6058,plain,
( ! [X0] :
( ~ class_Orderings_Opreorder(X0)
| class_Orderings_Opreorder(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2188,f4784]) ).
fof(f7877,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5106,f4474,f4802]) ).
fof(f5106,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4770,f4784]) ).
fof(f7876,plain,
( spl85_58
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7875,f4474,f4802,f4223]) ).
fof(f7875,plain,
( ! [X3,X4] :
( ~ hBOOL(v_F)
| X3 = X4 )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7874]) ).
fof(f7874,plain,
( ! [X3,X4] :
( X3 = X4
| ~ hBOOL(v_F)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7873,f4784]) ).
fof(f7873,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X3),c_FuncSet_Oextensional(X0,X2,X1)))
| X3 = X4
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f7872]) ).
fof(f7872,plain,
( ! [X2,X3,X0,X1,X4] :
( X3 = X4
| v_F != v_F
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X3),c_FuncSet_Oextensional(X0,X2,X1)))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7871,f4784]) ).
fof(f7871,plain,
( ! [X2,X3,X0,X1,X4] :
( X3 = X4
| v_F != hAPP(X3,sK3(X0,X1,X3,X4))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X3),c_FuncSet_Oextensional(X0,X2,X1)))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5125,f4784]) ).
fof(f5125,plain,
( ! [X2,X3,X0,X1,X4] :
( X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_Oextensional(X0,X2,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X3),c_FuncSet_Oextensional(X0,X2,X1)))
| v_F != hAPP(X3,sK3(X0,X1,X3,X4)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2199,f4784]) ).
fof(f7870,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7869,f4474,f4802]) ).
fof(f7869,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7868]) ).
fof(f7868,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7867,f4784]) ).
fof(f7867,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1)),v_F),sK83(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X2),X0,X3,X4,X5))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5400,f4784]) ).
fof(f5400,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X3)),X5),c_FuncSet_OPi(X0,X3,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X2),X4)))
| hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1)),v_F),sK83(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X1),X2),X0,X3,X4,X5))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3647,f4784]) ).
fof(f7855,plain,
( spl85_84
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7854,f4474,f4802,f6422]) ).
fof(f7854,plain,
( ! [X0,X1] :
( ~ hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X1,X0) )
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f7853]) ).
fof(f7853,plain,
( ! [X0,X1] :
( v_F != v_F
| c_Arrow__Order__Mirabelle_Odictator(X1,X0)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7852,f4784]) ).
fof(f7852,plain,
( ! [X0,X1] :
( ~ hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X1,X0)
| v_F != sK21(X0,X1) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5884,f4784]) ).
fof(f5884,plain,
( ! [X0,X1] :
( c_Arrow__Order__Mirabelle_Odictator(X1,X0)
| ~ hBOOL(v_F)
| sK21(X0,X1) != sK22(X0,X1) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2453,f4784]) ).
fof(f7848,plain,
( spl85_89
| ~ spl85_13
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6042,f4474,f3162,f6499]) ).
fof(f6042,plain,
( class_Orderings_Obot(v_F)
| ~ spl85_13
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3164,f4784]) ).
fof(f7836,plain,
( ~ spl85_76
| spl85_121
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7832,f4474,f7834,f4802]) ).
fof(f7834,plain,
( spl85_121
<=> ! [X2] : ~ c_Wellfounded_Oacyclic(X2,v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_121])]) ).
fof(f7832,plain,
( ! [X2] :
( ~ c_Wellfounded_Oacyclic(X2,v_F)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7831,f4784]) ).
fof(f7831,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Wellfounded_Oacyclic(X2,c_Set_Oinsert(tc_prod(X2,X2),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X0),X1),X3))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5519,f4784]) ).
fof(f5519,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),v_F),c_Transitive__Closure_Ortrancl(X2,X3)))
| ~ c_Wellfounded_Oacyclic(X2,c_Set_Oinsert(tc_prod(X2,X2),hAPP(hAPP(c_Product__Type_OPair(X2,X2),X0),X1),X3)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2414,f4784]) ).
fof(f7830,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7829,f4474,f4802]) ).
fof(f7829,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7828]) ).
fof(f7828,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7827,f4784]) ).
fof(f7827,plain,
( ! [X2,X3,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),X3),c_Relation_ODomain(X1,X1,X2)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5376,f4784]) ).
fof(f5376,plain,
( ! [X2,X3,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),v_F),c_Transitive__Closure_Ortrancl(X1,X2)))
| hBOOL(hAPP(hAPP(c_member(X1),X3),c_Relation_ODomain(X1,X1,X2))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2988,f4784]) ).
fof(f7820,plain,
( spl85_108
| ~ spl85_82
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7819,f4474,f6214,f7331]) ).
fof(f7819,plain,
( ! [X2,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,X2,X1) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7818,f4784]) ).
fof(f7818,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),v_F,v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,X2,X1) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7817,f4784]) ).
fof(f7817,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),v_F,hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1))
| c_Orderings_Oord__class_Oless__eq(v_F,X2,X1) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5394,f4784]) ).
fof(f5394,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),v_F,hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2325,f4784]) ).
fof(f2325,plain,
! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X2),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,X1) ),
inference(cnf_transformation,[],[f1631]) ).
fof(f1631,plain,
! [X0,X1,X2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X2),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X2),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,X1) ) ),
inference(rectify,[],[f1630]) ).
fof(f1630,plain,
! [X2,X0,X1] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X0)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0) ) ),
inference(nnf_transformation,[],[f858]) ).
fof(f858,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),X1,X0)
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X1),hAPP(hAPP(c_COMBC(X2,tc_fun(X2,tc_HOL_Obool),tc_HOL_Obool),c_member(X2)),X0)) ),
inference(rectify,[],[f242]) ).
fof(f242,axiom,
! [X34,X15,X8] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X15),hAPP(hAPP(c_COMBC(X8,tc_fun(X8,tc_HOL_Obool),tc_HOL_Obool),c_member(X8)),X34))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),X15,X34) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pred__subset__eq) ).
fof(f7808,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7807,f4474,f4802]) ).
fof(f7807,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7806]) ).
fof(f7806,plain,
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7805,f4784]) ).
fof(f7805,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_F),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7804]) ).
fof(f7804,plain,
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_F),c_Arrow__Order__Mirabelle_OLin))
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7803,f4784]) ).
fof(f7803,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_F),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5089,f4784]) ).
fof(f5089,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),hAPP(X2,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1))))
| ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),X2),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_F),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3623,f4784]) ).
fof(f7784,plain,
( spl85_120
| ~ spl85_1
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6088,f4474,f3099,f7781]) ).
fof(f7781,plain,
( spl85_120
<=> class_Orderings_Olinorder(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_120])]) ).
fof(f3099,plain,
( spl85_1
<=> class_Orderings_Olinorder(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_1])]) ).
fof(f6088,plain,
( class_Orderings_Olinorder(v_F)
| ~ spl85_1
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3101,f4784]) ).
fof(f3101,plain,
( class_Orderings_Olinorder(tc_Nat_Onat)
| ~ spl85_1 ),
inference(avatar_component_clause,[],[f3099]) ).
fof(f7769,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7768,f4474,f4802]) ).
fof(f7768,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7767]) ).
fof(f7767,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5258,f4784]) ).
fof(f5258,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X2)),X4),c_FuncSet_OPi(X1,X2,X0,X3)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2942,f4784]) ).
fof(f7753,plain,
( spl85_76
| spl85_58
| ~ spl85_25
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7752,f4474,f3223,f4223,f4802]) ).
fof(f7752,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(v_F) )
| ~ spl85_25
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7751]) ).
fof(f7751,plain,
( ! [X0,X1] :
( hBOOL(v_F)
| hBOOL(v_F)
| X0 = X1 )
| ~ spl85_25
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7750,f4784]) ).
fof(f7750,plain,
( ! [X0,X1] :
( hBOOL(v_F)
| X0 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),hAPP(v_F,v_Q____))) )
| ~ spl85_25
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5314,f4784]) ).
fof(f5314,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1)),hAPP(v_F,v_Q____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),hAPP(v_F,v_Q____))) )
| ~ spl85_25
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3633,f4784]) ).
fof(f7745,plain,
( spl85_76
| spl85_61
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5835,f4474,f4384,f4802]) ).
fof(f5835,plain,
( ! [X37] :
( ~ hBOOL(X37)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4121,f4784]) ).
fof(f7740,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7739,f4474,f4802]) ).
fof(f7739,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7738]) ).
fof(f7738,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7737,f4784]) ).
fof(f7737,plain,
( ! [X21,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X20,X21),X24)),X26),c_FuncSet_OPi(tc_fun(X20,X21),X24,c_FuncSet_OPi(X20,X21,X22,X23),X25)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f7736]) ).
fof(f7736,plain,
( ! [X21,X26,X24,X22,X25,X23,X20] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X20,X21),X24)),X26),c_FuncSet_OPi(tc_fun(X20,X21),X24,c_FuncSet_OPi(X20,X21,X22,X23),X25)))
| v_F != v_F )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7735,f4784]) ).
fof(f7735,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( v_F != hAPP(sK83(c_FuncSet_OPi(X20,X21,X22,X23),tc_fun(X20,X21),X24,X25,X26),sK72(X20,sK83(c_FuncSet_OPi(X20,X21,X22,X23),tc_fun(X20,X21),X24,X25,X26),X19,X22))
| hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X20,X21),X24)),X26),c_FuncSet_OPi(tc_fun(X20,X21),X24,c_FuncSet_OPi(X20,X21,X22,X23),X25))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5215,f4784]) ).
fof(f5215,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X20,X21)),X19),c_FuncSet_OPi(X20,X21,X22,X23)))
| v_F != hAPP(sK83(c_FuncSet_OPi(X20,X21,X22,X23),tc_fun(X20,X21),X24,X25,X26),sK72(X20,sK83(c_FuncSet_OPi(X20,X21,X22,X23),tc_fun(X20,X21),X24,X25,X26),X19,X22))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X20,X21),X24)),X26),c_FuncSet_OPi(tc_fun(X20,X21),X24,c_FuncSet_OPi(X20,X21,X22,X23),X25))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3608,f4784]) ).
fof(f7730,plain,
( spl85_105
| spl85_80
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6067,f4474,f6164,f7090]) ).
fof(f6067,plain,
( ! [X1] :
( ~ class_Lattices_Olattice(X1)
| class_Lattices_Osemilattice__inf(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2583,f4784]) ).
fof(f7729,plain,
( ~ spl85_119
| spl85_27
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5976,f4474,f3234,f7726]) ).
fof(f7726,plain,
( spl85_119
<=> v_F = v_b_H____ ),
introduced(avatar_definition,[new_symbols(naming,[spl85_119])]) ).
fof(f3234,plain,
( spl85_27
<=> v_a____ = v_b_H____ ),
introduced(avatar_definition,[new_symbols(naming,[spl85_27])]) ).
fof(f5976,plain,
( v_F != v_b_H____
| spl85_27
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3236,f4784]) ).
fof(f3236,plain,
( v_a____ != v_b_H____
| spl85_27 ),
inference(avatar_component_clause,[],[f3234]) ).
fof(f7723,plain,
( spl85_58
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7722,f4474,f4802,f4223]) ).
fof(f7722,plain,
( ! [X3,X0] :
( hBOOL(v_F)
| X0 = X3 )
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f7721]) ).
fof(f7721,plain,
( ! [X3,X0] :
( hBOOL(v_F)
| X0 = X3
| v_F != v_F )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7720,f4784]) ).
fof(f7720,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(v_F)
| X0 = X3
| v_F != c_Set_Oinsert(X2,X1,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7719,f4784]) ).
fof(f7719,plain,
( ! [X2,X3,X0,X1] :
( X0 = X3
| c_Set_Oinsert(X2,X1,X0) != c_Set_Oinsert(X2,X1,X3)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7718]) ).
fof(f7718,plain,
( ! [X2,X3,X0,X1] :
( X0 = X3
| c_Set_Oinsert(X2,X1,X0) != c_Set_Oinsert(X2,X1,X3)
| hBOOL(v_F)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5460,f4784]) ).
fof(f5460,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X2),X1),X3))
| X0 = X3
| c_Set_Oinsert(X2,X1,X0) != c_Set_Oinsert(X2,X1,X3)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2712,f4784]) ).
fof(f7717,plain,
( ~ spl85_118
| spl85_18
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5975,f4474,f3188,f7714]) ).
fof(f7714,plain,
( spl85_118
<=> v_F = v_b____ ),
introduced(avatar_definition,[new_symbols(naming,[spl85_118])]) ).
fof(f3188,plain,
( spl85_18
<=> v_a____ = v_b____ ),
introduced(avatar_definition,[new_symbols(naming,[spl85_18])]) ).
fof(f5975,plain,
( v_F != v_b____
| spl85_18
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3190,f4784]) ).
fof(f3190,plain,
( v_a____ != v_b____
| spl85_18 ),
inference(avatar_component_clause,[],[f3188]) ).
fof(f7711,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5911,f4474,f4802]) ).
fof(f5911,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2698,f4784]) ).
fof(f7700,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7699,f4474,f4802]) ).
fof(f7699,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7698]) ).
fof(f7698,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7697,f4784]) ).
fof(f7697,plain,
( ! [X11,X8,X6,X9] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(X6),sK72(X6,X11,X8,X9)),X9)) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7696]) ).
fof(f7696,plain,
( ! [X11,X8,X6,X9] :
( hBOOL(hAPP(hAPP(c_member(X6),sK72(X6,X11,X8,X9)),X9))
| hBOOL(v_F)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5498,f4784]) ).
fof(f5498,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X7)),X8),c_FuncSet_OPi(X6,X7,X9,X10)))
| hBOOL(hAPP(hAPP(c_member(X6),sK72(X6,X11,X8,X9)),X9)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3591,f4784]) ).
fof(f7686,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7685,f4474,f4802]) ).
fof(f7685,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7684]) ).
fof(f7684,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7683,f4784]) ).
fof(f7683,plain,
( ! [X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7682,f4784]) ).
fof(f7682,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25))) )
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f7681]) ).
fof(f7681,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25)))
| v_F != v_F
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5212,f4784]) ).
fof(f5212,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( v_F != hAPP(sK83(c_FuncSet_OPi(X19,X20,X22,X23),tc_fun(X19,X20),X24,X25,X26),sK72(X19,X21,sK83(c_FuncSet_OPi(X19,X20,X22,X23),tc_fun(X19,X20),X24,X25,X26),X22))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3615,f4784]) ).
fof(f7680,plain,
( spl85_79
| ~ spl85_22
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7679,f4474,f3208,f6161]) ).
fof(f7679,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(v_F,v_F,X1)
| ~ spl85_22
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7678,f4784]) ).
fof(f7678,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,v_F,X1)
| ~ spl85_22
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5748,f4784]) ).
fof(f5748,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(v_F,X1),X1)
| ~ spl85_22
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4001,f4784]) ).
fof(f4001,plain,
( ! [X2,X3,X1,X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool)),X2),X1),X1)
| ~ spl85_22 ),
inference(superposition,[],[f3995,f2728]) ).
fof(f7670,plain,
( spl85_76
| ~ spl85_9
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5852,f4474,f3140,f4802]) ).
fof(f5852,plain,
( hBOOL(v_F)
| ~ spl85_9
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3142,f4784]) ).
fof(f3142,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf))
| ~ spl85_9 ),
inference(avatar_component_clause,[],[f3140]) ).
fof(f7669,plain,
( ~ spl85_76
| ~ spl85_56
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5933,f4474,f4138,f4802]) ).
fof(f5933,plain,
( ~ hBOOL(v_F)
| ~ spl85_56
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4139,f4784]) ).
fof(f7667,plain,
( spl85_79
| ~ spl85_29
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7666,f4474,f3254,f6161]) ).
fof(f7666,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(v_F,v_F,X1)
| ~ spl85_29
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7665,f4784]) ).
fof(f7665,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,X1)
| ~ spl85_29
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5747,f4784]) ).
fof(f5747,plain,
( ! [X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(v_F,X1),X1)
| ~ spl85_29
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3999,f4784]) ).
fof(f3999,plain,
( ! [X2,X3,X1,X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat)),X2),X1),X1)
| ~ spl85_29 ),
inference(superposition,[],[f3994,f2728]) ).
fof(f7664,plain,
( ~ spl85_76
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7663,f4474,f4223,f4802]) ).
fof(f7663,plain,
( ! [X0,X1] :
( X0 = X1
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7662]) ).
fof(f7662,plain,
( ! [X0,X1] :
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| X0 = X1 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7661,f4784]) ).
fof(f7661,plain,
( ! [X0,X1] :
( ~ hBOOL(v_F)
| X0 = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK84(X0,X1)),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5311,f4784]) ).
fof(f5311,plain,
( ! [X0,X1] :
( X0 = X1
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),sK84(X0,X1)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),sK84(X0,X1)),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3619,f4784]) ).
fof(f7657,plain,
( spl85_77
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7656,f4474,f4802,f6128]) ).
fof(f7656,plain,
( ! [X46,X47,X45] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X46,X47,v_F,X45) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7655,f4784]) ).
fof(f7655,plain,
( ! [X40,X41,X46,X47,X45,X42,X43] :
( c_Predicate_ORangeP(X46,X47,c_COMBB(X40,X41,X42,X43),X45)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5054,f4784]) ).
fof(f5054,plain,
( ! [X40,X41,X46,X47,X45,X42,X43] :
( ~ hBOOL(hAPP(X43,v_F))
| c_Predicate_ORangeP(X46,X47,c_COMBB(X40,X41,X42,X43),X45) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4371,f4784]) ).
fof(f7650,plain,
( ~ spl85_82
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7649,f4474,f4802,f6214]) ).
fof(f7649,plain,
( hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7648,f4784]) ).
fof(f7648,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7647,f4784]) ).
fof(f7647,plain,
( ! [X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X5),v_F)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5017,f4784]) ).
fof(f5017,plain,
( ! [X8,X6,X9,X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X5),X6)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X7),X7,c_Wellfounded_Olex__prod(tc_Nat_Onat,X7,c_Wellfounded_Oless__than,hAPP(c_Transitive__Closure_Ortranclp(X8,X9),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X5),X6))),hAPP(hAPP(c_COMBS(X7,X7,tc_prod(tc_Nat_Onat,X7)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X7,tc_prod(tc_Nat_Onat,X7)),X7,c_Product__Type_OPair(tc_Nat_Onat,X7)),X4)),c_COMBI(X7)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X5),v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4095,f4784]) ).
fof(f7646,plain,
( spl85_77
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6068,f4474,f6128]) ).
fof(f6068,plain,
( ! [X202,X200,X201] : c_Predicate_ORangeP(X200,X201,v_F,X202)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4342,f4784]) ).
fof(f4342,plain,
! [X202,X200,X201] : c_Predicate_ORangeP(X200,X201,c_fequal,X202),
inference(resolution,[],[f2173,f3075]) ).
fof(f7645,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5927,f4474,f4802]) ).
fof(f5927,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3081,f4784]) ).
fof(f7638,plain,
( spl85_76
| ~ spl85_37
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5787,f4474,f3332,f4802]) ).
fof(f5787,plain,
( hBOOL(v_F)
| ~ spl85_37
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3585,f4784]) ).
fof(f7633,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7632,f4474,f4802]) ).
fof(f7632,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7631]) ).
fof(f7631,plain,
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7630,f4784]) ).
fof(f7630,plain,
( ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7629]) ).
fof(f7629,plain,
( ! [X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(v_F)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7628,f4784]) ).
fof(f7628,plain,
( ! [X0,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F),X0)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4954,f4784]) ).
fof(f4954,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),X1),X0)),X5))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X5),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F),X0)),X5)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3622,f4784]) ).
fof(f7621,plain,
( ~ spl85_117
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7616,f4474,f7618]) ).
fof(f7616,plain,
( v_F != c_Orderings_Obot__class_Obot(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7615,f4784]) ).
fof(f7615,plain,
( ! [X0] : v_F != c_Orderings_Obot__class_Obot(tc_fun(X0,v_F))
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6027,f4784]) ).
fof(f6027,plain,
( ! [X2,X0,X1] : c_Orderings_Obot__class_Obot(tc_fun(X0,v_F)) != c_Set_Oinsert(X0,X1,X2)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2646,f4784]) ).
fof(f7614,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5802,f4474,f4802]) ).
fof(f5802,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4090,f4784]) ).
fof(f7611,plain,
( spl85_58
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5828,f4474,f4802,f4223]) ).
fof(f5828,plain,
( ! [X0,X1] :
( ~ hBOOL(v_F)
| X0 = X1 )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2591,f4784]) ).
fof(f7603,plain,
( spl85_76
| ~ spl85_37
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5941,f4474,f3332,f4802]) ).
fof(f5941,plain,
( hBOOL(v_F)
| ~ spl85_37
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3334,f4784]) ).
fof(f7602,plain,
( spl85_77
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7601,f4474,f4802,f6128]) ).
fof(f7601,plain,
( ! [X38,X39,X37] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X38,X39,v_F,X37) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7600,f4784]) ).
fof(f7600,plain,
( ! [X38,X39,X37,X34,X35,X32,X33] :
( c_Predicate_ORangeP(X38,X39,hAPP(c_COMBS(X32,X33,X34),X35),X37)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5053,f4784]) ).
fof(f5053,plain,
( ! [X38,X39,X36,X37,X34,X35,X32,X33] :
( ~ hBOOL(hAPP(v_F,hAPP(X36,X37)))
| c_Predicate_ORangeP(X38,X39,hAPP(c_COMBS(X32,X33,X34),X35),X37) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4370,f4784]) ).
fof(f7594,plain,
( ~ spl85_76
| spl85_77
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7593,f4474,f6128,f4802]) ).
fof(f7593,plain,
( ! [X38,X39,X37] :
( c_Predicate_ORangeP(X38,X39,v_F,X37)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7592,f4784]) ).
fof(f7592,plain,
( ! [X31,X38,X39,X37,X34,X35,X32,X33] :
( c_Predicate_ORangeP(X38,X39,hAPP(hAPP(c_COMBC(X31,X32,X33),X34),X35),X37)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5045,f4784]) ).
fof(f5045,plain,
( ! [X31,X38,X39,X37,X34,X35,X32,X33] :
( ~ hBOOL(hAPP(hAPP(v_F,X35),X37))
| c_Predicate_ORangeP(X38,X39,hAPP(hAPP(c_COMBC(X31,X32,X33),X34),X35),X37) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4352,f4784]) ).
fof(f7579,plain,
( spl85_115
| spl85_116
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6060,f4474,f7576,f7573]) ).
fof(f6060,plain,
( ! [X1] :
( class_Orderings_Oord(v_F)
| ~ class_Orderings_Oord(X1) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2259,f4784]) ).
fof(f7571,plain,
( spl85_58
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7570,f4474,f4802,f4223]) ).
fof(f7570,plain,
( ! [X2,X3] :
( ~ hBOOL(v_F)
| X2 = X3 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5512,f4784]) ).
fof(f5512,plain,
( ! [X2,X3,X0,X1] :
( X2 = X3
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),v_F),c_Relation_OId__on(X1,X0))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2281,f4784]) ).
fof(f7568,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7567,f4474,f4802]) ).
fof(f7567,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7566]) ).
fof(f7566,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7565,f4784]) ).
fof(f7565,plain,
( ! [X31,X28,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7564]) ).
fof(f7564,plain,
( ! [X31,X28,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34)))
| hBOOL(v_F)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5700,f4784]) ).
fof(f5700,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X27,X28)),X29),c_FuncSet_OPi(X27,X28,X30,X31)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3595,f4784]) ).
fof(f7563,plain,
( spl85_76
| spl85_61
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5834,f4474,f4384,f4802]) ).
fof(f5834,plain,
( ! [X24] :
( ~ hBOOL(X24)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3749,f4784]) ).
fof(f7541,plain,
( spl85_106
| ~ spl85_26
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6047,f4474,f3229,f7195]) ).
fof(f6047,plain,
( class_Lattices_Osemilattice__sup(v_F)
| ~ spl85_26
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3231,f4784]) ).
fof(f7539,plain,
( spl85_108
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7538,f4474,f7331]) ).
fof(f7538,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(v_F,X1,X0)
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f7537]) ).
fof(f7537,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(v_F,X1,X0)
| v_F != v_F )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7536,f4784]) ).
fof(f7536,plain,
( ! [X3,X0,X1] :
( v_F != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),v_F),X1)
| c_Orderings_Oord__class_Oless__eq(v_F,X1,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7535,f4784]) ).
fof(f7535,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(v_F,X1,X0)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),v_F),X1) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X0),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5574,f4784]) ).
fof(f5574,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),v_F),X1) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X0),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2196,f4784]) ).
fof(f2196,plain,
! [X2,X3,X0,X1] :
( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X0),X2)),X1) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X0),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0) ),
inference(cnf_transformation,[],[f1525]) ).
fof(f1525,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X0),X2)),X1) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X0),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X0),X2)),X1) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X3,tc_HOL_Obool)),X0),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,X0) ) ),
inference(rectify,[],[f1524]) ).
fof(f1524,plain,
! [X1,X2,X3,X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,X1)
| hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),X3)),X2) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X3),X2)) )
& ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),X3)),X2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X3),X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,X1) ) ),
inference(nnf_transformation,[],[f822]) ).
fof(f822,plain,
! [X1,X2,X3,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X2,X1)
<=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),X3)),X2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X0,tc_HOL_Obool)),X1),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X3),X2)) ),
inference(rectify,[],[f419]) ).
fof(f419,axiom,
! [X8,X10,X47,X9] :
( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X10),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X9),X47)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X10),X9)),X47)
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),X47,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__assoc__eq) ).
fof(f7531,plain,
( spl85_76
| ~ spl85_82
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7530,f4474,f6214,f4802]) ).
fof(f7530,plain,
( ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7529,f4784]) ).
fof(f7529,plain,
( hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7528,f4784]) ).
fof(f7528,plain,
( ! [X28,X29,X27,X30] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X30,X30)),hAPP(hAPP(c_Product__Type_OPair(X30,X30),X28),X29)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X30),X30,c_Wellfounded_Olex__prod(tc_Nat_Onat,X30,c_Wellfounded_Oless__than,hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(X30,X30),X28),X29))),hAPP(hAPP(c_COMBS(X30,X30,tc_prod(tc_Nat_Onat,X30)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X30,tc_prod(tc_Nat_Onat,X30)),X30,c_Product__Type_OPair(tc_Nat_Onat,X30)),X27)),c_COMBI(X30)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4993,f4784]) ).
fof(f4993,plain,
( ! [X28,X29,X27,X30] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X27,X28),v_F)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X30,X30)),hAPP(hAPP(c_Product__Type_OPair(X30,X30),X28),X29)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X30),X30,c_Wellfounded_Olex__prod(tc_Nat_Onat,X30,c_Wellfounded_Oless__than,hAPP(c_fequal,hAPP(hAPP(c_Product__Type_OPair(X30,X30),X28),X29))),hAPP(hAPP(c_COMBS(X30,X30,tc_prod(tc_Nat_Onat,X30)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X30,tc_prod(tc_Nat_Onat,X30)),X30,c_Product__Type_OPair(tc_Nat_Onat,X30)),X27)),c_COMBI(X30))))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3923,f4784]) ).
fof(f7519,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7518,f4474,f4802]) ).
fof(f7518,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f7517]) ).
fof(f7517,plain,
( v_F != v_F
| ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7516,f4784]) ).
fof(f7516,plain,
( ! [X2] :
( v_F != c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7515,f4784]) ).
fof(f7515,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(v_F)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7514]) ).
fof(f7514,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5463,f4784]) ).
fof(f5463,plain,
( ! [X2,X0,X1,X6] :
( ~ hBOOL(hAPP(hAPP(c_member(X2),X6),X0))
| ~ hBOOL(v_F)
| c_Orderings_Obot__class_Obot(tc_fun(X2,tc_HOL_Obool)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X2,tc_HOL_Obool)),X0),X1) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3044,f4784]) ).
fof(f7512,plain,
( spl85_76
| spl85_114
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7508,f4474,f7510,f4802]) ).
fof(f7510,plain,
( spl85_114
<=> ! [X1,X3] :
( c_Orderings_Oord__class_Oless__eq(v_F,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,X3,v_F) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_114])]) ).
fof(f7508,plain,
( ! [X3,X1] :
( c_Orderings_Oord__class_Oless__eq(v_F,X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,X3,v_F)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7507,f4784]) ).
fof(f7507,plain,
( ! [X3,X0,X1] :
( hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,X3,X1) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7506,f4784]) ).
fof(f7506,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(v_F,X3,X1)
| hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,c_Set_Oinsert(X0,X2,X1)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5434,f4784]) ).
fof(f5434,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,X1)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,c_Set_Oinsert(X0,X2,X1))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2246,f4784]) ).
fof(f2246,plain,
! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,c_Set_Oinsert(X0,X2,X1))
| hBOOL(hAPP(hAPP(c_member(X0),X2),X3))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X3,X1) ),
inference(cnf_transformation,[],[f1568]) ).
fof(f7504,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5930,f4474,f4802]) ).
fof(f5930,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4771,f4784]) ).
fof(f4771,plain,
( ! [X1] : hBOOL(hAPP(hAPP(c_member(X1),v_F),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool))))
| ~ spl85_69 ),
inference(resolution,[],[f4476,f2711]) ).
fof(f7494,plain,
( spl85_95
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7493,f4474,f4802,f6693]) ).
fof(f7493,plain,
( ! [X6,X9,X7] :
( ~ hBOOL(v_F)
| X6 = X9
| X7 = X9 )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7492]) ).
fof(f7492,plain,
( ! [X6,X9,X7] :
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| X7 = X9
| X6 = X9 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7491,f4784]) ).
fof(f7491,plain,
( ! [X8,X6,X9,X7] :
( X6 = X9
| ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6)))
| X7 = X9 )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7490]) ).
fof(f7490,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(v_F)
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6)))
| ~ hBOOL(v_F)
| X7 = X9 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7489,f4784]) ).
fof(f7489,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X7)),X8))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6)))
| X7 = X9
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7488]) ).
fof(f7488,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6)))
| ~ hBOOL(v_F)
| X7 = X9
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X7)),X8))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7487,f4784]) ).
fof(f7487,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(v_F)
| X7 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X7)),X8))
| X6 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5321,f4784]) ).
fof(f5321,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6)))
| X7 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X6),X7)),X8))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X6)),c_Arrow__Order__Mirabelle_OLin))
| X6 = X9 )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3699,f4784]) ).
fof(f7485,plain,
( spl85_76
| ~ spl85_36
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5950,f4474,f3306,f4802]) ).
fof(f5950,plain,
( hBOOL(v_F)
| ~ spl85_36
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3308,f4784]) ).
fof(f7479,plain,
( spl85_78
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7478,f4474,f4802,f6145]) ).
fof(f7478,plain,
( ! [X15] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(v_F,X15) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7477,f4784]) ).
fof(f7477,plain,
( ! [X18,X16,X17,X15] :
( c_Arrow__Order__Mirabelle_Odictator(sK65(X16,X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18),X15)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7476]) ).
fof(f7476,plain,
( ! [X18,X16,X17,X15] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(sK65(X16,X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18),X15)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5846,f4784]) ).
fof(f5846,plain,
( ! [X18,X16,X17,X15] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17)),X18),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),c_COMBK(tc_fun(X17,tc_HOL_Obool),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X16))))
| c_Arrow__Order__Mirabelle_Odictator(sK65(X16,X17,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18),X15)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3951,f4784]) ).
fof(f7472,plain,
( spl85_113
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7468,f4474,f4802,f7470]) ).
fof(f7470,plain,
( spl85_113
<=> ! [X2,X0,X1] : c_Predicate_ODomainP(X2,X1,v_F,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_113])]) ).
fof(f7468,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(v_F)
| c_Predicate_ODomainP(X2,X1,v_F,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5560,f4784]) ).
fof(f5560,plain,
( ! [X2,X3,X0,X1] :
( c_Predicate_ODomainP(X2,X1,v_F,X0)
| ~ hBOOL(hAPP(hAPP(c_member(X2),X0),c_Relation_ODomain(X2,X1,X3))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2593,f4784]) ).
fof(f7464,plain,
( ~ spl85_112
| spl85_17
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5977,f4474,f3183,f7461]) ).
fof(f3183,plain,
( spl85_17
<=> v_b____ = v_a_H____ ),
introduced(avatar_definition,[new_symbols(naming,[spl85_17])]) ).
fof(f5977,plain,
( v_F != v_a_H____
| spl85_17
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3185,f4784]) ).
fof(f3185,plain,
( v_b____ != v_a_H____
| spl85_17 ),
inference(avatar_component_clause,[],[f3183]) ).
fof(f7455,plain,
( spl85_76
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5944,f4474,f4223,f4802]) ).
fof(f5944,plain,
( ! [X0,X1] :
( X0 = X1
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3394,f4784]) ).
fof(f7442,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7441,f4474,f4802]) ).
fof(f7441,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7440]) ).
fof(f7440,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7439,f4784]) ).
fof(f7439,plain,
( ! [X11,X8,X6,X9] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(X6),sK72(X6,X8,X11,X9)),X9)) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7438]) ).
fof(f7438,plain,
( ! [X11,X8,X6,X9] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(X6),sK72(X6,X8,X11,X9)),X9))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5499,f4784]) ).
fof(f5499,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X7)),X8),c_FuncSet_OPi(X6,X7,X9,X10)))
| hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(X6),sK72(X6,X8,X11,X9)),X9)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3598,f4784]) ).
fof(f7434,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7433,f4474,f4802]) ).
fof(f7433,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f7432]) ).
fof(f7432,plain,
( hBOOL(v_F)
| v_F != v_F
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7431,f4784]) ).
fof(f7431,plain,
( ! [X2,X3,X0,X5] :
( hBOOL(v_F)
| v_F != hAPP(X5,sK72(X0,X2,X5,X3)) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7430]) ).
fof(f7430,plain,
( ! [X2,X3,X0,X5] :
( hBOOL(v_F)
| v_F != hAPP(X5,sK72(X0,X2,X5,X3))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7429,f4784]) ).
fof(f7429,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,X4)))
| hBOOL(v_F)
| v_F != hAPP(X5,sK72(X0,X2,X5,X3)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5207,f4784]) ).
fof(f5207,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X0),sK83(X3,X0,X1,X4,X5)),X3))
| v_F != hAPP(X5,sK72(X0,X2,X5,X3))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,X4))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3611,f4784]) ).
fof(f7427,plain,
( spl85_87
| ~ spl85_22
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7426,f4474,f3208,f6484]) ).
fof(f7426,plain,
( ! [X2] : c_Orderings_Oord__class_Oless__eq(v_F,X2,v_F)
| ~ spl85_22
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5426,f4784]) ).
fof(f5426,plain,
( ! [X2] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X2,v_F)
| ~ spl85_22
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4003,f4784]) ).
fof(f4003,plain,
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool),X3),X2))
| ~ spl85_22 ),
inference(resolution,[],[f2380,f3210]) ).
fof(f2380,plain,
! [X2,X0,X1] :
( ~ class_Lattices_Olattice(X1)
| c_Orderings_Oord__class_Oless__eq(X1,X0,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X0)) ),
inference(cnf_transformation,[],[f1670]) ).
fof(f1670,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(X1,X0,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X1),X2),X0))
| ~ class_Lattices_Olattice(X1) ),
inference(rectify,[],[f1145]) ).
fof(f1145,plain,
! [X1,X2,X0] :
( c_Orderings_Oord__class_Oless__eq(X2,X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X0),X1))
| ~ class_Lattices_Olattice(X2) ),
inference(ennf_transformation,[],[f626]) ).
fof(f626,plain,
! [X2,X0,X1] :
( class_Lattices_Olattice(X2)
=> c_Orderings_Oord__class_Oless__eq(X2,X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X2),X0),X1)) ),
inference(rectify,[],[f396]) ).
fof(f396,axiom,
! [X49,X50,X8] :
( class_Lattices_Olattice(X8)
=> c_Orderings_Oord__class_Oless__eq(X8,X50,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(X8),X49),X50)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I4_J) ).
fof(f7417,plain,
( spl85_111
| ~ spl85_29
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6095,f4474,f3254,f7414]) ).
fof(f6095,plain,
( class_Lattices_Olattice(v_F)
| ~ spl85_29
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3256,f4784]) ).
fof(f7412,plain,
( ~ spl85_76
| spl85_53
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5779,f4474,f3629,f4802]) ).
fof(f5779,plain,
( ~ hBOOL(v_F)
| spl85_53
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3631,f4784]) ).
fof(f7411,plain,
( spl85_61
| spl85_76
| ~ spl85_26
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5838,f4474,f3229,f4802,f4384]) ).
fof(f5838,plain,
( ! [X14] :
( hBOOL(v_F)
| ~ hBOOL(X14) )
| ~ spl85_26
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3845,f4784]) ).
fof(f7408,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7407,f4474,f4802]) ).
fof(f7407,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7406]) ).
fof(f7406,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5191,f4784]) ).
fof(f5191,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X2)),X4),c_FuncSet_OPi(X0,X2,X3,c_COMBK(tc_fun(X2,tc_HOL_Obool),X0,X1))))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3493,f4784]) ).
fof(f7395,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7394,f4474,f4802]) ).
fof(f7394,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7393]) ).
fof(f7393,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7392,f4784]) ).
fof(f7392,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,X4))) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7391]) ).
fof(f7391,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,X4)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5262,f4784]) ).
fof(f5262,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X0),sK72(X0,X2,X5,X3)),X3))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,X4)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3597,f4784]) ).
fof(f7390,plain,
( spl85_76
| ~ spl85_16
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5815,f4474,f3178,f4802]) ).
fof(f5815,plain,
( hBOOL(v_F)
| ~ spl85_16
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3304,f4784]) ).
fof(f7389,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7388,f4474,f4802]) ).
fof(f7388,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7387]) ).
fof(f7387,plain,
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7386,f4784]) ).
fof(f7386,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X0)),X1)) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7385]) ).
fof(f7385,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X0)),X1))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7384,f4784]) ).
fof(f7384,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),X1))
| ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X0)),X1)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5278,f4784]) ).
fof(f5278,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X1),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X0)),X1))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),X1)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2792,f4784]) ).
fof(f7382,plain,
( spl85_78
| spl85_76
| ~ spl85_67
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7381,f4474,f4439,f4802,f6145]) ).
fof(f7381,plain,
( ! [X65] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(v_F,X65) )
| ~ spl85_67
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5844,f4784]) ).
fof(f5844,plain,
( ! [X65] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X65) )
| ~ spl85_67
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4440,f4784]) ).
fof(f7380,plain,
( spl85_76
| ~ spl85_33
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5793,f4474,f3283,f4802]) ).
fof(f5793,plain,
( hBOOL(v_F)
| ~ spl85_33
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3886,f4784]) ).
fof(f7378,plain,
( spl85_76
| ~ spl85_16
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7377,f4474,f3178,f4802]) ).
fof(f7377,plain,
( hBOOL(v_F)
| ~ spl85_16
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7376]) ).
fof(f7376,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_16
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5866,f4784]) ).
fof(f5866,plain,
( ! [X18] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
| ~ spl85_16
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3593,f4784]) ).
fof(f7373,plain,
( spl85_77
| ~ spl85_40
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6013,f4474,f3371,f6128]) ).
fof(f6013,plain,
( ! [X195,X199,X196] : c_Predicate_ORangeP(X195,X196,v_F,X199)
| ~ spl85_40
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4341,f4784]) ).
fof(f7370,plain,
( spl85_110
| ~ spl85_15
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6043,f4474,f3172,f7367]) ).
fof(f6043,plain,
( class_Lattices_Obounded__lattice__bot(v_F)
| ~ spl85_15
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3174,f4784]) ).
fof(f7365,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7364,f4474,f4802]) ).
fof(f7364,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5681,f4784]) ).
fof(f5681,plain,
( ! [X5] : hBOOL(hAPP(hAPP(c_member(X5),v_F),v_F))
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4774,f4784]) ).
fof(f4774,plain,
( ! [X6,X7,X5] : hBOOL(hAPP(hAPP(c_member(X5),v_F),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X5,tc_HOL_Obool)),X6),X7)))
| ~ spl85_69 ),
inference(resolution,[],[f4770,f2764]) ).
fof(f7359,plain,
( spl85_79
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7358,f4474,f6161]) ).
fof(f7358,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(v_F,v_F,X0)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5592,f4784]) ).
fof(f5592,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),v_F,X0)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2895,f4784]) ).
fof(f2895,plain,
! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X0),X0),
inference(cnf_transformation,[],[f2117]) ).
fof(f2117,plain,
! [X0,X1,X2] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X2),X0),X0),
inference(rectify,[],[f923]) ).
fof(f923,plain,
! [X2,X1,X0] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X1,tc_HOL_Obool)),X0),X2),X2),
inference(rectify,[],[f232]) ).
fof(f232,axiom,
! [X10,X8,X9] : c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X8,tc_HOL_Obool)),X10),X9),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower2) ).
fof(f7357,plain,
( spl85_76
| ~ spl85_4
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5809,f4474,f3115,f4802]) ).
fof(f5809,plain,
( hBOOL(v_F)
| ~ spl85_4
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3281,f4784]) ).
fof(f7354,plain,
( spl85_76
| ~ spl85_4
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5782,f4474,f3115,f4802]) ).
fof(f5782,plain,
( hBOOL(v_F)
| ~ spl85_4
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3397,f4784]) ).
fof(f3397,plain,
( ! [X0,X1] : hBOOL(hAPP(hAPP(c_member(X0),hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____)),hAPP(c_member(X1),c_Arrow__Order__Mirabelle_OProf)))
| ~ spl85_4 ),
inference(resolution,[],[f3281,f2711]) ).
fof(f7353,plain,
( ~ spl85_76
| spl85_90
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7352,f4474,f6538,f4802]) ).
fof(f6538,plain,
( spl85_90
<=> ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(v_F,X2,v_F)
| c_Relation_Orefl__on(X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_90])]) ).
fof(f7352,plain,
( ! [X2,X0,X1] :
( c_Relation_Orefl__on(X1,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,X0,v_F)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7351,f4784]) ).
fof(f7351,plain,
( ! [X2,X0,X1] :
( c_Relation_Orefl__on(X1,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,v_F)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5265,f4784]) ).
fof(f5265,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2)))
| c_Relation_Orefl__on(X1,X2,X0)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2230,f4784]) ).
fof(f7350,plain,
( spl85_76
| ~ spl85_33
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5942,f4474,f3283,f4802]) ).
fof(f5942,plain,
( hBOOL(v_F)
| ~ spl85_33
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3285,f4784]) ).
fof(f7347,plain,
( spl85_76
| ~ spl85_24
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5785,f4474,f3218,f4802]) ).
fof(f5785,plain,
( hBOOL(v_F)
| ~ spl85_24
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3466,f4784]) ).
fof(f7342,plain,
( spl85_87
| ~ spl85_82
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7341,f4474,f6214,f6484]) ).
fof(f7341,plain,
( ! [X6] :
( ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,X6,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7340,f4784]) ).
fof(f7340,plain,
( ! [X0,X1,X6] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X1,tc_HOL_Obool)),v_F,v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,X6,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7339,f4784]) ).
fof(f7339,plain,
( ! [X0,X1,X6] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1)))),X6),v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,X6,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7338,f4784]) ).
fof(f7338,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(v_F,X6,v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1)))),X6),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_COMBC(X0,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X2),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1))))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5101,f4784]) ).
fof(f5101,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),X6,v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1)))),X6),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_COMBC(X0,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X2),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1))))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4049,f4784]) ).
fof(f4049,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),X6,hAPP(X2,hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1)))),X6),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_COMBC(X0,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X2),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1))))) ),
inference(superposition,[],[f2345,f2728]) ).
fof(f7336,plain,
( spl85_108
| spl85_109
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7329,f4474,f7334,f7331]) ).
fof(f7334,plain,
( spl85_109
<=> ! [X3] :
( ~ class_Orderings_Oord(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,v_F,v_F) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_109])]) ).
fof(f7329,plain,
( ! [X2,X3,X1] :
( ~ class_Orderings_Oord(X3)
| c_Orderings_Oord__class_Oless__eq(v_F,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,v_F,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7328,f4784]) ).
fof(f7328,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Orderings_Oord(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,v_F,v_F)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X3),X1,X2) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5169,f4784]) ).
fof(f5169,plain,
( ! [X2,X3,X0,X1] :
( ~ class_Orderings_Oord(X3)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK56(X1,X2,X3)),v_F)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X3),X1,X2) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2647,f4784]) ).
fof(f2647,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,X3),X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(X3,hAPP(X1,sK56(X1,X2,X3)),hAPP(X2,sK56(X1,X2,X3)))
| ~ class_Orderings_Oord(X3) ),
inference(cnf_transformation,[],[f1906]) ).
fof(f7313,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7312,f4474,f4802]) ).
fof(f7312,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7311]) ).
fof(f7311,plain,
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7310,f4784]) ).
fof(f7310,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1),X2)))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5336,f4784]) ).
fof(f5336,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_F,X2)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X0)),c_Set_Oinsert(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X0),X1),X2))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3817,f4784]) ).
fof(f7307,plain,
( ~ spl85_82
| spl85_61
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7306,f4474,f4802,f4384,f6214]) ).
fof(f7306,plain,
( ! [X5] :
( hBOOL(v_F)
| ~ hBOOL(X5)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7305,f4784]) ).
fof(f7305,plain,
( ! [X5] :
( hBOOL(v_F)
| ~ hBOOL(X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7304,f4784]) ).
fof(f7304,plain,
( ! [X10,X11,X8,X6,X9,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X7),X8)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X9),X9,c_Wellfounded_Olex__prod(tc_Nat_Onat,X9,c_Wellfounded_Oless__than,c_COMBK(X10,X11,X5)),hAPP(hAPP(c_COMBS(X9,X9,tc_prod(tc_Nat_Onat,X9)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X9,tc_prod(tc_Nat_Onat,X9)),X9,c_Product__Type_OPair(tc_Nat_Onat,X9)),X6)),c_COMBI(X9)))))
| ~ hBOOL(X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5016,f4784]) ).
fof(f5016,plain,
( ! [X10,X11,X8,X6,X9,X7,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X6,X7),v_F)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X9,X9)),hAPP(hAPP(c_Product__Type_OPair(X9,X9),X7),X8)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X9),X9,c_Wellfounded_Olex__prod(tc_Nat_Onat,X9,c_Wellfounded_Oless__than,c_COMBK(X10,X11,X5)),hAPP(hAPP(c_COMBS(X9,X9,tc_prod(tc_Nat_Onat,X9)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X9,tc_prod(tc_Nat_Onat,X9)),X9,c_Product__Type_OPair(tc_Nat_Onat,X9)),X6)),c_COMBI(X9)))))
| ~ hBOOL(X5) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4082,f4784]) ).
fof(f7303,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5772,f4474,f4802]) ).
fof(f5772,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4101,f4784]) ).
fof(f7302,plain,
( spl85_42
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5790,f4474,f4802,f3379]) ).
fof(f5790,plain,
( ! [X7] :
( hBOOL(v_F)
| hBOOL(X7) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3730,f4784]) ).
fof(f7299,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5833,f4474,f4802]) ).
fof(f5833,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3644,f4784]) ).
fof(f7289,plain,
( spl85_98
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5917,f4474,f4802,f6883]) ).
fof(f5917,plain,
( ! [X0,X1] :
( hBOOL(v_F)
| c_Wellfounded_Oacyclic(X0,X1) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2175,f4784]) ).
fof(f7288,plain,
( spl85_76
| ~ spl85_4
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5853,f4474,f3115,f4802]) ).
fof(f5853,plain,
( hBOOL(v_F)
| ~ spl85_4
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3117,f4784]) ).
fof(f7281,plain,
( spl85_76
| ~ spl85_82
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7280,f4474,f4223,f6214,f4802]) ).
fof(f7280,plain,
( ! [X2,X3] :
( X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7279,f4784]) ).
fof(f7279,plain,
( ! [X2,X3] :
( hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,v_F)
| X2 = X3 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7278,f4784]) ).
fof(f7278,plain,
( ! [X2,X3,X1] :
( X2 = X3
| hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,hAPP(X1,X3)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4987,f4784]) ).
fof(f4987,plain,
( ! [X2,X3,X1] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt),tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt,c_Wellfounded_Oless__than,sK84(X3,X2)),hAPP(hAPP(c_COMBS(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Arrow__Order__Mirabelle_Oalt,tc_prod(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),tc_Arrow__Order__Mirabelle_Oalt,c_Product__Type_OPair(tc_Nat_Onat,tc_Arrow__Order__Mirabelle_Oalt)),X1)),c_COMBI(tc_Arrow__Order__Mirabelle_Oalt)))))
| X2 = X3
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,hAPP(X1,X3)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3917,f4784]) ).
fof(f7274,plain,
( spl85_87
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7273,f4474,f6484]) ).
fof(f7273,plain,
( ! [X5] : c_Orderings_Oord__class_Oless__eq(v_F,X5,v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7272,f4784]) ).
fof(f7272,plain,
( ! [X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X5,v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5766,f4784]) ).
fof(f5766,plain,
( ! [X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X5,hAPP(v_F,X5))
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4149,f4784]) ).
fof(f4149,plain,
! [X8,X6,X9,X7,X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_fun(X4,tc_HOL_Obool),X5,hAPP(hAPP(hAPP(c_COMBS(X7,X8,X9),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,tc_HOL_Obool))),X6),X5)),
inference(superposition,[],[f2791,f2728]) ).
fof(f2791,plain,
! [X2,X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X0)),
inference(cnf_transformation,[],[f666]) ).
fof(f666,plain,
! [X0,X1,X2] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool)),X2),X0)),
inference(rectify,[],[f408]) ).
fof(f408,axiom,
! [X9,X8,X10] : c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X10),X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper1) ).
fof(f7259,plain,
( spl85_76
| spl85_61
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5907,f4474,f4384,f4802]) ).
fof(f5907,plain,
( ! [X1] :
( ~ hBOOL(X1)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3359,f4784]) ).
fof(f7258,plain,
( spl85_76
| spl85_58
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7257,f4474,f4223,f4223,f4802]) ).
fof(f7257,plain,
( ! [X10,X8,X9,X7] :
( X7 = X8
| X9 = X10
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7256]) ).
fof(f7256,plain,
( ! [X10,X8,X9,X7] :
( X7 = X8
| hBOOL(v_F)
| X9 = X10
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7255,f4784]) ).
fof(f7255,plain,
( ! [X10,X8,X9,X7] :
( X9 = X10
| hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8),X7)),sK84(X9,X10)))
| X7 = X8 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5316,f4784]) ).
fof(f5316,plain,
( ! [X10,X8,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),sK84(X9,X10)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8),X7)),sK84(X9,X10)))
| X7 = X8
| X9 = X10 )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3635,f4784]) ).
fof(f7253,plain,
( spl85_58
| spl85_76
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7252,f4474,f4223,f4802,f4223]) ).
fof(f7252,plain,
( ! [X10,X8,X9,X7] :
( X7 = X8
| hBOOL(v_F)
| X9 = X10 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5309,f4784]) ).
fof(f5309,plain,
( ! [X10,X8,X9,X7] :
( X7 = X8
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK84(X9,X10)),X7),X8)))
| X9 = X10 )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3567,f4784]) ).
fof(f7246,plain,
( spl85_76
| spl85_92
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5490,f4474,f6565,f4802]) ).
fof(f5490,plain,
( ! [X2,X0,X1] :
( c_Relation_Osingle__valued(X0,X1,X2)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2618,f4784]) ).
fof(f7241,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7240,f4474,f4802]) ).
fof(f7240,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5237,f4784]) ).
fof(f5237,plain,
( ! [X2,X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Omkbot(X3,X2)))
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3027,f4784]) ).
fof(f7225,plain,
( spl85_76
| ~ spl85_35
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5773,f4474,f3297,f4802]) ).
fof(f5773,plain,
( hBOOL(v_F)
| ~ spl85_35
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3299,f4784]) ).
fof(f7222,plain,
( spl85_107
| spl85_100
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6063,f4474,f6981,f7220]) ).
fof(f6063,plain,
( ! [X0] :
( class_Orderings_Oorder(v_F)
| ~ class_Orderings_Oorder(X0) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2423,f4784]) ).
fof(f7215,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7214,f4474,f4802]) ).
fof(f7214,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5753,f4784]) ).
fof(f5753,plain,
( ! [X11,X12,X13] : hBOOL(hAPP(hAPP(c_member(tc_prod(X11,X12)),hAPP(hAPP(c_Product__Type_OPair(X11,X12),X13),v_F)),v_F))
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4776,f4784]) ).
fof(f4776,plain,
( ! [X11,X14,X15,X12,X13] : hBOOL(hAPP(hAPP(c_member(tc_prod(X11,X12)),hAPP(hAPP(c_Product__Type_OPair(X11,X12),X13),v_F)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(X11,X12),tc_HOL_Obool)),X14),X15)))
| ~ spl85_69 ),
inference(resolution,[],[f4770,f2208]) ).
fof(f7213,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7212,f4474,f4802]) ).
fof(f7212,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7211]) ).
fof(f7211,plain,
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7210,f4784]) ).
fof(f7210,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),c_Set_Oinsert(X0,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2),X3))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5360,f4784]) ).
fof(f5360,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Set_Oinsert(X0,v_F,X3)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X1)),c_Set_Oinsert(X0,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X1),X2),X3))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3957,f4784]) ).
fof(f7204,plain,
( ~ spl85_76
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7203,f4474,f4223,f4802]) ).
fof(f7203,plain,
( ! [X3,X4] :
( X3 = X4
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7202]) ).
fof(f7202,plain,
( ! [X3,X4] :
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| X3 = X4 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7201,f4784]) ).
fof(f7201,plain,
( ! [X2,X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(v_F)
| X3 = X4 )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7200]) ).
fof(f7200,plain,
( ! [X2,X3,X4] :
( ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4)),c_Arrow__Order__Mirabelle_OLin))
| X3 = X4
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7199,f4784]) ).
fof(f7199,plain,
( ! [X2,X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5312,f4784]) ).
fof(f5312,plain,
( ! [X2,X3,X4] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X2,X3,X4)),c_Arrow__Order__Mirabelle_OLin))
| X3 = X4
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3620,f4784]) ).
fof(f7198,plain,
( spl85_106
| ~ spl85_23
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6094,f4474,f3213,f7195]) ).
fof(f6094,plain,
( class_Lattices_Osemilattice__sup(v_F)
| ~ spl85_23
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3215,f4784]) ).
fof(f7192,plain,
( spl85_84
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7191,f4474,f4802,f6422]) ).
fof(f7191,plain,
( ! [X3,X4] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X4,X3) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7190]) ).
fof(f7190,plain,
( ! [X3,X4] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X4,X3)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5858,f4784]) ).
fof(f5858,plain,
( ! [X3,X4] :
( c_Arrow__Order__Mirabelle_Odictator(X4,X3)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK83(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin),X4)),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3867,f4784]) ).
fof(f7186,plain,
( spl85_76
| ~ spl85_35
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5781,f4474,f3297,f4802]) ).
fof(f5781,plain,
( hBOOL(v_F)
| ~ spl85_35
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3326,f4784]) ).
fof(f7181,plain,
( spl85_79
| ~ spl85_22
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7180,f4474,f3208,f6161]) ).
fof(f7180,plain,
( ! [X3] : c_Orderings_Oord__class_Oless__eq(v_F,v_F,X3)
| ~ spl85_22
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5420,f4784]) ).
fof(f5420,plain,
( ! [X3] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,v_F,X3)
| ~ spl85_22
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3980,f4784]) ).
fof(f3980,plain,
( ! [X2,X3] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),X2),X3),X3)
| ~ spl85_22 ),
inference(resolution,[],[f2278,f3210]) ).
fof(f7172,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5923,f4474,f4802]) ).
fof(f5923,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3032,f4784]) ).
fof(f3032,plain,
! [X2,X0] : hBOOL(hAPP(hAPP(c_member(X0),X2),c_Set_Oinsert(X0,X2,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool))))),
inference(equality_resolution,[],[f2563]) ).
fof(f2563,plain,
! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),X2),c_Set_Oinsert(X0,X1,c_Orderings_Obot__class_Obot(tc_fun(X0,tc_HOL_Obool)))))
| X1 != X2 ),
inference(cnf_transformation,[],[f1829]) ).
fof(f7151,plain,
( spl85_79
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7150,f4474,f6161]) ).
fof(f7150,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(v_F,v_F,X0)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5589,f4784]) ).
fof(f5589,plain,
( ! [X2,X0] : c_Orderings_Oord__class_Oless__eq(tc_fun(X2,tc_HOL_Obool),v_F,X0)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2852,f4784]) ).
fof(f7147,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7146,f4474,f4802]) ).
fof(f7146,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7145]) ).
fof(f7145,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7144,f4784]) ).
fof(f7144,plain,
( ! [X40,X38,X41,X39,X36,X37,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X36,X39),X38)),X42),c_FuncSet_OPi(tc_fun(X36,X39),X38,c_FuncSet_OPi(X36,X39,X40,X41),c_COMBK(tc_fun(X38,tc_HOL_Obool),tc_fun(X36,X39),X37))))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f7143]) ).
fof(f7143,plain,
( ! [X40,X38,X41,X39,X36,X37,X42] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X36,X39),X38)),X42),c_FuncSet_OPi(tc_fun(X36,X39),X38,c_FuncSet_OPi(X36,X39,X40,X41),c_COMBK(tc_fun(X38,tc_HOL_Obool),tc_fun(X36,X39),X37))))
| v_F != v_F )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7142,f4784]) ).
fof(f7142,plain,
( ! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(v_F)
| v_F != hAPP(sK65(X37,X38,c_FuncSet_OPi(X36,X39,X40,X41),tc_fun(X36,X39),X42),sK72(X36,sK65(X37,X38,c_FuncSet_OPi(X36,X39,X40,X41),tc_fun(X36,X39),X42),X35,X40))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X36,X39),X38)),X42),c_FuncSet_OPi(tc_fun(X36,X39),X38,c_FuncSet_OPi(X36,X39,X40,X41),c_COMBK(tc_fun(X38,tc_HOL_Obool),tc_fun(X36,X39),X37)))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5216,f4784]) ).
fof(f5216,plain,
( ! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X36,X39)),X35),c_FuncSet_OPi(X36,X39,X40,X41)))
| v_F != hAPP(sK65(X37,X38,c_FuncSet_OPi(X36,X39,X40,X41),tc_fun(X36,X39),X42),sK72(X36,sK65(X37,X38,c_FuncSet_OPi(X36,X39,X40,X41),tc_fun(X36,X39),X42),X35,X40))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X36,X39),X38)),X42),c_FuncSet_OPi(tc_fun(X36,X39),X38,c_FuncSet_OPi(X36,X39,X40,X41),c_COMBK(tc_fun(X38,tc_HOL_Obool),tc_fun(X36,X39),X37)))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3610,f4784]) ).
fof(f7141,plain,
( spl85_76
| ~ spl85_55
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5824,f4474,f4018,f4802]) ).
fof(f5824,plain,
( hBOOL(v_F)
| ~ spl85_55
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4020,f4784]) ).
fof(f7140,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7139,f4474,f4802]) ).
fof(f7139,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f7138]) ).
fof(f7138,plain,
( v_F != v_F
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7137,f4784]) ).
fof(f7137,plain,
( ! [X14,X17,X15,X12] :
( hBOOL(v_F)
| v_F != hAPP(X17,sK72(X12,X14,X17,X15)) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7136]) ).
fof(f7136,plain,
( ! [X14,X17,X15,X12] :
( hBOOL(v_F)
| v_F != hAPP(X17,sK72(X12,X14,X17,X15))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7135,f4784]) ).
fof(f7135,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16))))
| v_F != hAPP(X17,sK72(X12,X14,X17,X15))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5209,f4784]) ).
fof(f5209,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(X12),sK65(X16,X13,X15,X12,X17)),X15))
| v_F != hAPP(X17,sK72(X12,X14,X17,X15))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16)))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3613,f4784]) ).
fof(f7133,plain,
( spl85_76
| ~ spl85_82
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7132,f4474,f6214,f4802]) ).
fof(f7132,plain,
( ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7131,f4784]) ).
fof(f7131,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7130,f4784]) ).
fof(f7130,plain,
( ! [X28,X26,X27,X25] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X28,X28)),hAPP(hAPP(c_Product__Type_OPair(X28,X28),X26),X27)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X28),X28,c_Wellfounded_Olex__prod(tc_Nat_Onat,X28,c_Wellfounded_Oless__than,v_F),hAPP(hAPP(c_COMBS(X28,X28,tc_prod(tc_Nat_Onat,X28)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X28,tc_prod(tc_Nat_Onat,X28)),X28,c_Product__Type_OPair(tc_Nat_Onat,X28)),X25)),c_COMBI(X28)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5069,f4784]) ).
fof(f5069,plain,
( ! [X28,X26,X27,X25] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X25,X26),v_F)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X28,X28)),hAPP(hAPP(c_Product__Type_OPair(X28,X28),X26),X27)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X28),X28,c_Wellfounded_Olex__prod(tc_Nat_Onat,X28,c_Wellfounded_Oless__than,v_F),hAPP(hAPP(c_COMBS(X28,X28,tc_prod(tc_Nat_Onat,X28)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X28,tc_prod(tc_Nat_Onat,X28)),X28,c_Product__Type_OPair(tc_Nat_Onat,X28)),X25)),c_COMBI(X28))))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4781,f4784]) ).
fof(f4781,plain,
( ! [X28,X26,X27,X25] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X25,X26),hAPP(X25,X27))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X28,X28)),hAPP(hAPP(c_Product__Type_OPair(X28,X28),X26),X27)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X28),X28,c_Wellfounded_Olex__prod(tc_Nat_Onat,X28,c_Wellfounded_Oless__than,v_F),hAPP(hAPP(c_COMBS(X28,X28,tc_prod(tc_Nat_Onat,X28)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X28,tc_prod(tc_Nat_Onat,X28)),X28,c_Product__Type_OPair(tc_Nat_Onat,X28)),X25)),c_COMBI(X28))))) )
| ~ spl85_69 ),
inference(resolution,[],[f4770,f2974]) ).
fof(f7128,plain,
( spl85_76
| ~ spl85_38
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5943,f4474,f3341,f4802]) ).
fof(f5943,plain,
( hBOOL(v_F)
| ~ spl85_38
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3343,f4784]) ).
fof(f7121,plain,
( spl85_76
| spl85_78
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7120,f4474,f6145,f4802]) ).
fof(f7120,plain,
( ! [X7] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X7)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7119,f4784]) ).
fof(f7119,plain,
( ! [X10,X8,X9,X7] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(sK83(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,X9,X10),X7) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7118]) ).
fof(f7118,plain,
( ! [X10,X8,X9,X7] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(sK83(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,X9,X10),X7)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5848,f4784]) ).
fof(f5848,plain,
( ! [X10,X8,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8)),X10),c_FuncSet_OPi(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),X9)))
| hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(sK83(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8,X9,X10),X7) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3949,f4784]) ).
fof(f7117,plain,
( spl85_58
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7116,f4474,f4802,f4223]) ).
fof(f7116,plain,
( ! [X2,X0] :
( hBOOL(v_F)
| X0 = X2 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5296,f4784]) ).
fof(f5296,plain,
( ! [X2,X3,X0] :
( X0 = X2
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Omkbot(X3,X2))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3084,f4784]) ).
fof(f7115,plain,
( spl85_76
| spl85_102
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7114,f4474,f7012,f4802]) ).
fof(f7012,plain,
( spl85_102
<=> ! [X0] : ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_102])]) ).
fof(f7114,plain,
( ! [X0] :
( ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,X0)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7113,f4784]) ).
fof(f7113,plain,
( ! [X3,X0] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),v_F,X0)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5452,f4784]) ).
fof(f5452,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Set_Oinsert(X3,X2,X1),X0)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2548,f4784]) ).
fof(f7107,plain,
( spl85_79
| ~ spl85_82
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7106,f4474,f6214,f6161]) ).
fof(f7106,plain,
( ! [X6] :
( ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,v_F,X6) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7105,f4784]) ).
fof(f7105,plain,
( ! [X0,X1,X6] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X1,tc_HOL_Obool)),v_F,v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,v_F,X6) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7104,f4784]) ).
fof(f7104,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_COMBC(X0,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X2),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1)))),v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,v_F,X6) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7103,f4784]) ).
fof(f7103,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),v_F,X6)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_COMBC(X0,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X2),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1)))),v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5100,f4784]) ).
fof(f5100,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_COMBC(X0,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X2),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1)))),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1)))),X6))
| c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),v_F,X6) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4048,f4784]) ).
fof(f4048,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),hAPP(X2,hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1)))),X6)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_fun(X1,tc_HOL_Obool)),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_COMBC(X0,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool))),X2),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1)))),hAPP(hAPP(c_COMBC(X0,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_COMBC(X1,tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_prod(X0,X1)),tc_fun(X1,tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool)),X0,c_COMBB(tc_prod(X0,X1),tc_fun(tc_fun(tc_prod(X0,X1),tc_HOL_Obool),tc_HOL_Obool),X1,c_member(tc_prod(X0,X1)))),c_Product__Type_OPair(X0,X1)))),X6)) ),
inference(superposition,[],[f2345,f2728]) ).
fof(f7093,plain,
( spl85_105
| ~ spl85_7
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6091,f4474,f3130,f7090]) ).
fof(f6091,plain,
( class_Lattices_Osemilattice__inf(v_F)
| ~ spl85_7
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3132,f4784]) ).
fof(f7082,plain,
( spl85_76
| ~ spl85_37
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5869,f4474,f3332,f4802]) ).
fof(f5869,plain,
( hBOOL(v_F)
| ~ spl85_37
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3357,f4784]) ).
fof(f7078,plain,
( spl85_76
| ~ spl85_82
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7077,f4474,f6214,f4802]) ).
fof(f7077,plain,
( ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7076,f4784]) ).
fof(f7076,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7075,f4784]) ).
fof(f7075,plain,
( ! [X40,X41] :
( hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X40,X41),v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4995,f4784]) ).
fof(f4995,plain,
( ! [X40,X41,X44,X42,X43] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X43,X43)),hAPP(hAPP(c_Product__Type_OPair(X43,X43),X41),X42)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X43),X43,c_Wellfounded_Olex__prod(tc_Nat_Onat,X43,c_Wellfounded_Oless__than,c_Set_Oinsert(tc_prod(X43,X43),hAPP(hAPP(c_Product__Type_OPair(X43,X43),X41),X42),X44)),hAPP(hAPP(c_COMBS(X43,X43,tc_prod(tc_Nat_Onat,X43)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X43,tc_prod(tc_Nat_Onat,X43)),X43,c_Product__Type_OPair(tc_Nat_Onat,X43)),X40)),c_COMBI(X43)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X40,X41),v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3926,f4784]) ).
fof(f3926,plain,
! [X40,X41,X44,X42,X43] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X43,X43)),hAPP(hAPP(c_Product__Type_OPair(X43,X43),X41),X42)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X43),X43,c_Wellfounded_Olex__prod(tc_Nat_Onat,X43,c_Wellfounded_Oless__than,c_Set_Oinsert(tc_prod(X43,X43),hAPP(hAPP(c_Product__Type_OPair(X43,X43),X41),X42),X44)),hAPP(hAPP(c_COMBS(X43,X43,tc_prod(tc_Nat_Onat,X43)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X43,tc_prod(tc_Nat_Onat,X43)),X43,c_Product__Type_OPair(tc_Nat_Onat,X43)),X40)),c_COMBI(X43)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X40,X41),hAPP(X40,X42)) ),
inference(resolution,[],[f2974,f2539]) ).
fof(f7074,plain,
( ~ spl85_76
| spl85_78
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7073,f4474,f6145,f4802]) ).
fof(f7073,plain,
( ! [X94] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X94)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f7072]) ).
fof(f7072,plain,
( ! [X94] :
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(v_F,X94) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7071,f4784]) ).
fof(f7071,plain,
( ! [X90,X91,X89,X94,X92,X93] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X94)
| ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(X89,X90,X91,X92),X93)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7070,f4784]) ).
fof(f7070,plain,
( ! [X90,X91,X89,X94,X92,X93] :
( c_Arrow__Order__Mirabelle_Odictator(hAPP(c_COMBB(X89,X90,X91,X92),X93),X94)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(X89,X90,X91,X92),X93)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5076,f4784]) ).
fof(f5076,plain,
( ! [X90,X91,X89,X94,X92,X93] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X94,hAPP(c_COMBB(X89,X90,X91,X92),X93))),sK21(X94,hAPP(c_COMBB(X89,X90,X91,X92),X93)))),v_F))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),hAPP(c_COMBB(X89,X90,X91,X92),X93)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| c_Arrow__Order__Mirabelle_Odictator(hAPP(c_COMBB(X89,X90,X91,X92),X93),X94) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4286,f4784]) ).
fof(f7055,plain,
( spl85_76
| spl85_104
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7051,f4474,f7053,f4802]) ).
fof(f7053,plain,
( spl85_104
<=> ! [X2,X0,X3] : ~ c_Predicate_ORangeP(X2,X0,v_F,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_104])]) ).
fof(f7051,plain,
( ! [X2,X3,X0] :
( ~ c_Predicate_ORangeP(X2,X0,v_F,X3)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5557,f4784]) ).
fof(f5557,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X0),X3),c_Relation_ORange(X2,X0,X1)))
| ~ c_Predicate_ORangeP(X2,X0,v_F,X3) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2288,f4784]) ).
fof(f7044,plain,
( spl85_76
| ~ spl85_40
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5816,f4474,f3371,f4802]) ).
fof(f5816,plain,
( hBOOL(v_F)
| ~ spl85_40
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3652,f4784]) ).
fof(f7043,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5791,f4474,f4802]) ).
fof(f5791,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3819,f4784]) ).
fof(f3819,plain,
! [X8,X6,X9,X7] : hBOOL(hAPP(hAPP(c_member(X6),c_Set_Oinsert(X7,X8,X9)),hAPP(c_member(X7),X8))),
inference(resolution,[],[f2539,f2711]) ).
fof(f7036,plain,
( spl85_87
| ~ spl85_29
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7035,f4474,f3254,f6484]) ).
fof(f7035,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(v_F,X0,v_F)
| ~ spl85_29
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5428,f4784]) ).
fof(f5428,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_F)
| ~ spl85_29
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4002,f4784]) ).
fof(f4002,plain,
( ! [X0,X1] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X1),X0))
| ~ spl85_29 ),
inference(resolution,[],[f2380,f3256]) ).
fof(f7030,plain,
( ~ spl85_76
| spl85_103
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7026,f4474,f7028,f4802]) ).
fof(f7026,plain,
( ! [X48,X54,X55] :
( c_Predicate_ORangeP(X54,X55,X48,v_F)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5055,f4784]) ).
fof(f5055,plain,
( ! [X50,X51,X48,X49,X54,X55,X52,X53] :
( c_Predicate_ORangeP(X54,X55,X48,v_F)
| ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X51,X52,X53),X48),X50),X49)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4372,f4784]) ).
fof(f7017,plain,
( ~ spl85_76
| spl85_77
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7016,f4474,f6128,f4802]) ).
fof(f7016,plain,
( ! [X56,X57,X55] :
( c_Predicate_ORangeP(X56,X57,v_F,X55)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7015,f4784]) ).
fof(f7015,plain,
( ! [X50,X51,X49,X56,X57,X55,X52,X53] :
( c_Predicate_ORangeP(X56,X57,hAPP(c_COMBB(X49,X50,X51,X52),X53),X55)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5047,f4784]) ).
fof(f5047,plain,
( ! [X50,X51,X49,X56,X57,X55,X52,X53] :
( ~ hBOOL(hAPP(hAPP(X52,v_F),X55))
| c_Predicate_ORangeP(X56,X57,hAPP(c_COMBB(X49,X50,X51,X52),X53),X55) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4354,f4784]) ).
fof(f4354,plain,
! [X50,X51,X49,X56,X54,X57,X55,X52,X53] :
( ~ hBOOL(hAPP(hAPP(X52,hAPP(X53,X54)),X55))
| c_Predicate_ORangeP(X56,X57,hAPP(c_COMBB(X49,X50,X51,X52),X53),X55) ),
inference(superposition,[],[f2173,f2177]) ).
fof(f7014,plain,
( spl85_102
| spl85_87
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f7010,f4474,f6484,f7012]) ).
fof(f7010,plain,
( ! [X0,X1] :
( c_Orderings_Oord__class_Oless__eq(v_F,X1,v_F)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7009,f4784]) ).
fof(f7009,plain,
( ! [X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(v_F,X1,v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),v_F,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f7008,f4784]) ).
fof(f7008,plain,
( ! [X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),v_F,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5678,f4784]) ).
fof(f5678,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X2),X0)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2795,f4784]) ).
fof(f2795,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X2),X0) ),
inference(cnf_transformation,[],[f2039]) ).
fof(f2039,plain,
! [X0,X1,X2,X3] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X0))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X2),X0) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X0)) ) ),
inference(rectify,[],[f2038]) ).
fof(f2038,plain,
! [X3,X1,X2,X0] :
( ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X3))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,X2),X3) )
& ( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,X2),X3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X3)) ) ),
inference(nnf_transformation,[],[f967]) ).
fof(f967,plain,
! [X3,X1,X2,X0] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X0,tc_HOL_Obool)),X2),X3))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X0,tc_HOL_Obool),X1,X2),X3) ),
inference(rectify,[],[f490]) ).
fof(f490,axiom,
! [X8,X10,X9,X47] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X9),X47))
<=> c_Orderings_Oord__class_Oless__eq(tc_fun(X8,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X8,tc_HOL_Obool),X10,X9),X47) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset__conv) ).
fof(f7006,plain,
( spl85_76
| ~ spl85_46
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5822,f4474,f3437,f4802]) ).
fof(f5822,plain,
( hBOOL(v_F)
| ~ spl85_46
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3439,f4784]) ).
fof(f6996,plain,
( spl85_76
| ~ spl85_16
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6995,f4474,f3178,f4802]) ).
fof(f6995,plain,
( hBOOL(v_F)
| ~ spl85_16
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f6994]) ).
fof(f6994,plain,
( hBOOL(v_F)
| v_F != v_F
| ~ spl85_16
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6993,f4784]) ).
fof(f6993,plain,
( ! [X18] :
( hBOOL(v_F)
| v_F != hAPP(v_F,sK72(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18,v_F,c_Arrow__Order__Mirabelle_OProf)) )
| ~ spl85_16
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5220,f4784]) ).
fof(f5220,plain,
( ! [X18] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| v_F != hAPP(v_F,sK72(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X18,v_F,c_Arrow__Order__Mirabelle_OProf)) )
| ~ spl85_16
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3614,f4784]) ).
fof(f6992,plain,
( spl85_101
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6988,f4474,f4802,f6990]) ).
fof(f6988,plain,
( ! [X0,X1] :
( ~ hBOOL(v_F)
| ~ c_Wellfounded_Oacyclic(X1,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5377,f4784]) ).
fof(f5377,plain,
( ! [X0,X1] :
( ~ c_Wellfounded_Oacyclic(X1,X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),v_F),c_Transitive__Closure_Otrancl(X1,X0))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2723,f4784]) ).
fof(f6984,plain,
( spl85_100
| ~ spl85_8
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6040,f4474,f3135,f6981]) ).
fof(f3135,plain,
( spl85_8
<=> class_Orderings_Oorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_8])]) ).
fof(f6040,plain,
( class_Orderings_Oorder(v_F)
| ~ spl85_8
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3137,f4784]) ).
fof(f3137,plain,
( class_Orderings_Oorder(tc_HOL_Obool)
| ~ spl85_8 ),
inference(avatar_component_clause,[],[f3135]) ).
fof(f6975,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6974,f4474,f4802]) ).
fof(f6974,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6973]) ).
fof(f6973,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6972,f4784]) ).
fof(f6972,plain,
( ! [X31,X28,X29,X34,X32,X30,X33] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X28,X30),X33)),X29),c_FuncSet_OPi(tc_fun(X28,X30),X33,c_FuncSet_OPi(X28,X30,X31,X32),X34))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6971,f4784]) ).
fof(f6971,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X28,X30)),X27),c_FuncSet_OPi(X28,X30,X31,X32)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X28,X30),X33)),X29),c_FuncSet_OPi(tc_fun(X28,X30),X33,c_FuncSet_OPi(X28,X30,X31,X32),X34))) )
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f6970]) ).
fof(f6970,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( v_F != v_F
| hBOOL(hAPP(hAPP(c_member(tc_fun(X28,X30)),X27),c_FuncSet_OPi(X28,X30,X31,X32)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X28,X30),X33)),X29),c_FuncSet_OPi(tc_fun(X28,X30),X33,c_FuncSet_OPi(X28,X30,X31,X32),X34))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5218,f4784]) ).
fof(f5218,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( v_F != hAPP(sK57(X29,c_FuncSet_OPi(X28,X30,X31,X32),tc_fun(X28,X30),X33,X34),sK72(X28,sK57(X29,c_FuncSet_OPi(X28,X30,X31,X32),tc_fun(X28,X30),X33,X34),X27,X31))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X28,X30)),X27),c_FuncSet_OPi(X28,X30,X31,X32)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X28,X30),X33)),X29),c_FuncSet_OPi(tc_fun(X28,X30),X33,c_FuncSet_OPi(X28,X30,X31,X32),X34))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3609,f4784]) ).
fof(f6969,plain,
( spl85_76
| ~ spl85_34
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6968,f4474,f3290,f4802]) ).
fof(f6968,plain,
( hBOOL(v_F)
| ~ spl85_34
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5937,f4784]) ).
fof(f5937,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,v_F))
| ~ spl85_34
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3292,f4784]) ).
fof(f6966,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6965,f4474,f4802]) ).
fof(f6965,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6964]) ).
fof(f6964,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6963,f4784]) ).
fof(f6963,plain,
( ! [X2,X3,X0,X5] :
( hBOOL(hAPP(hAPP(c_member(X0),sK72(X0,X5,X2,X3)),X3))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6962]) ).
fof(f6962,plain,
( ! [X2,X3,X0,X5] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(X0),sK72(X0,X5,X2,X3)),X3))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5261,f4784]) ).
fof(f5261,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,X1)),X2),c_FuncSet_OPi(X0,X1,X3,X4)))
| hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(X0),sK72(X0,X5,X2,X3)),X3)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3590,f4784]) ).
fof(f6953,plain,
( spl85_84
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6952,f4474,f4802,f6422]) ).
fof(f6952,plain,
( ! [X2,X1] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X2,X1) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6951]) ).
fof(f6951,plain,
( ! [X2,X1] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5857,f4784]) ).
fof(f5857,plain,
( ! [X2,X1] :
( c_Arrow__Order__Mirabelle_Odictator(X2,X1)
| hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK65(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X2)),c_Arrow__Order__Mirabelle_OProf)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3866,f4784]) ).
fof(f6948,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6947,f4474,f4802]) ).
fof(f6947,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6946]) ).
fof(f6946,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6945,f4784]) ).
fof(f6945,plain,
( ! [X16,X14,X15,X12,X13] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16)))) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6944]) ).
fof(f6944,plain,
( ! [X16,X14,X15,X12,X13] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16))))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5692,f4784]) ).
fof(f5692,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(X12),sK72(X12,X17,X14,X15)),X15))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X13)),X14),c_FuncSet_OPi(X12,X13,X15,c_COMBK(tc_fun(X13,tc_HOL_Obool),X12,X16)))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3592,f4784]) ).
fof(f6943,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5764,f4474,f4802]) ).
fof(f5764,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3415,f4784]) ).
fof(f6942,plain,
( spl85_76
| ~ spl85_40
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5712,f4474,f3371,f4802]) ).
fof(f5712,plain,
( hBOOL(v_F)
| ~ spl85_40
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3372,f4784]) ).
fof(f6924,plain,
( spl85_58
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5922,f4474,f4802,f4223]) ).
fof(f5922,plain,
( ! [X2,X1] :
( ~ hBOOL(v_F)
| X1 = X2 )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2564,f4784]) ).
fof(f6923,plain,
( ~ spl85_76
| ~ spl85_40
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6922,f4474,f3371,f4802]) ).
fof(f6922,plain,
( ~ hBOOL(v_F)
| ~ spl85_40
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6921]) ).
fof(f6921,plain,
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| ~ spl85_40
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6920,f4784]) ).
fof(f6920,plain,
( ! [X14,X15,X13] :
( ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_Product__Type_OPair(X13,X14),X15)),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_40
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5371,f4784]) ).
fof(f5371,plain,
( ! [X14,X15,X13] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),hAPP(c_Product__Type_OPair(X13,X14),X15)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_Product__Type_OPair(X13,X14),X15)),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_40
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4237,f4784]) ).
fof(f6919,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6918,f4474,f4802]) ).
fof(f6918,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6917]) ).
fof(f6917,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5260,f4784]) ).
fof(f5260,plain,
( ! [X10,X8,X6,X9,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(X10),c_FuncSet_OPi(X5,X6,X8,X9)),hAPP(c_member(tc_fun(X5,X6)),X7)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3475,f4784]) ).
fof(f6908,plain,
( spl85_61
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5961,f4474,f4802,f4384]) ).
fof(f5961,plain,
( ! [X0] :
( ~ hBOOL(v_F)
| ~ hBOOL(X0) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2777,f4784]) ).
fof(f6907,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5900,f4474,f4802]) ).
fof(f5900,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4087,f4784]) ).
fof(f6892,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5805,f4474,f4802]) ).
fof(f5805,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4097,f4784]) ).
fof(f6891,plain,
( spl85_99
| spl85_95
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6887,f4474,f6693,f6889]) ).
fof(f6889,plain,
( spl85_99
<=> ! [X1,X3] : v_F != c_Set_Oinsert(X3,X1,v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_99])]) ).
fof(f6887,plain,
( ! [X2,X3,X0,X1,X4] :
( X0 = X4
| X0 = X2
| v_F != c_Set_Oinsert(X3,X1,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6886,f4784]) ).
fof(f6886,plain,
( ! [X2,X3,X0,X1,X4] :
( v_F != c_Set_Oinsert(X3,X1,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,v_F))))
| X0 = X4
| X0 = X2 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6017,f4784]) ).
fof(f6017,plain,
( ! [X2,X3,X0,X1,X4] :
( c_Set_Oinsert(X3,X1,c_Set_Oinsert(X3,X0,c_Orderings_Obot__class_Obot(tc_fun(X3,v_F)))) != c_Set_Oinsert(X3,X4,c_Set_Oinsert(X3,X2,c_Orderings_Obot__class_Obot(tc_fun(X3,v_F))))
| X0 = X4
| X0 = X2 )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2216,f4784]) ).
fof(f6885,plain,
( spl85_98
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5918,f4474,f4802,f6883]) ).
fof(f5918,plain,
( ! [X0,X1] :
( hBOOL(v_F)
| c_Wellfounded_Oacyclic(X1,X0) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2722,f4784]) ).
fof(f6879,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6878,f4474,f4802]) ).
fof(f6878,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f6877]) ).
fof(f6877,plain,
( v_F != v_F
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6876,f4784]) ).
fof(f6876,plain,
( ! [X3,X1] :
( hBOOL(v_F)
| v_F != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3,X1),tc_HOL_Obool)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5688,f4784]) ).
fof(f5688,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(v_F)
| c_Orderings_Obot__class_Obot(tc_fun(tc_fun(X3,X1),tc_HOL_Obool)) != c_FuncSet_OPi(X3,X1,X2,X0) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2637,f4784]) ).
fof(f6869,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6868,f4474,f4802]) ).
fof(f6868,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5289,f4784]) ).
fof(f5289,plain,
( ! [X2,X1] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Omktop(X2,X1)))
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3020,f4784]) ).
fof(f6845,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6844,f4474,f4802]) ).
fof(f6844,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f6843]) ).
fof(f6843,plain,
( hBOOL(v_F)
| v_F != v_F
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6842,f4784]) ).
fof(f6842,plain,
( ! [X40,X38,X41,X39,X36,X37,X35,X42] :
( v_F != hAPP(sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),sK72(X35,X37,sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),X38))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6841]) ).
fof(f6841,plain,
( ! [X40,X38,X41,X39,X36,X37,X35,X42] :
( v_F != hAPP(sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),sK72(X35,X37,sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),X38))
| hBOOL(v_F)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6840,f4784]) ).
fof(f6840,plain,
( ! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,X39)))
| hBOOL(v_F)
| v_F != hAPP(sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),sK72(X35,X37,sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),X38)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5217,f4784]) ).
fof(f5217,plain,
( ! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40))))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,X39)))
| v_F != hAPP(sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),sK72(X35,X37,sK65(X40,X41,c_FuncSet_OPi(X35,X36,X38,X39),tc_fun(X35,X36),X42),X38)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3617,f4784]) ).
fof(f6835,plain,
( spl85_95
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6834,f4474,f4802,f6693]) ).
fof(f6834,plain,
( ! [X6,X9,X7] :
( ~ hBOOL(v_F)
| X7 = X9
| X6 = X7 )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6833]) ).
fof(f6833,plain,
( ! [X6,X9,X7] :
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| X6 = X7
| X7 = X9 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6832,f4784]) ).
fof(f6832,plain,
( ! [X8,X6,X9,X7] :
( X7 = X9
| X6 = X7
| ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),X8)) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6831]) ).
fof(f6831,plain,
( ! [X8,X6,X9,X7] :
( X6 = X7
| ~ hBOOL(v_F)
| X7 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),X8))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6830,f4784]) ).
fof(f6830,plain,
( ! [X8,X6,X9,X7] :
( X6 = X7
| ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),X8))
| X7 = X9 )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6829]) ).
fof(f6829,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| X6 = X7
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),X8))
| X7 = X9 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6828,f4784]) ).
fof(f6828,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X6)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X7)))
| X6 = X7
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),X8))
| ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| X7 = X9 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5324,f4784]) ).
fof(f5324,plain,
( ! [X8,X6,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X7)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X8),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),X8))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X7),X6)),c_Arrow__Order__Mirabelle_Obelow(X8,X9,X7)))
| X6 = X7
| X7 = X9 )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3708,f4784]) ).
fof(f6815,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5935,f4474,f4802]) ).
fof(f5935,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4782,f4784]) ).
fof(f4782,plain,
( ! [X29] : hBOOL(hAPP(v_F,X29))
| ~ spl85_69 ),
inference(resolution,[],[f4770,f2710]) ).
fof(f6809,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6808,f4474,f4802]) ).
fof(f6808,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6807]) ).
fof(f6807,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5495,f4784]) ).
fof(f5495,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X2,X3)),X0),c_FuncSet_OPi(X2,X3,X1,X4))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2649,f4784]) ).
fof(f6806,plain,
( ~ spl85_76
| ~ spl85_47
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5774,f4474,f3442,f4802]) ).
fof(f5774,plain,
( ~ hBOOL(v_F)
| ~ spl85_47
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3443,f4784]) ).
fof(f6803,plain,
( spl85_97
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6799,f4474,f4223,f6801]) ).
fof(f6801,plain,
( spl85_97
<=> ! [X1] : v_F != hAPP(v_F,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_97])]) ).
fof(f6799,plain,
( ! [X3,X0,X1] :
( X0 = X3
| v_F != hAPP(v_F,X1) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5710,f4784]) ).
fof(f5710,plain,
( ! [X2,X3,X0,X1,X4] :
( X0 = X3
| v_F != hAPP(hAPP(c_Product__Type_OPair(X2,X4),X3),X1) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2787,f4784]) ).
fof(f6796,plain,
( spl85_77
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6086,f4474,f6128]) ).
fof(f6086,plain,
( ! [X203,X207,X204] : c_Predicate_ORangeP(X203,X204,v_F,X207)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4343,f4784]) ).
fof(f6786,plain,
( spl85_87
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6785,f4474,f6484]) ).
fof(f6785,plain,
( ! [X2] : c_Orderings_Oord__class_Oless__eq(v_F,X2,v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5676,f4784]) ).
fof(f5676,plain,
( ! [X2,X1] : c_Orderings_Oord__class_Oless__eq(tc_fun(X1,tc_HOL_Obool),X2,v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2791,f4784]) ).
fof(f6782,plain,
( spl85_77
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6781,f4474,f4802,f6128]) ).
fof(f6781,plain,
( ! [X94,X92,X93] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X93,X94,v_F,X92) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5049,f4784]) ).
fof(f5049,plain,
( ! [X90,X88,X89,X94,X92,X93] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X93,X94,c_COMBK(X88,X89,X90),X92) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4359,f4784]) ).
fof(f4359,plain,
! [X90,X88,X89,X94,X92,X93] :
( c_Predicate_ORangeP(X93,X94,c_COMBK(X88,X89,X90),X92)
| ~ hBOOL(hAPP(X90,X92)) ),
inference(superposition,[],[f2173,f2430]) ).
fof(f6778,plain,
( spl85_76
| ~ spl85_10
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5810,f4474,f3145,f4802]) ).
fof(f5810,plain,
( hBOOL(v_F)
| ~ spl85_10
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3339,f4784]) ).
fof(f3339,plain,
( ! [X6] : hBOOL(hAPP(hAPP(c_member(X6),c_Arrow__Order__Mirabelle_OProf),hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P_H____)))
| ~ spl85_10 ),
inference(resolution,[],[f3147,f2711]) ).
fof(f6774,plain,
( spl85_61
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6773,f4474,f4802,f4384]) ).
fof(f6773,plain,
( ! [X0] :
( ~ hBOOL(v_F)
| ~ hBOOL(X0) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6772]) ).
fof(f6772,plain,
( ! [X0] :
( ~ hBOOL(X0)
| ~ hBOOL(v_F)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6771,f4784]) ).
fof(f6771,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_COMBK(X1,X2,X0)))
| ~ hBOOL(v_F)
| ~ hBOOL(X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5369,f4784]) ).
fof(f5369,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_COMBK(X1,X2,X0)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(X0)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_COMBK(X1,X2,X0))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4081,f4784]) ).
fof(f6769,plain,
( ~ spl85_76
| spl85_77
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6768,f4474,f6128,f4802]) ).
fof(f6768,plain,
( ! [X6,X7,X5] :
( c_Predicate_ORangeP(X6,X7,v_F,X5)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5064,f4784]) ).
fof(f5064,plain,
( ! [X8,X6,X9,X7,X5] :
( c_Predicate_ORangeP(X6,X7,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X9),X5)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4675,f4784]) ).
fof(f4675,plain,
! [X8,X6,X9,X7,X4,X5] :
( ~ hBOOL(hAPP(X4,X5))
| c_Predicate_ORangeP(X6,X7,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X8,tc_HOL_Obool)),X9),X5) ),
inference(resolution,[],[f2894,f2173]) ).
fof(f6758,plain,
( spl85_76
| ~ spl85_40
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5886,f4474,f3371,f4802]) ).
fof(f5886,plain,
( hBOOL(v_F)
| ~ spl85_40
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4241,f4784]) ).
fof(f6757,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6756,f4474,f4802]) ).
fof(f6756,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6755]) ).
fof(f6755,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6754,f4784]) ).
fof(f6754,plain,
( ! [X21,X19,X22,X23,X20] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23))) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6753]) ).
fof(f6753,plain,
( ! [X21,X19,X22,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23)))
| hBOOL(v_F)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5505,f4784]) ).
fof(f5505,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3594,f4784]) ).
fof(f6738,plain,
( spl85_96
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6734,f4474,f4802,f6736]) ).
fof(f6734,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(v_F)
| c_Predicate_ODomainP(X3,X1,X2,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4889,f4784]) ).
fof(f4889,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ hBOOL(hAPP(v_F,X4))
| c_Predicate_ODomainP(X3,X1,X2,X0) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2844,f4784]) ).
fof(f6731,plain,
( spl85_76
| ~ spl85_38
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5795,f4474,f3341,f4802]) ).
fof(f5795,plain,
( hBOOL(v_F)
| ~ spl85_38
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3964,f4784]) ).
fof(f6725,plain,
( spl85_76
| spl85_90
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6724,f4474,f6538,f4802]) ).
fof(f6724,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(v_F,X2,v_F)
| c_Relation_Orefl__on(X0,X1,X2)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6723,f4784]) ).
fof(f6723,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,v_F)
| c_Relation_Orefl__on(X0,X1,X2)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5252,f4784]) ).
fof(f5252,plain,
( ! [X2,X0,X1] :
( hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,c_Product__Type_OSigma(X0,X0,X1,c_COMBK(tc_fun(X0,tc_HOL_Obool),X0,X1)))
| c_Relation_Orefl__on(X0,X1,X2) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2556,f4784]) ).
fof(f6708,plain,
( spl85_90
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6707,f4474,f4802,f6538]) ).
fof(f6707,plain,
( ! [X2,X0,X1] :
( hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,X0,v_F)
| c_Relation_Orefl__on(X1,X2,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6706,f4784]) ).
fof(f6706,plain,
( ! [X2,X0,X1] :
( hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,v_F)
| c_Relation_Orefl__on(X1,X2,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5492,f4784]) ).
fof(f5492,plain,
( ! [X2,X0,X1] :
( c_Relation_Orefl__on(X1,X2,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Product__Type_OSigma(X1,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X1,X2)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2231,f4784]) ).
fof(f6699,plain,
( ~ spl85_76
| spl85_78
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6698,f4474,f6145,f4802]) ).
fof(f6698,plain,
( ! [X15] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X15)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6697]) ).
fof(f6697,plain,
( ! [X15] :
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(v_F,X15) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6696,f4784]) ).
fof(f6696,plain,
( ! [X14,X15,X12,X13] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X15)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(X12,X13,X14)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5687,f4784]) ).
fof(f5687,plain,
( ! [X14,X15,X12,X13] :
( c_Arrow__Order__Mirabelle_Odictator(c_COMBK(X12,X13,X14),X15)
| ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),c_COMBK(X12,X13,X14)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3966,f4784]) ).
fof(f6695,plain,
( ~ spl85_76
| spl85_95
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6691,f4474,f6693,f4802]) ).
fof(f6691,plain,
( ! [X10,X8,X9] :
( X9 = X10
| ~ hBOOL(v_F)
| X8 = X9 )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6690]) ).
fof(f6690,plain,
( ! [X10,X8,X9] :
( X9 = X10
| ~ hBOOL(v_F)
| X8 = X9
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6689,f4784]) ).
fof(f6689,plain,
( ! [X10,X8,X9,X7] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)))
| ~ hBOOL(v_F)
| X9 = X10
| X8 = X9 )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6688]) ).
fof(f6688,plain,
( ! [X10,X8,X9,X7] :
( X9 = X10
| ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)))
| ~ hBOOL(v_F)
| X8 = X9 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6687,f4784]) ).
fof(f6687,plain,
( ! [X10,X8,X9,X7] :
( X9 = X10
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(v_F)
| X8 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10))) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6686]) ).
fof(f6686,plain,
( ! [X10,X8,X9,X7] :
( X9 = X10
| X8 = X9
| ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)))
| ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6685,f4784]) ).
fof(f6685,plain,
( ! [X10,X8,X9,X7] :
( ~ hBOOL(v_F)
| X9 = X10
| X8 = X9
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5318,f4784]) ).
fof(f5318,plain,
( ! [X10,X8,X9,X7] :
( X9 = X10
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X8),X10)),X7))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Obelow(X7,X9,X10)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X7),c_Arrow__Order__Mirabelle_OLin))
| X8 = X9 )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3687,f4784]) ).
fof(f6673,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6672,f4474,f4802]) ).
fof(f6672,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6671]) ).
fof(f6671,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6670,f4784]) ).
fof(f6670,plain,
( ! [X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6669]) ).
fof(f6669,plain,
( ! [X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5699,f4784]) ).
fof(f5699,plain,
( ! [X21,X19,X26,X24,X22,X25,X23,X20] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X19,X20)),X21),c_FuncSet_OPi(X19,X20,X22,X23)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X19,X20),X24)),X26),c_FuncSet_OPi(tc_fun(X19,X20),X24,c_FuncSet_OPi(X19,X20,X22,X23),X25))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3601,f4784]) ).
fof(f6666,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6665,f4474,f4802]) ).
fof(f6665,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6664]) ).
fof(f6664,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5691,f4784]) ).
fof(f5691,plain,
( ! [X10,X8,X6,X9,X7,X5] :
( hBOOL(hAPP(hAPP(c_member(X10),c_FuncSet_OPi(X5,X6,X8,c_COMBK(tc_fun(X6,tc_HOL_Obool),X5,X9))),hAPP(c_member(tc_fun(X5,X6)),X7)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3492,f4784]) ).
fof(f6663,plain,
( spl85_77
| ~ spl85_76
| ~ spl85_23
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6662,f4474,f3213,f4802,f6128]) ).
fof(f6662,plain,
( ! [X2,X3,X1] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X2,X3,v_F,X1) )
| ~ spl85_23
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5038,f4784]) ).
fof(f5038,plain,
( ! [X2,X3,X0,X1] :
( c_Predicate_ORangeP(X2,X3,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X0),X1)
| ~ hBOOL(v_F) )
| ~ spl85_23
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4345,f4784]) ).
fof(f4345,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(X0,X1))
| c_Predicate_ORangeP(X2,X3,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat),X0),X1) )
| ~ spl85_23 ),
inference(superposition,[],[f2173,f3828]) ).
fof(f6657,plain,
( spl85_76
| ~ spl85_33
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5868,f4474,f3283,f4802]) ).
fof(f5868,plain,
( hBOOL(v_F)
| ~ spl85_33
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3312,f4784]) ).
fof(f6656,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5803,f4474,f4802]) ).
fof(f5803,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3960,f4784]) ).
fof(f6651,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5924,f4474,f4802]) ).
fof(f5924,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2539,f4784]) ).
fof(f6648,plain,
( spl85_76
| spl85_61
| ~ spl85_7
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5831,f4474,f3130,f4384,f4802]) ).
fof(f5831,plain,
( ! [X14] :
( ~ hBOOL(X14)
| hBOOL(v_F) )
| ~ spl85_7
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3852,f4784]) ).
fof(f6643,plain,
( spl85_76
| ~ spl85_25
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5877,f4474,f3223,f4802]) ).
fof(f5877,plain,
( hBOOL(v_F)
| ~ spl85_25
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3225,f4784]) ).
fof(f6640,plain,
( spl85_76
| ~ spl85_40
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5891,f4474,f3371,f4802]) ).
fof(f5891,plain,
( hBOOL(v_F)
| ~ spl85_40
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4242,f4784]) ).
fof(f6639,plain,
( spl85_94
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6635,f4474,f4802,f6637]) ).
fof(f6635,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X2,X1,X3,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4814,f4784]) ).
fof(f4814,plain,
( ! [X2,X3,X0,X1] :
( c_Predicate_ORangeP(X2,X1,X3,X0)
| ~ hBOOL(hAPP(v_F,X0)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2173,f4784]) ).
fof(f6634,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6633,f4474,f4802]) ).
fof(f6633,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6632]) ).
fof(f6632,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6631,f4784]) ).
fof(f6631,plain,
( ! [X2,X1,X6,X5] :
( hBOOL(hAPP(hAPP(c_member(X1),sK83(X5,X1,X2,X6,v_F)),X5))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5193,f4784]) ).
fof(f5193,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X0,tc_fun(X1,X2))),X3),c_FuncSet_OPi(X0,tc_fun(X1,X2),X4,c_COMBK(tc_fun(tc_fun(X1,X2),tc_HOL_Obool),X0,c_FuncSet_OPi(X1,X2,X5,X6)))))
| hBOOL(hAPP(hAPP(c_member(X1),sK83(X5,X1,X2,X6,v_F)),X5)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3523,f4784]) ).
fof(f6616,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6615,f4474,f4802]) ).
fof(f6615,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6614]) ).
fof(f6614,plain,
( ~ hBOOL(v_F)
| ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6613,f4784]) ).
fof(f6613,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(c_Transitive__Closure_Ortranclp(X0,X1),v_F)))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5370,f4784]) ).
fof(f5370,plain,
( ! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(c_Transitive__Closure_Ortranclp(X0,X1),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3))),c_Arrow__Order__Mirabelle_OLin))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X3),X2)),hAPP(c_Transitive__Closure_Ortranclp(X0,X1),v_F))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4094,f4784]) ).
fof(f6607,plain,
( spl85_76
| ~ spl85_82
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6606,f4474,f6214,f4802]) ).
fof(f6606,plain,
( ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6605,f4784]) ).
fof(f6605,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6604,f4784]) ).
fof(f6604,plain,
( ! [X4,X5] :
( hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X5),v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5000,f4784]) ).
fof(f5000,plain,
( ! [X8,X6,X9,X7,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X7,X7)),hAPP(hAPP(c_Product__Type_OPair(X7,X7),X5),X6)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X7),X7,c_Wellfounded_Olex__prod(tc_Nat_Onat,X7,c_Wellfounded_Oless__than,c_Set_Oinsert(X8,hAPP(hAPP(c_Product__Type_OPair(X7,X7),X5),X6),X9)),hAPP(hAPP(c_COMBS(X7,X7,tc_prod(tc_Nat_Onat,X7)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X7,tc_prod(tc_Nat_Onat,X7)),X7,c_Product__Type_OPair(tc_Nat_Onat,X7)),X4)),c_COMBI(X7)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X4,X5),v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3958,f4784]) ).
fof(f6603,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6602,f4474,f4802]) ).
fof(f6602,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6601]) ).
fof(f6601,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5496,f4784]) ).
fof(f5496,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(hAPP(c_FuncSet_OPi(X0,X1,X3,X4),X2))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3467,f4784]) ).
fof(f6595,plain,
( spl85_76
| spl85_93
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6591,f4474,f6593,f4802]) ).
fof(f6591,plain,
( ! [X2,X3,X0,X1,X5] :
( c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,v_F)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f6590]) ).
fof(f6590,plain,
( ! [X2,X3,X0,X1,X5] :
( hBOOL(v_F)
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,v_F)
| v_F != v_F )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6589,f4784]) ).
fof(f6589,plain,
( ! [X2,X3,X0,X1,X5] :
( c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,v_F)
| hBOOL(v_F)
| v_F != hAPP(v_F,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6588,f4784]) ).
fof(f6588,plain,
( ! [X2,X3,X0,X1,X6,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK28(X0,X1,X2,X3,X5,X6)),X0)),X5))
| v_F != hAPP(v_F,X0)
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6587,f4784]) ).
fof(f6587,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( hAPP(v_F,X0) != hAPP(hAPP(X3,X4),X0)
| c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,v_F)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK28(X0,X1,X2,X3,X5,X6)),X0)),X5)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f4851,f4784]) ).
fof(f4851,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( c_Recdef_Owfrec__rel(X2,X1,X5,X3,X0,hAPP(hAPP(X3,X4),X0))
| hAPP(v_F,X0) != hAPP(hAPP(X3,X4),X0)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X2,X2)),hAPP(hAPP(c_Product__Type_OPair(X2,X2),sK28(X0,X1,X2,X3,X5,X6)),X0)),X5)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2486,f4784]) ).
fof(f6578,plain,
( spl85_76
| ~ spl85_40
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5806,f4474,f3371,f4802]) ).
fof(f5806,plain,
( hBOOL(v_F)
| ~ spl85_40
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4243,f4784]) ).
fof(f6577,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6576,f4474,f4802]) ).
fof(f6576,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6575]) ).
fof(f6575,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6574,f4784]) ).
fof(f6574,plain,
( ! [X10,X11,X6,X9,X7] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(X6),sK57(X11,X9,X6,X7,X10)),X9)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6573,f4784]) ).
fof(f6573,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X7)),X8),c_FuncSet_OPi(X6,X7,X9,X10)))
| hBOOL(hAPP(hAPP(c_member(X6),sK57(X11,X9,X6,X7,X10)),X9)) )
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f6572]) ).
fof(f6572,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X7)),X8),c_FuncSet_OPi(X6,X7,X9,X10)))
| hBOOL(hAPP(hAPP(c_member(X6),sK57(X11,X9,X6,X7,X10)),X9))
| v_F != v_F )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5208,f4784]) ).
fof(f5208,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( v_F != hAPP(X11,sK72(X6,X8,X11,X9))
| hBOOL(hAPP(hAPP(c_member(X6),sK57(X11,X9,X6,X7,X10)),X9))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X7)),X8),c_FuncSet_OPi(X6,X7,X9,X10))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3612,f4784]) ).
fof(f6567,plain,
( spl85_76
| spl85_92
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5489,f4474,f6565,f4802]) ).
fof(f5489,plain,
( ! [X2,X0,X1] :
( c_Relation_Osingle__valued(X0,X1,X2)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2620,f4784]) ).
fof(f6563,plain,
( spl85_87
| ~ spl85_23
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6562,f4474,f3213,f6484]) ).
fof(f6562,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(v_F,X0,v_F)
| ~ spl85_23
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5427,f4784]) ).
fof(f5427,plain,
( ! [X0] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,X0,v_F)
| ~ spl85_23
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4035,f4784]) ).
fof(f6560,plain,
( spl85_91
| ~ spl85_14
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6092,f4474,f3167,f6557]) ).
fof(f3167,plain,
( spl85_14
<=> class_Lattices_Odistrib__lattice(tc_Nat_Onat) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_14])]) ).
fof(f6092,plain,
( class_Lattices_Odistrib__lattice(v_F)
| ~ spl85_14
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3169,f4784]) ).
fof(f3169,plain,
( class_Lattices_Odistrib__lattice(tc_Nat_Onat)
| ~ spl85_14 ),
inference(avatar_component_clause,[],[f3167]) ).
fof(f6540,plain,
( spl85_90
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6536,f4474,f4802,f6538]) ).
fof(f6536,plain,
( ! [X2,X0,X1] :
( ~ hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,X2,v_F)
| c_Relation_Orefl__on(X0,X1,X2) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6535,f4784]) ).
fof(f6535,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,v_F)
| ~ hBOOL(v_F)
| c_Relation_Orefl__on(X0,X1,X2) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5486,f4784]) ).
fof(f5486,plain,
( ! [X2,X0,X1] :
( c_Relation_Orefl__on(X0,X1,X2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,c_Product__Type_OSigma(X0,X0,X1,c_COMBK(tc_fun(X0,tc_HOL_Obool),X0,X1)))
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2557,f4784]) ).
fof(f6530,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6529,f4474,f4802]) ).
fof(f6529,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6528]) ).
fof(f6528,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6527,f4784]) ).
fof(f6527,plain,
( ! [X40,X38,X41,X39,X36,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40))))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6526]) ).
fof(f6526,plain,
( ! [X40,X38,X41,X39,X36,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40))))
| hBOOL(v_F)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5767,f4784]) ).
fof(f5767,plain,
( ! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,X39)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40))))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3596,f4784]) ).
fof(f6521,plain,
( ~ spl85_76
| spl85_77
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6520,f4474,f6128,f4802]) ).
fof(f6520,plain,
( ! [X65,X66,X64] :
( c_Predicate_ORangeP(X65,X66,v_F,X64)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5048,f4784]) ).
fof(f5048,plain,
( ! [X65,X58,X59,X62,X63,X60,X66,X61,X64] :
( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_COMBS(X61,X62,X63),X58),X60),X59),X64))
| c_Predicate_ORangeP(X65,X66,v_F,X64) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4355,f4784]) ).
fof(f6510,plain,
( spl85_76
| spl85_61
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5893,f4474,f4384,f4802]) ).
fof(f5893,plain,
( ! [X16] :
( ~ hBOOL(X16)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4084,f4784]) ).
fof(f6509,plain,
( spl85_76
| ~ spl85_38
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5870,f4474,f3341,f4802]) ).
fof(f5870,plain,
( hBOOL(v_F)
| ~ spl85_38
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3358,f4784]) ).
fof(f6502,plain,
( spl85_88
| spl85_89
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6062,f4474,f6499,f6496]) ).
fof(f6062,plain,
( ! [X1] :
( class_Orderings_Obot(v_F)
| ~ class_Orderings_Obot(X1) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2391,f4784]) ).
fof(f6486,plain,
( spl85_80
| spl85_87
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6482,f4474,f6484,f6164]) ).
fof(f6482,plain,
( ! [X6,X5] :
( c_Orderings_Oord__class_Oless__eq(v_F,X6,v_F)
| ~ class_Lattices_Olattice(X5) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5760,f4784]) ).
fof(f5760,plain,
( ! [X6,X4,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X5),X6,v_F)
| ~ class_Lattices_Olattice(X5) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4004,f4784]) ).
fof(f4004,plain,
! [X6,X7,X4,X5] :
( ~ class_Lattices_Olattice(X5)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X5),X6,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X4,X5)),X7),X6)) ),
inference(resolution,[],[f2380,f2477]) ).
fof(f6473,plain,
( ~ spl85_76
| spl85_86
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6469,f4474,f4223,f6471,f4802]) ).
fof(f6469,plain,
( ! [X2,X0,X1,X4,X5] :
( X4 = X5
| ~ c_Relation_Osingle__valued(X0,X1,X2)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6468]) ).
fof(f6468,plain,
( ! [X2,X0,X1,X4,X5] :
( ~ hBOOL(v_F)
| X4 = X5
| ~ c_Relation_Osingle__valued(X0,X1,X2)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6467,f4784]) ).
fof(f6467,plain,
( ! [X2,X0,X1,X4,X5] :
( ~ hBOOL(v_F)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),v_F),X2))
| ~ c_Relation_Osingle__valued(X0,X1,X2)
| X4 = X5 )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5707,f4784]) ).
fof(f5707,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),hAPP(hAPP(c_Product__Type_OPair(X0,X1),X3),X5)),X2))
| ~ c_Relation_Osingle__valued(X0,X1,X2)
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(X0,X1)),v_F),X2))
| X4 = X5 )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2621,f4784]) ).
fof(f6466,plain,
( spl85_76
| spl85_61
| ~ spl85_12
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5832,f4474,f3155,f4384,f4802]) ).
fof(f5832,plain,
( ! [X14] :
( ~ hBOOL(X14)
| hBOOL(v_F) )
| ~ spl85_12
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3856,f4784]) ).
fof(f6446,plain,
( spl85_76
| ~ spl85_25
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5783,f4474,f3223,f4802]) ).
fof(f5783,plain,
( hBOOL(v_F)
| ~ spl85_25
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3399,f4784]) ).
fof(f6444,plain,
( spl85_85
| ~ spl85_21
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6045,f4474,f3203,f6441]) ).
fof(f3203,plain,
( spl85_21
<=> class_Orderings_Opreorder(tc_HOL_Obool) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_21])]) ).
fof(f6045,plain,
( class_Orderings_Opreorder(v_F)
| ~ spl85_21
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3205,f4784]) ).
fof(f3205,plain,
( class_Orderings_Opreorder(tc_HOL_Obool)
| ~ spl85_21 ),
inference(avatar_component_clause,[],[f3203]) ).
fof(f6425,plain,
( ~ spl85_76
| ~ spl85_41
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5934,f4474,f3376,f4802]) ).
fof(f5934,plain,
( ~ hBOOL(v_F)
| ~ spl85_41
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3377,f4784]) ).
fof(f6424,plain,
( spl85_84
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6420,f4474,f4802,f6422]) ).
fof(f6420,plain,
( ! [X6,X5] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(X6,X5) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6419]) ).
fof(f6419,plain,
( ! [X6,X5] :
( c_Arrow__Order__Mirabelle_Odictator(X6,X5)
| hBOOL(v_F)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5859,f4784]) ).
fof(f5859,plain,
( ! [X6,X5] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK57(X6,c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),c_Arrow__Order__Mirabelle_OProf))
| c_Arrow__Order__Mirabelle_Odictator(X6,X5) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3868,f4784]) ).
fof(f6418,plain,
( spl85_77
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6417,f4474,f4802,f6128]) ).
fof(f6417,plain,
( ! [X28,X29,X30] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X29,X30,v_F,X28) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5044,f4784]) ).
fof(f5044,plain,
( ! [X28,X29,X26,X30] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X29,X30,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X26,tc_HOL_Obool))),X28) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4351,f4784]) ).
fof(f4351,plain,
! [X28,X29,X26,X27,X30] :
( c_Predicate_ORangeP(X29,X30,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X26,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X26,tc_HOL_Obool))),X28)
| ~ hBOOL(hAPP(X27,X28)) ),
inference(superposition,[],[f2173,f2580]) ).
fof(f6413,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6412,f4474,f4802]) ).
fof(f6412,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6411]) ).
fof(f6411,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6410,f4784]) ).
fof(f6410,plain,
( ! [X38,X39,X36,X37,X35] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,X39)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6409]) ).
fof(f6409,plain,
( ! [X38,X39,X36,X37,X35] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,X39)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5770,f4784]) ).
fof(f5770,plain,
( ! [X40,X38,X41,X39,X36,X37,X35,X42] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X35,X36),X41)),X42),c_FuncSet_OPi(tc_fun(X35,X36),X41,c_FuncSet_OPi(X35,X36,X38,X39),c_COMBK(tc_fun(X41,tc_HOL_Obool),tc_fun(X35,X36),X40))))
| hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X35,X36)),X37),c_FuncSet_OPi(X35,X36,X38,X39))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3603,f4784]) ).
fof(f6407,plain,
( spl85_81
| spl85_82
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6406,f4474,f6214,f6207]) ).
fof(f6207,plain,
( spl85_81
<=> ! [X1] : ~ c_Orderings_Oord__class_Oless__eq(v_F,X1,v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_81])]) ).
fof(f6406,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,X0,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6405,f4784]) ).
fof(f6405,plain,
( ! [X0] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(v_F,tc_HOL_Obool),v_F,v_F)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,X0,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6404,f4784]) ).
fof(f6404,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,v_F)
| c_Orderings_Oord__class_Oless__eq(tc_fun(v_F,tc_HOL_Obool),v_F,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6403,f4784]) ).
fof(f6403,plain,
( ! [X2,X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Transitive__Closure_Ortrancl(X1,X2))
| c_Orderings_Oord__class_Oless__eq(tc_fun(v_F,tc_HOL_Obool),v_F,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6402,f4784]) ).
fof(f6402,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(v_F,tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X1,X0),v_F)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Transitive__Closure_Ortrancl(X1,X2)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5997,f4784]) ).
fof(f5997,plain,
( ! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(v_F,tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X1,X0),c_Transitive__Closure_Ortrancl(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Transitive__Closure_Ortrancl(X1,X2)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2558,f4784]) ).
fof(f2558,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X1,X0),c_Transitive__Closure_Ortrancl(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Transitive__Closure_Ortrancl(X1,X2)) ),
inference(cnf_transformation,[],[f1826]) ).
fof(f1826,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X1,X0),c_Transitive__Closure_Ortrancl(X1,X2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X1,X1),tc_HOL_Obool),X0,c_Transitive__Closure_Ortrancl(X1,X2)) ),
inference(rectify,[],[f1127]) ).
fof(f1127,plain,
! [X2,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X0,X2),c_Transitive__Closure_Ortrancl(X0,X1))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,c_Transitive__Closure_Ortrancl(X0,X1)) ),
inference(ennf_transformation,[],[f632]) ).
fof(f632,plain,
! [X0,X1,X2] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),X2,c_Transitive__Closure_Ortrancl(X0,X1))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X0,X0),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X0,X2),c_Transitive__Closure_Ortrancl(X0,X1)) ),
inference(rectify,[],[f234]) ).
fof(f234,axiom,
! [X8,X33,X19] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),X19,c_Transitive__Closure_Ortrancl(X8,X33))
=> c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(X8,X8),tc_HOL_Obool),c_Transitive__Closure_Ortrancl(X8,X19),c_Transitive__Closure_Ortrancl(X8,X33)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
fof(f6401,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6400,f4474,f4802]) ).
fof(f6400,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6399]) ).
fof(f6399,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6398,f4784]) ).
fof(f6398,plain,
( ! [X8,X9,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(X8),sK57(v_F,X12,X8,X9,X13)),X12))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5192,f4784]) ).
fof(f5192,plain,
( ! [X10,X11,X8,X9,X7,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X7,tc_fun(X8,X9))),X10),c_FuncSet_OPi(X7,tc_fun(X8,X9),X11,c_COMBK(tc_fun(tc_fun(X8,X9),tc_HOL_Obool),X7,c_FuncSet_OPi(X8,X9,X12,X13)))))
| hBOOL(hAPP(hAPP(c_member(X8),sK57(v_F,X12,X8,X9,X13)),X12)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3524,f4784]) ).
fof(f6392,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6391,f4474,f4802]) ).
fof(f6391,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6390]) ).
fof(f6390,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5798,f4784]) ).
fof(f5798,plain,
( ! [X18,X19,X16,X17,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X16,X18)),X20),c_FuncSet_OPi(X16,X18,X19,c_COMBK(tc_fun(X18,tc_HOL_Obool),X16,X17))))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3497,f4784]) ).
fof(f6381,plain,
( spl85_77
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6380,f4474,f4802,f6128]) ).
fof(f6380,plain,
( ! [X101,X98,X99] :
( hBOOL(v_F)
| c_Predicate_ORangeP(X98,X99,v_F,X101) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5885,f4784]) ).
fof(f5885,plain,
( ! [X101,X98,X99,X100] :
( c_Predicate_ORangeP(X98,X99,c_member(X100),X101)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4319,f4784]) ).
fof(f6379,plain,
( spl85_76
| ~ spl85_38
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5788,f4474,f3341,f4802]) ).
fof(f5788,plain,
( hBOOL(v_F)
| ~ spl85_38
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3589,f4784]) ).
fof(f6378,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6377,f4474,f4802]) ).
fof(f6377,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6376]) ).
fof(f6376,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6375,f4784]) ).
fof(f6375,plain,
( ! [X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X0),c_FuncSet_OPi(X1,X4,X3,X5)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6374,f4784]) ).
fof(f6374,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(X1),sK83(X3,X1,X4,X5,X2)),X3))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X0),c_FuncSet_OPi(X1,X4,X3,X5))) )
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f6373]) ).
fof(f6373,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X0),c_FuncSet_OPi(X1,X4,X3,X5)))
| hBOOL(hAPP(hAPP(c_member(X1),sK83(X3,X1,X4,X5,X2)),X3))
| v_F != v_F )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5204,f4784]) ).
fof(f5204,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( v_F != hAPP(X0,sK72(X1,X2,X0,X3))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X1,X4)),X0),c_FuncSet_OPi(X1,X4,X3,X5)))
| hBOOL(hAPP(hAPP(c_member(X1),sK83(X3,X1,X4,X5,X2)),X3)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3604,f4784]) ).
fof(f6370,plain,
( spl85_82
| ~ spl85_22
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6369,f4474,f3208,f6214]) ).
fof(f6369,plain,
( c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| ~ spl85_22
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6368,f4784]) ).
fof(f6368,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,v_F,v_F)
| ~ spl85_22
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5005,f4784]) ).
fof(f5005,plain,
( ! [X2,X3,X1,X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,v_F,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool)),X2),X1))
| ~ spl85_22
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4009,f4784]) ).
fof(f4009,plain,
( ! [X2,X3,X1,X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(X2,X1),hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Osemilattice__sup__class_Osup(tc_HOL_Obool)),X2),X1))
| ~ spl85_22 ),
inference(superposition,[],[f4003,f2728]) ).
fof(f6353,plain,
( spl85_76
| spl85_61
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5836,f4474,f4384,f4802]) ).
fof(f5836,plain,
( ! [X31] :
( ~ hBOOL(X31)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4112,f4784]) ).
fof(f6335,plain,
( spl85_76
| ~ spl85_40
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5771,f4474,f3371,f4802]) ).
fof(f5771,plain,
( hBOOL(v_F)
| ~ spl85_40
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4244,f4784]) ).
fof(f6332,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6331,f4474,f4802]) ).
fof(f6331,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6330]) ).
fof(f6330,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5497,f4784]) ).
fof(f5497,plain,
( ! [X10,X8,X6,X9,X7,X5] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(X10),c_FuncSet_OPi(X5,X6,X8,X9)),hAPP(c_member(tc_fun(X5,X6)),X7))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3468,f4784]) ).
fof(f6326,plain,
( spl85_76
| ~ spl85_9
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5808,f4474,f3140,f4802]) ).
fof(f5808,plain,
( hBOOL(v_F)
| ~ spl85_9
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3330,f4784]) ).
fof(f3330,plain,
( ! [X6] : hBOOL(hAPP(hAPP(c_member(X6),c_Arrow__Order__Mirabelle_OProf),hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____)))
| ~ spl85_9 ),
inference(resolution,[],[f3142,f2711]) ).
fof(f6314,plain,
( spl85_79
| ~ spl85_82
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6313,f4474,f6214,f6161]) ).
fof(f6313,plain,
( ! [X5] :
( ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,v_F,X5) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6312,f4784]) ).
fof(f6312,plain,
( ! [X0,X5] :
( c_Orderings_Oord__class_Oless__eq(v_F,v_F,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),v_F,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6311,f4784]) ).
fof(f6311,plain,
( ! [X0,X5] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),v_F,X5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),v_F,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6310,f4784]) ).
fof(f6310,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool)),X1),c_member(X0)),v_F)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),v_F,X5) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5111,f4784]) ).
fof(f5111,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool)),X1),c_member(X0)),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X5))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),v_F,X5) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3521,f4784]) ).
fof(f3521,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),hAPP(hAPP(hAPP(c_COMBS(X2,X3,X4),c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool)),X1),c_member(X0)),hAPP(hAPP(c_COMBC(X0,tc_fun(X0,tc_HOL_Obool),tc_HOL_Obool),c_member(X0)),X5))
| c_Orderings_Oord__class_Oless__eq(tc_fun(X0,tc_HOL_Obool),hAPP(X1,c_member(X0)),X5) ),
inference(superposition,[],[f2325,f2728]) ).
fof(f6309,plain,
( spl85_76
| ~ spl85_36
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5903,f4474,f3306,f4802]) ).
fof(f5903,plain,
( hBOOL(v_F)
| ~ spl85_36
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3535,f4784]) ).
fof(f6308,plain,
( spl85_82
| ~ spl85_22
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6307,f4474,f3208,f6214]) ).
fof(f6307,plain,
( c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| ~ spl85_22
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6306,f4784]) ).
fof(f6306,plain,
( c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,v_F,v_F)
| ~ spl85_22
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5002,f4784]) ).
fof(f5002,plain,
( ! [X2,X3,X1,X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool)),X2),X1),v_F)
| ~ spl85_22
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3985,f4784]) ).
fof(f3985,plain,
( ! [X2,X3,X1,X4,X5] : c_Orderings_Oord__class_Oless__eq(tc_HOL_Obool,hAPP(hAPP(hAPP(c_COMBS(X3,X4,X5),c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool)),X2),X1),hAPP(X2,X1))
| ~ spl85_22 ),
inference(superposition,[],[f3980,f2728]) ).
fof(f6305,plain,
( spl85_77
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6304,f4474,f4802,f6128]) ).
fof(f6304,plain,
( ! [X24,X25,X23] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X24,X25,v_F,X23) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5043,f4784]) ).
fof(f5043,plain,
( ! [X21,X24,X22,X25,X23] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X24,X25,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21,tc_HOL_Obool)),X22),X23) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4350,f4784]) ).
fof(f4350,plain,
! [X21,X24,X22,X25,X23] :
( c_Predicate_ORangeP(X24,X25,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X21,tc_HOL_Obool)),X22),X23)
| ~ hBOOL(hAPP(X22,X23)) ),
inference(superposition,[],[f2173,f2793]) ).
fof(f6302,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6301,f4474,f4802]) ).
fof(f6301,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6300]) ).
fof(f6300,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6299,f4784]) ).
fof(f6299,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X16)),X17),c_FuncSet_OPi(X12,X16,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X13),X14),c_COMBK(tc_fun(X16,tc_HOL_Obool),X12,X15))))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5402,f4784]) ).
fof(f5402,plain,
( ! [X16,X14,X17,X15,X12,X13] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),v_F),hAPP(hAPP(c_COMBC(X12,tc_fun(X12,tc_HOL_Obool),tc_HOL_Obool),c_member(X12)),X14)),sK65(X15,X16,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X13),X14),X12,X17)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X12,X16)),X17),c_FuncSet_OPi(X12,X16,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X12,tc_HOL_Obool)),X13),X14),c_COMBK(tc_fun(X16,tc_HOL_Obool),X12,X15)))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3649,f4784]) ).
fof(f6271,plain,
( spl85_76
| spl85_61
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5926,f4474,f4384,f4802]) ).
fof(f5926,plain,
( ! [X37] :
( ~ hBOOL(X37)
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3956,f4784]) ).
fof(f6270,plain,
( ~ spl85_76
| spl85_77
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6269,f4474,f6128,f4802]) ).
fof(f6269,plain,
( ! [X82,X80,X81] :
( c_Predicate_ORangeP(X81,X82,v_F,X80)
| ~ hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6268,f4784]) ).
fof(f6268,plain,
( ! [X82,X80,X81,X76,X77,X75] :
( ~ hBOOL(hAPP(c_Product__Type_OSigma(X75,X76,X77,v_F),X80))
| c_Predicate_ORangeP(X81,X82,v_F,X80) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5743,f4784]) ).
fof(f5743,plain,
( ! [X82,X80,X78,X81,X76,X77,X75] :
( c_Predicate_ORangeP(X81,X82,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X75,X76),tc_HOL_Obool)),c_Product__Type_OSigma(X75,X76,X77,X78)),X80)
| ~ hBOOL(hAPP(c_Product__Type_OSigma(X75,X76,X77,v_F),X80)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4357,f4784]) ).
fof(f4357,plain,
! [X82,X80,X78,X81,X79,X76,X77,X75] :
( c_Predicate_ORangeP(X81,X82,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X75,X76),tc_HOL_Obool)),c_Product__Type_OSigma(X75,X76,X77,X78)),X80)
| ~ hBOOL(hAPP(c_Product__Type_OSigma(X75,X76,X77,hAPP(hAPP(c_COMBS(X75,tc_fun(X76,tc_HOL_Obool),tc_fun(X76,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X76,tc_HOL_Obool),tc_fun(tc_fun(X76,tc_HOL_Obool),tc_fun(X76,tc_HOL_Obool)),X75,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X76,tc_HOL_Obool))),X78)),X79)),X80)) ),
inference(superposition,[],[f2173,f2930]) ).
fof(f2930,plain,
! [X2,X3,X0,X1,X4] : c_Product__Type_OSigma(X0,X3,X1,hAPP(hAPP(c_COMBS(X0,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),X2)),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X3),tc_HOL_Obool)),c_Product__Type_OSigma(X0,X3,X1,X2)),c_Product__Type_OSigma(X0,X3,X1,X4)),
inference(cnf_transformation,[],[f2147]) ).
fof(f2147,plain,
! [X0,X1,X2,X3,X4] : c_Product__Type_OSigma(X0,X3,X1,hAPP(hAPP(c_COMBS(X0,tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X3,tc_HOL_Obool),tc_fun(tc_fun(X3,tc_HOL_Obool),tc_fun(X3,tc_HOL_Obool)),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool))),X2)),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X3),tc_HOL_Obool)),c_Product__Type_OSigma(X0,X3,X1,X2)),c_Product__Type_OSigma(X0,X3,X1,X4)),
inference(rectify,[],[f653]) ).
fof(f653,plain,
! [X0,X2,X3,X1,X4] : c_Product__Type_OSigma(X0,X1,X2,hAPP(hAPP(c_COMBS(X0,tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X1,tc_HOL_Obool),tc_fun(tc_fun(X1,tc_HOL_Obool),tc_fun(X1,tc_HOL_Obool)),X0,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X1,tc_HOL_Obool))),X3)),X4)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X0,X1),tc_HOL_Obool)),c_Product__Type_OSigma(X0,X1,X2,X3)),c_Product__Type_OSigma(X0,X1,X2,X4)),
inference(rectify,[],[f345]) ).
fof(f345,axiom,
! [X8,X16,X69,X10,X9] : c_Product__Type_OSigma(X8,X16,X69,hAPP(hAPP(c_COMBS(X8,tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(X16,tc_HOL_Obool),tc_fun(tc_fun(X16,tc_HOL_Obool),tc_fun(X16,tc_HOL_Obool)),X8,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X16,tc_HOL_Obool))),X10)),X9)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(X8,X16),tc_HOL_Obool)),c_Product__Type_OSigma(X8,X16,X69,X10)),c_Product__Type_OSigma(X8,X16,X69,X9)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Sigma__Un__distrib2) ).
fof(f6267,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6266,f4474,f4802]) ).
fof(f6266,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6265]) ).
fof(f6265,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6264,f4784]) ).
fof(f6264,plain,
( ! [X31,X28,X29,X27,X30] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X27,X28)),X29),c_FuncSet_OPi(X27,X28,X30,X31))) )
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6263]) ).
fof(f6263,plain,
( ! [X31,X28,X29,X27,X30] :
( hBOOL(v_F)
| hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X27,X28)),X29),c_FuncSet_OPi(X27,X28,X30,X31))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5768,f4784]) ).
fof(f5768,plain,
( ! [X31,X28,X29,X27,X34,X32,X30,X33] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(X27,X28),X33)),X32),c_FuncSet_OPi(tc_fun(X27,X28),X33,c_FuncSet_OPi(X27,X28,X30,X31),X34)))
| hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X27,X28)),X29),c_FuncSet_OPi(X27,X28,X30,X31))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3602,f4784]) ).
fof(f6256,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6255,f4474,f4802]) ).
fof(f6255,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6254]) ).
fof(f6254,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6253,f4784]) ).
fof(f6253,plain,
( ! [X2] :
( hBOOL(v_F)
| hBOOL(hAPP(v_F,X2)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5149,f4784]) ).
fof(f5149,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(c_Wellfounded_Oaccp(X1,X0),X2))
| hBOOL(hAPP(v_F,X2)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2337,f4784]) ).
fof(f6239,plain,
( spl85_83
| spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6235,f4474,f4802,f6237]) ).
fof(f6235,plain,
( ! [X2,X3,X0,X1] :
( hBOOL(v_F)
| ~ c_Predicate_ORangeP(X2,X1,X3,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5124,f4784]) ).
fof(f5124,plain,
( ! [X2,X3,X0,X1] :
( ~ c_Predicate_ORangeP(X2,X1,X3,X0)
| hBOOL(hAPP(v_F,X0)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2174,f4784]) ).
fof(f6232,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6231,f4474,f4802]) ).
fof(f6231,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6230]) ).
fof(f6230,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6229,f4784]) ).
fof(f6229,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X10)),X9),c_FuncSet_OPi(X6,X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X8),X11))) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5401,f4784]) ).
fof(f5401,plain,
( ! [X10,X11,X8,X6,X9,X7] :
( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),v_F),hAPP(hAPP(c_COMBC(X6,tc_fun(X6,tc_HOL_Obool),tc_HOL_Obool),c_member(X6)),X8)),sK57(X9,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X8),X6,X10,X11)))
| hBOOL(hAPP(hAPP(c_member(tc_fun(X6,X10)),X9),c_FuncSet_OPi(X6,X10,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X6,tc_HOL_Obool)),X7),X8),X11))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3648,f4784]) ).
fof(f6226,plain,
( ~ spl85_76
| spl85_77
| ~ spl85_12
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6225,f4474,f3155,f6128,f4802]) ).
fof(f6225,plain,
( ! [X14,X15,X13] :
( c_Predicate_ORangeP(X14,X15,v_F,X13)
| ~ hBOOL(v_F) )
| ~ spl85_12
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5041,f4784]) ).
fof(f5041,plain,
( ! [X14,X15,X12,X13] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X14,X15,hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),X12),X13) )
| ~ spl85_12
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4348,f4784]) ).
fof(f4348,plain,
( ! [X14,X15,X12,X13] :
( c_Predicate_ORangeP(X14,X15,hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_HOL_Obool),X12),X13)
| ~ hBOOL(hAPP(X12,X13)) )
| ~ spl85_12 ),
inference(superposition,[],[f2173,f3847]) ).
fof(f6223,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6222,f4474,f4802]) ).
fof(f6222,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6221]) ).
fof(f6221,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5689,f4784]) ).
fof(f5689,plain,
( ! [X2,X3,X0,X1,X4] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_fun(X3,X1)),X4),c_FuncSet_OPi(X3,X1,X2,c_COMBK(tc_fun(X1,tc_HOL_Obool),X3,X0)))) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2719,f4784]) ).
fof(f6217,plain,
( ~ spl85_82
| spl85_76
| ~ spl85_40
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6212,f4474,f3371,f4802,f6214]) ).
fof(f6212,plain,
( hBOOL(v_F)
| ~ c_Orderings_Oord__class_Oless__eq(v_F,v_F,v_F)
| ~ spl85_40
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6211,f4784]) ).
fof(f6211,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,v_F)
| hBOOL(v_F)
| ~ spl85_40
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6210,f4784]) ).
fof(f6210,plain,
( ! [X21,X18,X19,X24,X22,X23,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(X21,X21)),hAPP(hAPP(c_Product__Type_OPair(X21,X21),X19),X20)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X21),X21,c_Wellfounded_Olex__prod(tc_Nat_Onat,X21,c_Wellfounded_Oless__than,hAPP(c_Product__Type_OPair(X22,X23),X24)),hAPP(hAPP(c_COMBS(X21,X21,tc_prod(tc_Nat_Onat,X21)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X21,tc_prod(tc_Nat_Onat,X21)),X21,c_Product__Type_OPair(tc_Nat_Onat,X21)),X18)),c_COMBI(X21)))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,v_F,v_F) )
| ~ spl85_40
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5022,f4784]) ).
fof(f5022,plain,
( ! [X21,X18,X19,X24,X22,X23,X20] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(X18,X19),v_F)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X21,X21)),hAPP(hAPP(c_Product__Type_OPair(X21,X21),X19),X20)),c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,X21),X21,c_Wellfounded_Olex__prod(tc_Nat_Onat,X21,c_Wellfounded_Oless__than,hAPP(c_Product__Type_OPair(X22,X23),X24)),hAPP(hAPP(c_COMBS(X21,X21,tc_prod(tc_Nat_Onat,X21)),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(X21,tc_prod(tc_Nat_Onat,X21)),X21,c_Product__Type_OPair(tc_Nat_Onat,X21)),X18)),c_COMBI(X21))))) )
| ~ spl85_40
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4238,f4784]) ).
fof(f6209,plain,
( spl85_79
| spl85_81
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6205,f4474,f6207,f6161]) ).
fof(f6205,plain,
( ! [X0,X1] :
( ~ c_Orderings_Oord__class_Oless__eq(v_F,X1,v_F)
| c_Orderings_Oord__class_Oless__eq(v_F,v_F,X0) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6204,f4784]) ).
fof(f6204,plain,
( ! [X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(v_F,v_F,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6203,f4784]) ).
fof(f6203,plain,
( ! [X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),v_F,X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5677,f4784]) ).
fof(f5677,plain,
( ! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2794,f4784]) ).
fof(f2794,plain,
! [X2,X3,X0,X1] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),c_Groups_Ominus__class_Ominus(tc_fun(X3,tc_HOL_Obool),X1,X2),X0)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(X3,tc_HOL_Obool),X1,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X3,tc_HOL_Obool)),X2),X0)) ),
inference(cnf_transformation,[],[f2039]) ).
fof(f6200,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6199,f4474,f4802]) ).
fof(f6199,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6198]) ).
fof(f6198,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5800,f4784]) ).
fof(f5800,plain,
( ! [X18,X19,X16,X17,X20] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(X16,X18)),X20),c_FuncSet_OPi(X16,X18,X17,X19)))
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3480,f4784]) ).
fof(f6197,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6196,f4474,f4802]) ).
fof(f6196,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(duplicate_literal_removal,[],[f6195]) ).
fof(f6195,plain,
( hBOOL(v_F)
| hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6194,f4784]) ).
fof(f6194,plain,
( ! [X2,X1] :
( hBOOL(v_F)
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),v_F),X2)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5381,f4784]) ).
fof(f5381,plain,
( ! [X2,X0,X1] :
( hBOOL(hAPP(hAPP(c_member(X1),X0),c_Wellfounded_Oacc(X1,X2)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(X1,X1)),v_F),X2)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f2525,f4784]) ).
fof(f6168,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5776,f4474,f4802]) ).
fof(f5776,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4102,f4784]) ).
fof(f6166,plain,
( spl85_79
| spl85_80
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6159,f4474,f6164,f6161]) ).
fof(f6159,plain,
( ! [X7,X5] :
( ~ class_Lattices_Olattice(X5)
| c_Orderings_Oord__class_Oless__eq(v_F,v_F,X7) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5755,f4784]) ).
fof(f5755,plain,
( ! [X7,X4,X5] :
( ~ class_Lattices_Olattice(X5)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X5),v_F,X7) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3981,f4784]) ).
fof(f3981,plain,
! [X6,X7,X4,X5] :
( ~ class_Lattices_Olattice(X5)
| c_Orderings_Oord__class_Oless__eq(tc_fun(X4,X5),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(X4,X5)),X6),X7),X7) ),
inference(resolution,[],[f2278,f2477]) ).
fof(f6147,plain,
( spl85_76
| spl85_78
| ~ spl85_69
| ~ spl85_75 ),
inference(avatar_split_clause,[],[f6143,f4730,f4474,f6145,f4802]) ).
fof(f6143,plain,
( ! [X65] :
( c_Arrow__Order__Mirabelle_Odictator(v_F,X65)
| hBOOL(v_F) )
| ~ spl85_69
| ~ spl85_75 ),
inference(forward_demodulation,[],[f5847,f4784]) ).
fof(f5847,plain,
( ! [X65] :
( hBOOL(v_F)
| c_Arrow__Order__Mirabelle_Odictator(sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),X65) )
| ~ spl85_69
| ~ spl85_75 ),
inference(backward_demodulation,[],[f4731,f4784]) ).
fof(f6139,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6138,f4474,f4802]) ).
fof(f6138,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5236,f4784]) ).
fof(f5236,plain,
( ! [X2,X3] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F),c_Arrow__Order__Mirabelle_Omktop(X2,X3)))
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3022,f4784]) ).
fof(f6130,plain,
( spl85_77
| ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6126,f4474,f4802,f6128]) ).
fof(f6126,plain,
( ! [X48,X46,X47] :
( ~ hBOOL(v_F)
| c_Predicate_ORangeP(X47,X48,v_F,X46) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6125,f4784]) ).
fof(f6125,plain,
( ! [X48,X46,X47,X44,X45] :
( c_Predicate_ORangeP(X47,X48,v_F,X46)
| ~ hBOOL(hAPP(hAPP(v_F,hAPP(X44,X45)),X46)) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5046,f4784]) ).
fof(f5046,plain,
( ! [X40,X41,X48,X46,X47,X44,X45,X42,X43] :
( c_Predicate_ORangeP(X47,X48,hAPP(hAPP(c_COMBS(X40,X41,X42),X43),X44),X46)
| ~ hBOOL(hAPP(hAPP(v_F,hAPP(X44,X45)),X46)) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f4353,f4784]) ).
fof(f6124,plain,
( spl85_76
| ~ spl85_16
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6123,f4474,f3178,f4802]) ).
fof(f6123,plain,
( hBOOL(v_F)
| ~ spl85_16
| ~ spl85_69 ),
inference(forward_demodulation,[],[f6122,f4784]) ).
fof(f6122,plain,
( ! [X18] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| ~ spl85_16
| ~ spl85_69 ),
inference(trivial_inequality_removal,[],[f6121]) ).
fof(f6121,plain,
( ! [X18] :
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))
| v_F != v_F )
| ~ spl85_16
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5221,f4784]) ).
fof(f5221,plain,
( ! [X18] :
( v_F != hAPP(v_F,sK72(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),v_F,X18,c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X18),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))) )
| ~ spl85_16
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3607,f4784]) ).
fof(f6118,plain,
( spl85_76
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5813,f4474,f4223,f4802]) ).
fof(f5813,plain,
( ! [X2,X3] :
( X2 = X3
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3395,f4784]) ).
fof(f6113,plain,
( spl85_76
| ~ spl85_34
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f5789,f4474,f3290,f4802]) ).
fof(f5789,plain,
( hBOOL(v_F)
| ~ spl85_34
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3684,f4784]) ).
fof(f6110,plain,
( spl85_76
| spl85_58
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f6109,f4474,f4223,f4802]) ).
fof(f6109,plain,
( ! [X2,X3] :
( X2 = X3
| hBOOL(v_F) )
| ~ spl85_69 ),
inference(forward_demodulation,[],[f5305,f4784]) ).
fof(f5305,plain,
( ! [X2,X3,X4] :
( hBOOL(hAPP(hAPP(c_member(X4),sK84(X2,X3)),hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),v_F)))
| X2 = X3 )
| ~ spl85_69 ),
inference(backward_demodulation,[],[f3463,f4784]) ).
fof(f4813,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f4794,f4474,f4802]) ).
fof(f4794,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(superposition,[],[f4770,f2580]) ).
fof(f4812,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f4792,f4474,f4802]) ).
fof(f4792,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(superposition,[],[f4770,f2397]) ).
fof(f4811,plain,
( spl85_42
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f4798,f4474,f3379]) ).
fof(f4798,plain,
( ! [X20] : hBOOL(X20)
| ~ spl85_69 ),
inference(superposition,[],[f4770,f2430]) ).
fof(f4810,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f4799,f4474,f4802]) ).
fof(f4799,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(superposition,[],[f4770,f2523]) ).
fof(f4809,plain,
( spl85_76
| ~ spl85_23
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f4788,f4474,f3213,f4802]) ).
fof(f4788,plain,
( hBOOL(v_F)
| ~ spl85_23
| ~ spl85_69 ),
inference(superposition,[],[f4770,f3828]) ).
fof(f4808,plain,
( spl85_76
| ~ spl85_26
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f4789,f4474,f3229,f4802]) ).
fof(f4789,plain,
( hBOOL(v_F)
| ~ spl85_26
| ~ spl85_69 ),
inference(superposition,[],[f4770,f3829]) ).
fof(f4807,plain,
( ~ spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f4786,f4474,f4802]) ).
fof(f4786,plain,
( ~ hBOOL(v_F)
| ~ spl85_69 ),
inference(resolution,[],[f4770,f2777]) ).
fof(f4806,plain,
( spl85_76
| ~ spl85_12
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f4791,f4474,f3155,f4802]) ).
fof(f4791,plain,
( hBOOL(v_F)
| ~ spl85_12
| ~ spl85_69 ),
inference(superposition,[],[f4770,f3847]) ).
fof(f4805,plain,
( spl85_76
| ~ spl85_69 ),
inference(avatar_split_clause,[],[f4793,f4474,f4802]) ).
fof(f4793,plain,
( hBOOL(v_F)
| ~ spl85_69 ),
inference(superposition,[],[f4770,f2793]) ).
fof(f4769,plain,
~ spl85_70,
inference(avatar_contradiction_clause,[],[f4765]) ).
fof(f4765,plain,
( $false
| ~ spl85_70 ),
inference(resolution,[],[f4482,f3081]) ).
fof(f4482,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool))))
| ~ spl85_70 ),
inference(avatar_component_clause,[],[f4480]) ).
fof(f4480,plain,
( spl85_70
<=> hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_70])]) ).
fof(f4734,plain,
( spl85_65
| spl85_66 ),
inference(avatar_split_clause,[],[f4600,f4435,f4431]) ).
fof(f4600,plain,
! [X10] :
( c_Arrow__Order__Mirabelle_Odictator(sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X10)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X10,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))),c_Arrow__Order__Mirabelle_OProf))
| c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool)) ),
inference(resolution,[],[f2451,f2323]) ).
fof(f4733,plain,
( spl85_65
| spl85_67 ),
inference(avatar_split_clause,[],[f4607,f4439,f4431]) ).
fof(f4607,plain,
! [X10] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X10,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))),sK21(X10,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))))),hAPP(sK20(X10,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))),X10)))
| c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool))
| c_Arrow__Order__Mirabelle_Odictator(sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X10) ),
inference(resolution,[],[f2452,f2323]) ).
fof(f4732,plain,
( spl85_65
| spl85_75 ),
inference(avatar_split_clause,[],[f4715,f4730,f4431]) ).
fof(f4715,plain,
! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X65,sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))),sK21(X65,sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))))),hAPP(sK20(X65,sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),X65)))
| c_Arrow__Order__Mirabelle_Odictator(sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),X65)
| c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool)) ),
inference(resolution,[],[f2929,f2452]) ).
fof(f4728,plain,
( spl85_65
| spl85_74 ),
inference(avatar_split_clause,[],[f4716,f4726,f4431]) ).
fof(f4716,plain,
! [X66] :
( c_Arrow__Order__Mirabelle_Odictator(sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))),X66)
| c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X66,sK82(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin))))),c_Arrow__Order__Mirabelle_OProf)) ),
inference(resolution,[],[f2929,f2451]) ).
fof(f4591,plain,
( spl85_73
| spl85_71 ),
inference(avatar_split_clause,[],[f4397,f4581,f4589]) ).
fof(f4589,plain,
( spl85_73
<=> ! [X16,X14,X15] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X15)),hAPP(sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK4(sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X16,X14,X15))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X15)),hAPP(v_F,X16)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X16),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X15)),hAPP(X16,sK4(sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X16,X14,X15))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X15)),hAPP(v_F,sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_73])]) ).
fof(f4581,plain,
( spl85_71
<=> c_Arrow__Order__Mirabelle_OProf = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_71])]) ).
fof(f4397,plain,
! [X16,X14,X15] :
( c_Arrow__Order__Mirabelle_OProf = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X15)),hAPP(sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK4(sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X16,X14,X15))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X15)),hAPP(v_F,sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X15)),hAPP(X16,sK4(sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X16,X14,X15))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X16),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X14),X15)),hAPP(v_F,X16))) ),
inference(resolution,[],[f2323,f2200]) ).
fof(f2200,plain,
! [X2,X3,X0,X1] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X0),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X1),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X1,sK4(X0,X1,X2,X3))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(X0,sK4(X0,X1,X2,X3))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X0)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X2),X3)),hAPP(v_F,X1))) ),
inference(cnf_transformation,[],[f1533]) ).
fof(f4587,plain,
( spl85_71
| spl85_72 ),
inference(avatar_split_clause,[],[f4396,f4585,f4581]) ).
fof(f4585,plain,
( spl85_72
<=> ! [X13,X12,X11] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),hAPP(X11,sK4(sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X11,X12,X13))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),hAPP(v_F,X11)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X11),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),hAPP(v_F,sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),hAPP(sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK4(sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X11,X12,X13)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_72])]) ).
fof(f4396,plain,
! [X11,X12,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),hAPP(X11,sK4(sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X11,X12,X13))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),hAPP(sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK4(sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X11,X12,X13))))
| c_Arrow__Order__Mirabelle_OProf = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),hAPP(v_F,sK12(c_Arrow__Order__Mirabelle_OProf,tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X11),c_Arrow__Order__Mirabelle_OProf))
| ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X12),X13)),hAPP(v_F,X11))) ),
inference(resolution,[],[f2323,f2201]) ).
fof(f4579,plain,
( spl85_58
| ~ spl85_61 ),
inference(avatar_split_clause,[],[f4501,f4384,f4223]) ).
fof(f4501,plain,
( ! [X24,X25] : X24 = X25
| ~ spl85_61 ),
inference(resolution,[],[f4385,f2949]) ).
fof(f4385,plain,
( ! [X179] : ~ hBOOL(X179)
| ~ spl85_61 ),
inference(avatar_component_clause,[],[f4384]) ).
fof(f4578,plain,
( spl85_42
| ~ spl85_61 ),
inference(avatar_split_clause,[],[f4539,f4384,f3379]) ).
fof(f4539,plain,
( ! [X69] : hBOOL(X69)
| ~ spl85_61 ),
inference(resolution,[],[f4385,f2866]) ).
fof(f4577,plain,
( spl85_58
| ~ spl85_61 ),
inference(avatar_split_clause,[],[f4494,f4384,f4223]) ).
fof(f4494,plain,
( ! [X18,X19] : X18 = X19
| ~ spl85_61 ),
inference(resolution,[],[f4385,f2948]) ).
fof(f4576,plain,
( spl85_42
| ~ spl85_61 ),
inference(avatar_split_clause,[],[f4527,f4384,f3379]) ).
fof(f4527,plain,
( ! [X63] : hBOOL(X63)
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3383]) ).
fof(f4575,plain,
( spl85_58
| ~ spl85_61 ),
inference(avatar_split_clause,[],[f4538,f4384,f4223]) ).
fof(f4538,plain,
( ! [X68,X67] : X67 = X68
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3394]) ).
fof(f4574,plain,
( ~ spl85_34
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4524]) ).
fof(f4524,plain,
( $false
| ~ spl85_34
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3314]) ).
fof(f4573,plain,
~ spl85_61,
inference(avatar_contradiction_clause,[],[f4487]) ).
fof(f4487,plain,
( $false
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3415]) ).
fof(f4572,plain,
( ~ spl85_37
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4535]) ).
fof(f4535,plain,
( $false
| ~ spl85_37
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3334]) ).
fof(f4571,plain,
( ~ spl85_34
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4537]) ).
fof(f4537,plain,
( $false
| ~ spl85_34
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3292]) ).
fof(f4570,plain,
~ spl85_61,
inference(avatar_contradiction_clause,[],[f4512]) ).
fof(f4512,plain,
( $false
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3644]) ).
fof(f4569,plain,
( ~ spl85_25
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4520]) ).
fof(f4520,plain,
( $false
| ~ spl85_25
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3288]) ).
fof(f4568,plain,
~ spl85_61,
inference(avatar_contradiction_clause,[],[f4515]) ).
fof(f4515,plain,
( $false
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3324]) ).
fof(f4567,plain,
( ~ spl85_25
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4492]) ).
fof(f4492,plain,
( $false
| ~ spl85_25
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3225]) ).
fof(f4566,plain,
~ spl85_61,
inference(avatar_contradiction_clause,[],[f4531]) ).
fof(f4531,plain,
( $false
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3075]) ).
fof(f4565,plain,
( ~ spl85_38
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4536]) ).
fof(f4536,plain,
( $false
| ~ spl85_38
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3343]) ).
fof(f4564,plain,
( ~ spl85_38
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4523]) ).
fof(f4523,plain,
( $false
| ~ spl85_38
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3358]) ).
fof(f4563,plain,
( ~ spl85_33
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4521]) ).
fof(f4521,plain,
( $false
| ~ spl85_33
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3312]) ).
fof(f4562,plain,
( ~ spl85_35
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4488]) ).
fof(f4488,plain,
( $false
| ~ spl85_35
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3299]) ).
fof(f4561,plain,
~ spl85_61,
inference(avatar_contradiction_clause,[],[f4529]) ).
fof(f4529,plain,
( $false
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3564]) ).
fof(f4560,plain,
( ~ spl85_4
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4497]) ).
fof(f4497,plain,
( $false
| ~ spl85_4
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3117]) ).
fof(f4559,plain,
( ~ spl85_4
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4516]) ).
fof(f4516,plain,
( $false
| ~ spl85_4
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3281]) ).
fof(f4558,plain,
( ~ spl85_33
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4534]) ).
fof(f4534,plain,
( $false
| ~ spl85_33
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3285]) ).
fof(f4557,plain,
~ spl85_61,
inference(avatar_contradiction_clause,[],[f4532]) ).
fof(f4532,plain,
( $false
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3016]) ).
fof(f4556,plain,
( ~ spl85_10
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4498]) ).
fof(f4498,plain,
( $false
| ~ spl85_10
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3147]) ).
fof(f4555,plain,
( ~ spl85_37
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4518]) ).
fof(f4518,plain,
( $false
| ~ spl85_37
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3585]) ).
fof(f4554,plain,
( ~ spl85_38
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4519]) ).
fof(f4519,plain,
( $false
| ~ spl85_38
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3589]) ).
fof(f4553,plain,
( ~ spl85_40
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4513]) ).
fof(f4513,plain,
( $false
| ~ spl85_40
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3652]) ).
fof(f4552,plain,
( ~ spl85_24
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4514]) ).
fof(f4514,plain,
( $false
| ~ spl85_24
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3295]) ).
fof(f4551,plain,
( ~ spl85_43
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4542]) ).
fof(f4542,plain,
( $false
| ~ spl85_43
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3389]) ).
fof(f4550,plain,
~ spl85_61,
inference(avatar_contradiction_clause,[],[f4540]) ).
fof(f4540,plain,
( $false
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3015]) ).
fof(f4549,plain,
( ~ spl85_37
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4522]) ).
fof(f4522,plain,
( $false
| ~ spl85_37
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3357]) ).
fof(f4548,plain,
( ~ spl85_24
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4500]) ).
fof(f4500,plain,
( $false
| ~ spl85_24
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3220]) ).
fof(f4547,plain,
( ~ spl85_33
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4517]) ).
fof(f4517,plain,
( $false
| ~ spl85_33
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3563]) ).
fof(f4546,plain,
( ~ spl85_9
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4496]) ).
fof(f4496,plain,
( $false
| ~ spl85_9
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3142]) ).
fof(f4545,plain,
( ~ spl85_40
| ~ spl85_61 ),
inference(avatar_contradiction_clause,[],[f4530]) ).
fof(f4530,plain,
( $false
| ~ spl85_40
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3372]) ).
fof(f4544,plain,
~ spl85_61,
inference(avatar_contradiction_clause,[],[f4528]) ).
fof(f4528,plain,
( $false
| ~ spl85_61 ),
inference(resolution,[],[f4385,f2539]) ).
fof(f4543,plain,
~ spl85_61,
inference(avatar_contradiction_clause,[],[f4511]) ).
fof(f4511,plain,
( $false
| ~ spl85_61 ),
inference(resolution,[],[f4385,f3035]) ).
fof(f4483,plain,
( spl85_70
| ~ spl85_16
| ~ spl85_65 ),
inference(avatar_split_clause,[],[f4450,f4431,f3178,f4480]) ).
fof(f4450,plain,
( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool))))
| ~ spl85_16
| ~ spl85_65 ),
inference(backward_demodulation,[],[f3180,f4433]) ).
fof(f4433,plain,
( c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool))
| ~ spl85_65 ),
inference(avatar_component_clause,[],[f4431]) ).
fof(f4477,plain,
( spl85_69
| ~ spl85_36
| ~ spl85_65 ),
inference(avatar_split_clause,[],[f4452,f4431,f3306,f4474]) ).
fof(f4452,plain,
( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool)),v_F))
| ~ spl85_36
| ~ spl85_65 ),
inference(backward_demodulation,[],[f3308,f4433]) ).
fof(f4445,plain,
( spl85_64
| spl85_68 ),
inference(avatar_split_clause,[],[f4406,f4443,f4426]) ).
fof(f4443,plain,
( spl85_68
<=> ! [X50,X49] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50),X49)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X49 = X50
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49),X50)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_68])]) ).
fof(f4406,plain,
! [X50,X49] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X50),X49)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X49),X50)),sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))
| X49 = X50 ),
inference(resolution,[],[f2323,f2888]) ).
fof(f4441,plain,
( spl85_65
| spl85_67 ),
inference(avatar_split_clause,[],[f4412,f4439,f4431]) ).
fof(f4412,plain,
! [X65] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),sK22(X65,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))),sK21(X65,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))))),hAPP(sK20(X65,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)))),X65)))
| c_Arrow__Order__Mirabelle_Odictator(sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X65)
| c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool)) ),
inference(resolution,[],[f2323,f2452]) ).
fof(f4437,plain,
( spl85_65
| spl85_66 ),
inference(avatar_split_clause,[],[f4413,f4435,f4431]) ).
fof(f4413,plain,
! [X66] :
( c_Arrow__Order__Mirabelle_Odictator(sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X66)
| hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),sK20(X66,sK12(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))))),c_Arrow__Order__Mirabelle_OProf))
| c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_HOL_Obool)) ),
inference(resolution,[],[f2323,f2451]) ).
fof(f4429,plain,
( spl85_63
| spl85_64 ),
inference(avatar_split_clause,[],[f4410,f4426,f4423]) ).
fof(f4423,plain,
( spl85_63
<=> ! [X61,X60] :
( X60 = X61
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X60),X61)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X60),X61))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_63])]) ).
fof(f4410,plain,
! [X60,X61] :
( c_Arrow__Order__Mirabelle_OLin = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool))
| X60 = X61
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),X60),X61)),hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove,sK12(c_Arrow__Order__Mirabelle_OLin,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),X60),X61))) ),
inference(resolution,[],[f2323,f3090]) ).
fof(f4390,plain,
( spl85_62
| spl85_61 ),
inference(avatar_split_clause,[],[f4375,f4384,f4388]) ).
fof(f4388,plain,
( spl85_62
<=> ! [X70,X73,X72] : c_Predicate_ORangeP(X72,X73,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X70,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X70,tc_HOL_Obool))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_62])]) ).
fof(f4375,plain,
! [X72,X70,X73,X71] :
( ~ hBOOL(X71)
| c_Predicate_ORangeP(X72,X73,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X70,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X70,tc_HOL_Obool))) ),
inference(superposition,[],[f2173,f2235]) ).
fof(f4386,plain,
( spl85_60
| spl85_61 ),
inference(avatar_split_clause,[],[f4337,f4384,f4381]) ).
fof(f4381,plain,
( spl85_60
<=> ! [X178,X176,X177,X175] : c_Predicate_ORangeP(X175,X176,c_member(X177),c_COMBI(X178)) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_60])]) ).
fof(f4337,plain,
! [X178,X179,X176,X177,X175] :
( ~ hBOOL(X179)
| c_Predicate_ORangeP(X175,X176,c_member(X177),c_COMBI(X178)) ),
inference(resolution,[],[f2173,f3359]) ).
fof(f4379,plain,
( spl85_59
| spl85_42 ),
inference(avatar_split_clause,[],[f4338,f3379,f4377]) ).
fof(f4377,plain,
( spl85_59
<=> ! [X182,X181,X180] : c_Predicate_ORangeP(X180,X181,c_member(X182),c_fNot) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_59])]) ).
fof(f4338,plain,
! [X180,X181,X182,X183] :
( hBOOL(X183)
| c_Predicate_ORangeP(X180,X181,c_member(X182),c_fNot) ),
inference(resolution,[],[f2173,f3383]) ).
fof(f4227,plain,
( spl85_58
| ~ spl85_42 ),
inference(avatar_split_clause,[],[f4211,f3379,f4223]) ).
fof(f4211,plain,
( ! [X233,X234] : X233 = X234
| ~ spl85_42 ),
inference(resolution,[],[f3380,f2346]) ).
fof(f3380,plain,
( ! [X6] : hBOOL(X6)
| ~ spl85_42 ),
inference(avatar_component_clause,[],[f3379]) ).
fof(f4226,plain,
( spl85_58
| ~ spl85_42 ),
inference(avatar_split_clause,[],[f4180,f3379,f4223]) ).
fof(f4180,plain,
( ! [X98,X99] : X98 = X99
| ~ spl85_42 ),
inference(resolution,[],[f3380,f2591]) ).
fof(f4225,plain,
( spl85_57
| spl85_58
| ~ spl85_42 ),
inference(avatar_split_clause,[],[f4170,f3379,f4223,f4220]) ).
fof(f4170,plain,
( ! [X58,X56,X57] :
( X57 = X58
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),X56),c_Arrow__Order__Mirabelle_OLin)) )
| ~ spl85_42 ),
inference(resolution,[],[f3380,f2997]) ).
fof(f4218,plain,
( spl85_11
| ~ spl85_42 ),
inference(avatar_contradiction_clause,[],[f4164]) ).
fof(f4164,plain,
( $false
| spl85_11
| ~ spl85_42 ),
inference(resolution,[],[f3380,f3152]) ).
fof(f4217,plain,
~ spl85_42,
inference(avatar_contradiction_clause,[],[f4183]) ).
fof(f4183,plain,
( $false
| ~ spl85_42 ),
inference(resolution,[],[f3380,f3081]) ).
fof(f4140,plain,
( spl85_56
| spl85_42 ),
inference(avatar_split_clause,[],[f4136,f3379,f4138]) ).
fof(f4136,plain,
! [X40,X41,X39,X42] :
( hBOOL(X42)
| ~ hBOOL(hAPP(hAPP(c_Product__Type_OPair(X40,X41),sK32(X40,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X39,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X39,tc_HOL_Obool))),X41)),sK31(X40,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X39,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X39,tc_HOL_Obool))),X41))) ),
inference(forward_demodulation,[],[f4122,f2580]) ).
fof(f4122,plain,
! [X40,X41,X39,X42] :
( hBOOL(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X39,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X39,tc_HOL_Obool))),X42))
| ~ hBOOL(hAPP(hAPP(c_Product__Type_OPair(X40,X41),sK32(X40,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X39,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X39,tc_HOL_Obool))),X41)),sK31(X40,hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(X39,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(X39,tc_HOL_Obool))),X41))) ),
inference(superposition,[],[f2501,f2580]) ).
fof(f4021,plain,
( spl85_11
| spl85_54
| ~ spl85_9
| spl85_55
| ~ spl85_4
| ~ spl85_24 ),
inference(avatar_split_clause,[],[f4010,f3218,f3115,f4018,f3140,f4014,f3150]) ).
fof(f4010,plain,
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,sK4(v_Q____,v_P____,v_a____,v_b____))))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,sK4(v_Q____,v_P____,v_a____,v_b____))))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_Q____)))
| ~ spl85_4
| ~ spl85_24 ),
inference(resolution,[],[f3311,f3220]) ).
fof(f3632,plain,
( ~ spl85_52
| ~ spl85_53
| ~ spl85_24 ),
inference(avatar_split_clause,[],[f3618,f3218,f3629,f3625]) ).
fof(f3618,plain,
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_b____),v_a____)),hAPP(v_F,v_P____)))
| ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_P____)),c_Arrow__Order__Mirabelle_OLin))
| ~ spl85_24 ),
inference(resolution,[],[f2792,f3220]) ).
fof(f3461,plain,
( spl85_50
| spl85_51 ),
inference(avatar_split_clause,[],[f3420,f3459,f3455]) ).
fof(f3459,plain,
( spl85_51
<=> ! [X20,X21,X19] : ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X19,X20,X21),c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),v_P_H____),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_51])]) ).
fof(f3420,plain,
! [X21,X19,X20] :
( ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X19,X20,X21),c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),v_P_H____),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)))) ),
inference(superposition,[],[f2672,f2728]) ).
fof(f2672,plain,
! [X0] :
( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,X0)))
| hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,X0))) ),
inference(cnf_transformation,[],[f1928]) ).
fof(f3453,plain,
( spl85_47
| spl85_49 ),
inference(avatar_split_clause,[],[f3419,f3450,f3442]) ).
fof(f3419,plain,
! [X18,X16,X17] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_Q____,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))))
| ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X16,X17,X18),c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),v_P____),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))) ),
inference(superposition,[],[f2449,f2728]) ).
fof(f3448,plain,
( spl85_47
| spl85_48 ),
inference(avatar_split_clause,[],[f3418,f3445,f3442]) ).
fof(f3418,plain,
! [X14,X15,X13] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a_H____),v_b_H____)),hAPP(v_P_H____,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))))
| ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X13,X14,X15),c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),v_P____),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))) ),
inference(superposition,[],[f2671,f2728]) ).
fof(f3440,plain,
( spl85_45
| spl85_46 ),
inference(avatar_split_clause,[],[f3417,f3437,f3434]) ).
fof(f3434,plain,
( spl85_45
<=> ! [X11,X12,X10] : ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X10,X11,X12),c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),v_Q____),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_45])]) ).
fof(f3417,plain,
! [X10,X11,X12] :
( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_P____,hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))))
| ~ hBOOL(hAPP(hAPP(hAPP(c_COMBS(X10,X11,X12),c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt))),v_Q____),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____))) ),
inference(superposition,[],[f2448,f2728]) ).
fof(f3393,plain,
( spl85_43
| spl85_44 ),
inference(avatar_split_clause,[],[f3384,f3391,f3387]) ).
fof(f3391,plain,
( spl85_44
<=> ! [X6,X4,X5,X3] : hBOOL(hAPP(c_fNot,hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_44])]) ).
fof(f3384,plain,
! [X3,X6,X4,X5] :
( hBOOL(hAPP(c_fNot,hAPP(hAPP(c_Product__Type_OPair(X3,X4),X5),X6)))
| hBOOL(sK33(c_fNot)) ),
inference(resolution,[],[f2866,f2500]) ).
fof(f2500,plain,
! [X2,X0,X1,X6,X7] :
( ~ hBOOL(hAPP(X1,sK33(X1)))
| hBOOL(hAPP(X1,hAPP(hAPP(c_Product__Type_OPair(X0,X2),X7),X6))) ),
inference(cnf_transformation,[],[f1773]) ).
fof(f3381,plain,
( spl85_41
| spl85_42 ),
inference(avatar_split_clause,[],[f3374,f3379,f3376]) ).
fof(f3374,plain,
! [X3,X6,X4,X5] :
( hBOOL(X6)
| ~ hBOOL(hAPP(hAPP(c_Product__Type_OPair(X4,X5),sK32(X4,c_COMBI(X3),X5)),sK31(X4,c_COMBI(X3),X5))) ),
inference(forward_demodulation,[],[f3360,f2523]) ).
fof(f3360,plain,
! [X3,X6,X4,X5] :
( ~ hBOOL(hAPP(hAPP(c_Product__Type_OPair(X4,X5),sK32(X4,c_COMBI(X3),X5)),sK31(X4,c_COMBI(X3),X5)))
| hBOOL(hAPP(c_COMBI(X3),X6)) ),
inference(superposition,[],[f2501,f2523]) ).
fof(f3373,plain,
( spl85_39
| spl85_40 ),
inference(avatar_split_clause,[],[f3366,f3371,f3368]) ).
fof(f3368,plain,
( spl85_39
<=> ! [X19] : ~ hBOOL(sK33(c_COMBI(X19))) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_39])]) ).
fof(f3366,plain,
! [X21,X19,X22,X23,X20] :
( hBOOL(hAPP(hAPP(c_Product__Type_OPair(X20,X21),X22),X23))
| ~ hBOOL(sK33(c_COMBI(X19))) ),
inference(forward_demodulation,[],[f3365,f2523]) ).
fof(f3365,plain,
! [X21,X19,X22,X23,X20] :
( hBOOL(hAPP(c_COMBI(X19),hAPP(hAPP(c_Product__Type_OPair(X20,X21),X22),X23)))
| ~ hBOOL(sK33(c_COMBI(X19))) ),
inference(superposition,[],[f2500,f2523]) ).
fof(f3344,plain,
( spl85_38
| ~ spl85_10 ),
inference(avatar_split_clause,[],[f3338,f3145,f3341]) ).
fof(f3338,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P_H____))
| ~ spl85_10 ),
inference(resolution,[],[f3147,f2710]) ).
fof(f3335,plain,
( spl85_37
| ~ spl85_9 ),
inference(avatar_split_clause,[],[f3329,f3140,f3332]) ).
fof(f3329,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_P____))
| ~ spl85_9 ),
inference(resolution,[],[f3142,f2710]) ).
fof(f3309,plain,
( spl85_36
| ~ spl85_16 ),
inference(avatar_split_clause,[],[f3303,f3178,f3306]) ).
fof(f3303,plain,
( hBOOL(hAPP(c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)),v_F))
| ~ spl85_16 ),
inference(resolution,[],[f3180,f2710]) ).
fof(f3300,plain,
( spl85_35
| ~ spl85_24 ),
inference(avatar_split_clause,[],[f3294,f3218,f3297]) ).
fof(f3294,plain,
( hBOOL(hAPP(hAPP(v_F,v_P____),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)))
| ~ spl85_24 ),
inference(resolution,[],[f3220,f2710]) ).
fof(f3293,plain,
( spl85_34
| ~ spl85_25 ),
inference(avatar_split_clause,[],[f3287,f3223,f3290]) ).
fof(f3287,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OLin,hAPP(v_F,v_Q____)))
| ~ spl85_25 ),
inference(resolution,[],[f3225,f2710]) ).
fof(f3286,plain,
( spl85_33
| ~ spl85_4 ),
inference(avatar_split_clause,[],[f3280,f3115,f3283]) ).
fof(f3280,plain,
( hBOOL(hAPP(c_Arrow__Order__Mirabelle_OProf,v_Q____))
| ~ spl85_4 ),
inference(resolution,[],[f3117,f2710]) ).
fof(f3278,plain,
spl85_32,
inference(avatar_split_clause,[],[f2553,f3275]) ).
fof(f3275,plain,
( spl85_32
<=> c_Arrow__Order__Mirabelle_OIIA(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_32])]) ).
fof(f2553,plain,
c_Arrow__Order__Mirabelle_OIIA(v_F),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
c_Arrow__Order__Mirabelle_OIIA(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I3_J) ).
fof(f3271,plain,
spl85_31,
inference(avatar_split_clause,[],[f2213,f3268]) ).
fof(f2213,plain,
class_Orderings_Obot(tc_Nat_Onat),
inference(cnf_transformation,[],[f514]) ).
fof(f514,axiom,
class_Orderings_Obot(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
fof(f3264,plain,
spl85_30,
inference(avatar_split_clause,[],[f2893,f3261]) ).
fof(f2893,plain,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f495]) ).
fof(f495,axiom,
class_Lattices_Obounded__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice) ).
fof(f3257,plain,
spl85_29,
inference(avatar_split_clause,[],[f2297,f3254]) ).
fof(f2297,plain,
class_Lattices_Olattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f511]) ).
fof(f511,axiom,
class_Lattices_Olattice(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
fof(f3244,plain,
spl85_28,
inference(avatar_split_clause,[],[f2475,f3241]) ).
fof(f3241,plain,
( spl85_28
<=> c_Arrow__Order__Mirabelle_Ounanimity(v_F) ),
introduced(avatar_definition,[new_symbols(naming,[spl85_28])]) ).
fof(f2475,plain,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
c_Arrow__Order__Mirabelle_Ounanimity(v_F),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).
fof(f3237,plain,
~ spl85_27,
inference(avatar_split_clause,[],[f2675,f3234]) ).
fof(f2675,plain,
v_a____ != v_b_H____,
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
v_a____ != v_b_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d2_I1_J) ).
fof(f3232,plain,
spl85_26,
inference(avatar_split_clause,[],[f2421,f3229]) ).
fof(f2421,plain,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
inference(cnf_transformation,[],[f516]) ).
fof(f516,axiom,
class_Lattices_Osemilattice__sup(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
fof(f3226,plain,
spl85_25,
inference(avatar_split_clause,[],[f2729,f3223]) ).
fof(f2729,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),hAPP(v_F,v_Q____)),c_Arrow__Order__Mirabelle_OLin)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096F_AQ_A_058_ALin_096) ).
fof(f3221,plain,
spl85_24,
inference(avatar_split_clause,[],[f2673,f3218]) ).
fof(f2673,plain,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_P____))),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_P____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_060_092_060_094bsub_062F_AP_092_060_094esub_062_Ab_096) ).
fof(f3216,plain,
spl85_23,
inference(avatar_split_clause,[],[f2907,f3213]) ).
fof(f2907,plain,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
inference(cnf_transformation,[],[f506]) ).
fof(f506,axiom,
class_Lattices_Osemilattice__sup(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
fof(f3211,plain,
spl85_22,
inference(avatar_split_clause,[],[f2549,f3208]) ).
fof(f2549,plain,
class_Lattices_Olattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f520]) ).
fof(f520,axiom,
class_Lattices_Olattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
fof(f3206,plain,
spl85_21,
inference(avatar_split_clause,[],[f2784,f3203]) ).
fof(f2784,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f519]) ).
fof(f519,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(f3201,plain,
spl85_20,
inference(avatar_split_clause,[],[f2851,f3198]) ).
fof(f2851,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(cnf_transformation,[],[f522]) ).
fof(f522,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(f3196,plain,
spl85_19,
inference(avatar_split_clause,[],[f2604,f3193]) ).
fof(f2604,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(cnf_transformation,[],[f513]) ).
fof(f513,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(f3191,plain,
~ spl85_18,
inference(avatar_split_clause,[],[f2274,f3188]) ).
fof(f2274,plain,
v_a____ != v_b____,
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d1_I1_J) ).
fof(f3186,plain,
~ spl85_17,
inference(avatar_split_clause,[],[f2920,f3183]) ).
fof(f2920,plain,
v_b____ != v_a_H____,
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
v_b____ != v_a_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d2_I2_J) ).
fof(f3181,plain,
spl85_16,
inference(avatar_split_clause,[],[f2418,f3178]) ).
fof(f2418,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
inference(cnf_transformation,[],[f44]) ).
fof(f44,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_F),c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),c_Arrow__Order__Mirabelle_OProf,c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool)),c_Arrow__Order__Mirabelle_OLin)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I1_J) ).
fof(f3175,plain,
spl85_15,
inference(avatar_split_clause,[],[f2342,f3172]) ).
fof(f2342,plain,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
inference(cnf_transformation,[],[f515]) ).
fof(f515,axiom,
class_Lattices_Obounded__lattice__bot(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
fof(f3170,plain,
spl85_14,
inference(avatar_split_clause,[],[f2562,f3167]) ).
fof(f2562,plain,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
inference(cnf_transformation,[],[f508]) ).
fof(f508,axiom,
class_Lattices_Odistrib__lattice(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Odistrib__lattice) ).
fof(f3165,plain,
spl85_13,
inference(avatar_split_clause,[],[f2599,f3162]) ).
fof(f2599,plain,
class_Orderings_Obot(tc_HOL_Obool),
inference(cnf_transformation,[],[f523]) ).
fof(f523,axiom,
class_Orderings_Obot(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
fof(f3158,plain,
spl85_12,
inference(avatar_split_clause,[],[f2207,f3155]) ).
fof(f2207,plain,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
inference(cnf_transformation,[],[f517]) ).
fof(f517,axiom,
class_Lattices_Osemilattice__inf(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
fof(f3153,plain,
~ spl85_11,
inference(avatar_split_clause,[],[f2565,f3150]) ).
fof(f2565,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_Q____))),
inference(cnf_transformation,[],[f965]) ).
fof(f965,plain,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_Q____))),
inference(flattening,[],[f534]) ).
fof(f534,negated_conjecture,
~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_Q____))),
inference(negated_conjecture,[],[f533]) ).
fof(f533,conjecture,
hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt)),hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),v_a____),v_b____)),hAPP(v_F,v_Q____))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f3148,plain,
spl85_10,
inference(avatar_split_clause,[],[f2473,f3145]) ).
fof(f2473,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P_H____),c_Arrow__Order__Mirabelle_OProf)),
inference(cnf_transformation,[],[f23]) ).
fof(f23,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P_H____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096P_H_A_058_AProf_096) ).
fof(f3143,plain,
spl85_9,
inference(avatar_split_clause,[],[f2393,f3140]) ).
fof(f2393,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_P____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096P_A_058_AProf_096) ).
fof(f3138,plain,
spl85_8,
inference(avatar_split_clause,[],[f2257,f3135]) ).
fof(f2257,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(cnf_transformation,[],[f521]) ).
fof(f521,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(f3133,plain,
spl85_7,
inference(avatar_split_clause,[],[f2291,f3130]) ).
fof(f2291,plain,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
inference(cnf_transformation,[],[f507]) ).
fof(f507,axiom,
class_Lattices_Osemilattice__inf(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
fof(f3128,plain,
~ spl85_6,
inference(avatar_split_clause,[],[f2331,f3125]) ).
fof(f2331,plain,
v_b_H____ != v_a_H____,
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
v_b_H____ != v_a_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_d1_I2_J) ).
fof(f3123,plain,
spl85_5,
inference(avatar_split_clause,[],[f2507,f3120]) ).
fof(f2507,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f512]) ).
fof(f512,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(f3118,plain,
spl85_4,
inference(avatar_split_clause,[],[f2251,f3115]) ).
fof(f2251,plain,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi,tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt,tc_Arrow__Order__Mirabelle_Oalt),tc_HOL_Obool))),v_Q____),c_Arrow__Order__Mirabelle_OProf)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096Q_A_058_AProf_096) ).
fof(f3113,plain,
spl85_3,
inference(avatar_split_clause,[],[f2701,f3110]) ).
fof(f2701,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f509]) ).
fof(f509,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(f3107,plain,
spl85_2,
inference(avatar_split_clause,[],[f2249,f3104]) ).
fof(f2249,plain,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
inference(cnf_transformation,[],[f518]) ).
fof(f518,axiom,
class_Lattices_Odistrib__lattice(tc_HOL_Obool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
fof(f3102,plain,
spl85_1,
inference(avatar_split_clause,[],[f2614,f3099]) ).
fof(f2614,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(cnf_transformation,[],[f510]) ).
fof(f510,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SCT128+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 12:56:31 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.20/0.53 % (27053)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.54 % (27061)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.55 % (27053)Instruction limit reached!
% 0.20/0.55 % (27053)------------------------------
% 0.20/0.55 % (27053)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55 % (27053)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55 % (27053)Termination reason: Unknown
% 0.20/0.55 % (27053)Termination phase: Preprocessing 1
% 0.20/0.55
% 0.20/0.55 % (27053)Memory used [KB]: 1918
% 0.20/0.55 % (27053)Time elapsed: 0.008 s
% 0.20/0.55 % (27053)Instructions burned: 8 (million)
% 0.20/0.55 % (27053)------------------------------
% 0.20/0.55 % (27053)------------------------------
% 0.20/0.55 % (27052)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.55 % (27055)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.55 % (27049)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.55 % (27048)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.56 % (27071)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.56 % (27068)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.56 % (27060)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.56 % (27047)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.57 % (27050)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.57 % (27069)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.57 % (27046)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.57 % (27073)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.57 % (27072)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.57 % (27051)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.57 % (27054)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.57 % (27054)Instruction limit reached!
% 0.20/0.57 % (27054)------------------------------
% 0.20/0.57 % (27054)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.57 % (27054)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.57 % (27054)Termination reason: Unknown
% 0.20/0.57 % (27054)Termination phase: Preprocessing 1
% 0.20/0.57
% 0.20/0.57 % (27054)Memory used [KB]: 1535
% 0.20/0.57 % (27054)Time elapsed: 0.004 s
% 0.20/0.57 % (27054)Instructions burned: 2 (million)
% 0.20/0.57 % (27054)------------------------------
% 0.20/0.57 % (27054)------------------------------
% 0.20/0.57 % (27074)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.57 % (27075)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.20/0.58 % (27062)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.58 % (27067)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.20/0.58 % (27070)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.58 % (27066)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.58 % (27065)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.58 % (27064)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.58 % (27063)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.59 % (27058)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.20/0.59 % (27057)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.59 % (27056)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.59 % (27059)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.71/0.63 % (27047)Instruction limit reached!
% 1.71/0.63 % (27047)------------------------------
% 1.71/0.63 % (27047)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.71/0.63 % (27047)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.71/0.63 % (27047)Termination reason: Unknown
% 1.71/0.63 % (27047)Termination phase: Function definition elimination
% 1.71/0.63
% 1.71/0.63 % (27047)Memory used [KB]: 3070
% 1.71/0.63 % (27047)Time elapsed: 0.023 s
% 1.71/0.63 % (27047)Instructions burned: 52 (million)
% 1.71/0.63 % (27047)------------------------------
% 1.71/0.63 % (27047)------------------------------
% 1.71/0.63 % (27061)Instruction limit reached!
% 1.71/0.63 % (27061)------------------------------
% 1.71/0.63 % (27061)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.71/0.63 % (27061)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.71/0.63 % (27061)Termination reason: Unknown
% 1.71/0.63 % (27061)Termination phase: Saturation
% 1.71/0.63
% 1.71/0.63 % (27061)Memory used [KB]: 3198
% 1.71/0.63 % (27061)Time elapsed: 0.082 s
% 1.71/0.63 % (27061)Instructions burned: 75 (million)
% 1.71/0.63 % (27061)------------------------------
% 1.71/0.63 % (27061)------------------------------
% 1.88/0.63 % (27051)Instruction limit reached!
% 1.88/0.63 % (27051)------------------------------
% 1.88/0.63 % (27051)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.88/0.63 % (27051)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.88/0.63 % (27051)Termination reason: Unknown
% 1.88/0.63 % (27051)Termination phase: Property scanning
% 1.88/0.63
% 1.88/0.63 % (27051)Memory used [KB]: 3070
% 1.88/0.63 % (27051)Time elapsed: 0.021 s
% 1.88/0.63 % (27051)Instructions burned: 48 (million)
% 1.88/0.63 % (27051)------------------------------
% 1.88/0.63 % (27051)------------------------------
% 1.88/0.63 % (27048)Instruction limit reached!
% 1.88/0.63 % (27048)------------------------------
% 1.88/0.63 % (27048)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.88/0.63 % (27048)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.88/0.63 % (27048)Termination reason: Unknown
% 1.88/0.63 % (27048)Termination phase: Property scanning
% 1.88/0.63
% 1.88/0.63 % (27048)Memory used [KB]: 3070
% 1.88/0.63 % (27048)Time elapsed: 0.021 s
% 1.88/0.63 % (27048)Instructions burned: 40 (million)
% 1.88/0.63 % (27048)------------------------------
% 1.88/0.63 % (27048)------------------------------
% 1.88/0.64 % (27055)Instruction limit reached!
% 1.88/0.64 % (27055)------------------------------
% 1.88/0.64 % (27055)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.88/0.64 % (27055)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.88/0.64 % (27055)Termination reason: Unknown
% 1.88/0.64 % (27055)Termination phase: Function definition elimination
% 1.88/0.64
% 1.88/0.64 % (27055)Memory used [KB]: 3070
% 1.88/0.64 % (27055)Time elapsed: 0.024 s
% 1.88/0.64 % (27055)Instructions burned: 52 (million)
% 1.88/0.64 % (27055)------------------------------
% 1.88/0.64 % (27055)------------------------------
% 1.88/0.64 % (27052)Instruction limit reached!
% 1.88/0.64 % (27052)------------------------------
% 1.88/0.64 % (27052)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.88/0.64 % (27052)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.88/0.64 % (27052)Termination reason: Unknown
% 1.88/0.64 % (27052)Termination phase: Function definition elimination
% 1.88/0.64
% 1.88/0.64 % (27052)Memory used [KB]: 3070
% 1.88/0.64 % (27052)Time elapsed: 0.024 s
% 1.88/0.64 % (27052)Instructions burned: 51 (million)
% 1.88/0.64 % (27052)------------------------------
% 1.88/0.64 % (27052)------------------------------
% 1.88/0.65 % (27049)Instruction limit reached!
% 1.88/0.65 % (27049)------------------------------
% 1.88/0.65 % (27049)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.88/0.65 % (27049)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.88/0.65 % (27049)Termination reason: Unknown
% 1.88/0.65 % (27049)Termination phase: Property scanning
% 1.88/0.65
% 1.88/0.65 % (27049)Memory used [KB]: 2814
% 1.88/0.65 % (27049)Time elapsed: 0.026 s
% 1.88/0.65 % (27049)Instructions burned: 54 (million)
% 1.88/0.65 % (27049)------------------------------
% 1.88/0.65 % (27049)------------------------------
% 1.88/0.65 % (27060)Instruction limit reached!
% 1.88/0.65 % (27060)------------------------------
% 1.88/0.65 % (27060)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.88/0.65 % (27060)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.88/0.65 % (27060)Termination reason: Unknown
% 1.88/0.65 % (27060)Termination phase: Property scanning
% 1.88/0.65
% 1.88/0.65 % (27060)Memory used [KB]: 3454
% 1.88/0.65 % (27060)Time elapsed: 0.031 s
% 1.88/0.65 % (27060)Instructions burned: 69 (million)
% 1.88/0.65 % (27060)------------------------------
% 1.88/0.65 % (27060)------------------------------
% 1.88/0.65 % (27050)Instruction limit reached!
% 1.88/0.65 % (27050)------------------------------
% 1.88/0.65 % (27050)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.88/0.65 % (27050)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.88/0.65 % (27050)Termination reason: Unknown
% 1.88/0.65 % (27050)Termination phase: Property scanning
% 1.88/0.65
% 1.88/0.65 % (27050)Memory used [KB]: 3070
% 1.88/0.65 % (27050)Time elapsed: 0.024 s
% 1.88/0.65 % (27050)Instructions burned: 52 (million)
% 1.88/0.65 % (27050)------------------------------
% 1.88/0.65 % (27050)------------------------------
% 1.88/0.65 % (27063)Instruction limit reached!
% 1.88/0.65 % (27063)------------------------------
% 1.88/0.65 % (27063)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.88/0.65 % (27063)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.88/0.65 % (27063)Termination reason: Unknown
% 1.88/0.65 % (27063)Termination phase: Property scanning
% 1.88/0.65
% 1.88/0.65 % (27063)Memory used [KB]: 3070
% 1.88/0.65 % (27063)Time elapsed: 0.026 s
% 1.88/0.65 % (27063)Instructions burned: 59 (million)
% 1.88/0.65 % (27063)------------------------------
% 1.88/0.65 % (27063)------------------------------
% 1.88/0.66 % (27076)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=388:si=on:rawr=on:rtra=on_0 on theBenchmark for (2998ds/388Mi)
% 1.88/0.67 % (27056)Instruction limit reached!
% 1.88/0.67 % (27056)------------------------------
% 1.88/0.67 % (27056)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.88/0.67 % (27056)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.88/0.67 % (27056)Termination reason: Unknown
% 1.88/0.67 % (27056)Termination phase: Function definition elimination
% 1.88/0.67
% 1.88/0.67 % (27056)Memory used [KB]: 3070
% 1.88/0.67 % (27056)Time elapsed: 0.025 s
% 1.88/0.67 % (27056)Instructions burned: 51 (million)
% 1.88/0.67 % (27056)------------------------------
% 1.88/0.67 % (27056)------------------------------
% 1.88/0.68 % (27072)Instruction limit reached!
% 1.88/0.68 % (27072)------------------------------
% 1.88/0.68 % (27072)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.88/0.68 % (27072)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.88/0.68 % (27072)Termination reason: Unknown
% 1.88/0.68 % (27072)Termination phase: Property scanning
% 1.88/0.68
% 1.88/0.68 % (27072)Memory used [KB]: 3454
% 1.88/0.68 % (27072)Time elapsed: 0.030 s
% 1.88/0.68 % (27072)Instructions burned: 70 (million)
% 1.88/0.68 % (27072)------------------------------
% 1.88/0.68 % (27072)------------------------------
% 2.36/0.72 % (27058)Instruction limit reached!
% 2.36/0.72 % (27058)------------------------------
% 2.36/0.72 % (27058)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.36/0.72 % (27058)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.36/0.72 % (27058)Termination reason: Unknown
% 2.36/0.72 % (27058)Termination phase: Saturation
% 2.36/0.72
% 2.36/0.72 % (27058)Memory used [KB]: 8187
% 2.36/0.72 % (27058)Time elapsed: 0.045 s
% 2.36/0.72 % (27058)Instructions burned: 101 (million)
% 2.36/0.72 % (27058)------------------------------
% 2.36/0.72 % (27058)------------------------------
% 2.36/0.74 % (27057)Instruction limit reached!
% 2.36/0.74 % (27057)------------------------------
% 2.36/0.74 % (27057)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.36/0.74 % (27057)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.36/0.74 % (27057)Termination reason: Unknown
% 2.36/0.74 % (27059)Instruction limit reached!
% 2.36/0.74 % (27059)------------------------------
% 2.36/0.74 % (27059)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.36/0.74 % (27057)Termination phase: Saturation
% 2.36/0.74
% 2.36/0.74 % (27059)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.36/0.74 % (27057)Memory used [KB]: 7675
% 2.36/0.74 % (27059)Termination reason: Unknown
% 2.36/0.74 % (27057)Time elapsed: 0.046 s
% 2.36/0.74 % (27059)Termination phase: Saturation
% 2.36/0.74
% 2.36/0.74 % (27057)Instructions burned: 100 (million)
% 2.36/0.74 % (27057)------------------------------
% 2.36/0.74 % (27057)------------------------------
% 2.36/0.74 % (27059)Memory used [KB]: 8059
% 2.36/0.74 % (27059)Time elapsed: 0.045 s
% 2.36/0.74 % (27059)Instructions burned: 100 (million)
% 2.36/0.74 % (27059)------------------------------
% 2.36/0.74 % (27059)------------------------------
% 2.36/0.74 % (27062)Instruction limit reached!
% 2.36/0.74 % (27062)------------------------------
% 2.36/0.74 % (27062)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.36/0.74 % (27062)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.36/0.74 % (27062)Termination reason: Unknown
% 2.36/0.74 % (27062)Termination phase: Saturation
% 2.36/0.74
% 2.36/0.74 % (27062)Memory used [KB]: 8059
% 2.36/0.74 % (27062)Time elapsed: 0.281 s
% 2.36/0.74 % (27062)Instructions burned: 100 (million)
% 2.36/0.74 % (27062)------------------------------
% 2.36/0.74 % (27062)------------------------------
% 2.36/0.74 % (27077)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=211:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/211Mi)
% 2.36/0.74 % (27065)Instruction limit reached!
% 2.36/0.74 % (27065)------------------------------
% 2.36/0.74 % (27065)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.36/0.74 % (27065)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.36/0.74 % (27065)Termination reason: Unknown
% 2.36/0.74 % (27065)Termination phase: Saturation
% 2.36/0.74
% 2.36/0.74 % (27065)Memory used [KB]: 3582
% 2.36/0.74 % (27065)Time elapsed: 0.045 s
% 2.36/0.74 % (27065)Instructions burned: 100 (million)
% 2.36/0.74 % (27065)------------------------------
% 2.36/0.74 % (27065)------------------------------
% 2.36/0.74 % (27064)Instruction limit reached!
% 2.36/0.74 % (27064)------------------------------
% 2.36/0.74 % (27064)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.36/0.74 % (27064)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.36/0.74 % (27064)Termination reason: Unknown
% 2.36/0.74 % (27064)Termination phase: Saturation
% 2.36/0.74
% 2.36/0.74 % (27064)Memory used [KB]: 8187
% 2.36/0.74 % (27064)Time elapsed: 0.046 s
% 2.36/0.74 % (27064)Instructions burned: 101 (million)
% 2.36/0.74 % (27064)------------------------------
% 2.36/0.74 % (27064)------------------------------
% 2.36/0.76 % (27080)ott+1_1:7_bd=off:i=934:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/934Mi)
% 2.36/0.76 % (27078)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/90Mi)
% 2.36/0.76 % (27082)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=655:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/655Mi)
% 2.36/0.76 % (27079)ott+1_1:2_i=920:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/920Mi)
% 2.68/0.77 % (27081)ott+10_1:50_bsr=unit_only:drc=off:fd=preordered:sp=frequency:i=747:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/747Mi)
% 2.68/0.77 % (27083)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/68Mi)
% 2.68/0.78 % (27084)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=940:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/940Mi)
% 2.68/0.78 % (27086)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/90Mi)
% 2.68/0.79 WARNING Broken Constraint: if sine_depth(2) has been set then sine_selection(off) is not equal to off
% 2.68/0.79 % (27085)ott+11_4:1_br=off:fde=none:s2a=on:sd=2:sp=frequency:urr=on:i=981:si=on:rawr=on:rtra=on_0 on theBenchmark for (2997ds/981Mi)
% 2.68/0.80 % (27067)Instruction limit reached!
% 2.68/0.80 % (27067)------------------------------
% 2.68/0.80 % (27067)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.68/0.80 % (27067)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.68/0.80 % (27067)Termination reason: Unknown
% 2.68/0.80 % (27067)Termination phase: Saturation
% 2.68/0.80
% 2.68/0.80 % (27067)Memory used [KB]: 8571
% 2.68/0.80 % (27067)Time elapsed: 0.064 s
% 2.68/0.80 % (27067)Instructions burned: 139 (million)
% 2.68/0.80 % (27067)------------------------------
% 2.68/0.80 % (27067)------------------------------
% 2.68/0.81 % (27087)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=2016:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/2016Mi)
% 2.68/0.81 % (27089)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=4958:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/4958Mi)
% 2.68/0.83 % (27088)dis+10_1:2_atotf=0.3:i=3735:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/3735Mi)
% 2.68/0.86 % (27066)Instruction limit reached!
% 2.68/0.86 % (27066)------------------------------
% 2.68/0.86 % (27066)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.68/0.86 % (27066)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.68/0.86 % (27066)Termination reason: Unknown
% 2.68/0.86 % (27066)Termination phase: Saturation
% 2.68/0.86
% 2.68/0.86 % (27066)Memory used [KB]: 8699
% 2.68/0.86 % (27066)Time elapsed: 0.084 s
% 2.68/0.86 % (27066)Instructions burned: 177 (million)
% 2.68/0.86 % (27066)------------------------------
% 2.68/0.86 % (27066)------------------------------
% 3.01/0.86 % (27090)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=4959:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/4959Mi)
% 3.01/0.87 % (27093)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/68Mi)
% 3.01/0.87 % (27091)ott+10_1:1_kws=precedence:tgt=ground:i=4756:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/4756Mi)
% 3.01/0.88 % (27073)Instruction limit reached!
% 3.01/0.88 % (27073)------------------------------
% 3.01/0.88 % (27073)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.01/0.88 % (27073)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.01/0.88 % (27073)Termination reason: Unknown
% 3.01/0.88 % (27073)Termination phase: Saturation
% 3.01/0.88
% 3.01/0.88 % (27073)Memory used [KB]: 4477
% 3.01/0.88 % (27073)Time elapsed: 0.082 s
% 3.01/0.88 % (27073)Instructions burned: 178 (million)
% 3.01/0.88 % (27073)------------------------------
% 3.01/0.88 % (27073)------------------------------
% 3.01/0.88 % (27094)ott+11_9:8_amm=off:bsd=on:etr=on:fsd=on:fsr=off:lma=on:newcnf=on:nm=0:nwc=3.0:s2a=on:s2agt=10:sas=z3:tha=some:i=1824:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/1824Mi)
% 3.01/0.88 % (27083)Instruction limit reached!
% 3.01/0.88 % (27083)------------------------------
% 3.01/0.88 % (27083)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.01/0.88 % (27083)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.01/0.88 % (27083)Termination reason: Unknown
% 3.01/0.88 % (27083)Termination phase: Property scanning
% 3.01/0.88
% 3.01/0.88 % (27083)Memory used [KB]: 3454
% 3.01/0.88 % (27083)Time elapsed: 0.029 s
% 3.01/0.88 % (27083)Instructions burned: 70 (million)
% 3.01/0.88 % (27083)------------------------------
% 3.01/0.88 % (27083)------------------------------
% 3.01/0.88 % (27095)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=2134:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/2134Mi)
% 3.01/0.88 % (27092)ott+3_1:1_atotf=0.2:fsr=off:kws=precedence:sp=weighted_frequency:spb=intro:tgt=ground:i=4931:si=on:rawr=on:rtra=on_0 on theBenchmark for (2996ds/4931Mi)
% 3.14/0.89 % (27078)Instruction limit reached!
% 3.14/0.89 % (27078)------------------------------
% 3.14/0.89 % (27078)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.14/0.89 % (27078)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.14/0.89 % (27078)Termination reason: Unknown
% 3.14/0.89 % (27078)Termination phase: Saturation
% 3.14/0.89
% 3.14/0.89 % (27078)Memory used [KB]: 7931
% 3.14/0.89 % (27078)Time elapsed: 0.238 s
% 3.14/0.89 % (27078)Instructions burned: 90 (million)
% 3.14/0.89 % (27078)------------------------------
% 3.14/0.89 % (27078)------------------------------
% 3.14/0.91 % (27086)Instruction limit reached!
% 3.14/0.91 % (27086)------------------------------
% 3.14/0.91 % (27086)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.14/0.91 % (27086)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.14/0.91 % (27086)Termination reason: Unknown
% 3.14/0.91 % (27086)Termination phase: Saturation
% 3.14/0.91
% 3.14/0.91 % (27086)Memory used [KB]: 8059
% 3.14/0.91 % (27086)Time elapsed: 0.239 s
% 3.14/0.91 % (27086)Instructions burned: 90 (million)
% 3.14/0.91 % (27086)------------------------------
% 3.14/0.91 % (27086)------------------------------
% 3.38/0.94 % (27096)ott-1_1:1_sp=const_frequency:i=2891:si=on:rawr=on:rtra=on_0 on theBenchmark for (2995ds/2891Mi)
% 3.38/0.97 % (27093)Instruction limit reached!
% 3.38/0.97 % (27093)------------------------------
% 3.38/0.97 % (27093)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.38/0.97 % (27093)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.38/0.97 % (27093)Termination reason: Unknown
% 3.38/0.97 % (27093)Termination phase: Property scanning
% 3.38/0.97
% 3.38/0.97 % (27093)Memory used [KB]: 3454
% 3.38/0.97 % (27093)Time elapsed: 0.028 s
% 3.38/0.97 % (27093)Instructions burned: 69 (million)
% 3.38/0.97 % (27093)------------------------------
% 3.38/0.97 % (27093)------------------------------
% 3.38/0.99 % (27098)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/90Mi)
% 3.58/1.01 % (27097)dis+2_1:64_add=large:bce=on:bd=off:i=4585:si=on:rawr=on:rtra=on_0 on theBenchmark for (2995ds/4585Mi)
% 3.58/1.02 % (27099)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=2016:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/2016Mi)
% 3.58/1.03 % (27100)dis+10_1:2_atotf=0.3:i=8004:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/8004Mi)
% 3.58/1.05 % (27101)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=9965:si=on:rawr=on:rtra=on_0 on theBenchmark for (2994ds/9965Mi)
% 3.75/1.07 % (27077)Instruction limit reached!
% 3.75/1.07 % (27077)------------------------------
% 3.75/1.07 % (27077)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.75/1.07 % (27077)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.75/1.07 % (27077)Termination reason: Unknown
% 3.75/1.07 % (27077)Termination phase: Saturation
% 3.75/1.07
% 3.75/1.07 % (27077)Memory used [KB]: 5500
% 3.75/1.07 % (27077)Time elapsed: 0.460 s
% 3.75/1.07 % (27077)Instructions burned: 211 (million)
% 3.75/1.07 % (27077)------------------------------
% 3.75/1.07 % (27077)------------------------------
% 3.75/1.11 % (27102)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=9877:si=on:rawr=on:rtra=on_0 on theBenchmark for (2993ds/9877Mi)
% 3.75/1.13 % (27098)Instruction limit reached!
% 3.75/1.13 % (27098)------------------------------
% 3.75/1.13 % (27098)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 3.75/1.13 % (27098)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 3.75/1.13 % (27098)Termination reason: Unknown
% 3.75/1.13 % (27098)Termination phase: Saturation
% 3.75/1.13
% 3.75/1.13 % (27098)Memory used [KB]: 8059
% 3.75/1.13 % (27098)Time elapsed: 0.236 s
% 3.75/1.13 % (27098)Instructions burned: 91 (million)
% 3.75/1.13 % (27098)------------------------------
% 3.75/1.13 % (27098)------------------------------
% 6.09/1.18 % (27076)Instruction limit reached!
% 6.09/1.18 % (27076)------------------------------
% 6.09/1.18 % (27076)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.09/1.18 % (27076)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.09/1.18 % (27076)Termination reason: Unknown
% 6.09/1.18 % (27076)Termination phase: Saturation
% 6.09/1.18
% 6.09/1.18 % (27076)Memory used [KB]: 11513
% 6.09/1.18 % (27076)Time elapsed: 0.537 s
% 6.09/1.18 % (27076)Instructions burned: 388 (million)
% 6.09/1.18 % (27076)------------------------------
% 6.09/1.18 % (27076)------------------------------
% 6.39/1.21 % (27075)Instruction limit reached!
% 6.39/1.21 % (27075)------------------------------
% 6.39/1.21 % (27075)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.39/1.21 % (27075)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.39/1.21 % (27075)Termination reason: Unknown
% 6.39/1.21 % (27075)Termination phase: Saturation
% 6.39/1.21
% 6.39/1.21 % (27075)Memory used [KB]: 12665
% 6.39/1.21 % (27075)Time elapsed: 0.765 s
% 6.39/1.21 % (27075)Instructions burned: 355 (million)
% 6.39/1.21 % (27075)------------------------------
% 6.39/1.21 % (27075)------------------------------
% 6.39/1.21 % (27103)ins+10_1:16_bce=on:fde=unused:igpr=on:igs=35:igwr=on:sp=const_frequency:tgt=full:to=lpo:i=9902:si=on:rawr=on:rtra=on_0 on theBenchmark for (2992ds/9902Mi)
% 6.66/1.24 % (27069)Instruction limit reached!
% 6.66/1.24 % (27069)------------------------------
% 6.66/1.24 % (27069)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.66/1.24 % (27069)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.66/1.24 % (27069)Termination reason: Unknown
% 6.66/1.24 % (27069)Termination phase: Saturation
% 6.66/1.24
% 6.66/1.24 % (27069)Memory used [KB]: 11769
% 6.66/1.24 % (27069)Time elapsed: 0.786 s
% 6.66/1.24 % (27069)Instructions burned: 467 (million)
% 6.66/1.24 % (27069)------------------------------
% 6.66/1.24 % (27069)------------------------------
% 6.66/1.26 % (27104)ott+11_9:8_amm=off:bsd=on:etr=on:fsd=on:fsr=off:lma=on:newcnf=on:nm=0:nwc=3.0:s2a=on:s2agt=10:sas=z3:tha=some:i=1824:si=on:rawr=on:rtra=on_0 on theBenchmark for (2992ds/1824Mi)
% 6.66/1.31 % (27105)dis+2_1:64_add=large:bce=on:bd=off:i=9989:si=on:rawr=on:rtra=on_0 on theBenchmark for (2991ds/9989Mi)
% 6.66/1.31 % (27074)Instruction limit reached!
% 6.66/1.31 % (27074)------------------------------
% 6.66/1.31 % (27074)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 6.66/1.31 % (27074)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 6.66/1.31 % (27074)Termination reason: Unknown
% 6.66/1.31 % (27074)Termination phase: Saturation
% 6.66/1.31
% 6.66/1.31 % (27074)Memory used [KB]: 12409
% 6.66/1.31 % (27074)Time elapsed: 0.865 s
% 6.66/1.31 % (27074)Instructions burned: 440 (million)
% 6.66/1.31 % (27074)------------------------------
% 6.66/1.31 % (27074)------------------------------
% 7.34/1.35 % (27106)ott-11_1:32_i=9707:si=on:rawr=on:rtra=on_0 on theBenchmark for (2991ds/9707Mi)
% 7.34/1.37 % (27107)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2991ds/90Mi)
% 7.72/1.40 % (27068)Instruction limit reached!
% 7.72/1.40 % (27068)------------------------------
% 7.72/1.40 % (27068)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 7.72/1.40 % (27068)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 7.72/1.40 % (27068)Termination reason: Unknown
% 7.72/1.40 % (27068)Termination phase: Saturation
% 7.72/1.40
% 7.72/1.40 % (27068)Memory used [KB]: 7419
% 7.72/1.40 % (27068)Time elapsed: 0.944 s
% 7.72/1.40 % (27068)Instructions burned: 498 (million)
% 7.72/1.40 % (27068)------------------------------
% 7.72/1.40 % (27068)------------------------------
% 7.72/1.43 % (27070)Instruction limit reached!
% 7.72/1.43 % (27070)------------------------------
% 7.72/1.43 % (27070)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 7.72/1.43 % (27070)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 7.72/1.43 % (27070)Termination reason: Unknown
% 7.72/1.43 % (27070)Termination phase: Saturation
% 7.72/1.43
% 7.72/1.43 % (27070)Memory used [KB]: 12537
% 7.72/1.43 % (27070)Time elapsed: 0.977 s
% 7.72/1.43 % (27070)Instructions burned: 484 (million)
% 7.72/1.43 % (27070)------------------------------
% 7.72/1.43 % (27070)------------------------------
% 7.72/1.45 % (27071)Instruction limit reached!
% 7.72/1.45 % (27071)------------------------------
% 7.72/1.45 % (27071)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 7.72/1.45 % (27071)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 7.72/1.45 % (27071)Termination reason: Unknown
% 7.72/1.45 % (27071)Termination phase: Saturation
% 7.72/1.45
% 7.72/1.45 % (27071)Memory used [KB]: 14839
% 7.72/1.45 % (27071)Time elapsed: 0.989 s
% 7.72/1.45 % (27071)Instructions burned: 500 (million)
% 7.72/1.45 % (27071)------------------------------
% 7.72/1.45 % (27071)------------------------------
% 7.72/1.45 % (27108)ott+3_1:1_abs=on:anc=none:bs=on:fsr=off:spb=goal_then_units:i=44001:si=on:rawr=on:rtra=on_0 on theBenchmark for (2990ds/44001Mi)
% 8.23/1.49 % (27107)Instruction limit reached!
% 8.23/1.49 % (27107)------------------------------
% 8.23/1.49 % (27107)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 8.23/1.49 % (27107)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 8.23/1.49 % (27107)Termination reason: Unknown
% 8.23/1.49 % (27107)Termination phase: Saturation
% 8.23/1.49
% 8.23/1.49 % (27107)Memory used [KB]: 8059
% 8.23/1.49 % (27107)Time elapsed: 0.215 s
% 8.23/1.49 % (27107)Instructions burned: 91 (million)
% 8.23/1.49 % (27107)------------------------------
% 8.23/1.49 % (27107)------------------------------
% 8.52/1.54 % (27109)ott+11_9:8_add=large:afp=10:amm=off:fsd=on:fsr=off:lma=on:nm=0:nwc=2.4:s2a=on:s2agt=10:sas=z3:sp=reverse_arity:tha=some:thi=overlap:i=4958:si=on:rawr=on:rtra=on_0 on theBenchmark for (2989ds/4958Mi)
% 8.76/1.54 % (27110)ott+1_27:428_av=off:awrs=converge:awrsf=8:bsr=unit_only:drc=off:fd=preordered:newcnf=on:nwc=1.5:skr=on:slsq=on:slsqc=2:slsql=off:slsqr=1,4:sp=reverse_frequency:uwa=one_side_constant:i=35256:si=on:rawr=on:rtra=on_0 on theBenchmark for (2989ds/35256Mi)
% 8.76/1.61 % (27111)dis+1002_1:1_fde=unused:nwc=10.0:s2a=on:s2at=3.0:sac=on:i=32293:si=on:rawr=on:rtra=on_0 on theBenchmark for (2988ds/32293Mi)
% 8.76/1.62 % (27112)ott+21_1:28_afr=on:anc=all_dependent:bs=on:bsr=unit_only:nicw=on:sp=const_frequency:uhcvi=on:i=37001:si=on:rawr=on:rtra=on_0 on theBenchmark for (2988ds/37001Mi)
% 11.42/1.88 % (27082)Instruction limit reached!
% 11.42/1.88 % (27082)------------------------------
% 11.42/1.88 % (27082)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 11.42/1.88 % (27082)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 11.42/1.88 % (27082)Termination reason: Unknown
% 11.42/1.88 % (27082)Termination phase: Saturation
% 11.42/1.88
% 11.42/1.88 % (27082)Memory used [KB]: 8571
% 11.42/1.88 % (27082)Time elapsed: 1.199 s
% 11.42/1.88 % (27082)Instructions burned: 655 (million)
% 11.42/1.88 % (27082)------------------------------
% 11.42/1.88 % (27082)------------------------------
% 12.58/2.02 % (27113)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=10187:si=on:rawr=on:rtra=on_0 on theBenchmark for (2984ds/10187Mi)
% 12.58/2.03 % (27081)Instruction limit reached!
% 12.58/2.03 % (27081)------------------------------
% 12.58/2.03 % (27081)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 12.58/2.04 % (27081)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 12.58/2.04 % (27081)Termination reason: Unknown
% 12.58/2.04 % (27081)Termination phase: Saturation
% 12.58/2.04
% 12.58/2.04 % (27081)Memory used [KB]: 15095
% 12.58/2.04 % (27081)Time elapsed: 1.368 s
% 12.58/2.04 % (27081)Instructions burned: 748 (million)
% 12.58/2.04 % (27081)------------------------------
% 12.58/2.04 % (27081)------------------------------
% 13.74/2.17 % (27114)ott+3_1:1_atotf=0.2:fsr=off:kws=precedence:sp=weighted_frequency:spb=intro:tgt=ground:i=29337:si=on:rawr=on:rtra=on_0 on theBenchmark for (2983ds/29337Mi)
% 14.38/2.28 % (27080)Instruction limit reached!
% 14.38/2.28 % (27080)------------------------------
% 14.38/2.28 % (27080)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 14.38/2.29 % (27080)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 14.38/2.29 % (27080)Termination reason: Unknown
% 14.38/2.29 % (27080)Termination phase: Saturation
% 14.38/2.29
% 14.38/2.29 % (27080)Memory used [KB]: 19957
% 14.38/2.29 % (27080)Time elapsed: 1.480 s
% 14.38/2.29 % (27080)Instructions burned: 934 (million)
% 14.38/2.29 % (27080)------------------------------
% 14.38/2.29 % (27080)------------------------------
% 15.06/2.31 TRYING [1]
% 15.61/2.37 % (27079)Instruction limit reached!
% 15.61/2.37 % (27079)------------------------------
% 15.61/2.37 % (27079)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 15.61/2.37 % (27079)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 15.61/2.37 % (27079)Termination reason: Unknown
% 15.61/2.37 % (27079)Termination phase: Saturation
% 15.61/2.37
% 15.61/2.37 % (27079)Memory used [KB]: 19957
% 15.61/2.37 % (27079)Time elapsed: 1.590 s
% 15.61/2.37 % (27079)Instructions burned: 920 (million)
% 15.61/2.37 % (27079)------------------------------
% 15.61/2.37 % (27079)------------------------------
% 15.96/2.42 TRYING [2]
% 15.96/2.42 % (27084)Instruction limit reached!
% 15.96/2.42 % (27084)------------------------------
% 15.96/2.42 % (27084)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 15.96/2.42 % (27084)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 15.96/2.42 % (27084)Termination reason: Unknown
% 15.96/2.42 % (27084)Termination phase: Saturation
% 15.96/2.42
% 15.96/2.42 % (27084)Memory used [KB]: 16247
% 15.96/2.42 % (27084)Time elapsed: 1.726 s
% 15.96/2.42 % (27084)Instructions burned: 941 (million)
% 15.96/2.42 % (27084)------------------------------
% 15.96/2.42 % (27084)------------------------------
% 16.09/2.45 % (27116)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=38056:si=on:rawr=on:rtra=on_0 on theBenchmark for (2979ds/38056Mi)
% 16.09/2.47 % (27115)ins+10_1:16_bce=on:fde=unused:igpr=on:igs=35:igwr=on:sp=const_frequency:tgt=full:to=lpo:i=10147:si=on:rawr=on:rtra=on_0 on theBenchmark for (2980ds/10147Mi)
% 16.09/2.50 % (27085)Instruction limit reached!
% 16.09/2.50 % (27085)------------------------------
% 16.09/2.50 % (27085)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 16.09/2.50 % (27085)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 16.09/2.50 % (27085)Termination reason: Unknown
% 16.09/2.50 % (27085)Termination phase: Saturation
% 16.09/2.50
% 16.09/2.50 % (27085)Memory used [KB]: 19445
% 16.09/2.50 % (27085)Time elapsed: 1.821 s
% 16.09/2.50 % (27085)Instructions burned: 981 (million)
% 16.09/2.50 % (27085)------------------------------
% 16.09/2.50 % (27085)------------------------------
% 16.71/2.53 % (27117)fmb+10_1:1_dr=on:fmbsr=2.0:newcnf=on:nm=2:i=33239:si=on:rawr=on:rtra=on_0 on theBenchmark for (2979ds/33239Mi)
% 17.16/2.62 % (27118)fmb+10_1:1_fmbas=predicate:gsp=on:nm=2:i=20987:si=on:rawr=on:rtra=on_0 on theBenchmark for (2978ds/20987Mi)
% 25.30/3.63 TRYING [1]
% 26.04/3.68 % (27094)Instruction limit reached!
% 26.04/3.68 % (27094)------------------------------
% 26.04/3.68 % (27094)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 26.04/3.68 % (27094)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 26.04/3.68 % (27094)Termination reason: Unknown
% 26.04/3.68 % (27094)Termination phase: Saturation
% 26.04/3.68
% 26.04/3.68 % (27094)Memory used [KB]: 10874
% 26.04/3.68 % (27094)Time elapsed: 2.660 s
% 26.04/3.68 % (27094)Instructions burned: 1826 (million)
% 26.04/3.68 % (27094)------------------------------
% 26.04/3.68 % (27094)------------------------------
% 26.23/3.70 TRYING [1]
% 26.44/3.77 TRYING [2]
% 26.44/3.80 % (27119)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=49917:si=on:rawr=on:rtra=on_0 on theBenchmark for (2966ds/49917Mi)
% 27.06/3.87 TRYING [2]
% 30.00/4.23 % (27087)Instruction limit reached!
% 30.00/4.23 % (27087)------------------------------
% 30.00/4.23 % (27087)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 30.00/4.23 % (27087)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 30.00/4.23 % (27087)Termination reason: Unknown
% 30.00/4.23 % (27087)Termination phase: Saturation
% 30.00/4.23
% 30.00/4.23 % (27087)Memory used [KB]: 17142
% 30.00/4.23 % (27087)Time elapsed: 3.524 s
% 30.00/4.23 % (27087)Instructions burned: 2016 (million)
% 30.00/4.23 % (27087)------------------------------
% 30.00/4.23 % (27087)------------------------------
% 30.99/4.30 TRYING [1]
% 31.33/4.39 % (27120)dis+2_1:64_add=large:bce=on:bd=off:i=19144:si=on:rawr=on:rtra=on_0 on theBenchmark for (2960ds/19144Mi)
% 31.87/4.45 % (27104)Instruction limit reached!
% 31.87/4.45 % (27104)------------------------------
% 31.87/4.45 % (27104)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 31.87/4.47 % (27104)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 31.87/4.47 % (27104)Termination reason: Unknown
% 31.87/4.47 % (27104)Termination phase: Saturation
% 31.87/4.47
% 31.87/4.47 % (27104)Memory used [KB]: 11001
% 31.87/4.47 % (27104)Time elapsed: 3.067 s
% 31.87/4.47 % (27104)Instructions burned: 1824 (million)
% 31.87/4.47 % (27104)------------------------------
% 31.87/4.47 % (27104)------------------------------
% 32.35/4.50 TRYING [2]
% 32.35/4.52 % (27099)Instruction limit reached!
% 32.35/4.52 % (27099)------------------------------
% 32.35/4.52 % (27099)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 32.35/4.52 % (27099)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 32.35/4.52 % (27099)Termination reason: Unknown
% 32.35/4.52 % (27099)Termination phase: Saturation
% 32.35/4.52
% 32.35/4.52 % (27099)Memory used [KB]: 18293
% 32.35/4.52 % (27099)Time elapsed: 3.600 s
% 32.35/4.52 % (27099)Instructions burned: 2016 (million)
% 32.35/4.52 % (27099)------------------------------
% 32.35/4.52 % (27099)------------------------------
% 33.22/4.59 % (27121)dis+10_1:128_bd=off:lcm=predicate:sac=on:sp=reverse_arity:urr=on:i=27492:si=on:rawr=on:rtra=on_0 on theBenchmark for (2958ds/27492Mi)
% 33.76/4.66 % (27122)ott-11_1:32_i=6101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2958ds/6101Mi)
% 35.02/4.82 % (27095)Instruction limit reached!
% 35.02/4.82 % (27095)------------------------------
% 35.02/4.82 % (27095)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 35.02/4.82 % (27095)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 35.02/4.82 % (27095)Termination reason: Unknown
% 35.02/4.82 % (27095)Termination phase: Saturation
% 35.02/4.82
% 35.02/4.82 % (27095)Memory used [KB]: 25713
% 35.02/4.82 % (27095)Time elapsed: 4.053 s
% 35.02/4.82 % (27095)Instructions burned: 2135 (million)
% 35.02/4.82 % (27095)------------------------------
% 35.02/4.82 % (27095)------------------------------
% 35.02/4.84 % (27089)First to succeed.
% 36.06/4.98 % (27123)dis+22_1:128_bsd=on:rp=on:slsq=on:slsqc=1:slsqr=1,6:sp=frequency:spb=goal:thsq=on:thsqc=16:thsqd=1:thsql=off:i=90:si=on:rawr=on:rtra=on_0 on theBenchmark for (2955ds/90Mi)
% 37.29/5.10 % (27123)Instruction limit reached!
% 37.29/5.10 % (27123)------------------------------
% 37.29/5.10 % (27123)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 37.29/5.10 % (27123)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 37.29/5.10 % (27123)Termination reason: Unknown
% 37.29/5.10 % (27123)Termination phase: Saturation
% 37.29/5.10
% 37.29/5.10 % (27123)Memory used [KB]: 7931
% 37.29/5.10 % (27123)Time elapsed: 0.227 s
% 37.29/5.10 % (27123)Instructions burned: 91 (million)
% 37.29/5.10 % (27123)------------------------------
% 37.29/5.10 % (27123)------------------------------
% 37.29/5.11 % (27089)Refutation found. Thanks to Tanya!
% 37.29/5.11 % SZS status Theorem for theBenchmark
% 37.29/5.11 % SZS output start Proof for theBenchmark
% See solution above
% 37.29/5.15 % (27089)------------------------------
% 37.29/5.15 % (27089)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 37.29/5.15 % (27089)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 37.29/5.15 % (27089)Termination reason: Refutation
% 37.29/5.15
% 37.29/5.15 % (27089)Memory used [KB]: 15223
% 37.29/5.15 % (27089)Time elapsed: 4.164 s
% 37.29/5.15 % (27089)Instructions burned: 2490 (million)
% 37.29/5.15 % (27089)------------------------------
% 37.29/5.15 % (27089)------------------------------
% 37.29/5.15 % (27045)Success in time 4.798 s
%------------------------------------------------------------------------------